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We address the problem of navigation data demodulation by an adaptive GPS receiver that utilizes a bank of single-satellite linear-tap-delay filters and employs antenna-array reception. The presence of an antenna array allows the receiver to operate in the spatial domain in addition to the temporal (code) domain. We investigate disjoint-domain as well as joint-domain space-time GPS signal processing techniques and we consider design criteria of conventional matched-filter (MF) type, minimum-mean-square-error (MMSE), minimum-variance-distortionless-response (MVDR) type and auxiliary-vector (AV) type. The proposed structures utilize filters that operate at a fraction of the navigation data bit period (1 ms) and are followed by hard-decision detectors. Hard decisions taken over a navigation data bit period (20 ms) are then combined according to a simple combining rule for further bit-error-rate (BER) performance improvements. Analytic, numerical, and simulation comparisons illustrate the relative merits of the investigated receiver design alternatives.