On Estimation Error Outage for Scalar Gauss-Markov Signals Sent Over Fading Channels

Measurements of a scalar linear Gauss-Markov process are sent over a fading channel. The fading channel is modeled as independent and identically distributed random variables with known realization at the receiver. The optimal estimator at the receiver is the Kalman filter. In contrast to the classical Kalman filter theory, given a random channel, the Kalman gain and the error covariance become random. Then the probability distribution function of expected estimation error and its outage probability can be chosen for estimation quality assessment. In this paper and in order to get the estimation error outage, we provide means to characterize the stationary probability density function of the random expected estimation error. Furthermore and for the particular case of the i.i.d. Rayleigh fading channels, upper and lower bounds for the outage probability are derived which provide insight and simpler means for design purposes. We also show that the bounds are tight for the high SNR regime, and that the outage probability decreases linearly with the inverse of the average channel SNR.Comment: 21 pages, 5 figures, conference version at EUSIPCO 2014, accepted for publication in IEEE Transactions on Signal Processin

Stability of Kalman Filtering with a Random Measurement Equation: Application to Sensor Scheduling with Intermittent Observations

Studying the stability of the Kalman filter whose measurements are randomly lost has been an active research topic for over a decade. In this paper we extend the existing results to a far more general setting in which the measurement equation, i.e., the measurement matrix and the measurement error covariance, are random. Our result also generalizes existing ones in the sense that it does not require the system matrix to be diagonalizable. For this general setting, we state a necessary and a sufficient condition for stability, and address its numerical computation. An important application of our generalization is a networking setting with multiple sensors which transmit their measurement to the estimator using a sensor scheduling protocol over a lossy network. We demonstrate how our result is used for assessing the stability of a Kalman filter in this multi-sensor setting