NASA NTRS1989
A novel multistage estimation scheme is presented for estimating the parameters of a received carrier signal possibly phase-modulated by unknown data, and experiencing very high Doppler, Doppler rate, etc. Such a situation arises, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity, acceleration and jerk of the GPS receiver. In the proposed multistage scheme, the first stage estimator operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency (an event termed cycle slip). The second state of the estimator operates on the error signal available from the first stage, refining the overall estimates, and in the process also reduces the number of cycle slips. The first stage algorithm is selected to be a modified least squares algorithm operating upon the differential signal model and referred to as differential least squares. This estimation stage provides relatively coarse estimates of the frequency and its derivatives. The second algorithm is simply an extended Kalman filter which also yields the estimate of the phase along with a more refined estimate of frequency as well. A major advantage of the proposed algorithm is a reduction in the threshold on received carrier power-to-noise power spectral density ratio as compared to the threshold achievable by either of these algorithms alone. In fact, it appears from the simulations that for the case of an unmodulated carrier, the proposed scheme achieves the same threshold as for an almost exact and computationally intensive implementation of the maximum likelihood estimator.