Answer L8-C3

** Here are the correct answers to this question:

* Answer A "Yes, because …" is NOT correct.
* Answer B "No, because …" is correct.

** Explanation

The question is about the values used in the covariance matrix for the correction part of a Kalman filter, based on the measurement of the pose of a destop robot using an overhead camera. On the right there is an illustration of a Thymio robot with a code on its top to be detetcted by a camera. The question is: "In a 2x2 m2 setup, you estimate the pose (cartesian coordinates in mm and angle in rad) of the Thymio robot by using a Kalman filter based on the odometry and the vision of a high resolution camera (2000x2000 pixels) looking from the top and extracting the position and orientation of a marker. With this vision approach you can have a resolution of 1mm in position and 1 degree in angle. In the Kalman filter, as covariance matrix related to the measurement by the camera, your colleague uses an identity matrix. Does this make sense?". 

Here the main issue is the value of the diagonal of the covariance in relationship with the units that should be mm^2 and rad^2. It is not realistic to have a covariance component of 1 on an angle in radians. 

Two statements are proposed:

* Statement A. "Yes, because …" is wrong. It is not realistic to have a covariance component of 1 on an angle in radians.
In the explanation of the student we would like to see that they understand the diagonal covariance matrix means that there is a variance of 1mm^2 on both coordinates, which could be reasonable, and a variance of 1rad^2 on the angle, which is really too much.

Statement B. "No, because …" is correct. It is not realistic to have a covariance component of 1 on an angle in radians.
In the explanation of the student we would like to see that they understand the diagonal covariance matrix means that there is a variance of 1mm^2 on both coordinates, which could be reasonable, and a variance of 1rad^2 on the angle, which is really too much.