# Covariance Matrix of various $x,y,z$ (cartesian coordinates)

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.

How can I get a covariance matrix?

EDIT1:

What I have tried so far?

I know the formulae

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

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

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

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

• @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. – orange14 Aug 2 '14 at 10:16
• Excellent. Don't worry about it now (since you're new) but here's a MathJax tutorial for formatting future questions, answers, comments, etc. :) – Shaun Aug 2 '14 at 11:01
• @Shaun Can you please assist me on the question – orange14 Aug 2 '14 at 11:31
• 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 :) – 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 $Z$.
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.