Tracking Multiple Targets Using Bearing-Only Measurements in Underwater Noisy Environments

This study handles tracking multiple objects under bearings-only measurements of multiple heterogeneous sonar sensors in cluttered underwater environments. In order to track multiple objects in clutter environments, we apply Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter. In the GM-PHD filter, the Extended Kalman Filter (EKF) is applied, since the EKF can cope with non-linearity of bearings-only measurements. However, range uncertainty of the object is large for bearings-only measurements, which can generate poor performance in the GM-PHD. The bearing measurements of any two passive sonar sensors can intersect at one point, and the point provides the viable location of an object. Hence, if an intersection point of two bearing sensors satisfies the maximum sensing range constraint, then the point can generate an object sample in our GM-PHD Kalman filter. In addition, every object sample is updated under the measurement update step of the EKF. To the best of our knowledge, this paper is novel in tracking multiple objects in clutter, under bearings-only measurements of multiple heterogeneous sonar sensors. The efficacy of the proposed GM-PHD Kalman filter is demonstrated under MATLAB simulations.

Gaussian mixture probability hypothesis density filter with dynamic probabilities: Application to road traffic surveillance

The Gaussian mixture probability hypothesis density (GM-PHD) filter has been widely adopted to track multiple targets, because it can effectively handle target birth/death without the track-to-measurement data association process. However, the GM-PHD filter is known to have serious problems related to birth intensity generation and target tractability. In addition, weight underestimation/overestimation may occur if there are missing detections or measurement clutters. Since these problems may lead to severe estimation errors, many researchers have tried to find solutions. However, none of the researchers have been successful at solving these problems simultaneously. In this paper, we propose a robust multitarget tracking scheme based on the GM-PHD filter to improve estimation accuracy, even if there are many false detections. The proposed scheme includes the processing step of evaluating multiple states/measurements, which is designed to overcome the weight underestimation/overestimation problems. Furthermore, it includes generating the birth intensity for the next iteration using measurements not associated with any tracked states. We also show that the proposed method can be extended to nonlinear Gaussian models. The simulation results demonstrate that the proposed scheme can provide relatively accurate multitarget estimates compared with the previous approaches when the measurements include many false positives/negatives.

An augmented state Gaussian mixture probability hypothesis density filter for multitarget tracking of autonomous underwater vehicles

In this paper, a novel moving target detection and tracking approach is presented based on Gaussian mixture probability hypothesis density (GMPHD) filter in synthetic aperture radar (SAR). Based on the advantages of GMPHD filter and the characteristics of moving target in SAR imagery, GMPHD filter is employed on potential moving target candidates extracted from a sequence of temporal and spatial sub-aperture SAR images to detect and track the moving targets in heavy clutter environment. Utilizing the tracking algorithm, the states and the number of moving targets are obtained over time. Simultaneously, the strong ground stationary clutter lacking of the dynamic behavior is eliminated finally. Both simulation and real Gotcha data set processing results are provided to demonstrate the effectiveness of the proposed approach.

Gaussian mixture probability hypothesis density (GM-PHD) filter is proposed as a closed form solution of PHD filter to estimate the first-order moment of the multi-target posterior density. Recently, different methods such as Competitive GM-PHD (CGM-PHD), Penalized GM-PHD (PGM-PHD) and Collaborative PGM-PHD (CPGM-PHD) are proposed to enhance the performance of GM-PHD filter for tracking closely spaced targets. These methods have no assumption about possible subsequent missed detections which occur in some practical applications. For this reason, the performance of these filters degrades in this condition. In this paper, we propose a novel improvement on GM-PHD filter to track targets in possible subsequent missed detections. In addition to targets weight, we define a probability of confirm (PC) for each target which is adaptively calculated in time. We also propose a new state refinement and state extraction methods based on the defined PC. The experimental results provided for different uncertainties show the effectiveness of the proposed method.

Refined GM-PHD tracker for tracking targets in possible subsequent missed detections

This paper describes the performance of the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter for multiple human tracking in an intelligent vision system. Human movement trajectories were observed with a camera and tracked by the GM-PHD filter. The filter multi-target tracking ability was validated by two random motion trajectories in the paper. To evaluate the filter performance in relation to the target movement, the motion velocity and angular velocity as key evaluation factors were proposed. A circular motion model was implemented for simplified analysis of the filter tracking performance. The results indicate that the mean absolute error defined as the difference between the filter prediction and the ground truth is proportional to the motion speed and angular velocity of the target. The error is only slightly affected by the tracking targets' number.

Modern vehicles equipped with Advanced Driver Assistance Systems (ADAS) rely heavily on sensor fusion to achieve a comprehensive understanding of their surrounding environment. Traditionally, the Kalman Filter (KF) has been a popular choice for this purpose, necessitating complex data association and track management to ensure accurate results. To address errors introduced by these processes, the application of the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filter is a good choice. This alternative filter implicitly handles the association and appearance/disappearance of tracks. The approach presented here allows for the replacement of KF frameworks in many applications while achieving runtimes below 1 ms on the test system. The key innovations lie in the utilization of sensor-based parameter models to implicitly handle varying Fields of View (FoV) and sensing capabilities. These models represent sensor-specific properties such as detection probability and clutter density across the state space. Additionally, we introduce a method for propagating additional track properties such as classification with the GM-PHD filter, further contributing to its versatility and applicability. The proposed GM-PHD filter approach surpasses a KF approach on the KITTI dataset and another custom dataset. The mean OSPA(2) error could be reduced from 1.56 (KF approach) to 1.40 (GM-PHD approach), showcasing its potential in ADAS perception.

