Target Tracking, Data Association and Sensor Fusion

Introduction and Context

Radar detection produces measurements, not target tracks. A measurement may be a range, bearing, elevation, Doppler frequency, amplitude, or a multidimensional combination of these quantities. Measurements are noisy, may be missing, and may include false alarms. Target tracking converts these observations into an estimate of target state—typically position, velocity, and sometimes acceleration—together with uncertainty and track quality.

Tracking is central to surveillance, air-traffic management, missile warning, autonomous vehicles, maritime monitoring, and integrated air-defence systems. In a modern sensor network, radar observations are also combined with electro-optical/infrared (EO/IR), GNSS, and communication-derived information. The fundamental engineering problem is therefore not only estimation, but also deciding which observations belong to which targets and how information from sensors with different accuracies, time references, coordinate systems, and failure modes should be combined.

This chapter develops the principal methods used in practical radar tracking: alpha-beta filtering, Kalman filtering, extended and nonlinear filters, maneuvering-target models, track initiation and termination, gating, data association, multi-target tracking, and multisensor fusion.

Learning Objectives

After studying this chapter, the reader should be able to:

1. Formulate a target-tracking problem in state-space form.

2. Explain and implement alpha-beta and Kalman filters.

3. Select suitable models for nonmaneuvering and maneuvering targets.

4. Apply prediction, validation gating, association, and track-management logic.

5. Distinguish nearest-neighbour, probabilistic, and multi-hypothesis association methods.

6. Explain the principles and limitations of EKF, UKF, and particle filtering.

7. Fuse radar data with EO/IR, GNSS, and communication sensors.

8. Evaluate tracking performance, robustness, cybersecurity, and operational risk.

1. State-Space Representation of a Tracking Problem

A target is represented by a state vector. For planar motion, a common constant-velocity state is

x_k = [x_k, y_k, v_x,k, v_y,k]^T,

where x and y are Cartesian position coordinates and v_x and v_y are velocity components. A discrete linear model is

x_k = F_k x_{k-1} + G_k u_k + w_k,

z_k = H_k x_k + v_k.

Here, z_k is the measurement at time k; F_k is the state-transition matrix; u_k is a known input, if present; G_k maps that input into the state; H_k is the observation matrix; w_k is process noise; and v_k is measurement noise. Usually, w_k and v_k are modelled as zero-mean random variables with covariance matrices Q_k and R_k, respectively. The standard Kalman assumptions additionally require linear models and approximately Gaussian noise.

For a constant-velocity model with sampling interval T,

F = [[1, 0, T, 0], [0, 1, 0, T], [0, 0, 1, 0], [0, 0, 0, 1]].

If radar directly measures Cartesian position, H selects the first two state components. If radar measures range r and bearing theta, the measurement is nonlinear:

h(x) = [sqrt(x^2+y^2), atan2(y,x)]^T.

The atan2 function is essential because it preserves the correct quadrant. Angles must be wrapped consistently, for example to the interval (-pi, pi].

A tracking system estimates both the state and its uncertainty. A point estimate without covariance is inadequate for gating, association, sensor fusion, and risk-based decision-making.

2. Alpha-Beta Filtering

The alpha-beta filter is a computationally efficient approximation to a constant-velocity Kalman filter. It is particularly useful when measurements are scalar, the sampling interval is regular, and processing resources are limited.

For one-dimensional position p and velocity v, prediction is

p_k^- = p_{k-1} + T v_{k-1},

v_k^- = v_{k-1}.

The residual, or innovation, is

r_k = z_k - p_k^-.

The update is

p_k = p_k^- + alpha r_k,

v_k = v_k^- + (beta/T) r_k.

The parameters alpha and beta are dimensionless gains, generally selected between zero and one, although their admissible values depend on the desired closed-loop behaviour and model assumptions. Alpha controls position correction and beta controls velocity correction. Small gains smooth noisy measurements but respond slowly to maneuvers; large gains respond quickly but pass more measurement noise into the track.

