Embee, let's review the goals with regards to attitude determination in an airplane absent conventional instrumentation or observation. Working and highly visible bog standard artificial horizon equipment may be the best way. But if somebody insists it is not there then GPS can provide some answers with a degree of roughness that depends on dynamics of the aircraft and expense you're willing to undergo.
Basically you need to know the relative positions of the two wing tips and the nose or tail to sufficient precision to determine an accurate attitude. GPS is one way to do it. Both differential GPS and phase tracking have been mentioned. A third method exists that might be called differential phase tracking, which can apply and will likely be cheaper to implement.
If we review differential GPS the conventional use requires, as you stated a precisely surveyed reference. Conventionally you need to know your position relative to physical features of the Earth. Thus the well surveyed reference position. Suppose a plane is flying near the surveyed site and you measure distances to both wing tipss and the nose. To get the attitude you play with the geometry of those three positions. The simple way is to note that the left wing tip is at some distance from the surface while the right wing tip is at some other distance. That gives you some attitude data. But it doesn't account for lateral distances along the surface of the Earth. Geometry gets messy.
Now presume the left wing tip is your "precisely determined position". Certainly it is, relative to the plane. And what you want is information about where the rest of the plane is relative to that wing tip. Once you know this you can shift the "reference" to the CG of the aircraft if that makes instrumentation read easier. What you need to know is all differences of position. If the left wing is higher than the right wing your plane is banked. You could care less if this is at FL 100 or FL 350. You know you are banked and can estimate how much. Instantaneous measurement precision for the GPS track for all three receivers limits your notion of how severely banked your plane is.
Phase tracking has a similar feature. It just gives more precise "where I am" information. If you simply measure relative carrier phases, which requires relatively little additional computer power you can get pretty accurate notions of position. (If you lose track you're more or less sunk, however. You have an ambiguity of 20 cm (roughly) to resolve. In turbulence it's fairly easy to have the dynamics kick the GPS
receiver out of lock. The loop time constants are large enough that the plane could move out of its established track by several times 20 cm quite easily.
So you're generally stuck with conventional differential GPS unless you have really good inertial measurement units to aid the GPS receivers in a military manner. (Or you can presume in designing the receiver that the loop time constants can be made much shorter to allow high dynamics tracking by sacrificing some of the GPS signals fairly dramatic anti-jamming margin. But I've already gotten too technical for this group, I suspect.)
GPS can be used. I'd need to see some analysis to show me it's usefulness for a differential GPS application before I'd endorse it for the application. It has promise. But the cost would probably make the artificial horizon gyroscopic approach sound exceptionally attractive.
JD-EE