Random Finite Set Research Articles

Posterior Cramér–Rao lower bounds for extended target tracking with PMBM conjugate recursion

AbstractThis letter considers the posterior Cramér–Rao lower bounds (PCRLB) problem for extended target tracking from a stack of measurement data that are modelled as random variables in the random finite sets framework. The scalars in the traditional PCRLB are converted into vectors based on random finite sets to derive a theoretical lower bound. In this way, the proposed method can be applied to the multi‐target tracking problem and accommodates scenarios with targets of varying. Moreover, solving the data association problem from four parts caused by the conjugate update of the Poisson multi‐Bernoulli mixture filter is considered. Simulation results are presented to verify the effectiveness of the derived PCRLB.

Probability hypothesis density filter for parameter estimation of multiple hazardous sources

This study introduces an advanced methodology for estimating the source term of multiple, variable-number biochemical hazard releases, where the exact count of sources is not predetermined. Focusing on environments monitored via a network of sensors, we tackle this challenge through a multi-source Bayesian filtering paradigm, employing the theory of random finite sets (RFS). Our novel approach leverages a modified particle filter-based probability hypothesis density (PHD) filter within the RFS framework, enabling simultaneous estimation of critical source characteristics (such as location, emission rate, and effective release height) and the quantification of source numbers. This method not only accurately estimates pertinent source parameters but is also adept at identifying the emergence of new sources and the cessation of existing ones within the monitored area. The efficacy of our approach is validated through extensive simulations, which mimic a range of scenarios with varying and unknown source counts, highlighting the proposed method’s robustness and precision.

Augmented LRFS-based filter: Holistic tracking of group objects

Aiming at the problem of accurate tracking of group objects, where multiple closely spaced objects within a group pose a coordinated motion, this paper develops a new type of labeled random finite set (LRFS), i.e., augmented LRFS, which inherently integrates group information such as the group geometry center and the group index into the definition of LRFS. Specifically, for each element in an augmented LRFS, the kinetic states, the track labels, and the corresponding group information of its represented object are incorporated. Then, by means of the proposed augmented LRFS-based filter, i.e., the labeled multi-Bernoulli filter with the proposed augmented LRFS, the group structure is iteratively propagated and updated during the tracking process, which achieves the holistic estimation of the kinetic states, track labels, and the corresponding group information of multiple group objects, and further improves the tracking performance. Finally, simulation experiments are conducted to verify the effectiveness of the proposed augmented LRFS-based filter.

Visual multi-object tracking with re-identification and occlusion handling using labeled random finite sets

This paper proposes an online visual multi-object tracking (MOT) algorithm that resolves object appearance–reappearance and occlusion. Our solution is based on the labeled random finite set (LRFS) filtering approach, which in principle, addresses disappearance, appearance, reappearance, and occlusion via a single Bayesian recursion. However, in practice, existing numerical approximations cause reappearing objects to be initialized as new tracks, especially after long periods of being undetected. In occlusion handling, the filter’s efficacy is dictated by trade-offs between the sophistication of the occlusion model and computational demand. Our contribution is a novel modeling method that exploits object features to address reappearing objects whilst maintaining a linear complexity in the number of detections. Moreover, to improve the filter’s occlusion handling, we propose a fuzzy detection model that takes into consideration the overlapping areas between tracks and their sizes. We also develop a fast version of the filter to further reduce the computational time.

