Distributed Fusion Estimation with Sensor Gain Degradation and Markovian Delays

Abstract

This paper investigates the distributed fusion estimation of a signal for a class of multi-sensor systems with random uncertainties both in the sensor outputs and during the transmission connections. The measured outputs are assumed to be affected by multiplicative noises, which degrade the signal, and delays may occur during transmission. These uncertainties are commonly described by means of independent Bernoulli random variables. In the present paper, the model is generalised in two directions: (i) at each sensor, the degradation in the measurements is modelled by sequences of random variables with arbitrary distribution over the interval [0, 1]; (ii) transmission delays are described using three-state homogeneous Markov chains (Markovian delays), thus modelling dependence at different sampling times. Assuming that the measurement noises are correlated and cross-correlated at both simultaneous and consecutive sampling times, and that the evolution of the signal process is unknown, we address the problem of signal estimation in terms of covariances, using the following distributed fusion method. First, the local filtering and fixed-point smoothing algorithms are obtained by an innovation approach. Then, the corresponding distributed fusion estimators are obtained as a matrix-weighted linear combination of the local ones, using the mean squared error as the criterion of optimality. Finally, the efficiency of the algorithms obtained, measured by estimation error covariance matrices, is shown by a numerical simulation example.