Is there some iterative way to compute heading and GPS projection at the same time?

Question

I have the following situation:

An off-road machine has a GPS antenna that is not at the center of the rear axle (this point is my path-tracking-control point). Let's say it's 3 meters from the rear axle and 2 meters from the left.

So, I should translate the GPS point to the center of the rear axle. For that, I need the current machine heading, given by delta latitude and delta longitude. So far, so good.

However, as my machine is turning, the heading of the rear axle and the heading of the GPS antenna are not the same.

For those, I'm looking for a method to, given an initial heading (GPS heading), start computing the antenna projection, and from that projection, calculate another heading (rear axle heading) until the system converges.

EDIT 1 - Some drawings POI goes for Point of Interest

Any ideas?