Tracking Motion Models, Track Lifecycle, and Metrics

Visual: track lifecycle state machine with birth, tentative, confirmed, coasting, deletion, motion model choice, gating, and metric outputs.

Tracking turns detections into persistent object hypotheses. A detector answers "what is visible now?" A tracker answers "which physical object is this over time, where is it going, and how uncertain am I?" The hard parts are not only Kalman equations. They are motion assumptions, data association, birth/death policy, occlusion handling, and metrics that reveal identity errors instead of hiding them inside detection scores.

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1. Related Docs

• Bayesian Filtering and Error-State Kalman Filters
• Data Association and Gating
• Probabilistic Multi-Object Association
• Particle Filters and Hypothesis Management
• Mahalanobis Distance, Chi-Square Gates, NIS, and NEES
• Detection Theory, ROC/PR Curves, and Operating Points
• Sensor Filtering: Alpha-Beta, Kalman, and Complementary

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2. State, Measurement, and Belief

A single-object tracker maintains a belief:

p(x_k | z_1:k)

where x_k may include position, velocity, acceleration, yaw, yaw rate, size, class, and existence probability.

A common linear Gaussian model is:

x_k = F x_(k-1) + q_k,     q_k ~ N(0, Q)
z_k = H x_k + r_k,         r_k ~ N(0, R)

The Kalman prediction/update is only one implementation. The modeling choices behind F, Q, H, R, gating, and lifecycle policy usually matter more than the matrix algebra.

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3. Motion Models

3.1 Constant Velocity

For one axis:

x = [ position, velocity ]^T
F = [ 1 dt ]
    [ 0 1  ]

With white acceleration noise spectral density sigma_a^2:

Q = sigma_a^2 * [ dt^4/4  dt^3/2 ]
                [ dt^3/2  dt^2   ]

Constant velocity is robust and simple. It fails during braking, turns, and stop-start motion unless process noise is large enough.

3.2 Constant Acceleration

x = [ position, velocity, acceleration ]^T
F = [ 1 dt 0.5 dt^2 ]
    [ 0 1  dt       ]
    [ 0 0  1        ]

This can reduce lag for maneuvering objects but may overfit noisy detections and create unstable acceleration estimates.

3.3 Coordinated Turn

For vehicles, yaw and yaw rate matter:

state = [px, py, speed, yaw, yaw_rate]

A coordinated-turn model predicts curved motion. It is better for lane turns and roundabouts but nonlinear and sensitive when yaw rate is near zero.

3.4 Interacting Multiple Model

An IMM runs several motion models and mixes their probabilities:

models = { constant_velocity, constant_acceleration, coordinated_turn }

The tracker estimates both state and mode. IMM is useful when objects switch between cruising, braking, and turning, but tuning mode transition probabilities is operationally important.

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4. Association and Gating

Before assigning detections to tracks, predict each track into measurement space:

z_hat = h(x_pred)
S = H P_pred H^T + R
nu = z - z_hat
d2 = nu^T S^-1 nu

A chi-square gate rejects unlikely candidates:

accept candidate if d2 <= gamma

Then an assignment solver, commonly Hungarian/min-cost matching, chooses a consistent set of detection-track matches. Costs may combine:

• Mahalanobis distance,
• 2D/3D IoU,
• class compatibility,
• appearance embedding distance,
• Doppler/radial velocity agreement,
• map/lane constraints.

SORT is the canonical simple baseline: Kalman filter prediction, bounding-box association, and Hungarian assignment. DeepSORT adds an appearance metric to reduce identity switches through occlusion.

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5. Track Lifecycle

Track lifecycle policy controls when tracks are created, confirmed, coasted, merged, split, and deleted.

tentative -> confirmed -> coasted/lost -> deleted

Typical fields:

• age: frames since birth,
• hits: associated detections,
• misses: consecutive missed updates,
• time_since_update,
• existence_probability,
• class_history,
• last_detection_time,
• last_update_source.

Birth

Create a tentative track when an unmatched detection passes quality gates. Do not immediately expose every tentative track to planning. Require confirmation:

confirm if hits >= M within N frames

Coast

When a confirmed track misses a detection, predict it forward:

x <- F x
P <- F P F^T + Q

Coasting preserves identity through short occlusions but increases false-track risk if deletion is too slow.

Death

Delete tracks when uncertainty, misses, or low existence probability exceed a policy:

delete if misses > max_misses
delete if existence_probability < p_min
delete if covariance too large for consumer

Lifecycle thresholds are operating points. They should be tuned against system costs, not only benchmark metrics.

