Gyro emulation using two accelerometers

[abiradla@hotmail.com]

Hi,
I'm looking for sensors to build an IMU. Classical IMU use 3
accelerometers and 3 gyros. For accelermeters we can find cheap sensor
(Freescale MMA7260Q 5$ for 3 axis). The gyros are more expensive (AD
ADXRS300 30$ per axis).
Do you know if we can measure the angle rate using using two
accelerometers separated by a small distance d (2 cm) ?
Can you point me to some articles that explain how we can do that.
I made some computations starting from the navigation equation and I
found that the difference between the two accelerometers outputs A1 and
A2 is directly :
A1-A3= W*W* d + 2*W*Phi*d

Where W = the earth rotation angle rate
Phi is the angle rate of accelerometer1 with respect to accelerometer2.

if A1 et A2 are at rest , Phi =0 and we can measure W.

I'm not sur that of my computation and I need help to relate A1-A2 to
the angle rate (W+Phi) given directly by a gyro.

Thanks.

 

[ChrisQuayle]

Hi,
I'm looking for sensors to build an IMU. Classical IMU use 3
accelerometers and 3 gyros. For accelermeters we can find cheap sensor
(Freescale MMA7260Q 5$ for 3 axis). The gyros are more expensive (AD
ADXRS300 30$ per axis).
Do you know if we can measure the angle rate using using two
accelerometers separated by a small distance d (2 cm) ?
Can you point me to some articles that explain how we can do that.
I made some computations starting from the navigation equation and I
found that the difference between the two accelerometers outputs A1 and
A2 is directly :
A1-A3= W*W* d + 2*W*Phi*d

Where W = the earth rotation angle rate
Phi is the angle rate of accelerometer1 with respect to accelerometer2.

if A1 et A2 are at rest , Phi =0 and we can measure W.

I'm not sur that of my computation and I need help to relate A1-A2 to
the angle rate (W+Phi) given directly by a gyro.

Thanks.

The only problem with accelerometers is that they will also sense
acceleration of the vehicle, which is probably not what's wanted and
difficult to compensate out. Have been doing some background work on a
solid state horizon and have collected books and other docs on inertial
nav along the way. The nasa tech reports server is a really rich
resource in particular and much of it is in pdf for download. Do a
search on inertial navigation and you get tech reports going back to the
sixties, when it really hard work and stretching the state of the art in
just about every way. eg: microcontroller power or less flight
computers. istr, there is a report covering just what you are trying to
do as well as early work on improved direction cosine algorithms etc.
Books which you might find usefull are:

Titterton and Weston: Strapdown Inertial Navigation Technology

Collinson: Introduction to Avionics

Both the above are fairly recent.

Savant, Howard, Salloway et al: Principles of Inertial Navigation

Parvin: Inertial Navigation

(Early 60's timeframe, missile applications etc)

You can usually find the above on ABE books at a fraction of new price
as well. Just plug in the Author or title...

Chris

 

[Ancient_Hacker]

Hi,
I'm looking for sensors to build an IMU.

First you should do some error budget calculations. For inertial
guidance you are doing double integrations, which require tremendous
absolute accuracy of the basic measurements in order to get even
mediocre end results. For example, calculate what happens if one of
your accelerometers is even 0.1% off zero. That's an error of 0.01
meters per second. That's an acceleration of 4.5MPH per minute. After
ten minutes your device thinks it's going 45MPH when it's actually
standing still. After an hour it's beaking the sound barrier while
just sitting there.

I don't think you can make a useful IMU out of $5 components. The
best Honeywell laser gyros have been in development for 30 years, cost
$70K each, and only promise 1 mile per hour drift.

 

[sdeyoreo@hotmail.com]

Hi,
I'm looking for sensors to build an IMU. Classical IMU use 3
accelerometers and 3 gyros. For accelermeters we can find cheap sensor
(Freescale MMA7260Q 5$ for 3 axis). The gyros are more expensive (AD
ADXRS300 30$ per axis).
Do you know if we can measure the angle rate using using two
accelerometers separated by a small distance d (2 cm) ?
Can you point me to some articles that explain how we can do that.
I made some computations starting from the navigation equation and I
found that the difference between the two accelerometers outputs A1 and
A2 is directly :
A1-A3= W*W* d + 2*W*Phi*d

Where W = the earth rotation angle rate
Phi is the angle rate of accelerometer1 with respect to accelerometer2.

if A1 et A2 are at rest , Phi =0 and we can measure W.

I'm not sur that of my computation and I need help to relate A1-A2 to
the angle rate (W+Phi) given directly by a gyro.

Thanks.

