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

• 成果类型: Article
• 署名作者: Kong, He; Sukkarieh, Salah; Arnold, Travis J.; Chen, Tianshi; Mu, Biqiang; Zheng, Wei Xing
• 署名单位: Southern University of Science & Technology; Southern University of Science & Technology; University of Sydney; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; The Chinese University of Hong Kong, Shenzhen; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Western Sydney University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3208338
• 发表日期: 2023
• 页码: 4459-4466
• 关键词: Arbitrary unknown input; estimation; Kalman filter; noise covariance estimation

摘要

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.