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digital integration

digital integration

digital integration

I am currently working on a project where I need to find a digital integration for acceleration data.  I believe I have found a sufficient integration filter that I have tested in matlab but after the first integration there is a dc offset that makes the second integration to get displacement data impossible.  It would be ideal to find another type of filter to remove the dc offset for my project.  I have tried basic high pass filters with no luck.  Is it possible to do such a thing?  and if so could someone advise me on a sufficient high pass filter?

RE: digital integration

Mac, Me thinks you are correct.  But in the chance that you are not...

Tenngineer, I would suggest that you look into methods of numerical integration.  From what little you have describe about what you are trying to accomplish, it looks to me as though you are making things too complex by worrying about filtering data.  A common form of numerical integration would be Runge Kata (spelling?) and you may consider searching for that term.  The book "Math toolkit for real time programming" by Jack Crenshaw is a wonderful resource for a solid how to when it comes to math programming for real time systems.

RE: digital integration

NO this is not a student post.  I work in the private industry at a testing facility for jet engines and we are having noise problems with all of our analog signals from the test facility.  We would like to convert them to digital directly at the accelerometer.

RE: digital integration

Better google Runge-Kutta.

Gunnar Englund
100 % recycled posting: Electrons, ideas, finger-tips have been used over and over again...

RE: digital integration

I do not think your problem is in your integration routine.  But you can publish your routine or test it with synthetic data.  I will think you will find the sticky reality issues with accelerometers and displacement estimation a difficult problem.  I have studied Jack Crenshaw's book and have been in contact with him on integration issues.  You will find his comments on why the Runga-Kutta method is not applicable to all real time problems informative.

Before you choose an integration routine you need to know if your sample rate meets Nyquist.  What is your noise density model?  Is your answer within the realm of expectations?

At the risk of copy write infringement I will copy only two lines from his book that I have used in industry.

First you will need both the present acceleration measurement and the past acceleration measurement.  Then you produce a predicted velocity.  Time now is "I", the past time isi-1, the future is i+1.  The time delta is "h", standing for height.  But buy the book if you want to know more.  

If you want more explanation;  Buy the book.  Even if you are mildly interested buy the book.  It is a great resource for understanding. "Math Toolkit for Real-Time Programming" Jack W. Crenshaw ISBN 1-929629-09-5.  I have one from CMP Books, but there is a new publisher according to Jack.

v(i+1) = v(i) + (h/2)*(3*f(i)-f(i-1))

The position is
x(i+1) = x(i) + (h/2)*(v(i+1)+v(i))

Without any other information this is a great thing to do.  It is a predictor corrector method, Adam, Bashforth, and Moulton are keywords.  Numerical Recipes for C++ recommends PC methods for most problems.  There are caveats.

Is your sample interval exactly uniform?  If not you could have some jitter problems.  So go with a lower order integrator with very small steps.  Jack Crenshaw explains how to make a sample rate independent system.  I did just that.  But it is a lot of work, especially the startup problem.  If you do not know what the startup problem is, buy the book!

I am not being facetious.  Integration problems are not trivial. I would need to know more to help.  I can not help with accelerometers.  Can others pipe in?


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