Joint Multi-innovation Recursive Extended Least Squares Parameter and State Estimation for a Class of State-space Systems

The relationship between the parameters and the states of state-space systems is nonlinear, which makes the identification problems of state-space systems complicated. This paper considers the joint parameter and state estimation issues for a class of state-space systems in the observer canonical form with the process noises and the observation noises. By means of the least squares principle and the Kalman filtering, we derive a Kalman filtering based recursive extended least squares algorithm. For purpose of achieving the higher estimation accuracy, a Kalman filtering based multi-innovation recursive extended least squares algorithm is proposed by utilizing a range of available data and more information at each recursion. Finally, the effectiveness of the proposed algorithms is validated through a simulation example.