Understanding MEMS Accelerometers: Converting and Integrating Data

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Discussion Overview

The discussion revolves around the conversion of accelerometer data from digital output to physical units, specifically focusing on the transition from acceleration to displacement. Participants explore the implications of integration in this context, addressing potential errors and assumptions involved in the process.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the units of displacement when converting accelerometer data, noting that the data is initially in bits and can be converted to gs or milli gs.
  • Another participant highlights the variability in outputs among different accelerometers and suggests checking the specific accelerometer's spec sheet for clarification.
  • A hypothetical scenario is presented where a digital accelerometer outputs a value of 256 decimal corresponding to 1g, raising questions about the implications of this conversion.
  • Concerns are raised about accumulating errors when integrating acceleration to obtain velocity and subsequently displacement, with a participant suggesting that using a displacement transducer may yield more accurate results.
  • One participant discusses the assumptions involved in converting counts to acceleration, noting that these assumptions may not hold true in practice, particularly regarding bias and non-linearity of accelerometers.
  • A participant acknowledges a missed multiplication factor of 9.8 in their calculations and seeks clarification on the resulting unit of displacement after integration.
  • Another participant advises converting counts directly to SI units to avoid complications with units, while also noting that issues related to dead reckoning remain problematic.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach to convert accelerometer data or the implications of integration, with multiple competing views and concerns about errors and assumptions remaining unresolved.

Contextual Notes

Participants mention various assumptions regarding the linearity of accelerometer outputs, the presence of bias, and the accuracy of spec sheets, indicating that these factors may complicate the conversion process and integration outcomes.

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I am bit confused on the units when you convert acceleration to displacement.

The accelerometer data is in bits. I can convert this to gs or milli gs.
When integrating, this will get multiplied by millisecs.

What will the displacement unit be in?
 
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Different accelerometers have different outputs. What does the spec sheet for your particular accelerometer say?
 
Let's assume the accelerometer has digital output and a value of 256 decimal is equal to 1g.
 
If you keep a continuous running total of the acceleration you will have velocity.
But there will be a zero velocity error and accumulating offset errors.

If you keep a continuous running total of the velocity total, you will have displacement.
But there will be a zero displacement error and accumulating errors.
Running totals are the equivalent of integration with unknown constants and so have square law errors.

If you want displacement you should measure it with a displacement transducer. You can then compute velocity and acceleration accurately from displacement. That involves differences and so will eliminate long term error accumulation. Differences are numerically stable.
 
Divide by 256 to get acceleration in gs, or divide my 256*9.80665 to get acceleration in SI units.

This simple division implicitly assumes three things, none of which is true. Dividing by 256 assumes that
  • A reported value of zero means zero acceleration.
    All (almost all) sensors have a bias. Accelerometers are no different in this regard.
  • The accelerometer output is linear.
    Linear sensors would be nice. Accelerometers oftentimes have a non-linearity to them.
  • That an output of 256 truly does mean 1g or (9.80665 m/s2).
    It would be so very nice if the spec sheet matched reality. It doesn't.
In a simple application you can ignore all these nuances. In more complex applications, the Kalman filter oftentimes incorporate bias, non-linearity, and scale factor error as a part of the state to be estimated by the filter.
 
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phew! I had completely missed multiplication by 9.8.

What about the unit of displacement?
While integrating, if the accn is multiplied by millisecs, velocity will be in m/millisec and displacement will be in mm. correct?
 
Convert those counts to SI units rather than gs and your unit-based headaches will go away.

Your dead reckoning headaches won't.
 

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