ARCOS, weighted ARCOS and Cramer-Rao bounds

Some insights are provided into the analysis of a recently proposed Doppler frequency estimator. The analysis of a multiplicative model and the algorithm used are reviewed. An optimal and a modified version of this algorithm are studied. The Cramer-Rao bounds for pole estimation of an equivalent autoregressive moving-average (ARMA) process are presented. Numerical simulations that described the statistical behavior of these estimators were performed. It is verified that the Doppler frequency is exactly the centroid of the set of ARMA pole frequencies. A novel algorithm (ARCOS), an optimally weighted version of ARCOS, and ARCOS modified by the Newton-Raphson (NR) technique are derived. Although a direct optimal estimator cannot be derived, it is shown that the basic and the optimal centroid are equivalent and below the ARMA bound. NRARCOS is shown to improve the variance, practically reaching the performance of the optimal centroid