The filter is attractive because it stores only a position and velocity estimate and avoids explicit covariance propagation. Its weaknesses are equally important: it provides no statistically rigorous uncertainty unless an additional covariance approximation is maintained, and gain selection is sensitive to sampling period, target dynamics, and noise conditions. It should not be treated as a universal replacement for a Kalman filter.

3. The Kalman Filter

The linear discrete Kalman filter consists of prediction and measurement-update stages.

Prediction

x_hat_k^- = F_k x_hat_{k-1} + G_k u_k,

P_k^- = F_k P_{k-1} F_k^T + Q_k.

The superscript minus denotes a prior estimate, and P is the error covariance matrix.

Measurement update

The innovation is

y_k = z_k - H_k x_hat_k^-.

Its covariance is

S_k = H_k P_k^- H_k^T + R_k.

The Kalman gain is

K_k = P_k^- H_k^T S_k^{-1}.

The updated state is

x_hat_k = x_hat_k^- + K_k y_k.

A numerically robust covariance update is the Joseph form:

P_k = (I-K_kH_k)P_k^-(I-K_kH_k)^T + K_kR_kK_k^T.

The simpler expression P_k = (I-K_kH_k)P_k^- is mathematically equivalent under exact arithmetic, but the Joseph form better preserves symmetry and positive semidefiniteness in finite-precision implementations.

The Kalman filter balances model prediction and measurement information according to their uncertainties. If R is large relative to predicted uncertainty, the filter trusts the model more. If P^- is large, the measurement receives greater weight. Q represents uncertainty in the motion model; underestimating Q makes the track sluggish during maneuvers, whereas overestimating Q makes it noisy.

Worked Example: Scalar Kalman Update

Suppose a predicted range is 1000 m with predicted variance 400 m². A radar measures 1010 m with measurement variance 100 m². Then

innovation = 1010 - 1000 = 10 m,

S = 400 + 100 = 500 m²,

K = 400/500 = 0.8.

The updated range is

1000 + 0.8(10) = 1008 m.

The updated variance is

(1 - 0.8)(400) = 80 m².

Thus the estimate moves close to the measurement, while its uncertainty decreases substantially. This scalar example assumes a direct measurement of the state and independent Gaussian errors.

4. Maneuvering Targets and Model Selection

A constant-velocity model is suitable for a target moving approximately straight and uniformly. It becomes inadequate when the target turns, accelerates, climbs, descends, or changes speed. Common alternatives include:

• Constant-acceleration (CA) model: state includes acceleration and assumes it remains approximately constant over a short interval.
• Coordinated-turn (CT) model: state includes turn rate and represents approximately constant-rate planar turning.
• Singer model: acceleration is a correlated random process with a specified correlation time, useful for aircraft and vehicles whose acceleration changes gradually.
• Multiple-model methods: several motion hypotheses are maintained and combined according to their likelihoods.

The interacting multiple model (IMM) filter is widely used. Each model independently performs a filter update. Model probabilities are then updated using the measurement likelihood, and state estimates are mixed before the next cycle. In conceptual form,

mu_k^i proportional to likelihood(z_k | model i) times predicted model probability.

The probabilities are normalized to sum to one. The combined state is a probability-weighted mixture of model estimates, with covariance including both within-model uncertainty and differences between model means.

IMM performance depends strongly on model diversity and transition probabilities. Models that are too similar cannot distinguish motion regimes; models that are too aggressive may produce unstable or noisy tracks. No finite model set represents every maneuver, so adaptive process-noise tuning and maneuver detection remain important.

5. Nonlinear Tracking: EKF, UKF and Particle Filters

Extended Kalman Filter

For nonlinear dynamics,

x_k = f(x_{k-1}) + w_k,

z_k = h(x_k) + v_k,

the extended Kalman filter linearizes the functions about the current estimate. Let F_k be the Jacobian of f and H_k the Jacobian of h. The ordinary Kalman equations are then applied using these local Jacobians.

