11. Laser Measurements Part 1

Variable Definitions

To reinforce was what discussed in the video, here is an explanation of what each variable represents:

• z is the measurement vector. For a lidar sensor, the $z$ vector contains the $position-x$ and $position-y$ measurements.
• ** H** is the matrix that projects your belief about the object's current state into the measurement space of the sensor. For lidar, this is a fancy way of saying that we discard velocity information from the state variable since the lidar sensor only measures position: The state vector $x$ contains information about $[p_x, p_y, v_x, v_y]$ whereas the $z$ vector will only contain $[px, py]$ . Multiplying Hx allows us to compare x, our belief, with z, the sensor measurement.
• What does the prime notation in the $x$ vector represent? The prime notation like $p_x'$ means you have already done the prediction step but have not done the measurement step yet. In other words, the object was at $p_x$ . After time $\Delta{t}$ , you calculate where you believe the object will be based on the motion model and get $p_x'$ .

H Matrix Quiz

Find the right $H$ matrix to project from a 4D state to a 2D observation space, as follows:

Here are your options:

A. $H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$

B. $H = \begin{pmatrix} 1 & 0 \\ 0 & 1 \\ 0 & 0 \\ 0 & 0 \end{pmatrix}$

C. $H = \begin{pmatrix} 1 & 1 \end{pmatrix}$

D. $H = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \end{pmatrix}$

(Hint: first consider the matrix dimensions, then try to use a 0 or 1 to correctly project the components into the measurement space.)

Select the correct H matrix given the projection above.

A

B

C

D

SOLUTION:

D