Performance Analysis of Kalman Filter Based Hybrid Estimation Algorithms

Kalman filter based hybrid estimation algorithms have been used in many applications. However, performance analysis of these algorithms is difficult because many of these algorithms use a set of Kalman filters that are coupled with each other. We present an algorithm to compute the means and cross-covariances of the residuals of the set of coupling (or interacting) Kalman filters. Specifically, we derive the cross-covariances, each of which is the covariance of the residuals of two interacting Kalman filters, to account for the mutual interactions between the Kalman filters. From the means and cross-covariances of the Kalman filter residuals, we then compute the means of the likelihood functions and the mean-squared estimation errors as performance measures of hybrid estimation algorithms. We consider the Interacting Multiple Model algorithm as an example in this paper. In general, the proposed algorithm could be applicable to various Kalman filter based hybrid estimation algorithms.