# Variance of the position noise

1. Jan 11, 2009

### ArixII

Hi,
I read an article in Kalman filtering. There is an example in introductory Mechanics. I just can not understand which formula for calculating the variance and covariance is used. The example is about a vehicle that is traveling straight on the road:

The postition is measured with an error of 10 feet (one standard deviation)
The command acceleration is a constant 1 foot/sec^2
The acceleration noise is 0.2 feet/sec^2 (one standard deviation)
The position is measured 10 times per second.

Since the position is proportional to 0.0005 times the acceleration, and the acceleration noise is 0.2 feet/sec^2, the variance of the position noise is (0.005)^2 * (0.2)^2 = 10^(-6)
...

[and what formula is used to calculate this? ]

[author continues]
...Similarly, since the velocity is proportional to 0.1 times the acceleration, the variance of the velocity noise is (0.1)^2 * (0.2)^2 = 4 * 10^(-4). Finally, the covariance of the position noise and velocity noise is equal to the standard deviation of the position noise times the standard deviation of the velocity noise, which can be calculated as (0.005 * 0.2) * (0.1 * 0.2) = 2 * 10^(-5).
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Well I know that:
cov(X,Y) = E[(X - mu_x) * (Y - mu_y)]
but this is not what he used, right? does somebody knows the formulas used in such calculations?

Thank you!