A Solution to the Filtering Problem for Stochastic Systems with Multi-Sensor Uncertain Observations

Abstract

In this paper, the least-squares linear and quadratic filtering problems are studied in discrete-time linear stochastic systems with uncertain observations coming from multiple sensors, when the variables describing the uncertainty in the observations are correlated at instants that differ two units of time. The least-squares linear filter is obtained by using an approach based on innovations. The least-squares quadratic estimation problem is solved by defining an appropriate augmented system, whose state linear filtering estimate provides the quadratic filtering estimate of the original state vector. A numerical simulation example shows the effectiveness of the proposed estimation algorithms.