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 article considers the identifiability of Q / R using the correlation-based measurement difference approach. More specifically, we establish 1) necessary conditions under which Q and R can be uniquely jointly identified; 2) necessary and sufficient conditions under which Q can be uniquely identified, when R is known; 3) 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.  

　　Publication:  

　　IEEE Transactions on Automatic Control, Volume: 68, Issue: 7, July 2023  

　　http://dx.doi.org/10.1109/TAC.2022.3208338  

　　Author:  

　　He Kong  

　　Shenzhen Key Laboratory of Biomimetic Robotics and Intelligent Systems, Department of Mechanical and Energy Engineering, Southern University of Science and Technology, Shenzhen, China  

　　Guangdong Provincial Key Laboratory of Human-Augmentation and Rehabilitation Robotics in Universities, Southern University of Science and Technology, Shenzhen, China  

　　Salah Sukkarieh  

　　Sydney Institute for Robotics and Intelligent Systems, The University of Sydney, Sydney, NSW, Australia  

　　Travis J. Arnold  

　　Tianshi Chen  

　　School of Data Science and Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China  

　　Biqiang Mu  

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China  

　　Email: bqmu@amss.ac.cn  

　　Wei Xing Zheng  

　　School of Computer, Data and Mathematical Sciences, Western Sydney University, Sydney, NSW, Australia