A Kalman Filter with Intermittent Observations and Reconstruction of Data Losses

• Published in: International journal of applied mathematics and computer science 2022-06, Vol.32 (2), p.241-253
• Main Authors: Rhouma, Taouba, Keller, Jean-Yves, Abdelkrim, Mohamed Naceur
• Format: Article
• Language: English
• Subjects: Communication channels; Covariance matrix; Data integrity; Data loss; Data transmission; Discrete time systems; Fault diagnosis; Filter design (mathematics); intermittent observation; intermittent unknown inputs; Kalman filter; Kalman filters; linear system; Linear systems; Markov analysis; Mathematical analysis; Reconstruction; Sensors; Sequences; State estimation
• ISSN: 1641-876X; 2083-8492
• DOI: 10.34768/amcs-2022-0018

This paper deals with the problem of joint state and unknown input estimation for stochastic discrete-time linear systems subject to intermittent unknown inputs on measurements. A Kalman filter approach is proposed for state prediction and intermittent unknown input reconstruction. The filter design is based on the minimization of the trace of the state estimation error covariance matrix under the constraint that the state prediction error is decoupled from active unknown inputs corrupting measurements at the current time. When the system is not strongly detectable, a sufficient stochastic stability condition on the mathematical expectation of the random state prediction errors covariance matrix is established in the case where the arrival binary sequences of unknown inputs follow independent random Bernoulli processes. When the intermittent unknown inputs on measurements represent intermittent observations, an illustrative example shows that the proposed filter corresponds to a Kalman filter with intermittent observations having the ability to generate a minimum variance unbiased prediction of measurement losses.