Research Article Kalman Filter-Based Hybrid Indoor...

Hindawi Publishing CorporationInternational Journal of Navigation and ObservationVolume 2013 Article ID 570964 13 pageshttpdxdoiorg1011552013570964

Research ArticleKalman Filter-Based Hybrid Indoor Position EstimationTechnique in Bluetooth Networks

Fazli Subhan1 Halabi Hasbullah2 and Khalid Ashraf2

1 National University of Modern Languages Sector H-91 Islamabad-44000 Pakistan2Universiti Teknologi PETRONAS Bandar Seri Iskandar 31750 Tronoh Perak Malaysia

Correspondence should be addressed to Fazli Subhan fazlisugmailcom

Received 7 June 2013 Revised 22 July 2013 Accepted 29 July 2013

Academic Editor Sandro Radicella

Copyright copy 2013 Fazli Subhan et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper presents an extended Kalman filter-based hybrid indoor position estimation technique which is based on integrationof fingerprinting and trilateration approach In this paper Euclidian distance formula is used for the first time instead of radiopropagation model to convert the received signal to distance estimates This technique combines the features of fingerprinting andtrilateration approach in a more simple and robust way The proposed hybrid technique works in two stages In the first stage ituses an online phase of fingerprinting and calculates nearest neighbors (NN) of the target node while in the second stage it usestrilateration approach to estimate the coordinate without the use of radio propagation model The distance between calculated NNand detective access points (AP) is estimated using Euclidian distance formula Thus distance between NN and APs provides radiifor trilateration approach Therefore the position estimation accuracy compared to the lateration approach is better Kalman filteris used to further enhance the accuracy of the estimated position Simulation and experimental results validate the performanceof proposed hybrid technique and improve the accuracy up to 5364 and 2558 compared to lateration and fingerprintingapproaches respectively

1 Introduction

Position estimation is the process which calculates objectposition with reference to some coordinate system Theposition of object can be specified as absolute coordinatesconsisting of (latitude longitude) and (x y) coordinates orin a symbolic form such as room number 1 of the 2nd flooror specific location represented by name Global positioningsystem (GPS) is the world first position estimation systemwhich was originally developed by the US Department ofDefense for military purpose in order to track the movementof enemies [1] GPS was originally designed for navigationpurpose to track the movement of objects from satellitesHowever this technology is used for outdoor applicationsThe signals transmitted from GPS satellites do not penetrateinside the buildings hence it is not applicable for indoorenvironment [2] In order to provide an alternate solutionfor indoor environment the research community is focusingon low-cost and highly accurate indoor position estimationtechniques which can be used for indoor environment [3]

The applications of indoor position estimation systems aredifferent from GPS and not limited to navigation or objecttracking Also apart from this GPS provides an accuracyfrom 5 to 10 meters which is sufficient for outdoor appli-cation but for indoor environment which comprises limitedgeographical area and the accuracy required is not sufficientfor indoor environment GPS [4] Therefore there is a direneed to develop an accurate indoor position estimationtechnique In order to improve the accuracy first of all it isnecessary to identify the factors which significantly affect theaccuracy of indoor position estimation systems theoreticallyand experimentally

Bluetooth is a short-range wireless radio technologywhich uses Bluetooth-enabled electrical devices to commu-nicate in the 245GHz ISM (license-free) frequency band [5]The communication changes the transmitting and receivingfrequency 1600 times per second using 79 different fre-quencies The range of Bluetooth network can be 0 to 100meters It is used to transmit both synchronous as well asasynchronous data The bandwidth of Bluetooth network at

2 International Journal of Navigation and Observation

physical layer is 21Mbits In the domain of indoor positionestimation there are also other wireless communicationstandards which can be used for indoor position estimationsuch as wireless local area networks (WLAN) and ZigBeeHowever in this paper Bluetooth technology is used forindoor position estimation due to its low cost low power andvast usage

This paper presents the design of an extended hybridtechnique for position estimation using the idea originallyproposed in [6] The hybrid technique combines the goodfeatures of fingerprinting- and lateration-based approaches ina simple and robust wayThe proposed hybrid technique firstuses fingerprintingmethod to calculate the nearest neighbors(NN) and then calculates the distance between each NN andanchor nodes using Euclidian distance formula When thedistance between each NN and anchor nodes is known thenthe position of target node is calculated using trilaterationtechnique The calculated position is then given to Kalmanfilter to minimize the effect of noise The next sectionelaborates design of proposed hybrid technique in moredetails The remainder of this paper is structured as followSection 2 discusses the existing indoor position estimationtechniques which is mainly focussed on fingerprinting- andlateration-based position estimation techniques Section 3presents the proposed extended hybrid position estimationtechnique Section 4 presents experimental setup and datacollection Section 5 presents numerical results and finallyconclusion and future research directions are presented inSection 6

2 Position Estimation Techniques

Positing estimation is the process to locate an object withreference to some coordinate system [2] In RF-basedwirelesscommunication position estimation is performed using RSSwhich is the parameter used to estimate distance betweenmobile and anchor nodes or APs [7 8] The standardradio propagation models are used to convert RSS measure-ments into distance estimates [9] There are generally twokinds of position estimation techniques that is laterationand fingerprinting-based position estimation techniquesLateration-based position estimation techniques use theradio propagation model to convert RSS measurements todistance estimates Fingerprinting-based position estimationtechniques use the pattern matching approach to estimatethe position of target node The following section providesan overview of the lateration-based position estimationtechniques

21 Lateration-Based Position Estimation TechniquesLateration-based position estimation techniques are amongthe widely usedmethods to estimate the location of the target[10ndash12] Lateration-based position estimation techniquesestimate the target position by measuring distance betweenthe target and anchor nodes The standard radio propagationmodel is used to convert RSS measurements to distanceestimates [1 13 14] The conversion process requiresradio propagation constants This process requires the

characterization of radio propagation constants specific tothe environment where RSS measurements are collectedThe distance estimation process strongly depends on thepropagation constants Once the distance estimates areknown then the position is estimated using equation ofcircles [15 16] The following subsection discusses thewell-known lateration-based position estimation techniques

211 Trilateration andMultilateration The term trilaterationrefers to the process which estimates the target position basedon measurements of distances from three fixed positions Insimple words it is a technique which estimates the point ofintersection from three fixed points [17] Trilateration refersto measurement the distance from three anchor nodes ofwhile multilateration measures the distance from more thanthree anchor nodes Trilateration and multilateration are themostly used lateration-based position estimation algorithmswhich use the radio propagation model to convert RSSmeasurements to distance estimates Trilateration algorithmcomputes the object position by taking the RSS measure-ments from at least three anchor nodes and the locations ofanchor nodes which measure the RSS are already fixed Formultilateration more than three anchor nodes are requiredto locate an object Both algorithms require distances fromtarget to anchor nodes [18] The distance 119889 is obtainedfrom RSS received at the anchor nodes The standard radiopropagation model is used to convert RSS readings fromtarget nodes to distances for estimation of target position[19 20] The distance between anchor nodes and fixedpoints depends on the radio propagation constants whichare represented in the form of numerical values required toconvert RSS measurements to distance estimates [21] Themathematical equations of trilateration and multilaterationare given as follows Let 119860(119909

1 1199101) 119861(119909

2 1199102) 119862(119909

3 1199103) and

119863(1199094 1199104) be the anchor and be 119879(119909 119910) be the target node

then distance 119889119894between anchor and target nodes can be

obtained using the following equation [22]

119889119894= radic(119909 minus 119909

119894)2

+ (119910 minus 119910119894)2

for 119894 = 1 2 3 119899 minus 1 (1)

The solution set of (1) using minimum mean square error(MMSE) which is a technique designed to minimize thevariance of the estimation errors is as follow

119860 = (2)

or

= 119860minus1 (3)

The estimated target position lies at the point of intersec-tion In ideal conditions the circles will intersect at onlyone point However the distance estimates contain noisewhich produces variations in RSS measurements Thereforeestimated position of target nodemay not be the unique pointof intersection In that case the MMSE technique is usedto estimate the coordinates of target node with minimumposition estimation error [23]

International Journal of Navigation and Observation 3

212 Maximum Likelihood Estimation MLE is a kind oflateration-based position estimation techniqueMLE is basedon the statistical consideration that the set of RSS measure-ments comes from anchor nodes containing noise The mainidea behind this approach is to minimize the mean squareerror (MSE) [24] First of all distance estimate is derivedfrom each of the anchor node using RSS measurement Thenthe estimated target node defines an error 119890

119894which is the

error between the estimated and the actual distance using thefollowing formula [25]

119890119894(1199090 1199100)

= 119889119894minus radic(119909

0minus 119909119894)2

+ (1199100minus 119910119894)2 for 119894 = 1 2 3 119899 minus 1

(4)

where (1199090 1199100) is the unknown position of target node

and (119909119894 119910119894) is the position of 119894th anchor node The detail

mathematical formulation is discussed in Section 34 Themain objective of MLE method is to minimize the meanerror This algorithm is mainly used for large-scale indoorpositioning Unfortunately for small scale the number ofmeasures is normally limited therefore for three anchors theperformance of this algorithm may be unsatisfactory

