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Journal articles on the topic 'Cardinalized probability hypothesis density'

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Author: Grafiati

Published: 10 March 2023

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1

Li, Bo, and Fu-Wen Pang. "Improved cardinalized probability hypothesis density filtering algorithm." Applied Soft Computing 24 (November 2014): 692–703. http://dx.doi.org/10.1016/j.asoc.2014.08.023.

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2

Vo, Ba-Tuong, Ba-Ngu Vo, and Antonio Cantoni. "Analytic Implementations of the Cardinalized Probability Hypothesis Density Filter." IEEE Transactions on Signal Processing 55, no. 7 (July 2007): 3553–67. http://dx.doi.org/10.1109/tsp.2007.894241.

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3

Ma, Yue, Jian-zhang Zhu, Qian-qing Qin, and Yi-jun Hu. "Convolution kernels implementation of cardinalized probability hypothesis density filter." Acta Mathematicae Applicatae Sinica, English Series 29, no. 4 (October 2013): 739–48. http://dx.doi.org/10.1007/s10255-013-0252-0.

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4

LIN, Zai-Ping, Yi-Yu ZHOU, and Wei AN. "Track-Before-Detect algorithm based on cardinalized probability hypothesis density filter." Journal of Infrared and Millimeter Waves 32, no. 5 (2013): 437. http://dx.doi.org/10.3724/sp.j.1010.2013.00437.

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5

Song, L., M. Liang, and H. Ji. "Box-Particle Implementation and Comparison of Cardinalized Probability Hypothesis Density Filter." Radioengineering 25, no. 1 (April 14, 2016): 177–86. http://dx.doi.org/10.13164/re.2016.0177.

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6

Ulmke, Martin, Ozgur Erdinc, and Peter Willett. "GMTI Tracking via the Gaussian Mixture Cardinalized Probability Hypothesis Density Filter." IEEE Transactions on Aerospace and Electronic Systems 46, no. 4 (October 2010): 1821–33. http://dx.doi.org/10.1109/taes.2010.5595597.

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7

Li, Bo, Huawei Yi, and Xiaohui Li. "Innovative unscented transform–based particle cardinalized probability hypothesis density filter for multi-target tracking." Measurement and Control 52, no. 9-10 (October 21, 2019): 1567–78. http://dx.doi.org/10.1177/0020294019877494.

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Multi-target tracking is widely applied in video surveillance systems. As we know, although the standard particle cardinalized probability hypothesis density filter can estimate state of targets, it is difficult to define the proposal distribution function in prediction stage. Since the robust particles cannot be effectively drawn, the actual tracking accuracy should be enhanced. In this paper, an innovative unscented transform–based particle cardinalized probability hypothesis density filter is derived. Considering the different state spaces, we use the auxiliary particle method and then draw robust particles from the modified distributions in order to estimate the position of targets. Simultaneously, we present the recursion of the optimized Kalman gain to improve the general unscented transform for the velocity estimates. Using the track label, we further integrate them in the framework of the jump Markov model. The simulation results show that the proposed filter has advances in the multi-target tracking scenes. Moreover, the experiments indicate that the filter can track mobile targets with satisfactory results.

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8

Zhai Dai-Liang, Lei Hu-Min, Li Hai-Ning, Zhang Xu, and Li Jiong. "Derivation of cardinalized probability hypothesis density filter via the physical-space approach." Acta Physica Sinica 63, no. 22 (2014): 220204. http://dx.doi.org/10.7498/aps.63.220204.

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9

Lian, Feng, Chongzhao Han, Weifeng Liu, Jing Liu, and Jian Sun. "Unified cardinalized probability hypothesis density filters for extended targets and unresolved targets." Signal Processing 92, no. 7 (July 2012): 1729–44. http://dx.doi.org/10.1016/j.sigpro.2012.01.009.

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10

Franken, D., M. Schmidt, and M. Ulmke. ""Spooky Action at a Distance" in the Cardinalized Probability Hypothesis Density Filter." IEEE Transactions on Aerospace and Electronic Systems 45, no. 4 (October 2009): 1657–64. http://dx.doi.org/10.1109/taes.2009.5310327.

