Statistics of the RSS estimation algorithm for Gaussian measurement noise

Author

Agate, Craig S. ; Iltis, Ronald A.

Author_Institution

Dept. of Electr. & Comput. Eng., California Univ., Santa Barbara, CA, USA

Volume

47

Issue

1

fYear

1999

fDate

1/1/1999 12:00:00 AM

Firstpage

22

Lastpage

32

Abstract

The large and small sample properties of the reduced sufficient statistics (RSS) estimator of Kulhavy (1990, 1992) are derived for the nonlinear additive white Gaussian noise measurement model. The RSS algorithm recursively propagates a set of sufficient statistics for a mixture density that approximates the true posterior density of a parameter vector. The joint probability density function for the weighting coefficients of the mixture density is derived for the case of additive white Gaussian noise. Through integration of this density, the estimator bias and mean-squared error are determined. The results are applied to a scalar phase estimation problem in which the sample-averaged statistics are compared with those derived from numerical integration of the density function. The asymptotic bias and variance of the RSS estimator are also derived and compared with simulation results

Keywords

AWGN; integration; mean square error methods; nonlinear estimation; phase estimation; signal sampling; RSS estimation algorithm; additive white Gaussian noise; asymptotic bias; estimator bias; joint probability density function; mean-squared error; mixture density; nonlinear additive white Gaussian noise measurement model; parameter vector; reduced sufficient statistics; sample-averaged statistics; scalar phase estimation problem; true posterior density; variance; weighting coefficients; Additive white noise; Covariance matrix; Density functional theory; Density measurement; Filters; Gaussian noise; Noise measurement; Noise reduction; Probability density function; Statistics;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.738236

Filename

738236