Radar_tracker - Wikiparency

# Radar tracker A **radar tracker** is a component of a radar system, or of a command-and-control system built around one, that associates consecutive detections, or plots, of the same object into a continuous track rather than leaving every scan's detections as unrelated points. It becomes essential the moment a system reports several targets at once or draws plots from more than one radar or sensor, since deciding which plot belongs to which object, and smoothing the noisy sequence that results into a stable estimate of position and velocity, is a separate problem from detecting a target in the first place. A microsim companion in three.js, a variant of the Kalman-filter sketch, renders exactly this problem: a single track carried across a run of scans in which some of the expected measurements simply fail to arrive. A tracker's output is what supports scan modes such as track-while-scan, in which a [[Radar|radar]] continues to search a volume while still keeping every established track alive between the looks that renew it. ## Role of the radar tracker Without a tracker, each scan produces a fresh, disconnected set of plots, and nothing links this scan's return near a given point to the previous scan's return nearby: two separate detections of the same aircraft look identical to two detections of two different aircraft flying close together. A tracker resolves that ambiguity by carrying forward an expectation of where an established target should appear next and comparing new plots against that expectation, which is also what lets a system report a target's velocity and heading rather than only its instantaneous position, since velocity is only ever visible across more than one measurement. The role grows further in a data-fusion setting, where a track may be built from a mix of primary radar returns, an aircraft's own replies to [[Secondary_surveillance_radar|secondary surveillance radar]] interrogation, or reports handed over from an entirely different sensor or site; the tracker is the component that decides whether all of these separate reports describe one object or several. ## General approach Almost every radar tracker runs the same cycle on each new batch of plots: predict where each existing track should be by the time of the new scan, associate the fresh plots with those predictions, update each matched track's state with the plot it was given, and maintain the population of tracks by confirming, coasting or deleting them as the evidence warrants. The predict step uses a motion model, commonly constant velocity or constant acceleration over one scan interval, to project a track's position forward and to grow its uncertainty appropriately, since more time between looks means less confidence in exactly where the target has gone. The update step then folds a matched plot back into the estimate, shrinking the uncertainty the prediction step grew. This cycle repeats indefinitely, and its steady operation, more than any single equation inside it, is what a radar tracker actually delivers. ## Plot to track association Association decides which, if any, of the current scan's plots belongs to which existing track, and it starts by drawing a validation gate around each track's predicted position, sized from the track's own predicted uncertainty so that a genuine measurement falls inside it with high probability while unrelated plots mostly fall outside. A tighter gate, available to a system with better angular accuracy such as a [[Monopulse_radar|monopulse]] antenna, rejects more clutter and more of a nearby second target's plots at the cost of occasionally excluding a genuine but unusually noisy measurement. The plots offered to a tracker may come from a simple threshold detector or from a [[Pulse-Doppler_radar|pulse-Doppler]] system whose own measured Doppler shift narrows the gate further by ruling out any candidate whose radial velocity does not match. The simplest rule assigns the single nearest plot inside the gate to the track, but nearest-neighbour assignment fails visibly when two tracks' gates overlap or when more than one plot falls in a single gate, which is common near a real target embedded in residual [[Clutter_(radar)|clutter]] or close to another track. More careful schemes weigh every plot in the gate by a [[Probability_density_function|probability density]] centred on the prediction rather than committing to the closest one outright, folding the position of every candidate plot into the update in proportion to how likely it is to be the real return. ## Track initiation A track cannot be trusted the moment a single plot suggests one, since an isolated plot is exactly what a strong clutter residual or a random noise excursion also looks like; initiation logic instead holds a candidate as tentative until a run of scans confirms it, typically requiring detections in some minimum number of looks out of a slightly larger window before the track is promoted to confirmed and released to the tracker's normal maintenance cycle. Raising that confirmation bar cuts down on tracks started from noise or from a [[Constant_false_alarm_rate|constant-false-alarm-rate]] detector's residual false alarms, at the cost of a slightly slower reaction to a genuinely new target entering the coverage volume, so the initiation threshold is itself a tuned trade between false tracks and a track's time to first confirmation. ## Track maintenance An established track is rarely fed a clean, unbroken stream of matching plots. A target can fade below the detection threshold