Kalman-Based Joint Estimation for Generalized Time-Varying Parameter Systems With the Unknown Invariant Matrix

This article delves into the exploration of state-space methods applied to the modeling and estimation of systems with time-varying parameters. While typically existing approaches rely on the assumption that the parameters satisfy the Markov evolution and require the knowledge of the transfer matrix, this article develops an explicit autoregressive (AR) model for time-varying parameters in which the invariant matrix represents the dynamic changes in the parameters. Unlike the previous work, the state-space model is constructed by stacking the invariant matrix and time-varying parameters into the unknown state vector. Then, the joint state estimation (JSE) algorithm is deduced based on the Kalman filtering principle, aiming to reduce the dependence on the prior knowledge of the invariant matrix. Through the numerical simulation and Monte Carlo test, it is indicated that the developed algorithm maintains reliability under various random white noises. In addition, the practical estimation results with the real-time series also verify the validity.