Joint Parameter and State Estimation of Errors‐in‐Variables Nonlinear Systems Based on the Adaptive Kalman Filter

ABSTRACT This paper develops a hybrid strategy for identifying the nonlinear errors‐in‐variables (EIV) Wiener state‐space systems subjected to the unknown states. The Wiener nonlinear system with the noisy input is investigated, and a state‐space subsystem affected by the process disturbance is considered. The unbiased parameter estimation of the EIV Wiener systems with nonideal observations and polynomial nonlinearities is realized using the proposed bias‐compensated recursive least squares algorithm. Specifically, the estimated bias caused by the noisy measurements is eliminated, and the analytic formulas for estimating unmeasurable nonlinear intermediate variables are derived. Furthermore, based on the adaptive Kalman filtering principle, a state observer is designed to simultaneously estimate the subsystem states and the unknown noise variances in the estimated bias. The presented algorithms in the hybrid framework achieve the joint estimation of the parameters and states for EIV Wiener state‐space systems. The convergence analysis shows that the parameter estimates can converge to their true values. Finally, a numerical simulation and a quarter‐car model simulation demonstrate the effectiveness of the proposed algorithm.