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Technical Briefs

Nonlinear Estimation Techniques Applied on Target Tracking Problems

[+] Author and Article Information
Andrew Gadsden

Department of Mechanical Engineering,  McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadagadsden@mcmaster.ca

Saeid Habibi

Department of Electrical and Computer Engineering,  McMaster University 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadahabibi@mcmaster.ca

Darcy Dunne

Department of Mechanical Engineering,  McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadaddunne@mcmaster.ca

T. Kirubarajan

Department of Electrical and Computer Engineering,  McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4L7, Canadakiruba@mcmaster.ca

J. Dyn. Sys., Meas., Control 134(5), 054501 (Jun 05, 2012) (13 pages) doi:10.1115/1.4006374 History: Received October 05, 2009; Revised March 04, 2012; Published June 05, 2012; Online June 05, 2012

This paper discusses the application of four nonlinear estimation techniques on two benchmark target tracking problems. The first problem is a generic air traffic control (ATC) scenario, which involves nonlinear system equations with linear measurements. The second study is a classical ground surveillance problem, where a moving airborne platform with a sensor is used to track a moving target. The tracking scenario is set in two dimensions, with the measurement providing nonlinear bearing-only observations. These two target tracking problems provide a good benchmark for comparing the following nonlinear estimation techniques: the common extended and unscented Kalman filters (EKF/UKF), the particle filter (PF), and the relatively new smooth variable structure filter (SVSF). The results of applying the SVSF on the two target tracking problems demonstrate its stability and robustness. Both of these attributes make use of the SVSF advantageous over other popular methods. The filters performances are quantified in terms of robustness, resilience to poor initial conditions and measurement outliers, and tracking accuracy and computational complexity. The purpose of this paper is to demonstrate the effectiveness of applying the SVSF on nonlinear target tracking problems, which in the past have typically been solved by Kalman or particle filters.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Distribution of sigma point set for the UKF in 2D space [22]

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Figure 2

SVSF estimation concept [8]

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Figure 3

Aircraft trajectory

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Figure 4

Platform and target trajectory

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Figure 5

Results for Sec. 41, normal conditions: (a) EKF results, (b) UKF results, (c) PF results, and (d) SVSF results

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Figure 6

Results for Sec. 41, PCRLB and RMSE results: (a) uniform motion model and (b) coordinated turn model

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Figure 7

Results for Sec. 42, poor initial conditions: (a) EKF results, (b) UKF results, (c) PF results, and (d) SVSF results

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Figure 8

Results for Sec. 43, presence of a measurement outlier: (a) EKF results, (b) UKF results, (c) PF results, and (d) SVSF results

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Figure 9

Results for Sec. 44, poor initial conditions and outlier: (a) EKF results, (b) UKF results, (c) PF results, and (d) SVSF results

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Figure 10

Results for Sec. 41, normal conditions: (a) estimated position of target and (b) estimated velocity of target

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Figure 11

Results for Sec. 41, normal conditions: (a) RMS position error and (b) RMS velocity error

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Figure 12

Results for Sec. 42, poor initial conditions: (a) RMS position error and (b) RMS velocity error

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Figure 13

Results for Sec. 42, poor initial conditions: (a) estimated position of target and (b) estimated velocity of target

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