What is Trajectory Probability Hypothesis Density Filter?
Trajectory Probability Hypothesis Density Filter is an assumed-density multi-object tracker that propagates first-order intensity over a Random Finite Set of Trajectories using a Poisson multitrajectory approximation.
Quick Facts
| Specification | Official Specification |
|---|
How It Works
Project the multitrajectory posterior onto Poisson intensity
The TPHD and TCPHD derivation obtains the best Poisson multitrajectory approximation in the stated Kullback-Leibler direction. Prediction extends surviving histories and adds newborn one-state trajectories; update uses the measurement set at the current-time projection while changing weights and state histories.
The resulting intensity lives on trajectory space. Integrating over a region of start times, lengths, and state sequences gives the expected number of trajectories in that region. It is not a normalized density for one track, and a component weight is expected trajectory mass rather than an existence probability.
Store history without inventing identity certainty
A Gaussian-mixture TPHD component contains a mean vector and covariance across the represented state sequence, not only the latest state. This permits current measurements to refine recent historical states and produces trajectories from the declared posterior approximation.
TPHD does not retain explicit mutually exclusive global association hypotheses. Two nearby objects can still merge into one intensity mode, and extracting one track per component can overstate identity certainty. The method is principled about its trajectory state but remains a first-moment approximation.
Bound history cost with an L-scan approximation
Full trajectory covariance grows with track length. An L-scan implementation updates only the most recent L states and leaves older states fixed, reducing matrix and storage cost while giving up later corrections beyond that lag. Pruning and merging must respect trajectory history, not only current-state proximity.
A Pulse-Doppler TPHD/TCPHD study independently demonstrates trajectory-space recursions, Gaussian sequential implementations, and L-scan trade-offs under its radar model. Its simulation results do not establish universal superiority outside those measurement and clutter conditions.
Key Characteristics
- Propagates first-order intensity on a set-of-trajectories state space
- Uses a Poisson multitrajectory assumed-density approximation
- Represents start time and a sequence of states in each component
- Forms trajectory estimates without adding labels to state-only PHD peaks
- Supports Gaussian-mixture and L-scan implementations
- Does not preserve a general count distribution or global association mixture
Common Use Cases
- Low-complexity radar or sonar tracking that requires track histories
- Trajectory baselines for maneuvering-object tracking experiments
- Fixed-lag refinement of recent states under a bounded memory budget
- Comparing state-only PHD extraction with trajectory-space inference
- Applications where first-moment summaries are acceptable
Example
Loading code...Frequently Asked Questions
How is TPHD different from a standard PHD filter?
Standard PHD intensity is defined over current object states, so connecting extracted peaks across time requires extra heuristics. TPHD intensity is defined over complete trajectory variables with a start time and state sequence, allowing trajectory extraction from the represented approximation itself.
Does each TPHD component represent exactly one object?
No. A component contributes expected trajectory mass under a Poisson intensity and is not a Bernoulli existence variable. Component management and peak extraction can produce useful tracks, but they must not be interpreted as a full posterior over mutually exclusive object identities.
What does the L value mean in an L-scan TPHD filter?
The lag `L` is the number of most recent trajectory states whose joint density remains open to measurement updates. Older states are frozen. A larger lag permits more retrospective correction but increases covariance, memory, and computation.
When should TCPHD be used instead of TPHD?
TCPHD is appropriate when uncertainty over the number of trajectories matters beyond its expectation. It propagates an explicit cardinality distribution with trajectory intensity, while TPHD uses a Poisson count assumption and is generally simpler.
How should a TPHD filter be evaluated?
Report T-GOSPA or another trajectory metric, count error, localization, missed and false objects, switches, extraction sensitivity, component count, runtime, and memory. Hold detections, birth, survival, clutter, pruning, lag, and compute budget constant across comparisons.