213 MinMax Algorithm MinMax is also a kind oflateration-based position estimation technique whichprovides a very simple trigonometric solution for positionestimation Like other lateration-based position estimationtechniques the position estimation process requires radiopropagation model to convert RSS measurements todistance estimates In MinMax algorithm a bounding box isconstructed for each anchor node using the given distancegenerated from propagation model The intersection of thesebounding boxes from anchor nodes will give the position oftarget node The bounding box is generated for each anchornode by adding and subtracting the estimated distance 119889from fixed anchor nodes [24 26] The mathematical formulafor MinMax algorithm is as follows

(max(119909119894minus119889119894)

max(119910119894minus119910119894)

) lowast (min(119909119894+119889119894)

min(119910119894+119910119894)

) (5)

where (119909119894 119910119894) is the position of anchor node and 119889

119894is the

distance between anchor and target node Compared totrilateration approach the mean error of MinMax approachis better in real-time scenarios However the MinMaxalgorithm is also based on radio propagation model andthe distance estimations are obtained based on the radiopropagation model On the other hand fingerprinting-basedapproaches provide better accuracy [24 27 28]

22 Fingerprinting-Based Position Estimation Techniques Inthe domain of position estimation fingerprinting is a tech-nique which determines location of a mobile terminal basedon the received signal fingerprints It is also termed as apattern matching technique in which RSS measurementsare matched with the stored set of RSS measurements Theposition estimation based on fingerprinting technique hastwo operational phases the online and offline phases The

offline phase is the training learning phase in which theRSS fingerprints which are the measured signal propertiesagainst respective location coordinates of reference points(RPs) are collected empirically to build up the fingerprintdatabase radio map of the concerned indoor environmentDuring the online positioning phase the measured signalquantities at target location are compared with the stored fin-gerprints using an appropriate database correlation method(DCM)The estimated location coordinates are derived fromthe RPs stored in the database which have similar signalcharacteristics to the target location The popular algorithmdeveloped by the researchers for database correlation inlocation fingerprinting-based technique is K-nearest neigh-bors (K-NN) [29] The fingerprints of K-NN-based positionestimation technique consist of average signal strengths (SS)over a time period taken at RPs

221 K-Nearest Neighbors (K-NN) K-NN is the most pop-ular fingerprinting-based position estimation techniqueswhich use RSS patterns to estimate the position of targetnode The term 119870 represents the numbers of the nearestneighbors to target node All fingerprinting-based positionestimation techniques estimate the target position in twostages that is offline and online stage Similarly K-NNestimates the target position in two stages that is in thefirst stage it uses an offline database which contains the RSSpattern collected at known locations In the second stagewhich is position estimation stage it calculates the positionof target node based on K-nearest neighbors The estimatedposition is average value of coordinates of the NNs Hencethe position is estimated based on the predefined value of 119870The value of 119870 is not fixed corresponding to the number ofNNs For example if the value of 119870 is 2 then a total of 2NNs will be calculated Similarly if the value of119870 is 119899 then 119899number of NNs will be calculated [30ndash32]

The position estimation process is carried in two stagesthat is offline and online Offline stage requires a databaseof RSS measurements collected at known locations Thisoffline phase is very time-consuming because the databasegeneration requires a lot of effort to construct the databaseThat is divide the whole area into equal size grids collecthundreds of RSS measurements at each location calculatethe mean value and store in the database Once the databaseis generated then position estimation is performed in theonline phase The online phase requires measurement ofthe RSS signals from the target node It compares RSSpatterns with stored database by measuring the Euclidiandistance between the measured and stored RSS value againsta predefined locationThe Euclidian distance formula is usedto estimate the distance between observed and stored RSSmeasurementThe distance between observed and stored RSSmeasurements is calculated and based on the value of 119870which is fixed 119870 shortest distances are calculated which istermed as NNsWhen the NNs are calculated then the targetposition is estimated by averaging the coordinates of the NNs[1 7]

K-NN is considered as the most accurate indoor positionestimation technique for stationary objects but due to time-consuming offline phase it is rarely used for dynamically


changing environments The RSS disagreements depend onthe environment where the measurements are collected Theadvantage of K-NN-based position estimation techniquesis the high accuracy On the other hand there are twomain limitations of K-NN First of all the time requiredto construct offline phase makes it impracticable for indoorenvironment Secondly the position of target node is alwaysestimated by taking the average value of NNs In case oflarge-size grid the error will be large For example if thecalculated NNs lie at corners of a 2-square meters grid thenestimated position will be the center point of grid which isnot always the case Hence position estimation error dependson the grid size If grid size is small then the correspondingtime taken to construct the offline stage will be more [33]Therefore based on these two drawbacks fingerprinting-based position estimation techniques are mostly not feasiblefor real-time position estimations

23Hybrid Indoor Position EstimationTechnique Anattemptis being made to combine the features of fingerprintingand lateration-based position estimation techniques in orderto enhance the position estimation accuracy In [6] theauthor proposed a hybrid indoor positioning algorithmusingWLANThe hybrid technique estimates the target position intwo steps In the first phase it uses fingerprinting algorithmto calculate the NN and in second stage the basic trilater-ation approach is applied to estimate target position How-ever like lateration-based position estimation techniques anempirical radio propagation model is used to convert RSSmeasurements to distance estimates This is almost similarto radio propagation model To convert RSSI measurementsto distance estimates the authors used empirical propagationconstants for different sets of environment The author thencompared position estimation accuracy with trilateration-and fingerprinting-based K-NN approach According tonumerical results obtained the position estimation accuracyis better than trilateration approach because target node liesnear the NN After this the distance between NNs and targetnode is calculated based on the radio propagation modelThe numerical results obtained using WLAN show that theproposed algorithm is better than basic trilateration approachhowever the position estimation error of the proposedtechnique is greater than K-NN algorithm [34]

The hybrid approach performs better than trilaterationapproach due to limited range that is when the NNs arecalculated then it is assumed that target node would existsomewhere near the NNs Therefore position estimationaccuracy of the proposed hybrid approach is comparativelybetter than basic lateration approach However the accuracyis still worse than K-NN

In [35] the authors proposed another hybrid indoorposition estimation technique which worked in three stagesIn the first stage it generated a database which modeledthe relation between distance and RSSI Then based ongenerated database the binary search algorithm was appliedto estimate distance between anchor and target node In thethird stage it used basic trilateration approach to estimatethe target position The author claims that the performance

of the proposed hybrid approach is better than the basictrilateration while the position estimation error is almostsimilar toK-NN [36]Thedistance between target and anchornodes which are fixed was estimated using a binary searchtechnique The position estimation process was carried outusing the basic trilateration

In summary both of the hybrid approaches use trilater-ation approach at the end to estimate target position withassumption that position of the target node lies when circlesintersect at one point only The positioning error provesthat the point of intersection is not unique or position oftarget node lies at the projected point of intersection Thelimitation of this hybrid approach is the complex binarysearch algorithm to estimate distance between anchor andtarget nodes The position estimation process is carried outin three instead of two steps The hybrid approach uses themodified K-NN approach in which the NNs are calculatedbased on probability of each 119870 elements The numericalresults show that the hybrid approach is comparatively betterthan trilateration and almost similar to K-NN

24 Related Work RADAR was the first RF-based posi-tion estimation technique for user tracking developed atMicrosoft Research RADAR is basically developed utilizingwireless local area networks (WLAN) using themost popularfingerprinting-based position estimation technique that isK-NN [30] The idea of using RF for indoor position estima-tion is experimentally verified and tested in order to estimatethe stationary object According to the experimental resultsthe accuracy for estimating the stationary object is around 3to 4meters RADAR uses RSSI as a signal parameter for posi-tion estimation together with the radio propagation modelFurthermore the authors opened the gate to develop an RF-based position estimation technique which can estimate theuser within a building The authors claimed that the positionestimation accuracy can be further enhanced by minimizingthe variations in RSSI measurements Kotanen presentedlocal positioning system based on received power level Theaccuracy obtained using extended Kalman filter was 376meters with radio propagationmodelThis technique is basedon the RX power level and used EKF for position estimation[37] Bluetooth technology is used for position estimationusing connection-based RSSI The measurements were thenconverted to RX power level by establishing a relationshipusing radio propagation model The conversion process wasperformed based on the GRPR The author finally suggestedthat the accuracy of the position estimation techniques can beimproved if the variations in RSSI are minimized In [38] theauthors compared lateration- and fingerprinting-based posi-tion estimation techniques and outlined themajor advantagesand disadvantages Furthermore the authors concluded thatfingerprinting-based position estimation techniques providebetter accuracy than lateration-based techniques howeverdue to the time-consuming offline stage it is rarely used forreal-time position estimation where frequent changes in theenvironment occurOn the other hand lateration-based posi-tion estimation techniques namely trilateration approach isvery simple and efficient but due to the radio propagation


model constants the accuracy is comparatively lesser thanfingerprinting-based position estimation techniques

