What is Generalized Labeled Multi-Bernoulli Filter?
Generalized Labeled Multi-Bernoulli Filter is a labeled Random Finite Set tracker whose posterior is a weighted mixture over object-label sets and association histories, preserving the GLMB family under the standard multi-object Bayesian recursion.
Quick Facts
| Specification | Official Specification |
|---|
How It Works
Preserve mutually exclusive labeled hypotheses
A GLMB component assigns probability mass to a label set and stores label-conditioned state densities. Delta-GLMB components additionally index association histories, so two explanations that reuse the same detection or imply incompatible label sets remain separate rather than being averaged into independent tracks.
Vo and Vo's conjugate-prior paper establishes a GLMB family that is closed under the standard multi-object Chapman-Kolmogorov prediction and Bayes update. The guarantee depends on the stated point-target, independent-survival, independent-detection, and Poisson-clutter model.
Truncate the mixture without hiding lost probability
Prediction branches over surviving and newborn label sets; update branches over feasible positive one-to-one measurement maps. The exact symbolic posterior can therefore contain an impractically large number of components. Production filters gate candidates and retain only high-weight hypotheses using ranked assignment, shortest paths, Gibbs sampling, or related methods.
The efficient GLMB implementation combines prediction and update and uses Gibbs sampling to reduce wasted hypothesis generation. Its complexity result belongs to that implementation and model; retained probability mass, convergence diagnostics, hypothesis caps, and latency still need reporting.
Distinguish GLMB from LMB, MHT, and PMBM
LMB marginalizes a richer labeled mixture into independent per-label Bernoulli components, trading dependence for smaller state. MHT also maintains competing association histories, but its classical track trees and scores are not the same probability representation as GLMB. PMBM separates never-detected objects into a Poisson process and detected objects into a multi-Bernoulli mixture.
Evaluate GLMB with GOSPA and trajectory metrics, count error, ID switches, fragmentation, hypothesis probability mass, existence calibration, localization consistency, memory, and latency. A mathematically closed family does not protect against model mismatch, poor birth intensity, missed hypotheses, or bad detections.
Key Characteristics
- Represents a weighted mixture over distinct object-label sets
- Can index components by complete association histories
- Is conjugate under the standard labeled multi-object model
- Preserves dependencies and mutual exclusion across labeled tracks
- Requires practical gating and hypothesis truncation
- Supports direct labeled state and trajectory extraction
Common Use Cases
- Multi-object tracking through crossings and temporary occlusion
- Radar or sonar tracking with explicit identity management
- Multi-sensor tracking with joint association hypotheses
- Computer vision or cell tracking that needs labeled trajectories
- Reference-quality comparison for approximate LMB or PMBM variants
Example
Loading code...Frequently Asked Questions
What does a GLMB hypothesis represent?
A GLMB hypothesis represents a possible set of object labels together with association-history context, a normalized weight, and conditional state densities for those labels. Competing hypotheses retain mutually exclusive explanations of the same measurements.
Why is GLMB called a conjugate family?
Under the standard labeled point-target transition and measurement models, applying Chapman-Kolmogorov prediction and Bayes update to a GLMB prior yields another GLMB density. This is closure of the functional form, not a promise that all resulting components are cheap to enumerate.
What is the difference between GLMB and delta-GLMB?
GLMB names the broader distribution family. Delta-GLMB is an implementation-oriented parameterization whose components explicitly select a label set and typically carry an association history. In tracking literature, GLMB filter often refers to this delta-GLMB recursion.
How is GLMB different from LMB?
GLMB retains a mixture of global label and association hypotheses, including dependencies among objects. LMB collapses that mixture into independent Bernoulli components per label. LMB is smaller, while GLMB can preserve ambiguity that matters during crossings and occlusions.
What limits a practical GLMB filter?
The number of survival, birth, and association hypotheses can grow rapidly. Gating, ranked assignment, sampling, pruning, and capping make computation feasible but may remove important probability mass. Detection quality, birth modeling, and likelihood calibration remain equally important.