Filtering difference of correlated measurements
I have a couple thoughts on your problem:


Regarding the handling of atmospherically-induced biases to the GPS receivers' reported positions, I don't think you need to do anything at all. If there is a truly common bias inherent in both positions, then it will simply cancel when you take the difference of the two positions. Thus, I would just treat each platform independently and subtract the time-aligned positions to yield your displacement vector estimate.

This is essentially the technique of differential GPS (DGPS), which was used successfully to combat the effects of the US government's policy of selective availability (SA) on the publically-available GPS carrier. SA was implemented by pseudorandomly dithering the timebase of the spacecraft; this would result in small position errors reported by GPS receivers. 

This type of implementation meant that the SA error was highly correlated with the receiver position, such that two receivers in close proximity would experience approximately the same SA error. In the typical DGPS case, if one receiver's position is known precisely, one can solve for the SA error and resolve the second receiver's absolute position accurately, cancelling out the effects of SA. In 2000, the US government ended the use of selective availability, so this isn't much of an issue any more.

Your case is similar but slightly different, in that you don't know the absolute position of either receiver, but that doesn't seem to be what you care most about. Instead, you only care about the differential displacement between the two. Therefore, you can apply a similar technique; if there is a constant position bias inherent in both, then calculating the difference of the two positions will cancel it out, just as DGPS systems did for SA error.
It's not likely that you can improve the performance of the GPS receivers' reported positions by filtering them further. Dynamics tracking systems are a key part of any GPS receiver, and a lot of work has gone into their development. Especially if the receivers that you are using are of a recent vintage, I would hazard that any additional filtering that you would apply would be superfluous.

That's not to say that you would never want to process the reported positions further. There are some exceptions to my above statement:


If you have data from other instruments to fuse with the GPS readings, that can yield a gain. Sensors used for dead reckoning (e.g. gyroscopes or accelerometers) can yield measurements that can help to improve tracking of platform dynamics in periods where the GPS receiver outputs are unreliable or inaccurate. However, in time periods where the receiver measurements are assumed to be accurate, an optimal tracker would rely proportionally more upon the GPS measurements in lieu of the higher-variance dead reckoning sensors.
If you have some specific knowledge of your platform's dynamics that you know the GPS receiver isn't taking into account, then you may be able to obtain some gains. If you can specifically configure your receiver for maritime operation, you may be able to obtain better performance, as its tracker can make certain assumptions about your platform's position (e.g. zero altitude relative to sea level, no vertical velocity or acceleration). Failing that, it's possible that you could take the receivers' position outputs and apply some filtering to improve things, but your results will be very specific to the equipment that you use and whatever processing is applied by their internal trackers.