The EKF is efficient and often effective for range-bearing radar, but it can be inaccurate when uncertainty is large, nonlinearities are strong, or the estimate is far from the true state. Bearing residuals must be angle-wrapped, and coordinate singularities—such as a target near the sensor origin—must be handled explicitly.

Unscented Kalman Filter

The unscented Kalman filter propagates a deterministically selected set of sigma points through the nonlinear functions. It avoids explicitly calculating Jacobians and often provides better moment approximations than first-order linearization. It remains fundamentally a unimodal, approximately Gaussian estimator and can be computationally more expensive than an EKF.

Particle Filter

A particle filter represents the posterior distribution by weighted samples:

p(x_k | z_{1:k}) approximately equals sum_i w_k^i delta(x_k - x_k^i),

where x_k^i are particles, w_k^i are normalized weights, and delta denotes a point mass. Each particle is propagated through the motion model, weighted according to measurement likelihood, and resampled when degeneracy becomes significant.

Particle filters are suitable for multimodal distributions, severe nonlinearities, non-Gaussian noise, and ambiguous observations. Their disadvantages include high computational cost, sampling impoverishment, sensitivity to proposal distributions, and the need for enough particles to cover the relevant state space. They are especially useful when terrain, occlusion, multiple hypotheses, or nonstandard sensor likelihoods make Gaussian assumptions unreliable.

6. Track Initiation, Maintenance and Termination

A detector output should not immediately become a confirmed track. False alarms, sidelobes, interference, and transient clutter can otherwise create large numbers of false tracks.

A practical track-management state machine may contain tentative, confirmed, coasted, and deleted states. A tentative track is formed when detections are consistent with a plausible motion model. It becomes confirmed after a logic such as M-of-N: at least M validated detections in the most recent N scans. For example, 3-of-5 means that three supporting detections are required within five scans; the exact rule must be selected using false-alarm rate, revisit time, and operational risk.

A confirmed track may be coasted through a limited number of missed detections. During coasting, prediction continues but covariance grows because no measurement update is available. The track is deleted after too many consecutive misses, excessive uncertainty, or a confirmed exit from the surveillance region.

Track initiation methods include:

• Threshold initiation: create a track from a single detection, fast but vulnerable to false alarms.
• Logic-based initiation: require several detections satisfying kinematic consistency.
• Hough or Radon methods: accumulate evidence along candidate trajectories.
• Batch or maximum-likelihood initiation: evaluate a group of measurements jointly.

Initiation thresholds should be designed using measured clutter statistics rather than arbitrary values.

7. Validation Gating

Before assigning a measurement to a track, the system rejects observations that are physically or statistically implausible. The innovation covariance S defines the uncertainty ellipsoid. The squared Mahalanobis distance is

D^2 = y^T S^{-1} y.

For an m-dimensional measurement and a Gaussian innovation, a gate may be defined by

D^2 <= gamma,

where gamma is selected from a chi-square distribution for the chosen probability of gate coverage. For example, with two independent measurement dimensions and a 95% gate, gamma is approximately 5.991. This value applies only when the innovation is correctly normalized, the measurement dimension is two, and the Gaussian model is appropriate.

Gating reduces computational load and prevents grossly incompatible observations from corrupting a track. It is not a substitute for association logic: several measurements may lie inside one gate, and a genuine measurement may fall outside because of model error or an abrupt maneuver.

Practical gates may combine statistical and physical constraints, such as maximum speed, acceleration, altitude, field of view, and sensor detection range. Gate inflation can be used during maneuvers, but uncontrolled inflation increases false associations.

8. Data Association

Data association determines which measurement, if any, belongs to each track.

