Tracking¶

Code: radarsim/tracking/tracker.py, kalman.py, ekf.py, monopulse.py.

The engine feeds every detection, converted from measured range, azimuth and elevation to a position on the ground plane, to a track-while-scan tracker.

Filter¶

Each track is a constant-velocity Kalman filter on \([x, y, \dot x, \dot y]\) with continuous white-noise acceleration (Bar-Shalom, Li & Kirubarajan 2001, §6.2.2):

\[ Q(\Delta t) = q\begin{bmatrix} \Delta t^3/3 & \Delta t^2/2 \\ \Delta t^2/2 & \Delta t \end{bmatrix} \otimes I_2, \qquad q = \sigma_a^2 \cdot 1\,\mathrm{s}. \]

Unlike the discrete-step variant, the covariance added over a revisit interval does not depend on how many simulation steps it is split into. The default \(\sigma_a\) = 10 m/s² suits transport aircraft; close_air_combat raises it to 40 m/s² to hold a 4.7 g turn. An extended Kalman filter with polar measurements and SNR-dependent noise is available through TrackManager.set_ekf_mode.

Association¶

Detections are assigned to tracks by global nearest neighbour (Hungarian algorithm) with a χ² gate at 99.73 % on the normalised innovation squared. A track with only one detection has no velocity yet, so it uses a velocity gate instead, \(|z_2 - z_1| \le v_{max}\,\Delta t + 3\sqrt{2}\,\sigma_z\), and on the second hit is initialised by two-point differencing (velocity from the two positions, covariance from the measurement noise).

Life cycle¶

tentative after the first detection; dropped after two misses;
confirmed after three consecutive hits (configurable);
coasting after a miss, back to confirmed on the next hit;
lost after three misses, or when it has not been updated for 3.5 revisit periods (a target that left a sector scan for good).

A miss is only charged when the beam actually looked at the track's predicted position in that step and the track has not already been updated during the current scan, so tracks between beam passes simply coast.

Monopulse¶

With Monopulse on, angles come from an amplitude-comparison estimator instead of fixed angle noise. Two Gaussian beams squinted by \(\pm\theta_s\) give

\[ \varepsilon(\theta) = \frac{\Delta}{\Sigma} = \tanh\!\left(\frac{4\ln 2\,\theta\,\theta_s}{\theta_3^2}\right), \qquad k_m = \frac{4\ln 2\,\theta_s}{\theta_3}, \]

linear near boresight and saturating off axis. Thermal noise gives the accuracy \(\sigma_\theta = \theta_3 / (k_m\sqrt{2\,\mathrm{SNR}})\) (Barton 2005), applied to \(\varepsilon\) before inversion.

Validity¶

Single-model filters only (no IMM); hard manoeuvres need a larger \(\sigma_a\).
Tracks are two-dimensional; altitude is not estimated.