READ THIS!!! Inertial Navigation Sytems. Very Good !!!
http://www.frc.ri.cmu.edu/~alonzo/course/pos_ins.frm.pdf
For a gyro, look at AD22304

For IMU info, search on Alonzo Kelly, a researcher at Carnegie-Mellon
Robotics Institute.

 

[YAZ]

Thank you all for your answers.

In fact I think using a GPS to aide the low cost IMU. GPS module these
days are cheap (< 20$).
your comments about the accurracy of cheap accelerometers made me doubt
about the faisability of such IMU even with a GPS. GPS can correct evey
second when it's outdoor. But when the GPS is OFF the low cost IMU
error can be greater than 1000 meters after 1 minute !!!.
What kind of accelerometers are used in commercial IMU ?
About my equation. It's wrong. I found this very usefull paper about
Gyro-Free IMU:
http://www.auto.fcu.edu.tw/~newsletr/f94/f9411/b10.pdf
If we want to simpify the computations using 6 accelermeters we must
choose a suitable position for each accelerometer.

My GPS works fine indoor but sometimes it take one hour to fix if not
aided. So my IMU can be usefull if the error growth don't exceed 500
meters after one hour. If it cann't meet these performances then i'll
not call it IMU.
If the main source of error is the accelerometer offset then it can be
cancelled during calibration. If it's a zero mean noise then it will
zero mean error in the position (right ?). If it's a drift then we can
do nothing because we integrate (and don't differentiate Helas).

Sincerely

 

[Nico Coesel]

Thank you all for your answers.

In fact I think using a GPS to aide the low cost IMU. GPS module these
days are cheap (< 20$).
your comments about the accurracy of cheap accelerometers made me doubt
about the faisability of such IMU even with a GPS. GPS can correct evey
second when it's outdoor. But when the GPS is OFF the low cost IMU
error can be greater than 1000 meters after 1 minute !!!.
What kind of accelerometers are used in commercial IMU ?

Look at www.xsens.com

My GPS works fine indoor but sometimes it take one hour to fix if not
aided. So my IMU can be usefull if the error growth don't exceed 500

The error of a GPS can be close to 100meters when you are in an area
with a lot of buildings.

 

[Jan Panteltje]

Look at www.xsens.com

http://www.xsens.com/index.php?mainmenu=order&submenu=price_list
100 euro for a cable?

mmm

 

[Rene Tschaggelar]

Hi,
I'm looking for sensors to build an IMU. Classical IMU use 3
accelerometers and 3 gyros. For accelermeters we can find cheap sensor
(Freescale MMA7260Q 5$ for 3 axis). The gyros are more expensive (AD
ADXRS300 30$ per axis).
Do you know if we can measure the angle rate using using two
accelerometers separated by a small distance d (2 cm) ?
Can you point me to some articles that explain how we can do that.
I made some computations starting from the navigation equation and I
found that the difference between the two accelerometers outputs A1 and
A2 is directly :
A1-A3= W*W* d + 2*W*Phi*d

Where W = the earth rotation angle rate
Phi is the angle rate of accelerometer1 with respect to accelerometer2.

if A1 et A2 are at rest , Phi =0 and we can measure W.

I'm not sur that of my computation and I need help to relate A1-A2 to
the angle rate (W+Phi) given directly by a gyro.

Don't forget the noise and offset of the output. Plus
there may be a dependency on supply voltage and
temperature.

Rene

 

[Rene Tschaggelar]

http://www.xsens.com/index.php?mainmenu=order&submenu=price_list
100 euro for a cable?

Yes, the cable is the show stopper. Whatever the other
items are priced, they appear as overpriced as the cable.
Rather not sell the cable at all.

Rene

 

[Tim Wescott]

Hi,
I'm looking for sensors to build an IMU. Classical IMU use 3
accelerometers and 3 gyros. For accelermeters we can find cheap sensor
(Freescale MMA7260Q 5$ for 3 axis). The gyros are more expensive (AD
ADXRS300 30$ per axis).
Do you know if we can measure the angle rate using using two
accelerometers separated by a small distance d (2 cm) ?
Can you point me to some articles that explain how we can do that.
I made some computations starting from the navigation equation and I
found that the difference between the two accelerometers outputs A1 and
A2 is directly :
A1-A3= W*W* d + 2*W*Phi*d

Where W = the earth rotation angle rate
Phi is the angle rate of accelerometer1 with respect to accelerometer2.

if A1 et A2 are at rest , Phi =0 and we can measure W.

I'm not sur that of my computation and I need help to relate A1-A2 to
the angle rate (W+Phi) given directly by a gyro.

Thanks.

FYI:

http://www.strapdownassociates.com/Inertial Sensors Measure.pdf
http://www.strapdownassociates.com/Accels Measure.pdf
http://www.strapdownassociates.com/Gyros Measure.pdf

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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