A State Estimation Method for Rectangular Singular Systems Based on State Decomposition

This paper proposes a state estimation method of linear discrete rectangular singular systems. The system is observable and regular, and the system matrix is rectangular without full column rank. To give the estimation of the state, the state is decomposed into two parts based on QR factorization, and the weighted least squares method is used to obtain the prediction of one part of the state. Then, the partial measurement equation is used to obtain the prediction of the other part of the state, and the projection theorem is used to obtain the state estimation value. Combined with the data-driven idea, a Kalman filtering algorithm based on historical data modeling is established. Finally, the feasibility and effectiveness of our approach is discussed and verified through performance analysis and numerical simulation perspectives.