Block Diagonally Dominant Positive Definite Sub-optimal Filters and Smoothers

TL;DR

This paper introduces suboptimal filters and smoothers for stochastic systems with nearly block diagonal matrices, ensuring positive semi-definiteness and improved numerical stability, especially useful in distributed systems like pixel imaging.

Contribution

The paper proposes a novel class of filters and smoothers tailored for nearly block diagonal matrices, enhancing stability and positivity in distributed dynamical systems.

Findings

Filters are always positive semi-definite.

Numerical stability is improved in the proposed methods.

Applications include distributed pixel imaging systems.

Abstract

We examine stochastic dynamical systems where the transition matrix, $\Phi$, and the system noise, $\bf{\Gamma}\bf{Q}\bf{\Gamma}^T$, covariance are nearly block diagonal. When $\bf{H}^T \bf{R}^{-1} \bf{H}$ is also nearly block diagonal, where $\bf{R}$ is the observation noise covariance and $\bf{H}$ is the observation matrix, our suboptimal filter/smoothers are always positive semi-definite, and have improved numerical properties. Applications for distributed dynamical systems with time dependent pixel imaging are discussed.