Kalman Filters & accelerometers - linear vs extended, what do I need?

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SUMMARY

The discussion centers on integrating accelerometer data with an extended Kalman filter (EKF) to accurately model displacement and velocity curves over short time spans, particularly in response to impact forces. The user expresses concerns about drift and error amplification in accelerometer readings and aims to validate these against data from a Linear Variable Differential Transformer (LVDT). The proposed method involves combining outputs from both the accelerometer and LVDT through EKF to derive a reliable displacement curve over time.

PREREQUISITES
  • Understanding of Kalman Filters, specifically linear and extended Kalman filters.
  • Familiarity with accelerometer data processing and integration techniques.
  • Knowledge of Linear Variable Differential Transformers (LVDT) and their application in displacement measurement.
  • Basic principles of signal processing and error analysis in sensor data.
NEXT STEPS
  • Research the implementation of Extended Kalman Filters (EKF) in sensor fusion applications.
  • Study the mathematical foundations of double integration in motion tracking.
  • Explore techniques for minimizing drift in accelerometer readings.
  • Investigate best practices for validating sensor data against reference measurements like those from LVDTs.
USEFUL FOR

Engineers, data scientists, and researchers involved in motion tracking, sensor fusion, and displacement measurement, particularly those working with accelerometers and Kalman filtering techniques.

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Hello,
I have a problem for work where I am attempting to integrate (a single) accelerometer readout in order to gain insight into the resulting velocity and position curves with respect to time. From experience I know this is a tricky task due to drift and error being amplified when integrated.

Just some background: displacement of our subject will most likely occur over a short time span - millisecond scale due to an impact force during the test. A http://en.wikipedia.org/wiki/LVDT" will also be implemented during the test in an attempt to directly measure displacement with time. However, I believe this data will be erroneous and spotty at best due to the high sample rates involved (possibly tens of khz) Worst case, the LVDT will give us a very accurate total displacement value with which we can check our accelerometer against.

Based on my reading and intermediate understanding of the linear Kalman filter, I am suspecting that I will require an extended Kalman filter (EKF) in order to model the nonlinear accelerometer data and LVDT displacement curve.

Since both of these tools can eventually measure the same thing (displacement) it is my thinking that their results can be combined and filtered to eventually wind up with a displacement curve w.r.t time that agrees with the total displacement measured by the LVDT. Please see this flow chart:

[Accelerometer data] + [EKF] -> [Double integration] --> [Displacement curve 1]

[LVDT] + [EKF] --> [Displacement curve 2]

EKF {[Displacement curve 1] + [Displacement curve 2]} --> [Most trustworthy displacement curve]

I want to figure out from those with more experience if this is feasible and if I am on the right track..? Thank you for reading and I appreciate any tips/criticism or suggested reading you may offer.
 
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