Inertial Navigation System - what do I need?

3 questions :

1) Is it possible to build a simple but accurate INS using a 3 axis accelerometer and 3 axis inclinometer? Or do I need something more than that? Is the inclinometer even needed or would just an accelerometer surfice?

2) Is a gyroscopic chip required to measure the yaw or can that be handled by the accelerometer above? Is it true that accelerometers cannot measure yaw but can measure pitch and roll only? Do I need a 3 axis gyroscope as well in that case?

3) If I am in a car parked on a hill, how does the INS know I'm not accelerating forward but rather that the acceleration is just due to gravity? This gets back to my question of whether an inclinometer is needed I'm guessing.

Crap I have not even started and its already sounding complicated. Please, a simple explaination only as I'm already somewhat befuddled.

Reply to
vorange
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On Wed, 26 Dec 2007 03:58:30 -0800 (PST), I said, "Pick a card, any card" and vorange instead replied:

You've got some of the basics but go back even further. You need a way to pinpoint your position on earth and your initial vectors from true north and flat/level with the surface of this accommodating sphere known as earth.

From that, three accelerometers will do the trick but there are other factors such as coreolis effect, drift of your accelerometers, and a means to keep the accelerometer platform stable. As you noted, a gyro will do that.

-- Ray

Reply to
Ray Haddad

Very important: define "accurate." A few meters over the space of a few minutes of operation? Hours? Days? Operating within a few meters of its starting point? Kilometers? Hundreds of kilometers? Thousands?

WRT your questions:

An ideal accelerometer responds only to acceleration along its sensitive axis and not at all to rotation. You can infer tilt from a two-axis accelerometer provided it's not accelerating.

Typical inclinometers presume they are operating in a non-accelerating frame of reference, so you'd need to do the math to compensate, using the information from the accelerometers to correct the acceleration-induced change in the tilt. It's also possible to add something like wheel sensors to independently derive acceleration and feed that info back to compensate.

Inertial systems that I'm familiar with, however, all use rate gyros to sense rotation, and integrate once to get angular position.

Accelerometers can only measure pitch or roll if they are in a non-accelerating frame of reference. No good for yaw.

A navigation-grade INS can sense earth rate rotation during initial alignment and with that information will independently determine north, east, and down as well as its present latitude (although it will generally align better/faster if it's helped out by being told a correct initial latitude).

They ain't cheap.

More feasible (and affordable) would be to provide the INS with an initial position and orientation. Once it stabilizes, it navigates with deltas from that initial fix. For local operation (more or less, out to the horizon from where it starts) a flat earth approximation is fine.

You can also add a "digital" compass (see

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to help out with the yaw problem and provide periodic position updates from a GPS module (see
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It's a good topic and the source of a lot of interesting math and real-world problem solving.

The guys working on autonomous helicopters (the hobby guys not the corporate mega-buck R&D lab guys) have some informative web sites that discuss their approaches as well as some open source implementations that you could use as a starting point.

Sparkfun has some six degree of freedom assemblies for a reasonable price, as well as various other modules that might come in handy.

--
Rich Webb     Norfolk, VA
Reply to
Rich Webb

No.

No and No.

You need a lot more then that.

Yes and No.

Yes.

You got to account for the gravitation and the rotation of the Earth, as well as for the tide force from the Moon.

Crap, Yes.

As simple as that.

Vladimir Vassilevsky DSP and Mixed Signal Consultant

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Reply to
Vladimir Vassilevsky

No. An inclinometer is just a type of accelerometer, and accelerometers alone aren't sufficient.

You need three axes of acceleration, and three axes of angular rate.

Assuming perfect accelerometers, gyros, and geodetic database information, and assuming that the INS is properly initialized, the INS will "know" that the car has rotated and stopped, and will be able to null out the effect of gravity.

Yes it is. And you've just scratched the surface.

If you can only survive on simplicity you're screwed. There. That's simple.

Inertial navigation is a complex subject. Sensors good enough to do the job purely from inertial measurements are exceedingly expensive (i.e. a rather large fraction of $1M), and if you do want to do it purely inertially you need a pretty detailed knowledge of the geodetic properties of the earth.

GPS-aided inertial navigation can use much less expensive sensors, because the data from a GPS system tends to fill in the gaps left by the sensors (and visa-versa), but now instead of combining information from six sensors and a big database, you have to combine three bits of data from the GPS with six bits of data from your sensors, and the required Kalman filter is neither linear nor time invariant.

If you really want to do this instead of buying a solution the AIAA

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has how-to books -- but in order to understand them you need most of a Master's degree in the right sort of signal processing mathematics. Only you can say if you're up to it, but it's not the sort of thing you'll do in a few evenings with a high-school math background unless you're _really_ an astounding person.

