I have around 1000 values of gps receiver positions as follows: I have to calculate the covariance matrix with all these values.

All of the following values represent a SINGLE POINT.

First few values

How can I get a covariance matrix?


What I have tried so far?

I know the formulae covariance matrix

Then I decided to find $\operatorname{Var}(Y)$ and $\operatorname{Cov}(X,Y)$

I know $\operatorname{Cov}(X,Y)$ formulae is this:

enter image description here

and $\operatorname{Var}(Y)$ I am trying to find using the following formulae: enter image description here

Do you think this is the correct way to go? Do I need additional values to compute this.

  • 1
    $\begingroup$ @Shaun I have edited the doc to show where I am standing right now. I am confused and I only have x,y,z cooridnate data. And I have to computer covariance matrix. $\endgroup$ – orange14 Aug 2 '14 at 10:16
  • $\begingroup$ Excellent. Don't worry about it now (since you're new) but here's a MathJax tutorial for formatting future questions, answers, comments, etc. :) $\endgroup$ – Shaun Aug 2 '14 at 11:01
  • $\begingroup$ @Shaun Can you please assist me on the question $\endgroup$ – orange14 Aug 2 '14 at 11:31
  • $\begingroup$ I'm afraid I can't. I'm not trained in Statistics enough to assist you without spending more time than I have available. I'm sorry. I just thought I'd help get used to the site :) $\endgroup$ – Shaun Aug 2 '14 at 11:38

What you wrote is the covariance matrix of the random variables $X$, $Y$ and $Z$, where the random variables $X$, $Y$ and $Z$ represent the stochastic processes that can produce the data you have collected. In your case they are the 3 coordinate positions recorded by the gps. The finite amount of data you have stored is a sampling of the population of all possible outcomes of the random variables $X$, $Y$ and $Z$.

As you are dealing with a sampling (of about 1000 observations per coordinate/ random variable), then you should consider the sample covariance matrix, instead.

The number $N$ is the number of coordinate observations: in your case about 1000. Any statistical software is able to compute the sample covariance matrix.

  • $\begingroup$ Can you please give me an example of statistical software which can compute covariance matrix. $\endgroup$ – orange14 Aug 3 '14 at 0:22
  • $\begingroup$ R, Matlab, SPSS and even Excel $\endgroup$ – Avitus Aug 3 '14 at 9:44

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