GNSS-based timing synchronization

A time synchronization method, wherein the method uses a processor coupled with stored instructions implementing the method, wherein the instructions, when executed by the processor carry out steps of the method, comprising:

• receiving pseudorange measurements from a set of antennas of at least one Global Navigation Satellite System (GNSS) receiving system that operates the set of antennas at known positions according to a clock with an unknown time bias to receive signals from satellites in sight of each antenna of the set of antennas;
• comparing the pseudorange measurements of the set of antennas to produce an antenna-specific clock offset for each antenna of the set of antennas, wherein a first antenna-specific clock offset for an antenna k of the set of antennas is determined using a belief propagation as a probabilistic belief bt(αk) at time t on a marginal distribution of an antenna-specific clock offset αk using a product of a prior distribution of the probabilistic belief bt(αk) and incoming belief messages from all antennas of the set of antennas except the antenna k;
• correcting the pseudorange measurement of the set of antennas according to the antenna-specific clock offset for each antenna of the set of antennas to produce corrected pseudorange measurements;
• determining the time bias of the clock using the corrected pseudorange measurements;
• and
• correcting the time of the clock using the determined time bias.

A non-transitory computer readable storage medium embodied thereon a program executable by a processor for performing a method, the method comprising:

• receiving pseudorange measurements from a set of antennas of at least one Global Navigation Satellite System (GNSS) receiving system that operates the set of antennas at known positions according to a clock with an unknown time bias to receive signals from satellites in sight of each antenna of the set of antennas;
• comparing the pseudorange measurements of the set of antennas to produce an antenna-specific clock offset for each antenna of the set of antennas by:
• determining, for each pair of antennas from the set of antennas, a difference pseudorange residual between pseudorange measurements of a pair of antennas of the set of antennas, wherein a pseudorange residual of a first antenna of the set of antennas removes known components from the pseudorange measurement of the first antenna, and wherein the difference pseudorange residual between the pair of antennas of the set of antennas removes common components in the pseudorange measurements of the pair of antennas of the set of antennas, such that the difference pseudorange residual includes a difference between the antenna-specific clock offsets of the pair of antennas of the set of antennas subject to noise;
• and
• comparing the difference pseudorange residuals between different pairs of antennas of the set of antennas to produce the antenna-specific clock offset for each antenna of the set of antennas;
• correcting the pseudorange measurement of the set of antennas according to the antenna-specific clock offset for each antenna of the set of antennas to produce corrected pseudorange measurements;
• determining the time bias of the clock using the corrected pseudorange measurements;
• and
• outputting the determined time bias.