Joachim:
I will attempt to help however I must preface all of these comments by stating that I am not a trained avionics guy. I have just had my face pressed into the glass for a few decades while struggling to figure all of this out…
A course deviation indicator (generally) accepts a signal from two wires that have a voltage between them that varies between plus 150 mV and -150 mV. If a CDI indicator sees a voltage vary between those limits it will move the indicator appropriately.
An simple autopilot like the single axis century (or an associated nav coupler) would accept that voltage signal from those two wires and commence a turn, left or right and to greater or lower degrees of bank depending on the strength and polarity of the signal. Some couplers may be more complex and actually track an intercept heading rather than an arbitrary turn from the signal.
Any device that outputs that signal could be routed into the autopilot and produce the same effect. Almost all analog CDI use that same +- 150 mV DC signal and almost all devices that produce a navigation output can drive an analog CDI that uses that signal. So, in general, you very likely could route your GPS CDI signal directly into the autopilot (or its nav coupler) and it would work.
The devil is in the details. There are some technical issues that may mean that whatever particular arrangement cannot be certified for IFR, for example. I once successfully routed a digital serial IO signal from a modern hand-held GPS into a +/- 150 mV signal that was then used to drive an old single axis Century II autopilot in a 1970 Cherokee successfully. Completely experimental and utterly not certified for use in an actual airplane – but it did work and so it can be done.
Now, whether or not that can be done in a practical manner for a reasonable amount of money in a certified IFR aircraft is between yourself and your avionics shop.
William
