Multiple Extended Target Tracking Research Articles

Multiple Extended Target Tracking Algorithm Based on Spatio-Temporal Correlation

In the clutter environment, the measurement of a set of multiple extended targets, with an unknown number of targets, poses challenges in partitioning, and the computational cost is high. In particular, the multiple extended target tracking method, based on distance partition, has obvious potential estimation errors when the extended targets intersect. This paper proposes a partition algorithm, based on spatio-temporal correlation, which considers the correlation between adjacent moments of the extended target and uses this prior information to divide the measurement set into a survival target measurement set and a born target measurement set for the first time. Then, the survival target measurement set is clustered by the K-means++ algorithm, and the extended target tracking is transformed into point target tracking. The born target measurement undergoes preprocessing by the DBSCAN clustering algorithm, and then uses the directed graph with shared nearest neighbors (SNN) dividing the measurement set. The method proposed in this paper significantly reduces the number of partitions and the computational time. The effectiveness of the algorithm is demonstrated through experimental simulations.

Generalised covariance intersection‐Gamma Gaussian Inverse Wishart‐Poisson multi‐Bernoulli Mixture: An intelligent multiple extended target tracking scheme for mobile aquaculture sensor networks

AbstractPoisson multi‐Bernoulli Mixture (PMBM) filter has been known as an available or practical point and multiple extended target tracking (METT) method. The authors present an improved PMBM filter with adaptive detection probability and adaptive newborn distributions, accompanying with an associated distributed fusion strategy for the tracking extended multiple targets. First, the augmented state of unknown and changing target detection probability is assumed as Gamma (GAM) distribution. Second, extended states are described by Inverse Wishart (IW) distribution based on this augmented state, accompanying with dynamic states presented by Gaussian distribution. And then, an adaptive newborn distribution is adopted to describe the newborn targets appearing arbitrarily. Consequently, the closed‐form solutions of the proposed filter can be derived by approximating the intensity of newborn and potential targets to the Gamma Gaussian Inverse Wishart (GGIW) form. Moreover, the fused means that Generalised Covariance Intersection (GCI) is performed in such a large‐scale aquaculture sensor network. Experiments are presented to verify the availability of the GCI‐GGIW‐PMBM method, and comparisons with other METT filters also demonstrate that tracking behaviours are improved largely.

A Bi-Direction People Counting Method Based on Multiscale Clustering and Multiple Extended Target Tracking Using MIMO Radar

A Bi-Direction People Counting Method Based on Multiscale Clustering and Multiple Extended Target Tracking Using MIMO Radar

RFS-Based Multiple Extended Target Tracking With Resolved Multipath Detections in Clutter

RFS-Based Multiple Extended Target Tracking With Resolved Multipath Detections in Clutter

PMBM Filter for Multiple Extended Targets With Unknown Clutter Rate and Detection Probability

In a multi-target tracking (MTT) scenario, the prior knowledge of parameters such as clutter rate and detection probability are usually uncertain or estimated offline from training data. However, significant parameters mismatch in the clutter and detection model will result in biased estimates. In such cases, the ability to adaptively online estimate clutter rate and detection probability is critical in MTT under the random finite sets (RFS) framework. In this paper, we propose a robust Poisson multi-Bernoulli mixture (PMBM) filter that can accommodate model mismatch in clutter rate and detection probability for multiple extended target tracking problems. Moreover, the closed-form solution to the proposed method is derived by the use of Beta and Gamma Gaussian inverse-Wishart (GGIW) distribution, where Beta is used to describe unknown detection probability and GGIW is used to model extended target extension as an ellipse. Simulation results are presented to verify the effectiveness of the proposed method.

Hierarchical Network-Based Tracklets Data Association for Multiple Extended Target Tracking with Intermittent Measurements.

The key issue of multiple extended target tracking is to differentiate the origins of the measurements. The association of measurements with the possible origins within the target's extent is difficult, especially for occlusions or detection blind zones, which cause intermittent measurements. To solve this problem, a hierarchical network-based tracklet data association algorithm (ET-HT) is proposed. At the low association level, a min-cost network flow model based on the divided measurement sets is built to extract the possible tracklets. At the high association level, these tracklets are further associated with the final trajectories. The association is formulated as an integral programming problem for finding the maximum a posterior probability in the network flow model based on the tracklets. Moreover, the state of the extended target is calculated using the in-coordinate interval Kalman smoother. Simulation and experimental results show the superiority of the proposed ET-HT algorithm over JPDA- and RFS-based methods when measurements are intermittently unavailable.

