# What's the precision of a modern Inertial Measurement Unit, and how is it obtained?

This recent comment reports that:

the IMU on new (plane) would localize the aircraft to within 3 feet after a cross-country flight, without any GPS input other than the starting location.

I somewhat doubt about this statement, at least for an IMU based solely on inertial measurement: over the duration of a flight, I fear much more error accumulates.

So what's the precision of a modern Inertial Measurement Unit over say the duration of a flight, and from what sources is that obtained? If some source (in particular, GPS) becomes unavailable, how does it degrade that accuracy?

• For a country the size of Monaco the statement might be true... Mar 24, 2014 at 11:59
• the wiki article of INS states (unreffed) that "The inaccuracy of a good-quality navigational system is normally less than 0.6 nautical miles per hour in position and on the order of tenths of a degree per hour in orientation" Mar 24, 2014 at 12:01
• @ratchet freak: From my minimal understanding of Inertial Measurement, the error in a purely inertial mode should grow as the square of the time; or at least significantly faster than linearly with time. That makes me doubt of that source, although I think it is much less far off than the bragging I quote. Mar 24, 2014 at 12:10
• All INS units that I am aware of have max drift rates specified in NM/Hour so is linear. Mar 24, 2014 at 12:39
• @fgrieu Due to the Schuler tuning, the error is only growing quadratically during the first 10 minutes or so. The errors are oscillating with a period of 84 minutes. Mar 24, 2014 at 12:40

Let's have a look at documentation of actual modern IRS. It says (on page 6) that if GPS data is lost, it will maintain RNP0.1 for 8 minutes, RNP0.3 for 20 minutes and RNP1 for 2 hours. That means that in 8 minutes the error is no more than 0.1 nautical mile with 95% confidence, in 20 minutes it is no more than 0.3 nm with 95% confidence and in 2 hours the error is no more than 1 nm again with 95% confidence.

For general description how it works see What is an Inertial Navigation System? How does it work? and of course the appropriate Wikipedia article. Basically it measures acceleration and rotation (with gyroscopes) and integrates it over time. Modern systems do the calculations digitally with sophisticated filters to smooth over some errors.

• Those are the certified values. The actual accuracy of the INS is likely significantly better, but the manufacturer can't/won't guarantee that for certification purposes. There's always a safety margin and in systems like this it's usually a pretty large margin. Mar 27, 2014 at 15:41
• @dvnrrs: The certification only requires 95% confidence here, which is pretty low. So I suspect the margin does not have to be that large in this case. Mar 27, 2014 at 16:32
• @dvnrrs: A safety margin is built into the RNP procedures where the actual clearance from terrain is always higher (I believe at least twice, but am not sure whether it's not more) than the required RNP rating. Mar 27, 2014 at 16:35

In addition to Jan's answer, there are other means than GPS to provide location data to an INS.
VOR and NBD triangulation has been used for decades, long before GPS even existed.
And there's always the good old sextant, which a trained crew member can use to get a pretty accurate position with, in combination with a good clock.

Both can provide location information to update an INS. Of course the update will only be as good as the skill of the crew performing the position calculation.

• I am not sure how many IRS are capable of in-flight realignment to those inputs and suspect not many. The older ones certainly can't (I've seen report of an incident where a plane had to land because they switched off INS by mistake and it couldn't be reinitialized in flight). Mar 27, 2014 at 16:32
• @JanHudec the 747-200 I know could be updated in flight using VOR data. Not reinitialised, but updated. Initialisation of INS requires the aircraft to be stationary, even strong wind can cause problems in some aircraft. Mar 31, 2014 at 6:33