"The filter was chosen as an EKF for simplicity (and it seemed to work fine).\n",
"\n",
"##### **Initialization**\n",
"The tracks were initialized at the measurement (converted to the positional domain) with a $0$ velocity. The initial uncertainty was set to $\\mathbf{P}_0=\\mathsc{diag}[100, 100, 1000, 1000]$ to account for the unknown initial velocity. The track score is initially set to $L_t=0$.\n"
"The tracks were initialized at the measurement (converted to the positional domain) with a $0$ velocity. The initial uncertainty was set to $\\mathbf{P}_0=\\mathrm{diag}[100, 100, 1000, 1000]$ to account for the unknown initial velocity. The track score is initially set to $L_t=0$.\n"
]
},
{
...
...
@@ -337,6 +339,17 @@
"#### Comments\n",
"Both the GNN and JPDA manage to keep both tracks the entire time. The GNN results in two \"U\"-shaped tracks whereas the JPDA results in \"S\"-shaped tracks. Without more information, it is impossible to say which is correct. However, the JPDA tracker results in a smoother trajectory, probably because of the soft measurement assignments."
A GNN tracker and a JPDA tracker were implemented, see src.trackers. The model setup is as follows
##### **Sensor Model**
The sensor model is the standard distance and bearing radar with $\mathbf{R}=\mathrm{diag}[10, 0.001]^2$. The probability of detection is set to $P_D=0.9$.
##### **Gating**
Mahalanobis gating is used with $\gamma=9.2$.
##### **Clutter Model**
The volume is rectangular with $0\leq x\leq 2500$ and $0\leq y\leq2000$. Further, $\beta_{FA}V=2$.
##### **Track Logic**
A score-based track logic was used with an exponential forgetting factor to avoid integrator wind-up. The forgetting factor was tuned to $\lambda=0.6$. The new target rate $\beta_{NT}=\beta_{FA}$. Further, the probability of confirming false tracks $P_{FC}0.1\%$ and the probability of rejecting true tracks is $P_{TM}=1\%$.
##### **Motion Model**
The motion model is chosen as a CV model with $\mathbf{Q}=10\mathbf{I}$ which yielded good tracking performance for both GNN and JPDA.
##### **Filter**
The filter was chosen as an EKF for simplicity (and it seemed to work fine).
##### **Initialization**
The tracks were initialized at the measurement (converted to the positional domain) with a $0$ velocity. The initial uncertainty was set to $\mathbf{P}_0=\mathsc{diag}[10, 10, 100, 100]$ to account for the unknown initial velocity. The track score is initially set to $L_t=0$.
Both the GNN and JPDA capture all four tracks good. The GNN has a slightly lower RMSE overall which seems reasonable given the "low" clutter rate and only a few track cross-overs.
A GNN and a JPDA tracker were applied to the mysterious data set. The design choices are listed below.
##### **Sensor Model**
The sensor model is the standard distance and bearing radar as before with the same noise parameters. The probability of detection was set to $P_D=0.9$.
##### **Gating**
Mahalanobis gating was used with $\gamma=9.2$.
##### **Clutter Model**
The tracking volume was established by inspecting the measurement data in the positional domain. The volume is rectangular with $-2000\leq x\leq 2000$ and $-21000\leq y\leq-17000$. As before $\beta_{FA}V=2$.
##### **Track Logic**
A score-based track logic was used with an exponential forgetting factor to avoid integrator wind-up. The forgetting factor was tuned to $\lambda=0.95$. The new target rate $\beta_{NT}=\beta_{FA}$. Further, the probability of confirming false tracks $P_{FC}0.1\%$ and the probability of rejecting true tracks is $P_{TM}=1\%$.
##### **Motion Model**
After inspection of the measurement data in the positional domain, a CV model was chosen as the motion model. The process noise was tuned to $\mathbf{Q}=5e4\mathbf{I}$ which yielded good tracking performance for both GNN and JPDA.
##### **Filter**
The filter was chosen as an EKF for simplicity (and it seemed to work fine).
##### **Initialization**
The tracks were initialized at the measurement (converted to the positional domain) with a $0$ velocity. The initial uncertainty was set to $\mathbf{P}_0=\mathsc{diag}[100, 100, 1000, 1000]$ to account for the unknown initial velocity. The track score is initially set to $L_t=0$.
The tracks were initialized at the measurement (converted to the positional domain) with a $0$ velocity. The initial uncertainty was set to $\mathbf{P}_0=\mathrm{diag}[100, 100, 1000, 1000]$ to account for the unknown initial velocity. The track score is initially set to $L_t=0$.
Both the GNN and JPDA manage to keep both tracks the entire time. The GNN results in two "U"-shaped tracks whereas the JPDA results in "S"-shaped tracks. Without more information, it is impossible to say which is correct. However, the JPDA tracker results in a smoother trajectory, probably because of the soft measurement assignments.
