A Student’s T Mixture Cardinality-Balanced Multi-Target Multi-Bernoulli Filter With Heavy-Tailed Process and Measurement Noises
10 Sep 2018-IEEE Access (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 6, pp 51098-51109
TL;DR: Simulation results demonstrate that robust multi-target tracking can be achieved in the presence of outliers in process and measurement noises, and the proposed algorithm is a generalization of existing Gaussian mixture CBMeMBer (GM-CBMe MBer) filter.
Abstract: The cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter is a promising solution for multi-target tracking. However, the performance of the CBMeMBer filter will be degraded severely by outliers in the presence of heavy-tailed process noise and measurement noise. To address this challenging issue, a novel CBMeMBer filter called the Student’s t mixture CBMeMBer (STM-CBMeMBer) filter is proposed in this paper, by assuming that the joint probability density function (pdf) of the state and process noise and the joint pdf of the state and measurement noise follow joint Student’s t distributions. Following that, a closed-form solution of the CBMeMBer recursion is obtained by approximating the probability density parameter of the multi-Bernoulli as a STM. The proposed algorithm is a generalization of existing Gaussian mixture CBMeMBer (GM-CBMeMBer) filter, and it reduces to the GM-CBMeMBer filter in some special cases. Simulation results demonstrate that robust multi-target tracking can be achieved in the presence of outliers in process and measurement noises.
Citations
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TL;DR: The novel GSTM distributed Kalman filter has the important advantage over the RSTKF that the adaptation of the mixing parameter is much more straightforward than learning the degrees of freedom parameter.
Abstract: In this paper, a novel Gaussian–Student's t mixture (GSTM) distribution is proposed to model non-stationary heavy-tailed noises. The proposed GSTM distribution can be formulated as a hierarchical Gaussian form by introducing a Bernoulli random variable, based on which a new hierarchical linear Gaussian state-space model is constructed. A novel robust GSTM distribution based Kalman filter is proposed based on the constructed hierarchical linear Gaussian state-space model using the variational Bayesian approach. The Kalman filter and robust Student's t based Kalman filter (RSTKF) with fixed distribution parameters are two existing special cases of the proposed filter. The novel GSTM distributed Kalman filter has the important advantage over the RSTKF that the adaptation of the mixing parameter is much more straightforward than learning the degrees of freedom parameter. Simulation results illustrate that the proposed filter has better estimation accuracy than those of the Kalman filter and RSTKF for a linear state-space model with non-stationary heavy-tailed noises.
142 citations
Cites methods from "A Student’s T Mixture Cardinality-B..."
...The Student’s t filter has been also extended to the application of multi-target tracking to cope with outlier-corrupted state and measurement noises, and many robust Student’s t mixture filters have been proposed, such as the Student’s t mixture probability hypothesis density filter [16], [17], the Student’s t mixture labeled multi-Bernoulli filter [18], and the Student’s t mixture cardinality-balanced multi-target multi-Bernoulli filter [19]....
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TL;DR: The simulation results and the theoretical analysis indicate that the new PM-PHD filter can deal with a harsh tracking environment and can handle the problems of miss-detection and false alarm effectively.
Abstract: Compared with the single sensor tracking system, the multi-sensor tracking system has several advantages in target tracking, such as a larger field of view and higher tracking accuracy. Different from the multi-sensor filters based on the random finite set (RFS) theory, the product multi-sensor probability hypothesis density (PM-PHD) filter with a modified cardinality coefficient performs well in estimating the number of targets. Since the PM-PHD filter employs the iterative fusion structure, its state estimation is sensitive to the sensor parameters. Furthermore, to improve the cardinality estimation, the PM-PHD filter may estimate some false targets when miss-detection occurs. Addressing the above problems, this paper changes the fusion structure of the PM-PHD filter and presents a novel version of the PM-PHD filter. The main idea of the proposed algorithm is the combinations of measurement subsets and other factors. Both the cardinality estimation and the state estimation are obtained by fusing the target numbers and normalized PHDs of these combinations. Compared with other multi-sensor PHD filters, the proposed algorithm can handle the problems of miss-detection and false alarm effectively. Moreover, the simulation results and the theoretical analysis indicate that the new PM-PHD filter can deal with a harsh tracking environment.
9 citations
Cites background from "A Student’s T Mixture Cardinality-B..."
...filter [11], [12], cardinality probability hypothesis density (CPHD) filter [13] and cardinality balanced MeMBer (CBMeMBer) filter [14], [15]....
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TL;DR: The theoretical analysis and experiment results of different tracking scenarios show that the proposed methods perform well in both state estimation and cardinality estimation.