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11

Sun, Jie, and Dong Li. "Multiple Model CPHD Filter for Tracking Maneuvering Targets." Applied Mechanics and Materials 556-562 (May 2014): 3238–41. http://dx.doi.org/10.4028/www.scientific.net/amm.556-562.3238.

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A multiple model cardinalized probability hypothesis density (CPHD) filter is proposed for tracking multiple maneuvering targets. The augmented state is established by combining the target motion mode with the kinematic state. Both the posterior cardinality distribution of the targets and the posterior probability hypothesis density (PHD) of the augmented state are jointly propagated by using CPHD recursion. Simulation results show that the proposed filter improves the estimation accuracy of target number and target states over the multiple model PHD filter and single model CPHD filter respectively.

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12

Chen, Xiao, Yaan Li, Yuxing Li, and Jing Yu. "Active Sonar Target Tracking Based on the GM-CPHD Filter Algorithm." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 36, no. 4 (August 2018): 656–63. http://dx.doi.org/10.1051/jnwpu/20183640656.

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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.

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13

Zhang, Jungen. "Bearings-only multitarget tracking based onRao-Blackwellized particle CPHD filter." International Journal of Circuits, Systems and Signal Processing 14 (January 13, 2021): 1129–36. http://dx.doi.org/10.46300/9106.2020.14.141.

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Following Mahler’s framework forinformation fusion, this paper develops a implementationof cardinalized probability hypothesis density (CPHD)filter for bearings-only multitarget tracking.Rao-Blackwellized method is introduced in the CPHDfiltering framework for mixed linear/nonlinear state spacemodels. The sequential Monte Carlo (SMC) method is usedto predict and estimate the nonlinear state of targets.Kalman filter (KF) is adopted to estimate the linear stateswith the information embedded in the estimated nonlinearstates. The multitarget state estimates are extracted byutilizing the kernel density estimation (KDE) theory andmean-shift algorithm to enhance tracking performance.Moreover, the computational load of the filter is analyzedby introducing equivalent flop measure. Finally, theperformance of the proposed Rao-Blackwellized particleCPHD filter is evaluated through a challengingbearings-only multitarget tracking simulation experiment.

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14

Kim, Sun Young, Chang Ho Kang, and Chan Gook Park. "SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking." Applied Sciences 12, no. 3 (January 27, 2022): 1369. http://dx.doi.org/10.3390/app12031369.

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We propose a sequential Monte Carlo-based cardinalized probability hypothesis density (SMC-CPHD) filter with adaptive survival probability for multiple frequency tracking to enhance the tracking performance. The survival probability of the particles in the filter is adjusted using the pre-designed exponential function related to the distribution of the estimated particle points. In order to ensure whether the proposed survival probability affects the stability of the filter, the error bounds in the prediction process are analyzed. Moreover, an inverse covariance intersection-based compensation method is added to enhance cardinality tracking performance by integrating two types of cardinality information from the CPHD filter and data clustering process. To evaluate the proposed method’s performance, MATLAB-based simulations are performed. As a result, the tracking performance of the multiple frequencies has been confirmed, and the accuracy of cardinality estimates are improved compared to the existing filters.

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15

Wang, Sen, Qinglong Bao, and Zengping Chen. "Refined PHD Filter for Multi-Target Tracking under Low Detection Probability." Sensors 19, no. 13 (June 26, 2019): 2842. http://dx.doi.org/10.3390/s19132842.

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Radar target detection probability will decrease as the target echo signal-to-noise ratio (SNR) decreases, which has an adverse influence on the result of multi-target tracking. The performances of standard multi-target tracking algorithms degrade significantly under low detection probability in practice, especially when continuous miss detection occurs. Based on sequential Monte Carlo implementation of Probability Hypothesis Density (PHD) filter, this paper proposes a heuristic method called the Refined PHD (R-PHD) filter to improve multi-target tracking performance under low detection probability. In detail, this paper defines a survival probability which is dependent on target state, and labels individual extracted targets and corresponding particles. When miss detection occurs due to low detection probability, posterior particle weights will be revised according to the prediction step. Finally, we transform the target confirmation problem into a hypothesis test problem, and utilize sequential probability ratio test to distinguish real targets and false alarms in real time. Computer simulations with respect to different detection probabilities, average numbers of false alarms and continuous miss detection durations are provided to corroborate the superiority of the proposed method, compared with standard PHD filter, Cardinalized PHD (CPHD) filter and Cardinality Balanced Multi-target Multi-Bernoulli (CBMeMBer) filter.

