A Tightly Coupled Positioning Solution for Land Vehicles...

Research ArticleA Tightly Coupled Positioning Solution forLand Vehicles in Urban Canyons

Xu Li1 Rong Jiang1 Xianghui Song2 and Bin Li2

1School of Instrument Science and Engineering Southeast University Nanjing China2Key Laboratory of Technology on Intelligent Transportation Systems Ministry of TransportResearch Institute of Highway Ministry of Transport Beijing 100088 China

Correspondence should be addressed to Xu Li lixumail163com

Received 14 November 2016 Revised 11 January 2017 Accepted 6 February 2017 Published 5 March 2017

Academic Editor Pietro Siciliano

Copyright copy 2017 Xu Li et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The integration between Global Navigation Satellite System (GNSS) and on-board sensors is widely used for vehicle positioningHowever as the main information source in the integration the positioning performance of single- or multiconstellation GNSSs isseverely degraded in urban canyons due to the effects of Non-Line-Of-Sight (NLOS) and multipath propagations How to mitigatesuch effects is vital to achieve accurate positioning performance in urban canyonsThis paper proposes a tightly coupled positioningsolution for land vehicles fusing dual-constellation GNSSs with other low-cost complementary sensors First the nonlinear filtermodel is established based on a cost-effective reduced inertial sensor system with 3D navigation solution Then an adaptive fuzzyunscentedKalman filter (AF-UKF) algorithm is developed to achieve the global fusion In the implementation of AF-UKF the fuzzycalibration logic (FCL) is designed and introduced to adaptively adjust the dependence on each received satellite measurementto effectively mitigate the NLOS and multipath interferences in urban areas Finally the proposed solution is evaluated throughexperiments The results validate the feasibility and effectiveness of the proposed solution

1 Introduction

The importance of accuracy and integrity in a positioningsystem has increasingly been emphasized in many intelligenttransportation system or intelligent vehicle applications suchas advanced driver assistance systems intersection collisionwarnings and traffic control [1ndash3] During the past years thesatellite-based positioning system like the Global PositioningSystem (GPS) has become the primary solution for vehiclenavigation However in critical environments such as urbancanyons the satellite signal is often blocked andor reflectedby surrounding objects causing multipath and Non-Line-Of-Sight (NLOS) signal interferences [4 5] The multipathmeans that the direct path and reflected path are receivedtogether In contrast the NLOS signal is only received viareflection that is no direct Light of Sight (LOS) path existsIn such environments the standalone GPS cannot guaranteean accurate and continuous positioning

To solve the issues mentioned above there have beena number of techniques presented in the literature Among

them the fusion of GPS with inertial navigation system(INS) andor odometer and so forth has been a commonone due to their complementary natures [6ndash8] To fuse theinformation from multiple sensors the Kalman filter andextended Kalman filter (EKF) are widely utilized [9ndash11]Although the EKF-based methods can provide an efficientperformance in many practical applications its linearizationprocess may suffer from divergence due to approximationsduring the linearization process and system mismodellingBesides note that nowadays only the low-cost INS basedonmicroelectromechanical systems (MEMS) is affordable forland vehicle applications [12 13] However such low-costINS and odometer errors diverge rapidly over time and thusthe fusion above still cannot provide acceptable navigationperformance for long GPS signal outages or in the event ofconsiderable NLOS delays

With the rapid development of other Global NavigationSatellite Systems (GNSS) such as GLONASS and BeiDou apossible way to fill this gap is to adopt the multiconstellationapproach [14ndash16] Just like GPS GLONASS has also been

HindawiJournal of SensorsVolume 2017 Article ID 5965716 11 pageshttpsdoiorg10115520175965716

2 Journal of Sensors

fully operational BeiDou attained initial regional operationalstatus at the end of December 2011 It can now providepositioning navigation and timing services in the wholeAsia-Pacific region and is expected to be fully operational in2020 The combination of GPS BeiDou and other satelliteconstellations will provide far superior satellite geometryand signal availability compared to GPS alone Howeverdue to the serious impact of NLOS and multipath on thepositioning accuracy in urban areas such improvements inthe availability of satellite signals do not necessarily facilitatehigh-precision positioning at the same time

A series of technologies has been developed to mitigatethe multipath and NLOS effects For the multipath theyare mainly cataloged into three antenna-based receiver-based and navigation-processor-based techniques [17ndash20]Generally speaking themultipath can be effectivelymitigatedvia such techniques (the error is less than few meters) Incontrast the NLOS signals have more severe impact (cancause the positioning error as large as a few hundred meters)and are difficult to be discriminated in urban canons Inrecent years various 3D maps have been proposed andconstructed to detect exclude or compensate NLOS delays[4 21ndash24] Though viable and useful it is prerequisite tomeasure and map the building height information of thedriving environments beforehand Moreover it may leadto huge errors if the constructed 3D map has not enoughaccuracy Generally how to mitigate the NLOS effect toimprove the positioning result is still an open research topic

In this paper we propose a tightly coupled position-ing solution for land vehicles in urban environmentswhich fuses low-cost complementary sensors including dual-constellation GNSSs in-vehicle sensors and electronic com-pass The nonlinear filter model is firstly established basedon a cost-effective reduced inertial sensor system with 3Dnavigation solution Further the adaptive fuzzy unscentedKalman filter (AF-UKF) algorithm is developed to executethe global fusion Specifically a fuzzy calibration logic (FCL)is designed and introducedwhich candetermine the depend-able degree of each received satellite measurement accordingto its features including current geometrical distribution andcarrier-to-noise ratio Through such mechanism the NLOSand multipath interferences can be effectively mitigated andaccurate positioning in urban canyons can be achieved The

main novel aspect of the proposed solution is that it does notneed the prior information about the driving environmentand has better adaptability and accuracy

The remainder of this paper is organized as follows InSection 2 the filter model used for multisensor fusion is pre-sented in detailThen the fusion algorithm for implementingmultisensor integrated positioning is proposed in Section 3Experimental results are provided in Section 4 Section 5 isdevoted to the conclusion

2 Nonlinear Filter Model

21 System Model A nonlinear motion model involving theposition velocity and attitude states based on a reducedinertial sensor system (RISS) is adopted in this paper to cutthe cost Specifically the RISS integrates the measurementsfrom the vertically aligned gyroscope and two horizontalaccelerometers with speed readings provided by wheel speedsensors Though reduced it can still provide an effective 3Dnavigation solution for land vehicles via 3D RISS calculationmechanization [25]

211 Position and Velocity Calculation Before describingthe system equations for position and velocity the relationbetween the vehicle velocity in the body frame and in thelocal-level frame is given by

[[[[

V119864119896V119873119896V119880119896

]]]]= R119897119887119896

[[[0V1199081198960]]]= [[[V119908119896 sin119860119896 cos119901119896V119908119896 cos119860119896 cos119901119896

V119908119896 sin119901119896]]] (1)

where

V119864 V119873 and V119880 denote the velocity components alongeast north and up directions respectively

