CISOID PARAMETER-ESTIMATION IN THE COLORED NOISE CASE - ASYMPTOTIC CRAMER-RAO BOUND, MAXIMUM-LIKELIHOOD, AND NONLINEAR LEAST-SQUARES

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