I have an application with two separated GPS receivers giving live positions and I'm deriving a heading/displacement from the vector between them. Each set of position measurements is noisy and has dropouts but I do have a quality estimate. So far it's classic Kalman filter.
The relation between the two antennas isn't fixed, both are moving independently and generally one is moving at higher rate than the other.
But obviously some of the error is correlated between the two receivers, so do I filter each antennae location separately or the filter the displacement? Or is there a cleverer alternative?
edit: As an example suppose you have a GPS on a boat and on a towed sonar array - and you are trying to track the relative position of the sonar receiver.
The general uncertainties on each antennae position are similar. But some errors will correlate between them - eg. if an atmospheric effect moves both readings 10m North this has zero effect on the difference but would effect any filter/average of each position.
Arguing against simply averaging/filtering on the displacement vector is that the motion of each receiver is different, the boat is relatively steady - the sonar bounces around in the waves. So the statistics of each if you have any sort of averaging filter are different.