What is Trajectory Cardinality Probability Hypothesis Density Filter?
Trajectory Cardinality Probability Hypothesis Density Filter is an assumed-density multi-object tracker that propagates trajectory intensity and a trajectory-cardinality distribution under an independent and identically distributed cluster approximation.
Quick Facts
| Specification | Official Specification |
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How It Works
Match both the trajectory PHD and cardinality distribution
The original TPHD/TCPHD paper derives TCPHD by projecting prediction and update results onto an IID-cluster multitrajectory density. The approximation preserves the cardinality distribution and the trajectory PHD, unlike TPHD's Poisson family, whose count variance and probability mass function follow from its mean.
The trajectory PHD integrates to expected trajectory count, while the separate cardinality distribution determines probabilities for zero, one, or more trajectories. Their expected counts must agree; normalization or truncation errors that break this consistency indicate an invalid implementation.
Update count uncertainty and trajectory states together
Prediction combines surviving trajectories with a birth process in both the intensity and count domains. Update uses the full measurement set, detection probability, clutter model, and symmetric measurement statistics to correct the cardinality distribution and trajectory intensity together.
TCPHD avoids enumerating a persistent global association mixture. That reduces cost relative to hypothesis-rich methods but also removes dependence needed to distinguish some crossing histories. A precise count posterior does not by itself guarantee correct trajectory continuity.
Control state growth and compare under matched assumptions
Gaussian-mixture TCPHD stores cross-time mean and covariance for each trajectory component. L-scan implementations leave states older than the chosen lag unchanged, while pruning and merging reduce component count. Those policies alter history accuracy and must be included in reproducible evaluation.
Independent Pulse-Doppler work applies both TPHD and TCPHD with sequential Gaussian updates and L-scan approximations. Its results support implementability under that radar model, not a claim that TCPHD universally beats TPHD, TPMBM, or labeled trackers.
Key Characteristics
- Propagates a probability mass function over trajectory cardinality
- Propagates first-order intensity over complete trajectory variables
- Uses an IID-cluster approximation conditional on trajectory count
- Retains more count uncertainty than the Poisson TPHD approximation
- Supports Gaussian-mixture and fixed-lag L-scan implementations
- Does not preserve explicit global association hypotheses or identities
Common Use Cases
- Multi-object tracking where trajectory count uncertainty matters
- Radar or sonar scenes with births, deaths, missed detections, and clutter
- Trajectory estimation under a lower hypothesis budget than TPMBM
- Fixed-lag tracking when recent history may be revised
- Benchmarking Poisson and IID-cluster trajectory approximations
Example
Loading code...Frequently Asked Questions
What does TCPHD add to TPHD?
TPHD propagates trajectory intensity under a Poisson multitrajectory approximation, so its count distribution is determined by the mean. TCPHD also propagates an arbitrary cardinality probability mass function under an IID-cluster approximation, retaining more information about count uncertainty.
Does TCPHD preserve target identity?
It represents complete trajectory variables, so it forms histories from its own state space rather than tagging current peaks. However, its IID-cluster approximation does not retain explicit object-specific existence or global association hypotheses, so ambiguous crossings can still lose dependence.
Why must TCPHD intensity and cardinality stay consistent?
The integral of trajectory intensity and the mean of the cardinality distribution describe the same expected number of trajectories. If they disagree after numerical truncation or normalization, the stored quantities no longer describe one valid IID-cluster approximation.
What does L-scan change in a TCPHD implementation?
It keeps only the latest `L` states of each trajectory open to joint correction and freezes older states. This bounds covariance and memory growth but prevents later measurements from revising history outside the lag window.
How should TCPHD and TPHD be compared?
Use identical detections, dynamic and birth models, clutter, pruning, merging, lag, extraction rules, and compute limits. Report cardinality calibration and RMSE, T-GOSPA components, localization, missed and false objects, switches, runtime, and memory.