# Inertial Navigation System - what do I need?

Started by December 26, 2007
```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.
```
```On Wed, 26 Dec 2007 03:58:30 -0800 (PST), I said, "Pick a card, any
card" and vorange <orangepic@yahoo.com> instead replied:

>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.

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
```
```vorange wrote:
> 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?

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?

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.

> 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?

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

> 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.

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
http://en.wikipedia.org/wiki/Fluxgate_compass) to help out with the yaw
problem and provide periodic position updates from a GPS module (see
http://en.wikipedia.org/wiki/Kalman_filter).

> Crap I have not even started and its already sounding complicated.

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
```
```"vorange" <orangepic@yahoo.com> wrote in message
> 3 questions :
>
> 1)  Is it possible to build a simple but accurate INS

No.

> using a 3 axis
> accelerometer and 3 axis inclinometer?

No and No.

> Or do I need something more
> than that?

You need a lot more then that.

> 2) Is a gyroscopic chip required to measure the yaw

Yes and No.

> Do I need a 3
> axis gyroscope as well in that case?

Yes.

> 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?

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

> Crap I have not even started and its already sounding complicated.

Crap, Yes.

As simple as that.

DSP and Mixed Signal Consultant
www.abvolt.com

```
```On Wed, 26 Dec 2007 03:58:30 -0800, vorange wrote:

> 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?

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

> 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?

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

> 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.

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.

> Crap I have not even started and its already sounding complicated.

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
(http://www.aiaa.org) 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
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
```
```"vorange" <orangepic@yahoo.com> wrote in message
> 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.

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.

```
```On Dec 26, 10:42 am, Tim Wescott <t...@seemywebsite.com> wrote:
> On Wed, 26 Dec 2007 03:58:30 -0800, vorange wrote:
> > 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?
>
> No.  An inclinometer is just a type of accelerometer, and accelerometers
> alone aren't sufficient.
>
> > 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?
>
> You need three axes of acceleration, and three axes of angular rate.
>
> > 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.
>
> 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.
>
> > Crap I have not even started and its already sounding complicated.
>
> Yes it is.  And you've just scratched the surface.
>
> > Please, a simple explanation only as I'm already somewhat befuddled.
>
> 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.

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.

>
> If you really want to do this instead of buying a solution the AIAA
> (http://www.aiaa.org) 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.

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.

>
> I hope this helps, even if the answer may not be what you want to hear.
>
> --
> Tim Wescott
> Control systems and communications consultinghttp://www.wescottdesign.com
>
> Need to learn how to apply control theory in your embedded system?
> "Applied Control Theory for Embedded Systems" by Tim Wescott
> Elsevier/Newnes,http://www.wescottdesign.com/actfes/actfes.html

```
```linnix wrote:
[snip...snip...]
> 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.

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 www.ee.ucr.edu/~farrell/faq_errata.pdf

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
```
```On Dec 26, 6:58=A0am, vorange <orange...@yahoo.com> wrote:
> 3 questions :
>
> 1) =A0Is it possible to build a simple but accurate INS using a 3 axis
> accelerometer and 3 axis inclinometer? =A0Or do I need something more
> than that? =A0Is 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? =A0Is it true that accelerometers
> cannot measure yaw but can measure pitch and roll only? =A0Do 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? =A0This 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.

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:

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.

APPLICATIONS:

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

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

Have fun.

- Tom Gootee

http://www.fullnet.com/~tomg/index.html
```
```tomg@fullnet.com wrote:
> 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:
>