119860 119901 and 119903 are the azimuth pitch and roll angles ofvehicle respectively

V119908 is the vehicle speed derived from the vehiclersquoswheel speed

R119897119887119896 is represented as

R119897119887119896 = [[[[[

cos119860119896 cos 119903119896 + sin119860119896 sin119901119896 sin 119903119896 sin119860119896 cos119901119896 cos119860119896 sin 119903119896 minus sin119860119896 sin119901119896 cos 119903119896minus sin119860119896 cos 119903119896 + cos119860119896 sin119901119896 sin 119903119896 cos119860119896 cos119901119896 minus sin119860119896 sin 119903119896 minus cos119860119896 sin119901119896 cos 119903119896

minus cos119901119896 sin 119903119896 sin119901119896 cos119901119896 cos 119903119896]]]]] (2)

In (1) the velocity in the body frame is assumed to consistonly of the forward longitudinal speed of the vehicle whilethe transversal and vertical components are assumed to bezeros Such constraints are very effective to improve the stateestimates along the lateral and vertical directions

Further the latitude can be expressed as

120593119896 = 120593119896minus1 + V119873119896119877119872 + ℎ119896Δ119905 (3)

Similarly the longitude is

120582119896 = 120582119896minus1 + V119864119896(119877119873 + ℎ119896) cos120593119896Δ119905 (4)

Journal of Sensors 3

The altitude is

ℎ119896 = ℎ119896minus1 + V119880119896 Δ119905 (5)

where120593 120582 and ℎ denote the latitude longitude and altitudeof vehicle respectively119877119872 is the meridian radius of curvature of the Earth119877119873 is the normal radius of curvature of the EarthΔ119905 is the sampling time

212 Pitch Roll and Azimuth Calculation When the vehicleis moving the forward accelerometer measures the forwardvehicle acceleration as well as the component due to gravityTo calculate the pitch angle the vehicle acceleration derivedfrom the odometer measurements is removed from theforward accelerometer measurements

119901119896 = sinminus1 (119891119910119896 minus 119886119908119896119892 ) (6)

Similarly the transversal accelerometer measures thenormal component of the vehicle acceleration as well asthe component due to gravity and to calculate the rollangle the transversal accelerometer measurement must becompensated for the normal component of acceleration

119903119896 = minussinminus1 (119891119909119896 + V119908119896 120596119911119896119892 cos119901119896 ) (7)

Besides the azimuth angle directly in local-level framecan be written as

119860119896 = 119860119896minus1 minus 120596119911119896Δ119905 + (120596119890 sin120593119896minus1) Δ119905+ V119864119896minus1 tan120593119896minus1(119877119873 + ℎ119896minus1) Δ119905

(8)

where119886119908 is the vehicle acceleration derived from the vehi-clersquos wheel speed119891119909 and 119891119910 devote the transversal accelerometer mea-surement and forward accelerometer measurementrespectively120596119911 is the angular rate obtained from the verticallyaligned gyroscope120596119890 is the Earthrsquos rotation rate119892 is the acceleration of gravity

213 Stochastic Errors In order to compensate for thestochastic errors associated with the gyroscope and thevehiclersquos wheel speed and enhance the estimation accuracy ofthe filter these stochastic errors are also included as stateswhich are modeled by a Gauss-Markov model

[120575119865119908119896120575120596119911119896] = [(1 minus 120574119908Δ119905) 120575119865119908119896minus1(1 minus 120573119911Δ119905) 120575120596119911119896minus1] + [[

radic21205741199081205902119908Δ119905radic21205731199111205902119911Δ119905

]] (9)

where

120575119865119908 is the scale factor error of the wheel speed120575120596119885 is the stochastic gyroscope drift120574119908 is the reciprocal of the autocorrelation time for thescale factor of the wheel speed

120573119911 is the reciprocal of the autocorrelation time for thegyroscopersquos stochastic drift

1205902119908 is the variance of the noise associated with thewheel speed

1205902119911 is the variance of the noise associated with thegyroscopersquos stochastic drift

Based on 3D RISS as described by (1)ndash(9) the nonlinearsystem transition model about vehicle states is given by

XRISS119896 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

120593119896120582119896ℎ119896V119864119896

V119873119896

V119880119896119901119896119903119896119860119896120575119865119908119896120575120596119885119896

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

120593119896minus1 + V119873119896119877119872 + ℎ119896Δ119905120582119896minus1 + V119864119896(119877119873 + ℎ119896) cos120593119896Δ119905ℎ119896minus1 + V119880119896 Δ119905

V119908119896 sin119860119896 cos119901119896V119908119896 cos119860119896 cos119901119896

V119908119896 sin119901119896sinminus1 (119891119910119896 minus 119886119908119896119892 )

minussinminus1 (119891119909119896 + V119908119896 120596119911119896119892 cos119901119896 )119860119896minus1 minus 120596119911119896Δ119905 + (120596119890 sin120593119896minus1) Δ119905 + V119864119896minus1 tan120593119896minus1(119877119873 + ℎ119896minus1) Δ119905(1 minus 120574119908Δ119905) 120575119865119908119896minus1

(1 minus 120573119911Δ119905) 120575120596119885119896minus1

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

(10)


Moreover the receiverrsquos clock bias and drift errors of GPSand BeiDou can be modeled as

XGPS119896 = [120575119887GPS119896120575119889GPS119896 ] = [120575119887GPS119896minus1 + 120575119889GPS119896minus1Δ119905120575119889GPS119896minus1 ]

XBDS119896 = [120575119887BDS119896120575119889BDS119896 ] = [120575119887BDS119896minus1 + 120575119889BDS119896minus1Δ119905120575119889BDS119896minus1 ]

(11)

where 120575119887GPS and 120575119889GPS are GPS receiverrsquos clock offsetand drift error respectively 120575119887BDS and 120575119889BDS are BeiDoureceiverrsquos clock offset and drift error respectively

Combining (10) and (11) we can obtain the full systemstate transition model for the overall tightly coupled integra-tion as

X (119896) = f (X (119896 minus 1) U (119896 minus 1) W (119896 minus 1) T (119896 minus 1)) (12)

where X and U represent the state and input vectors of thesystem respectively and W and T are the correspondingsystem and input noise vectors respectively f(sdot) is thenonlinear system function where the function componentscan be determined based on (10) and (11) X and U can berepresented by

X = [120593 120582 ℎ V119864 V119873 V119880 119901 119903 119860 120575119865119908 120575120596119911 120575119887GPS 120575119889GPS 120575119887BDS 120575119889BDS]119879 U = [V119908 119886119908 119891119909 119891119910 120596119911]119879

(13)

22 Measurement Model In the tightly coupled integrationthe pseudorange measurements of dual-constellation GNSSsact as the observation vector Therefore the measurementmodel can be given as

Z (119896) = h (X (119896)) + 120576 (119896) (14)

where Z is the measurement vector h(sdot) is the process func-tion of the measurement model and 120576 is the measurementGaussian noise vector Z can be depicted as