The multiple pairwise Markov chain model-based labeled multi-Bernoulli filter

Most of existing multi-target tracking (MTT) algorithms, which are rooted in random finite set theory, generally rely on two hypotheses, i.e., the single dynamic model hypothesis and the hidden Markov chain (HMC) hypothesis, and the HMC hypothesis requires the target state to conform to a Markov process and the detection process to be independent. Unfortunately, these hypotheses may not always hold at the same time in many practical situations. Therefore, it is important to study the MTT algorithms in such scenarios when the HMC hypothesis and the single dynamic model hypothesis fail simultaneously. As a result, this paper presents a multiple model MTT algorithm, which is designed to tackle the MTT problem effectively in scenarios where both hypotheses are invalid. Firstly, when the HMC hypothesis is not satisfied, an MTT algorithm was presented based on pairwise Markov chain (PMC) and the labeled multi-Bernoulli filter (PMC-LMB). Secondly, in case that both hypotheses are not met, a multiple model MTT algorithm was proposed by extending the previously presented PMC-LMB filter to multiple PMC model case. Finally, extensive simulation was done to demonstrate the efficiency of the presented algorithms.

Robust and Convergent Distributed Cooperative Localization With Labeled Bernoulli Random Finite Set

Robust and Convergent Distributed Cooperative Localization With Labeled Bernoulli Random Finite Set

A Network-Group Target State and Network Topology Estimation Method Based on Signals Containing Delay, Doppler and Address

Network-group targets are a set of objectives that adhere to a shared communication protocol, perform common tasks, and exhibit relatively coordinated movements. Typically, network-group targets emit radar and communication signals. However, they often employ a silent mode to evade our perception. Despite this, they continue to exchange data through their communication networks. By intercepting the communication signals of these targets, this paper proposes a method for estimating the state and network topology of network-group targets based on random finite set (RFS) theory. This method is based on the modeling of network-group targets using a labeled multi-Bernoulli (LMB) RFS. In state estimation, the usual method involves extracting the localization parameters from the signals in the first step and use these parameters for target tracking in the second step. This study focused on estimating the kinematic states of network-group targets using communication signals containing delay and Doppler information received by multiple mobile sensor platforms. The proposed method considers the coherency between frequency-hopping pulses in the signals, resulting in an improved estimation performance. In addition, considering that network-group targets require network access for information exchange, graph theory concepts were utilized to estimate the network topology of network-group targets by address measurement. The simulation results validated the effectiveness of the proposed method and demonstrated its superior performance.

Generalized Labeled Multi-Bernoulli Filter-Based Passive Localization and Tracking of Radiation Sources Carried by Unmanned Aerial Vehicles

This paper discusses a key technique for passive localization and tracking of radiation sources, which obtains the motion trajectory of radiation sources carried by unmanned aerial vehicles (UAVs) by continuously or periodically localizing it without the active participation of the radiation sources. However, the existing methods have some limitations in complex signal environments and non-stationary wireless propagation that impact the accuracy of localization and tracking. To address these challenges, this paper extends the δ-generalized labeled multi-Bernoulli (GLMB) filter to the scenario of passive localization and tracking based on the random finite-set (RFS) framework and provides the extended Kalman filter (EKF) and unscented Kalman filter (UKF) implementations of the δ-GLMB filter, which fully take into account the nonlinear motion of the radiation source. By modeling the “obstacle scenario” and the influence of external factors (e.g., weather, terrain), our proposed GLMB filter can accurately track the target and capture its motion trajectory. Simulation results verify the effectiveness of the GLMB filter in target identification and state tracking.

Distributed Joint Detection, Tracking, and Classification via Labeled Multi-Bernoulli Filtering.

In this article, we propose a novel approach to distributed joint detection, tracking, and classification (D-JDTC) of multiple targets by means of a multisensor network. The proposed approach relies on labeled multi-Bernoulli (LMB) random finite set modeling of the multisensor state, and consists of two main tasks, that is, local filtering in each individual node and data fusion among multiple nodes. For local filtering, the LMB filter is extended to JDTC by augmenting the target state to incorporate class and mode information. Further, the well-known generalized covariance intersection and recently developed minimum information loss fusion paradigms are exploited for data fusion among sensors. The effectiveness of the resulting algorithm, called D-JDTC-LMB, is assessed via simulation experiments.

