Bounding the Estimation Error Covariance for Nonlinear Systems

TL;DR

This paper introduces a method to compute upper bounds on the estimation error covariance in nonlinear systems using quadratic constraints and semidefinite programming, enhancing the analysis of extended Kalman filter performance.

Contribution

It proposes a novel approach combining quadratic constraints and semidefinite programming to bound estimation errors in nonlinear filtering.

Findings

Upper bounds on estimation error covariance are computable for nonlinear systems.

The method utilizes quadratic constraints to handle nonlinearities.

Semidefinite programs are used to find bounds for each covariance matrix entry.

Abstract

This paper presents preliminary work on computing upper bounds on the estimation error covariance in the framework of the extended Kalman filter. The approach taken is using quadratic constraints to bound the dynamic nonlinearities and use of semidefinite programs to find the upper bound of each entry of the estimation error covariance matrix.