Z

= [120588GPS1 120588GPS2 sdot sdot sdot 120588GPS1198981 120588BDS1 120588BDS2 sdot sdot sdot 120588BDS1198982]119879 (15)

where 120588GPS and 120588BDS are the corrected GPS and BeiDoupseudorange measurements respectively 1198981 and 1198982 arethe numbers of received GPS and BeiDou satellites whoseelevation angle and carrier-to-noise ratio are both morethan certain thresholds (eg 35∘ and 30 db-Hz resp in thispaper) respectively In urban areas through such thresholdprocessing that is abandoning the measurements of thesatellites with low elevation angle and low carrier-to-noiseratio the impact of NLOS andmultipath can be preliminarilyalleviated to some degree

Note that in common INSGNSS tightly coupled inte-gration each of received satellite measurements is generallyregarded as Gaussian noise with the same noise covariance

1198770 That is 120576 is usually assumed to have the noise covariancematrix R which has equal diagonal elements that is

R (119896) = diag [1198770 sdot sdot sdot 1198770] (16)

where R has1198981 + 1198982 dimensionSatellite clock bias and ionospheric errors can be calcu-

lated from the satellitersquos navigationmessage and troposphericerror can also be estimated using an appropriate model [25]Hence after correcting all the errors except receiver clockerrors the corrected pseudoranges 120588GPS and 120588BDS can bedescribed as

120588GPS = 10038171003817100381710038171003817r minus rGPS10038171003817100381710038171003817 + 120575119887GPS + 120576GPS120588120588BDS = 10038171003817100381710038171003817r minus rBDS10038171003817100381710038171003817 + 120575119887BDS + 120576BDS120588

(17)

where r = [119909 119910 119911] is the receiverrsquos rectangular coordi-nates in e-frame rGPS = [119909GPS 119910GPS 119911GPS] and rBDS =[119909BDS 119910BDS 119911BDS] are satellitesrsquo rectangular coordinates ine-frame 120575119887GPS and 120575119887BDS are the GPS and BeiDou receiverrsquosclock biases respectively 120576GPS120588 and 120576BDS120588 are the total effectof residual errors

The coordinate transformation between geodetic e-frameand rectangular e-frame is

119909 = (119877119873 + ℎ) cos120593 cos 120582119910 = (119877119873 + ℎ) cos120593 sin 120582119911 = [119877119873 (1 minus 1198902) + ℎ] sin120593

(18)

where 119890 is the eccentricity of ellipsoid Utilizing this transfor-mation the measurement equation can be obtained as


Z (119896)

=

[[[[[[[[[[[[[[[[[[[[

radic((119877119873 + ℎ119896) cos120593119896 cos 120582119896 minus 119909GPS1119896 )2 + ((119877119873 + ℎ119896) cos120593119896 sin 120582119896 minus 119910GPS1119896 )2 + [119877119873 (1 minus 1198902) + ℎ119896] sin120593119896 minus 119911GPS1119896 2 + 120575119887GPS119896radic((119877119873 + ℎ119896) cos120593119896 cos 120582119896 minus 119909GPS1198981119896

)2 + ((119877119873 + ℎ119896) cos120593119896 sin 120582119896 minus 119910GPS1198981119896)2 + [119877119873 (1 minus 1198902) + ℎ119896] sin120593119896 minus 119911GPS1198981119896

2 + 120575119887GPS119896radic((119877119873 + ℎ119896) cos120593119896 cos 120582119896 minus 119909BDS1119896 )2 + ((119877119873 + ℎ119896) cos120593119896 sin 120582119896 minus 119910BDS1119896 )2 + [119877119873 (1 minus 1198902) + ℎ119896] sin120593119896 minus 119911BDS1119896 2 + 120575119887BDS119896

radic((119877119873 + ℎ119896) cos120593119896 cos 120582119896 minus 119909BDS1198982119896)2 + ((119877119873 + ℎ119896) cos120593119896 sin 120582119896 minus 119910BDS1198982119896

)2 + [119877119873 (1 minus 1198902) + ℎ119896] sin120593119896 minus 119911BDS11989821198962 + 120575119887BDS119896

]]]]]]]]]]]]]]]]]]]]

(19)

3 Fusion Positioning Algorithm

31 EKF Algorithm The extended Kalman filter (EKF) hasbeen widely used for INSGNSS integration For systemstate model (12) and measurement model (19) the systeminput and measurement noises are assumed to be Gaussianwith zero mean and their covariance matrices Q Γ and Rrespectively Further the corresponding EKF process can bedivided into the following two phases

Prediction

X (119896 119896 minus 1) = f (X (119896 minus 1) U (119896 minus 1) 0 0) P (119896 119896 minus 1) = A (119896 119896 minus 1)P (119896 minus 1)A119879 (119896 119896 minus 1)

+ B (119896 119896 minus 1) Γ (119896 minus 1)B119879 (119896 119896 minus 1)+Q (119896 minus 1)

(20)

Update

K (119896) = P (119896 119896 minus 1) sdotH119879 (119896)sdot [H (119896)P (119896 119896 minus 1)H119879 (119896) + R (119896)]minus1

X (119896) = X (119896 119896 minus 1)+ K (119896) [Z (119896) minus h (X (119896 119896 minus 1))]

P (119896) = [I minus K (119896) sdotH (119896)] sdot P (119896 119896 minus 1)

(21)

where I is an identity matrix A and B are the Jacobianmatrices of the system function f(sdot) with respect to X and Uand H is the Jacobian matrix of the measurement functionh(sdot) with respect to X that is

A[119894][119895] = 120597f[119894]120597119909[119895] (X (119896 119896 minus 1) U (119896 minus 1) 0 0) B[119894][119895] = 120597f[119894]120597119906[119895] (X (119896 119896 minus 1) U (119896 minus 1) 0 0)

H[119894][119895] = 120597h[119894]120597119909[119895] (X (119896 119896 minus 1)) (22)

32 UKF Algorithm As shown in (12) and (19) both systemand measurement models are nonlinear Although the EKFcan deal with such fusion through linearization it willinevitably cause the approximation error To enhance theintegration performance nonlinear estimation techniquesthat do not require linearized dynamic models should beconsidered to be used The unscented Kalman filter (UKF) isone of the effective nonlinear Bayes filters which can directlyuse nonlinear system and measurement models without anylinearization [26 27] Generally it can achieve a good balancebetween computational complexity and accuracy [28] Incontrast to the EKF the UKF does not need to compute theJacobian matrix and can predict the means and covariancecorrectly up to the fourth order

For (12) and (19) we can execute the recursive procedureof UKF according to the following steps [26 27]

Step 1 Calculate weights coefficient and sigma points

120596(119898)0 = 120578119899 + 120578 119894 = 0120596(119888)0 = 120578119899 + 120578 + (1 minus 12057212 + 1205722) 119894 = 0120596(119898)119894 = 120596(119898)119894 = 12 (119899 + 120578) 119894 = 1 2 2119899

120585119894 (119896 minus 1) = X (119896 minus 1) 119894 = 0120585119894 (119896 minus 1) = X (119896 minus 1) + (radic(119899 + 120578)P (119896))

