Have to agree with Jackdaw, but not 100%. However, Doppler must be accounted for during start up and during operations. As he noted, the carrier frequency of the satellite is shifting and start high at acquisition and ends low at loss of signal. The GPS terminal must track this shift or the low data rate messages will be lost. I believe ephemeris data of each bird is transmitted during the messages so the GPS receiver knows where to look, when to look, and how much shift (mathematically) the receiver must adjust per channel.
For those who are not familiar with Doppler, it is how a tone appears high in frequency when the sound source is approaching you, then as it moves away, the tone gets lower in frequency. Doppler is also used in light to determine if a star is moving away from earth or towards it (Red Shift / Blue Shift). Doppler is in everything.
Now, TOD (Time of Day) is also important. All the components of the GPS signal work in tangent. Not individual parts, but the sum of all the parts.
Just so you know, I have been working with GEOs, MEOs,and LEOs for many years. Not GPS system mind you, but the theory is all the same. A satellite in orbit exhibits characteristics based on it altitude and velocity.
So, back to the OP, I am unsure of why a vessel would appear to moving backwards. Maybe this is a fundamental flaw in AIS.
This has been a great read. Love it.