# Using many cheap accelerometers to reduce error

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JS
Guest

Sat Feb 09, 2019 10:45 pm

Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

Thanks.

Guest

Sat Feb 09, 2019 11:45 pm

On Saturday, February 9, 2019 at 3:47:32 PM UTC-5, JS wrote:
Quote:
Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

It would if the errors are all random. Are they?

Rick C.

George Herold
Guest

Sat Feb 09, 2019 11:45 pm

On Saturday, February 9, 2019 at 4:53:39 PM UTC-5, gnuarm.del...@gmail.com wrote:
Quote:
On Saturday, February 9, 2019 at 3:47:32 PM UTC-5, JS wrote:
Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

It would if the errors are all random. Are they?

Rick C.

Right, systematic vs random differences.
A systematic error (like a DC offset vs. bias
voltage (or temperature)) Can't be improved
(as much) with averaging.

George H.

Guest

Sun Feb 10, 2019 12:45 am

On Saturday, February 9, 2019 at 6:13:07 PM UTC-5, John Larkin wrote:
Quote:
On Sat, 9 Feb 2019 12:47:28 -0800 (PST), JS <js5071921_at_gmail.com
wrote:

Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly better
than a cheap MEMS or some such.

What if they charge more for the MEMS? Does that make it more accurate?

Rick C.

John Larkin
Guest

Sun Feb 10, 2019 12:45 am

On Sat, 9 Feb 2019 12:47:28 -0800 (PST), JS <js5071921_at_gmail.com>
wrote:

Quote:
Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly better
than a cheap MEMS or some such.

--

John Larkin Highland Technology, Inc

lunatic fringe electronics

Sylvia Else
Guest

Sun Feb 10, 2019 2:45 am

On 10/02/2019 9:39 am, George Herold wrote:
Quote:
On Saturday, February 9, 2019 at 4:53:39 PM UTC-5, gnuarm.del...@gmail.com wrote:
On Saturday, February 9, 2019 at 3:47:32 PM UTC-5, JS wrote:
Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

It would if the errors are all random. Are they?

Rick C.

Right, systematic vs random differences.
A systematic error (like a DC offset vs. bias
voltage (or temperature)) Can't be improved
(as much) with averaging.

George H.

Even if there is no systematic error, the random errors may still be
skewed in one direction, since the set of all sets of random values has
to contain sets with that property.

Seems to me that if you need a particular accuracy, your options are
limited.

a) Get a part specified to have that accuracy.

b) Get a part not so specified, but which is specified not to drift, and
which you have measured to determine that it has the required accuracy [*].

Any approach using large numbers of less accurate parts is not
guaranteed to give you the accuracy you want.

Sylvia.

[*] If such even exists - why wouldn't the manufacturer measure the part
and sell it at a higher price?

Guest

Sun Feb 10, 2019 4:45 am

On Saturday, February 9, 2019 at 8:23:20 PM UTC-5, Sylvia Else wrote:
Quote:
On 10/02/2019 9:39 am, George Herold wrote:
On Saturday, February 9, 2019 at 4:53:39 PM UTC-5, gnuarm.del...@gmail.com wrote:
On Saturday, February 9, 2019 at 3:47:32 PM UTC-5, JS wrote:
Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

It would if the errors are all random. Are they?

Rick C.

Right, systematic vs random differences.
A systematic error (like a DC offset vs. bias
voltage (or temperature)) Can't be improved
(as much) with averaging.

George H.

Even if there is no systematic error, the random errors may still be
skewed in one direction, since the set of all sets of random values has
to contain sets with that property.

Seems to me that if you need a particular accuracy, your options are
limited.

a) Get a part specified to have that accuracy.

b) Get a part not so specified, but which is specified not to drift, and
which you have measured to determine that it has the required accuracy [*].

Any approach using large numbers of less accurate parts is not
guaranteed to give you the accuracy you want.

Sylvia.

[*] If such even exists - why wouldn't the manufacturer measure the part
and sell it at a higher price?

If the starting point is that the error is random, your arguments all fade away. Averaging many measurements will result in a lower range of error with some probability. No measurement is contained in an error window with 100% probability.

Rick C.