119894

119894 = 1 2 119899120585119894 (119896 minus 1) = X (119896 minus 1) minus (radic(119899 + 120578)P (119896))

119894

119894 = 119899 + 1 119899 + 2 2119899

(23)


where 120578 = 12057212(119899+1205723)minus119899 is a scaling parameterThe constant1205721 determines the spread of the sigma points around a meanof state X and is usually set to a small positive value Theconstant 1205723 is usually set to 0 1205722 is used to incorporate priorknowledge of the distribution of X and is optimally set to 2for Gaussian distributions 119899 is the dimension of state vector

Step 2 Estimate a priori state X(119896 119896 minus 1) and a priorierror covariance P(119896 119896 minus 1) and then obtain the predictedobservation by the unscented transform of which inputs arethe sigma points and the weights

120585119894 (119896 119896 minus 1) = f (120585119894 (119896 minus 1)) 119894 = 0 1 2119899X (119896 119896 minus 1) = 2119899sum

119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0

120596(119888)119894 [120585119894 (119896 119896 minus 1) minus X (119896 119896 minus 1)]sdot [120585119894 (119896 119896 minus 1) minus X (119896 119896 minus 1)]119879

120577119894 (119896 119896 minus 1) = h (120585119894 (119896 119896 minus 1)) 119894 = 0 1 2119899Z (119896 119896 minus 1) = 2119899sum

119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)

Step 3 Calculate the UKF gain

P119885119885 = R (119896) + 2119899sum119894=0

120596(119888)119894 [120577119894 (119896 119896 minus 1) minus Z (119896 119896 minus 1)]sdot [120577119894 (119896 119896 minus 1) minus Z (119896 119896 minus 1)]119879

(25)

P119883119885 = 2119899sum119894=0

120596(119888)119894 [120585119894 (119896 119896 minus 1) minus X (119896 119896 minus 1)]sdot [120577119894 (119896 119896 minus 1) minus Z (119896 119896 minus 1)]119879

(26)

K (119896) = P119883119885P119885119885minus1 (27)

Step 4 Update the system state and error covariance

X (119896) = X (119896 119896 minus 1) + K (119896) (Z (119896) minus Z (119896 119896 minus 1)) P (119896) = P (119896 119896 minus 1) minus K (119896)P119885119885K (119896)119879 (28)

33 AF-UKF Algorithm For the UKF above the noisecovariance matrix R(119896) in (25) is usually set to be a constantdiagonal one This setting is generally appropriate in theopen-sky situations but is not suitable for urban canyons Asmentioned earlier the satellite signals in urban areas are oftenblocked andor reflected by surrounding objects causingNLOS and multipath interferences For the received LOSsatellites their measurement accuracy is superior Howeverif one received satellite signal belongs to multipath and

NLOS its measurement accuracy is poor Through simplethreshold processing mentioned above only partly obviousNLOS and multipath interferences can be alleviated That issuch alleviation is very limited and rough For the remainingsatellite signals it is still necessary to adaptively adjust thedependence on each satellite measurement whether fromBeiDou or from GPS according to its specific conditionsrather than utilize it invariably

Generally in unban canyon scenarios the LOS satellitesignals may be different from the satellite signals affectedby the NLOS and multipath interferences in several aspectsFirst the satellite signals along the vehiclersquos longitudinaldirection (ie along the street) are not obstructed by build-ings and trees while the signals going along the vehiclersquoslateral direction (ie across the street) are prone to beblocked or reflected as illustrated in Figure 1 Besides thesatellite signals with low elevation angles are more likely tobe influenced than those with high elevation angles in urbancanyonsMoreover the LOS signals often have higher carrier-to-noise ratio (ie C1198730) than the NLOS and multipathsignals [29]

Obviously if we can take full advantages of the above-mentioned features to determine the degree of dependenceon the measurement of each received satellite signal theimpact ofNLOS andmultipath interferences can bemitigatedand thus the positioning accuracy can be enhancedHowevernote that how to utilize the features above to ascertain thedependence degree on the measurement of each receivedsatellite signal is a nonlinear process with some uncertaintyand fuzziness rather than a strict or rigorous process Thusit is reasonable to adopt fuzzy logic to model this decisionprocess that is based on the features of received satellitesignals

Based on the discussions above the fuzzy calibration logic(FCL) here is designed using three inputs that is the azimuthdifference 120579119894 between the received 119894th satellite and the vehiclethe elevation angle 120574119894 of the received 119894th satellite and thecarrier-to-noise ratio 119875119894 (ie C1198730) and one output thescaling coefficient 120583119894 which is used to adjust the pseudorangemeasurement noise level In actual implementation 120579 isdetermined by

120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)

where 119860119878119894 denotes the azimuth angle of the received 119894thsatellite and 119860119862 is the azimuth angle measured by theelectronic compass If 120579119894 is small it means that the signalof received 119894th satellite is nearly along the canyonrsquos directionand its observation noise covariance should not be enlargedOn the other hand large 120579119894 means that the signal of received119894th satellite significantly deviates the canyonrsquos direction andits observation noise covariance should be enlarged 120583119894represents the enlarged degree about the observation noisecovariance of the received 119894th satellite that is

1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)

The range of 120583119894 is set mainly according to the knowledge orexperience about the observation noise and then is adjusted


MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)

Figure 1 Illustration of NLOS and multipath interferences in urban canyons (a) Front view (b) Top view

many times by trial and error to obtain better estimationperformance

Three membership functions Large (L) Middle (M)and Small (S) and three membership functions Low Eleva-tion (LowE) Middle Elevation (MidE) and High Elevation(HighE) are used to describe two input variables 120579119894 and 120574119894respectively Besides two membership functions Low Power(LowP) and High Power (HighP) are utilized to describe theinput variable 119875119894 For the output six membership functionsare defined as Normal (N-A) Slight Amplification (SL-A)Small Amplification (SM-A) Middle Amplification (M-A)Large Amplification (L-A) and Very Large Amplification(VL-A)The fuzzymembership functions for three inputs andone output are shown in Figure 2

The fuzzy reasoning rules are mainly based on thefollowing prior considerations First if 120579119894 is Small 120574119894 is HighElevation and 119875119894 is High Power then it means that thereceived 119894th satellite is not interfered and its observation noisecovariance should not be enlarged (ie Normal) Besides if120579119894 is Large and 120574119894 is Low Elevation it reveals that the received119894th satellite is very likely to be affected by urban canyonsand thus its observation noise covariance should be amplifiedlargely or very largely Finally in the cases of other inputcombinations the observation noise covariance should beenlarged moderately Table 1 gives the complete fuzzy rulebase

When the enlarged degree about the observation noisecovariance of each received satellite is determined utilizingthe FCL above we can achieve the global fusion via theUKF algorithm presented in Section 32 For clarity wesummarize the proposed adaptive fuzzy UKF (AF-UKF)algorithm briefly as follows

Step 1 Calculate weights coefficient and sigma points accord-ing to (23)

