# Using many cheap accelerometers to reduce error

• posted

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.

• posted

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

Rick C.

• posted

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.

• posted

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```
• posted

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

Rick C.

• posted

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?
• posted

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.

• posted

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.

• posted

Sylvia Else wrote in news:gc9co2Fmqn1U1 @mid.individual.net:

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.

• posted

Sylvia Else wrote in news: snipped-for-privacy@mid.individual.net:

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.

• posted

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

• posted

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

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

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.

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

• posted

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.

• posted

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

• posted

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

Within a chip yes.

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

• posted

Perhaps you are saying this in a tongue in cheek way, but ITAR is one of th ose things where you are expected to know your device is restricted without anyone in the government telling you. Not only are you required to not se ll it to the wrong people, but you are supposed to know that the people you sell it to won't sell it to the wrong people.

Rick C.

• posted

It might be interesting to try out say 16 to see how much of an improvement is obtained and how much of it is systematic error.

A 10 fold performance improvement with 100 or 128 might be worthwhile if they are cheap enough to fabricate in bulk.

```--
Regards,
Martin Brown```
• posted

The problem is the square root relationship. That means you need N^2 more units to get an N factor improvement which means a *lot* more units.

Rick C.

• posted

A UK seismometer company did (does?) just this, 16 MEMS accelerometers per axis. I don't know what the improvement is, but I'm certain they'd lie about it knowing the customer couldn't check. [That's why I only stayed there a few months, shocking quality and shocking performance exaggeration.]

Cheers

```--
Clive```
• posted

If the MEMS parts use vibrating cantilevers, they would want to sync up. I don't know if that is good or bad.

```--
John Larkin         Highland Technology, Inc

lunatic fringe electronics```

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