Kalman filtering based gradient estimation algorithms for observer canonical state-space systems with moving average noises

Abstract

This paper focuses on the joint parameter and state estimation issue for observer canonical state-space systems with white noises in state equations and moving average noises in output equations. By means of the Kalman filtering and the gradient search, we derive a Kalman filtering based extended stochastic gradient algorithm. For purpose of achieving the higher parameter estimation accuracy, a Kalman filtering based multi-innovation extended stochastic gradient algorithm is proposed on the basis of the multi-innovation identification theory. Finally, the effectiveness of the proposed algorithms is validated through a numerical example.