Noise modeling with Markov modeling

In summary, the conversation discusses using an accelerometer and horizontal gyroscope to replace GPS, and modeling noise with a first order Markov process for use in a Kalman filter. The individual has recorded measurements and computed auto-correlation, but is unsure of how to fix the value of "P" (correlation). They also mention the use of a Gauss-Markov process and question the need for a Kalman filter to estimate position error.
  • #1
ramesses
17
0
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
 
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  • #2
Noise is usually modeled as a stationary process, not a Markov process.
 
  • #3
Gauss-Markov process ?
 
  • #4
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.
 
  • #5
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
 
  • #6
Sorry - Ican't answer your specific questions. I have not worked with the specific process or Kalman filters.
 

1. What is noise modeling with Markov modeling?

Noise modeling with Markov modeling is a statistical approach used to analyze and predict the behavior of complex systems that involve random or unpredictable events. It involves creating a mathematical model based on the Markov process, which is a type of stochastic process that uses probability to describe changes in a system over time.

2. How does Markov modeling help with noise modeling?

Markov modeling is useful for noise modeling because it allows us to account for the random and unpredictable nature of noise in a system. By using mathematical equations and probability calculations, we can better understand and predict how noise will affect a system over time.

3. What are the steps involved in noise modeling with Markov modeling?

The first step is to identify the system and the sources of noise. Then, data is collected and analyzed to determine the patterns and characteristics of the noise. Next, a Markov model is created based on this data, and simulations are run to predict the behavior of the system with different levels and types of noise. Finally, the results are compared to real-world observations to validate the model.

4. What are the limitations of noise modeling with Markov modeling?

One limitation is that Markov models assume that the system is in a steady state, meaning that the probabilities of events occurring do not change over time. This may not always be the case in real-world systems. Additionally, the accuracy of the model depends on the quality and quantity of data used to create it.

5. How is noise modeling with Markov modeling used in practical applications?

Noise modeling with Markov modeling has various practical applications, such as predicting stock market trends, weather forecasting, and analyzing the performance of communication networks. It is also commonly used in engineering and industrial settings to optimize system performance and reduce the impact of noise on operations.

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