Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

Abstract

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.

Keywords:

• random parameter matrices
• correlated noises
• optimal least-squares estimation
• innovation approach

Additional information

Funding

This research is supported by Ministerio de Ciencia e Innovación [FPU programme] [grant number MTM2011-24718].

Notes on contributors

J. Linares-Pérez

Josefa Linares-Pérez received the MSc degree in mathematics (statistics) and her PhD in stochastic differential equations, both from the University of Granada (Spain), in 1980 and 1982, respectively. She is currently a professor at the Department of Statistics and Operations Research, University of Granada (Spain). Her research interest involves the areas of stochastic calculus and estimation in stochastic systems.

R. Caballero-Águila

Raquel Caballero-Águila received her MSc degree in mathematics (statistics) from the University of Granada (Spain) in 1997 and her PhD in polynomial filtering in systems with uncertain observations in 1999. In 1997 she joined University of Jaén (Spain), where she is now an associate professor at the Department of Statistics and Operations Research. Her research interest is mainly focused on stochastic systems, filtering, prediction and smoothing.

I. García-Garrido

Irene García-Garrido received her BSc in mathematics and her BSc in statistics, both from the University of Granada (Spain), in 2008 and 2010, respectively. She also received the MSc in applied statistics in 2010. Currently, she is a PhD student of mathematics and statistics at the Department of Statistics and Operations Research, University of Granada (Spain). Her research is focused on filtering estimation in discrete-time linear systems.