An improved measurement noise covariance estimation method based on envelope pseudo-measurement system in adaptive Kalman filter

Accurate estimation of the measurement noise covariance matrix is crucial for adaptive Kalman filtering in non-stationary environments. Existing methods mainly couple measurement noise covariance matrix estimation with state estimation. In contrast, the emerging second-order mutual difference (SOMD) technique achieves state-independent estimation through redundant measurements. However, this approach comes at the cost of requiring additional sensor resources. To overcome this limitation, this paper proposes a pseudo-measurement-based method that replaces redundant measurements using the mean of the upper and lower signal envelopes. Our analysis reveals that traditional envelope construction methods often suffer from coverage gaps; therefore, we categorize the envelope signals into three trend-based groups and address them comprehensively. Additionally, outliers are detected using the interquartile range (IQR) and replaced by the mean of the neighboring measurements at time steps k−1 and k+1. The performance of the proposed improved envelope pseudo-measurement noise covariance estimate (IEPMNCE) method is evaluated through numerical and motion model simulations. The numerical simulation results show that systematic errors do not affect IEPMNCE. Furthermore, IEPMNCE demonstrates greater resistance to outliers, yielding more accurate state estimation than other methods in motion model simulation. These findings highlight the effectiveness of IEPMNCE in improving measurement noise covariance estimation accuracy. The method is particularly well-suited for adaptive filtering in dynamic environments.