CPHD Filter Research Articles

A Gaussian Mixture CPHD Filter for Multi-Target Tracking in Target-Dependent False Alarms

The estimation of the target number and individual tracks are two major tasks in multi-target tracking. The main shortcoming of traditional tracking methods is the cumbersome data association between measurements and targets. The cardinalized probability hypothesis density filter (CPHD) proposed in recent years can achieve the requirement for multitarget tracking. This kind of filter jointly estimates the cardinality distribution and the posterior density, which can achieve a more stable estimate of the target number. However, targets with complex micro-Doppler signatures (drones, birds, etc.) may generate target-dependent false alarms, which is contrary to the traditional uniform distribution assumption. In this case, the estimates of traditional CPHD filter will suffer from the abnormal transfer of PHD mass, causing the degradation of filtering performance. This paper studies the individual tracking of group targets with an improved GM-CPHD filter. First, the target-dependent false alarms are modeled with a general independent and identically distributed (I.I.D.) cluster process. Second, the update equations of cardinality and PHD density in target-dependent false alarms are derived. Finally, a practical solution using the Gaussian mixture method is proposed. The effectiveness of the proposed filter is verified by the simulation and experimental results.

The trajectory CPHD filter for spawning targets

This paper proposes a new trajectory cardinality probability hypothesis density (TCPHD) filter to track multiple spawning targets, referred to as the S-TCPHD filter. Firstly, we build the spawning events of single trajectory as a zero-inflated Poisson process and present corresponding trajectory set dynamic model. Then, the prediction equations of the S-TCPHD filter is derived based on the dynamic model, while the update step is the same as the TCPHD. In addition, we also develop the linear Gaussian mixture (LGM) implementations of the prediction step. The resulting S-TCPHD filter can estimate the trajectory information of targets, thereby being versatile and suitable for spawning target applications. The trajectory probability hypothesis density (TPHD) filter for spawning targets, namely S-TPHD, can be directly obtained from the S-TCPHD filter. Finally, the simulation results verify the tracking performance of the proposed S-TCPHD/S-TPHD filters in a multiple spawning targets tracking scenario.

Kernel-based learning of birth process from evolving spatiotemporal RFS data stream in SMC[sbnd]CPHD filter for multi-target tracking

This paper presents a kernel-based framework to estimate the birth process in the sequential Monte Carlo cardinalized probability hypothesis density (SMCCPHD) filter from the evolving spatiotemporal birth random finite set data stream that can enhance the performance of the SMCCPHD based trackers when tracking targets with no a priori information on where and when targets can appear. The time-varying spatial distribution of birth events is modelled as a map with adaptive grid points and their corresponding density values. While the spatial distribution of birth density is estimated from the elements of the birth random finite sets (RFSs), the time-varying birth cardinality distribution is estimated from the cardinality of the birth RFSs. The corresponding estimations are eventually used by a SMCCPHD based tracker to adjust its filtering strength spatially and temporally for target tracking. Experimental results on both the synthetic and real video surveillance datasets show that the proposed algorithm can improve the tracking accuracy by more precisely eliminating clutters and more effectively capturing newborn targets.

SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking

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.

Frequency tracking and mitigation method based on CPHD filter and adaptive multiple linear Kalman notch filter for multiple GNSS interference

NAVIGATIONVolume 67, Issue 1 p. 213-213 ERRATUMFree Access Frequency tracking and mitigation method based on CPHD filter and adaptive multiple linear Kalman notch filter for multiple GNSS interference This article corrects the following: Frequency tracking and mitigation method based on CPHD filter and adaptive multiple linear Kalman notch filter for multiple GNSS interference Sun Young Kim Chang Ho Kang Chan Gook Park Volume 66Issue 4Navigation pages: 803-830 First Published online: January 14, 2020 First published: 20 March 2020 https://doi.org/10.1002/navi.351AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinked InRedditWechat In Kim et al,1 the Acknowledgements section was published with missing content. The text “This work was done while the first author was a member of the Department of Mechanical and Aerospace Engineering, Seoul National University.” should be added. The complete Acknowledgements section is shown below: ACKNOWLEDGEMENTS A preliminary version of this paper was presented at the ION GNSS+ 2018 conference. This work has been supported by the National GNSS Research Center program of the Defense Acquisition Program Administration and Agency for Defense Development, and the Ministry of Science and ICT of the Republic of Korea through the Space Core Technology Development Program (No. NRF- 2018M1A3A3A02065722). This work was done while the first author was a member of the Department of Mechanical and Aerospace Engineering, Seoul National University. The online version was already corrected. We apologize for this error. REFERENCE 1Kim SY, Kang CH, Park CG. Frequency tracking and mitigation method based on CPHD filter and adaptive multiple linear Kalman notch filter for multiple GNSS interference. NAVIGATION. 2019; 66(4): 803- 830. https://doi.org/10.1002/navi.332Wiley Online LibraryWeb of Science®Google Scholar Volume67, Issue1Spring 2020Pages 213-213 ReferencesRelatedInformation

