Treatment of bias in recursive filtering

Author

Friedland, Bernard

Author_Institution

Singer-General Precision, Incorporated, Little Falls, NJ, USA

Volume

14

Issue

4

fYear

1969

fDate

8/1/1969 12:00:00 AM

Firstpage

359

Lastpage

367

Abstract

The problem of estimating the state $x$ of a linear process in the presence of a constant but unknown bias vector $b$ is considered. This bias vector influences the dynamics and/or the observations. It is shown that the optimum estimate $\\hat{x}$ of the state can be expressed as $\\hat{x} = x + V_{x}\\hat{b}$ (1) where $\\tilde{x}$ is the bias-free estimate, computed as if no bias were present, $\\hat{b}$ is the optimum estimate of the bias, and Vxis a matrix which can be interpreted as the ratio of the covariance of $\\tilde{x}$ and $\\hat{b}$ to the variance of $\\hat{b}$ . Moreover, $\\hat{b}$ can be computed in terms of the residuals in the bias-free estimate, and the matrix Vxdepends only on matrices which arise in the computation of the bias-free estimates. As a result, the computation of the optimum estimate $\\tilde{x}$ is effectively decoupled from the estimate of the bias $\\hat{b}$ , except for the final addition indicated by (1).

Keywords

Recursive digital filters; State estimation; Covariance matrix; Equations; Error correction; Filtering; Nonlinear filters; Recursive estimation; State estimation; Vectors;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.1969.1099223

Filename

1099223