Laser Measurements Part 1

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' .

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

\begin{pmatrix} p_x \\ p_y \end{pmatrix} = H \begin{pmatrix} p_x' \\ p_y' \\ v_x' \\ v_y' \end{pmatrix}

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.)

SOLUTION:

D