Arithmetic average density fusion - Part I: Some statistic and information-theoretic results

Finite mixture such as the Gaussian mixture is a flexible and powerful probabilistic modeling tool for representing the multimodal distribution widely involved in many estimation and learning problems. The core of it is representing the target distribution by the arithmetic average (AA) of a finite number of sub-distributions which constitute a mixture. While the mixture has been widely used for single sensor filter design, it is only recent that the AA fusion demonstrates compelling performance for multi-sensor filter design. In this paper, some statistic and information-theoretic results are given on the covariance consistency, mean square error, mode-preservation capacity, and the information divergence of the AA fusion approach. In particular, based on the concept of conservative fusion, the relationship of the AA fusion with the existing conservative fusion approaches such as covariance union and covariance intersection is exposed. A suboptimal weighting approach has been proposed, which jointly with the best mixture-fit property of the AA fusion leads to a max–min optimization problem. Linear Gaussian models are considered for algorithm illustration and simulation comparison, resulting in the first-ever AA fusion-based multi-sensor Kalman filter. This is the first part of a series of papers that provide a comprehensive and thorough study of the AA fusion methodology and its application for target tracking. Extension and derivation of the AA fusion in the context of random finite set filters are provided in the consequent papers.

Anomaly detection of defect using energy of point pattern features within random finite set framework

In this paper, we propose a lightweight approach for industrial defect detection that is modeled based on anomaly detection using point pattern data. Most recent works use global features for feature extraction to summarize image content. However, global features are not robust against lighting and viewpoint changes and do not describe images’ geometrical information which, thus, cannot be fully utilized in manufacturing industry. To the best of our knowledge, we are the first to propose using transfer learning of local/point pattern features to overcome these limitations and capture geometrical information of the interested image regions. We model these local/point pattern features as a random finite set (RFS). In addition, we propose RFS energy, in contrast to RFS likelihood as an anomaly score. The similarity distribution of point pattern features of the normal sample has been modeled as a multivariate Gaussian. Parameters learning of the proposed RFS energy does not require any heavy computation. We evaluate the proposed approach on the MVTec AD dataset, a multi-object defect detection dataset. Experimental results show the outstanding performance of our proposed approach compared to the state-of-the-art methods, and the proposed RFS energy outperforms the state-of-the-art in the few shot learning settings. Also, we evaluated the proposed approach on needle dataset, a real life application, to detect defective needle samples given three different views. The results show superior performance compared to DiffeNet.

A Modified δ-Generalized Labeled Multi-Bernoulli Filtering for Multi-Source DOA Tracking With Coprime Array

For the target tracking problem where the number of targets fluctuates with time and the measurement is a point measurement, the random finite set (RFS) class filtering is an available solution. However, in direction of arrival (DOA) tracking, the array observation is a super-positional value, and the tracking performance can be severely impaired if the RFS-based filter approach is applied. As a result, a novel measurement association mapping (NMAP) approach has been presented to cope with the mapping problem between the array observations and sources. Nevertheless, the tracking performance is poor when the number of particles is small. In this paper, a modified delta-Generalized Labeled Multi-Bernoulli (δ-GLMB) DOA tracking particle filter is proposed in combination with the NMAP strategy, which can achieve the same tracking performance with a smaller number of particles by modifying the particles in the δ-GLMB prediction step. Furthermore, the approach is extended to a coprime array and can achieve better DOA tracking performance than a uniform linear array. Simulation experiments validate the effectiveness of the proposed algorithm.