In [26] the authors compared the lateration-based posi-tion estimation techniques namely MLH MinMax andmultilateration The authors experimentally compared allthe techniques and concluded that MinMax performs bet-ter than trilateration- and multilateration-based positionestimation techniques Furthermore the authors performedsimulations to see the effect of increasing anchor nodes onposition estimation accuracy According to the simulation-based numerical results the accuracy of MLH increaseswith the increasing number of anchor nodes compared toMinMax and multilateration approach However accord-ing to the concluding remarks of authors the accuracystill depends on selection of radio propagation constantsand variations in RSSI In [39] the authors discussedthe fingerprinting-based position estimation techniques andfocused on the offline stage of fingerprinting-based posi-tion estimation techniques The authors modeled the userbehavior in constructing an offline stage for fingerprinting-based position estimation techniques The authors arguedthat user feed is necessary to generate an offline databasewhich is required to design a fingerprinting-based posi-tion estimation technique in order to minimize the time-consuming offline stage in fingerprinting-based positionestimation technique In [29] the authors extended theidea of Kotanen [37] to WLAN using extended Kalmanfilter for real-time position estimation in indoor environ-ment The authors compared trilateration and fingerprintingtechniques with the proposed EKF-based indoor positionestimation The numerical results obtained from the pro-posed EKF-based position estimation technique confirmthat the mean error of EKF is better than trilaterationand worse than K-NN The authors claimed that the meanerror obtained using EKF is 375 meters in typical indoorenvironments

In [24] the authors compared themost popular lateration-based position estimation techniques namely trilaterationMinMax and Maximum Likelihood (MLH) using real-timeRSSImeasurementsThenumerical results presented confirmthat lateration-based position estimation techniques stronglydepend on radio propagation constants The authors mod-eled the radio propagation constants using a mathematicalapproach and identified the radio propagation constantsempirically Furthermore the computational complexity ofeach algorithm was also calculated Based on the real-time RSSI measurements from IEEE 802154 wireless sensornetworks (WSN) it is observed that MinMax algorithmperforms better than trilateration and MLH for averageRSSI measurement The authors also used the concept ofmultiple antennas in order to improve the accuracy ofposition estimation Furthermore authors conclude that theexisting lateration-based position estimation techniques canbe effectively used to develop a successful indoor positionestimation system if the variations in RSSI are minimizedand radio propagation model constants are accurately used

In [2 9 17 40] the authors conclude that lateration-basedapproaches can be effectively used to design an indoor posi-tion estimation technique if the radio propagation constants

and variations in RSSI measurements are minimized Inlateration-based position estimation techniques the difficultstage is to model the radio propagation constants in such away that the effect noise which increases variations in RSSIis minimized

In summary lateration-based approaches can be effec-tively used to design an indoor position estimation techniqueif the radio propagation constants and variations in RSSmeasurements are minimized In lateration-based positionestimation techniques the difficult stage is tomodel the radiopropagation constants in such a way that the effect noisewhich increases the variations in RSS is minimized Themajority of these works consider IEEE 802154 and its succes-sor IEEE 802154a However these twowireless personal areanetworking technologies are not yet widespread Moreoverthe 802154a standard is specifically designed for positioningbut UWB-based commercial systems for positioning arestill at a prototyping phase On the other hand most ofportable devices and mobile phones include a Bluetoothtechnology hence a position estimation technique based onthis technology could be easily deployed with no costs for theend users Therefore based on the above facts positioningsystem based on Bluetooth technology provides a low-costsolution for indoor position estimation

3 Design of Proposed Hybrid Indoor PositionEstimation Technique

The proposed hybrid indoor position estimation techniquecalculates target position in two stages In the first stage NNsare calculated by comparing theRSSmeasurements observedat target position with the RSS stored in a database using K-NN algorithm When the NNs are calculated then distancebetween coordinates of NNs and anchors is calculated usingEuclidian distance formula In second stage the positionof target node is calculated using trilateration techniqueThe calculated coordinates usually contain noise due to thevariations in RSS measurements Noise is an unpredictablephenomenon and its values are unknown but it can beassumed that the values belong to a probability distributionfunction In the proposed hybrid technique the properties ofnoise are assumed to be Gaussian and normally distributedAs the noise is assumed to be Gaussian Kalman filter isapplied to estimate position of target node and removes theeffects of Gaussian noise

The proposed hybrid estimation technique possessesfeatures of fingerprinting and lateration-based techniques Infingerprinting-based technique the most popular approach isK-NN which calculates119870 nearest neighbors and position oftarget node is calculated by averaging the coordinates of NNsIn lateration-based technique trilateration and MinMax arethe most popular position estimation techniques [24] In thispaper the proposed hybrid approach integrates K-NN withtrilateration approach Other than trilateration approachMinMax can also be integrated with K-NN However theposition estimation error using MinMax is greater comparedto using trilateration-based technique The reason behindthis is the use of radio propagation model which is used


to convert RSS measurements to distance estimates Hencetrilateration-based hybrid approach is considered as a betterapproach The main contribution of the proposed techniqueis to completely eliminate the use of a radio propagationmodel which is normally used to convert RSS measure-ments to distance estimates The proposed hybrid indoorposition estimation technique is completely independent ofthe environmental conditions as it does not consider radiopropagationmodelThe proposed hybrid position estimationtechnique minimizes the time-consuming offline stage byusing a model-based radio map generation utility to buildthe RSS map during offline stage To achieve this the firststep is to calculate experimentally the relation between RSSand distanceThe RSSmeasurements are collected by varyingthe distance between master and mobile node at a fixed stepsize up to maximum range of the device used In order toaccommodate orientation of device the measurements needto be collected in different directions The average valuesof measurements for each step size are required Each RSSmeasurement is stored in a table against its recorded distanceThe RSS map is then generated based on the relationshipmodel developed using RSS and distance relationship Thedistance between each grid and AP is calculated usingEuclidian distance formula

31 Stage 1 (Offline Phase) In the offline stage offingerprinting-based approach the whole area is dividedinto equal size grids The RSS samples are collected at eachgrid several times The average of measured RSS valuesis calculated and stored in a lookup of table with theircorresponding coordinates If the area of position estimationsystem is 100 square meters then the RSSI samples arecollected at 100 locations from each anchor node Thisapproach is very time-consuming and a lot of effort isrequired to build the RSS map Any small change in the areacan affect the accuracy The limitations of fingerprinting-based approach are the time-consuming offline stage whichrequires effort to construct the radio map Therefore fordynamic indoor environment where frequent changes comefingerprinting approach is rarely used [39] In this paperan attempt is made to minimize the time-consuming offlinestage by an automatic map generation utility which is basedon the distance to RSS relationshipThe following subsectionelaborates automatic map generation utility

32 Automatic RSS Map Generation Utility In order to buildan RSSmap a simple method is tomeasure the RSSmeasure-ments from a single anchor node in all directions dependingon range of Bluetooth devicesThe step size is fixed to 1meterA minimum of two devices are required to build the mapOne is considered as master node and the second as mobilenode The master node is fixed while the mobile node ismovingThe experiment was conducted in lab at Departmentof Computer and Information system Universiti TeknologiPETRONAS The RSS samples were collected by moving theslave node away from master node with a fixed step size of 1meter to a maximum of 10 meters The process was repeatedfor all directions in order to consider the orientation ofmaster

node At each step a total of 50 RSS measurements werecollected Three mobile devices of the same specificationswere used simultaneously to save time For each locationthe average value is calculated Based on the mean RSSmeasurements the RSSmap can be generated using Euclidiandistance formula Consider an example of area of 10 squaremeters which have 100 locations The distance between eachgrid having known coordinates from the respective anchornodes can be calculated using Euclidian distance formulaThe minimum value of RSS value is minus90 dBm which isassigned to the maximum rounded distance of 13 metersThe Euclidian distances are converted to round numbersbased on the significant digit rule Once the relationshipbetween distance and RSS is established the RSS map canthen be generated using Euclidian distance formulaThe ideaof automatic map generation is useful to large area whenthere are many anchor nodes and the radio map generationis difficult and time-consuming The benefit of knowing thisrelationship can also beworthful in identifying accurate radiopropagation constants Furthermore this relationship canalso help to filter RSS values Knowing the upper and lowerboundary of RSS measurements filtering and predicting RSSvalues in noisy environment can be worthful

33 Online Phase In this stage the proposed hybrid positionestimation algorithm uses the online stage of fingerprinting-based K-NN algorithm to calculate the NN based on filteredRSS received at anchor nodes The NNs are calculated basedon the shortest Euclidian distance between the RSS obtainedat target node and the corresponding RSS in database storedin the offline stage The formula for calculating the NN isexpressed as follows

119889 = radic

119899

sum

119894=1

(119904119894minus 1199041198941015840)2

(6)

where 119889 shows Euclidian distance 119904119894represents RSS received

at the target location and 1199041198941015840 shows the corresponding RSS

in database while 119899 is the number of anchor nodes forwhich the Euclidian distance is calculated The number ofNN represents value of 119870 If the value of 119870 = 3 thenonly three NNs will be calculated In the proposed hybridposition estimation technique theminimum value of119870mustbe greater than 2 the number NN required to estimateposition of target node For trilateration approach at least 3NNs are required The coordinates of the calculated NNs arealready identified and also the coordinates of anchor nodesare fixed in advance Hence the position of target node canbe estimated using lateration-based approach

