Performance comparison of Gaussian-based filters using information measures

In many situations, solutions to nonlinear discrete- time filtering problems are available through approximations. Many of these solutions are based on approximating the posterior distributions of the states with Gaussian distributions. In this letter, we compare the performance of Gaussian-based filters including the extended Kalman filter, the unscented Kalman filter, and the Gaussian particle filter. To that end, we measure the distance between the posteriors obtained by these filters and the one estimated by a sequential Monte Carlo (particle filtering) method. As a distance metric, we apply the Kullback-Leibler and X² information measures. Through computer simulations, we rank the performance of the three filters.