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16

Wang, Yun, Guo-ping Hu, and Hao Zhou. "Group Targets Tracking Using Multiple Models GGIW-CPHD Based on Best-Fitting Gaussian Approximation and Strong Tracking Filter." Journal of Sensors 2016 (2016): 1–13. http://dx.doi.org/10.1155/2016/7294907.

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Gamma Gaussian inverse Wishart cardinalized probability hypothesis density (GGIW-CPHD) algorithm was always used to track group targets in the presence of cluttered measurements and missing detections. A multiple models GGIW-CPHD algorithm based on best-fitting Gaussian approximation method (BFG) and strong tracking filter (STF) is proposed aiming at the defect that the tracking error of GGIW-CPHD algorithm will increase when the group targets are maneuvering. The best-fitting Gaussian approximation method is proposed to implement the fusion of multiple models using the strong tracking filter to correct the predicted covariance matrix of the GGIW component. The corresponding likelihood functions are deduced to update the probability of multiple tracking models. From the simulation results we can see that the proposed tracking algorithm MM-GGIW-CPHD can effectively deal with the combination/spawning of groups and the tracking error of group targets in the maneuvering stage is decreased.

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17

Zhang, Li, and Sun. "Multisensor RFS Filters for Unknown and Changing Detection Probability." Electronics 8, no. 7 (June 30, 2019): 741. http://dx.doi.org/10.3390/electronics8070741.

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The detection probability is an important parameter in multisensor multitarget tracking. The existing multisensor multi-Bernoulli (MS-MeMBer) filter and multisensor cardinalized probability hypothesis density (MS-CPHD) filter require that detection probability is a priori. However, in reality, the value of the detection probability is constantly changing due to the influence of sensors, targets, and other environmental characteristics. Therefore, to alleviate the performance deterioration caused by the mismatch of the detection probability, this paper applies the inverse gamma Gaussian mixture (IGGM) distribution to both the MS-MeMBer filter and the MS-CPHD filter. Specifically, the feature used for detection is assumed to obey the inverse gamma distribution and is statistically independent of the target’s spatial position. The feature is then integrated into the target state to iteratively estimate the target detection probability as well as the motion state. The experimental results demonstrate that the proposed methods can achieve a better filtering performance in scenarios with unknown and changing detection probability. It is also shown that the distribution of the sensors has a vital influence on the filtering accuracy, and the filters perform better when sensors are dispersed in the monitoring area.

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18

Li, Cuiyun, Rong Wang, Jinbin Wang, and Yuhen Hu. "Cardinalised probability hypothesis density tracking algorithm for extended objects with glint noise." IET Science, Measurement & Technology 10, no. 5 (August 1, 2016): 528–36. http://dx.doi.org/10.1049/iet-smt.2016.0004.

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19

Chi, Luo-jia, Xin-xi Feng, and Lu Miao. "Generalized Labeled Multi-Bernoulli Extended Target Tracking Based on Gaussian Process Regression." MATEC Web of Conferences 176 (2018): 01017. http://dx.doi.org/10.1051/matecconf/201817601017.

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For the problems that Gamma Gaussian Inverse Wishart Cardinalized Probability Hypothesis Density (GGIW-CPHD) filter cannot accurately estimate the extended target shape and has a bad tracking performance under the condition of low SNR, a new generalized labeled multi-Bernoulli algorithm based on Gaussian process regression is proposed. The algorithm adopts the star convex to model the extended target, and realizes the online learning of the Gaussian process by constructing the state space model to complete the estimation of the extended target shape. At the same time, in the low SNR environment, the target motion state is tracked by the good tracking performance of the generalized label Bernoulli filter. Simulation results show that for any target with unknown shape, the proposed algorithm can well offer its extended shape and in the low SNR environment it can greatly improve the accuracy and stability of target tracking.