S M L

LowE HighEMidE

LowP HighP

N-A SL-A SM-A M-A L-A VL-A

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65

Figure 2 Membership functions for 120579119894 120574119894 and 119875119894


Table 1 Fuzzy rules for proposed FCL

120579119894 119875119894 120574119894HighE MidE LowE

S HighP N-A SL-A SL-ALowP N-A SM-A SM-A

M HighP N-A SM-A M-ALowP SM-A L-A L-A

L HighP SL-A M-A L-ALowP SM-A L-A VL-A

Step 2 Estimate a priori state and its error covariance andthen calculate the predict observation based on (24)

Step 3 For each received satellite signal its azimuth differ-ence 120579119894 is ascertained according to (29) and then the corre-sponding scaling coefficient 120583119894 can be determined utilizingthe FCL aboveWhen all satellite signals are judged thewholeadaptive noise covariance matrix Ra can be obtained

Ra (119896)= diag [(12058311198770)2 sdot sdot sdot (1205831198941198770)2 sdot sdot sdot (1205831198981+11989821198770)2]

(31)

Step 4 Substitute R in (25) with Ra and then calculate theUKF gain according to (25)ndash(27)

Step 5 Update the system state and error covariance basedon (28)

From the discussion above the established FCL is mainlybased on the information about the urban environmentknowledge and received satellite signal features

4 Experimental Results

41 Experiment Setup To verify the positioning performanceof the proposed solution experiments were conducted on aChery TIGGO5 SUV vehicle The information about wheelspeeds could be directly obtained from the in-vehicle CANnetwork Besides a low-cost NovAtel C260-AT GPSBeiDoudual-constellation receiver MEMSIC MEMS-based IMUVG440CA-200 inertial sensors and KVH C100plus elec-tronic compass were installed The sensor accuracies (1120590)are 5m for GPS and BeiDou pseudorange measurements01ms2 for the accelerometers 02∘s for the yaw rate sensor05∘ for the yaw angle of electronic compass and 005msfor wheel speed sensors Moreover an accurate and reliableNovAtel SPAN-CPT system was used as a reference whichcan provide accurate positioning reference via postprocessingeven under adverse environments [30]

The experiments were executed along a typical urban-canyon trajectory in the downtown of Nanjing City whichis a metropolitan city in East China and has a population ofover 8 million Figure 3 shows this trajectoryThere are manytall buildings and skyscrapers along the two sides of the testtrajectory The same FCL calibration parameters are utilizedthroughout the whole experiment

I

II

III

IV

Figure 3 Test trajectory for the performance evaluation (Courtesyof Google Earth)

54

GPSBeiDouGPS + BeiDou

100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8

Figure 4 Number of received satellites

42 Satellite Availability Evaluation Figure 4 shows the num-ber of received satellites whose elevation angle and carrier-to-noise ratio are more than 35∘ and 30 db-Hz respectivelyAs shown in Figure 4 it is obvious that with more satelliteconstellations utilized more satellites can be available in citycanyons

With standalone GPS used the number of availablesatellites is less than four at over 501 epochs which isnot sufficient to provide a positioning solution With onlyBeiDou utilized the percentage of the situation when thenumber of available satellites is less than four can be reducedto 52 In contrast with the combination of GPS andBeiDou the satellite availability can be obviously enhancedThe percentage of the situation when the number of availablesatellites is insufficient to provide a positioning solution (ielt5) can be decreased to only 12 These results show themulticonstellation GNSSs have the potential to improve thepositioning performance in challenging urban environmentsHowever note that the multiconstellation GNSSs can still notensure providing 100 positioning solution in urban canons


Table 2 Statistics of Euclidean distance errors in four regions (unit m)

Region number EKF UKF AF-EKF AF-UKFMax RMS Max RMS Max RMS Max RMS

I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)

Figure 5 Euclidean distance errors of GNSS only and RISS only inRegion IV

43 Positioning Performance Evaluation Firstly we evaluatethe performance of using GNSS only and RISS only Thepositioning result in Region IV shown in Figure 5 is selectedas an example to demonstrate the performance of GNSS onlyand RISS only due to the fact that similar results can beobtained from other regions For the RISS only its initialposition is set to the reference position at the start of RegionIV The Euclidean distance error (horizontal positioningerrors) of RISS only growswith time and reaches 190m in 80 sGNSS outage which can be attributed to the accumulationof inertial sensor errors The performance of GNSS only isbetter than the RISS only but the maximum error of GNSSonly is up to 445m owing to the NLOS and multipathinterferences From this we can find that the performancesof using GNSS only or RISS only are so poor that theycannot satisfy the requirements of vehicle positioning inurban canyons Therefore we focus on the evaluation ofpositioning performance fusing GNSS and other low-costcomplementary sensors in the following sections

The positioning performance of the proposed AF-UKFsolution is assessed through comparing with three otherrepresentative positioning methods that is EKF and UKFpresented in Sections 31 and 32 and AF-EKF Note thatfour typical driving regions where dense tall buildings andskyscrapers are located nearby that is Regions IndashIV inFigure 3 are selected to make the statistical analysis

For four positioningmethods Table 2 gives their statisticsof Euclidean distance errors (horizontal positioning errors) infour selected regions To provide a clear description Figures6 and 7 illustrate the positioning results of threemethods (ieEKF UKF and AF-UKF) on the map in Regions I and IV

AF-UKFReferenceEKF

UKF

Figure 6 Positioning results of threemethods on themap in RegionI

respectively For brevity the results in two other regions arenot shown

From the results above all three fusion positioningmethods can obtain 100 positioning solution during thetest which can overcome the disadvantage of the positioningmethod of multiconstellation GNSSs alone discussed inSection 42

As far as the EKF and UKF are concerned the UKFexhibits better nonlinear adaptability and can achieve betterperformance than the EKF in most cases For instance inRegion I the maximum and RMS values of Euclidean dis-tance error of EKF is 847m and 361m respectively whereasthose of UKF are decreased to 815m and 342m respectivelyHowever in the situation where there exist obvious NLOSand multipath interferences (eg in Regions IIndashIV) theiradverse effect cannot be effectively mitigated by both of theEKF and UKF methods As illustrated in Regions IIndashIVwhether for EKF or for UKF the corresponding maximumvalues of Euclidean distance error are large

Compared with the EKF andUKFmethods both the AF-EKF and AF-UKF can significantly enhance the positioningperformance However the proposed AF-UKF is able toobtain better performance than AF-EKF in most cases FromTable 2 in all regions the AF-UKF solution can achieve the


AF-UKFReferenceEKF

UKF

Figure 7 Positioning results of threemethods on themap in RegionIV

best positioning accuracy Specifically even in the environ-ments of heavy NLOS andmultipath interferences it can stillprovide reasonable and acceptable accurate positioning forcommon positioning applications For example in Region IVwhere there are dense tall buildings and skyscrapers nearbyas shown in Figure 7 the maximum values of Euclideandistance error of EKF and UKF reach 6068m and 4692mrespectively In contrast the value of AF-UKF is only 1152mthat is the significant improvement of about 81 and 75over EKF and UKF respectively It can be attributed to thefact that the proposed fuzzy calibration logic in AF-UKFcan effectively alleviate the impact of NLOS and multipathpropagations

