https://www.jstage.jst.go.jp/article/jsprs1975/37/6/37_6_39/_pdf

1998 IEEE International Conference on SMCに参加して

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.

A Novel Robust Gaussian–Student's t Mixture Distribution Based Kalman Filter

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.

/pdf/multi-sensor-multi-target-tracking-using-probability-434ndwmias.pdf

Multi-Sensor Multi-Target Tracking Using Probability Hypothesis Density Filter

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.

/pdf/multi-target-tracking-by-associating-and-fusing-the-multi-2bpgvwx6gy.pdf

Multi-Target Tracking by Associating and Fusing the Multi-Bernoulli Parameter Sets

Due to its low computational cost, the Gaussian mixture (GM) implementation of the probability hypothesis density (PHD) filter is a good candidate for multi-target tracking (MTT), especially in real-time processing applications. In this study, we propose an explicit track continuity algorithm based on the GM-PHD filter with unknown target birth intensity for online MTT. In this approach, the identity labels of Gaussian components are divided into three classes, and the labels of confirmed components are unchanged through the overall filtering process, this can provide explicit MTT. Based on the measurements not associated with the predicted components, the adaptive target birth intensity is obtained. The simulation results demonstrate that the proposed approach can achieve explicit MTT under the unknown target birth intensity scenes.

An explicit track continuity algorithm based on the GM-PHD filter with adaptive birth intensity

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.

A Student’s T Mixture Cardinality-Balanced Multi-Target Multi-Bernoulli Filter With Heavy-Tailed Process and Measurement Noises

Appropriately modelling target-birth intensity is a significant but challenging issue in multi-target tracking systems. In existing cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filters, a priori knowledge about the locations where targets appear is required to model the target-birth intensity. Since the newborn targets can appear anywhere within the observation region, it is impractical to obtain such prior information. In this study, a novel CBMeMBer filter with adaptive target-birth intensity is presented, considering the newborn and surviving targets separately. The target-birth function of the target-birth intensity is modelled using current measurements rather than the known birth locations, and the target-birth magnitude is assigned by an allocation function rather than equally assigned. The new CBMeMBer filter can remove the restriction on the requirement of prior birth location information and can adapt well after continuous missing detection occurs. Simulations of the sequential Monte Carlo and Gaussian mixture implementations demonstrate the effectiveness of the proposed filter.

https://ietresearch.onlinelibrary.wiley.com/doi/epdf/10.1049/iet-spr.2017.0567

CBMeMBer filter with adaptive target birth intensity

The probability hypothesis density (PHD) filter is a promising filter for multi-target tracking which propagates the posterior intensity of the multi-target state. In this paper, a Gaussian mixture particle flow PHD (GMPF-PHD) filter is proposed which uses a bank of particles to represent the Gaussian components in the Gaussian mixture PHD (GM-PHD) filter. Then a particle flow is implemented to migrate the particles to a more appropriate region in order to obtain a more accurate approximation of the posterior intensity. To verify the effectiveness of the algorithm, both linear and nonlinear multi-target tracking problem are designed, and the performance are compared with the classical approaches such as the GM-PHD filter, the Gaussian mixture particle PHD (GMP-PHD) filter, and the particle PHD filter. Simulation results show that the proposed filter can achieve a good performance with a reasonable computational cost.

Mingjie Wang

Papers

A Student’s T Mixture Cardinality-Balanced Multi-Target Multi-Bernoulli Filter With Heavy-Tailed Process and Measurement Noises

CBMeMBer filter with adaptive target birth intensity

Gaussian mixture particle flow probability hypothesis density filter