Distributed Tracking Using Kalman Filtering

By: Aaron Dyreson (aaron.dyreson@mavs.uta.edu)Supervising Professor: Dr. Ioannis Schizas (schizas@uta.edu)

IntroductionTopic of Research: The performance of

different distributed Kalman Filtering Algorithms in wireless sensor networks

What is Kalman Filtering?Brief HistoryApplications

Wireless Sensor NetworksCentralizedAd Hoc

Extended Kalman Filtering (1/2)Data Model Assumptions:

A: State transition matrixh: Observation function

Noise vectors wk and vkPhysical Interpretationwk and vk are zero mean with covariance

matrices Q and R respectively

Extended Kalman Filtering (2/2)Algorithm

Prediction Update:

Linearization

Kalman Gain Calculation:

Measurement Update:

Wireless Sensor Networks Topologies to be simulated in research

Centralized Ad Hoc

Methodology/ProcedureChoose system to studyDerive physical data model for system Simulations in MATLAB:

Wireless sensor network (WSN) with N sensorsTrajectory of object according constant velocity

modelRange and bearing measurements for each sensor

Perform extended Kalman filtering in MATLAB to obtain estimates for state of system

Calculate localization error between estimate and true

Results (1/4)Simulations completed so far:

Centralized Extended Kalman Filtering with range and bearing measurments

Centralized Extended Kalman filtering with range measurements

Results (2/4)Example plots for range and bearing Kalman

Filter

0 20 40 60 80 100 1200

20

40

60

80

100

120

x-position

y-po

sitio

n

True and Estimated Tracks for WSN with 3 Sensors

KalmanTrue

Results (3/4)

0 10 20 30 40 50 60 70 80 90 1000

0.2

0.4

0.6

0.8

1

1.2

1.4RMS Error between True and Estimate

Time (100 ms)

RM

S

Results (4/4)Range and Bearing Range Only

Number of Sensors

Average RMS Error(100

Simulations)

Number of Sensors

Average RMS Error(100

Simulations)1 16.6199 m 1 434.8799 m2 .5834 m 2 .8813 m3 .3187 m 3 .4957 m4 .2496 m 4 .2301 m5 .2311 m 5 .2003 m10 .1622 m 10 .1473 m25 .1104 m 25 .1036 m

ConclusionStill to be researched:

Simulation of Ad Hoc topologiesAlgorithms associated with Ad Hoc topologies

More data collection and analysis for centralized distributed Kalman filtering.

Any questions?