5 Conclusion

In this paper we propose a tightly coupled position-ing solution for land vehicles based on the adaptivefuzzy unscented Kalman filter (AF-UKF) integrating dual-constellation GNSSs with other low-cost complementarysensors

The nonlinear filter model is first built based on a cost-effective reduced inertial sensor system with 3D navigationsolution Then the adaptive fuzzy unscented Kalman filteralgorithm is proposed which can effectively mitigate theNLOS and multipath interferences and achieve accuratepositioning in urban canyons Finally the proposed solutionis validated through experiments in real urban canyons Themain advantage of the proposed solution is that it doesnot need the accurate prior information about the drivingenvironment and owns superior adaptability and accuracy

It should be noted that the proposed solution also hasits own limitation Under certain conditions the observation

noise covariance of some satellites which seem suspicious butare actually healthy would be amplified largely or very largelyand may cause the loss in the positioning accuracy to someextent If 3D city map can be utilized the performance ofthe proposed solution will be further improved Our futureresearch will consider this aspect

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no 61273236) the JiangsuProvincial Basic Research Program (Natural Science Foun-dation Grant no BK2010239) and the Scientific ResearchFoundation of Graduate School of Southeast University (noYBJJ1637)

References

[1] A Vu A Ramanandan A Chen J A Farrell and M BarthldquoReal-time computer visionDGPS-aided inertial navigationsystem for lane-level vehicle navigationrdquo IEEE Transactions onIntelligent Transportation Systems vol 13 no 2 pp 899ndash9132012

[2] K Jo K Chu and M Sunwoo ldquoInteracting multiple modelfilter-based sensor fusion of GPS with in-vehicle sensors forreal-time vehicle positioningrdquo IEEE Transactions on IntelligentTransportation Systems vol 13 no 1 pp 329ndash343 2012

[3] I Skog and P Handel ldquoIn-car positioning and navigationtechnologiesmdasha surveyrdquo IEEE Transactions on Intelligent Trans-portation Systems vol 10 no 1 pp 4ndash21 2009

[4] Y Gu L-T Hsu and S Kamijo ldquoGNSSonboard inertial sensorintegration with the aid of 3-D building map for lane-levelvehicle self-localization in urban canyonrdquo IEEE Transactions onVehicular Technology vol 65 no 6 pp 4274ndash4287 2016

[5] F PeyretD Betaille P Carolina R Toledo-MoreoA FGomez-Skarmeta and M Ortiz ldquoGNSS autonomous localizationNLOS satellite detection based on 3-Dmapsrdquo IEEERobotics andAutomation Magazine vol 21 no 1 pp 57ndash63 2014

[6] Z Wu M Yao H Ma and W Jia ldquoImproving accuracy of thevehicle attitude estimation for low-cost INSGPS integrationaided by the GPS-measured course anglerdquo IEEE Transactionson Intelligent Transportation Systems vol 14 no 2 pp 553ndash5642013

[7] X Li Q Xu C Chan B Li W Chen and X Song ldquoA hybridintelligent multisensor positioning methodology for reliablevehicle navigationrdquoMathematical Problems in Engineering vol2015 Article ID 176947 13 pages 2015

[8] S Godha and M E Cannon ldquoGPSMEMS INS integratedsystem for navigation in urban areasrdquo GPS Solutions vol 11 no3 pp 193ndash203 2007

[9] A Angrisano S Gaglione and C Gioia ldquoPerformance assess-ment of aided global navigation satellite system for land naviga-tionrdquo IET Radar Sonar amp Navigation vol 7 no 6 pp 671ndash6802013

[10] Z Ren and H Wang ldquoFusion estimation algorithm withuncertain noises and its application in navigation systemrdquo


Mathematical Problems in Engineering vol 2015 Article ID218561 9 pages 2015

[11] S-B Kim J-C Bazin H-K Lee K-H Choi and S-Y ParkldquoGround vehicle navigation in harsh urban conditions by inte-grating inertial navigation system global positioning systemodometer and vision datardquo IET Radar Sonar and Navigationvol 5 no 8 pp 814ndash823 2011

[12] R Toledo-Moreo M A Zamora-Izquierdo B Ubeda-Minarroand A F Gomez-Skarmeta ldquoHigh-integrity IMM-EKF-basedroad vehicle navigation with low-cost GPSSBASINSrdquo IEEETransactions on Intelligent Transportation Systems vol 8 no 3pp 491ndash511 2007

[13] J Georgy A Noureldin M J Korenberg and M M BayoumildquoModeling the stochastic drift of a MEMS-based gyroscope ingyroodometerGPS integrated navigationrdquo IEEE Transactionson Intelligent Transportation Systems vol 11 no 4 pp 856ndash8722010

[14] X Li M Ge X Dai et al ldquoAccuracy and reliability of multi-GNSS real-time precise positioning GPS GLONASS BeiDouandGalileordquo Journal of Geodesy vol 89 no 6 pp 607ndash635 2015

[15] P D Groves ldquoShadow matching a new GNSS positioningtechnique for urban canyonsrdquo Journal of Navigation vol 64 no3 pp 417ndash430 2011

[16] F Meng B Zhu and S Wang ldquoA new fast satellite selectionalgorithm for BDS-GPS receiversrdquo in Proceedings of the IEEEWorkshop on Signal Processing Systems (SiPS rsquo13) pp 371ndash376Taipei Taiwan October 2013

[17] G A McGraw R S Y Young K Reichenauer J Stevens andF Ventrone ldquoGPS multipath mitigation assessment of digitalbeam forming antenna technology in a JPALS dual frequencysmoothing architecturerdquo in Proceedings of the Institute of Navi-gation National Meeting (NTM rsquo04) pp 561ndash572 January 2004

[18] N Kubo T Suzuki A Yasuda and R Shibazaki ldquoAn effec-tive method for multipath mitigation under severe multipathenvironmentsrdquo in Proceedings of the 18th International TechnicalMeeting of the Satellite Division of The Institute of Navigation(ION GNSS rsquo05) pp 2187ndash2194 Long Beach Calif USASeptember 2005

[19] P Xie and M G Petovello ldquoMeasuring GNSS multipath distri-butions in urban canyon environmentsrdquo IEEE Transactions onInstrumentation and Measurement vol 64 no 2 pp 366ndash3772015

[20] L-T Hsu ldquoIntegration of vector tracking loop and multipathmitigation technique and its assessmentrdquo in Proceedings of the26th International Technical Meeting of the Satellite Divisionof the Institute of Navigation (ION GNSS rsquo13) pp 3263ndash3278Nashville Tenn USA September 2013

[21] L Wang P D Groves and M K Ziebart ldquoMulti-constellationGNSS performance evaluation for urban canyons using largevirtual reality city modelsrdquo Journal of Navigation vol 65 no3 pp 459ndash476 2012