Distributed Large-Scale Swarm Control in Obstacle Environment Based on Random Finite Set Theory

Distributed Large-Scale Swarm Control in Obstacle Environment Based on Random Finite Set Theory

A Labeled RFS-Based Framework for Multiple Integrity Attackers Detection and Identification in Cyber–Physical Systems

The problem of multiple integrity attacks (attackers) detection and identification (MIADI) in cyber-physical systems (CPSs) is still a challenging problem to date. The goal of this paper is to develop a knowledge-based method capable of simultaneously detecting and identifying multiple integrity attacks aiming at different sensors in a CPS. In this paper, with the help of labeled random finite set (RFS) theory, a new solution to solve the MIADI problem is proposed. The main contributions of this paper, lie in the the following two aspects, the first is the novel formulation of the MIADI problem, in which labeled RFSs are used to model the behaviors of multiple integrity attackers for the first time, and the second is the proposed labeled RFS-based solution, which provides an elegant framework to cope with the MIADI problem. Numerical experiments are conducted and experimental results demonstrate the effectiveness of the proposed solution. This proposed solution further extends the feasibility of the labeled RFS theory in the context of CPSs cybersecurity.

Adaptive Marginal Multi-Target Bayes Filter without Need for Clutter Density for Object Detection and Tracking

The random finite set (RFS) approach for multi-target tracking is widely researched because it has a rigorous theoretical basis. However, many prior parameters such as the clutter density, survival probability and detection probability of the target, pruning threshold, merging threshold, initial state of the birth object and its error covariance matrix are required in the standard RFS-based filters. In real application scenes, it is difficult to obtain these prior parameters. To address this problem, an adaptive marginal multi-target Bayes filter without the need for clutter density is proposed. This filter obviates the need for prior clutter density and survival probability. Instead of using the prior initial states of newborn targets and their error covariance matrices, it uses two scans of observations to generate the initial states of potential birth targets and their error covariance matrices according to the least squares technique. Simulation results reveal that the proposed adaptive filter has smaller OSPA and OSPA(2) errors as well as less cardinality error than the adaptive RFS-based filters. The OSPA and OSPA(2) errors have been reduced by more than 20% compared to those of the adaptive RFS-based filters.

Automating multi-target tracking of singing humpback whales recorded with vector sensors.

Passive acoustic monitoring is widely used for detection and localization of marine mammals. Typically, pressure sensors are used, although several studies utilized acoustic vector sensors (AVSs), that measure acoustic pressure and particle velocity and can estimate azimuths to acoustic sources. The AVSs can localize sources using a reduced number of sensors and do not require precise time synchronization between sensors. However, when multiple animals are calling concurrently, automated tracking of individual sources still poses a challenge, and manual methods are typically employed to link together sequences of measurements from a given source. This paper extends the method previously reported by Tenorio-Hallé, Thode, Lammers, Conrad, and Kim [J. Acoust. Soc. Am. 151(1), 126-137 (2022)] by employing and comparing two fully-automated approaches for azimuthal tracking based on the AVS data. One approach is based on random finite set statistics and the other on message passing algorithms, but both approaches utilize the underlying Bayesian statistical framework. The proposed methods are tested on several days of AVS data obtained off the coast of Maui and results show that both approaches successfully and efficiently track multiple singing humpback whales. The proposed methods thus made it possible to develop a fully-automated AVS tracking approach applicable to all species of baleen whales.

Coordinated target localization and tracking with node scheduling for a network of autonomous underwater vehicles

Underwater mobile sensor networks (UMSNs) have the advantages of large area coverage, flexible network structure, and good local resolution. Particularly, spatial diversity can be exploited through node mobility to get more target information. To take those advantages in the context of regional cooperative target localization and tracking, a joint node scheduling and acoustic model fusion method is proposed for an UMSN consisting of multiple autonomous underwater vehicles (AUVs). First, a target tracking algorithm framework based on the random finite set theory is established. To take the acoustic environment into account, the a priori acoustic field and target distribution information are combined to evaluate the detection probability. A path-planning scheme with node scheduling is then developed based on the information gain to optimize the detection performance. To achieve effective node scheduling, three reward functions with different information gains respectively derived from the Rényi divergence and Fisher information matrix are proposed and compared. The rationale and the performance of the developed method are verified via simulations. A simplified version of the approach is also tested in field experiments with three AUVs, verifying the effectiveness of node scheduling in a realistic scenario.

