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

Abstract

This paper proposes an efficient implementation of the multi-sensor generalized labeled multi-Bernoulli (GLMB) filter. The solution 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 quadratic complexity in the number of hypothesized object and linear in the number of measurements of each individual sensors. Index TermsRandom finite sets, generalized labeled multi-Bernoulli, multi-object tracking, data association, Gibbs sampling The classical PHD and CPHD filters are developed for single-sensors. Since the multi-sensor PHD, CPHD and multi-Bernoulli filters are combinatiorial [4], [30], the most commonly used approximate multi-sensor PHD, CPHD and multi-Bernoulli filter are the heuristic "iterated corrector" versions [31] that apply single-sensor updates, once for each sensor in turn. This approach yields final solutions that depend on the order in which the sensors are processed. Multi-sensor PHD and CPHD filters that are principled, computationally tractable, and independent of sensor order have been proposed in [4] (Section 10.6).However, this approach as well as the heuristic "iterated corrector" involve two levels of approximation since the exact multi-sensor PHD, CPHD and multi-Bernoulli filters are approximations of the Bayes multi-sensor multi-object filter.An exact solution to the Bayes multi-object filter is the Generalized Labeled Multi-Bernoulli (GLMB) filter, which also outputs multi-object trajectories [32], [33]. Moreover, given a cap on the number of GLMB components, recent works show that the GLMB filter can be implemented with linear complexity in the number of measurements and quadratic in the number of hypothesized objects [34]. The GLMB density is flexible enough to approximate any labeled RFS density with matching intensity function and cardinality distribution [35], and also enjoys a number of nice analytical properties, e.g. the void probability functional-a necessary and sufficient statistic-of a GLMB, the Cauchy-Schwarz divergence between two GLMBs, the L 1 -distance between a GLMB and its truncation, can all be computed in closed form [36], [33]. Recent research in approximate GLMB filters [37], [38] as well as applications in tracking from merged measurements [39], extended targets [40], maneuvering targets [41], [42], trackbefore-detect [35], [43], computer vision [44]-[47], sensor scheduling [36], [48], field robotics [49], and distributed multi-object tracking [50], demonstrate the versatility of the GLMB filter, and suggest that it is an important tool in multi-object systems.In this work we present an implementation of the multi-sensor GLMB filter. The major hurdle in the multi-sensor GLMB filter implementation is the NP-hard multi-dimensional ranked assignment problem.A multi-sensor version of an approximation of the GLMB filter, known as the marginalized GLMB filter, was proposed in [38]. While this multi-sensor solution is scalable in the number of sensors, it...

Multi-Target Localization and Tracking Using TDOA and AOA Measurements Based on Gibbs-GLMB Filtering

“…Given the multi-target state X, each (x, l) ∈ X is either detected with probability p D,m (x, l) and generates observation z with likelihood function g (z |x, l ). For S sensors, the multi-sensor and multi-target mapping [56] is defined by θ (m)…”

“…GLMB RFS has been applied in many fields, such as tracking with merged measurements [39], extended targets [40], computer vision [41][42][43], cell tracking [44,45], track-before-detect [46,47], sensor scheduling [48,49], field robotics [50][51][52], distributed tracking [53,54] and cell microscopy [55]. The GLMB solution has also been applied to the multi-sensor case [56] and the multi-scan case [57]. The multi-sensor GLMB filter [56] is the first multi-sensor solution with linear complexity in the sum of number of measurements.…”

“…The GLMB solution has also been applied to the multi-sensor case [56] and the multi-scan case [57]. The multi-sensor GLMB filter [56] is the first multi-sensor solution with linear complexity in the sum of number of measurements. The multi-scan GLMB filter [57] is the first solution that is demonstrated to handle as much as 100 scans as well as providing posterior statistics about the set of target trajectories.…”

GLMB Tracker with Partial Smoothing

“…Consequently, truncation-based unlabeled RFS algorithms are heuristics [51]. Numerically, labeled RFS filters such as the GLMB have been demonstrated to be scalable in the number of objects [52], number of scans [50], and number of sensors [53]. Hence, the GLMB is a versatile class of models for multi-sensor multi-object problems.…”

Resolvable Group State Estimation with Maneuver Based on Labeled RFS and Graph Theory

“…So, the GLMB filter can obtain the number of targets and their tracks at the same time, which is a very significant breakthrough. It has been proven to be a Bayes optimal filter [26]. Vo et al also proposed an implementation method called the δ-GLMB filter, also known as the Vo-Vo filter.…”