Nearest-neighbour methods

Nearest-neighbour (NN) association selects the validated measurement with minimum distance, commonly Mahalanobis distance. Global nearest neighbour (GNN) assigns measurements to tracks jointly, preventing two tracks from receiving the same detection. These methods are simple and effective in sparse, well-separated scenes but fail when targets are close or clutter density is high.

Probabilistic data association

The probabilistic data association filter (PDAF) assigns probabilities to all validated measurements and to the missed-detection event. The state update uses a weighted innovation rather than one selected measurement. PDAF is useful for one target in clutter, but its assumptions become problematic when several tracks compete for the same observations.

Joint probabilistic data association (JPDAF) computes probabilities over feasible joint associations for multiple targets. It reduces hard assignment errors but can become computationally demanding and may cause track coalescence when targets are close.

Multiple-hypothesis tracking

Multiple-hypothesis tracking (MHT) maintains alternative association histories over several scans. Hypotheses are scored using measurement likelihoods, detection probability, clutter density, and track-existence assumptions. Pruning, merging, and N-scan-back decisions are essential to control combinatorial growth. MHT can be highly effective in dense and ambiguous scenes, but it requires substantial computation and careful management of delayed decisions.

Association quality depends on detection probability, clutter intensity, target separation, sensor resolution, model accuracy, and timing accuracy. A sophisticated filter cannot compensate for poor association.

9. Multi-Target Tracking Architecture

A multi-target tracker typically performs the following cycle:

1. Predict every existing track.

2. Generate validation gates.

3. Form a track-to-measurement cost matrix.

4. Solve an association problem or maintain association hypotheses.

5. Update assigned tracks.

6. Coast unassigned tracks.

7. Initiate tentative tracks from unexplained detections.

8. Confirm, merge, split, or delete tracks according to management logic.

The cost matrix may use Mahalanobis distance, negative log likelihood, or a composite cost including amplitude, classification, and kinematic consistency. Assignment algorithms such as the Hungarian method provide efficient one-to-one assignment for a selected cost matrix, but they do not by themselves represent uncertainty over alternative associations.

Track coalescence occurs when nearby targets receive similar updates and estimates converge. Track splitting can occur when one target generates detections distributed across several hypotheses. Track identity management therefore requires continuity features, quality scores, and sometimes target classification information.

10. Sensor Fusion

Fusion combines information from sensors that differ in modality, geometry, sampling rate, precision, latency, and reliability. The first requirement is a common reference: time synchronization, coordinate transformation, sensor calibration, and uncertainty representation.

Measurement-level, track-level and decision-level fusion

Measurement-level fusion combines raw or lightly processed observations before estimation. It can preserve information but requires accurate calibration, common timing, compatible likelihood models, and high bandwidth.

Track-level fusion combines local sensor tracks. It is more scalable and protects sensor autonomy, but local filters may have correlated errors. Simply adding covariances as if tracks were independent can produce overconfident estimates.

Decision-level fusion combines classifications or detections, such as target/no-target or threat/non-threat decisions. It is robust to heterogeneous interfaces but discards information and is difficult to calibrate probabilistically.

Radar with EO/IR

Radar supplies all-weather range and often Doppler and angle. EO/IR supplies high-resolution bearing, imagery, and target classification, but performance is affected by illumination, weather, atmospheric obscuration, and background clutter. Fusion commonly uses radar to cue a narrow camera search, then uses EO/IR bearing and classification to refine or confirm the radar track. Accurate boresight calibration and time alignment are essential.

Radar with GNSS

GNSS can provide precise position or velocity for cooperative platforms, reference stations, or instrumented targets. GNSS is vulnerable to jamming, spoofing, blockage, and multipath. A fusion system must attach integrity indicators to GNSS data and avoid treating reported precision as proof of correctness. Radar can provide an independent consistency check.

Radar with communication sensors

Communication systems may provide cooperative identity, position reports, or time information. Examples include aircraft surveillance broadcasts and networked platform reports. Communication-derived data should be associated with radar observations using identity, time, position uncertainty, and kinematic consistency. Authentication, replay protection, and trust management are necessary because a validly formatted message may still be false or compromised.

