Non-linear least squares estimation for harmonics in multiplicative and additive noise

Author

Ghogho, Mounir ; Swami, Ananthram ; Nandi, Asoke

Author_Institution

Dept. of Electron. & Electr. Eng., Strathclyde Univ., Glasgow, UK

fYear

1998

fDate

14-16 Sep 1998

Firstpage

407

Lastpage

410

Abstract

We consider the problem of estimating the frequency of a complex harmonic in Doppler radar signals in the presence of additive and multiplicative noise, which may be colored and non-Gaussian. Two nonlinear least-squares (NLLS) estimators, NLLS₁ and NLLS₂, are proposed, which consist of matching the data and the squared data, respectively, with a constant amplitude harmonic. Expressions for the asymptotic covariances of the NLLS estimators are derived. It is shown that for high SNR, NLLS₂ should be used instead of NLLS₁, regardless of the value of the intrinsic SNR (ISNR) of the random amplitude. On the other hand, for low SNR, there is a trade-off between NLLS₁ and NLLS₂. The former is superior to the latter when the ISNR is below a threshold which is a function of the SNR and the kurtosis of the additive noise

Keywords

Doppler radar; amplitude modulation; frequency estimation; least squares approximations; nonlinear estimation; radar signal processing; random noise; Doppler radar signals; additive noise; asymptotic covariances; colored noise; complex harmonic; constant amplitude harmonic; data matching; frequency estimation; intrinsic SNR; multiplicative noise; non-Gaussian noise; nonlinear least-squares estimators; random amplitude; Additive noise; Amplitude estimation; Amplitude modulation; Colored noise; Frequency estimation; Least squares approximation; Noise level; Powders; Signal processing; Signal to noise ratio;

fLanguage

English

Publisher

ieee

Conference_Titel

Statistical Signal and Array Processing, 1998. Proceedings., Ninth IEEE SP Workshop on

Conference_Location

Portland, OR

Print_ISBN

0-7803-5010-3

Type

conf

DOI

10.1109/SSAP.1998.739421

Filename

739421