Laser Measurements Part 2

H Matrix Quiz Explanation

H = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix}

In order to obtain our measurement (x and y) we need to determine the H matrix. (x and y) is found by multiplying H with the state vector.

So let’s find out first what is the dimension of our H matrix. Here we have a 2 by 1 matrix, and that came from our m by n H matrix times the four row and one column matrix. Now, from the matrix multiplication we know that the number of columns of the first matrix should be equal with the number of rows of a second matrix, which is 4. And also the number of rows of the first matrix is the same with the number of rows of the result matrix, which is 2. So our H is a matrix of 2 rows and 4 columns. And finally we put ones and zeroes so that the px and py coordinates are propagated to the result Z.

Measurement Noise Covariance Matrix R

Now, let's take a look at the covariance matrix, R, which represents the uncertainty in our sensor measurements. The dimensions of the R matrix is square and each side of its matrix is the same length as the number of measurements parameters. Before diving into the details, let's have a quick quiz to test your intuition about what this matrix might look like for the laser sensor.

SOLUTION:

2 rows by 2 columns

Next Concept