Sequential Monte Carlo Probability Hypothesis Density Research Articles

SA-HPMHT for Maritime Dim Targets Tracking With Sensor Location Uncertainty

To address the problem of tracking low signal-to-clutter ratio (SCR) maritime targets with sensor location uncertainty, an effective track-before-detect (TBD) method, called the state augmentation histogram probabilistic multihypothesis tracking (SA-HPMHT) algorithm, is proposed in this article. In this algorithm, the initialization of new tracks is realized based on the constant false alarm rate (CFAR) detector with a low threshold and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${K}$ </tex-math></inline-formula> -means clustering algorithm. The target and sensor states are then simultaneously estimated in an iterative manner via a synthetic histogram and state augmentation (SA) method. In each iteration, we update the estimated sensor state and yield more accurate measured images, allowing for improved performance of detection and tracking targets. Finally, an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${M}/{N}$ </tex-math></inline-formula> logic technology is invoked to confirm or terminate the tracks. The results of simulation and real dataset verification show that the SA-HPMHT algorithm has a better performance compared with the histogram probabilistic multihypothesis tracking (H-PMHT) algorithm and the sequential Monte Carlo probability hypothesis density (SMC-PHD) algorithm.

Scene-Specialized Multitarget Detector with an SMC-PHD Filter and a YOLO Network.

You only look once (YOLO) is one of the most efficient target detection networks. However, the performance of the YOLO network decreases significantly when the variation between the training data and the real data is large. To automatically customize the YOLO network, we suggest a novel transfer learning algorithm with the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter and Gaussian mixture probability hypothesis density (GM-PHD) filter. The proposed framework can automatically customize the YOLO framework with unlabelled target sequences. The frames of the unlabelled target sequences are automatically labelled. The detection probability and clutter density of the SMC-PHD filter and GM-PHD are applied to retrain the YOLO network for occluded targets and clutter. A novel likelihood density with the confidence probability of the YOLO detector and visual context indications is implemented to choose target samples. A simple resampling strategy is proposed for SMC-PHD YOLO to address the weight degeneracy problem. Experiments with different datasets indicate that the proposed framework achieves positive outcomes relative to state-of-the-art frameworks.

A novel SMC-PHD filter for multi-target tracking without clustering

The probability hypothesis density (PHD) filter has been regarded as a practicable multi-target tracking algorithm which can alleviate the computational difficulty of the multi-target Bayes filter due to the multiple high-dimensional space integrals. As one of the major implementations of the PHD filter, sequential Monte Carlo PHD (SMC-PHD) is suitable for highly nonlinear systems. However, in scenarios with missing detections, the false-estimation problem occurs which leads to estimation performance degradation. To reduce the negative effects of missing detections, this paper develops a compensatory measurements generating mechanism and presents a novel measurement compensation based SMC-PHD filter, which can avoid the unreliable clustering. Comparative results verify the proposed filter, indicating good application prospects.

A Robust SMC-PHD Filter for Multi-Target Tracking with Unknown Heavy-Tailed Measurement Noise.

In multi-target tracking, the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter is a practical algorithm. Influenced by outliers under unknown heavy-tailed measurement noise, the SMC-PHD filter suffers severe performance degradation. In this paper, a robust SMC-PHD (RSMC-PHD) filter is proposed. In the proposed filter, Student-t distribution is introduced to describe the unknown heavy-tailed measurement noise where the degrees of freedom (DOF) and the scale matrix of the Student-t distribution are respectively modeled as a Gamma distribution and an inverse Wishart distribution. Furthermore, the variational Bayesian (VB) technique is employed to infer the unknown DOF and scale matrix parameters while the recursion estimation framework of the RSMC-PHD filter is derived. In addition, considering that the introduced Student- t distribution might lead to an overestimation of the target number, a strategy is applied to modify the updated weight of each particle. Simulation results demonstrate that the proposed filter is effective with unknown heavy-tailed measurement noise.

Automated extraction of dolphin whistles-A sequential Monte Carlo probability hypothesis density approach.

The need for automated methods to detect and extract marine mammal vocalizations from acoustic data has increased in the last few decades due to the increased availability of long-term recording systems. Automated dolphin whistle extraction represents a challenging problem due to the time-varying number of overlapping whistles present in, potentially, noisy recordings. Typical methods utilize image processing techniques or single target tracking, but often result in fragmentation of whistle contours and/or partial whistle detection. This study casts the problem into a more general statistical multi-target tracking framework and uses the probability hypothesis density filter as a practical approximation to the optimal Bayesian multi-target filter. In particular, a particle version, referred to as a sequential Monte Carlo probability hypothesis density (SMC-PHD) filter, is adapted for frequency tracking and specific models are developed for this application. Based on these models, two versions of the SMC-PHD filter are proposed and the performance of these versions is investigated on an extensive real-world dataset of dolphin acoustic recordings. The proposed filters are shown to be efficient tools for automated extraction of whistles, suitable for real-time implementation.