34 Stage 2 (Position Computation Using TrilaterationApproach) [26] When the 119870 number of NNs are cal-culated the distance between their respective coordi-nates and anchor nodes can be calculated using (6)For example NN

1(1198831 1198841) NN

2(1198832 1198842) NN

3(1198833 1198843) and

NN4(1198834 1198844) are the nearest candidate points and locations

of anchor nodes are AP1(1198831 1198841) AP2(1198832 1198842) AP3(1198833 1198843)

and AP4(1198834 1198844) hence the Euclidian distance formula is


used to calculate distance between these points When thedistances are given then trilateration approach can be usedto calculate coordinates of the target location using thefollowing equation for circle Consider that (119909

1 1199101) (1199092 1199102)

(1199093 1199103) and (119909

4 1199104) are the AP location and (119909 119910) is the

target node Hence the equation of circle becomes

(1199091minus 119909)2

+ (1199101minus 119910)2

= 1198892

1 (7a)

(1199092minus 119909)2

+ (1199102minus 119910)2= (1198892)2

(7b)

(1199093minus 119909)2

+ (1199103minus 119910)2

= (1198893)2

(7c)

(1199094minus 119909)2

+ (1199104minus 119910)2

= (1198894)2

(7d)

Similarly (119909119899minus 119909)2

+ (119910119899minus 119910)2

= (119889119899)2 for 119894 = 1 2 4

(7e)

To solve the above simultaneous equations in order to find theposition of target node (119909 119910) subtract (7d) from (7a) (7b)and (7c) respectively

(1199091minus 119909)2

minus (1199094minus 119909)2

+ (1199101minus 119910)2

minus (1199104minus 119910)2

= (1198891)2

minus (1198894)2

(8a)

(1199092minus 119909)2

minus (1199094minus 119909)2

+ (1199102minus 119910)2

minus (1199104minus 119910)2

= (1198892)2

minus (1198894)2

(8b)

(1199093minus 119909)2

minus (1199094minus 119909)2

+ (1199103minus 119910)2

minus (1199104minus 119910)2

= (1198893)2

minus (1198894)2

(8c)

Rearrange (7a) (7b) and (7c) respectively to get the linearequations

2 (1199094minus 1199091) 119909 + 2 (119910

4minus 1199101) 119910

= (1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(9a)

2 (1199094minus 1199092) 119909 + 2 (119910

4minus 1199102) 119910

= (1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(9b)

2 (1199094minus 1199093) 119909 + 2 (119910

4minus 1199103) 119910

= (1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

(9c)

Rewrite the earlier equation in matrix form as follows

2[

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

[

[

119909

119910

]

]

=[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(10)

Hence the linear systemobtained inmatrix form is as follows

119860 lowast = (11)

Simultaneous linear equations can be solved using (11) where

119860 = [

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

119909 = [

[

119909

119910

]

]

119887 =[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(12)

Equation (11) can be solved using the following Equation (13)

= 119860minus1sdot (13)

The solution of (13) exists only if 119899 = 119898 and 119860minus1 wheren = number of equations corresponding to number of anchornodes and 119898 = coordinates of the target node In case of119899 gt 119898 then the system is considered as determined systemof equations which can be solved using minimum meansquare error (MMSE) method To minimize the distanceerror which occurs due to various environmental conditionsand over determined system of equations MMSE techniqueis used to minimize the mean square error [26]

119860119909 minus 1198872 997888rarr 119860119879119860119909 = 119860

119879119887

119909 = (119860119879119860)minus1

119860119879119887

(14)

The position estimation using trilateration approach assumesthat target node lies at the point of intersection In idealcondition the solution set of (13) will exist only if all thethree or four circles intersect at only one point Then thesolution set will be existing but in real-time scenariosthe circles do not intersect Therefore based on the real-time scenarios this hybrid algorithm is designed As hybridalgorithm first calculates the NNs and then measures the dis-tance between fixed anchor nodes and NNs using Euclidiandistance therefore it is clear that the circles will not intersectEquation (13) calculates the position of target node based onprojected point of intersection similar to basic trilaterationapproach Normally in an area of 100 square meters if thereare four anchor nodes there is only one point where all thecircles will intersect Therefore the proposed hybrid indoorposition estimation algorithm considers measuring distancebetween anchor nodes andNNHence tominimize the effectof position estimation error Kalman filter can be used toestimate position of target node [41]

341 Kalman Filter Kalman filter is a standard filter devel-oped by Rudolf Kalman in 1960 which removes noise froma series of data [42] Kalman filter is widely used in controlsystems to estimate the state of a process in presence ofnoisy measurements It estimates the states of a process byminimizing mean square error between the ideal and realsystem states Kalman filter estimates the states of a process intwo steps that is time update step (also known as prediction)andmeasurement update step (also known as correction) Let


a linear time-invariant systembe represented by the followingequations [43]

119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)

where 119865 represents the system matrix 119883 represents state attime 119905 and119884 represent observations of at time 119905 where119865 and119867 represent the system matrices and 119876 and 119877 are covarianceofmeasurement noise Consider that an object ismovingwitha constant velocity The new estimated position is the oldposition plus velocity and noise Hence the matrices become

119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)

As the position of target node is estimated using orientationalspace therefore state size is 4 and observation size is 2becausewe are only estimating the position of the target nodeThe measurement parameters of Kalman filter equations aretuned to adjust to the value of 119876 and 119877 in order to minimizeerror in position estimation After repeated processing thenumerical values adjusted are 119876 = 001 and 119877 = 116The numerical values are selected after extensive simulationsstudies in order to adjust the values based on the mean errorbetween actual and estimated position

4 Experimental Setup and Data Collection forReal-Time Analysis

An experiment was performed to collect the RSS mea-surement in order to verify the proposed hybrid positionestimation technique The location of testbed lies in secondfloor of Department of Computer and Information SciencesWireless Communication Lab The dimension of lab is(1420m times 16m) having an area of 2272 square metersOut of this an area of (10m times 10m) was selected for theexperiment The devices which were used in the experimentsare Bluetooth USB dongles from Cambridge Silicon havingclass 1 specifications Four anchor nodes which representedthe master nodes were used to collect RSS measurementsAll the anchor nodes and mobile devices had the samespecifications The whole area was divided into grids havingsize equal to 1 square meter A total of 100 grids were createdThe data collector program was running simultaneously onall anchor nodes using BlueZ programming language TheSecure Shell (SSH) utility was configured using WLAN IPin order to synchronize the time for data collection At eachgrid the mobile device was placed in the middle of gridand 100 RSS measurements were collectedThe data collectorprogram was programmed for collecting RSS readings usinginquirymodeTheRSS samples collected by the data collectorprogram were stored in an excel sheet The average values foreach grid were calculated Figure 1 shows the experimentalsetup with known anchor and mobile nodes The anchornodes were fixed and their actual position is necessary for theproposed hybrid approach to estimate the position of mobile

node Out of 100 grids the mobile nodes were placed in 10random locations as shown in the experimental setup

The following subsection discusses a comparative analysisusing real-time RSS measurements obtained from the exper-iment conducted

5 Results and Discussions

The performance of proposed algorithm was tested for 10target nodes the positions of which were already knownBased on the mean RSS values position of mobile nodeswere estimated using trilateration MinMax K-NN and theproposed hybrid indoor position estimation technique Themean error and standard deviation of position estimationerror were calculated for analysis Table 1 shows the meanerror analysis of trilateration MinMax K-NN and proposedhybrid indoor position estimation technique The positionof mobile client was calculated using 3 and 4 anchor nodesThe numerical results obtained from real-time RSS measure-ments using sample size of 100 RSS measurements showthat the mean error of trilateration is 332 and 302 metersfor 10 target nodes using 3 and 4 anchor nodes respec-tively The performance of lateration-based algorithms isgreatly dependent on radio propagation constantsThereforefor radio propagation constants Bluetooth channel modelerwas used which identifies the radio propagation constantsthrough a mathematical approach The mean error observedfor MinMax is 293 and 258 meters while mean error ofK-NN is 246 and 192 meters for 3 and 4 anchor nodesrespectively On the other hand mean error of the proposedhybrid approach is only 199 and 140 meters for 3 and 4anchor nodes respectively

Table 1 shows standard deviation of position estimationerror The numerical results indicate that standard deviationof the proposed hybrid algorithm is better than K-NN how-ever compared to trilateration for 3 anchor nodes it is greaterGenerally increase in number of anchor nodes decreasesthe mean error and standard deviation proportionally Theproposed hybrid approach uses Kalman filter tominimize theeffect of noise in dynamic environment The Kalman filterassumes that the estimated position contains Gaussian noisetherefore output of the proposed hybrid approach is givento Kalman filter to minimize the effect of Gaussian noiseThe Kalman filter further minimizes mean error of estimatedposition The Kalman filter improves the accuracy of theproposed algorithm by 18 As Kalman filter minimizesthe position estimation error by 18 hence it is observedthat estimated position contains noise Hence based on thereal-time offline RSS measurements it is confirmed that theproposed hybrid approach performs better than trilaterationMinMax and K-NN in terms of position estimation error

