Combined estimation of the parameters and states for a multivariable state‐space system in presence of colored noise

Summary This article addresses the combined estimation issues of parameters and states for multivariable systems in the state‐space form disturbed by colored noises. By utilizing the Kalman filtering principle and the coupling identification concept, we derive a Kalman filtering based partially coupled recursive generalized extended least squares (KF‐PC‐RGELS) algorithm to jointly estimate the parameters and the states. Using the past and the current data in parameter estimation, we propose a Kalman filtering based multi‐innovation partially coupled recursive generalized extended least‐squares algorithm to enhance the parameter estimation accuracy of the KF‐PC‐RGELS algorithm. Finally, a simulation example is provided to test and compare the performance of the proposed algorithms.