State estimation under nonlinear state inequality constraints. A tracking application

This paper proposes a general method for dealing with state estimation under nonlinear state soft inequality constraints. This method is based on the projection approach, and then has the advantage to be compatible with any kind of state estimator. In order to be taken into account, the nonlinear constraints are linearized about the constrained state using an iterated approach. The proposed algorithm is tested on a three- dimension tracking application with nonlinear constraints on the moving body acceleration. The results are compared with those of an unconstrained Kalman filter.

[1]  Petros G. Voulgaris,et al.  On optimal ℓ∞ to ℓ∞ filtering , 1995, Autom..

[2]  Pramod K. Varshney,et al.  A tracking algorithm of maneuvering targets , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[3]  Hugh F. Durrant-Whyte,et al.  Model-based multi-sensor data fusion , 1992, Proceedings 1992 IEEE International Conference on Robotics and Automation.

[4]  M. Tahk,et al.  Generalized input-estimation technique for tracking maneuvering targets , 1999 .

[5]  Dan Simon,et al.  Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches , 2006 .

[6]  P. Bogler.  Tracking a Maneuvering Target Using Input Estimation , 1987, IEEE Transactions on Aerospace and Electronic Systems.

[7]  Y. Bar-Shalom,et al.  Variable Dimension Filter for Maneuvering Target Tracking , 1982, IEEE Transactions on Aerospace and Electronic Systems.

[8]  D. Simon,et al.  Kalman filtering with inequality constraints for turbofan engine health estimation , 2006 .

[9]  Y. Chan,et al.  A Kalman Filter Based Tracking Scheme with Input Estimation , 1979, IEEE Transactions on Aerospace and Electronic Systems.

[10]  Yaakov Bar-Shalom,et al.  Multitarget/Multisensor Tracking: Applications and Advances -- Volume III , 2000 .

[11]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[12]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[13]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[14]  Mohinder S. Grewal,et al.  Global Positioning Systems, Inertial Navigation, and Integration , 2000 .

[15]  T. M. Williams.  Practical Methods of Optimization. Vol. 2 — Constrained Optimization , 1982 .

[16]  Silvio Simani,et al.  Model-based fault diagnosis in dynamic systems using identification techniques , 2003 .

[17]  J. Ragot,et al.  A discrete-time Sliding Window Observer for Markovian Switching System , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

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

[19]  Pramod K. Varshney,et al.  A tracking algorithm for maneuvering targets , 1993 .

[20]  Yaakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking , 1995 .

[21]  Yaakov Bar-Shalom,et al.  Multitarget-Multisensor Tracking: Applications and Advances , 1992 .