Recursive performance ranking of Kalman filter with mismatched noise covariances. Issue 4 (28th January 2019)

• Record Type: Journal Article
• Authors: Shao, Teng; Duan, Zhansheng; Ge, Quanbo; Liu, Huaping
• Is Part Of: IET control theory & applications. Volume 13:Issue 4(2019)
• Page Start: 459
• Page End: 466
• Publication Date: 2019-01-28
• Subjects: mean square error methods -- recursive estimation -- covariance matrices -- state estimation -- Kalman filters -- target tracking -- mathematical programming; Kalman filter -- mismatched noise covariances -- unknown noise covariances -- recursive performance ranking -- recursive state estimator -- mean squared errors -- filter calculated MSE -- FMSE -- true MSE -- TMSE -- target tracking -- semidefinite deviation; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.5064
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : The Kalman filter is a powerful recursive state estimator and has been widely used in many applications. To guarantee its optimality, the noise covariances should to be exactly known. In reality, however, for most practical applications, it is difficult or unrealistic to obtain the noise covariances. A typical practice is to use some pre‐determined alternatives for unknown noise covariances. The main issue concerning this is how the pre‐determined alternatives will affect the performance of the Kalman filter. In this study, the authors study recursive performance ranking of Kalman filter with mismatched noise covariances. For this purpose, three types of mean squared errors (MSEs) have been used, i.e., the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE). This study considers the recursive ranking of these three types of MSEs at each time step. It is found that for the case with positive semi‐definite deviation from the truth, they have FMSE ⪰ TMSE ⪰ IMSE at each time step recursively. On the contrary, for the case with negative semi‐definite deviation, they have TMSE ⪰ IMSE ⪰ FMSE at each time step recursively. Target tracking examples further verify these results.