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Number 2 - June 2022
Volume 32 - 2022
A Kalman filter with intermittent observations and reconstruction of data losses
Taouba Rhouma, Jean-Yves Keller, Mohamed Naceur Abdelkrim
Abstract
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.
Keywords
Kalman filter, intermittent unknown inputs, linear system, intermittent observation