09. State Prediction

State Prediction

The State Transition Matrix

\begin{pmatrix} p_x' \\\ p_y' \\\ v_x' \\\ v_y' \\\ \end{pmatrix} = \begin{pmatrix} 1 & 0 & \Delta t & 0 \\\ 0 & 1 & 0 & \Delta t \\\ 0 & 0 & 1 & 0 \\\ 0 & 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} p_x \\\ p_y \\\ v_x \\\ v_y \end{pmatrix} + \begin{pmatrix} \nu_{px} \\\\ \nu_{py} \\\\ \nu_{vx} \\\\ \nu_{vy} \end{pmatrix}

As a reminder, the above equation is x' = Fx + noise

Motion noise and process noise refer to the same case: uncertainty in the object's position when predicting location. The model assumes velocity is constant between time intervals, but in reality we know that an object's velocity can change due to acceleration. The model includes this uncertainty via the process noise.

Measurement noise refers to uncertainty in sensor measurements, which will be discussed in more detail later.

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Suppose you have a pedestrian state X. I want you to compare two scenarios: in the first predict the state 0.1s into the future and in the second 5s into the future. Which of these two scenarios leads to a higher uncertainty? In answering this, consider whether or not random noise has an increasing effect with increasing gaps between prediction times.

SOLUTION: A time difference of 5s leads to a higher uncertainty.

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Let's say we use our linear motion model with fixed time increments, but the pedestrian is randomly changing her velocity (accelerating), sometimes speeding up, slowing down or changing direction. However, the overall mean change is zero. This introduces a noise in the tracking process - what kind of noise is it?

SOLUTION: Process noise

From the examples I’ve just showed you we can clearly see that the process noise depends on both: the elapsed time and the uncertainty of acceleration. So, how can we model the process noise by considering both of these factors? Keep going to find out :)

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