A method and device to acquire navigational satellite signals combines non-coherent and coherent integrations and can efficiently acquire both strong and weak signals. Successive steps eliminate lower powered and less likely combinations of code offsets and carrier frequencies or dwells of a given satellite signal. Only remaining dwells then are correlated and integrated over larger time duration to obtain the most probable dwell or dwells, which results in reduced computational load. The selection of most likely dwells is based on Parseval's theorem on equivalence of power in time and frequency domains. An optimal estimator algorithm efficiently estimates the probable navigation data bits embedded in the received signal. In case of an ambiguity due to several possible dwells, the steps are repeated with a new set of signal samples.