Kalman Filter With Recursive Covariance Estimation-Sequentially Estimating Process Noise Covariance

• Published in: IEEE transactions on industrial electronics (1982) Vol. 61; no. 11; pp. 6253 - 6263
• Main Authors: Feng, Bo, Fu, Mengyin, Ma, Hongbin, Xia, Yuanqing, Wang, Bo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2014; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithm design and analysis; Algorithms; Covariance matrices; Kalman filter; Kalman filters; Noise; Noise measurement; process noise covariance matrix; recursive covariance estimating; Stability analysis; unknown covariance matrix; unknown covariance matrix; recursive covariance estimating; Kalman filter; stability analysis; process noise covariance matrix
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2014.2301756

The Kalman filter has been found to be useful in vast areas. However, it is well known that the successful use of the standard Kalman filter is greatly restricted by the strict requirements on a priori information of the model structure and statistics information of the process, and measurement noises. Generally speaking, the covariance matrix of process noise is harder to be determined than that of the measurement noise by routine experiments, since the statistical property of process noise cannot be obtained directly by collecting a large number of sensor data due to the intrinsic coupling of process noise and system dynamics. Considering such background of wide applications, this paper introduces one algorithm, recursive covariance estimation (RCE) algorithm, to estimate the unknown covariance matrix of noise from a sample of signals corrupted with the noise. Based on this idea, for a class of discrete-time linear-time-invariant systems where the covariance matrix of process noise is completely unknown, a new Kalman filtering algorithm named, Kalman filter with RCE, is presented to resolve this challenging problem of state estimation without the statistical information of process noise, and the rigorous stability analysis is given to show that this algorithm is optimal in the sense that the covariance matrix and state estimations are asymptotically consistent with the ideal Kalman filter when the exact covariance matrix of process noise is completely known a priori. Extensive simulation studies have also verified the theoretical results and the effectiveness of the proposed algorithm.