Robust fusion of GM-PHD filters based on geometric average

This paper proposes a Bayesian set-based estimator applied to the adaptive mapping of objects resting on the seabed, through the design and the implementation of a Gaussian Mixture - Probability Hypothesis Density (GM-PHD) filter. Starting from the noisy measures provided by an Autonomous Underwater Vehicle (AUV) equipped with side-scan sonar, the GM-PHD filter produces an on-line estimation of the map of the explored area. The mapping performance are demonstrated through simulations providing the effectiveness of the filter in localizing and mapping new findings and decreasing the spatial uncertainty of the position of known objects.

This work applies the Gaussian Mixture Probability Hypothesis Density (GMPHD) Filter to multi-object tracking in video data. In order to take advantage of additional visual information, Kernelized Correlation Filters (KCF) are evaluated as a possible extension of the GMPHD tracking-by-detection scheme to enhance its performance. The baseline GMPHD filter and its extension are evaluated on the UA-DETRAC benchmark, showing that combining both methods leads to a higher recall and a better quality of object tracks to the cost of increased computational complexity and increased sensitivity to false-positives.

In this paper, we propose a highly feasible fully online multi-object tracking and segmentation (MOTS) method that uses instance segmentation results as an input. The proposed method is based on the Gaussian mixture probability hypothesis density (GMPHD) filter, a hierarchical data association (HDA), and a mask-based affinity fusion (MAF) model to achieve high-performance online tracking. The HDA consists of two associations: segment-to-track and track-to-track associations. One affinity, for position and motion, is computed by using the GMPHD filter, and the other affinity, for appearance is computed by using the responses from single object trackers such as kernalized correlation filter, SiamRPN, and DaSiamRPN. These two affinities are simply fused by using a score-level fusion method such as min-max normalization referred to as MAF. In addition, to reduce the number of false positive segments, we adopt mask IoU-based merging (mask merging). The proposed MOTS framework with the key modules: HDA, MAF, and mask merging, is easily extensible to simultaneously track multiple types of objects with CPU-only execution in parallel processing. In addition, the developed framework only requires simple parameter tuning unlike many existing MOTS methods that need intensive hyperparameter optimization. In the experiments on the two popular MOTS datasets, the key modules show some improvements. For instance, ID-switch decreases by more than half compared to a baseline method in the training sets. In conclusion, our tracker achieves state-of-the-art MOTS performance in the test sets.

In the extended target tracking using Gaussian process (GP) or other methods to estimate the extension state, all of them is necessary to obtain the measurement model, and the deviation from the true kinematic state affects the extension result easily. Meanwhile, with the growth of the shape complexity, the corresponding covariance matrix dimension increases, leading to a very high computational burden. To this end, we present an extended target tracking algorithm based on deep learning, which adopts Gaussian mixture (GM) probability hypothesis density (PHD) filter for extended target (ET) tracking, called the ET-GM-PHD filter, to estimate the kinematic state, and uses convolutional conditional neural process (ConvCNP) to estimate the extension state (i.e., the shape of the target) avoiding the complex computation and dependence on priors. Therefore, the proposed algorithm is named as the ConvCNP-GM-PHD filter. In our algorithm, ConvCNP lies on the neural network (NN) and GP, where the former can learn the rules from a large amount of data without any priors, while the latter uses the covariance function to express the distribution over possible functions according to a small number of context observations. Due the proposed algorithm can effectively combine the advantages of both, it is reliable to get a model via training which is able to realize function regression flexibly. Thus, ConvCNP is able to estimate the shape function by putting the angles and radial value between the kinematic state and associated measurements into the pre-trained model. The results show that the accuracy of the extension state estimation of the proposed ConvCNP-GM-PHD filter is improved and its computational complexity is also reduced. It implies that the proposed algorithm is more real-time and effective, and has a good application prospect.

In this paper, we consider the problem of tracking multiple targets in a passive multi-static radar system using Doppler-only measurements. The number of targets is assumed unknown and time-varying. The Doppler measurements are subject to additive noise, clutter, and missed detections. Doppler-only measurements from a single sensor provide incomplete information about the target state, commonly referred to as single-sensor unobservability. In a passive multi-static radar system, the availability of multiple bistatic links naturally lends itself to the fusion of measurements from spatially distributed sensors. However, data fusion emerges as a computationally intensive problem in multi-sensor multi-target tracking algorithms. We propose a two-step sequential approach to solve the underlying problem. We first cast the underlying problem as a group sparse problem in a discretized position-velocity space. A group sparsity based algorithm is applied to simultaneously exploit the multi-static Doppler frequency measurements to directly obtain the instantaneous target state estimates in the Cartesian coordinate system. These estimates are then fed as inputs to the linear Gaussian mixture probability hypothesis density (GMPHD) filter, which removes the false measurements, compensates for missed detections and reduces the localization error. The optimal sub-pattern assignment metric, which jointly comprises a weighted contribution of cardinality error and localization error, is used to evaluate the performance of the proposed method. Simulation results show that the proposed method successfully handles the multi-target tracking problem and outperforms the existing random receiver selection based multi-sensor implementation of the GMPHD filter.