# Using many cheap accelerometers to reduce error

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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.

Re: Using many cheap accelerometers to reduce error
On Saturday, February 9, 2019 at 3:47:32 PM UTC-5, JS wrote:

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

Rick C.

Re: Using many cheap accelerometers to reduce error
On Saturday, February 9, 2019 at 4:53:39 PM UTC-5, snipped-for-privacy@gmail.com wrote:

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.

Re: Using many cheap accelerometers to reduce error
On 10/02/2019 9:39 am, George Herold wrote:

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?

Re: Using many cheap accelerometers to reduce error
On Saturday, February 9, 2019 at 8:23:20 PM UTC-5, Sylvia Else wrote:

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.

Re: Using many cheap accelerometers to reduce error
On 10/02/2019 2:38 pm, snipped-for-privacy@gmail.com wrote:

Random doesn't mean equally distributed. If you found that every set you
obtained were equally distributed, you'd be forced to conclude that they
were not random.

So the question becomes that of how likely it is that a random selection
will be distributed in a way that the combined error exceeds what you want.

If I select 1% resistors, I'll be pretty annoyed if more than a very
small number show a 2% error.

By contrast, if I select 10% resistors, and group then in sets of ten in
parallel, I'll expect the combined result to exceed a 2% error quite often.

Sylvia.

Re: Using many cheap accelerometers to reduce error
wrote:

I'd be very surprised if you actually did get 2% error.  I'd expect a
reel to be skewed one way or another with perhaps very few individual
resistors in tens of reels within 5%, even.

Re: Using many cheap accelerometers to reduce error
On Monday, February 11, 2019 at 2:59:12 PM UTC+11, snipped-for-privacy@notreal.com wrote:

il.com wrote:

sample size), does having many accelerometers and then averaging their outp
ut therefore reduce their overall error?

ters rather than one expensive one like a laser ring gyro?

as
and
y [*].

art
fade away.  Averaging many measurements will result in a lower range of err
or with some probability.  No measurement is contained in an error window w
ith 100% probability.

nt.

en.

If the errors were normally distributed and the 10% tolerance represented t
hree standard deviations away from the mean, 67% of the resistors in the sa
mple would lie with +/3% of the mean. Putting ten resistors out of such a s
election in parallel would mean that 67% of your samples of ten in parallel
would be within +/-1% of the mean.

There's no obligation  on the manufacturer to make the resistors in a way t
hat generates a normal distribution, and some manufacturers are claimed to
measure all the resistors that they did make and sort them into bins.

The +/-1% bin would then get the centre of the distributions, the +/-2% bin
would get the two bands around it, the +/-5% bins gets the next two bands
out from there, and the +/-10% bin gets all the resistors between +5% and +
10% as well as all the resistors between -5% and -10%.

I've no idea precisely what they actually do, but anybody whose distributio
n is centred 5% or more away from the target value would end up throwing ou
t a lot of resistors.

--
Bill Sloman, Sydney

Re: Using many cheap accelerometers to reduce error
On Sunday, February 10, 2019 at 10:11:29 PM UTC-5, Sylvia Else wrote:

l.com wrote:

ample size), does having many accelerometers and then averaging their outpu
t therefore reduce their overall error?

ers rather than one expensive one like a laser ring gyro?

s
nd
[*].

rt
ade away.  Averaging many measurements will result in a lower range of erro
r with some probability.  No measurement is contained in an error window wi
th 100% probability.

t.

n.

What's your point?  Did you do the math correctly?  Maybe that's why you do
n't see the right values.

To get a five fold improvement in accuracy, I believe 10 resistors is not t
he correct number.  I'd have to do some digging to get the right number and
come up with a probability of being within 2%, so I'll let you do your own
homework.  Bottom line is you can get whatever accuracy you desire to what
ever probability you desire by combining resistors or any other components
if the values are randomly distributed with a known average.

Rick C.

Re: Using many cheap accelerometers to reduce error
On Monday, February 11, 2019 at 5:30:27 PM UTC+11, snipped-for-privacy@gmail.com wrote:

It's 25. The probability of the set being within 2% of the nominal value depends on the way the resistance values are distributed within the set of parts you are selecting from, which is not guaranteed by anybody, and I've never seen it pulbished.

