Gaussian Mixture Cardinalized Probability Hypothesis 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.

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.

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.

Chernoff fusion of Gaussian mixtures based on sigma-point approximation

The use of a sigma-point approximation is proposed for the Chernoff fusion of Gaussian mixtures. The superiority of the proposed method to its best alternatives in the literature is shown on both a simple density fusion problem and a distributed multiple target tracking example, where the outputs of Gaussian mixture cardinalized probability hypothesis density filters are fused.

Ground target tracking with RCS estimation based on signal strength measurements

The discrimination of closely spaced targets is a major challenge in the ground target-tracking domain based on measurements of airborne ground moving target indication radar. Being a standard output of modern radar systems, the measured signal strength of a radar detection can be used to estimate the characteristic mean radar cross section (RCS) of a ground target, which is then used as additional target attribute information to improve the tracking performance in situations with closely spaced targets. For this method to work, the fluctuations of the target RCS are assumed to follow the analytically tractable Swerling-I and Swerling-III cases. In this work, the RCS estimation scheme originally developed for air targets [1, 2] is generalized to ground-moving objects and then implemented into the Gaussian mixture cardinalized probability hypothesis density filter. The performance of the resulting algorithm is analyzed based on single and multiple-target simulation scenarios. In the latter case, a modified version of the optimal subpattern assignment metric that also accounts for labeling errors is used.

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

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.

GMTI Tracking via the Gaussian Mixture Cardinalized Probability Hypothesis Density Filter

The cardinalized probability hypothesis density (CPHD) filter is a recursive Bayesian algorithm for estimating multiple target states with a varying target number in clutter. In particular the Gaussian mixture variant (GMCPHD), which provides closed-form prediction and update equations for the filter in the case of linear Gaussian systems, is a candidate for real time multi-target tracking. The following three issues are addressed. First we show the equivalence between the GMCPHD filter and the standard multi hypothesis tracker (MHT) in the case of a single target. Second by using a Gaussian sum approach, we extend the GMCPHD filter to incorporate digital road maps for road constrained targets. The use of such external information leads to more precise tracks and faster and more reliable target number estimates. Third we model the effect of Doppler blindness by a target state-dependent detection probability, which leads to a more stable target-number estimation in the case of low-Doppler targets.