Method and system for carrier recovery and estimation of Doppler shift from a signal source that is moving relative to a signal receiver. A pure carrier preamble for the received signal is processed through each of two stages of a linear predictor to obtain a successively more accurate estimation of a Doppler frequency offset for the carrier. The received signal is downconverted by each stage estimation of the Doppler frequency offset, and the downconverted signal is processed through a decision feedback phase locked loop to provide a signal in which substantially all of the Doppler offset and/or phase angle are identified and removed. The system has low complexity, is fast, and is accurate to within an estimated few tens of Hertz and will work with signals having relatively low signal-to-noise ratios. The invention is useful for receipt of signals from satellites in low earth orbits (LEOs) and other non-geosynchronous orbits, and wherever a transmitter and receiver are moving relative to each other.