Sadly, that's not what the manufacturers claim. All they say is that none of the resistors that they sell you with +/-10% tolerance lies outside that tolerance.

The joke example is where they have a process that generates nice stable resistors but with a perfect Gaussian distribution around the nominal value, and they measure everything.

+/-1% are samples taken from the peak of the distribution, and probablity distribution would be pretty much flat.

+/-2% are actually -2% to -1% and +1% to +2%, with nothing within the +/1% band.

And so on.

In reality, tight tolerance resistors are almost always trimmed after manufacture, but if you do it faster you do it, the trimming process is less precise. It presumably leads to rather messy statistics.

--
Bill Sloman, Sydney

Re: Using many cheap accelerometers to reduce error
On Sun, 10 Feb 2019 22:57:40 -0800 (PST), snipped-for-privacy@ieee.org wrote:

If the resistor is supposed to belong to the E12 series, an inaccuracy
more than +/-10 % would be falling in next or previous bin and should
be labeled as such.

Do they really measure each and every such low cost component
individually ?

Re: Using many cheap accelerometers to reduce error
On Monday, February 11, 2019 at 7:29:20 PM UTC+11, snipped-for-privacy@downunder.com wrote:

Depend when the value is marked on the resistor - before or after measurement.

It seems unlikely. I did label it a joke example.

As I've posted elsewhere in the thread, I've no idea precisely what they actually do.

--
Bill Sloman, Sydney

Re: Using many cheap accelerometers to reduce error
snipped-for-privacy@ieee.org wrote in

He said E12 series.

Resistors all follow a standard progression in values.

Usually a full deviation from center spec will NOT take the part into
the next value bin.

If the deviation is that wide, then the table of values it fits into
would be wider, IOW not E12.

Re: Using many cheap accelerometers to reduce error
On Tuesday, February 12, 2019 at 2:01:40 AM UTC+11, snipped-for-privacy@decadence.org wrote:

If the resistor gets its value marking before its resistance was measured, you wouldn't put it into the next bin up, even if it did measure out as qualifying.

<snip>

--
Bill Sloman, Sydney

Re: Using many cheap accelerometers to reduce error
On Tuesday, 12 February 2019 00:13:26 UTC+1, snipped-for-privacy@ieee.org  wrote:

Practical example:

Most nowadays look like the China one. Offset gausian

Cheers

Klaus

Re: Using many cheap accelerometers to reduce error
On Tuesday, February 12, 2019 at 10:50:30 AM UTC+11, snipped-for-privacy@gmail.com w
rote:

to

ed, you wouldn't put it into the next bin up, even if it did measure out as
qualifying.

re_are_manufactured_oc/

Not all that gaussian. There's perceptible skew, and probably some kurtotis
as well. The numbers of samples in each bin aren't large, so the standard
deviations on each would be four or five, but my guess would be that there'
s something slightly odd going on - perhaps samples drawn from two adjacent
(but slightly offset) gaussians.

--
Bill Sloman, Sydney

--
Bill Sloman, Sydney

Re: Using many cheap accelerometers to reduce error
snipped-for-privacy@ieee.org wrote in

Precision resistors get matched and culled before any markings are
applied.  Some even get laser trimmed to spec.

Precision SMTs usually do not even have a marking.

Re: Using many cheap accelerometers to reduce error
@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.

Re: Using many cheap accelerometers to reduce error
On Sunday, 10 February 2019 05:08:13 UTC+1, snipped-for-privacy@decadence.org
wrote:

That is not my experience. Resistors are tuned in the process, which means
that one lot will typically have more or less the same distribution, but it
is offset from the nominal. If they measure its's within the specs (1%), t
hen they do not alter the process to pull it in. They just press the big "G
O" button

Thus more resistors in parallel gets you nowhere

Cheers

Klaus

Re: Using many cheap accelerometers to reduce error
snipped-for-privacy@gmail.com wrote in

They do when they are multi-gigohm.  So two 10G in paralell makes
a closer than rated 5G resistor.  Usually.