Nonlinear Estimation Techniques Applied on Target Tracking Problems

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.

[1]  D. Simon.  Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches , 2006 .

[2]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[3]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[4]  Simon J. Julier,et al.  The spherical simplex unscented transformation , 2003, Proceedings of the 2003 American Control Conference, 2003..

[5]  Hiromitsu Kumamoto,et al.  Random sampling approach to state estimation in switching environments , 1977, Autom..

[6]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[7]  S. Haykin.  Kalman Filtering and Neural Networks , 2001 .

[8]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[9]  Robert J. Elliott,et al.  Discrete-Time Nonlinear Filtering Algorithms Using Gauss–Hermite Quadrature , 2007, Proceedings of the IEEE.

[10]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice Using MATLAB , 2001 .

[11]  D. Mayne,et al.  Monte Carlo techniques to estimate the conditional expectation in multi-stage non-linear filtering† , 1969 .

[12]  Rudolph van der Merwe,et al.  Sigma-Point Kalman Filters for Integrated Navigation , 2004 .

[13]  Andrew Blake,et al.  A Probabilistic Exclusion Principle for Tracking Multiple Objects , 2000, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[14]  Jang-Sub Kim,et al.  Joint estimation of time delay and channel amplitude by simplex unscented filter without assisted pilot in CDMA systems , 2005, The 7th International Conference on Advanced Communication Technology, 2005, ICACT 2005..

[15]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[16]  Xiaobei Zhao,et al.  The square-root spherical simplex unscented Kalman filter for state and parameter estimation , 2008, 2008 9th International Conference on Signal Processing.

[17]  Thiagalingam Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation , 2001 .

[18]  Petar M. Djuric,et al.  Guest editorial special issue on monte carlo methods for statistical signal processing , 2002, IEEE Trans. Signal Process..

[19]  Nando de Freitas,et al.  Sequential Monte Carlo Methods in Practice , 2001, Statistics for Engineering and Information Science.

[20]  Hugh F. Durrant-Whyte,et al.  A new method for the nonlinear transformation of means and covariances in filters and estimators , 2000, IEEE Trans. Autom. Control..

[21]  S. Habibi,et al.  The Variable Structure Filter , 2003 .

[22]  J. Hammersley,et al.  Poor Man's Monte Carlo , 1954 .

[23]  Y. Bar-Shalom,et al.  Multisensor resource deployment using posterior Cramer-Rao bounds , 2004, IEEE Transactions on Aerospace and Electronic Systems.

[24]  Carlos H. Muravchik,et al.  Posterior Cramer-Rao bounds for discrete-time nonlinear filtering , 1998, IEEE Trans. Signal Process..

[25]  Saeid Habibi,et al.  The Smooth Variable Structure Filter , 2007, Proceedings of the IEEE.

[26]  Thiagalingam Kirubarajan,et al.  Precision large scale air traffic surveillance using IMM/assignment estimators , 1999 .

[27]  Saeid Habibi,et al.  Estimation using a new variable structure filter , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[28]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[29]  Stuart J. Russell,et al.  Stochastic simulation algorithms for dynamic probabilistic networks , 1995, UAI.

[30]  Norman S. Nise,et al.  Control Systems Engineering , 1991 .

[31]  Stephen Andrew Gadsden,et al.  SMOOTH VARIABLE STRUCTURE FILTERING: THEORY AND APPLICATIONS , 2011 .

[32]  P. Moral.  Measure-valued processes and interacting particle systems. Application to nonlinear filtering problems , 1998 .

[33]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[34]  Youmin Tang,et al.  Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems , 2009 .

[35]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.