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

In this paper, the least-squares linear and quadratic filtering pro-blems are studied in discrete-time linear stochastic systems with un-certain 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 sys-tem, 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. 888 I. Garćıa-Garrido et a