Gaussian Process Gaussian Mixture PHD Filter for 3D Multiple Extended Target Tracking

This paper addresses the problem of tracking multiple extended targets in three-dimensional space. We propose the Gaussian process Gaussian mixture probability hypothesis density (GP-PHD) filter, which is capable of tracking multiple extended targets with complex shapes in the presence of clutter. Our approach combines the Gaussian process regression measurement model with the probability hypothesis density filter to estimate both the kinematic state and the shape of the targets. The shape of the extended target is described by a 3D radial function and is estimated recursively using the Gaussian process regression model. Furthermore, we transform the recursive Gaussian process regression problem into a state estimation problem by deriving a state space model such that the estimation of the extent can be integrated into the kinematic part. We derive the predicted likelihood function of the PHD filter and provide a closed-form Gaussian mixture implementation. To evaluate the performance of the proposed filter, we simulate a typical extended target tracking scenario and compare the GP-PHD filter with the traditional Gamma Gaussian Inverse-Wishart PHD (GGIW-PHD) filter. Our results demonstrate that the proposed algorithm outperforms the GGIW-PHD filter in terms of estimating both kinematic states and shape. We also investigate the impact of the measurement rates on both filters; it is observed that the proposed filter exhibits robustness across various measurement rates, while the GGIW-PHD filter suffers under low-measurement-rate conditions.

An Overview of the PAKF-JPDA Approach for Elliptical Multiple Extended Target Tracking Using High-Resolution Marine Radar Data

Ground radar stations observing specific regions of interest nowadays provide detections in the form of point-clouds. This article focuses on a framework that consists of an elliptical multitarget tracker, referred to as Principal-Axes based Kalman Filter (PAKF)-based Joint Probabilistic Data Association (JPDA) (PAKF-JPDA), to enable maritime traffic monitoring. The framework touches on two major stages, target detection and target tracking. For the former, we employed a clustering approach and for the latter, we presented a data-association-based version of the PAKF tracker with an automatic track management functionality. The framework’s benefits are demonstrated when it is applied to the radar streaming in a harbor setting based on a homogeneous multisensor tracking system by comparing our results against their corresponding reference data with visualizations, including performance measures.

Multiple extended target tracking based on distributed multi‐sensor fusion and shape estimation

AbstractDistributed multi‐sensor fusion based on the generalised covariance intersection (GCI) fusion has been widely integrated into the Random Finite Set theory, which is promising for multi‐target tracking with an unknown number of targets. However, it has not been widely investigated in the multiple extend target tracking (METT) field, and there is still an open problem on how to solve the inconsistency of label space among the sensors. For these problems, we first introduce the GCI fusion into the METT and proposed an association algorithm by considering the estimated shapes and the target positions to avoid the phenomenon of the label inconsistency as well as to reduce the computational burden. Simulation results show that the proposed algorithm has a better tracking performance than the traditional METT algorithms.

Multiple extended target tracking based on gamma box particle and labeled random finite sets

A gamma box particle (GBP) implementation of the extended target generalized labeled multi-Bernoulli (ET-GLMB) filter is proposed in this paper, named the ET-GBP-GLMB filter. The filter can simultaneously estimate the unknown number, measurement rate states, kinematics states, extension states and tracks of extended targets in the presence of clutter, missed detection and data association uncertainty. In order to obtain the GLMB recursion of the ET-GBP-GLMB filter, an appropriate measurement likelihood function that comprehensively considers the measurement rate state, kinematics state and extension state of each extended target is introduced for a given measurement partition cell, and the specific implementation steps of the filter are derived with necessary interval operations and approximations. Further, an extended target GBP labeled multi-Bernoulli (ET-GBP-LMB) filter is proposed as an effective approximation of the ET-GBP-GLMB filter. The advantages and disadvantages of the two proposed filters are presented in simulation examples. The simulation results show that, compared with the gamma sequential Monte Carlo (GSMC) implementation of the ET-GLMB filter, the GBP implementation of the ET-GLMB filter can effectively reduce the number of particles and the amount of computation. Compared with the ET-GBP-GLMB filter, the ET-GBP-LMB filter can further reduce the computational burden. Compared with the extended target box particle probability hypothesis density (ET-BP-PHD) filter, the two proposed filters can obtain better estimation results.

