Omur Yuksel Bas

Proportional-Integral Kalman Filter Design with Applications to Target Tracking

June 8, 2000
10:00 AM
406 Egan

Abstract

In this thesis, we introduce several optimal design strategies for the Proportional- Integral (PI) Kalman filter. The design of the PI Kalman filter, in its most general form, involves the design of four matrices: The proportional and integral gains, the fading constant and the integral effect coefficient. The methods given in this thesis provide optimal proportional and integral gains. Guidelines for the design of the fading constant and the integral effect coefficient are discussed as well, wherever possible. Four methods of PI Kalman filter design are introduced here, each with their own advantages and disadvantages. For each method, the design algorithms are given in detail, with some mathematical analysis to form a basis of comparison with the proportional Kalman filter. Simulations are performed where the PI Kalman filter algorithms are tested as associated filters. We also provide a robustness analysis of the filter with unknown inputs and modeling errors. The second portion of this thesis is about the use of the PI Kalman filter design methods to develop an extended Kalman filter for multiple target tracking. This filter is based on Symmetrical Measurement Equations, which is a very intuitive method for multiple target tracking without data association. Prior work showed that an extended Kalman filter enhanced with integral action was effective in overcoming stability problems associated with the symmetrical measurement equation method. Here we establish a systematic design method for the PI extended Kalman filter and demonstrate its effectiveness. We also include simulation results to demonstrate the performance of each method and verify guidelines for design parameters.

Thesis Committee:
Prof. B. Shafai (advisor)
Prof. H. Lev-Ari
Prof. M. Maliutov (Mathematics Department)