Precision? accuracy? And how to tell if there are games going on in the software!

It gets harder unless we doggedly insist on being hard-heads about it. I guess the temptation among those sales oriented folk is overwhelming, and gaming the software to give you a nice warm "Gosh - that must be accurate" feeling is only one small step away from going the whole 9 yards like Volkswagen did with the software "recognizing" that an emissions test was under way.

For me, it is often about angular resolution using encoder kit in satellite tracking Earth station antennas

Stuff like this -->

http://www.renishaw.com/en/optical-encoders--6433
One of the products offers 26 bits, and for an extra £15, one can have 32 bits resolution, of a full circle.

No surprise then that a computer sampling at 40 times/sec (in between lots of other tasks) sees all the digits to the right of the true accuracy dancing about randomly.

Worse, the numbers are being crunched by a hard-working DSP (Digital Signal Processor), hard-programmed hardware to do trigonometric math on these useless extra numbers.

1/(2^32) = 1/4294967296 = 2.32830643654e-10 . Try 0.3 milli-arc-seconds! Is that about the height of a pencil in NY, if one is in London? I don't know. It is beyond the ability of the calculator trig function.

OK - so it strains credulity. Maybe there is some kind of very special application that requires it.. (might be?)

So I try the 26-bit product. Keep in mind these things are

*very* expensive!

1/(2^26) = 1/67108864. Even then, the display will not allow those random digits to stand still.

We have to discard the last bit because of the +/-1 bit uncertainty about the state of the least significant bit.

Eventually, finding that the communication to encoder protocol to the servos can only do 22 bits.. Hmm the digits still dance about sampling noise!

1/(2^22) = 1/ 4194304 (of a circle), or 85.83 micro-degrees, or 0.309 arc-seconds. Better than the theodolite!

OK - we can have the system working fine, but that does not stop the sales guys bragging that it has (looking at the encoder) 32 bits accuracy.

In fact, the seismic vibrations of me stomping about on the concrete floor were making the last two digits jump!

Getting the terms used correctly may be near impossible amid the sales culture (yeah - mostly telling sort of lies!)