Robust Poisson multi-Bernoulli mixture filter using adaptive birth distributions for extended targets

This paper presents a robust Poisson multi-Bernoulli mixture (PMBM) filter using adaptive birth distributions for the tracking of multiple extended targets. Firstly, in order to be immune to the uncertainty of target birth, we present a novel measurement-driven adaptive birth distribution that is robust to the arbitrariness of locations where new targets appear. Then, to enhance practicability of algorithm, the Beta distribution is employed to describe unknown detection probability augmented into the extended target state. On these bases, the detailed recursion and closed-form solutions to the proposed filter are derived by means of approximating the intensity of target birth and potential targets to Beta gamma Gaussian inverse Wishart (BGGIW) mixture form and density of existing Bernoulli component to a single BGGIW form. Moreover, the computational bottleneck caused by data associations is settled by truncating the PMBM filtering density using the Gibbs sampler of the Metropolis Hasting Markov Chain Monte Carlo (MCMC). Simulation results show the robustness and effectiveness of the proposed method.

Distributed GGIW-CPHD-Based Extended Target Tracking Over a Sensor Network

Multiple extended target tracking (METT) is a common and challenging problem. Various solutions for METT have been proposed, however, most of them focus on the single-sensor or centralized multi-sensor scenarios. In this letter, we explore the multi-sensor METT problem in a distributed fusion framework. Specifically, there are two stages in the implementation process: 1) to perform a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gamma Gaussian Inverse Wishart Cardinalized Probability Hypothesis Density</i> (GGIW-CPHD) filter for each sensor node, and 2) to perform a fusion by resorting to the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Generalized Covariance Intersection</i> (GCI) fusion rule. In the fusion stage, we derive an approximate GGIW mixture form of the fused spatial density. Lastly, simulation experiments via a consensus sensor network are provided to verify the effectiveness of the proposed approach.

A Measurement Set Partitioning Algorithm Based on CFSFDP for Multiple Extended Target Tracking in PHD Filter

A Measurement Set Partitioning Algorithm Based on CFSFDP for Multiple Extended Target Tracking in PHD Filter

Multiple extended target tracking by truncated JPDA in a clutter environment

Data association is a crucial part of target tracking systems with clutter measurements. In general, its complexity increases sharply with a number of targets and measurements. Recently, high-resolution sensors have given rise to extended target tracking problems and more than one measurements can emerge from each target, making the association problems more complex. In this study, a tractable algorithm based on the Gaussian process measurement model and truncated joint probabilistic data association technique is proposed for multiple extended target tracking in the presence of measurement origin uncertainty. Based on the marginal association probabilities, the calculation amount is effectively reduced by truncating the association events with low probabilities in the shortest path problem. The effectiveness of the proposed algorithm is verified by the test of multiple extended targets tracking and compared with the linear-time joint probabilistic data association as well as the algorithm on random finite sets. Simulation results show that the proposed algorithm can track multiple extended targets accurately, which is significant in high-resolution radar tracking systems.

Joint tracking and classification of multiple extended targets via the PHD filter and star-convex RHM

For joint tracking and classification (JTC) of multiple extended targets in the presence of clutter and detection uncertainty, this paper proposes a recursive algorithm based on the probability hypothesis density (PHD) filter and star-convex random hypersurface model (RHM), resulting in the JTC-RHM-PHD filter. By modeling the extent state via the star-convex RHM, the JTC-RHM-PHD filter can classify the extended targets using the feature information of size and shape, instead of the size information only in the random matrix model (RMM)-based JTC method. To integrate the prior class-dependent information into the tracking procedure and obtain the recursive expressions of the JTC-RHM-PHD filter, the relationship between the instantaneous extent state and prior class-dependent information is first constructed. Then, the target state is remodeled by two vectors: one for the kinematic state and another for the extent state. The kinematic state is estimated via a Kalman-like filter. For the extent state, the measurement-based extent state and class-based extent state are obtained via the sensor measurements and prior class-dependent information, respectively. The two kinds of extent states are used to determine the target class. At last, a Gamma-Gaussian-Gaussian mixture implementation of the JTC-RHM-PHD filter is presented. Simulation results indicate that: (1) Compared with the RMM-based JTC method, the proposed JTC-RHM-PHD filter can correctly classify multiple extended targets with similar sizes. (2) Compared with the RHM-PHD filter, the proposed JTC-RHM-PHD filter has superior tracking performance with a similar algorithm complexity.

Joint detection and tracking of non‐ellipsoidal extended targets based on cubature Kalman‐CBMeMBer sub‐random matrices filter

Joint detection and tracking of multiple extended targets (ETs) from image observations is a challenging radar technology; especially for extended stealth targets (ESTs). This work provides a new approach for the ESTs tracking under the non-linear Gaussian system based on track-before-detect (TBD) approach. The sequential Monte Carlo cardinality-balanced multi-target multi-Bernoulli (SMC-CBMeMBer) filter provides a good framework to cope with TBD approach. However, this filter suffers from the particles’ degradation problem seriously; especially for ETs tracking. Recently, the cubature Kalman (CK)-CBMeMBer filter which employs a third-degree spherical-radical cubature rule has been proposed to handle the non-linear models, the CK-CBMeMBer filter is more accurate and more principled in mathematical terms compared to SMC-CBMeMBer filter. To this point, the authors address a TBD of ESTs with extended CK-CBMeMBer filter based on random matrix model (RMM), which is an efficient way to track ellipsoidal ESTs. In RMM-ESTs scenarios, although the extension ellipsoid is efficient, it may not be accurate enough because of lacking useful information, such as size, shape, and orientation. Therefore, they introduce a filter composed of sub-ellipses; each one is represented by a RMM. The results confirm the effectiveness and robustness of the proposed filter.

