Sub-microsecond time transfer in a GPS/GNSS receiver using a weak GPS/GNSS signal is provided. The digitized complex baseband signal and the generated PN code are cross-correlated for each code period so as to output a complex correlation value at each code epoch of the generated PN code, where a sequence of the output correlation values form a data stream representing the navigation message. Bit synchronization generates bit sync pulses at bit boundaries. The location of a target segment having a known sequence at a known bit location in the navigation message is detected by searching through a plurality of sub-frames and accumulating search results for the plurality of subframes. Transmission time of the target segment is determined from the detected location of the target segment, with a certain time ambiguity. Accurate local time is determined by solving the time ambiguity using approximate time obtained from an external source.