Correlated estimates and track-to-track fusion

If two local tracks use common measurements, a common navigation source, or exchanged prior information, their errors are correlated. The cross-covariance is often unavailable. Covariance intersection provides a conservative fusion method:

P^{-1} = omega P_1^{-1} + (1-omega)P_2^{-1},

x = P[omega P_1^{-1}x_1 + (1-omega)P_2^{-1}x_2],

where 0 <= omega <= 1 is selected to minimize a chosen uncertainty measure, such as determinant or trace of P. This method avoids unjustified independence assumptions but may be conservative. When cross-covariance is known, an optimal correlated fusion method should be used instead.

11. Performance Evaluation

A tracker should be assessed using both estimation and operational metrics. Common measures include position and velocity root-mean-square error, track continuity, probability of track initiation, probability of track loss, false-track rate, latency, and computational load. Multi-target metrics include OSPA, GOSPA, track purity, identity switches, and fragmentation.

Evaluation must use representative scenarios: dense clutter, crossing targets, intermittent detection, maneuvers, sensor outages, timing errors, and adversarial inputs. Average accuracy alone can conceal catastrophic association failures. Confidence calibration is also important: a 95% confidence region should contain the true state approximately 95% of the time under the stated conditions.

12. Illustrative Case: Coastal Surveillance with Radar and EO/IR

Background

Consider an illustrative coastal surveillance system with a rotating coastal radar and a steerable EO/IR turret. The radar supplies range, bearing, and Doppler detections every two seconds. The camera has higher angular resolution but a narrow field of view and can be affected by haze.

Problem

Small boats create intermittent radar detections because of sea clutter. Two boats may pass close to one another, and an occasional communication report provides a position that may be delayed or unreliable.

Analysis

A constant-velocity Kalman filter is used initially, with an IMM component containing constant-velocity and coordinated-turn models. Radar measurements are converted into a common local Cartesian frame, with bearing residuals wrapped correctly. A 95% chi-square validation gate is applied, supplemented by speed and shoreline constraints. Tentative tracks require three detections in five scans. Confirmed tracks are coasted for three missed scans.

When two tracks approach within overlapping gates, nearest-neighbour association is replaced by JPDAF. The radar track predicts the EO/IR line of sight, and the camera is cued only when the predicted uncertainty ellipse intersects its field of view. EO/IR detections are fused at track level after boresight and timestamp correction. Communication reports are used as auxiliary observations only after identity, latency, and kinematic consistency checks.

Outcome

The system reduces false track initiation in sea clutter and maintains track continuity through occasional radar misses. JPDAF reduces identity swaps during close approach, while the IMM responds faster to turning boats than a constant-velocity filter alone. GNSS-like communication reports improve accuracy when trustworthy but are rejected when their residuals and integrity indicators are inconsistent.

Learning Points

The case demonstrates that tracking performance depends on the complete chain: detection quality, motion modelling, gating, association, calibration, timing, and track management. Sensor fusion is not achieved merely by averaging measurements. Reliability and independence assumptions must be explicit.

13. Implementation, Governance and Emerging Developments

A professional implementation should use numerically stable matrix operations, validate covariance symmetry, monitor innovation statistics, and log association decisions for post-mission analysis. Filter tuning should be based on measured sensor and maneuver data. Unit tests should include angle wrapping, coordinate singularities, missed detections, out-of-sequence measurements, and nearly singular covariance matrices.

Out-of-sequence measurements require buffering and retrodiction or state reconstruction. Asynchronous sensors require precise timestamps and latency models. Track databases should preserve provenance: which sensor produced each update, when it was received, and what transformations were applied.

Machine-learning methods are increasingly used for detection confidence, motion-model adaptation, re-identification, and learned proposal distributions for particle filters. They should complement rather than obscure probabilistic tracking logic. Training-data bias, distribution shift, explainability, adversarial examples, and failure under rare maneuvers are significant concerns.

