A Single-Pass Noise Covariance Estimation Algorithm in Nonswitching Multiple-Model Adaptive Kalman Filters for Nonstationary Systems

This paper presents a single-pass stochastic gradient descent (SGD) algorithm for estimating unknown noise covariances. The proposed algorithm is designed for nonswitching multiple-model adaptive Kalman filters, where the noise covariances can occasionally jump up or down by an unknown magnitude. Compared to our previous batch estimation or multipass decision-directed estimation methods, the proposed algorithm has the advantage of reading measurement data exactly once, leading to a significant improvement in computational efficiency and practicality. Moreover, the algorithm achieves an acceptable level of root mean square error (RMSE) in state estimates, making it suitable for real-time industrial applications. The proposed algorithm utilizes recursive fading memory estimates of the sample cross-correlations of the innovations and employs the root mean square propagation (RMSprop) accelerated SGD algorithm. The combination of these techniques enables the algorithm to achieve high accuracy in estimating the unknown noise covariances while maintaining superior computational efficiency over iterative batch methods. The paper presents a comparative evaluation of the proposed method on several test cases, which demonstrate its effectiveness in terms of computational efficiency and estimation accuracy. Overall, the proposed algorithm offers a promising approach for real-time noise covariance estimation in multiple-model adaptive Kalman filters. © 2024 JAIF.