Abstract: A Least Mean Squares (LMS) polynomial estimator is disclosed. The LMS polynomial estimator may be a LMS moving window polynomial estimator capable of performing real-time polynomial estimation and evaluation of successive time derivatives of a function of a single variable up to a specified polynomial order. The estimator makes a unique use system memory that allows for the evaluation of the least squares normal equations with a very low computational footprint. This allows the estimator to be realizable in computationally-constrained environments such as embedded systems. The LMS polynomial estimator may be implemented in a frequency estimator for estimation of the phase, frequency, Doppler, delta Doppler, and/or higher order time derivatives of phase. Estimates may be performed in real time, running at the same rate as the inbound signal.