Kalman Filter for Linear Discrete-Time Rectangular Singular Systems Considering Causality

Abstract

This paper proposes a Kalman filter for linear rectangular singular discrete-time systems, where the singular matrix in the system is a rectangular matrix without full column rank. By using two different restricted equivalent transformation methods and adding the measurement equation to the state equation, the system is transformed into a square singular system satisfying regularity and observability. During this process, the causality of the system is taken into account, and multiple matrix transformations are applied accordingly. Based on these modifications, state estimation results are obtained using the Kalman filter. Finally, a numerical example is employed to demonstrate the effectiveness of our approach.

Keywords

• rectangular singular systems
• Kalman filter
• non-causal system