Linear Systems Homework Assignment 6
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
µx = [12,33]T (1)
and its covariance is Cx = [1 2; 1 1] (2)
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.
PLOT THIS FOR PROBLEM #1
Fig. 1. Covariance estimation error and Kalman filtering
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