Guest

Sun Feb 10, 2019 5:45 am

gnuarm.deletethisbit_at_gmail.com wrote in

Quote:
On Saturday, February 9, 2019 at 6:13:07 PM UTC-5, John Larkin
wrote:
On Sat, 9 Feb 2019 12:47:28 -0800 (PST), JS <js5071921_at_gmail.com
wrote:

Hi all,

Given that the random error in a sample is proportional to
1/sqrt(sample size), does having many accelerometers and then
averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap
accelerometers rather than one expensive one like a laser ring
gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly
better than a cheap MEMS or some such.

What if they charge more for the MEMS? Does that make it more
accurate?

Rick C.

There are some pretty damned good MEMS based accelerometers out
there.

All of your basic quad rotor craft use pretty good 'cheap' models,
so the high end is even more resolved.

Guest

Sun Feb 10, 2019 5:45 am

Sylvia Else <sylvia_at_email.invalid> wrote in news:gc9co2Fmqn1U1
@mid.individual.net:

Quote:
Any approach using large numbers of less accurate parts is not
guaranteed to give you the accuracy you want.

One exception might be when paralelling resistors. 1% resistors in
paralell will generally be more accurate than the original spec. Maybe
due to the way precision classed resistor sets get matched and culled.
One can generally count on the members of the set to actually be more
accurate than the spec they claim to be at least as good as.

Guest

Sun Feb 10, 2019 5:45 am

Sylvia Else <sylvia_at_email.invalid> wrote in
news:gc9co2Fmqn1U1_at_mid.individual.net:

Quote:
[*] If such even exists - why wouldn't the manufacturer measure
the part and sell it at a higher price?

The same reason that a mil-spec part had additional testing done on it.
Cost. higher class chips cost more, but not always due to hard
internal differences so much as exceptional performance compared to the
rest of the lot.

Intel cpus still got sold when they exhibited too much heat ran at
speced rate. Ran slower. Tag it with a different name, and sell it as
a slower version. The 486's that had failed math cos still got sold.
Intel die issues. Have to keep to a minimum the number of failed units
on a single platter.

JS
Guest

Sun Feb 10, 2019 7:45 am

Quote:
JS wrote in

On Sunday, February 10, 2019 at 1:13:07 AM UTC+2, John Larkin
wrote:
On Sat, 9 Feb 2019 12:47:28 -0800 (PST),
wrote:

Hi all,

Given that the random error in a sample is proportional to
1/sqrt(sample size), does having many accelerometers and then
averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap
accelerometers rather than one expensive one like a laser ring
gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly
better than a cheap MEMS or some such.

--

John Larkin Highland Technology, Inc

lunatic fringe electronics

OK I did the sums. Based on the random walk of a laser ring gyro
(0.0035 deg/sqrt-hour) and that of a MEMS accelerometer (2.25
deg/sqrt-hour) [1], you need about 400k MEMS accelerometers to
approach the accuracy of a laser ring gyro.

It sounds like a lot of components to solder together but if done
in a chip fab, it should be possible.

What makes you think they need to be 'together'? Simply on the
same superstructure should be enough.

Incorrect. On the same superstructure there will be additional structural vibrations whose amplitude and frequency are position-dependent. While these vibrations do not result in a net spatial or angular translation (you would hope so!) for the math to work the accelerometers have to be at the same location, the closer the better, sampling the same thing.

Quote:

Is it possible to make a commercial accelerometer with no export
restrictions by using such an array?

Is it possible to feesibly make such an array, cost, logistics,
etc. at all?

Within a chip yes.

Quote:

Or will ITAR or the like be
slapped on such a device once its accuracy is published in a
brochure?

ITAR restricts YOU the maker long before you go publishing product
performance numbers. If you make certain items, you 'learn' the
restrictions (long) before you get past single proto stage.

Refs:
[1] Honeywell GG1320AN Digital Laser Gyro brochure
[2] Error and Performance Analysis of MEMS-based Inertial Sensors
with a Low-Cost GPS Receiver. Park, M & Gao, Y. [2008] Sensors Vol
8

Perhaps they are an order of magnitude better since 2008. The gear
they based their numbers on was perhaps even older than that.

The accuracy is good enough, especially if the gyros are only used in portions of the journey where other sensors (e.g. GPS) are unavailable, such as indoors or underground.