for a scan or two, sit briefly behind terrain or another obstruction, or simply fall outside the beam for an interval, and a well-built tracker coasts through a limited run of missed detections by continuing to predict the track forward on its motion model alone rather than deleting it at the first gap; the delay-and-dropout behaviour a real system must tolerate is exactly what this article's three.js companion renders. Coasting cannot continue indefinitely, since a track with no fresh measurements is only ever a prediction whose uncertainty keeps growing, so maintenance logic also tracks a quality score or a consecutive-miss count and deletes a track once it falls too far below confidence to be worth carrying. Real dropouts have real causes beyond a simple fade: [[Multipath_propagation|multipath]] near the ground, a deep [[Radar_cross_section|radar cross-section]] null at a particular aspect angle, or a scan cycle too slow to keep pace with a fast manoeuvre can all interrupt the plot stream a tracker was otherwise built to expect. ## Track smoothing Track smoothing is the part of the cycle that turns a noisy sequence of associated plots into a stable estimate of a target's state, and the algorithms used for it range from a fixed, hand-tuned rule to a fully adaptive statistical filter. ### Alpha-beta tracker The alpha-beta tracker updates a position-and-velocity estimate with two fixed gains, conventionally named α and β, applied to the difference between a new plot and the track's own prediction: position is corrected by a fraction α of that difference and velocity by a fraction β divided by the scan interval, with both gains chosen once at design time rather than recomputed from the data as the track runs.[^benedict62] Its appeal is computational cost low enough for the earliest tracking radars to run in real time, at the price of gains that are only ever a compromise, tuned for a particular mix of measurement noise and target manoeuvre rather than adapting when either one changes. ### Kalman filter The [[Kalman_filter|Kalman filter]], introduced by Rudolf Kálmán in 1960 as a recursive solution to linear filtering and prediction problems, replaces the alpha-beta tracker's fixed gains with a gain recomputed on every scan from the track's own predicted uncertainty and the measurement's known noise.[^kalman60] Because that gain, usually written K, shrinks automatically as a track's confidence grows and rises again after a manoeuvre inflates the uncertainty, a Kalman filter behaves like an alpha-beta tracker whose gains retune themselves continuously rather than sitting fixed at values chosen in advance, and for a linear motion model with Gaussian noise it is the statistically optimal choice of gain rather than merely a convenient one. ### Multiple hypothesis tracker (MHT) Rather than committing to a single association decision on each scan, a multiple hypothesis tracker carries forward several competing explanations of how the recent plots might belong to tracks, deferring a final commitment until later scans make one hypothesis clearly more probable than its rivals and allowing the rest to be pruned away.[^reid79] This costs considerably more computation than a single-hypothesis tracker, since the number of candidate hypotheses can grow quickly with the number of tracks and plots under consideration, but it copes far better with a dense, ambiguous scene in which the single most likely association on one scan is sometimes simply wrong. ### Random finite sets A random-finite-set tracker treats the entire population of targets, whose count is itself unknown and changes as targets appear and disappear, as a single set-valued random variable rather than as a fixed list of individually labelled tracks to be associated one by one, an approach formalised by Ronald Mahler through the probability hypothesis density filter.[^mahler03] Propagating and updating that set directly avoids making an explicit plot-to-track assignment at all, folding the association problem into the same recursive update that estimates the targets' states, at the cost of a considerably more demanding mathematical and computational framework than assigning plots to tracks one at a time. ### Interacting multiple model (IMM) An interacting multiple model tracker runs several motion models in parallel, typically a steady, constant-velocity model alongside one or more manoeuvring models, and blends their estimates according to probabilities that shift, scan by scan, toward whichever model has been predicting the recent plots best.[^blom88] This lets a single tracker follow a target that cruises for long stretches and then turns sharply without needing either a sluggish, heavily smoothed filter that struggles through the turn or a noisy, lightly smoothed one that jitters during the cruise, a mixing idea related to the switching linear systems studied more generally in [[Control_theory|control theory]]. ## Nonlinear tracking algorithms A Kalman filter is exact only when the motion model and the measurement model are both linear functions of the state, and a radar tracker routinely violates the second condition even when the first is a reasonable approximation, since range and bearing are [[Nonlinear_system|nonlinear]] functions of a target's Cartesian position. Several extensions handle that nonlinearity without giving up the basic predict-update structure that makes recursive tracking practical in real time. ### Extended Kalman filter (EKF) The extended Kalman filter linearises the nonlinear motion or measurement function afresh at every scan, computing a local slope, or Jacobian, around the current estimate and running the ordinary linear Kalman recursion on that local approximation; the technique reached practical maturity in the 1960s as part of the effort to fly the Apollo missions' onboard navigation on hardware with only a fraction of a modern tracker's computing power.