Linear and quadratic estimation using uncertain observations from multiple sensors with correlated uncertainty

In this paper, filtering algorithms are derived for the least-squares linear and quadratic estimation problems in linear systems with uncertain observations coming from multiple sensors with different uncertainty characteristics. It is assumed that, at each sensor, the state is measured in the presence of additive white noise and that the Bernoulli random variables describing the uncertainty are correlated at consecutive sampling times but independent otherwise. The least-squares linear estimation problem is solved by using an innovation approach, and the quadratic estimation problem is reduced to a linear estimation one in a suitable augmented system. The performance of the linear and quadratic estimators is illustrated by a numerical simulation example wherein a scalar signal is estimated from correlated uncertain observations coming from two sensors with different uncertainty characteristics.