New advances in the estimation problem in systems with random failures

Abstract

The aim of this PhD thesis is to address least-squares estimation problems in discrete-time linear systems from noisy measurements derived from multiple sensors, affected by random parameters which model different situations of failure in the mechanism or the transmission of the measurements. According to the kind of systems considered, the main contributions of this PhD thesis are summarized below: Sensor network systems with uncertain observations. These systems describe situations in which the mechanism of measurements may be randomly interrupted, in the sense that, at each instant of time, there is a positive probability that the corresponding observation is only noise, i.e., the observations may not contain information about the state. This kind of uncertainty is modeled by including in the observation equation not only an additive noise, but also a multiplicative noise component described by a sequence of Bernoulli random variables whose values, one or zero, indicate the presence or absence of the state in the corresponding measurement. In cases in which the Bernoulli variables are assumed to be correlated at instants that differ by m units of time, on the one hand, centralized and distributed fusion linear estimators are designed (Chapter 1) and, on the other, in order to improve the linear estimators, quadratic estimators are obtained using the centralized fusion method (Chapter 2). Sensor network systems with failures in the measurements, in which the observations from the different sensors may contain only partial information about the state. This kind of failure is more general than the previous one and it is described by a sequence of independent random variables with discrete probability distribution over the interval [0; 1]. For this class of systems, under the assumption that the system additive noises are autocorrelated and also cross-correlated, recursive linear filtering algorithms are derived using the centralized and distributed fusion methods (Chapter 3). Sensor network systems with random parameter matrices. This kind of systems constitute a more general framework than the previous ones since the state and/or the observation equations may be affected by random parameter matrices, thus covering numerous real situations with random failures in the measurements. First, we consider independent random state transition matrices, and one-step correlated and cross-correlated random parameter matrices in the observation equation; it is also assumed that the system noises are autocorrelated and cross-correlated. Using the centralized fusion method, a recursive linear filtering algorithm is obtained and the results are applied to multi-sensor systems with failures in the measurements described by random variables with discrete distribution over the interval [0; 1], and to multi-sensor systems with randomly delayed observations (Chapter 4). Second, the linear estimation problem in systems with independent random parameter matrices and correlated noises is addressed, using the distributed fusion method (Chapter 5). Finally, centralized quadratic estimators are obtained in systems with independent random parameter matrices and noises, and they are applied to systems with random failures in the measurements, described by different sequences of random variables with discrete probability distribution over the interval [0; 1] (Chapter 6).