Title: Least-squares quadratic filtering in linear stochastic systems with random parameter matrices and correlated noises
Authors: Raquel Caballero-Aguila - Universidad de Jaen (Spain)
Irene Garcia-Garrido - Universidad de Jaén (Spain) [presenting]
Josefa Linares-Perez - Universidad de Granada (Spain)
Abstract: A quadratic filtering algorithm in linear discrete-time stochastic systems with random parameter matrices is designed. The additive noises involved in the system are supposed to be autocorrelated and cross-correlated. To address the quadratic estimation problem under the least-squares (LS) optimality criterion, the system hypotheses must include the knowledge of the fourth-order moments of the processes involved. Defining a suitable augmented system by stacking the original state and observation vectors with their second-order Kronecker powers, the quadratic estimation problem is then reformulated as a linear estimation problem, whose approach requires to study the second-order statistical properties of the processes involved in this augmented system. By an innovation approach, a recursive algorithm for the LS linear filter of the augmented state based on the augmented observations is derived, from which the required LS quadratic filter of the original state is obtained. The proposed algorithm can be applied to multisensor systems with random uncertainties in both the state and measurement equations. The performance of the proposed estimator is illustrated by a numerical simulation example where a scalar state process is estimated from multisensor missing measurements. The quadratic estimation accuracy is analyzed in terms of their error variances for different missing probabilities and the superiority of the quadratic filter in comparison with the linear one is also shown.