UC San Diego

The problem of state estimation for a linear, time-varying, gaussian system from measurements which are communicated over an imperfect channel is considered from several perspectives. The communication imperfections include intermittency, channel noise, quantization, etc. The first part of the thesis examines the stochastic behavior of the state estimation error and of the regulated state itself in situations of intermittent and quantized measurements via the formulation of an escape time problem dealing with the cumulative distribution function of the probability of escape of these signals from a given set. This is compared to and contrasted with earlier analyses which considered the behavior of Kalman filters with intermittent data based on moments and conditional moments, and the evaluation of the minimal number of bits required for mean square stabilization. The main result shows the escape time is characterized by a Markov chain which is amenable to explicit analysis through the calculation of the its cumulative distribution function. The second part of the thesis focuses on developing an exact formulation of the conditional probability density function of the system state given quantized innovations signals communicated from a linear Kalman filter at the transmitter. This is based on Bayesian filtering and extends previous works on the subject but without the requirement for simplifying assumptions. This latter result follows from a simple observation concerning the correct choice of state for the transmitter, which includes the transmitters’ Kalman filter estimate. This leads to an exact and recursive approach.