DB-Tracker: Multi-Object Tracking for Drone Aerial Video Based on Box-MeMBer and MB-OSNet

Drone aerial videos offer a promising future in modern digital media and remote sensing applications, but effectively tracking several objects in these recordings is difficult. Drone aerial footage typically includes complicated sceneries with moving objects, such as people, vehicles, and animals. Complicated scenarios such as large-scale viewing angle shifts and object crossings may occur simultaneously. Random finite sets are mixed in a detection-based tracking framework, taking the object’s location and appearance into account. It maintains the detection box information of the detected object and constructs the Box-MeMBer object position prediction framework based on the MeMBer random finite set point object tracking. We develop a hierarchical connection structure in the OSNet network, build MB-OSNet to get the object appearance information, and connect feature maps of different levels through the hierarchy such that the network may obtain rich semantic information at different sizes. Similarity measurements are computed and collected for all detections and trajectories in a cost matrix that estimates the likelihood of all possible matches. The cost matrix entries compare the similarity of tracks and detections in terms of position and appearance. The DB-Tracker algorithm performs excellently in multi-target tracking of drone aerial videos, achieving MOTA of 37.4% and 46.2% on the VisDrone and UAVDT data sets, respectively. DB-Tracker achieves high robustness by comprehensively considering the object position and appearance information, especially in handling complex scenes and target occlusion. This makes DB-Tracker a powerful tool in challenging applications such as drone aerial videos.

Likelihood function modelling of radar targets under high‐speed observation

AbstractThe likelihood ratio function of the target plays a crucial role in applications such as tracking before detection (TBD). In the framework of random finite sets, the performance of radar target TBD based on particle filters is limited by the performance of the likelihood ratio function. Traditional likelihood ratio functions only consider the likelihood ratio between the target and background noise, thus requiring a high signal‐to‐noise (SNR) ratio for the input signal. In scenarios where the observation time interval is extremely short, there exists a strong autocorrelation between the complex amplitudes of the radar target at different time instants. Based on this characteristic, an autoregressive model is utilized to establish the autocorrelation of the target complex amplitudes and update the target's complex amplitudes using a Kalman filter. The likelihood ratio is derived from the model and it is compared with the traditional likelihood ratio under pulse‐Doppler radar. This comparison aims to demonstrate the effectiveness of the proposed likelihood ratio. Due to the fact that this likelihood ratio only requires the extraction of the complex amplitudes of the target scattering centre, without the need to extract the energy around the scattering centre like traditional point spread function methods, the algorithm complexity is greatly reduced, enabling real‐time operation of the proposed method.

An RFS Time-Frequency Model for Decomposing Chirp Modes With Dynamic Cross, Appearance, and Disappearance

In this paper, the decomposition and retrieval of the chirp modes with dynamic cross, appearance, and/or disappearance in a signal are formulated as a process of tracking time-frequency (TF) trajectories. Analyses show that the amplitude and frequency evolutions of each chirp mode in the signal can be described by polynomial prediction models. When all these evolutions are viewed as state equations, it is illustrated that the random appearance and/or disappearance of these modes will make the state equations into a state random finite set (RFS). If the amplitudes and frequencies obtained by the short-time spectrum of the signal are taken as the measurements of the state equations, a measurement RFS model in the presence of data association and detection uncertainties is coined when the statistical properties of the existing and newborn chirp modes as well as the noise/clutter are taken into consideration. So, a RFS TF model for tracking the TF trajectories in a signal is established. It is then demonstrated that a modified probability hypothesis density filter can be used to infer the amplitude and frequency posterior distributions of the chirp modes in the signal when the intensity of the RFS states is modelled as a Gaussian mixture. Numerical simulation experiments verify the effectiveness of our model and analytical results. Meanwhile, a superior performance is achieved especially for the high readability, extractability, and decomposability of instantaneous frequency trajectories with dynamic cross, appearance, and disappearance in a signal.