Operational systems must address privacy and proportionality where imaging or communication data identify persons or vehicles. Security controls should protect sensor interfaces, track databases, and fusion networks against spoofing, replay, denial of service, and data poisoning. Safety-critical decisions require human oversight, auditable confidence information, and clearly defined rules for uncertain or conflicting tracks.

Best-Practice Design Guidance

1. Define the state, coordinate frame, timing convention, and noise assumptions before selecting a filter.

2. Use covariance-aware gating and never associate solely by Euclidean distance when measurement scales differ.

3. Match motion-model complexity to the maneuver environment; use IMM or adaptive methods when one model is inadequate.

4. Separate estimation from track management, association, and classification, while allowing controlled information exchange.

5. Treat false alarms, missed detections, latency, and correlation as first-class design variables.

6. Preserve uncertainty and provenance throughout sensor fusion.

7. Test close-target, cluttered, intermittent, adversarial, and sensor-outage cases—not only nominal trajectories.

8. Prefer conservative decisions when sensor independence or integrity cannot be established.

Chapter Summary

Target tracking transforms noisy, intermittent sensor detections into state estimates with quantified uncertainty. The alpha-beta filter offers simplicity, while the Kalman filter provides a principled recursive solution for linear Gaussian models. EKF, UKF, and particle filters extend tracking to nonlinear and non-Gaussian situations. Maneuvering targets require appropriate dynamic models, often combined through IMM methods.

Track quality also depends on management functions. Initiation prevents isolated false alarms from becoming tracks; validation gates reject implausible observations; data association assigns detections to tracks; and confirmation, coasting, and deletion maintain a reliable track population. Nearest-neighbour methods are efficient in sparse scenes, whereas PDAF, JPDAF, and MHT address increasing levels of ambiguity and computational cost.

Sensor fusion with EO/IR, GNSS, and communication sensors can improve observability, classification, and continuity, but only when time, coordinates, calibration, uncertainty, correlation, and integrity are handled correctly. Performance must be evaluated using accuracy, continuity, false-track, identity, latency, and computational metrics. Robust engineering additionally requires cybersecurity, auditability, human oversight, and testing under nonideal and adversarial conditions.

Key Terms

State estimate: The estimated target position, velocity, and other dynamic variables.

Process noise: Random uncertainty representing unmodelled target or system dynamics.

Measurement noise: Random error in a sensor observation.

Innovation: Difference between an actual measurement and its predicted value.

Covariance: Matrix describing estimation uncertainty and correlations.

Alpha-beta filter: A simplified position-velocity tracking filter using two correction gains.

Kalman filter: Recursive minimum-variance estimator for linear systems with Gaussian noise.

Extended Kalman filter: Kalman filter using local linearization of nonlinear models.

Unscented Kalman filter: Nonlinear filter based on propagation of sigma points.

Particle filter: Sampling-based estimator representing a posterior distribution with weighted particles.

IMM filter: Multiple-model estimator that mixes motion-model hypotheses according to likelihood.

Validation gate: Region containing measurements considered plausible for a track.

Mahalanobis distance: Covariance-normalized innovation distance.

Data association: Assignment of observations to tracks.

PDAF: Probabilistic data association filter for one target in clutter.

JPDAF: Joint probabilistic data association filter for competing multiple targets.

MHT: Multiple-hypothesis tracking over alternative association histories.

Track coasting: Continuing prediction during temporary absence of validated detections.

Track coalescence: Unwanted convergence of estimates for nearby targets.

Covariance intersection: Conservative fusion method for estimates with unknown correlation.

