A Pareto based comparison approach for nonlinear state estimation algorithms

The Kalman filter obtains optimal estimates, with respect to the mean square error, of states from observations of linear systems. For state estimation of nonlinear systems, closed-form optimal filter similar to the Kalman filter exists only in some specific cases. In practice, most of the suggested filters for state estimation of nonlinear systems refer to specific classes of systems and are suboptimal filters. There exist many suboptimal filters in the literature. Each filter has its own advantages and disadvantages. Furthermore, each filter has at least one tuning parameter which needs to be adjusted to each nonlinear problem separately. It is difficult to determine analytically which filter is most suitable for a specific problem. Our work proposes a methodical approach for appropriate and meaningful comparison of filter performance for a given state estimation problem. The comparison is made using the Pareto front paradigm and is accordingly called the Pareto Based Comparison (PBC) approach. The proposed procedure plots the settling time versus the steady state error for all relevant values of the tuning parameter, thus circumventing the different tuning of each nonlinear filter. Thus the PBC approach enables comparison on common basis of the various filters. In order to examine the proposed approach, several nonlinear filters were simulated for the nonlinear state estimation problem of a target performing a 2-D barrel roll with a constant but unknown angular velocity.