[^mcgee85] It is inexpensive and often adequate when the estimate stays close to the true state, but the linearisation can drift badly out of step with reality when a target manoeuvres hard enough that the local slope taken at the last update no longer describes its motion well. ### Unscented Kalman filter (UKF) The unscented Kalman filter avoids linearising anything at all, instead passing a small, deterministically chosen set of sample points, called sigma points, through the true nonlinear functions directly and reconstructing a mean and covariance from how those points land.[^ju97] Because it never needs a Jacobian, it extends naturally to a motion or measurement model too awkward to differentiate cleanly, and it tends to track the true nonlinear statistics more faithfully than a linearised [[Kalman_filter|Kalman filter]] does whenever the nonlinearity is strong enough to matter. ### Particle filter A [[Particle_filter|particle filter]] represents a track's entire probability distribution with a large population of weighted sample states, called particles, propagating each one through the true motion model and reweighting the population against each new measurement rather than summarising the distribution by a mean and a covariance at all.[^gordon93] This lets it represent a distribution that is multimodal, such as a target that might have turned left or right behind an obstruction, or otherwise far from Gaussian in a way no Kalman-family filter can express, at a computational cost that grows with the number of particles carried rather than staying fixed as a Kalman filter's does. ## Microsims The three.js companion built for this article is a variant of the Kalman-filter sketch that follows a single track through a run of scans in which some of the expected measurements are deliberately withheld, showing how the track's estimate and its uncertainty behave while coasting through a dropout and how quickly both recover once measurements resume. Its specific controls and readouts belong to that companion and are not repeated here. *Try:* in the [[Kalman_filter]] sketch, raise the measurement-noise slider and watch the filter lean more heavily on its motion model through a turn, lagging the true path; a radar tracker's gain makes exactly that trade between a fresh, noisy plot and an existing track's own prediction on every scan. *Try:* in the [[Radar]] sketch, freeze the antenna sweep and compare where a moving target's glow last appeared with where the beam is pointed now; the gap between the two is the same predicted displacement a tracker's motion model has to bridge between one look and the next. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Radar_tracker) : [Wikitube](https://en.wikitube.io/wiki/Radar_tracker) Skeleton mirrored at revision 1310376815. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Constant_false_alarm_rate]] - [[Pulse-Doppler_radar]] - [[Monopulse_radar]] - [[Kalman_filter]] - [[Particle_filter]] - [[Clutter_(radar)]] - [[Radar]] ## References [^benedict62]: Benedict, T. R.; Bordner, G. W. "Synthesis of an Optimal Set of Radar Track-While-Scan Smoothing Equations." *IRE Transactions on Automatic Control*, vol. AC-7, no. 4, July 1962, pp. 27-32. [^kalman60]: Kalman, R. E. "A New Approach to Linear Filtering and Prediction Problems." *Journal of Basic Engineering*, vol. 82, no. 1, March 1960, pp. 35-45. https://doi.org/10.1115/1.3662552 [^reid79]: Reid, D. B. "An Algorithm for Tracking Multiple Targets." *IEEE Transactions on Automatic Control*, vol. 24, no. 6, December 1979, pp. 843-854. [^mahler03]: Mahler, R. P. S. "Multitarget Bayes Filtering via First-Order Multitarget Moments." *IEEE Transactions on Aerospace and Electronic Systems*, vol. 39, no. 4, October 2003, pp. 1152-1178. [^blom88]: Blom, H. A. P.; Bar-Shalom, Y. "The Interacting Multiple Model Algorithm for Systems with Markovian Switching Coefficients." *IEEE Transactions on Automatic Control*, vol. 33, no. 8, August 1988, pp. 780-783. [^mcgee85]: McGee, L. A.; Schmidt, S. F. *Discovery of the Kalman Filter as a Practical Tool for Aerospace and Industry*. NASA Technical Memorandum 86847, Ames Research Center, November 1985. Archived by the NASA Technical Reports Server: https://ntrs.nasa.gov/ . [^ju97]: Julier, S. J.; Uhlmann, J. K. "New Extension of the Kalman Filter to Nonlinear Systems." *Proceedings of SPIE*, vol. 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 1997, pp. 182-193. [^gordon93]: Gordon, N. J.; Salmond, D. J.; Smith, A. F. M. "Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation." *IEE Proceedings F (Radar and Signal Processing)*, vol. 140, no. 2, 1993, pp. 107-113. https://doi.org/10.1049/ip-f-2.1993.0015 ## Further reading - Ellingson, S. *Radio Systems Engineering - Revised First Edition* (2023), CC BY-NC. https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Dyer, J.; Davis, C. *Measurement and Instrumentation: An Introduction to Concepts and Methods - 1st Edition* (2020), CC BY-NC-SA. https://open.umn.edu/opentextbooks/textbooks/measurement-and-instrumentation-an-introduction-to-concepts-and-methods ## External links - The three.js companion for this article (see Microsims) will be linked here once published.