Design of optimal gains for the proportional integral Kalman filter with application to single particle tracking

In this paper, we introduce an optimal design strategy for the proportional-integral (PI) Kalman filter. The design of the PI Kalman filter involves the design of four matrices: The proportional and integral gains, the fading constant and the integral effect coefficient. The method in this paper provides optimal proportional and integral gains. Guidelines for the design of the fading constant and the integral effect coefficient are discussed as well. The suggested algorithm was tested as a single particle tracking system, for a maneuvering target.