models

Tracking models can be chosen from the ros parameter ~tracking_model:

Each model has its own parameters, which can be set in the ros parameter server.

• model name
  • parameter name for general
  • override parameter name for each tracking object class

linear constant acceleration model

• prediction

\[ \begin{bmatrix} x_{k+1} \\ y_{k+1} \\ v_{x_{k+1}} \\ v_{y_{k+1}} \\ a_{x_{k+1}} \\ a_{y_{k+1}} \end{bmatrix} = \begin{bmatrix} 1 & 0 & dt & 0 & \frac{1}{2}dt^2 & 0 \\ 0 & 1 & 0 & dt & 0 & \frac{1}{2}dt^2 \\ 0 & 0 & 1 & 0 & dt & 0 \\ 0 & 0 & 0 & 1 & 0 & dt \\ 0 & 0 & 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} x_k \\ y_k \\ v_{x_k} \\ v_{y_k} \\ a_{x_k} \\ a_{y_k} \end{bmatrix} + noise \]

• noise model

  • random walk in acc: 2 parameters(currently disabled)
  • random state noise: 6 parameters $$\begin{align} noise &= \begin{bmatrix} \frac{dt^{3}}{6} \\ 0\\ \frac{dt^{2}}{2} \\ 0 \\ dt \\0 \end{bmatrix} \nu_{ax_k} + \begin{bmatrix} 0 \\ \frac{dt^{3}}{6} \\ 0 \\ \frac{dt^{2}}{2} \\ 0 \\ dt \end{bmatrix} \nu_{ay_k} & \text{(random walk in acc)} \\ noise &= \begin{bmatrix} \nu_{x_k} \\ \nu_{y_k} \\ \nu_{v_{x_k}} \\ \nu_{v_{y_k}} \\ \nu_{a_{x_k}} \\ \nu_{a_{y_k}} \end{bmatrix} & \text{(random state noise)} & \end{align}$$

• observation
  • observation: x,y,vx,vy
  • observation noise: 4 parameters

constant turn rate and velocity model

Just idea, not implemented yet.

\[ \begin{align} x_{k+1} &= x_k + \frac{v_k}{\omega_k} (sin(\theta_k + \omega_k dt) - sin(\theta_k)) \\ y_{k+1} &= y_k + \frac{v_k}{\omega_k} (cos(\theta_k) - cos(\theta_k + \omega_k dt)) \\ v_{k+1} &= v_k \\ \theta_{k+1} &= \theta_k + \omega_k dt \\ \omega_{k+1} &= \omega_k \end{align} \]