Gaussian Mixture Cardinalized Probability Hypothesis Density Research Articles

Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD): A Distributed Filter Based on the Intersection of Parallel Inverse Covariances

A distributed GM-CPHD filter based on parallel inverse covariance crossover is designed to attenuate the local filtering and uncertain time-varying noise affecting the accuracy of sensor signals. First, the GM-CPHD filter is identified as the module for subsystem filtering and estimation due to its high stability under Gaussian distribution. Second, the signals of each subsystem are fused by invoking the inverse covariance cross-fusion algorithm, and the convex optimization problem with high-dimensional weight coefficients is solved. At the same time, the algorithm reduces the burden of data computation, and data fusion time is saved. Finally, the GM-CPHD filter is added to the conventional ICI structure, and the generalization capability of the parallel inverse covariance intersection Gaussian mixture cardinalized probability hypothesis density (PICI-GM-CPHD) algorithm reduces the nonlinear complexity of the system. An experiment on the stability of Gaussian fusion models is organized and linear and nonlinear signals are compared by simulating the metrics of different algorithms, and the results show that the improved algorithm has a smaller metric OSPA error than other mainstream algorithms. Compared with other algorithms, the improved algorithm improves the signal processing accuracy and reduces the running time. The improved algorithm is practical and advanced in terms of multisensor data processing.

Estimations of time-varying birth cardinality distribution and birth intensity in Gaussian mixture CPHD filter for multi-target tracking

Cardinalized probability hypothesis density (CPHD) filter is a promising algorithm for multi-target tracking. However, the performance of standard CPHD is degraded when the target birth process is unknown and dynamically changing. To remove this limitation, a discrete kernel estimator in conjunction with exponential weighted moving average scheme is introduced in this study to estimate the time-varying target birth cardinality distribution (i.e., probability distribution on number of newborn targets appearing during one sampling time) at each processing step. The target birth intensity is then updated according to the resulting estimated birth cardinality distribution. The estimated birth intensity and cardinality distribution can be employed by a tracker based on Gaussian mixture CPHD (GMCPHD) to modulate its filtering strength for target tracking. The performance of the proposed framework is demonstrated by both numerical simulations and experiment on a video surveillance dataset. Results show that the proposed algorithm can reduce the delay of standard GMCPHD filter's response to the changes in the number of targets, and thus improve the accuracy of cardinality estimates. Satisfactory estimation of cardinality can be obtained even when there is a fast change in the rate of birth.

A GM-CPHD Filtering Algorithm Assisted by Luminance Information

Optical tracking of small and weak targets in space, has problems such as a large and unknown number of targets, dense clutter, close measurement of neighboring targets, and false detection and missed detection. In this paper, a Gaussian mixture cardinalized probability hypothesis density (GM-CPHD) filtering algorithm assisted by luminance information is proposed. By establishing the luminance likelihood function, the luminance information is introduced into the CPHD filtering process, and the Gaussian mixture implementation method is given. The simulation results indicate that the proposed algorithm can effectively adapt to the dense clutter environment, and compared with the traditional GM-CPHD filtering algorithm, its tracking accuracy for multiple targets is significantly improved.

Distributed GM-CPHD Filter Based on Generalized Inverse Covariance Intersection

In this paper, we propose a distributed Gaussian mixture cardinalized probability hypothesis density (GM-CPHD) filter based on generalized inverse covariance intersection that fuses multiple node information effectively for multi-target tracking applications. Covariance intersection (CI) is a well-known fusion method that produces a conservative estimate of the joint covariance regardless of the actual correlation between the different nodes. Inverse covariance intersection (ICI) is the updated version to obtain fusion results that guarantee consistency and less conservative than CI. However, the ICI is not extended to multi-sensor multi-target tracking system yet. Since the ICI formula can be re-structured as naïve fusion with covariance inflation in Gaussian pdf, this method was applied to the GM-CPHD with generalization. The formula for random finite set (RFS) fusion was derived in the same way as the conventional generalized covariance intersection (GCI) based fusion. The simulation results for multi-target tracking show that the proposed algorithm has smaller optimal sub-pattern assignment (OSPA) errors than naïve fusion and the GCI-based fusions.

