Robust CAWOF Kalman predictors for uncertain multi‐sensor generalized system

Abstract

Robust centralized and weighted observation fusion (CAWOF) prediction algorithm is addressed in this article for an uncertain multi-sensor generalized system with linear correlation between observation noises and an input white noise. This uncertainty in the generalized system primarily means that the variances of the aforementioned types of noise, as well as the multiplicative noise variances, are uncertain. Through singular value decomposition and virtual noise compensation, the original generalized system is changed to non-generalized reduced-order subsystems in which only noise variances are uncertain. Utilizing the minimax robustness estimation criterion, robust CAWOF Kalman predictors are put forward on account of the first subsystem with conservative upper bounds of noise variances. Eventually, robust observation fusion Kalman predictors of the original generalized system are proposed.The Lyapunov equation method is applied to verify two fusion predictors' robustness. With regard to all permissible uncertain practical noise variances, CAWOF predictors are robust, namely, the practical prediction error variances of two robust predictors will have minimum upper bounds. This equivalence between CAWOF Kalman predictors is proved by an information filter. In this article, the precision relationship of fusion predictors is given. Meanwhile, robust Kalman predictors for steady-state case are proposed, and the astringency of robust time-variant Kalman predictors is analyzed through the analysis of dynamic error system. The validity and correctness of proposed algorithm are proved by the simulation example of random dynamic input and output system in an economic system.

Robust weighted fusion Kalman estimators for systems with uncertain noise variances, multiplicative noises, missing measurements, packets dropouts and two‐step random measurement delays

“…Besides that, the generalized system can be transformed into non-generalized reduced-order subsystems by using singular value decomposition, and then the proposed methods can be used to address the robust estimation problem. 51,52 AUTHOR CONTRIBUTIONS Chunshan Yang: Conceptualization, formal analysis, investigation, methodology, software, visualization, writing-original draft, writing-review and editing. Ying Zhao: Conceptualization, formal analysis, methodology, supervision, writing-original draft, writing-review and editing.…”

“…This extension work is in the investigation. Besides that, the generalized system can be transformed into non‐generalized reduced‐order subsystems by using singular value decomposition, and then the proposed methods can be used to address the robust estimation problem 51,52 …”

Robust Fusion Kalman Estimator of the Multi-Sensor Descriptor System with Multiple Types of Noises and Packet Loss

“…Time delay is not considered in references [ 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 ]. Meanwhile, references [ 19 , 20 , 21 ] do not consider missing measurement, references [ 19 , 21 , 27 ] ignore the multiplicative noise, and references [ 19 , 20 , 25 , 27 ] do not consider packet dropouts.…”

“…However, it should be noted that reference [ 19 ] only considers the descriptor with a one-step measurement delay, and other uncertainties are not considered. In [ 20 ], the robust centralized and weighted observation fusion (CAWOF) prediction algorithm is derived for the uncertain MSDS with multiplicative noise by using the SVD method and the minimax robustness estimation criterion. Reference [ 20 ] only considers the descriptor system with multiplicative noise and uncertain noise.…”

“…In [ 20 ], the robust centralized and weighted observation fusion (CAWOF) prediction algorithm is derived for the uncertain MSDS with multiplicative noise by using the SVD method and the minimax robustness estimation criterion. Reference [ 20 ] only considers the descriptor system with multiplicative noise and uncertain noise. However, packet loss and measurement delay problems have not been taken into account.…”