The noise covariances of linear Gaussian systems with unknown inputs are not uniquely identifiable using autocovariance least-squares

Kong，He1; Sukkarieh，Salah2; Arnold，Travis J.3; Chen，Tianshi4; Zheng，Wei Xing5

2022-04-01

10.1016/j.sysconle.2022.105172

SYSTEMS & CONTROL LETTERS   影响因子和分区

0167-6911

1872-7956

Existing works in optimal filtering for linear Gaussian systems with arbitrary unknown inputs assume perfect knowledge of the noise covariances in the filter design. This is impractical and raises the question of whether and under what conditions one can identify the noise covariances of linear Gaussian systems with arbitrary unknown inputs. This paper considers the above identifiability question using the correlation-based autocovariance least-squares (ALS) approach. In particular, for the ALS framework, we prove that (i) the process noise covariance Q and the measurement noise covariance R cannot be uniquely jointly identified; (ii) neither Q nor R is uniquely identifiable, when the other is known. This not only helps us to have a better understanding of the applicability of existing filtering frameworks under unknown inputs (since almost all of them require perfect knowledge of the noise covariances) but also calls for further investigation of alternative and more viable noise covariance methods under unknown inputs. Especially, it remains to be explored whether the noise covariances are uniquely identifiable using other correlation-based methods. We are also interested to use regularization for noise covariance estimation under unknown inputs, and investigate the relevant property guarantees for the covariance estimates. The above topics are the main subjects of our current and future work.

Arbitrary unknown input Estimation Kalman filter Noise covariance estimation

SCI ; EI

英语

第一 ; 通讯

Chinese University of Hong Kong, Shenzhen[2014.0003.23] ; [PF. 01.000249]

Automation & Control Systems ; Operations Research & Management Science

Automation & Control Systems ; Operations Research & Management Science

WOS:000788749000008

ELSEVIER

20221011757255

Correlation methods ; Gaussian distribution

Probability Theory:922.1 ; Mathematical Statistics:922.2

ENGINEERING

2-s2.0-85125697580

Scopus

1.Department of Mechanical and Energy Engineering,Southern University of Science and Technology,Shenzhen,518055,China
2.Australian Centre for Field Robotics,University of Sydney,NSW,2006,Australia
3.Independent researcher,Tucson,85756,United States
4.School of Data Science and Shenzhen Research Institute of Big Data,The Chinese University of Hong Kong,Shenzhen,518172,China
5.School of Computer,Data and Mathematical Sciences,Western Sydney University,Sydney,NSW 2751,Australia

Kong，He,Sukkarieh，Salah,Arnold，Travis J.,et al. The noise covariances of linear Gaussian systems with unknown inputs are not uniquely identifiable using autocovariance least-squares[J]. SYSTEMS & CONTROL LETTERS,2022,162.

Kong，He,Sukkarieh，Salah,Arnold，Travis J.,Chen，Tianshi,&Zheng，Wei Xing.(2022).The noise covariances of linear Gaussian systems with unknown inputs are not uniquely identifiable using autocovariance least-squares.SYSTEMS & CONTROL LETTERS,162.

Kong，He,et al."The noise covariances of linear Gaussian systems with unknown inputs are not uniquely identifiable using autocovariance least-squares".SYSTEMS & CONTROL LETTERS 162(2022).