Constrained two-stage Kalman filter for real-time state estimation of systems with time-varying measurement noise covariance

Considering the statistical properties of the measurement noise are not deterministic, which is very common in engineering and may bring large errors to system state estimation, a novel constrained two-stage Kalman filter algorithm is proposed. Based on the prior estimate of system states, the covariance update model is established and the constraint algorithm is introduced to accurately estimate the measurement noise covariance. The results are subsequently substituted back into the main-filter to obtain the posterior estimate of system states. Finally, the proposed algorithm is validated by two simulation cases, and the performance is compared with that of Kalman filter and adaptive Kalman filter. The results show that the proposed method is more effective than conventional methods when facing the time-varying measurement noise covariance problem.