Identification of non-causal systems with arbitrary switching modes

TL;DR

This paper introduces an EM-based method for identifying non-causal systems with arbitrary switching modes, addressing challenges in estimating causal and anticausal components amid random switching sequences.

Contribution

It presents a novel EM-based approach combining a modified Kalman filter and switching least-squares for accurate system identification in complex non-causal, switching environments.

Findings

The method converges under mild conditions.

Parameter estimation errors are bounded.

Numerical simulations validate effectiveness.

Abstract

We consider the identification of non-causal systems with arbitrary switching modes (NCS-ASM), a class of models essential for describing typical power load management and department store inventory dynamics. The simultaneous identification of causal-and-anticausal subsystems, along with the presence of possibly random switching sequences, however, make the overall identification problem particularly challenging. To this end, we develop an expectation-maximization (EM) based system identification technique, where the E-step proposes a modified Kalman filter (KF) to estimate the states and switching sequences of causal-and-anticausal subsystems, while the M-step consists in a switching least-squares algorithm to estimate the parameters of individual subsystems. We establish the main convergence features of the proposed identification procedure, also providing bounds on the parameter estimation errors under mild conditions. Finally, the effectiveness of our identification method is validated through two numerical simulations.