Method and system for reconstructing time of transmit from assisted or weak signal GPS observations

A method for determining a time of transmit of a Global Navigation Satellite System (GNSS) signal to a receiver that is not moving or is slowly moving relative to the earth, the method comprising:

• (a) acquiring and tracking, in the receiver, a code phase and a carrier frequency of the GNSS signal;
• (b) obtaining bit synchronization based on the code phase and the carrier frequency by performing non-coherent correlations over rounds of coherent correlations of the GNSS signal using multiple offsets at a predetermined spacing;
• (c) pre-integrating the bit synchronized GNSS signal over data bit periods to form bit-aligned partial integrals;
• (d) storing the bit-aligned partial integrals in a signal store;
• (e) multiplying the stored bit-aligned partial integrals by data test bits;
• and
• (f) applying a mathematical transformation on the product of the stored bit-aligned partial integrals and the data test bits to provide correlation values to be compared with at least one threshold thereby providing an ambiguity resolution candidate for time of transmit of the GNSS signal.