Generalized Labeled multi-Bernoulli Research Articles

Multi-object tracking with an adaptive generalized labeled multi-Bernoulli filter

The challenges in multi-object tracking mainly stem from the random variations in the cardinality and states of objects during the tracking process. Further, the information on locations where the objects appear, their detection probabilities, and the statistics of the sensor’s false alarms significantly influence the tracking accuracy of the filter. However, this information is usually assumed to be known and provided by the users. In this paper, we propose an adaptive generalized labeled multi-Bernoulli (GLMB) filter which can track multiple objects without prior knowledge of the aforementioned information. Experimental results show that the performance of the proposed filter is comparable to an ideal GLMB filter supplied with correct information of the tracking scenarios.

Decomposed POMDP Optimization-Based Sensor Management for Multi-Target Tracking in Passive Multi-Sensor Systems

This paper presents an efficient information-theoretic sensor management method to maximize the performance of the passive multi-sensor system for multi-target tracking. We model the multi-target state as a generalized labeled multi-Bernoulli (GLMB) random finite set and formulate the dynamic sensor selection process as a partially observable Markov decision process (POMDP). The optimization objective is to maximum the information gain obtained from the observed data, which is measured by the Cauchy-Schwarz divergence. This is accomplished with two main technical innovations. The first is a tractable decomposed POMDP based sensor selection solution, in which the informative sensors are selected sequentially from the candidates based on the Cauchy-Schwarz divergence. The second is a novel dual-stage multi-sensor fusion strategy based on the iterated-corrector GLMB filter. Since the uncertainty of the passive multi-sensor system is generally large, the performance of the iterated-corrector scheme can be greatly influenced by the order of sensor updates. To fix this problem, the selected sensors are ranked in order of the Cauchy-Schwarz divergence obtained in sensor selection, followed by the iterated-corrector update. For the multi-sensor fusion, the effect of poor performance sensors is weakened and that of better performance sensors is enhanced. Simulation studies demonstrate the effectiveness and efficiency of the proposed method in challenging passive multi-target tracking scenarios.

Time-Varying DOA Tracking Algorithm Based on Generalized Labeled Multi-Bernoulli

Direction of arrival (DOA) tracking for multi-sources is a hot issue in array signal processing. To deal with the problem that sources DOA and their number are time-varying, a DOA tracking algorithm based on Generalized Labeled Multi-Bernoulli (GLMB) filter is proposed. Since the measurement value has only one set of data, the measurement association mapping (MAM) does not match, which leads to deviations in the GLMB filter update step. In this regard, we used the estimated sources number of the previous time step as the measurement number of the current time step, and successfully achieved MAM matching. Subsequently, particle filtering is used to approximate the posterior distribution of DOA, where the particle likelihood function can be calculated by the multi-signal classification (MUSIC) spatial spectrum function. In addition, by exponentially weighting the likelihood function, the number of particles in the high likelihood region of the posterior distribution increases, which makes the GLMB filter pruning and merging operations more effective. Simulation results show that the method is better than the probability hypothesis density DOA (PHD-DOA) algorithm in tracking state sources and estimating the number of targets.

Robust Generalized Labeled Multi-Bernoulli Filter for Multitarget Tracking With Unknown Non- Stationary Heavy-Tailed Measurement Noise

A robust generalized labeled multi-Bernoulli (GLMB) filter is presented to perform multitarget tracking (MTT) with unknown non-stationary heavy-tailed measurement noise (HTMN). The HTMN is modeled as a multivariate Student's t-distribution with unknown and time-varying mean. The proposed filter relaxes the restrictive assumption that the mean of HTMN is zero, and can effectively deal with MTT under the condition that the mean of HTMN is unknown and time-varying. The variational Bayesian (VB) approximation is applied in the GLMB filtering framework with the augmented state. The marginal likelihood function is obtained via minimizing the Kullback-Leibler divergence by the variational lower bound. The simulation results demonstrate that the proposed filter can effectively track multiple targets in both linear and nonlinear scenarios when the mean of HTMN is unknown and time-varying.