[22] L-T Hsu Y Gu and S Kamijo ldquoNLOS correctionexclusionfor GNSSmeasurement using RAIM and city building modelsrdquoSensors vol 15 no 7 pp 17329ndash17349 2015

[23] D Betaille F Peyret M Ortiz S Miquel and L FontenayldquoA new modeling based on urban trenches to improve GNSSpositioning quality of service in citiesrdquo IEEE Intelligent Trans-portation Systems Magazine vol 5 no 3 pp 59ndash70 2013

[24] M Obst S Bauer P Reisdorf and G Wanielik ldquoMultipathdetection with 3D digital maps for robust multi-constellationGNSSINS vehicle localization in urban areasrdquo in Proceedings

of the IEEE Intelligent Vehicles Symposium (IV rsquo12) pp 184ndash190Madrid Spain June 2012

[25] A Noureldin T B Karamat and J Georgy Fundamentalsof Inertial Navigation Satellite-Based Positioning and TheirIntegration Springer 2012

[26] J Kong X Mao and S Li ldquoBDSGPS dual systems positioningbased on the modified SR-UKF algorithmrdquo Sensors vol 16 no5 article no 635 2016

[27] K Jung J Kim J Kim E Jung and S Kim ldquoPositioningaccuracy improvement of laser navigation using UKF and FISrdquoRobotics and Autonomous Systems vol 62 no 9 pp 1241ndash12472014

[28] M St-Pierre and D Gingras ldquoComparison between theunscented Kalman filter and the extended Kalman filter forthe position estimation module of an integrated navigationinformation systemrdquo in Proceedings of the IEEE IntelligentVehicles Symposium pp 831ndash835 Parma Italy June 2004

[29] P D Groves and Z Jiang ldquoHeight aiding CN0 weighting andconsistency checking for gnss nlos and multipath mitigation inurban areasrdquo Journal of Navigation vol 66 no 5 pp 653ndash6692013

[30] httpwwwnovatelcomsupportinfodocuments564

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpswwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



fully operational BeiDou attained initial regional operationalstatus at the end of December 2011 It can now providepositioning navigation and timing services in the wholeAsia-Pacific region and is expected to be fully operational in2020 The combination of GPS BeiDou and other satelliteconstellations will provide far superior satellite geometryand signal availability compared to GPS alone Howeverdue to the serious impact of NLOS and multipath on thepositioning accuracy in urban areas such improvements inthe availability of satellite signals do not necessarily facilitatehigh-precision positioning at the same time

A series of technologies has been developed to mitigatethe multipath and NLOS effects For the multipath theyare mainly cataloged into three antenna-based receiver-based and navigation-processor-based techniques [17ndash20]Generally speaking themultipath can be effectivelymitigatedvia such techniques (the error is less than few meters) Incontrast the NLOS signals have more severe impact (cancause the positioning error as large as a few hundred meters)and are difficult to be discriminated in urban canons Inrecent years various 3D maps have been proposed andconstructed to detect exclude or compensate NLOS delays[4 21ndash24] Though viable and useful it is prerequisite tomeasure and map the building height information of thedriving environments beforehand Moreover it may leadto huge errors if the constructed 3D map has not enoughaccuracy Generally how to mitigate the NLOS effect toimprove the positioning result is still an open research topic

In this paper we propose a tightly coupled position-ing solution for land vehicles in urban environmentswhich fuses low-cost complementary sensors including dual-constellation GNSSs in-vehicle sensors and electronic com-pass The nonlinear filter model is firstly established basedon a cost-effective reduced inertial sensor system with 3Dnavigation solution Further the adaptive fuzzy unscentedKalman filter (AF-UKF) algorithm is developed to executethe global fusion Specifically a fuzzy calibration logic (FCL)is designed and introducedwhich candetermine the depend-able degree of each received satellite measurement accordingto its features including current geometrical distribution andcarrier-to-noise ratio Through such mechanism the NLOSand multipath interferences can be effectively mitigated andaccurate positioning in urban canyons can be achieved The

main novel aspect of the proposed solution is that it does notneed the prior information about the driving environmentand has better adaptability and accuracy

The remainder of this paper is organized as follows InSection 2 the filter model used for multisensor fusion is pre-sented in detailThen the fusion algorithm for implementingmultisensor integrated positioning is proposed in Section 3Experimental results are provided in Section 4 Section 5 isdevoted to the conclusion

2 Nonlinear Filter Model

21 System Model A nonlinear motion model involving theposition velocity and attitude states based on a reducedinertial sensor system (RISS) is adopted in this paper to cutthe cost Specifically the RISS integrates the measurementsfrom the vertically aligned gyroscope and two horizontalaccelerometers with speed readings provided by wheel speedsensors Though reduced it can still provide an effective 3Dnavigation solution for land vehicles via 3D RISS calculationmechanization [25]

211 Position and Velocity Calculation Before describingthe system equations for position and velocity the relationbetween the vehicle velocity in the body frame and in thelocal-level frame is given by

[[[[

V119864119896V119873119896V119880119896

]]]]= R119897119887119896

[[[0V1199081198960]]]= [[[V119908119896 sin119860119896 cos119901119896V119908119896 cos119860119896 cos119901119896

V119908119896 sin119901119896]]] (1)

where

V119864 V119873 and V119880 denote the velocity components alongeast north and up directions respectively

119860 119901 and 119903 are the azimuth pitch and roll angles ofvehicle respectively

V119908 is the vehicle speed derived from the vehiclersquoswheel speed

R119897119887119896 is represented as

R119897119887119896 = [[[[[

cos119860119896 cos 119903119896 + sin119860119896 sin119901119896 sin 119903119896 sin119860119896 cos119901119896 cos119860119896 sin 119903119896 minus sin119860119896 sin119901119896 cos 119903119896minus sin119860119896 cos 119903119896 + cos119860119896 sin119901119896 sin 119903119896 cos119860119896 cos119901119896 minus sin119860119896 sin 119903119896 minus cos119860119896 sin119901119896 cos 119903119896

minus cos119901119896 sin 119903119896 sin119901119896 cos119901119896 cos 119903119896]]]]] (2)

In (1) the velocity in the body frame is assumed to consistonly of the forward longitudinal speed of the vehicle whilethe transversal and vertical components are assumed to bezeros Such constraints are very effective to improve the stateestimates along the lateral and vertical directions

Further the latitude can be expressed as

120593119896 = 120593119896minus1 + V119873119896119877119872 + ℎ119896Δ119905 (3)

Similarly the longitude is

120582119896 = 120582119896minus1 + V119864119896(119877119873 + ℎ119896) cos120593119896Δ119905 (4)


The altitude is

ℎ119896 = ℎ119896minus1 + V119880119896 Δ119905 (5)



119901119896 = sinminus1 (119891119910119896 minus 119886119908119896119892 ) (6)