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6. Failure Modes

Failure	Cause	Consequence
track fragmentation	deletion too aggressive or detector flicker	one object becomes many short tracks
identity switch	association ambiguity during crossing/occlusion	prediction and behavior history attach to wrong object
ghost track	false detections confirmed or stale coast	planner reacts to nonexistent object
track lag	motion model too smooth or low process noise	braking/cut-in detected late
track jitter	detection noise trusted too much	unstable velocity and object box
class flapping	class updated every frame without smoothing	downstream behavior changes abruptly
duplicate tracks	birth policy ignores existing uncertain tracks	planner sees multiple obstacles
covariance inconsistency	Q/R not matched to errors	gates reject true detections or accept clutter

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7. Metrics

7.1 Detection Metrics Are Not Tracking Metrics

Frame-level precision/recall ignores identity. A tracker can have good detection counts and still switch IDs at every occlusion. Tracking metrics must evaluate:

• localization,
• detection presence,
• identity association over time,
• fragmentation,
• false tracks and missed tracks.

7.2 CLEAR MOT

MOTA combines false positives, false negatives, and ID switches:

MOTA = 1 - (FN + FP + IDSW) / GT

MOTP measures localization precision over matched objects. MOTA is widely known but can be dominated by detection errors and may hide association quality.

7.3 IDF1

IDF1 measures identity precision/recall over matched identity trajectories:

IDF1 = 2 * IDTP / (2 * IDTP + IDFP + IDFN)

It is useful when maintaining consistent object identity matters.

7.4 HOTA

HOTA was introduced to balance detection, association, and localization. Its high-level intuition is:

HOTA ~= geometric mean of detection accuracy and association accuracy

It is often more diagnostic than a single MOTA score because it decomposes tracking behavior into interpretable components.

7.5 OSPA

OSPA is common in multi-target tracking theory. It measures distance between sets while penalizing both localization error and cardinality error:

OSPA_p,c(X, Y) =
  [ (1/n) ( min_assignment sum d_c(x_i, y_pi(i))^p
            + c^p * (n - m) ) ]^(1/p)

where d_c is capped at cutoff c, and n >= m. OSPA is useful when the number of targets varies and the metric should remain a true set distance.

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8. How It Appears in AV and Robotics

Consumer	Tracker requirement
prediction	stable velocity, yaw, and identity history
planning	conservative existence and occupancy during occlusion
behavior	class and intent should not flicker
mapping	dynamic tracks should be removed from static map updates
safety	close-range false negatives are costlier than far false positives
evaluation	metrics should separate misses, false tracks, localization, and IDs

The tracker is a contract between perception and planning. A box without covariance, age, source, and lifecycle state is often not enough.

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9. Implementation Checklist

• Define track state per class: pedestrian, cyclist, vehicle, unknown, static obstacle may need different dynamics.
• Tune measurement covariance by detector range, object size, occlusion, and sensor modality.
• Use chi-square gating before assignment to reduce impossible matches.
• Keep unmatched high-quality detections for birth; suppress births inside gates of existing tracks unless duplicate evidence is clear.
• Separate tentative tracks from planner-visible confirmed tracks.
• Carry covariance and existence probability through coast periods.
• Smooth class probabilities rather than hard-switching class labels per frame.
• Log association costs, gate distances, lifecycle transitions, and deletion reasons.
• Evaluate after the full tracking pipeline, not only detector outputs.
• Slice metrics by range, occlusion, density, turning, weather, and object class.
• Replay known crossing/occlusion scenarios whenever changing lifecycle policy.

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10. Sources

• Yaakov Bar-Shalom, X. Rong Li, and Thiagalingam Kirubarajan, "Estimation with Applications to Tracking and Navigation": https://www.wiley.com/en-us/Estimation+with+Applications+to+Tracking+and+Navigation-p-9780471416555
• Samuel Blackman and Robert Popoli, "Design and Analysis of Modern Tracking Systems": https://us.artechhouse.com/Design-and-Analysis-of-Modern-Tracking-Systems-P982.aspx
• Alex Bewley et al., "Simple Online and Realtime Tracking": https://arxiv.org/abs/1602.00763
• Nicolai Wojke, Alex Bewley, and Dietrich Paulus, "Simple Online and Realtime Tracking with a Deep Association Metric": https://arxiv.org/abs/1703.07402
• Keni Bernardin and Rainer Stiefelhagen, "Evaluating Multiple Object Tracking Performance: The CLEAR MOT Metrics": https://link.springer.com/article/10.1155/2008/246309
• Jonathon Luiten et al., "HOTA: A Higher Order Metric for Evaluating Multi-Object Tracking": https://arxiv.org/abs/2009.07736
• Dominic Schuhmacher, Ba-Ngu Vo, and Ba-Tuong Vo, "A Consistent Metric for Performance Evaluation of Multi-Object Filters": https://doi.org/10.1109/TSP.2008.920469