Algorithm for Performance Analysis of the IMM Algorithm

The interacting multiple model (IMM) algorithm has been used in many applications. However, performance analysis of the IMM algorithm is difficult because it uses 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 and state estimation errors of these Kalman filters. Specifically, we derive the cross-covariances, each of which is the covariance of the residuals of two Kalman filters, to account for the mutual interactions. From the means and cross-covariance terms, we then compute the means of the likelihood functions and the mean-squared estimation errors as performance measures of the IMM algorithm.