Abstract: The Cardinality Balanced MeMBer (CBMeMBer) filter is a single sensor multi-target tracking method based on the random finite set. Compared with the single sensor system, the multi-sensor system can achieve more stable and better performance in tracking targets. However, some problems exist in multi-sensor system based on the CBMeMBer filter. Tracks in the CBMeMBer filter are described by parameter sets which may be generated by miss-detection, targets and clutters. It is difficult to associate the parameter sets correctly because of their complex forms and various types. Moreover, the filter reacts slowly to disappeared targets, which leads to a cardinality overestimation. This problem may be more serious in the multi-sensor system. To deal with the above problems, the parameter sets association and fusion methods are presented in this paper. By three association processes with the adaptive thresholds selection approaches, parameter sets corresponding to the same target are grouped into one parameter set partition. Parameter sets have different association thresholds because of their different accuracies. The fusion method considers the types and relationships of parameter sets in the partition simultaneously and uses a joint credibility to accelerate changes in existence probability. The cardinality estimation decreases rapidly when the target disappears. The theoretical analysis and experiment results of different tracking scenarios show that the proposed methods perform well in both state estimation and cardinality estimation.
2 citations
Cites methods from "A Student’s T Mixture Cardinality-B..."
...In [10] and [11], the Student’s t-distribution is used to handle the problems of observation noise of the PHD filter and the CBMeMBer filter, respectively....
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TL;DR: In this article , a distributed multi-target tracking (DMT) algorithm for asynchronous non-uniform multisensor networks (AN-WSN) is studied, and the fusion rule of AAD consensus is derived to construct the fusion process of the proposed DMT algorithm.
Abstract: With more and more extensive applications of target tracking, distributed multitarget tracking (DMT) becomes an important research direction. However, the synchronization characteristics of some sensor networks cannot be effectively guaranteed due to communication delay, nonuniform sampling, etc. Therefore, a DMT algorithm for asynchronous nonuniform multisensor networks (AN-WSN) is studied in this article. First, a CD-CPHD algorithm with the multistep birth process and time-triggered structure (TCD-CPHD) is proposed by using the continuous-discrete multitarget dynamic (CD) model and the cardinalized probability hypothesis density (CPHD); second, a TCD-CPHD trigger structure based on asymmetric alpha-divergence (AAD) is designed to reduce the communication rate of TCD-CPHD by adaptively calculating the time-trigger index; third, the fusion rule of AAD consensus is derived to construct the fusion process of the proposed DMT algorithm; finally, by combining the above structures and the fusion rule, the implementation processes of the proposed DMT algorithm are given. Theoretical analysis and exhaustive experimental analysis show the effectiveness of the proposed algorithm.
06 Jul 2020
TL;DR: Simulation results demonstrated that the proposed Student's t mixture $\delta$-GLMB filter can achieve a good trade-off between efficiency and tracking accuracy.
Abstract: To solve the problem of multi-target tracking with heavy-tailed process noise and measurement noise, a Student's t mixture $\delta$ -generalized labeled multi-Bernoulli ( $\delta$ -GLMB) filter is proposed for nonlinear systems. A third-degree Spherical-Radial rule is utilized to calculate the probability density functions of the prediction and update of target states for nonlinear multi-target models. The performance of the proposed Student's t mixture $\delta$ -GLMB filter for nonlinear systems is compared with the Sequential Monte Carlo $\delta$ -GLMB (SMC- $\delta$ -GLMB) filter through simulation experiments. Simulation results demonstrated that the proposed filter can achieve a good trade-off between efficiency and tracking accuracy.
Cites methods from "A Student’s T Mixture Cardinality-B..."
...In order to deal with the multi-target tracking issue of in the presence of process and measurement noise outliers, many robust Student’s t mixture filters have been proposed, including the Student’s t mixture PHD filter [18], [19], and the Student’s t mixture CBMeMBer filter [20]....
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References
More filters
Book•
01 Jan 1988
4,098 citations
"A Student’s T Mixture Cardinality-B..." refers background in this paper
...Generally, the joint probabilistic data association (JPDA) filter [1], [2], the multiple hypothesis tracking (MHT) [3], [4], and the random finite set (RFS) theory [5] are the most commonly used approaches for multitarget tracking....
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Book•
01 Aug 1999
TL;DR: The Basics of Target Tracking and Multi Target Tracking with an Agile Beam Radar, and Multiple Hypothesis Tracking System Design and Application.
