Noise modeling with Markov modeling

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Discussion Overview

The discussion revolves around modeling noise in sensor data using a first-order Markov process, particularly in the context of replacing GPS with accelerometer and gyroscope measurements. Participants explore the implications of using Markov processes in noise modeling and their integration with Kalman filters.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant describes their approach of using a first-order Markov process to model noise and seeks guidance on determining the correlation value "P."
  • Another participant suggests that noise is typically modeled as a stationary process rather than a Markov process.
  • A question is raised about the Gauss-Markov process and its relevance to the discussion.
  • It is noted that a noise process generally has a mean of 0, while a Markov process's mean is influenced by the last known sample.
  • A participant mentions that the Gauss-Markov process yields good results but questions the necessity of using a Kalman filter for estimating position errors instead of directly integrating the Gauss-Markov sequence.
  • One participant expresses their inability to answer specific questions related to the process or Kalman filters due to lack of experience.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of modeling noise as a Markov process versus a stationary process, indicating a lack of consensus on the best approach. Questions remain regarding the integration of the Gauss-Markov process with Kalman filters.

Contextual Notes

There are unresolved questions regarding the determination of the correlation value "P" and the specific characteristics of the noise process being modeled. The discussion does not clarify the assumptions underlying the use of Markov processes in this context.

ramesses
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Hi
I'm using accelerometer & horizontal gyroscope in order to replace GPS. Now, I'want to model the noise with first order markov process, to use it in kalman filter.
I recorded measurement on all axes and computed auto-correlation.
This picture represents auto-correlation on one of axes.
http://picpaste.com/pics/autocorrelation_x-qjpnbYJk.1437477728.png

Now, I know that the first order markov process takes the following equation :
w = white noise which has the same variance.
and P is the correlation

My problem is how to fix the value of "P" (know as correlation) ?
thank you
 
Last edited by a moderator:
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Noise is usually modeled as a stationary process, not a Markov process.
 
Gauss-Markov process ?
 
In general, a noise process has a mean of 0. A Markov process has a mean, at a given time, the value at the last known sample.
 
The Gauss-Markov process gives a good result as you see in this picture.
Now, I don't understand why I need to use kalman filter in-order to estimate the position's error ?
why we don't integrate directly the Gauss-Markov sequence ?
2A5Bmqzc2uO9.png
 
Sorry - Ican't answer your specific questions. I have not worked with the specific process or Kalman filters.
 

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