51 Comparative Analysis Using Simulations To investigateperformance of the proposed algorithm simulation wasperformed using three and four anchor nodes The ideabehind simulation-based analysis is to see performance ofthe proposed hybrid approach using random RSS samples inorder to validate the position estimation accuracy for larger


0

2

4

6

8

10

12

0 2 4 6 8 10 12

Experimental setup for real-time analysis

Target nodeAnchor node

minus2

minus2 X-axisY

-axi

s

Figure 1 Experimental setup showing actual positions of anchor nodes and selected target nodes

Table 1 Mean error (ME)standard deviation (St D) analysisof trilateration K-NN MinMax and proposed hybrid technique(sample size 100)

Actualposition(119909 119910)

Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122

Table 2 Simulation studies mean error (ME)standard deviation(St D) analysis of trilateration K-NN MinMax and proposedhybrid technique (sample size 100)


Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098

locationThe simulationmodel actually depicts the variationsoccurring in RSS measurements in order to validate theperformance of the proposed hybrid position estimationtechnique on large scale According to initial experimentalobservation the standard deviation of RSS measurementsobtained from a stationary object is 10 dBm Hence themethodology adopted to test performance of the proposed

technique follows real-time standard deviation of RSSThere-fore target node is placed in middle of the anchor nodesTheactual position of target node is stored and a total of 100 RSSrandom samples were generated with a standard deviationof 10 dBm The simulation was performed using three andfour anchor nodes The position of the anchor nodes wasnot fixed The simulation was repeated 3 times by changingthe actual position of the anchor nodes and each time themobile nodes were assumed to be in the middle of the anchornodes The statistical parameters that were used for simula-tion results were mean error and standard deviation of theposition estimation error The random RSS measurementsthat were generated ignored the communication holes Thefollowing subsection presents a comparative analysis of theproposed hybrid approach with the K-NN trilateration andMinMax Table 2 shows the simulation results of trilaterationMinMax K-NN and proposed hybrid approach using 3 and4 anchor nodes As position of target node lies in the middletherefore mean error of trilateration and K-NN algorithm islow However it is clear from Table 2 that the mean errorof proposed hybrid approach is better than trilaterationMinMax and also K-NN As the proposed algorithm usesKalman filter to minimize the Gaussian noise thereforecompared to K-NN the mean error of proposed algorithmis better In general the performance of lateration-basedposition estimation technique increases with the increase innumber of anchor nodes but in this case the performanceof lateration-based algorithm using 3 anchor nodes is betterThe reason behind this is position of the target node and alsothe variation is constant for all anchor nodes According tothe literature studies the performance of MinMax algorithmis better than trilateration approach [24 44] Table 2 alsoconfirms that the mean error of MinMax is lesser thantrilateration approach however it is greater than K-NNapproach In case of increasing number of anchor nodes theaccuracy increases proportionally but the case is differentin simulations due to the fixed radio propagation constantsHence the mean error of MinMax for 3 anchor nodes isbetter than 4 anchor nodes Therefore based on 100 randomRSS measurements with a standard deviation of 10 dBm it is


Table 3 Mean error analysis of trilateration K-NN and proposedhybrid technique (sample size 10)

Actual position(119909 119910)

Trilateration (m) K-NN (m) Hybridapproach (m)

(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079

observed that the position estimation error of the proposedhybrid approach is lesser than K-NN trilateration and alsobetter than MinMax The performance of proposed hybridtechnique is analyzed using twomethods that is using offlineand online RSS measurements Offline RSS measurementsmean that the RSS measurements were collected at knownlocations and the mean value was calculated from 100 RSSsamples at each location The performance of the proposedapproach is then analyzed using mean RSS value calculatedduring offline phase

While online RSS measurements mean that for each andevery real-time RSSmeasurement obtained the performanceof proposed hybrid approach is tested and compared withtrilateration MinMax and K-NN In this way the real-timeRSS fluctuations are also considered

The above numerical results demonstrate the perfor-mance of the proposed hybrid approach using offline RSSmeasurements based on mean RSS value The sample sizeof offline measurements was 100 The following subsectionpresents a comparative analysis using real-time online RSSmeasurement for every measurement observed

52 Comparative Analysis Using Real-Time RSSMeasurements(Online) In order to check the performance of the proposedalgorithm based on real-time online RSS measurementsan experiment was performed and the position of targetnode was calculated based on online RSS measurementsThe experimental setup was the same using the same setof Bluetooth dongles Eight random positions were selectedand the RSS measurements were observed using SSH()command to remotely access the client computers [45] Thetime synchronization is important for the client computerstherefore the data collector program was executed usingLinuxSSH() command for 15 seconds During this time 10samples were recorded The RSS measurements containedthe effect of noise therefore the measurements were filteredusing extended gradient RSS predictor and filter

Tables 3 and 4 represent a comparative analysis of pro-posed hybrid approach with trilateration and K-NN A totalof 8 positions were selected for mobile node and the RSSmeasurements were observed for 15 seconds at each positionTable 3 shows the actual positions of mobile clientThemeanerror and standard deviation of the estimated position error

Table 4 Standard deviation of error in trilateration K-NN andhybrid algorithm (sample size 10)



(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041

were observed In Tables 3 and 4 column 1 represents theactual position of target node and column 2 represents themean and standard deviation of trilateration Similarly inTables 3 and 4 column 3 represents mean and standarddeviation of the proposed hybrid approach According toreal-time online numerical results using 4 anchor nodesthe mean error of proposed hybrid approach is better thantrilateration and K-NN for each point except the middlepoint that is (5 6) When mobile node lies in the middleof anchor nodes then it is possible that at certain places thepoint of intersection is more closer than hybrid approach Asthe proposed hybrid position estimation technique assumesthat the point of intersection is not unique therefore basedon this assumption the position of target node is estimated bymeasuring the distance between calculated NN and Anchornodes Therefore if the target node is placed at the centerthen the position estimation accuracy is better than theproposed hybrid position estimation approach

Table 4 shows the standard deviation of trilateration K-NN and proposed hybrid approach In case of real-timeonline observations the fluctuations in RSS measurementsexist therefore it is possible that standard deviation of theproposed hybrid approach is more than the trilateration andK-NN

Based on the numerical results presented in Tables 3 and4 it is observed that performance of the proposed hybridtechnique is better than trilateration and K-NN

53 Comparison of the ProposedHybrid Technique with Trilat-eration Approach The performance of the proposed hybridapproach is further compared with trilateration approach inorder to visualize the calculated position As discussed earliertrilateration approach assumes that target position lies at thepoint of intersection The radius of circle is equal to thedistance between anchor and target node But in real-timescenarios due to noise in RSS measurements the circles donot intersect at one point Therefore the position of targetnode lies at the projected line of interaction from three circlesIn case of hybrid approach first of all the NNs are calculatedand then the distance between NNs and anchor nodes iscalculated using Euclidian distance formula The circles aredrawn with the radii equal to the distance between NNs andanchor nodes In all the figures the black square (if printed in


0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)

X-axis (m)minus4 minus3 minus2 minus1

Position estimation error using trilaterationversus hybrid technique (0 5)

Figure 2 Position estimation error of trilateration and hybridtechnique (0 5)

2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)



color) represents the center of the circleThe proposed hybridapproach ensures that the estimated position will be near toNN Following is the explanation of each case

Figure 2 represents the case when actual position of nodeis at (0 5) As indicated in Figure 2 the actual positionlies at point (0 5) the calculated NNs are very close tothe actual position and hence the estimated position usinghybrid approach is also near to NN that is the projectedpoint of intersection The circumference of each circle ispassing through NNTherefore the point of intersection andactual position are closer to each other As shown in Figure 2the estimated position using trilateration approach is away

3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid

Figure 4 Position estimation error of K-NN and hybrid technique(0 5)

1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)

Position estimation error using K-NNversus hybrid technique (6 4)


from the actual position It means that in case of trilaterationthe projected point of intersection lies away from the actualposition The calculated mean error of trilateration approachis 213 meters while the mean error of proposed hybridapproach is 077 meters Figure 3 shows the case when theactual location of mobile device is (6 4) As the point liesin the middle of the anchor nodes so position estimationerror is better than K-NN approach The mean error oftrilateration approach is approximately equal to the proposedhybrid approach that is 169 and 166 meters respectivelyFigure 3 shows that the proposed hybrid approach estimatesthe position of mobile node somewhere near to NN This isthe scenario where trilateration algorithm performs better


Figures 2 and 3 show the comparative analysis of proposedapproach with trilateration approach The following sub-section presents a comparative analysis of the proposedhybrid technique with K-NN

54 Comparison of the ProposedHybrid TechniquewithK-NNTheposition estimation error is visualized in order to analyzethe difference between K-NN approach and proposed hybridapproach Figures 4 and 5 present the position estimationerror of K-NN and proposed hybrid technique when actualpositions of the mobile node are at (0 5) and (6 4) Asdiscussed earlier K-NN algorithm computes position oftarget node by averaging the coordinates of NN Figure 4shows estimated position using K-NN approach within themiddle of NN Therefore in case of 1 or 2 meters grid sizethe position error depends on size of grid For example ifsize of grid is 2 square meters then the target node lies atthe corner of 2 square meters grid instead of center locationFigure 4 clarifies the scenario inwhich the estimated positionis at the middle of the anchor nodes However the proposedhybrid approach estimates target position based on projectedpoint of intersection which can be any where near NNs Thecalculated mean error of the proposed hybrid approach is080 meters while the K-NN is 2 meters Figure 5 shows thecase when actual position of the mobile node is at (6 4) Thistime the position estimation error is more than trilaterationapproach because actual position lies in the middle of anchornodes The mean error of K-NN is again 2 meters which isgreater than trilateration and the proposed hybrid approach

