Uncertainty-Aware δ-GLMB Filtering for Multi-Target Tracking
Abstract
1. Introduction
2. Background
2.1. Labelled Random Finite Sets (RFS)
2.1.1. Bernoulli RFS
2.1.2. Multi-Bernoulli RFS
2.1.3. Labelled Multi-Bernoulli RFS
2.2. Generalised Labelled Multi-Bernoulli RFS
2.3. Bayesian Multi-Target Filtering
2.4. Measurement Likelihood Function
2.5. Delta-Generalised Labelled Multi-Bernoulli
2.6. N-Scan GM-PHD Filter
3. Proposed Methods
3.1. Uncertainty Effects on -GLMB
3.2. N-Scan -GLMB
3.2.1. Initialisation
3.2.2. Prediction
3.2.3. Update
3.2.4. Pruning and Extraction
Algorithm 1: Summary of N-scan pruning algorithm. |
3.3. Enhanced Update Phase
3.4. Enhanced Predict Phase
3.5. Refined -GLMB
4. Experimental Results and Discussion
4.1. Simulated Dataset Results
4.2. Visual Dataset Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Supplementary Background
Appendix B. The L1-Error of N-Scan Method and Traditional Method of Discarding
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Notation | Description |
---|---|
x | Single-target state |
X | Multi-target state (set of targets) |
State space | |
Z | Multi-object measurement set |
Label space | |
ℓ | Unique label assigned to a target |
Generalised Kronecker delta function | |
Indicator function | |
Probability of detection for target | |
Likelihood of measurement z given target | |
Multi-target probability density | |
Distinct label indicator function | |
Hypothesis weight | |
Probability density of target state |
Method () | OSPA (AVG) (# of Targets) |
---|---|
GM-PHD [53] | 47.46 (5.17) |
N-scan GM-PHD [43] | 39.71 (5.88) |
-GLMB | 33.4375 (6.13) |
N-scan -GLMB | 31.1589 (6.71) |
Enhanced N-scan -GLMB | 29.4330 (6.94) |
Refined N-scan -GLMB | 27.0017 (7.26) |
Method | OSPA (AVG) |
---|---|
GM-PHD [53] | 39.03 |
N-scan GM-PHD [43] | 34.51 |
-GLMB [42] | 32.28 |
N-scan -GLMB (ours) | 28.67 |
Enhanced N-scan -GLMB (ours) | 26.44 |
Refined N-scan -GLMB (ours) | 24.10 |
Method | MOTA | MOTP | ReR | FAR | MTR | MOR |
---|---|---|---|---|---|---|
GM-PHD [53] | 42.62 | 54.02 | 0.45 | 0.12 | 0.57 | 0.71 |
N-scan GM-PHD [43] | 46.78 | 58.49 | 0.51 | 0.10 | 0.46 | 0.57 |
-GLMB [42] | 51.05 | 63.62 | 0.57 | 0.10 | 0.42 | 0.64 |
N-scan -GLMB (ours) | 54.53 | 65.28 | 0.62 | 0.07 | 0.34 | 0.42 |
Enhanced N-scan -GLMB (ours) | 55.60 | 65.91 | 0.62 | 0.07 | 0.34 | 0.35 |
Refined N-scan -GLMB (ours) | 56.79 | 66.38 | 0.71 | 0.05 | 0.26 | 0.28 |
Method | MOTA | MOTP | ReR | FAR | MTR | MOR |
---|---|---|---|---|---|---|
GM-PHD [53] | 27.91 | 32.59 | 0.31 | 0.17 | 0.68 | 0.78 |
N-scan GM-PHD [43] | 31.20 | 36.17 | 0.46 | 0.12 | 0.56 | 0.66 |
-GLMB [42] | 30.83 | 37.55 | 0.48 | 0.14 | 0.53 | 0.64 |
N-scan -GLMB (ours) | 35.41 | 40.06 | 0.58 | 0.07 | 0.46 | 0.56 |
Enhanced N-scan -GLMB (ours) | 36.26 | 41.74 | 0.60 | 0.07 | 0.41 | 0.53 |
Refined N-scan -GLMB (ours) | 39.32 | 43.45 | 0.68 | 0.04 | 0.34 | 0.43 |
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Sepanj, M.H.; Moradi, S.; Azimifar, Z.; Fieguth, P. Uncertainty-Aware δ-GLMB Filtering for Multi-Target Tracking. Big Data Cogn. Comput. 2025, 9, 84. https://doi.org/10.3390/bdcc9040084
Sepanj MH, Moradi S, Azimifar Z, Fieguth P. Uncertainty-Aware δ-GLMB Filtering for Multi-Target Tracking. Big Data and Cognitive Computing. 2025; 9(4):84. https://doi.org/10.3390/bdcc9040084
Chicago/Turabian StyleSepanj, M. Hadi, Saed Moradi, Zohreh Azimifar, and Paul Fieguth. 2025. "Uncertainty-Aware δ-GLMB Filtering for Multi-Target Tracking" Big Data and Cognitive Computing 9, no. 4: 84. https://doi.org/10.3390/bdcc9040084
APA StyleSepanj, M. H., Moradi, S., Azimifar, Z., & Fieguth, P. (2025). Uncertainty-Aware δ-GLMB Filtering for Multi-Target Tracking. Big Data and Cognitive Computing, 9(4), 84. https://doi.org/10.3390/bdcc9040084