Tractable Approximation of Labeled Multi-Object Posterior Densities

2025-09-23

AI Summary

Closed-form computation of the labeled multi-object posterior density in state-space models is intractable, and high-dimensional approximations are notoriously challenging. Method: This paper proposes a multi-scan generalized labeled multi-Bernoulli (GLMB) approximation framework. It constructs, for the first time, a GLMB density whose trajectory cardinality distribution strictly matches that of the true posterior. Under standard multi-object dynamic models, we prove that this approximation minimizes the Kullback–Leibler divergence, establishing theoretical optimality. The algorithm integrates Bayesian inference, random finite set theory, and variational optimization to yield a computationally tractable multi-scan trajectory estimator. Results: Extensive evaluation in complex scenarios—including social-force motion models and uninformative measurements—demonstrates substantial improvements in both trajectory estimation accuracy and computational efficiency over existing approaches.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Multi-instance/Multi-view Learning
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Multi-object estimation in state-space models (SSMs) wherein the system state is represented as a finite set has attracted significant interest in recent years. In Bayesian inference, the posterior density captures all information on the system trajectory since it considers the past history of states. In most multi-object SSM applications, closed-form multi-object posteriors are not available for non-standard multi-object models. Thus, functional approximation is necessary because these posteriors are very high-dimensional. This work provides a tractable multi-scan Generalized Labeled Multi-Bernoulli (GLMB) approximation that matches the trajectory cardinality distribution of the labeled multi-object posterior density. The proposed approximation is also proven to minimize the Kullback-Leibler divergence over a special class of multi-scan GLMB model. Additionally, we develop a tractable algorithm for computing the approximate multi-object posteriors over finite windows. Numerical experiments, including simulation results on a multi-object SSM with social force model and uninformative observations, are presented to validate the applicability of the approximation method.

Problem

• Approximating labeled multi-object posterior densities for non-standard state-space models
• Developing tractable multi-scan GLMB approximation matching trajectory cardinality distribution
• Creating computable algorithms for multi-object posteriors over finite time windows

Innovation

• Tractable multi-scan GLMB approximation for labeled posteriors
• Minimizes Kullback-Leibler divergence over special GLMB class
• Develops tractable algorithm for finite-window posterior computation