Writting an INS for the G1000

[VORTIME]

Hi folks,

Is it possible using the solid state gyros, accelerometres and enroute fixes to write a simple peice of software to record and INS position and display it on a G1000. What technical difficulties would this encounter and are the gyros/accelerometres from Garmin upto the task or would they need to be upgraded.

In theory - one could add a INS to their SEP with a few lines of code (in theory...)

VT

[IO540]

No, the long term stability of the gyros used in the G1000 is not good enough for long distance enroute nav, by several orders of magnitude.

The problem is you have to integrate the acceleration signal to get velocity, then integrate that to get distance travelled, so any drift soon becomes dominant.

A lot of people are working on this, I can assure you...

Fibre optic gyros are coming down in price. The U.S. smart bomb (JDAM) guidance package has them, with a mil-spec jam-resistant GPS thrown in, and the whole thing is reportedly US$ 20k. In reasonable volumes, of course ;)

Give it another 10 years...

[bookworm]

No, the long term stability of the gyros used in the G1000 is not good enough for long distance enroute nav, by several orders of magnitude.

Depends on what sort of timescale you're looking for, doesn't it? If you're prepared to calibrate position against the GPS every minute or two, then it might work. But why would you want to?

[englishal]

The G1000 switches to a DR mode if GPS is lost if I recall correctly........Not INS of course, but better than stopwatch and compass.....;)

[JP1]

I think you'll find that its a lot more than a few lines of code!!

The problem is not the software or the algorithms, but the accuracy of any solution that you might obtain.

The biggest problem is that the INS platform, the triad of 3 accelerometers, has to be gyro-compassed so that the platform is level, (the x and y accelerometers sensing no gravitational component) and the x axis aligned with north, or the offset to North known. This is the reference point from which any accelerations sensed can de dead reckoned into a position solution.

INS systems gyro-compass by using a gimballed platform to mechanically level, or calculate a mathematical level (known as strapdown systems). The actual levelling of the system is achieved by the accelerometers sensing gravity and the earth’s rotational rate measured from the gyros.

So here we start to list your problems

1) Your system will never gyro-compass accurately since the errors in the accelerometers and gyros prevent the platform levelling to any reasonable accuracy. So before we even start to move, the system might think its pointing North, when in fact its pointing nearer to east! Don’t forget the error on the other axes as well.

2) The triad of sensors (gyro and accelerometers) have to be orthogonal. (the 3 axes at 90 degrees to each other). Any errors here will mean that the rates are not measured along the true axis. Any low grade Inertial measurement unit will have extremely crude alignment of the axes, many order of magnitudes too low

3) The sensors will be subject to scale factor errors, temperature effects, non-linearity, the list goes on.
For the type of IMU that you refer to, the above errors mean that a position solution will be accurate in the order of 10’s of seconds, before it just ramps off to some horrendous error.

Medium grade INS (defined as a 0.8nm hour system, which means that after 1 hour of flight the system would be in error by about 0.8nm) cost in today’s money about £250k. ( or did do a few years ago). The large cost is because of the mechanical tolerances and the accuracy of the components required. The algorithms are software, so are cheap!!!

Good luck.

[S-Works]

give me a GPS anyday......:)

[JP1]

Just so you have an idea of error, and this is an extremely optimistic calculation considering 1 error source out of hundreds.

Say that you start your system and the horizontal error of the platform is 5 degrees. So the x accelerometer is pitched up at 5 degrees. It’s now measuring a component of gravity.

X accl = 9.8 x cos(90-5) = 0.087 metres per sec squared, but you are stationary

And using the equation

distance = ut + at2 /2

Over 10 minutes, your error is (0.087 *600*600)/2 = 15.7 kilometres.

All the time your gyros are drifting and that 5 degree pitch up is increasing, add in all the other error sources and this drift is not obtained in 10 minutes, but 10 seconds!! (Well something certainly a lot shorter).

[IO540]

Do you actually design this stuff, JP1?

I ask because I looked into developing an INS for GA a couple of years ago. It isn't that hard to put a working platform together, and most of the obvious error sources can be compensated for with a combination of sensing and software.

But one would still need a GPS update every few minutes, which isn't really very useful. The minimum requirement, IMHO, is to be able to fly through the Luton/Stansted gap from Duxford to Stapleford, and doing the usual three go-arounds at the latter :)

The breakthrough, assuming anybody is going to bother (unlikely, since GPS works so well) will be done with FOGs. They are down to about US$5k per axis, in small quantities, but last I heard they are still export controlled (due to the obvious weapon usage) which is no good.

[JP1]

But I spent my first 10 years of my career doing so. I was involved with intergrated navigation and worked at RAE Farnborough.

I worked on algorithm design of Kalman filters for INS/GPS data blending and INS error correction.

[Nipper2]

JP1 is quite right about the problem with errors. It's not quite as bad as his example with some clever modern devices, but still out of the price performance bracket required to make the whole thing a sensible proposition.

We use some small cheap (circa £1000) units http://www.xsens.com/index.php?mainmenu=products&submenu=machine_motion&subsubmenu=MTi
in a marine application and they work very well. The secret here is the use of magnetometers to compenaste for drift and set the reference azimuth so not really a pure INS. We also cheat and use GPS as a reference when we can and keep the gyros and accelerometers for the high frequency stuff.

An interesting discussion though.