What is Poisson Multi-Bernoulli Mixture Filter?
Poisson Multi-Bernoulli Mixture Filter is a Bayesian multi-object tracker that represents never-detected objects with a Poisson Point Process and detected objects with a mixture of Bernoulli-track hypotheses.
Quick Facts
| Specification | Official Specification |
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How It Works
Separate undetected objects from detected tracks
The PPP intensity carries expected object mass that has not yet generated a detection. Prediction applies survival and motion to that intensity and adds a birth PPP. During update, missed detection thins the PPP; each measurement creates a Bernoulli hypothesis whose existence probability compares target-generated evidence from the PPP with clutter intensity.
Detected objects live in an MBM. Each Bernoulli has an existence probability and conditional state density, while each global hypothesis selects one local hypothesis per track subject to a compatible measurement assignment.
Exploit conjugacy without confusing form and cost
The direct PMBM derivation shows that the family is conjugate for the standard point-target measurement model and gives a linear Gaussian implementation. It also relates a labeled multi-Bernoulli mixture to delta-GLMB; this structural connection does not make PMBM and GLMB identical in track representation or birth handling.
Conjugacy says the posterior remains PPP plus MBM. Association branching can still grow combinatorially, so gating, clustering, Murty-style assignment or sampling, pruning, recycling, merging, and N-scan policies determine practical cost and approximation error.
Measure discovery, association, and trajectory quality
The PMBM author's overview distinguishes point-target, extended-target, general-measurement, continuous-discrete, and trajectory variants. A Trajectory PMBM Filter makes complete histories the state; its likelihood and state space are not interchangeable with a standard point-target PMBM or an extended-object variant.
Report GOSPA or OSPA decomposition, T-GOSPA or identity metrics when trajectories are represented, first-detection delay, false initiation, cardinality error, existence calibration, retained hypothesis mass, runtime, and memory. Compare under the same detector, birth intensity, clutter model, extraction policy, and compute budget.
Key Characteristics
- Uses a PPP to represent objects that have never been detected
- Uses an MBM to represent detected objects and association ambiguity
- Creates probabilistic new-track hypotheses from measurements
- Is conjugate under the declared standard point-target model
- Retains global association hypotheses for detected objects
- Requires pruning, recycling, and hypothesis-management policies
Common Use Cases
- Radar or sonar tracking with uncertain object births
- Autonomous-driving tracking-by-detection with false positives
- Extended-object tracking with a separately derived measurement model
- Trajectory estimation with PMBM distributions on sets of trajectories
- Bayesian comparison with MHT, GLMB, LMB, and PHD-family filters
Example
Loading code...Frequently Asked Questions
Why does PMBM use both a Poisson process and a multi-Bernoulli mixture?
The Poisson process represents objects that may exist but have never been detected, where no individual track identity is yet justified. The multi-Bernoulli mixture represents detected objects, their existence probabilities, and competing measurement-association explanations.
How does a PMBM filter initiate a new track?
A measurement branches into a clutter explanation and a first-detection explanation supported by the undetected PPP intensity. Their relative evidence determines a new Bernoulli existence probability and state density. Birth and clutter calibration therefore directly affect initiation.
How is PMBM related to multiple hypothesis tracking?
Both retain global association hypotheses for detected tracks. PMBM supplies an explicit Bayesian RFS density, probabilistic existence for tracks, and a Poisson representation for never-detected objects. Classical MHT implementations may use different scores, trees, initiation, and pruning semantics.
What is the difference between PMBM and PMB?
PMBM retains a mixture of multi-Bernoulli global hypotheses. PMB approximates that mixture with one multi-Bernoulli, usually reducing memory and association cost while discarding dependencies. The approximation method and recycling policy determine how much information is lost.
Does PMBM always outperform GLMB or LMB?
No universal ordering follows from the distribution names. Results depend on the target and measurement models, detector, birth intensity, pruning budget, implementation, and metric. Compare accuracy, identity, discovery delay, calibration, runtime, and memory under matched conditions.