Joint detection and tracking of extended stealth targets from image observations based on subrandom matrices

The challenge of joint detection and tracking of multiple extended targets (ETs) arises in many radar applications, especially for extended stealth targets (ESTs) with small signal-to-noise ratio (SNR). Recently, the multi-Bernoulli (MB) filter-based random matrix model (RMM) has been proposed for tracking ellipsoidal ETs. The MB-RMM filter depends on the measurements (position and range rate), which are extracted by thresholding the received signal. It is acceptable if SNR is high. The threshold must be less than the sufficient probability to avoid a high rate of false detections. This assumption is unsuitable for tracking extended-stealth targets (ESTs) with unknown detection probability. To this point, we address a track-before-detect-MB-RMM approach, which is an efficient way to solve the unknown detection profile issue. There is a considerable advantage of using unthresholded data in simultaneous detection and tracking. In this scenario, although the extension ellipsoid is efficient, it may not be accurate enough because of a lack of useful information, such as size, shape, and orientation. Therefore, we introduce a filter composed of subellipses where each one is represented by an RMM. Furthermore, a sequential Monte Carlo implementation is applied to estimate nonlinear kinematic ESTs’ state. The results confirm the effectiveness and robustness of the proposed filter.

Extended Target Marginal Distribution Poisson Multi-Bernoulli Mixture Filter.

The existence of clutter, unknown measurement sources, unknown number of targets, and undetected probability are problems for multi-extended target tracking, to address these problems; this paper proposes a gamma-Gaussian-inverse Wishart (GGIW) implementation of a marginal distribution Poisson multi-Bernoulli mixture (MD-PMBM) filter. Unlike existing multiple extended target tracking filters, the GGIW-MD-PMBM filter computes the marginal distribution (MD) and the existence probability of each target, which can shorten the computing time while maintaining good tracking results. The simulation results confirm the validity and reliability of the GGIW-MD-PMBM filter.

Tracking of Multiple Closely Spaced Extended Targets Based on Prediction-Driven Measurement Sub-Partitioning Algorithm

For multiple extended target tracking, the accuracy of measurement partitioning directly affects the target tracking performance, so the existing partitioning algorithms tend to use as many partitions as possible to obtain accurate estimates of target number and states. Unfortunately, this may create an intolerable computational burden. What is worse is that the measurement partitioning problem of closely spaced targets is still challenging and difficult to solve well. In view of this, a prediction-driven measurement sub-partitioning (PMS) algorithm is first proposed, in which target predictions are fully utilized to determine the clustering centers for obtaining accurate partitioning results. Due to its concise mathematical forms and favorable properties, redundant measurement partitions can be eliminated so that the computational burden is largely reduced. More importantly, the unreasonable target predictions may be marked and replaced by PMS for solving the so-called cardinality underestimation problem without adding extra measurement partitions. PMS is simple to implement, and based on it, an effective multiple closely spaced extended target tracking approach is easily obtained. Simulation results verify the benefit of what we proposed—it has a much faster tracking speed without degrading the performance compared with other approaches, especially in a closely spaced target tracking scenario.

Fast measurement partitioning algorithm for multiple extended target tracking

For tracking of multiple extended targets with unknown and varying target number, the measurements partitioning is indispensable and plays an important role in achieving good performance. However, the number of possible partitions grows very fast with the increasing of total number of measurements, which causes heavy computational burden. Thus this Letter proposes a fast measurement partitioning algorithm, in which the target predictive information is explicitly considered and used to determine the clustering centres for measurement partitioning. To guarantee its robustness, the target predictions are further modified when the target number is overestimated. This flexible strategy reduces the dependence on original predictive information and significantly improves the accuracy of partitioning results. Besides, the proposed algorithm greatly reduces the partition number by fully considering possible changes of the number of newborn targets and spawned targets. It not only eliminates unreasonable and redundant measurement partitions for tracking performance improvement, but also fits well with the tracking of newborn targets and spawned targets. Simulation results verify the benefit of what the authors proposed.