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20

Zheng, Jihong, and Meiguo Gao. "Tracking Ground Targets with a Road Constraint Using a GMPHD Filter." Sensors 18, no. 8 (August 18, 2018): 2723. http://dx.doi.org/10.3390/s18082723.

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The Gaussian mixture probability hypothesis density (GMPHD) filter is applied to the problem of tracking ground moving targets in clutter due to its excellent multitarget tracking performance, such as avoiding measurement-to-track association, and its easy implementation. For the existing GMPHD-based ground target tracking algorithm (the GMPHD filter incorporating map information using a coordinate transforming method, CT-GMPHD), the predicted probability density of its target state is given in road coordinates, while its target state update needs to be performed in Cartesian ground coordinates. Although the algorithm can improve the filtering performance to a certain extent, the coordinate transformation process increases the complexity of the algorithm and reduces its computational efficiency. To address this issue, this paper proposes two non-coordinate transformation roadmap fusion algorithms: directional process noise fusion (DNP-GMPHD) and state constraint fusion (SC-GMPHD). The simulation results show that, compared with the existing algorithms, the two proposed roadmap fusion algorithms are more accurate and efficient for target estimation performance on straight and curved roads in a cluttered environment. The proposed methods are additionally applied using a cardinalized PHD (CPHD) filter and a labeled multi-Bernoulli (LMB) filter. It is found that the PHD filter performs less well than the CPHD and LMB filters, but that it is also computationally cheaper.

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21

Li, Xiaohua, Bo Lu, Wasiq Ali, and Haiyan Jin. "Passive Tracking of Multiple Underwater Targets in Incomplete Detection and Clutter Environment." Entropy 23, no. 8 (August 20, 2021): 1082. http://dx.doi.org/10.3390/e23081082.

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A major advantage of the use of passive sonar in the tracking multiple underwater targets is that they can be kept covert, which reduces the risk of being attacked. However, the nonlinearity of the passive Doppler and bearing measurements, the range unobservability problem, and the complexity of data association between measurements and targets make the problem of underwater passive multiple target tracking challenging. To deal with these problems, the cardinalized probability hypothesis density (CPHD) recursion, which is based on Bayesian information theory, is developed to handle the data association uncertainty, and to acquire existing targets’ numbers and states (e.g., position and velocity). The key idea of the CPHD recursion is to simultaneously estimate the targets’ intensity and the probability distribution of the number of targets. The CPHD recursion is the first moment approximation of the Bayesian multiple targets filter, which avoids the data association procedure between the targets and measurements including clutter. The Bayesian-filter-based extended Kalman filter (EKF) is applied to deal with the nonlinear bearing and Doppler measurements. The experimental results show that the EKF-based CPHD recursion works well in the underwater passive multiple target tracking system in cluttered and noisy environments.

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22

LIAN, Feng, Chong-Zhao HAN, Wei-Feng LIU, and Xiang-Hui YUAN. "Multiple-model Probability Hypothesis Density Smoother." Acta Automatica Sinica 36, no. 7 (August 3, 2010): 939–50. http://dx.doi.org/10.3724/sp.j.1004.2010.00939.

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23

Sithiravel, Rajiv, Xin Chen, Ratnasingham Tharmarasa, Bhashyam Balaji, and Thiagalingam Kirubarajan. "The Spline Probability Hypothesis Density Filter." IEEE Transactions on Signal Processing 61, no. 24 (December 2013): 6188–203. http://dx.doi.org/10.1109/tsp.2013.2284139.

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24

Mahler, R. P. S., Ba-Tuong Vo, and Ba-Ngu Vo. "Forward-Backward Probability Hypothesis Density Smoothing." IEEE Transactions on Aerospace and Electronic Systems 48, no. 1 (January 2012): 707–28. http://dx.doi.org/10.1109/taes.2012.6129665.

