What sampling rate is needed for demodulating and decoding GPS signal data?
A more detailed understanding of the Nyquist rate would show that it requires sampling at twice the information bandwidth, not the carrier frequency. In the GPS case, there is no information at the carrier rate (1575 MHz) -- just in the modulation.
The modulation is much lower (10.23 MHz), and sampling at just over twice this would theoretically be sufficient. However to do this, you would also need a filter to keep any modulation (or noise) outside 10.23 MHz from getting to the sampler, so in practice you would need sampling at well over 30 MHz to allow a practical filter.
Note that GPS signals are quite weak, and it is unlikely a simple SDR will have sufficient signal-to-noise (SNR) ratio to function.