What is Trajectory Poisson Multi-Bernoulli Mixture Filter?
Trajectory Poisson Multi-Bernoulli Mixture Filter is a Bayesian multi-object tracker that represents undetected and detected objects with a Poisson Multi-Bernoulli Mixture density defined on a Random Finite Set of Trajectories.
Quick Facts
| Specification | Official Specification |
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How It Works
Represent undetected mass and detected histories separately
The trajectory PPP carries potential histories for objects that exist but have never generated a detection. A first detection creates a Bernoulli trajectory hypothesis with uncertainty over its start time and state sequence. Detected objects remain in an MBM whose global hypotheses encode compatible measurement histories.
Each Bernoulli stores an existence probability and a conditional single-trajectory density. A global hypothesis selects local histories jointly, retaining association dependence that TPHD and TCPHD discard. This does not make association uncertainty disappear; it makes that uncertainty explicit.
Filter alive trajectories, all trajectories, or a time window
The TPMBM derivation gives separate recursions for trajectories alive now and for all trajectories that have existed. It also proves a PMBM time-marginalization result for declared trajectory intervals under the standard model.
The alive formulation limits stored histories but omits terminated tracks from its current state. The all-trajectory formulation supports retrospective estimation and end-time uncertainty but grows over time. A chosen time window must match the downstream question; marginalizing to current targets gives PMBM state information, not the discarded joint history.
Make hypothesis and history reduction auditable
Exact symbolic conjugacy does not bound the number of association branches or trajectory-state dimension. Practical filters use ellipsoidal gating, ranked assignment, N-scan pruning, recycling, Gaussian moment or information forms, and L-scan covariance approximations. Report retained hypothesis probability mass and history lag with runtime and memory.
An independent shallow-water study applies TPMBM to intermittent acoustic sources with a specialized matched-field likelihood. Its results support one application and measurement model; they do not transfer automatically to point detections, cameras, or extended objects.
Key Characteristics
- Defines a PMBM posterior on a Random Finite Set of Trajectories
- Uses a trajectory PPP for objects that have never been detected
- Uses an MBM for detected trajectories and association histories
- Supports separate alive-trajectory and all-trajectory recursions
- Permits time-window marginalization under the declared standard model
- Needs explicit hypothesis, component, and history reduction in practice
Common Use Cases
- Radar and sonar tracking with uncertain births and long occlusions
- Multi-scan association when later observations may revise track history
- Retrospective estimation of trajectories that have already ended
- Tracking-by-detection with probabilistic first-track initiation
- Bayesian comparison with MHT, GLMB, TPHD, and TCPHD
Example
Loading code...Frequently Asked Questions
How is TPMBM different from a standard PMBM filter?
Standard PMBM filtering represents the current set of object states. TPMBM defines PPP and MBM components over complete trajectory variables, preserving uncertainty about start times, histories, and, in the all-trajectory formulation, end times.
What is the difference between alive and all-trajectory TPMBM filters?
The alive filter retains trajectories present at the current time. The all-trajectory filter also retains terminated histories. Both can be Bayesian recursions under their stated models, but the all-trajectory representation needs stronger history management as time grows.
Why does TPMBM still need pruning if it is conjugate?
Conjugacy preserves the PMBM functional form; it does not prevent the number of global and local association hypotheses from growing. Gating, ranked assignment, pruning, recycling, N-scan decisions, and lag approximations make the representation computationally finite.
How is TPMBM different from TPMB?
TPMBM retains a mixture of global multi-Bernoulli trajectory hypotheses. TPMB approximates that mixture with one trajectory multi-Bernoulli, usually reducing assignment and memory costs while discarding association dependence. The approximation method determines the loss.
How should a TPMBM filter be evaluated?
Report T-GOSPA components, count and first-detection error, existence calibration, retained hypothesis mass, smoothing lag, runtime, and memory. Comparisons must share detections, likelihoods, birth and clutter models, extraction rules, and compute budgets.