Francesco Papi

Generalized Labeled Multi-Bernoulli Approximation of Multi-Object Densities

In multiobject inference, the multiobject 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 multiobject density is generally intractable and tractable implementations usually require statistical independence assumptions between objects. In this paper we propose a tractable multiobject 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 multiobject 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 multiobject tracking algorithm for generic measurement models. Simulation results for a multiobject Track-Before-Detect example using radar measurements in low signal-to-noise ratio (SNR) scenarios verify the applicability of the proposed approach.

A Particle Multi-Target Tracker for Superpositional Measurements Using Labeled Random Finite Sets

In this paper we present a general solution for multi-target tracking with superpositional measurements. Measurements that are functions of the sum of the contributions of the targets present in the surveillance area are called superpositional measurements. We base our modelling on Labeled Random Finite Set (RFS) in order to jointly estimate the number of targets and their trajectories. This modelling leads to a labeled version of Mahlers multi-target Bayes filter. However, a straightforward implementation of this tracker using Sequential Monte Carlo (SMC) methods is not feasible due to the difficulties of sampling in high dimensional spaces. We propose an efficient multi-target sampling strategy based on Superpositional Approximate CPHD (SA-CPHD) filter and the recently introduced Labeled Multi-Bernoulli (LMB) and Vo-Vo densities. The applicability of the proposed approach is verified through simulation in a challenging radar application with closely spaced targets and low signal-to-noise ratio.

Scalable Multisensor Multitarget Tracking Using the Marginalized δ-GLMB Density.

Existing multisensor multitarget tracking solutions have complexities that grow super-exponentially w.r.t. the number of sensors. In this letter, we propose a novel algorithm for multisensor multitarget tracking that is scalable w.r.t. the number of sensors. Our approach is based on the class of marginalized δ-generalized labeled multi-Bernoulli (Mδ-GLMB) densities, which can be used to define a principled approximation to the δGLMB density representing the true posterior in the sense of the multitarget Bayes filter. We derive the update equations of an MδGLMB density that matches the δ-GLMB density in cardinality distribution and first moment, as well as minimizes the Kullback- Leibler divergence w.r.t. the true δ-GLMB density over the class of Mδ-GLMB densities. The proposed Mδ-GLMB density is then used to define an approximate multisensor sequential update step. Simulations in multisensor scenarios with radar and range-only measurements verify the applicability of the proposed approach.

Multiple target tracking in video data using labeled random finite set

This paper demonstrates how the δ-Generalized Labeled Multi-Bernoulli (δ-GLMB) filter can be applied to track moving targets on videos. The tracking is performed directly on the original images which are not preprocessed into point measurements and estimates the number of targets on frame along with their states. In that sense this concept bears resemblance to the track before detect (TBD) approach employed under low signal to noise ratio conditions. Image sequences from the CAVIAR1 dataset are used in simulations to prove the aptitude of this method.

Multi-target Track-Before-Detect using labeled random finite set

Multi-target tracking requires the joint estimation of the number of target trajectories and their states from a sequence of observations. In low signal-to-noise ratio (SNR) scenarios, the poor detection probability and large number of false observations can greatly degrade the tracking performance. In this case an approach called Track-Before-Detect (TBD) that operates on the pre-detection signal, is needed. In this paper we present a labeled random finite set solution to the multi-target TBD problem. To the best of our knowledge this is the first provably Bayes optimal approach to multi-target tracking using image data. Simulation results using realistic radar-based TBD scenarios are also presented to demonstrate the capability of the proposed approach.

Bayesian Track-Before-Detect for closely spaced targets

Track-Before-Detect (TBD) is an effective approach to multi-target tracking problems with low signal-to-noise (SNR) ratio. In this paper we propose a novel Labeled Random Finite Set (RFS) solution to the multi-target TBD problem for a generic pixel based measurement model. In particular, we discuss the applicability of the Generalized Labeled Multi-Bernoulli (GLMB) distribution to the TBD problem for low SNR and closely spaced targets. In such case, the commonly used separable targets assumption does not hold and a more sophisticated algorithm is required. The proposed GLMB recursion is effective in the sense that it matches the cardinality distribution and Probability Hypothesis Density (PHD) function of the true joint posterior density. The approach is validated through simulation results in challenging scenarios.

Multi-Sensor d-GLMB Filter for Multi-Target Tracking using Doppler only Measurements

Multi-target tracking using Doppler-shift only measurements is a difficult problem due to the lack of local observability. Multiple Doppler sensors are required to estimate in time the velocity and position vectors of a single-target. The situation is more complicated in multi-target scenarios due to the measurement-to-track assignment problem and approximations usually required in multi-sensor algorithms. In this paper, we consider the use of a δ-Generalized Labeled Multi Bernoulli (δ-GLMB) filter for centralized processing of the Doppler only measurements received from multiple sensors. The approach is a natural multi-sensor extension of the single-sensor δ-GLMB filter and represents a closed-form solution the multi-target tracking problem. Simulation results for challenging Doppler only multi-target scenarios are reported to verify the applicability of the proposed approach.

OSPA-based sensor control

This paper presents a new sensor control method for multi-object filtering, that is designed based on maximizing a measure of confidence in state estimation accuracy. Confidence of estimation is quantified by measuring the dispersion of the multi-object posterior about its statistical mean using Optimal Sub-Pattern Assignment (OSPA). The proposed method is generic and the presented algorithm can be used with common statistical filters. Implementation of the algorithm in conjunction with a labeled multi-Bernoulli filter is presented. Simulation studies demonstrate that the proposed method works in a challenging sensor control for multi-target tracking scenario.

Bayesian multi-target tracking with superpositional measurements using labeled random finite sets

In this paper we present a general solution for multi-target tracking problems with superpositional measurements. In a superpositional sensor model, the measurement collected by the sensor at each time step is a superposition of measurements generated by each of the targets present in the surveillance area. We use the Bayes multi-target filter with Labeled Random Finite Set (RFS) in order to jointly estimate the number of targets and their trajectories. We propose an implementation of this filter using Sequential Monte Carlo (SMC) methods with an efficient multi-target sampling strategy based on the Approximate Superpositional Cardinalized Probability Hypothesis Density (CPHD) filter.

Constrained d-GLMB Filter for Multi-Target Track-Before-Detect using Radar Measurements

Multi-target Track-Before-Detect (TBD) algorithms are of great interest in many surveillance applications using Radar measurements. When low sensor resolution and/or low Signal-to-Noise Ratio (SNR) limit the tracking performance, exploiting additional information about the targets and/or the scenario becomes fundamental. In this paper, we consider a novel application of the d-Generalized Labeled Multi-Bernoulli (d-GLMB) filter for ground and/or maritime TBD problems where additional information is modeled using constraints on the target dynamics. Specifically, state constraints are used to model the additional information about the surveillance area, and a generalized likelihood function is derived to enforce the constraints in the update step of the d-GLMB filter. Simulations results for a scenario with low resolution and low SNR verify the applicability of the proposed approach.