On-Line Visual Tracking with Occlusion Handling.

One of the core challenges in visual multi-target tracking is occlusion. This is especially important in applications such as video surveillance and sports analytics. While offline batch processing algorithms can utilise future measurements to handle occlusion effectively, online algorithms have to rely on current and past measurements only. As such, it is markedly more challenging to handle occlusion in online applications. To address this problem, we propagate information over time in a way that it generates a sense of déjà vu when similar visual and motion features are observed. To achieve this, we extend the Generalized Labeled Multi-Bernoulli (GLMB) filter, originally designed for tracking point-sized targets, to be used in visual multi-target tracking. The proposed algorithm includes a novel false alarm detection/removal and label recovery methods capable of reliably recovering tracks that are even lost for a substantial period of time. We compare the performance of the proposed method with the state-of-the-art methods in challenging datasets using standard visual tracking metrics. Our comparisons show that the proposed method performs favourably compared to the state-of-the-art methods, particularly in terms of ID switches and fragmentation metrics which signifies occlusion.

Improved generalized labeled multi-Bernoulli filter for non-ellipsoidal extended targets or group targets tracking based on random sub-matrices

For non-ellipsoidal extended targets and group targets tracking, using an ellipsoid to approximate the target extension may not be accurate enough because of lacking shape and orientation information. In consideration of this, we model a non-ellipsoidal extended target or target group as a combination of multiple ellipsoidal sub-objects, each represented by a random matrix. Besides, in practical tracking scenes, the knowledge of detection probability is of critical importance, which, however, is prior unknown due to the fluctuation of target parameters. Thus based on the aforementioned random sub-matrices model, an improved generalized labeled multi-Bernoulli (GLMB) filter is presented for the tracking of non-ellipsoidal extended targets or group targets in the case of unknown detection probability. In addition, a cheaper Gibbs sampling based joint prediction and updating implementation of the proposed GLMB filter is given, within which the extended targets or group targets are modeled using Beta gamma Gaussian inverse Wishart (BGGIW) distributions, achieving the estimation to detection probability, measurement rate, and extension state of each sub-object and the kinematic state with the positions of all sub-objects and unified kinematics for each extended target or target group. The simulation results demonstrate the effectiveness of the proposed filter.

Multidimensional Information Fusion in Active Sonar via the Generalized Labeled Multi-Bernoulli Filter

Under the conditions of low detection probabilities, high clutter rates, low data-sampling rates, large measurement errors, and unknown prior information of the target position, multi-object tracking is difficult. This paper proposes a multidimensional information fusion method in active sonar via the generalized labeled multi-Bernoulli (GLMB) filter. After modeling the position measurement, radial velocity measurement and amplitude measurement of the target and clutter, new target births are adaptively generated by the measurement-driven model, predictions are made by the target motion model and updates are performed via multidimensional measurements with the generalized likelihood in the GLMB filter, which enables the measurement information of different dimensions to be elegantly applied to information fusion and significantly improves the filter performance. The contribution of specific dimension measurement to fusion can be evaluated by the Kullback-Leibler (KL) divergence. In the efficient implementation, we propose flat Gibbs sampling to realize multiple hypothesis optimization. Moreover, the filtering recursion is derived from Gaussian mixtures. Simulations are presented to verify the proposed method.

Multi-Sensor Multi-Object Tracking With the Generalized Labeled Multi-Bernoulli Filter

This paper proposes an efficient implementation of the multi-sensor generalized labeled multi-Bernoulli (GLMB) filter. Like its single-sensor counterpart, such implementation requires truncating the GLMB sum. However the single-sensor case requires solving 2-D ranked assignment problems whereas the multi-sensor case require solving multi-dimensional ranked assignment problems, which are NP-hard. The proposed implementation exploits the GLMB joint prediction and update together with a new technique for truncating the GLMB filtering density based on Gibbs sampling. The resulting algorithm has a quadratic complexity in the number of hypothesized objects and linear in the total number of measurements from all sensors.