Audio–Visual Particle Flow SMC-PHD Filtering for Multi-Speaker Tracking

Sequential Monte Carlo probability hypothesis density (SMC-PHD) filtering is a popular method used recently for audio-visual (AV) multi-speaker tracking. However, due to the weight degeneracy problem, the posterior distribution can be represented poorly by the estimated probability, when only a few particles are present around the peak of the likelihood density function. To address this issue, we propose a new framework where particle flow (PF) is used to migrate particles smoothly from the prior to the posterior probability density. We consider both zero and non-zero diffusion particle flows (ZPF/NPF), and developed two new algorithms, AV-ZPF-SMC-PHD and AV-NPF-SMC-PHD, where the speaker states from the previous frames are also considered for particle relocation. The proposed algorithms are compared systematically with several baseline tracking methods using the AV16.3, AVDIAR and CLEAR datasets, and are shown to offer improved tracking accuracy and average effective sample size (ESS).

A novel SMC-PHD filter based on particle compensation

As a typical implementation of the probability hypothesis density (PHD) filter, sequential Monte Carlo PHD (SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.

A Novel Sequential Monte Carlo-Probability Hypothesis Density Filter for Particle Impoverishment Problem

As a typical implementation of the probability hypothesis density (PHD) filter, sequential Monte Carlo PHD (SMC-PHD) is widely employed in highly nonlinear systems. However, diversity loss of particles introduced by the resampling step, which can be called particle impoverishment problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this paper, a novel SMC-PHD filter based on particle compensation is proposed to solve the problem. Firstly, based on an analysis of the particle impoverishment problem, a new particle compensatory method is developed to improve the particle diversity. Then, all the particles are integrated into the SMC-PHD filter framework. Compared with the SMC-PHD filter, simulation results demonstrate that the proposed particle compensatory SMC-PHD filter is capable of overcoming the particle impoverishment problem, which indicate good application prospects.

Multi-Target State Extraction for the SMC-PHD Filter.

The sequential Monte Carlo probability hypothesis density (SMC-PHD) filter has been demonstrated to be a favorable method for multi-target tracking. However, the time-varying target states need to be extracted from the particle approximation of the posterior PHD, which is difficult to implement due to the unknown relations between the large amount of particles and the PHD peaks representing potential target locations. To address this problem, a novel multi-target state extraction algorithm is proposed in this paper. By exploiting the information of measurements and particle likelihoods in the filtering stage, we propose a validation mechanism which aims at selecting effective measurements and particles corresponding to detected targets. Subsequently, the state estimates of the detected and undetected targets are performed separately: the former are obtained from the particle clusters directed by effective measurements, while the latter are obtained from the particles corresponding to undetected targets via clustering method. Simulation results demonstrate that the proposed method yields better estimation accuracy and reliability compared to existing methods.

Cubature Information SMC-PHD for Multi-Target Tracking.

In multi-target tracking, the key problem lies in estimating the number and states of individual targets, in which the challenge is the time-varying multi-target numbers and states. Recently, several multi-target tracking approaches, based on the sequential Monte Carlo probability hypothesis density (SMC-PHD) filter, have been presented to solve such a problem. However, most of these approaches select the transition density as the importance sampling (IS) function, which is inefficient in a nonlinear scenario. To enhance the performance of the conventional SMC-PHD filter, we propose in this paper two approaches using the cubature information filter (CIF) for multi-target tracking. More specifically, we first apply the posterior intensity as the IS function. Then, we propose to utilize the CIF algorithm with a gating method to calculate the IS function, namely CISMC-PHD approach. Meanwhile, a fast implementation of the CISMC-PHD approach is proposed, which clusters the particles into several groups according to the Gaussian mixture components. With the constructed components, the IS function is approximated instead of particles. As a result, the computational complexity of the CISMC-PHD approach can be significantly reduced. The simulation results demonstrate the effectiveness of our approaches.

SMC-PHD algorithm based on squared cubature particles

Most of the conventional sequential Monte Carlo probability hypothesis density( SMC-PHD)approaches adopt the state transition density as importance sampling function. When targets are with nonlinear motions,such a selection makes few particles with large weights,leading to inaccurate estimation and particle divergence. To avoid such problems,a novel importance sampling function approximation approach with the squared cubature Kalman filter( SCKF) and statistical gating method was proposed. To design such an importance sampling function,the mean and covariance of importance sampling function were predicted at first.Then,the statistical gating method were utilized to extract observations associated with the importance sampling particle from the current observation set. Merging the extracted observations with corresponding weights,the mean and covariance of importance sampling function were updated. Using the designed importance sampling function,the intensity of particles can be predicted and updated,according to the conventional SMCPHD method. At last,the states and number of multi-target can be approximated by the intensity of particles.The simulation results demonstrate that the proposed approach has the advantages of high accuracy and stable estimation in nonlinear target tracking.