Gaussian Mixture Particle Jump-Markov-CPHD Fusion for Multitarget Tracking Using Sensors With Limited Views

In this article, we propose a multisensor cardinalized probability density hypothesis (CPHD) filter for tracking an unknown number of targets that may maneuver over time by using a sensor network with partially overlapping fields of views (PO-FoVs). We develop a novel, Gaussian mixture particle (GMP) implementation of the jump-Markov CPHD filter to deal with highly non-linear/non-Gaussian models and target maneuvers. The concepts of zero-forcing and zero-avoiding originally used in density approximation are introduced to elucidate a key difference between geometric and arithmetic averaging approaches, which are extended for joint target-state and mode fusion with regard to each PO-FoV for which distributed flooding is used for internode communication. The resulting GMP-JMCPHD fusion algorithm comprises three FoV-oriented steps: splitting, fusion, and merging. Simulations are provided to demonstrate the effectiveness of the proposed approaches.

Sequential Monte Carlo Cardinalized probability hypothesized density filter based on Track-Before-Detect for fluctuating targets in heavy-tailed clutter

In this paper, a Sequential Monte Carlo Cardinalized Probability Hypothesized Density (SMC-CPHD) filter based on Track-Before-Detect (TBD) algorithm in heavy-tailed clutter is proposed. The CPHD filter, which jointly propagates the first-order statistical moment and cardinality distribution, is an effective and efficient solution to multitarget filter problem in the presence of data association uncertainty, detect uncertainty, and time-varying. The TBD algorithm is extremely sensitive to the presence of clutter spikes in the data as the formulation of the TBD filter is dependent on knowledge of underlying clutter behavior. Therefore, the clutter is modeled in terms of K distribution with sea surface background and G0 distribution with primary forest background, while the popular Swerling targets of type 1 and 3 are considered to capture the target amplitude fluctuation frame-to-frame in this paper. The utilization of K distribution and G0 distribution clutter models instead of conventional Rayleigh distribution are verified through analysis of simulated and realistic data. The relevant results prove that proposed SMC-CPHD-TBD algorithm based on K distribution model and G0 distribution model can improve the detect and tracking performance over the conventional method in heavy-tailed clutter scenario. Additionally, the numerical simulations show that proposed CPHD-TBD algorithm can output the multitarget trajectories in the better precision with considerably less computational complexity compared with DP-TBD algorithm.

A Particle Multi-Target Tracker for Superpositional Measurements Using Labeled Random Finite Sets

In this paper we present a general solution for multi-target tracking with superpositional measurements. Measurements that are functions of the sum of the contributions of the targets present in the surveillance area are called superpositional measurements. We base our modelling on Labeled Random Finite Set (RFS) in order to jointly estimate the number of targets and their trajectories. This modelling leads to a labeled version of Mahler's multi-target Bayes filter. However, a straightforward implementation of this tracker using Sequential Monte Carlo (SMC) methods is not feasible due to the difficulties of sampling in high dimensional spaces. We propose an efficient multi-target sampling strategy based on Superpositional Approximate CPHD (SA-CPHD) filter and the recently introduced Labeled Multi-Bernoulli (LMB) and Vo-Vo densities. The applicability of the proposed approach is verified through simulation in a challenging radar application with closely spaced targets and low signal-to-noise ratio.

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.