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Bounding the Estimation Error Covariance for Nonlinear Systems

Sze Kwan Cheah, Yingjie Hu

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.

Bounding the Estimation Error Covariance for Nonlinear Systems

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.

Paper Structure

This paper contains 5 sections, 2 theorems, 28 equations.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Bounding of Covariance for Nonlinear Equations
  4. Description of Algorithm
  5. Conclusions

Key Result

Theorem III.1

Consider the time update equation described by eq:eom_dt_1-eq:eom_dt_last with white process noise satisfying $\mathbb{E}(\mathbf{w}_k\mathbf{w}_k^{\mathsf{T}})=\mathbf{Q}$, an estimation error covariance at time step $k$ of $\mathbb{E} \left(\delta \mathbf{x}_k \delta \mathbf{x}_k^{\mathsf{T}}\righ then

Theorems & Definitions (4)

  • Theorem III.1
  • proof
  • Theorem III.2
  • proof