Active Sonar Target Tracking Based on the GM-CPHD Filter Algorithm

The estimation of underwater multi-target state has always been the difficult problem of active sonar target tracking.In order to get the variable number of target and their state, the random finite set theory is applied to multi-target tracking system.This theory not only effectively avoids the problem of multi-target tracking data association, and also realizes the estimation of time-varying number of targets and their states.Due to Probability Hypothesis Density(PHD) recursion propagates cardnality distribution with only a single parameter, a new generalization of the PHD recursion called Cardinalized Probability Hypothesis Density(CPHD) recursion, which jointly propagates the intensity function and the cardnality distribution, while have a big computation than PHD.Also there did not have closed-form solution for PHD recursion and CPHD recursion, so for linear Gaussian multi-target tracking system, the Gaussian Mixture Probability Hypothesis Density and Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD) filter algorithm is put forward.GM-CPHD is more accurate than GM-PHD in estimation of the time-varying number of targets.In this paper, we use the ellipse gate tracking strategy to reduce computation in GM-CPHD filtering algorithm.At the same time, according to the characteristics of underwater target tracking, using active sonar equation, we get the relationship between detection probability, distance and false alarm, when fixed false alarm, analytic formula of the relationship between adaptive detection probability and distance is obtained, we puts forward the adaptive detection probability GM-CPHD filtering algorithm.Simulation shows that the combination of ellipse tracking gate strategy and adaptive detection probability GM-CPHD filtering algorithm can realize the estimation of the time-varying number of targets and their state more accuracy in dense clutter environment.

PHD and CPHD Algorithms Based on a Novel Detection Probability Applied in an Active Sonar Tracking System

Underwater multi-targets tracking has always been a difficult problem in active sonar tracking systems. In order to estimate the parameters of time-varying multi-targets moving in underwater environments, based on the Bayesian filtering framework, the Random Finite Set (RFS) is introduced to multi-targets tracking, which not only avoids the problem of data association in multi-targets tracking, but also realizes the estimation of the target number and their states simultaneously. Usually, the conventional Probability Hypothesis Density (PHD) and Cardinalized Probability Hypothesis Density (CPHD) algorithms assume that the detection probability is known as a priori, which is not suitable in many applications. Some methods have been proposed to estimate the detection probability, but most assume that it is constant both in time and surveillance region. In this paper, we model the detection probability through the active sonar equation. When fixed the false detection probability, we can get the analytic expression for the detection probability, which is related to target position. In addition, this novel detection probability is used in PHD and CPHD algorithms and applied to underwater active sonar tracking systems. Also, we use the adaptive ellipse gate strategy to reduce the computational load in PHD and CPHD algorithms. Under the linear Gaussian assumption, the proposed detection probability is illustrated in both Gaussian Mixture Probability Hypothesis Density (GM-PHD) and Gaussian Mixture Cardinalized Probability Hypothesis Density (GM-CPHD), respectively. Simulation results show that the proposed Pd-GM-PHD and Pd-GM-CPHD algorithms are more realistic and accuratein underwater active sonar tracking systems.