6 Conclusions and Future Work

This paper presented an extended Kalman filter-based hybridindoor position estimation technique The main objectiveof this approach is to increase the accuracy by minimizingthe mean error Other than this the existing gradient RSSIpredictor and filter is modified based on the most recent RSSmeasurement in order to predict andfilter theRSS in presenceof communication gap termed as communication hole Inproposed hybrid approach the filtering process is performedas a preprocessing tool to handle the variations occurringin RSS due to environmental conditions The numerical andgraphical result presented in this paper concludes that theproposed extended Kalman filter-based hybrid indoor posi-tion estimation technique improves the position estimationaccuracy compared to the trilateration MinMax and K-NNThe novel idea presented in this paper is the eliminationof radio propagation model for distance estimation whichsignificantly improves the position estimation accuracy Astandard Kalman filter is used after the trilateration approachwhich further enhances the position estimation accuracy

The proposed hybrid positioning algorithm can be easilyimplemented on other wireless platforms such as WLAN orZigBee standard The idea of automatic map generation canfurther simplify fingerprinting-based approach and also thetime to build the radio map Future research is needed to testthe hybrid approach on other platforms and on large scale

Acknowledgments

The authors would like to thank Dr Emanuele Goldoni atUniversity of Pavia Italy and Salman Ahmed at University ofAlberta Canada for providing useful suggestions and help

References

[1] F Forno G Malnati and G Portelli ldquoDesign and implementa-tion of a bluetooth ad hoc network for indoor positioningrdquo IEEProceedings Software vol 152 no 5 pp 223ndash228 2005

[2] G Mao B Fidan and B D O Anderson ldquoWireless sensornetwork localization techniquesrdquo Computer Networks vol 51no 10 pp 2529ndash2553 2007

[3] M P Kodde ldquoBluetooth communication and positioning forlocation based servicesrdquo Report For the Course Location BasedServices TU-Delft The Netherlands 2005

[4] K Nguyen Robot-based evaluation of bluetooth fingerprinting[MS thesis] Queensrsquo College Computer Laboratory Universityof Cambridge UK 2011

[5] Bluetooth Special Intrest Group ldquoFast-factsrdquo 2011[6] B Li A Dempster C Rizos and J Barnes ldquoHybrid method

for localization using wlanrdquo in Proceedings of the InternationalConferene on Spatial Intelligence Innovation and Praxis pp297ndash303

[7] L Dong and W Jiancheng ldquoResearch of indoor local posi-tioning based on bluetooth technologyrdquo in Proceedings of the5th International Conference on Wireless Communications Net-working and Mobile Computing (WiCOM rsquo09) Beijing ChinaSeptember 2009

[8] M Sugano T Kawazoe Y Ohta and M Murata ldquoIndoorlocalization system using RSSI measurement of wireless sensornetwork based on ZigBee standardrdquo in Proceedings of theInternational Conference on Wireless Sensor Networks (IASTEDrsquo06) p 6s Alberta Canada July 2006

[9] L Peneda A Azenha and A Carvalho ldquoTrilateration forindoors positioning within the framework of wireless commu-nicationsrdquo in Proceedings of the 35th Annual Conference of theIEEE Industrial Electronics Society (IECON rsquo09) pp 2732ndash2737Porto Portugal November 2009

[10] J Hightower and G Borriello ldquoLocation systems for ubiquitouscomputingrdquo Computer vol 34 no 8 pp 57ndash66 2001

[11] D Zhang F Xia Z Yang L Yao and W Zhao ldquoLocalizationtechnologies for indoor human trackingrdquo in Proceedings of the5th International Conference on Future Information Technology(FutureTech rsquo10) Busan Republic of Korea May 2010

[12] S Zhou and J K Pollard ldquoPosition measurement using blue-toothrdquo IEEE Transactions on Consumer Electronics vol 52 no2 pp 555ndash558 2006

[13] J Yang and Y Chen ldquoIndoor localization using improved rss-based lateration methodsrdquo in Proceedings of the IEEE GlobalTelecommunications Conference GLOBECOM rsquo09) HonoluluHawaii USA December 2009

[14] C Alippi and G Vanini ldquoA RSSI-based and calibrated cen-tralized localization technique for wireless sensor networksrdquo inProceedings of the 4th Annual IEEE International Conference onPervasive Computing and CommunicationsWorkshops (PerComrsquo06) pp 306ndash311 Pisa Italy March 2006

[15] E-E Lau and W-Y Chung ldquoEnhanced RSSI-based real-timeuser location tracking system for indoor and outdoor environ-mentsrdquo in Proceedings of the 2nd International Conference on


Convergent Information Technology (ICCIT rsquo07) pp 1213ndash1218Republic of Korea November 2007

[16] W Xinwei B Ole L Rainer and P Steffen ldquoLocalization inwireless ad-hoc sensor networks using multilateration withRSSI for logistic applicationsrdquo Procedia Chemistry vol 1 no 1pp 461ndash464 2009

[17] A V Bosisio ldquoPerformances of an RSSI-based positioningand tracking algorithmrdquo in Proceedings of the InternationalConference on Indoor Positioning and Indoor Navigation (IPINrsquo11) Guimaraes Portugal September 2011

[18] A Boukerche H A B F Oliveira E F Nakamura and A A FLoureiro ldquoLocalization systems for wireless sensor networksrdquoIEEE Wireless Communications vol 14 no 6 pp 6ndash12 2007

[19] S Pandey and P Agrawal ldquoDistance measurement model basedon RSSI in wsnrdquo Wireless Sensor Network Scientific Researchvol 29 no 7 pp 606ndash6011 2010

[20] H Jeffrey and B Gaetano ldquoLocation sensing techniquesrdquo TechRep UW CSE 2001-07- 30 vol 34 2001

[21] R M Pellegrini S Persia D Volponi and G MarconeldquoRF propagation analysis for ZigBee Sensor Network usingRSSI measurementsrdquo in Proceedings of the 2nd InternationalConference on Wireless Communication Vehicular TechnologyInformation Theory and Aerospace and Electronic Systems Tech-nology (Wireless VITAE rsquo11) Chennai India March 2011

[22] S William and J Murphy Determination of a position usingapproximate distances and trilateration [MS thesis] Trustees ofthe Colorado School of Mines Colo USA 2007

[23] K Langendoen and N Reijers ldquoDistributed localization inwireless sensor networks a quantitative comparisonrdquoComputerNetworks vol 43 no 4 pp 499ndash518 2003

[24] E Goldoni A Savioli M Risi and P Gamba ldquoExperimentalanalysis of RSSI-based indoor localization with IEEE 802154rdquoin Proceedings of the EuropeanWireless Conference (EW rsquo10) pp71ndash77 Lucca Italy April 2010

[25] X Kuang and H Shao ldquoMaximum likelihood localization algo-rithm using wireless sensor networksrdquo in Proceedings of the 1stInternational Conference on Innovative Computing Informationand Control (ICICIC rsquo26) pp 263ndash266 2003

[26] G Zanca F Zorzi A Zanella and M Zorzi ldquoExperimentalcomparison of RSSI-based localization algorithms for indoorwireless sensor networksrdquo in Proceedings of the 3rd Workshopon Real-World Wireless Sensor Networks (REALWSN rsquo08) pp 1ndash5 April 2008

[27] R Priwgharm and P Chemtanomwong ldquoA comparative studyon indoor localization based on RSSI measurement in wirelesssensor networkrdquo in Proceedings of the 8th International JointConference on Computer Science and Software Engineering(JCSSE rsquo11) pp 1ndash6 May 2011

[28] CWang and X Li ldquoSensor localization under limitedmeasure-ment capabilitiesrdquo IEEE Network vol 21 no 3 pp 16ndash23 2007

[29] J Yim S Jeong K Gwon and J Joo ldquoImprovement of Kalmanfilters for WLAN based indoor trackingrdquo Expert Systems withApplications vol 37 no 1 pp 426ndash433 2010

[30] P Bahl and V N Padmanabhan ldquoRADAR an in-building RF-based user location and tracking systemrdquo in Proceedings ofthe 19th Annual Joint Conference of the IEEE Computer andCommunications Societies (IEEE INFOCOM rsquo00) pp 775ndash784March 2000

[31] W Liu S Gong Y Zhou and P Wang ldquoTwo-phase indoorpositioning technique in wireless networking environmentrdquoin Proceedings of the 2010 IEEE International Conference onCommunications (ICC rsquo10) Cape Town South AfricaMay 2010

[32] XNguyen andT Rattentbury ldquoLocalization algorithms for sen-sor networks using RF signal strengthrdquo Tech Rep University ofCalifornia at Berkeley 2003

