Statistical Analysis of Non Linear Least Squares Estimation for Harmonic Signals in Multiplicative and Additive Noise

The nonlinear least squares (NLLS) estimators, NLLS 1 and NLLS 2 proposed by Ghogho et al. (1999b) to estimate the coherent model parameters for single-component harmonic signal, are generalized to the multicomponent harmonic signals for the cases of nonzero- and zero-mean multiplicative noise, respectively.

By statistical analysis, some asymptotic results of the NLLS estimators are derived, including the strong consistency, the strong convergence rate and the asymptotic normality. Furthermore, the NLLS 1 - and NLLS 2 - based estimators are proposed to estimate the noncoherent model parameters for the cases of nonzero- and zero-mean multiplicative noise, respectively, meanwhile the strong consistency and the asymptotic normality of the NLLS-based estimators are also derived.