Weighted Multi-Innovation Stochastic Gradient Identification of CAR Models

In this paper, the identification problems for CAR models have been researched by combining the multi-innovation principle and the weighted idea. The weighted multi-innovation stochastic gradient identification algorithm for CAR models is proposed. The convergence performance of the proposed algorithm is analyzed, and it is proven that the parameter estimation errors converge to zero for any initial values under persistent excitation. The computation burden of the MISG algorithm and the proposed WMISG algorithm is also analyzed. Finally, it is shown by a numerical example that the WMISG algorithm can possess higher convergence precision compared with the MISG algorithm if the weighting factor is appropriately chosen.