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25

Schikora, Marek, Amadou Gning, Lyudmila Mihaylova, Daniel Cremers, and Wolfgang Koch. "Box-particle probability hypothesis density filtering." IEEE Transactions on Aerospace and Electronic Systems 50, no. 3 (July 2014): 1660–72. http://dx.doi.org/10.1109/taes.2014.120238.

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26

Cao, Chenghu, Yongbo Zhao, Xiaojiao Pang, Baoqing Xu, and Zhiling Suo. "Sequential Monte Carlo Cardinalized probability hypothesized density filter based on Track-Before-Detect for fluctuating targets in heavy-tailed clutter." Signal Processing 169 (April 2020): 107367. http://dx.doi.org/10.1016/j.sigpro.2019.107367.

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27

Sithiravel, Rajiv, Michael McDonald, Bhashyam Balaji, and Thiagalingam Kirubarajan. "Multiple model spline probability hypothesis density filter." IEEE Transactions on Aerospace and Electronic Systems 52, no. 3 (June 2016): 1210–26. http://dx.doi.org/10.1109/taes.2016.140750.

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28

He, Xiangyu, and Guixi Liu. "Improved Gaussian mixture probability hypothesis density smoother." Signal Processing 120 (March 2016): 56–63. http://dx.doi.org/10.1016/j.sigpro.2015.08.011.

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29

Vo, B. N., and W. K. Ma. "The Gaussian Mixture Probability Hypothesis Density Filter." IEEE Transactions on Signal Processing 54, no. 11 (November 2006): 4091–104. http://dx.doi.org/10.1109/tsp.2006.881190.

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30

Tang, Xu, Xin Chen, Michael McDonald, Ronald Mahler, Ratnasingham Tharmarasa, and Thiagalingam Kirubarajan. "A Multiple-Detection Probability Hypothesis Density Filter." IEEE Transactions on Signal Processing 63, no. 8 (April 2015): 2007–19. http://dx.doi.org/10.1109/tsp.2015.2407322.

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31

Nadarajah, N., T. Kirubarajan, T. Lang, M. Mcdonald, and K. Punithakumar. "Multitarget Tracking using Probability Hypothesis Density Smoothing." IEEE Transactions on Aerospace and Electronic Systems 47, no. 4 (2011): 2344–60. http://dx.doi.org/10.1109/taes.2011.6034637.

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32

Wu, Wei Hua, Jing Jiang, Chong Yang Liu, and Xiong Hua Fan. "Fast Gaussian Mixture Probability Hypothesis Density Filter." Applied Mechanics and Materials 568-570 (June 2014): 550–56. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.550.

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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.

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33

Ma, Tianli, Xinmin Wang, and Ting Li. "Multiple-model multiple hypothesis probability hypothesis density filter with blind zone." International Journal of Industrial and Systems Engineering 27, no. 2 (2017): 180. http://dx.doi.org/10.1504/ijise.2017.086271.

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Li, Ting, Xinmin Wang, and Tianli Ma. "Multiple-model multiple hypothesis probability hypothesis density filter with blind zone." International Journal of Industrial and Systems Engineering 27, no. 2 (2017): 180. http://dx.doi.org/10.1504/ijise.2017.10007097.

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35

Shen, Xinglin, Luping Zhang, Moufa Hu, Shanzhu Xiao, and Huamin Tao. "Arbitrary clutter extended target probability hypothesis density filter." IET Radar, Sonar & Navigation 15, no. 5 (April 8, 2021): 510–22. http://dx.doi.org/10.1049/rsn2.12041.

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36

DU Hang-yuan, 杜航原, 郝燕玲 HAO Yan-ling, 赵玉新 ZHAO Yu-xin, and 杨永鹏 YANG Yong-peng. "Implementation of SLAM by probability hypothesis density filter." Optics and Precision Engineering 19, no. 12 (2011): 3064–73. http://dx.doi.org/10.3788/ope.20111912.3064.

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37

Zhang, Feihu, and Alois Knoll. "Vehicle Detection Based on Probability Hypothesis Density Filter." Sensors 16, no. 4 (April 9, 2016): 510. http://dx.doi.org/10.3390/s16040510.