Dolphin Whistle Track Estimation Using Sequential Monte Carlo Probability Hypothesis Density Filter

This article focuses on possible automation of dolphin whistle track estimation process within the context of Multiple Target Tracking (MTT). It provides automatic whistle track estimation from raw hydrophone measurements using the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) filter. Hydrophone measurements for three different types of species namely bottlenose dolphin (Tursiops truncates), common dolphin (Delphinus delphis) and striped dolphin (Stenella coeruleoalba) have been used to benchmark the tracking performance of the SMC-PHD filter against three major challenges- the presence of multiple whistles, spontaneous death/birth of whistles and multiple whistles crossing each other. Quantitative analysis of the whistle track estimation accuracy is not possible since there is no ground truth type track for the dolphin whistles. Hence visual inspection of estimated tracks has been used corroborate the satisfactory tracking performance in the presence of all three challenges. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21954 Dhaka Univ. J. Sci. 62(1): 17-20, 2014 (January)

Fast Gaussian Mixture Probability Hypothesis Density Filter

Although the Gaussian mixture probability hypothesis density (GMPHD) filter is a multi-target tracker that can alleviate the computational intractability of the optimal multi-target Bayes filter and its computational complex is lower than that of sequential Monte Carlo probability hypothesis density (SMCPHD), its computational burden can be reduced further. In the standard GMPHD filter, each observation should be matched with each component when the PHD is updated. In practice, time cost of evaluating many unlikely measurements-to-components parings is wasteful, because their contribution is very limited. As a result, a substantial reduction in complexity could be obtained by directly setting relative value associated with these parings. A fast GMPHD algorithm is proposed in the paper based on gating strategy. Simulation results show that the fast GMPHD can save computational time by 60%~70% without any degradation in performance compared with standard GMPHD.

Multi-target tracking with PHD filter using Doppler-only measurements

In this paper, we address the problem of multi-target detection and tracking over a network of separately located Doppler-shift measuring sensors. For this challenging problem, we propose to use the probability hypothesis density (PHD) filter and present two implementations of the PHD filter, namely the sequential Monte Carlo PHD (SMC-PHD) and the Gaussian mixture PHD (GM-PHD) filters. Performances of both filters are carefully studied and compared for the considered challenging tracking problem. Simulation results show that both PHD filter implementations successfully track multiple targets using only Doppler shift measurements. Moreover, as a proof-of-concept, an experimental setup consisting of a network of microphones and a loudspeaker was prepared. Experimental study results reveal that it is possible to track multiple ground targets using acoustic Doppler shift measurements in a passive multi-static scenario. We observed that the GM-PHD is more effective, efficient and easy to implement than the SMC-PHD filter.

The Spline Probability Hypothesis Density Filter

The Probability Hypothesis Density (PHD) filter is a multitarget tracker that can alleviate the computational intractability of the optimal multitarget Bayes filter. The PHD filter recursively estimates the number of targets and their PHD from a set of observations and works well in scenarios with false alarms and missed detections. Two distinct PHD filter implementations are available in the literature: the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) and the Gaussian Mixture Probability Hypothesis Density (GM-PHD) filters. While particle-based PHD implementations may suffer from degeneracy, GM-based methods may not be suitable for highly nonlinear non-Gaussian systems. This paper proposes a B-Spline based Spline Probability Hypothesis Density (SPHD) filter, which has the capability to better approximate any arbitrary probability density function. The resulting algorithm can handle linear, non-linear, Gaussian, and non-Gaussian models. The SPHD filter can provide continuous estimates of the probability density function of the system state and it is immune to the degeneracy problem. The SPHD filter can maintain highly accurate tracks by taking advantage of dynamic knot movement, but at the expense of higher computational complexity, which makes it suitable for tracking a few high-value targets under difficult conditions. The SPHD filter derivations and simulations are provided in this paper.

Efficient importance sampling function design for sequential Monte Carlo PHD filter

In this paper, we propose a novel implementation of the probability hypothesis density (PHD) filter based on the sequential Monte Carlo (SMC) method called SMC-PHD filter. The SMC-PHD filter is analogous to the sequential importance sampling which generates samples using an importance sampling (IS) function. Even though this filter permits general class of IS density function, many previous implementations have simply used the state transition density function. However, this approach leads to a degeneracy problem and renders the filter inefficient. Thus, we propose a novel IS function for the SMC-PHD filter using a combination of an unscented information filter and a gating technique. Further, we use measurement-driven birth target intensities because they are more efficient and accurate than selecting birth targets selected using arbitrary or expected mean target states. The performance of the SMC-PHD filter with the proposed IS function was subsequently evaluated through a simulation and it was shown to outperform the standard SMC-PHD filter and recently proposed auxiliary PHD filter.

Extensions of the SMC-PHD filters for jump Markov systems

The probability hypothesis density (PHD) filter is a promising algorithm for multitarget tracking, which can be extended for jump Markov systems (JMS). Since the existing multiple model sequential Monte Carlo PHD (MM SMC-PHD) filter is not interacting, two extensions of the SMC-PHD filters are developed in this paper. The interacting multiple-model (IMM) SMC-PHD filter approximates the model conditional PHD of target states by particles, and performs the interaction by resampling without any a priori assumption of the noise. The IMM Rao-Blackwellized particle (RBP) PHD filter uses the idea of Rao-Blackwellized to further enhance the performance of target state estimation for JMS with mixed linear/nonlinear state space models. The simulation results show that the proposed algorithms have better performances than the existing MM SMC-PHD filter in terms of state filtering and target number estimation.