Maneuvering multi-target tracking based on variable structure multiple model GMCPHD filter

The traditional multiple model cardinalized probability hypothesis density (MMCPHD) filter uses a fixed model set for all targets. It is clearly inefficient and may cause the decrease of performance in the situations where the size of the model set is large and the scene is complicated. This paper presents a variable structure multiple model (VSMM) version of the Gaussian mixture cardinalized probability hypothesis density (GMCPHD) filter based on the expected mode augmentation (EMA) for the multiple maneuvering target tracking. The GMCPHD filter which is suitable for the VSMM is derived, thus different model sets can be used for different targets. Then EMA algorithm which is an efficient model set adaptation method is introduced and applied to the VSMM version of the GMCPHD (VSMM-GMCPHD) filter. This method costs less computational time and has better estimate precision than that of the traditional multiple model version of GMCPHD (MM-GMCPHD) filter. The gating technique is utilized to further improve the computational efficiency. Simulation results verify the performance of the proposed methods. The estimate precision of VSMM-GMCPHD filters with and without the gate are almost the same, however the former one is more cost-effective. Both of the two VSMM-GMCPHD filters outperform the MM-GMCPHD filter.

Global tracking of space debris via CPHD and consensus

Space debris tracking is of great importance for safe operation of spacecraft. This paper presents an algorithm that achieves global tracking of space debris with a multi-sensor network. The sensor network has unknown and possibly time-varying topology. A consensus algorithm is used to effectively counteract the effects of data incest. Gaussian Mixture-Cardinalized Probability Hypothesis Density (GM-CPHD) filtering is used to estimate the state of the space debris. As an example of the method, 45 clusters of sensors are used to achieve global tracking. The performance of the proposed approach is demonstrated by simulation experiments.

Multi-Target Tracking Using an Improved Gaussian Mixture CPHD Filter.

The cardinalized probability hypothesis density (CPHD) filter is an alternative approximation to the full multi-target Bayesian filter for tracking multiple targets. However, although the joint propagation of the posterior intensity and cardinality distribution in its recursion allows more reliable estimates of the target number than the PHD filter, the CPHD filter suffers from the spooky effect where there exists arbitrary PHD mass shifting in the presence of missed detections. To address this issue in the Gaussian mixture (GM) implementation of the CPHD filter, this paper presents an improved GM-CPHD filter, which incorporates a weight redistribution scheme into the filtering process to modify the updated weights of the Gaussian components when missed detections occur. In addition, an efficient gating strategy that can adaptively adjust the gate sizes according to the number of missed detections of each Gaussian component is also presented to further improve the computational efficiency of the proposed filter. Simulation results demonstrate that the proposed method offers favorable performance in terms of both estimation accuracy and robustness to clutter and detection uncertainty over the existing methods.

Situation Assessment: An End-to-End Process for the Detection of Objects of Interest

Semiautomatic approaches are developed for wide area situation assessment in near-real-time. The two-step method consists of two granularity levels. The first entity assessment uses a new multi-target tracking (MTT) algorithm (hybridization of Gaussian mixture-Cardinalized probability hypothesis density (GM-CPHD) filter and multiple hypothesis tracker (MHT) with road constraints) on ground moving target indicator (GMTI) data. The situation is then assessed by detecting objects of interest such as convoys with other data types (synthetic aperture radar (SAR), video). These detections are based on Bayesian networks and their credibilistic counterpart.

Consensus CPHD Filter for Distributed Multitarget Tracking

The paper addresses distributed multitarget tracking over a network of heterogeneous and geographically dispersed nodes with sensing, communication and processing capabilities. The contribution has been to develop a novel consensus Gaussian Mixture-Cardinalized Probability Hypothesis Density (GM-CPHD) filter that provides a fully distributed, scalable and computationally efficient solution to the problem. The effectiveness of the proposed approach is demonstrated via simulation experiments on realistic scenarios.

