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With upcoming GNSS systems that have better accuracy than GPS, could there be an GNSS based attitude indicator? Does maybe one already exist?
I could imagine having 4 sensors (front, aft, left wingtip, right wingtip) that then calculate the attitude.
I suppose you could but what benefit wound a GNSS based system offer over traditional gyroscopic and AHARS based attitudes systems while offering better redundancy against a system reliant on outside radio sources and risks with system outages, etc?
Part of the attitude determination on the ISS is done that way. The size of the space station makes for a larger measurement base then on an aircraft, but the idea is the same. Further, the ISS has an unobstructed view of the navigation satellites, and has lower rotation rates than one can expect on an aircraft, which makes it an easier problem. But, a quick search finds plenty of research for doing the same for aircraft.
There has been quite a bit of research on the topic and units have even been built. Ultimately it will trickle its way out there if the price of the unit drops below AHARS or Gyro equivalent units and its accuracy is equal or better than modern AI's. However you can get a good, small, drop in, AHARS style AI for fairly reasonable (considering the cost of avionics). The FAA seems to allow GNSS signals to supplement AHARS data I cant find a copy of TSO-C4c which outlines the certification limits for pitch and bank instruments but may shed more light on the topic.
Side note: to escape the mechanical dependence of gyros and if you want something different than what your run of the mill AHARS unit has, some of the newer high performance stuff uses a Ring Laser Gyro.
This isn't a direct answer to your question, but there has been research on a simpler gyro-free and GPS-free absolute attitude determination method based on a trio of 3-axis magnetometers and a trio of 3-axis accelerometers.
Very much like you imagine 4 GNSS sensors, they use a trio of 3-axis magnetometers -- each detecting the 3-axis direction of magnetic north.
They don't need to be at the extremities of the aircraft, just separated in space for sufficient magnetic and rotational accuracy.
The challenge to overcome lies with the fact that "the aircraft environment is very poor for the performance of the magnetometer, with large electromagnetic transients that cannot be calibrated out of the measurements". Their solution is to integrate a trio of accelerometers, and a time-filtered sampling method to reject transient magnetic readings.
They validated with limited test flights, but there is insufficient information to know how it might hold up to less-than-transient magnetic phenomena in the real world due to storms, static charges, etc.
The paper was published by Stanford in 2000...
One future possibility might be to create an attitude detection system which incorporated all three methods (relative "digital" laser-gyro, motion extraction from a trio of accelerometers, vector extraction from a trio of 3-axis magnetometers, and absolute position extraction from four extremity mounted WAAS GNSS sensors), and used each to backup and reject spurious data from the others.
This would not only provide the least likelyhood of inaccurate attitude indication, but it would also provide extensive data on when there is divergence between the different methods.
