Identifiability Analysis of Noise Covariances for LTI Stochastic Systems with Unknown Inputs

作     者：Kong, He Sukkarieh, Salah Arnold, Travis J. Chen, Tianshi Mu, Biqiang Zheng, Wei Xing 

作者机构： Shenzhen518055 China Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities SUSTech Shenzhen518055 China Sydney Institute for Robotics and Intelligent Systems The University of Sydney NSW2006 Australia MadisonWI53704 United States School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen518172 China Key Laboratory of Systems and Control Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Computer Data and Mathematical Sciences Western Sydney University SydneyNSW2751 Australia 

出 版 物：《arXiv》 (arXiv)

年 卷 期：2022年

核心收录：

主　　题：Stochastic systems 

摘      要：Most existing works on optimal filtering of linear time-invariant (LTI) stochastic systems with arbitrary unknown inputs assume perfect knowledge of the covariances of the noises in the filter design. This is impractical and raises the question of whether and under what conditions one can identify the process and measurement noise covariances (denoted as Q and R, respectively) of systems with unknown inputs. This paper considers the identifiability of Q/R using the correlation-based measurement difference approach. More specifically, we establish (i) necessary conditions under which Q and R can be uniquely jointly identified;(ii) necessary and sufficient conditions under which Q can be uniquely identified, when R is known;(iii) necessary conditions under which R can be uniquely identified, when Q is known. It will also be shown that for achieving the results mentioned above, the measurement difference approach requires some decoupling conditions for constructing a stationary time series, which are proved to be sufficient for the well-known strong detectability requirements established by Hautus. © 2022, CC BY.