Abstract: The Basics of Target Tracking. Sensor and Source Characteristics. Kinematic State Estimation: Filtering and Prediction. Modelling and Tracking Dynamic Targets. Passive Sensor Tracking. Basic Methods for Data Association. Advanced Methods for MTT Data Association. Attribute Data Fusion. Multiple Sensor Tracking -- Issues and Methods. Multiple Sensor Tracking -- System Implementation and Applications. Reasoning Schemes for Situation Assessment and Sensor Management. Situation Assessment. Tracking System Performance Prediction, and Evaluation. Multi Target Tracking with an Agile Beam Radar. Sensor Management. Multiple Hypothesis Tracking System Design and Application. Detection and Tracking of Dim Targets in Clutter.
2,774 citations
TL;DR: Recursion Bayes filter equations for the probability hypothesis density are derived that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets and it is shown that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.
Abstract: The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.
2,088 citations
"A Student’s T Mixture Cardinality-B..." refers background in this paper
...51108 VOLUME 6, 2018 [12] B. Ristic, D. Clark, B.-N. Vo, and B.-T. Vo, ‘‘Adaptive target birth intensity for PHD and CPHD filters,’’ IEEE Trans....
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...[11] T. Zajic and R. P. S. Mahler, ‘‘Particle-systems implementation of the PHD multitarget-tracking filter,’’ Proc....
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...Moreover, the number of the Student’s t components to represent each multi-Bernoulli component increases with recursion similar to the GM-PHD filter [8]....
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...To address this issue, the probability hypothesis density (PHD) [6] and cardinalized PHD (CPHD) [7] filters have been proposed....
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...These operations are similar to that of the GM-PHD and GM-CBMeMBer [8], [17]....
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Book•
28 Feb 2007
TL;DR: This comprehensive resource provides an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm.
Abstract: This comprehensive resource provides you with an in-depth understanding of finite-set statistics (FISST) - a recently developed method which unifies much of information fusion under a single probabilistic, in fact Bayesian, paradigm. The book helps you master FISST concepts, techniques, and algorithms, so you can use FISST to address real-world challenges in the field. You learn how to model, fuse, and process highly disparate information sources, and detect and track non-cooperative individual/platform groups and conventional non-cooperative targets. You find a rigorous Bayesian unification for many aspects of expert systems theory. Moreover, the book presents systematic integral and differential calculus for multisource-multitarget problems, providing a methodology for devising rigorous new techniques. This accessible and detailed book is supported with over 3,000 equations, 90 clear examples, 70 explanatory figures, and 60 exercises with solutions.
2,004 citations
"A Student’s T Mixture Cardinality-B..." refers background or methods in this paper
...THE CBMeMBer FILTER The MeMBer filter [5] can be used to track targets through propagating the approximated posterior density recursively, which is represented by a multi-Bernoulli parameter set π = {(r (i), p)}i=1 with r (i) representing the existence probability and p(i) representing the probability density, respectively....
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...In addition, another Bayesianmulti-target approximation, named the multi-target multi-Bernoulli (MeMBer) filter, was proposed in [5] by recursively propagating the multi-target posterior density....
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...Generally, the joint probabilistic data association (JPDA) filter [1], [2], the multiple hypothesis tracking (MHT) [3], [4], and the random finite set (RFS) theory [5] are the most commonly used approaches for multitarget tracking....
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TL;DR: Under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture and closed-form recursions for propagating the means, covariances, and weights of the constituent Gaussian components of the posteriorintensity are derived.
Abstract: A new recursive algorithm is proposed for jointly estimating the time-varying number of targets and their states from a sequence of observation sets in the presence of data association uncertainty, detection uncertainty, noise, and false alarms. The approach involves modelling the respective collections of targets and measurements as random finite sets and applying the probability hypothesis density (PHD) recursion to propagate the posterior intensity, which is a first-order statistic of the random finite set of targets, in time. At present, there is no closed-form solution to the PHD recursion. This paper shows that under linear, Gaussian assumptions on the target dynamics and birth process, the posterior intensity at any time step is a Gaussian mixture. More importantly, closed-form recursions for propagating the means, covariances, and weights of the constituent Gaussian components of the posterior intensity are derived. The proposed algorithm combines these recursions with a strategy for managing the number of Gaussian components to increase efficiency. This algorithm is extended to accommodate mildly nonlinear target dynamics using approximation strategies from the extended and unscented Kalman filters
1,805 citations
"A Student’s T Mixture Cardinality-B..." refers methods or result in this paper
...Moreover, the number of the Student’s t components to represent each multi-Bernoulli component increases with recursion similar to the GM-PHD filter [8]....
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...Note that both of the filters can be implemented by Gaussian mixture [8], [9] and particle methods [10], [11]....
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...These operations are similar to that of the GM-PHD and GM-CBMeMBer [8], [17]....
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