Regularized Robust Filtering for Discrete Time Uncertain Time-Delayed Stochastic Systems

摘要

The Kalman filter is the optimal linear least-mean-squares estimator for systems that are described by linear state-space Markovian models. However, when the model is not accurately known, the performance of the filter can deteriorate appreciably. There have been many approaches to robust filtering in the literature (see, e.g., [2]). In [3, 4], frameworks for robust filter designs were discussed that perform regularization as opposed to de-regularization. In this paper, we pursue the design of such regularized robust filters for state-delayed systems. We also allow for stochastic uncertainties in the state matrices and deterministic uncertainties for the output matrices and design a robust filter that bounds the state error covariance matrix.