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38

Yang, Feng, Xi Shi, Keli Liu, Yan Liang, and Hao Chen. "Global track extraction for probability hypothesis density filter." Journal of Systems Engineering and Electronics 27, no. 6 (December 20, 2016): 1151–57. http://dx.doi.org/10.21629/jsee.2016.06.03.

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39

Li, Bo, and Fu-Wen Pang. "Improved probability hypothesis density filter for multitarget tracking." Nonlinear Dynamics 76, no. 1 (November 21, 2013): 367–76. http://dx.doi.org/10.1007/s11071-013-1131-1.

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40

Whiteley, Nick, Sumeetpal Singh, and Simon Godsill. "Auxiliary Particle Implementation of Probability Hypothesis Density Filter." IEEE Transactions on Aerospace and Electronic Systems 46, no. 3 (July 2010): 1437–54. http://dx.doi.org/10.1109/taes.2010.5545199.

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41

Liu, Weifeng, and Xiaobin Xu. "The Probability Hypothesis Density filter with evidence fusion." Journal of Electronics (China) 26, no. 6 (November 2009): 746–53. http://dx.doi.org/10.1007/s11767-010-0286-x.

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42

Gao, Li, Huaiwang Liu, and Hongyun Liu. "Probability hypothesis density filter with imperfect detection probability for multi-target tracking." Optik 127, no. 22 (November 2016): 10428–36. http://dx.doi.org/10.1016/j.ijleo.2016.08.060.

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Ya-Dong Wang, Jian-Kang Wu, A. A. Kassim, and Weimin Huang. "Data-Driven Probability Hypothesis Density Filter for Visual Tracking." IEEE Transactions on Circuits and Systems for Video Technology 18, no. 8 (August 2008): 1085–95. http://dx.doi.org/10.1109/tcsvt.2008.927105.

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Gao, Li, and Yang Wang. "Improved measurement-driven Gaussian mixture probability hypothesis density filter." Optik 127, no. 12 (June 2016): 5021–28. http://dx.doi.org/10.1016/j.ijleo.2016.02.052.

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45

Hernandez, S., and M. Frean. "BAYESIAN MULTIPLE PERSON TRACKING USING PROBABILITY HYPOTHESIS DENSITY SMOOTHING." International Journal on Smart Sensing and Intelligent Systems 4, no. 2 (2011): 285–312. http://dx.doi.org/10.21307/ijssis-2017-440.

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46

Barbieri, Florian, Corentin Rifflart, Ba-Tuong Vo, Sumedha Rajakaruna, and Arindam Ghosh. "Intrahour Cloud Tracking Based on Probability Hypothesis Density Filtering." IEEE Transactions on Sustainable Energy 9, no. 1 (January 2018): 340–49. http://dx.doi.org/10.1109/tste.2017.2733258.

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47

Li, Yun-xiang, Huai-tie Xiao, Zhi-yong Song, Hong-qi Fan, and Qiang Fu. "Free clustering optimal particle probability hypothesis density (PHD) filter." Journal of Central South University 21, no. 7 (July 2014): 2673–83. http://dx.doi.org/10.1007/s11771-014-2229-4.

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48

Gayraud, Ghislaine. "Minimax Hypothesis Testing about the Density Support." Bernoulli 7, no. 3 (June 2001): 507. http://dx.doi.org/10.2307/3318499.

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49

LIN, Zai-Ping, Yi-Yu ZHOU, and Wei AN. "Improved multitarget track-before-detect using probability hypothesis density filter." JOURNAL OF INFRARED AND MILLIMETER WAVES 31, no. 5 (November 29, 2012): 475–80. http://dx.doi.org/10.3724/sp.j.1010.2012.00475.

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Imtiaz Ahmed, Imtiaz Ahmed. "Multiple Track Estimation using Gaussian Mixture Probability Hypothesis Density Filter." IOSR journal of VLSI and Signal Processing 2, no. 4 (2013): 37–42. http://dx.doi.org/10.9790/4200-0243742.

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