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

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, NLLS/sub 1/ and NLLS/sub 2/, 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, NLLS/sub 2/ should be used instead of NLLS/sub 1/, 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 NLLS/sub 1/ and NLLS/sub 2/. 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.