How is GPS RAIM availability calculated?

I recently had someone ask me if there was a GPS RAIM availability calculator available for the iPad. There isn't, but it got me thinking that I could write one. After doing some searching, I can't find a good explanation of how to calculate RAIM availability, so am looking for the formulas used to calculate it for a specific route.

I want this to be an offline tool, so the calculations need to be complete, rather than relying on a website for the information.

The website that Ralgha points out is indeed the one to look at for the US. They also provide a SOAP interface should you want to create your own app for the IPAD.

For RAIM to be available, you need to check firstly that at least 5 satellites (Space Vehicles in GPS language) are visible from you position, or 4 if your RAIM algorithm uses Baro-aiding. They have to be well above the horizon. How much depends on your satellite receiver, the FAA uses 5 degrees on their website. There are some receivers that use a masking angle of only 3 degrees.

Orbital equations can be taken from the GPS interface control document, section 30.3.3.1.3. They take almanac data as input. Apart from the Space Vehicle orbits, you also need to take into account their health from the NANU's.

With the satellites available, you need to calculate the RAIM containment bound. This is the maximum size that a position error can grow due to a faulty satellite signal without the RAIM algorithm noticing it within 10 seconds (with a 99.9% probability). If that containment bound is more than 1 nautical mile, RAIM is said to be unavailable for terminal procedures. For NPA a 0.3 nautical mile radius is used.

The containment bound depends very much on the geometry of the satellites, more that on the number of satellites available.

The problem with the RAIM algorithms is that they aren't standardized. There are several ways to perform RAIM and because GPS manufacturers use proprietary solutions there is little information available to the public. So calculating the containment bound is where you will get stuck.

So there is no easy way to implement RAIM prediction on an IPad, apart from using the FAA website.

Europe has also a RAIM prediction website; AUGUR.

• Good info, but I want to be able to do this offline so don't want to rely on the SOAP interface. I'll update my question with that – Lnafziger Jan 14 '14 at 12:31
• Well, than you're up for some very serious mathematics. I'd like to help out, but as far as I know there are no RAIM algorithms simply available to the public. – DeltaLima Jan 14 '14 at 12:37
• Hmm, I figured that surely someone would have them (although I haven't been able to find any either, lol). – Lnafziger Jan 14 '14 at 12:39
• These algorithms are carefully kept company secrets apparently – DeltaLima Jan 14 '14 at 12:40
• I know there are basically two ways to do it, but I have not done the full math on either. The concept is quite complex and involves geometry and a lot of probabilistic. – DeltaLima Jan 14 '14 at 12:42

RAIM availability calculations are simply checking to see if at least 5 satellites will be visible, that's all it is. You'll need the orbital equations to calculate that though. It would probably be easier to pull data from one of the websites that provide RAIM information. http://www.raimprediction.net is the FAA's site.

Details of RAIM calculation is explained in the paper : GPS EASY Suite II: easy13 - RAIM by Kai Borre http://www.insidegnss.com/auto/julyaug09-borre.pdf Also the author gives a Matlab implementation. Hope it helps.

• could you try to summirize it briefly in your answer? – Federico May 2 '14 at 6:50
• Interesting article, but it seems to calculate RAIM as part of the position calculation, not RAIM availability. – Lnafziger May 2 '14 at 16:12