A general approach for designing the MWGS-based information-form Kalman filtering methods

• Published in: European journal of control Vol. 56; pp. 86 - 97
• Main Authors: Tsyganova, Julia V., Kulikova, Maria V., Tsyganov, Andrey V.
• Format: Journal Article
• Language: English
• Published: Philadelphia Elsevier Ltd 01.11.2020; Elsevier Limited
• Subjects: Algorithms; Array algorithms; Arrays; Decomposition; Equivalence; Information filter; Iterative methods; Kalman filter; Kalman filters; MWGS orthogonalization; Random variables; Robustness (mathematics); Roundoff error; Signal processing; Array algorithms; MWGS orthogonalization; Kalman filter; Information filter
• ISSN: 0947-3580; 1435-5671
• DOI: 10.1016/j.ejcon.2020.02.001

•An unified approach for designing the MWGS-based information-form Kalman filter implementation methods is proposed.•The solution is based on the modified Cholesky factorization and the utilization of numerically stable Modified Weighted Gram-Schmidt (MWGS) orthogonal transformation for updating the MWGS factors of the filter information matrix involved.•The factorization based implementation strategies are recognized to enhance the numerical robustness with respect to roundoff errors and, hence, they are the preferred implementations when solving applications with high reliability requirements.•To illustrate the suggested general approach, two MWGS-based information-form methods are developed. Their theoretical properties, computational complexities are discussed and numerical comparison with the existing array information implementations is performed for determining the most reliable implementations.•The newly-suggested extended eMWGS-aIF method is found out to be the most reliable implementations in the class of square-root-free information-form Kalman filtering algorithms, which allows the ill-conditioned state estimation problems to be solved accurately. The paper addresses a general approach to MWGS (Modified Weighted Gram-Schmidt) orthogonalization based Kalman filtering (KF) implementation methods. We propose two new numerically favored and convenient array information formulations of the MWGS-based KF that are the MWGS-based array Information Filter (algorithm MWGS-aIF) and the extended MWGS-based array Information Filter (algorithm eMWGS-aIF). To confirm the correctness of our results, we have proved that the newly constructed MWGS-based array computational schemes are algebraically equivalent to the “straight” (conventional) information filter. Although all these information-type algorithms are theoretically equivalent, their computational properties are different. The newly proposed algorithms are numerically robust to machine roundoff errors due to the numerically stable orthogonal transformations applied on each iteration. The obtained numerical results confirm this statement. Additionally, algorithm eMWGS-aIF has the extended array form, i. e., it allows for updating all required filter quantities with the use of the numerically stable MWGS orthogonalization procedure, only. Thus, our results extend the existing class of numerically efficient KF implementation methods and can be used in practical applications.