(8)




radic21205741199081205902119908Δ119905radic21205731199111205902119911Δ119905

]] (9)

where






XRISS119896 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

120593119896120582119896ℎ119896V119864119896

V119873119896

V119880119896119901119896119903119896119860119896120575119865119908119896120575120596119885119896

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[


V119908119896 sin119860119896 cos119901119896V119908119896 cos119860119896 cos119901119896



(1 minus 120573119911Δ119905) 120575120596119885119896minus1

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

(10)





(11)






(13)


Z (119896) = h (X (119896)) + 120576 (119896) (14)


Z









(17)




(18)



Z (119896)

=

[[[[[[[[[[[[[[[[[[[[






]]]]]]]]]]]]]]]]]]]]

(19)



Prediction



(20)

Update




(21)



H[119894][119895] = 120597h[119894]120597119909[119895] (X (119896 119896 minus 1)) (22)




120596(119898)0 = 120578119899 + 120578 119894 = 0120596(119888)0 = 120578119899 + 120578 + (1 minus 12057212 + 1205722) 119894 = 0120596(119898)119894 = 120596(119898)119894 = 12 (119899 + 120578) 119894 = 1 2 2119899


119894


119894

119894 = 119899 + 1 119899 + 2 2119899

(23)





119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0



119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)


P119885119885 = R (119896) + 2119899sum119894=0


(25)

P119883119885 = 2119899sum119894=0


(26)

K (119896) = P119883119885P119885119885minus1 (27)








120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)


1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)



MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










The altitude is

ℎ119896 = ℎ119896minus1 + V119880119896 Δ119905 (5)



119901119896 = sinminus1 (119891119910119896 minus 119886119908119896119892 ) (6)





(8)




radic21205741199081205902119908Δ119905radic21205731199111205902119911Δ119905

]] (9)

where






XRISS119896 =

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[

120593119896120582119896ℎ119896V119864119896

V119873119896

V119880119896119901119896119903119896119860119896120575119865119908119896120575120596119885119896

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

=

[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[[


V119908119896 sin119860119896 cos119901119896V119908119896 cos119860119896 cos119901119896



(1 minus 120573119911Δ119905) 120575120596119885119896minus1

]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]]

(10)





(11)






(13)


Z (119896) = h (X (119896)) + 120576 (119896) (14)


Z









(17)




(18)



Z (119896)

=

[[[[[[[[[[[[[[[[[[[[






]]]]]]]]]]]]]]]]]]]]

(19)



Prediction



(20)

Update




(21)



H[119894][119895] = 120597h[119894]120597119909[119895] (X (119896 119896 minus 1)) (22)




120596(119898)0 = 120578119899 + 120578 119894 = 0120596(119888)0 = 120578119899 + 120578 + (1 minus 12057212 + 1205722) 119894 = 0120596(119898)119894 = 120596(119898)119894 = 12 (119899 + 120578) 119894 = 1 2 2119899


119894


119894

119894 = 119899 + 1 119899 + 2 2119899

(23)





119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0



119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)


P119885119885 = R (119896) + 2119899sum119894=0


(25)

P119883119885 = 2119899sum119894=0


(26)

K (119896) = P119883119885P119885119885minus1 (27)








120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)


1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)



MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













(11)






(13)


Z (119896) = h (X (119896)) + 120576 (119896) (14)


Z









(17)




(18)



Z (119896)

=

[[[[[[[[[[[[[[[[[[[[






]]]]]]]]]]]]]]]]]]]]

(19)



Prediction



(20)

Update




(21)



H[119894][119895] = 120597h[119894]120597119909[119895] (X (119896 119896 minus 1)) (22)




120596(119898)0 = 120578119899 + 120578 119894 = 0120596(119888)0 = 120578119899 + 120578 + (1 minus 12057212 + 1205722) 119894 = 0120596(119898)119894 = 120596(119898)119894 = 12 (119899 + 120578) 119894 = 1 2 2119899


119894


119894

119894 = 119899 + 1 119899 + 2 2119899

(23)





119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0



119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)


P119885119885 = R (119896) + 2119899sum119894=0


(25)

P119883119885 = 2119899sum119894=0


(26)

K (119896) = P119883119885P119885119885minus1 (27)








120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)


1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)



MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Z (119896)

=

[[[[[[[[[[[[[[[[[[[[






]]]]]]]]]]]]]]]]]]]]

(19)



Prediction



(20)

Update




(21)



H[119894][119895] = 120597h[119894]120597119909[119895] (X (119896 119896 minus 1)) (22)




120596(119898)0 = 120578119899 + 120578 119894 = 0120596(119888)0 = 120578119899 + 120578 + (1 minus 12057212 + 1205722) 119894 = 0120596(119898)119894 = 120596(119898)119894 = 12 (119899 + 120578) 119894 = 1 2 2119899


119894


119894

119894 = 119899 + 1 119899 + 2 2119899

(23)





119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0



119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)


P119885119885 = R (119896) + 2119899sum119894=0


(25)

P119883119885 = 2119899sum119894=0


(26)

K (119896) = P119883119885P119885119885minus1 (27)








120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)


1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)



MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119894=0

120596(119898)119894 120585119894 (119896 119896 minus 1) P (119896 119896 minus 1) = Q (119896)

+ 2119899sum119894=0



119894=0

120596(119898)119894 120577119894 (119896 119896 minus 1)

(24)


P119885119885 = R (119896) + 2119899sum119894=0


(25)

P119883119885 = 2119899sum119894=0


(26)

K (119896) = P119883119885P119885119885minus1 (27)








120579119894 = 10038161003816100381610038161003816119860119878119894 minus 11986011986210038161003816100381610038161003816 (119894 = 1 1198981 + 1198982) (29)


1198771198942 = (120583119894 times 1198770)2 (119894 = 1 1198981 + 1198982) (30)



MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










MultipathLOS

NLOS

Blocked

(a)

LOS Multipath

Blocked

NLOS

(b)







S M L

LowE HighEMidE

LowP HighP


002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

002040608

1

Deg

ree o

f mem

bers

hip

706030 40 50 80 9010 200휃i

40 50 60 70 80 9030훾i

40 50 60 70 80 90 10030Pi

1 15 2 25 3 35휇i

4 45 5 55 6 65




120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120579119894 119875119894 120574119894HighE MidE LowE







(31)







I

II

III

IV


54


100 200 300 400 500 600 700 8000Time (s)

Num

ber o

f sat

ellit

es 12

10

14

6

4

2

8







I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












I 847 361 815 342 628 322 531 310II 369 1309 2934 996 1081 489 972 462III 2187 605 2254 621 1011 454 1004 459IV 6068 1285 4692 1073 1197 473 1152 469

RISSGNSS

020406080

100120140160180200

Eucli

dean

dist

ance

erro

r (m

)

10 20 30 40 50 60 70 80 900Time (s)





AF-UKFReferenceEKF

UKF







AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


Acknowledgments


References




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










AF-UKFReferenceEKF

UKF



5 Conclusion





Competing Interests


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









A Tightly Coupled Positioning Solution for Land Vehicles...

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Transcript of A Tightly Coupled Positioning Solution for Land Vehicles...