Sensor - accelerations to displacements, error

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Discussion Overview

The discussion revolves around the challenges of converting acceleration readings from a sensor into displacement measurements. Participants explore various integration methods and the associated errors that arise during this process, focusing on both theoretical and practical aspects of the problem.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant describes using MATLAB's cumtrapz function for integrating acceleration data to obtain displacement, noting some discrepancies with known distances.
  • Another participant questions the effectiveness of cumtrapz and suggests considering Simpson's rule as a potentially better integration method.
  • A participant clarifies that cumtrapz is based on the trapezoidal rule and expresses uncertainty about whether Simpson's rule would resolve their accuracy issues given their discrete data.
  • One participant points out that errors in acceleration measurements can lead to constant offsets in velocity, which may affect displacement calculations over time.
  • Another participant suggests creating a test case with sinusoidal data to identify where errors might be originating in the calculations.
  • A later reply mentions observing quadratic drift in velocity, which raises concerns about its impact on position data and expresses uncertainty about how to correct this issue.

Areas of Agreement / Disagreement

Participants express differing opinions on the best integration method and the nature of the errors encountered. There is no consensus on how to improve accuracy or rectify the observed issues.

Contextual Notes

Participants acknowledge limitations related to measurement errors, the nature of the data (discrete vs. continuous), and the challenges of correcting for drift in velocity. Specific assumptions about the data and integration methods remain unresolved.

Who May Find This Useful

This discussion may be of interest to those working with sensor data, particularly in fields involving motion analysis, signal processing, or numerical integration techniques.

Maria Redericki
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Hello everybody, apologies from outset for bad English.

I wonder if anyone can give me some advice regarding my problem. I have a sesnor that gives acceleration readings. I have been working hard to turn these readings into position or displacements. I tried many method but MATLAB cumptrapz was most effective. I integrated my data twice and got position

This has been quite successful but I have recently had some test data where by I know exactly the distance traveled because I was able to measure it at the time. I now see that displacement given by cumtrap is out by a small amount. How can I improve upon accuracy. I have looked at centering my velocity aound before carrying out the second integration i have also made sure of these things such as start at point where acceleration is zero and where velocity is zero but I still have some problems. Also I find to completely do these things is tricky so I have do it with some slight error. Can you advise for me some help?
Thank you
 
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What ever in the world is cumtrapz?

Just guessing that it might be a routine based on trapezoidal integration, you might us a better integration algorithm such as Simpson's rule.
 
Hello Doctor, This is a algoirthm on Mathlab based upon the trapezium rule as you suggest. I think everything around simpsons rule they have on there needs function and I just have discrete data? Do you think this will solve my problem of being a little out in terms of distance it is not by much but I want to correct
 
An acceleration sensor will always give lead to some errors - a small measurement error early on leads to a constant offset in the velocity, even with an impossible perfect integration scheme.

Is the deviation between estimated and measured distance getting worse over time?
 
Maia, it is hard to say what will correct your problem when I do not know ith certainty what is wrong.

Simpson's rule works (approximately) with both discrete and continuous data.

You can make up a test case, perhaps pure sinusoidal data, to check the calcs to see where the error is coming in.
 
Well when I examine the velocity I see that I have drift and it is quadratic. This makes me think that it could be causing error in the position data but I am not sure how to rectify this.
 

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