Detection finds a target. Tracking keeps following it.
10.1 Sequential lobing
The simplest tracking: alternate the antenna beam between two slightly offset positions and compare the returns. If the target is centered between the two positions, returns are equal. If the target is off-axis toward position A, the A return is larger. The difference drives a servo to point the antenna at the target.
Slow (each measurement takes two pulses) and vulnerable to amplitude fluctuations of the target. Used in 1940s fire-control radars. Largely obsolete now.
10.2 Conical scan
The feed of the dish is offset slightly and rotated around the axis at, say, 30 Hz, so the beam scribes a cone in space. If the target sits exactly on the cone's axis, the return amplitude is constant. If the target is off-axis, the return is modulated at 30 Hz, with phase that indicates direction.
Conical scan was widely used in the 1950s and 60s. Its weakness: an enemy can radiate a signal at the scan frequency to confuse the tracker into pointing at a phantom location. This is conical-scan jamming, a classic countermeasure.
10.3 Monopulse: the modern standard
A monopulse tracker generates pointing information from a single pulse. The antenna has multiple feeds; sum and difference channels are formed in real time. With four feeds A, B, C, D arranged in a 2x2 pattern, the radar computes:
- (sum, the conventional beam)
- (azimuth difference)
- (elevation difference)
The ratio in each axis gives the angular error of the target from boresight. One pulse, one measurement, in two axes simultaneously.
Monopulse defeats conical-scan-style jamming because there is no scanning to lock onto. Almost every fire-control and missile-seeker radar built since 1965 is monopulse. Patriot, AMRAAM, modern naval AAW systems, and the Aegis tracker all use monopulse.
10.4 Range tracking with split gates
The radar's range tracker maintains two "gates" of 50% overlap centered on the target's predicted position. If the target is centered, returns into the early and late gates are equal. If the target is closer, the early gate fills more; if farther, the late gate fills more. The difference drives the gate to follow the target.
A leading-edge tracker uses only the leading edge of the return (the earliest part), making it harder for a deceptive jammer to "pull" the tracker by gradually delaying its repeated false echoes.
10.5 Track-while-scan and Kalman filters
Modern radars do track-while-scan: the antenna keeps scanning for new targets while the signal processor maintains tracks for confirmed targets, updated each time the beam revisits them. A tracker fits a smoothed trajectory through the noisy measurements.
The mathematical workhorse is the Kalman filter, which propagates a state estimate (position, velocity, acceleration) and its covariance forward in time using a motion model, then updates with each new measurement, weighting prediction and measurement by their relative uncertainties. The filter naturally handles missed detections (skip the update), unequal time intervals, and changing motion models.
Kalman filter loop (one tracker, one target):
┌──────────────────┐
│ Predict state │←───────────┐
│ x⁻ = F x⁺ │ │
│ P⁻ = F P⁺ Fᵀ + Q │ │
└────────┬─────────┘ │
│ │
┌────────┴─────────┐ │
│ Wait for new │ │
│ measurement z │ │
└────────┬─────────┘ │
│ │
┌────────┴─────────┐ │
│ Innovation │ │
│ y = z - H x⁻ │ │
│ S = H P⁻ Hᵀ + R │ │
│ K = P⁻ Hᵀ S⁻¹ │ │ every PRI or
│ x⁺ = x⁻ + K y │ │ every revisit
│ P⁺ = (I-KH) P⁻ │ │
└────────┬─────────┘ │
│ │
└──────────────────────┘A real radar runs hundreds of such trackers in parallel, one per confirmed target, plus a separate detection processor watching for new tracks to spawn.