I hope this helps, even if the answer may not be what you want to hear.

--
Tim Wescott
Control systems and communications consulting
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Reply to
Tim Wescott

You have to deal with a fundamental problem in modern physics - gravity is indistiguishable from acceleration without additional information. You also need to worry about the accumulation of errors if you are calculating position by integrating twice from acceleration.

Reply to
Richard Henry

GPS is accurate but slow. By the time you finish all the calcuations, you are way-off from the original position. Accelerometers can apply quick but inaccurate corrections to GPS. Combining the two is not so difficult in theory, but of course in practice.

Two years of undergrad maths should be enough. It's just spatial geometry and linear algebra. Some high school students do study this stuff. Oh wait, may be not in the U.S.

Reply to
linnix

linnix wrote: [snip...snip...]

Heh. Yeah, if it's not on the Standards of Learning exams ...

There are lots of introductions out there but one that I like is "The Global Positioning System and Inertial Navigation" by Farrell and Barth. Like most (all?) technical pubs there are a few errors/typos; the authors have an errata at

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The OP hasn't been seen since the original post but the issues of implementing an INS are really pretty interesting. I'm assuming he's doing this out of curiosity and as a learning exercise and not trying to engineer the next gen Trident missile.

--
Rich Webb     Norfolk, VA
Reply to
Rich Webb

Hi vorange,

Depending on what you're going to try to use it for, it might not be NEARLY as difficult or expensive as you've been led to believe.

Maybe the Analog Devices ADIS16355 "High-Precision Tri-Axis Inertial Sensor" would work for your application:

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It's only $30 in quantity and has built-in tri-axis gyroscope with

+/-75 to +/-300 deg/sec dynamic range (14 bits), and built-in tri-axis accelerometer (+/-10g, 14 bits), and 350 Hz bandwidth.

=46rom the ADIS16355 datasheet:

APPLICATIONS:

Guidance and control Platform control and stabilization Motion control and analysis Inertial measurement units General navigation Image stabilization Robotics

Analog Devices has quite a few other interesting-looking MEMS devices listed, too.

Have fun.

- Tom Gootee

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Reply to
tomg

Actually, it is $359 in quantity, and not quite available yet, but other than that you got it right 8^)

Marc

Reply to
Marc Ramsey

and since you have to order 1000 for that price, that is quite an order. can i put it on my visa card?

alan nishioka

Reply to
Alan Nishioka

Oops. You are correct. I was looking at the wrong table-entry. Thanks for pointing that out.

It's still pretty cheap, for what it can do. And if the OP doesn't need the high-precision version, there is a somewhat-lower-cost model that is similar.

Reply to
tomg

I don't know. CAN you? :-)

Maybe we can all get free samples.

I wonder what the qty 1 price might end up at, from a distributor, and what it might go down to, in a few years.

Reply to
tomg

It's better to say that GPS is accurate over the long term, but not the short, while accelerometers (and gyros) are accurate over the short term but not the long.

It's just spatial geometry, linear algebra, multivariate statistics, with some real analysis if you want to understand how the math goes together instead of just following someones recipe. Add to that the fact that you need to know and understand the characteristics of your sensors and a good dose of how GPS works.

You may be able to understand some of the _principals_ if you're an ordinary high school student, and even reason out a solution that kinda works -- but I doubt that even one high school student in 100, in any given country, could begin to understand all of the issues inherent in a professional-grade INS solution.

--
Tim Wescott
Control systems and communications consulting
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Reply to
Tim Wescott

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The principals will be a problem only if the student steps out of line and neglects his study of the principles.

Reply to
Richard Henry

My statement about high school student is just sarcastic, considering the low interest in science in the U.S. (driven by misguided government policies).

However, colleges are more competitive, mostly due to foreign students anyway.

But I maintained that the first two years of undergrad math should be enough. GPS is nothing more than translating time delays into spatial coordinates and Accelerometers are applied Newtonian physics. I know of some heavy duty research facility in these areas, but they are not in the U.S.

Unfortunately, the applications are often in sensitive areas (fast moving projectiles) and the interesting stuffs are always hidden. I am probably saying too much already.

Reply to
linnix

Mathematics is no longer taught in the United States.

Reply to
larwe

Hey, that's a really really good link there, I see a bunch of books I've added to my wishlist. Thanks!

Reply to
larwe

Eh? The only vaguely mathematical thing I saw on that page is a talking calculator, which if anything is arithmetic rather than mathematics.

Reply to
larwe

Obligatory "The missile knows where it is" lecture...

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Reply to
Jim Stewart

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