JS
Guest

Sun Feb 10, 2019 7:45 am

On Sunday, February 10, 2019 at 1:13:07 AM UTC+2, John Larkin wrote:
Quote:
On Sat, 9 Feb 2019 12:47:28 -0800 (PST),
wrote:

Hi all,

Given that the random error in a sample is proportional to 1/sqrt(sample size), does having many accelerometers and then averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap accelerometers rather than one expensive one like a laser ring gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly better
than a cheap MEMS or some such.

--

John Larkin Highland Technology, Inc

lunatic fringe electronics

OK I did the sums. Based on the random walk of a laser ring gyro (0.0035 deg/sqrt-hour) and that of a MEMS accelerometer (2.25 deg/sqrt-hour) [1], you need about 400k MEMS accelerometers to approach the accuracy of a laser ring gyro.

It sounds like a lot of components to solder together but if done in a chip fab, it should be possible.

Is it possible to make a commercial accelerometer with no export restrictions by using such an array? Or will ITAR or the like be slapped on such a device once its accuracy is published in a brochure?

Refs:
[1] Honeywell GG1320AN Digital Laser Gyro brochure
[2] Error and Performance Analysis of MEMS-based Inertial Sensors with a Low-Cost GPS Receiver. Park, M & Gao, Y. [2008] Sensors Vol 8

Guest

Sun Feb 10, 2019 7:45 am

JS <js5071921_at_gmail.com> wrote in

Quote:
On Sunday, February 10, 2019 at 1:13:07 AM UTC+2, John Larkin
wrote:
On Sat, 9 Feb 2019 12:47:28 -0800 (PST),
wrote:

Hi all,

Given that the random error in a sample is proportional to
1/sqrt(sample size), does having many accelerometers and then
averaging their output therefore reduce their overall error?

So would it be worthwhile to have say 100 or 1000 cheap
accelerometers rather than one expensive one like a laser ring
gyro?

Thanks.

sqrt(1000) is only 32. I'd expect the ring gyro to be vastly
better than a cheap MEMS or some such.

--

John Larkin Highland Technology, Inc

lunatic fringe electronics

OK I did the sums. Based on the random walk of a laser ring gyro
(0.0035 deg/sqrt-hour) and that of a MEMS accelerometer (2.25
deg/sqrt-hour) [1], you need about 400k MEMS accelerometers to
approach the accuracy of a laser ring gyro.

It sounds like a lot of components to solder together but if done
in a chip fab, it should be possible.

What makes you think they need to be 'together'? Simply on the
same superstructure should be enough.
Quote:

Is it possible to make a commercial accelerometer with no export
restrictions by using such an array?

Is it possible to feesibly make such an array, cost, logistics,
etc. at all?

Quote:
Or will ITAR or the like be
slapped on such a device once its accuracy is published in a
brochure?

ITAR restricts YOU the maker long before you go publishing product
performance numbers. If you make certain items, you 'learn' the
restrictions (long) before you get past single proto stage.

Quote:
Refs:
[1] Honeywell GG1320AN Digital Laser Gyro brochure
[2] Error and Performance Analysis of MEMS-based Inertial Sensors
with a Low-Cost GPS Receiver. Park, M & Gao, Y. [2008] Sensors Vol
8

Perhaps they are an order of magnitude better since 2008. The gear
they based their numbers on was perhaps even older than that.

Guest

Sun Feb 10, 2019 7:45 am

JS <js5071921_at_gmail.com> wrote in

MEMs have come a long way over the years.

FOG and MEMS compete with ring laser gyros in many applications
because at certain points increased accuracy yields no gain in
performance for that particular application.

<https://www.analog.com/en/technical-articles/the-battle-between-mems-
and-fogs-for-precision-guidance.html>

Guest

Sun Feb 10, 2019 7:45 am

news:q3ofp9\$nmo\$2_at_gioia.aioe.org:

Quote:
JS <js5071921_at_gmail.com> wrote in

MEMs have come a long way over the years.

FOG and MEMS compete with ring laser gyros in many applications
because at certain points increased accuracy yields no gain in
performance for that particular application.

https://www.analog.com/en/technical-articles/the-battle-between-
me
ms- and-fogs-for-precision-guidance.html

Found a lot of good info in this pdf about position
tagging/tracking/placement science.

<https://www.analog.com/media/en/technical-documentation/data-