Problem 1

Figure 1-left a Monte Carlo simulation of a random variable and its error ellipse.

- From the error ellipse shown in Figure 1a, what is the mean value? Give an approximate value.
- Plot the data points and the error ellipse knowing that the mean value of a random Guassian variable is
*µ*= [12_{x }*,*33](1)^{T }and its covariance is

*C*= [1 2; 1 1] (2)_{x }You can use Matlab function randn of other functions. Questions 1) and 2) do not necessarily refer to the same variable.

- Another variable is define as
*y*=*Ax*(3) - Plot the data points and the error ellipse of
*y*. Is*y*Gaussian? - Find the variance and mean of
*y*using the data points. - Find the variance and mean of
*y*using the error propagation equation. Compare with previous question.

Fig. 1. Covariance estimation error and Kalman filtering

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