[33] J Xu H Luo F Zhao R Tao and Y Lin ldquoDynamic indoorlocalization techniques based on RSSI inWLAN environmentrdquoin Proceedings of the 6th International Conference on PervasiveComputing and Applications (ICPCA rsquo11) pp 417ndash421 PortElizabeth South Africa October 2011

[34] J Lloret J Tomas M Garcia and A Canovas ldquoA hybridstochastic approach for self-location of wireless sensors inindoor environmentsrdquo Sensors vol 9 no 5 pp 3695ndash37122009

[35] H Wang and F Jia ldquoA hybrid modeling for WLAN positioningsystemrdquo in Proceedings of the International Conference onWireless Communications Networking and Mobile Computing(WiCOM rsquo07) pp 2152ndash2155 Shanghai China September 2007


[37] K Antti H Marko L Helena and H Timo ldquoExperimentson local positioning with bluetoothrdquo in Proceedings of theInternational Conference on Information Technology Computersand Communications pp 297ndash303 IEEE Computer Society2003

[38] W Ting and B Scott ldquoIndoor localization method comparisonfingerprinting and trilateration algorithmrdquo International Jour-nal of Control In press

[39] W Ting and B Scott ldquoIndoor localization methodcomparison fingerprinting and trilateration algorithmrdquohttprosegeogmcgillcaskisystemfilesfm2011Weipdf

[40] R Priwgharm and P Chemtanomwong ldquoA comparative studyon indoor localization based on RSSI measurement in wirelesssensor networkrdquo in Proceedings of the 8th International JointConference on Computer Science and Software Engineering(JCSSE rsquo11) pp 1ndash6 Nakhon Pathom Thailand May 2011

[41] B Deen A software solution for absolute position estimationusing wlan for robotics [MS thesis] EEMCSElectrical Engi-neering Control Engineeringy University of Twente Nether-lands 2008

[42] National Academy of Engineering ldquoBiography of RudolfKalmanrdquo 2011

[43] K Murphy ldquoKalman filter toolbox for matlabrdquo 2004[44] B Dawes and K-W Chin ldquoA comparison of deterministic

and probabilistic methods for indoor localizationrdquo Journal ofSystems and Software vol 84 no 3 pp 442ndash451 2011

[45] A K M M Hossain and W-S Soh ldquoA comprehensive studyof bluetooth signal parameters for localizationrdquo in Proceedingsof the 18th Annual IEEE International Symposium on PersonalIndoor andMobile RadioCommunications (PIMRC rsquo07) AthensGreece September 2007

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



physical layer is 21Mbits In the domain of indoor positionestimation there are also other wireless communicationstandards which can be used for indoor position estimationsuch as wireless local area networks (WLAN) and ZigBeeHowever in this paper Bluetooth technology is used forindoor position estimation due to its low cost low power andvast usage

This paper presents the design of an extended hybridtechnique for position estimation using the idea originallyproposed in [6] The hybrid technique combines the goodfeatures of fingerprinting- and lateration-based approaches ina simple and robust wayThe proposed hybrid technique firstuses fingerprintingmethod to calculate the nearest neighbors(NN) and then calculates the distance between each NN andanchor nodes using Euclidian distance formula When thedistance between each NN and anchor nodes is known thenthe position of target node is calculated using trilaterationtechnique The calculated position is then given to Kalmanfilter to minimize the effect of noise The next sectionelaborates design of proposed hybrid technique in moredetails The remainder of this paper is structured as followSection 2 discusses the existing indoor position estimationtechniques which is mainly focussed on fingerprinting- andlateration-based position estimation techniques Section 3presents the proposed extended hybrid position estimationtechnique Section 4 presents experimental setup and datacollection Section 5 presents numerical results and finallyconclusion and future research directions are presented inSection 6

2 Position Estimation Techniques

Positing estimation is the process to locate an object withreference to some coordinate system [2] In RF-basedwirelesscommunication position estimation is performed using RSSwhich is the parameter used to estimate distance betweenmobile and anchor nodes or APs [7 8] The standardradio propagation models are used to convert RSS measure-ments into distance estimates [9] There are generally twokinds of position estimation techniques that is laterationand fingerprinting-based position estimation techniquesLateration-based position estimation techniques use theradio propagation model to convert RSS measurements todistance estimates Fingerprinting-based position estimationtechniques use the pattern matching approach to estimatethe position of target node The following section providesan overview of the lateration-based position estimationtechniques

21 Lateration-Based Position Estimation TechniquesLateration-based position estimation techniques are amongthe widely usedmethods to estimate the location of the target[10ndash12] Lateration-based position estimation techniquesestimate the target position by measuring distance betweenthe target and anchor nodes The standard radio propagationmodel is used to convert RSS measurements to distanceestimates [1 13 14] The conversion process requiresradio propagation constants This process requires the

characterization of radio propagation constants specific tothe environment where RSS measurements are collectedThe distance estimation process strongly depends on thepropagation constants Once the distance estimates areknown then the position is estimated using equation ofcircles [15 16] The following subsection discusses thewell-known lateration-based position estimation techniques

211 Trilateration andMultilateration The term trilaterationrefers to the process which estimates the target position basedon measurements of distances from three fixed positions Insimple words it is a technique which estimates the point ofintersection from three fixed points [17] Trilateration refersto measurement the distance from three anchor nodes ofwhile multilateration measures the distance from more thanthree anchor nodes Trilateration and multilateration are themostly used lateration-based position estimation algorithmswhich use the radio propagation model to convert RSSmeasurements to distance estimates Trilateration algorithmcomputes the object position by taking the RSS measure-ments from at least three anchor nodes and the locations ofanchor nodes which measure the RSS are already fixed Formultilateration more than three anchor nodes are requiredto locate an object Both algorithms require distances fromtarget to anchor nodes [18] The distance 119889 is obtainedfrom RSS received at the anchor nodes The standard radiopropagation model is used to convert RSS readings fromtarget nodes to distances for estimation of target position[19 20] The distance between anchor nodes and fixedpoints depends on the radio propagation constants whichare represented in the form of numerical values required toconvert RSS measurements to distance estimates [21] Themathematical equations of trilateration and multilaterationare given as follows Let 119860(119909

1 1199101) 119861(119909

2 1199102) 119862(119909

3 1199103) and

119863(1199094 1199104) be the anchor and be 119879(119909 119910) be the target node

then distance 119889119894between anchor and target nodes can be

obtained using the following equation [22]

119889119894= radic(119909 minus 119909

119894)2

+ (119910 minus 119910119894)2

for 119894 = 1 2 3 119899 minus 1 (1)

The solution set of (1) using minimum mean square error(MMSE) which is a technique designed to minimize thevariance of the estimation errors is as follow

119860 = (2)

or

= 119860minus1 (3)

The estimated target position lies at the point of intersec-tion In ideal conditions the circles will intersect at onlyone point However the distance estimates contain noisewhich produces variations in RSS measurements Thereforeestimated position of target nodemay not be the unique pointof intersection In that case the MMSE technique is usedto estimate the coordinates of target node with minimumposition estimation error [23]



119894which is the


119890119894(1199090 1199100)

= 119889119894minus radic(119909

0minus 119909119894)2

+ (1199100minus 119910119894)2 for 119894 = 1 2 3 119899 minus 1

(4)





(max(119909119894minus119889119894)

max(119910119894minus119910119894)

) lowast (min(119909119894+119889119894)

min(119910119894+119910119894)

) (5)


119894is the































119889 = radic

119899

sum

119894=1

(119904119894minus 1199041198941015840)2

(6)





1(1198831 1198841) NN

2(1198832 1198842) NN

3(1198833 1198843) and






1 1199101) (1199092 1199102)

(1199093 1199103) and (119909



(1199091minus 119909)2

+ (1199101minus 119910)2

= 1198892

1 (7a)

(1199092minus 119909)2

+ (1199102minus 119910)2= (1198892)2

(7b)

(1199093minus 119909)2

+ (1199103minus 119910)2

= (1198893)2

(7c)

(1199094minus 119909)2

+ (1199104minus 119910)2

= (1198894)2

(7d)

Similarly (119909119899minus 119909)2

+ (119910119899minus 119910)2

= (119889119899)2 for 119894 = 1 2 4

(7e)


(1199091minus 119909)2

minus (1199094minus 119909)2

+ (1199101minus 119910)2

minus (1199104minus 119910)2

= (1198891)2

minus (1198894)2

(8a)

(1199092minus 119909)2

minus (1199094minus 119909)2

+ (1199102minus 119910)2

minus (1199104minus 119910)2

= (1198892)2

minus (1198894)2

(8b)

(1199093minus 119909)2

minus (1199094minus 119909)2

+ (1199103minus 119910)2

minus (1199104minus 119910)2

= (1198893)2

minus (1198894)2

(8c)


2 (1199094minus 1199091) 119909 + 2 (119910

4minus 1199101) 119910

= (1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(9a)

2 (1199094minus 1199092) 119909 + 2 (119910

4minus 1199102) 119910

= (1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(9b)

2 (1199094minus 1199093) 119909 + 2 (119910

4minus 1199103) 119910

= (1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

(9c)


2[

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

[

[

119909

119910

]

]

=[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(10)


119860 lowast = (11)


119860 = [

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

119909 = [

[

119909

119910

]