GLMB Tracker with Partial Smoothing.

In this paper, we introduce a tracking algorithm based on labeled Random Finite Sets (RFS) and Rauch–Tung–Striebel (RTS) smoother via a Generalized Labeled Multi-Bernoulli (GLMB) multi-scan estimator to track multiple objects in a wide range of tracking scenarios. In the forward filtering stage, we use the GLMB filter to generate a set of labels and the association history between labels and the measurements. In the trajectory-estimating stage, we apply a track management strategy to eliminate tracks with short lifespan compared to a threshold value. Subsequently, we apply the information of trajectories captured from the forward GLMB filtering stage to carry out standard forward filtering and RTS backward smoothing on each estimated trajectory. For the experiment, we implement the tracker with standard GLMB filter, the hybrid track-before-detect (TBD) GLMB filter, and the GLMB filter with objects spawning. The results show improvements in tracking performance for all implemented trackers given negligible extra computational effort compared to standard GLMB filters.

A Multi-Scan Labeled Random Finite Set Model for Multi-Object State Estimation

State-space models in which the system state is a finite set–called the multi-object state–have generated considerable interest in recent years. Smoothing for state-space models provides better estimation performance than filtering. In multi-object state estimation, the multi-object filtering density can be efficiently propagated forward in time using an analytic recursion known as the generalized labeled multi-Bernoulli (GLMB) recursion. In this paper, we introduce a multi-scan version of the GLMB model to accommodate the multi-object posterior recursion, and develop efficient numerical algorithms for computing this so-called multi-scan GLMB posterior.

Exact Closed-Form Multitarget Bayes Filters.

The finite-set statistics (FISST) foundational approach to multitarget tracking and information fusion has inspired work by dozens of research groups in at least 20 nations; and FISST publications have been cited tens of thousands of times. This review paper addresses a recent and cutting-edge aspect of this research: exact closed-form—and, therefore, provably Bayes-optimal—approximations of the multitarget Bayes filter. The five proposed such filters—generalized labeled multi-Bernoulli (GLMB), labeled multi-Bernoulli mixture (LMBM), and three Poisson multi-Bernoulli mixture (PMBM) filter variants—are assessed in depth. This assessment includes a theoretically rigorous, but intuitive, statistical theory of “undetected targets”, and concrete formulas for the posterior undetected-target densities for the “standard” multitarget measurement model.

An efficient approximate implementation for labeled random finite set filtering

Abstract In this paper, we propose an approximate implementation for labeled random finite set filtering with low computational cost. In contrast to the earlier implementations of the generalized labeled multi-Bernoulli (GLMB) filter and the labeled multi-Bernoulli (LMB) filter, the proposed approach adopts a sampler based on marginaling the joint association probability that can generate the components of the GLMB density from marginal probabilities with high parallel level. Additionally, this marginal probability approximation results in an efficient implementation of the LMB filter, which calculates the parameter set of the filtering LMB density from the marginal probabilities. Furthermore, we exploit a simplified belief propagation algorithm to obtain approximate marginal probabilities with linear complexity in the number of measurements and objects. Simulations show that the proposed implementation can handle both linear and non-linear scenarios and is more efficient against the existing implementations.

Robust Distributed Fusion With Labeled Random Finite Sets

This paper considers the problem of the distributed fusion of multi-object posteriors in the labeled random finite set filtering framework, using Generalized Covariance Intersection (GCI) method. Our analysis shows that GCI fusion with labeled multi-object densities strongly relies on label consistencies between local multi-object posteriors at different sensor nodes, and hence suffers from a severe performance degradation when perfect label consistencies are violated. Moreover, we mathematically analyze this phenomenon from the perspective of Principle of Minimum Discrimination Information and the so called yes-object probability. Inspired by the analysis, we propose a novel and general solution for the distributed fusion with labeled multi-object densities that is robust to label inconsistencies between sensors. Specifically, the labeled multi-object posteriors are firstly marginalized to their unlabeled posteriors which are then fused using GCI method. We also introduce a principled method to construct the labeled fused density and produce tracks formally. Based on the developed theoretical framework, we present tractable algorithms for the family of generalized labeled multi-Bernoulli (GLMB) filters including $\delta$-GLMB, marginalized $\delta$-GLMB and labeled multi-Bernoulli filters. The robustness and efficiency of the proposed distributed fusion algorithm are demonstrated in challenging tracking scenarios via numerical experiments.

