Kalman Filtering in Correlated Losses

In this project we consider the problem of estimating the state of an unstable system in presence of correlated losses using a Kalman Filter . This scenario arises in performing vehicle tracking or navigation over a wireless channel. Since wireless channels are inherently lossy in nature, it is possible for the Kalman estimator to lose some observations. We study the behavior of Kalman filter in such correlated losses. To model a channel with correlated losses, we consider a Gilbert Elliott channel which is a simple two state Markov model with a good and a bad state. The observations are received with no error when the channel is in good state and all observations in bad state are lost. We show that the channel memory ha adverse effect on the performance of Kalman filter. We also show that considering the usual metric of average error covariance is not useful since the estimator has huge oscillations in its error covariance. We then define a new metric which gives a probabilistic definition of stability. This new metric upper bounds the error covariance with some desired probability. We then derive conditions on channel parameters that meet this metric in the case of scalar systems.