Review Questions

Short Answer Questions

1. What are the roles of the state-transition matrix and measurement matrix in a Kalman filter?

2. Why does a tracker require covariance in addition to a point estimate?

3. Define validation gating and state why Mahalanobis distance is useful.

4. What is the principal difference between PDAF and nearest-neighbour association?

5. Why can GNSS or communication-derived position reports not be accepted solely on the basis of their stated accuracy?

Long Answer Questions

1. Derive and explain the prediction and update equations of the discrete linear Kalman filter, including the meaning of Q and R.

2. Compare constant-velocity, constant-acceleration, coordinated-turn, Singer, and IMM approaches for maneuvering targets.

3. Explain track initiation, confirmation, coasting, and deletion, and discuss how M-of-N logic affects false-track and missed-track performance.

4. Compare NN, GNN, PDAF, JPDAF, and MHT in terms of ambiguity handling, computational cost, and operational suitability.

5. Discuss measurement-level, track-level, and decision-level fusion for a radar–EO/IR–GNSS surveillance system, including correlation and integrity issues.

Analytical / Application Questions

1. A radar track has a predicted two-dimensional measurement covariance S and a residual y. Explain how you would calculate the Mahalanobis gate test and select a chi-square threshold for a specified gate probability.

2. Design a tracking architecture for two aircraft that frequently cross in dense clutter. Justify the motion models, association method, track-management logic, and performance metrics.

3. Two local sensors provide position tracks but their common navigation source creates unknown error correlation. Explain why naive covariance-weighted fusion is unsafe and propose a conservative alternative.

Multiple Choice Questions with Answers

Question 1

In a linear Kalman filter, what does the innovation represent?

A. The difference between the actual and predicted measurement

B. The process-noise covariance

C. The predicted state covariance

D. The probability that a track is confirmed

Correct Answer: A. The difference between the actual and predicted measurement

Question 2

For a two-dimensional Gaussian innovation, the approximate chi-square threshold for a 95% validation gate is:

A. 1.386

B. 3.000

C. 5.991

D. 9.210

Correct Answer: C. 5.991

Question 3

Which filter is specifically designed to maintain several motion-model hypotheses and combine them probabilistically?

A. Alpha-beta filter

B. Interacting multiple model filter

C. Nearest-neighbour filter

D. Constant-position filter

Correct Answer: B. Interacting multiple model filter

Question 4

What is the main purpose of track coasting?

A. To increase radar transmit power

B. To continue prediction during temporary missed detections

C. To remove all covariance from a track

D. To force two tracks to merge

Correct Answer: B. To continue prediction during temporary missed detections

Question 5

Which association method maintains alternative association histories over multiple scans?

A. MHT

B. Simple nearest neighbour

C. Scalar alpha filter

D. Single-scan thresholding

Correct Answer: A. MHT

Question 6

In an alpha-beta filter, the beta gain primarily controls correction of the estimated:

A. Measurement dimension

B. Velocity

C. Sensor bias only

D. Track existence probability

Correct Answer: B. Velocity

Question 7

Which condition most directly motivates use of a particle filter?

A. A strictly linear model with Gaussian noise

B. A scalar measurement with fixed sampling

C. A strongly nonlinear or multimodal posterior distribution

D. A situation with no process uncertainty

Correct Answer: C. A strongly nonlinear or multimodal posterior distribution

Question 8

Why is the Joseph covariance update form useful in implementation?

A. It removes the need for measurements

B. It improves numerical preservation of covariance properties

C. It guarantees zero estimation error

D. It converts polar measurements to Cartesian coordinates

Correct Answer: B. It improves numerical preservation of covariance properties

Question 9

What is a major risk of naive track-to-track fusion when estimates share information?

A. The fused estimate may become overconfident

B. The radar wavelength changes

C. The measurement dimension becomes zero

D. The target cannot maneuver

Correct Answer: A. The fused estimate may become overconfident

Question 10

Which sensor is typically most affected by illumination and atmospheric visibility conditions?

A. EO/IR camera

B. Inertial clock

C. Radar Doppler processor

D. Covariance matrix

Correct Answer: A. EO/IR camera