Cisoid parameter estimation in the colored noise case: asymptotic Cramer-Rao bound, maximum likelihood, and nonlinear least-squares

Abstract

The problem of estimating the parameters of complex-valued sinusoidal signals (cisoids, for short) from data corrupted by colored noise occurs in many signal processing applications. We present a simple formula for the asymptotic (large-sample) Cramer-Rao bound (CRB) matrix associated with this problem. The maximum likelihood method (MLM), which estimates both the signal and noise parameters, attains the performance corresponding to the asymptotic CRB, as the sample length increases. More interestingly, we show that a computationally much simpler nonlinear least-squares method (NLSM), which estimates the signal parameters only, achieves the same performance in large samples.