Constrained target motion modeling — Part I: Straight line track

Straight line motion is one of the most fundamental target motions. Its modeling has been well studied for unconstrained targets, e.g., air targets. However, the existing straight line motion models can not be directly used for the constrained case on straight line tracks, which has wide application, e.g., in ground target tracking. In this paper, modeling of the constrained target motion on a straight line track is considered. First, the constraints imposed by the straight track are explicitly set up. Then both direct elimination and projection along-track are applied to obtain two forms of constrained motion models in the 2D Cartesian plane and 3D Cartesian space. The connections between these two forms are studied. It is found that the traditional linear Gaussian assumption is still valid for the nearly constant velocity models, the nearly constant acceleration models and the Singer model. Inspired by this, a general condition under which the traditional linear Gaussian assumption is valid for modeling of constrained motion on a straight track is also discussed.

[1]  Dennis S. Bernstein,et al.  State estimation for equality-constrained linear systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[2]  C. Yang,et al.  Nonlinear constrained tracking of targets on roads , 2005, 2005 7th International Conference on Information Fusion.

[3]  Zhansheng Duan,et al.  Constrained target motion modeling — Part II: Circular track , 2013, Proceedings of the 16th International Conference on Information Fusion.

[4]  Joseph J. LaViola,et al.  On Kalman Filtering With Nonlinear Equality Constraints , 2007, IEEE Transactions on Signal Processing.

[5]  N. Gupta,et al.  Kalman Filtering in the Presence of State Space Equality Constraints , 2006, 2007 Chinese Control Conference.

[6]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[7]  R. Bitmead,et al.  STATE ESTIMATION OF LINEAR SYSTEMS WITH STATE EQUALITY CONSTRAINTS , 2005 .

[8]  Robert R. Bitmead,et al.  State estimation for linear systems with state equality constraints , 2007, Autom..

[9]  Erik Blasch,et al.  Fusion of Tracks with Road Constraints , 2008, J. Adv. Inf. Fusion.

[10]  F. Markley,et al.  Unscented Filtering for Spacecraft Attitude Estimation , 2003 .

[11]  D. Simon,et al.  Kalman filtering with state equality constraints , 2002 .

[12]  Zhansheng Duan,et al.  Best linear unbiased state estimation with noisy and noise-free measurements , 2009, 2009 12th International Conference on Information Fusion.

[13]  F. Chang,et al.  Filtering method for nonlinear systems with constraints , 2002 .

[14]  Jie Zhou,et al.  The Linear Minimum Mean-Square Error Estimation with Constraints and Its Applications , 2006, 2006 International Conference on Computational Intelligence and Security.

[15]  Chun Yang,et al.  Kalman Filtering with Nonlinear State Constraints , 2009 .

[16]  J. Speyer,et al.  Target tracking problems subject to kinematic constraints , 1990 .

[17]  D. Bernstein,et al.  Compartmental modelling and second-moment analysis of state space systems , 1993 .

[18]  Zhansheng Duan,et al.  Design and analysis of linear equality constrained dynamic systems , 2012, 2012 15th International Conference on Information Fusion.

[19]  Zhansheng Duan,et al.  Modeling and State Estimation for Dynamic Systems With Linear Equality Constraints , 2013, IEEE Transactions on Signal Processing.

[20]  X. R. Li,et al.  Survey of maneuvering target tracking. Part I. Dynamic models , 2003 .

[21]  Michael T. Heath,et al.  A Robust Null Space Method for Linear Equality Constrained State Estimation , 2010, IEEE Transactions on Signal Processing.

[22]  Krishna R. Pattipati,et al.  Ground target tracking with variable structure IMM estimator , 2000, IEEE Trans. Aerosp. Electron. Syst..

[23]  Zhansheng Duan,et al.  The Role of Pseudo Measurements in Equality-Constrained State Estimation , 2013, IEEE Transactions on Aerospace and Electronic Systems.