]

119887 =[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(12)


= 119860minus1sdot (13)


119860119909 minus 1198872 997888rarr 119860119879119860119909 = 119860

119879119887

119909 = (119860119879119860)minus1

119860119879119887

(14)





119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)


119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)











0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119894which is the


119890119894(1199090 1199100)

= 119889119894minus radic(119909

0minus 119909119894)2

+ (1199100minus 119910119894)2 for 119894 = 1 2 3 119899 minus 1

(4)





(max(119909119894minus119889119894)

max(119910119894minus119910119894)

) lowast (min(119909119894+119889119894)

min(119910119894+119910119894)

) (5)


119894is the































119889 = radic

119899

sum

119894=1

(119904119894minus 1199041198941015840)2

(6)





1(1198831 1198841) NN

2(1198832 1198842) NN

3(1198833 1198843) and






1 1199101) (1199092 1199102)

(1199093 1199103) and (119909



(1199091minus 119909)2

+ (1199101minus 119910)2

= 1198892

1 (7a)

(1199092minus 119909)2

+ (1199102minus 119910)2= (1198892)2

(7b)

(1199093minus 119909)2

+ (1199103minus 119910)2

= (1198893)2

(7c)

(1199094minus 119909)2

+ (1199104minus 119910)2

= (1198894)2

(7d)

Similarly (119909119899minus 119909)2

+ (119910119899minus 119910)2

= (119889119899)2 for 119894 = 1 2 4

(7e)


(1199091minus 119909)2

minus (1199094minus 119909)2

+ (1199101minus 119910)2

minus (1199104minus 119910)2

= (1198891)2

minus (1198894)2

(8a)

(1199092minus 119909)2

minus (1199094minus 119909)2

+ (1199102minus 119910)2

minus (1199104minus 119910)2

= (1198892)2

minus (1198894)2

(8b)

(1199093minus 119909)2

minus (1199094minus 119909)2

+ (1199103minus 119910)2

minus (1199104minus 119910)2

= (1198893)2

minus (1198894)2

(8c)


2 (1199094minus 1199091) 119909 + 2 (119910

4minus 1199101) 119910

= (1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(9a)

2 (1199094minus 1199092) 119909 + 2 (119910

4minus 1199102) 119910

= (1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(9b)

2 (1199094minus 1199093) 119909 + 2 (119910

4minus 1199103) 119910

= (1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

(9c)


2[

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

[

[

119909

119910

]

]

=[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(10)


119860 lowast = (11)


119860 = [

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

119909 = [

[

119909

119910

]

]

119887 =[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(12)


= 119860minus1sdot (13)


119860119909 minus 1198872 997888rarr 119860119879119860119909 = 119860

119879119887

119909 = (119860119879119860)minus1

119860119879119887

(14)





119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)


119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)











0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































119889 = radic

119899

sum

119894=1

(119904119894minus 1199041198941015840)2

(6)





1(1198831 1198841) NN

2(1198832 1198842) NN

3(1198833 1198843) and






1 1199101) (1199092 1199102)

(1199093 1199103) and (119909



(1199091minus 119909)2

+ (1199101minus 119910)2

= 1198892

1 (7a)

(1199092minus 119909)2

+ (1199102minus 119910)2= (1198892)2

(7b)

(1199093minus 119909)2

+ (1199103minus 119910)2

= (1198893)2

(7c)

(1199094minus 119909)2

+ (1199104minus 119910)2

= (1198894)2

(7d)

Similarly (119909119899minus 119909)2

+ (119910119899minus 119910)2

= (119889119899)2 for 119894 = 1 2 4

(7e)


(1199091minus 119909)2

minus (1199094minus 119909)2

+ (1199101minus 119910)2

minus (1199104minus 119910)2

= (1198891)2

minus (1198894)2

(8a)

(1199092minus 119909)2

minus (1199094minus 119909)2

+ (1199102minus 119910)2

minus (1199104minus 119910)2

= (1198892)2

minus (1198894)2

(8b)

(1199093minus 119909)2

minus (1199094minus 119909)2

+ (1199103minus 119910)2

minus (1199104minus 119910)2

= (1198893)2

minus (1198894)2

(8c)


2 (1199094minus 1199091) 119909 + 2 (119910

4minus 1199101) 119910

= (1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(9a)

2 (1199094minus 1199092) 119909 + 2 (119910

4minus 1199102) 119910

= (1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(9b)

2 (1199094minus 1199093) 119909 + 2 (119910

4minus 1199103) 119910

= (1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

(9c)


2[

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

[

[

119909

119910

]

]

=[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(10)


119860 lowast = (11)


119860 = [

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

119909 = [

[

119909

119910

]

]

119887 =[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(12)


= 119860minus1sdot (13)


119860119909 minus 1198872 997888rarr 119860119879119860119909 = 119860

119879119887

119909 = (119860119879119860)minus1

119860119879119887

(14)





119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)


119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)











0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











1 1199101) (1199092 1199102)

(1199093 1199103) and (119909



(1199091minus 119909)2

+ (1199101minus 119910)2

= 1198892

1 (7a)

(1199092minus 119909)2

+ (1199102minus 119910)2= (1198892)2

(7b)

(1199093minus 119909)2

+ (1199103minus 119910)2

= (1198893)2

(7c)

(1199094minus 119909)2

+ (1199104minus 119910)2

= (1198894)2

(7d)

Similarly (119909119899minus 119909)2

+ (119910119899minus 119910)2

= (119889119899)2 for 119894 = 1 2 4

(7e)


(1199091minus 119909)2

minus (1199094minus 119909)2

+ (1199101minus 119910)2

minus (1199104minus 119910)2

= (1198891)2

minus (1198894)2

(8a)

(1199092minus 119909)2

minus (1199094minus 119909)2

+ (1199102minus 119910)2

minus (1199104minus 119910)2

= (1198892)2

minus (1198894)2

(8b)

(1199093minus 119909)2

minus (1199094minus 119909)2

+ (1199103minus 119910)2

minus (1199104minus 119910)2

= (1198893)2

minus (1198894)2

(8c)


2 (1199094minus 1199091) 119909 + 2 (119910

4minus 1199101) 119910

= (1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(9a)

2 (1199094minus 1199092) 119909 + 2 (119910

4minus 1199102) 119910

= (1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(9b)

2 (1199094minus 1199093) 119909 + 2 (119910

4minus 1199103) 119910

= (1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

(9c)


2[

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

[

[

119909

119910

]

]

=[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(10)


119860 lowast = (11)


119860 = [

[

1199094minus 1199091

1199104minus 1199101

1199094minus 1199092

1199104minus 1199102

1199094minus 1199093

1199104minus 1199103

]

]

119909 = [

[

119909

119910

]

]

119887 =[[

[

(1198892

1minus 1198892

4) minus (119909

2

1minus 1199092

4) minus (119910

2

1minus 1199102

4)

(1198892

2minus 1198892

4) minus (119909

2

2minus 1199092

4) minus (119910

2

2minus 1199102

4)

(1198892

3minus 1198892

4) minus (119909

2

3minus 1199092

4) minus (119910

2

3minus 1199102

4)

]]

]

(12)


= 119860minus1sdot (13)


119860119909 minus 1198872 997888rarr 119860119879119860119909 = 119860

119879119887

119909 = (119860119879119860)minus1

119860119879119887

(14)





119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)


119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)











0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119883119905+1= 119865119909119905+ noise (119876)

119884119905= 119867119909119905+ noise (119877)

(15)


119865 =[[[

[

1 0 1 0

0 1 0 1

0 0 1 0

0 0 0 1

]]]

]

119867 = [1 0 0 0

0 1 0 0] (16)











0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0

2

4

6

8

10

12

0 2 4 6 8 10 12



minus2

minus2 X-axisY

-axi

s




Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 332 293 246 199

Anchors 4(ME) 302 258 192 144

Anchors 3(St D) 179 174 153 153

Anchors 4(St D) 191 186 122 122



Trilateration(m)

MinMax(m)

K-NN(m)

Hybridapproach (m)

Anchors 3(ME) 529 246 19 138

Anchors 4(ME) 414 213 22 155

Anchors 3(StD) 383 157 148 113

Anchors 4(StD) 385 193 14 098







(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(0 5) 200 207 165(2 3) 362 255 212(2 5) 176 117 089(5 0) 251 075 068(5 6) 053 145 144(3 7) 215 167 131(8 8) 170 177 063(0 8) 378 1 079









(0 5) 238 119 114(2 3) 157 114 077(2 5) 083 068 076(5 0) 147 081 074(5 6) 011 105 083(3 7) 193 182 107(8 8) 137 029 043(0 8) 127 039 041






0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 1 2 3 43

4

5

6

7

8

9

10

11

NNReal position

TrilaterationHybrid

Y-a

xis (

m)




2 3 4 5 6 7 81

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)





3

4

5

6

7

8

9

10

11

0 1 2 3 4

Y-a

xis (

m)



NNReal position

K-NNHybrid


1 2 3 4 5 6 7 8 9

0

1

2

3

4

5

6

7

NNReal position

K-NNHybrid

Y-a

xis (

m)

X-axis (m)










Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation















Acknowledgments


References


















































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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