Adaptive moving horizon state estimation for linear time-varying systems with unknown model parameters and noise statistics

A novel state estimator with adaptive moving horizon for linear time-varying systems with unknown noise statistics and model parameters is proposed to reduce computational burden and enhance estimation performance. First, the Q-learning algorithm is used to derive a policy for obtaining state estimates, addressing the issue of unknown model parameters. Next, to improve estimation accuracy, an influence function is introduced to quantitatively analyze the impact of past sample data on current estimate. The window length of moving horizon is adaptively adjusted according to the computed impact weights. Then, the estimation policy is evaluated based on the adaptive window length to update the state estimation values. Finally, the proposed algorithm is applied to estimate the states of a two-state polynomial system and the water levels of a quadruple water tank system, demonstrating the effectiveness of the algorithm.