Tracking of Midcourse Ballistic Target Group on Space-based Infrared Focal Plane using GM-CPHD Filter

Tracking of midcourse ballistic target group on space-based infrared focal plane plays a key role in the space-based early warning system. This paper proposes the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter to solve this problem. The multi-target states and measurements on infrared focal plane are modeled by random finite set (RFS). The intensity function of RFS of multi-target states and the probability distribution of target number are jointly propagated by cardinalized probability hypothesis density (CPHD) recursion. Under the assumptions of linear Gaussian multi-target models, the Gaussian-mixture implementations of CPHD are presented, and the target number and the multi-target states on infrared focal plane are estimated. In order to enable track continuity, we propose 0-1 integer programming to associate the estimated states between frames. The simulation results show that the GM-CPHD filter can dramatically improve the accuracy of estimated target number and estimated target states compared with the Gaussian-mixture probability hypothesis density filter, and that the track continuity can be successfully achieved. Defence Science Journal, 2012, 62(6), pp.431-436 , DOI:http://dx.doi.org/10.14429/dsj.62.1199

The GM-CPHD Tracker Applied to Real and Realistic Multistatic Sonar Data Sets

The Gaussian mixture-cardinalized probability hypothesis density (GM-CPHD) tracker was applied to three real and simulated multistatic sonar data sets. The goal was to test the versatility of the tracker on data of increasing difficulty. The first two data sets presented minor challenges for the tracker and in our opinion demonstrate that it is, indeed, a tracking paradigm that is ready for “prime time.” The last data set was considerably more challenging. Without some means to use data from multiple sensors success would be in doubt. However, since a practicable multisensor form of the probability hypothesis density (PHD) filter is still unclear, predetection fusion (contact sifting) was considered a necessary first step before tracking. On all the data sets investigated, the GM-CPHD proved to be easily adaptable (e.g., to low probability of detection, large number of sensors), discovered all the targets and generated satisfactory tracks for them. Plots of the tracks obtained and the associated metrics of performance are provided.

Set JPDA Filter for Multitarget Tracking

In this article, we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, which we call set JPDA (SJPDA). Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, Kullback-Leibler SJPDA (KLSJPDA), which provides optimal Gaussian approximations in the Kullback-Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean optimal subpattern assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter.

Hybrid Algorithms for Multitarget Tracking using MHT and GM-CPHD

The Gaussian mixture cardinalized probability hypothesis density (GM-CPHD) is a new original algorithm for multitarget tracking adapted to false alarms, nondetection and closely spaced objects. It models the target set as a random finite set (RFS) and estimates the target state as the first-order moment of a joint probability distribution. In the classical version no track assignment is implemented; this is a limit to scene understanding in a multitarget context. A technique for choosing the peak to track association is therefore proposed. With this implementation the main strength of the GM-CPHD is shown: it drastically improves the performances concerning the estimation of the number of targets and gives acceptable performances concerning the state of each individual target even if targets are close together, but it cannot rival an interacting multiple model estimator with multiple hypothesis tracking (IMM-MHT) in regards to velocity estimation, which is also the case with other multitarget tracking algorithms not equiped with IMM. However, MHT performance decreases due to poor estimation of the number of targets when targets are close together. It is worth noting that combining a probability hypothesis density (PHD) filter with a multiple-model approach should improve the velocity estimation but is unnecessary because we have developed a hybrid algorithm, combining the precision of the estimation of the number of targets given by the GM-CPHD, used in a labeled version, with the precision of the estimation of each individual state given by the MHT. These noteworthy performances can be observed for individual targets as well as for convoys. This hybrid algorithm is extended by using an IMM-MHT with road constraints.

Gaussian mixture CPHD filter with gating technique

Cardinalized probability hypothesis density (CPHD) filter provides more accurate estimates of target number than the probability hypothesis density (PHD) filter, and hence, also of the states of targets. This additional capability comes at the price of greater computational complexity: O ( N M 3 ) , where N is the number of targets and M is the cardinality of measurement set at each time index. It is shown that the computational cost of CPHD filter can be reduced by means of reducing the cardinality of measurement set. In practice, the cardinality of measurement set can be reduced by gating techniques as done in traditional tracking algorithms. In this paper, we develop a method of reducing the computational cost of Gaussian mixture CPHD filter by incorporating the elliptical gating technique. Computer simulation results show that the computational cost is reduced and that the tracking performance loss incurred is not significant.