Quadratic Filtering Algorithm Based on Covariances Using Correlated Uncerta in Observations Coming from Different Sensors

R. Caballero-Á guila ； A. Hermoso-Carazo ； J. Linares-Pérez

《ISRN Applied Mathematics》 2011 (2011/12) Pp. 685-702

並列摘要

The least-squares quadratic estimation problem of signals from observations coming from multiple sensors is addressed when there is a nonzero probability that each observation does not contain the signal to be estimated. We assume that, at each sensor, the uncertainty about the signal being present or missing in the observation is modeled by correlated Bernoulli random variables, whose probabilities are not necessarily the same for all the sensors. A recursive algorithm is derived without requiring the knowledge of the signal state-space model but only the moments (up to the fourth-order ones) of the signal and observation noise, the uncertainty probabilities, and the correlation between the variables modeling the uncertainty. The estimators require the auto covariance and cross-covariance functions of the signal and their second-order powers in a semi-degenerate kernel form. The recursive quadratic filtering algorithm is derived from a linear estimation algorithm for a suitably defined augmented system.