Void Probabilities and Cauchy–Schwarz Divergence for Generalized Labeled Multi-Bernoulli Models

The generalized labeled multi-Bernoulli (GLMB) is a family of tractable models that alleviates the limitations of the Poisson family in dynamic Bayesian inference of point processes. In this paper, we derive closed form expressions for the void probability functional and the Cauchy–Schwarz divergence for GLMBs. The proposed analytic void probability functional is a necessary and sufficient statistic that uniquely characterizes a GLMB, while the proposed analytic Cauchy–Schwarz divergence provides a tractable measure of similarity between GLMBs. We demonstrate the use of both results on a partially observed Markov decision process for GLMBs, with Cauchy–Schwarz divergence based reward, and void probability constraint.

A Generalized Labeled Multi-Bernoulli Filter With Object Spawning

Previous labeled random finite set filter developments use a motion model that only accounts for survival and birth. While such a model provides the means for a multi-object tracking filter such as the Generalized Labeled Multi-Bernoulli (GLMB) filter to capture object births and deaths in a wide variety of applications, it lacks the capability to capture spawned tracks and their lineages. In this paper, we propose a new GLMB based filter that formally incorporates spawning, in addition to birth. This formulation enables the joint estimation of a spawned object's state and information regarding its lineage. Simulations results demonstrate the efficacy of the proposed formulation.

An Efficient Implementation of the Generalized Labeled Multi-Bernoulli Filter

This paper proposes an efficient implementation of the generalized labeled multi-Bernoulli (GLMB) filter by combining the prediction and update into a single step. In contrast to an earlier implementation that involves separate truncations in the prediction and update steps, the proposed implementation requires only one truncation procedure for each iteration. Furthermore, we propose an efficient algorithm for truncating the GLMB filtering density based on Gibbs sampling. The resulting implementation has a linear complexity in the number of measurements and quadratic in the number of hypothesized objects.

Multiple Extended Target Tracking With Labeled Random Finite Sets

Targets that generate multiple measurements at a given instant in time are commonly known as extended targets. These present a challenge for many tracking algorithms, as they violate one of the key assumptions of the standard measurement model. In this paper, a new algorithm is proposed for tracking multiple extended targets in clutter, that is capable of estimating the number of targets, as well the trajectories of their states, comprising the kinematics, measurement rates and extents. The proposed technique is based on modelling the multi-target state as a generalised labelled multi-Bernoulli (GLMB) random finite set (RFS), within which the extended targets are modelled using gamma Gaussian inverse Wishart (GGIW) distributions. A cheaper variant of the algorithm is also proposed, based on the labelled multi-Bernoulli (LMB) filter. The proposed GLMB/LMB-based algorithms are compared with an extended target version of the cardinalised probability hypothesis density (CPHD) filter, and simulation results show that the (G)LMB has improved estimation and tracking performance.

Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities

In multi-object inference, the multi-object probability density captures the uncertainty in the number and the states of the objects as well as the statistical dependence between the objects. Exact computation of the multi-object density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multi-object density approximation that can capture statistical dependence between objects. In particular, we derive a tractable Generalized Labeled Multi-Bernoulli (GLMB) density that matches the cardinality distribution and the first moment of the labeled multi-object distribution of interest. It is also shown that the proposed approximation minimizes the Kullback-Leibler divergence over a special tractable class of GLMB densities. Based on the proposed GLMB approximation we further demonstrate a tractable multi-object tracking algorithm for generic measurement models. Simulation results for a multi-object Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.