Robust Kalman Filter For 2-D Nonlinear Systems

Abstract

Kalman filter (KF), being an optimal estimator for linear systems and known statistics of Gaussian noise, is an optimal filter thus widely used method for state estimation. However, the central obstruction in its implementation is that the dynamics of the model must be exactly known. Many advances in robust control and estimation to reduce the effects of model uncertainties have attracted various studies on robust Kalman filtering. There are three renowned approaches for robust linear state estimation i.e. H∞ filtering, set valued filtering and guaranteed cost (GC) filtering; all of them are used with Kalman filtering framework due to its wider applicability. Since, the exact minimum of estimation error variance is not mathematically computed, the usual choice, therefore, is to enforce a constant upper bound on error variances for all acceptable uncertainties. This upper bound is then minimized instead of obtaining (global) minimum variance. Thus, the robust KFs (RKFs) are sub-optimal but adaptable to practical scenarios. Since, all of the above methods perform de-regularization, they either suffer from inherent conservativeness or existence conditions. Practically, these conditions cannot be ensured to be satisfied at all arbitrary iterations. If the conditions are not met at any iteration, the filter may perform poorly. However, a RKF based on least square (LS) approach employed unique Regularized Least Square (RLS) criterion for uncertain models. The distinctive features of this method are it performs regularization thus avoids existence conditions and vector optimization problem is reduced to scalar minimization problem. Hence, this approach, according to the best of our knowledge, is most suitable for online implementation.