Provided herein are systems and methods for achieving long integration of an input signal by compensating the frequency and phase of each sample of the input signal. In an embodiment, a Numerical Controlled Oscillator (NCO) of the receiver is modified to include a variable control input that allows the output frequency of the NCO to be adjusted based on a rate of change of frequency. The rate of change of frequency may be estimated based on the relative velocity of a satellite to the receiver computed from satellite orbit parameters or ephemeris. The rate of change of frequency may also be estimated based on frequency measurements of previous samples. The modified NCO may be used as a carrier NCO or code NCO of the receiver to provide frequency and phase compensation of each sample of the input signal.