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

In this paper, we introduce a tracking algorithm based on labeled Random Finite Sets (RFS) and Rauch-Tung-Striebel (RTS) smoother via a Generalized Labeled Multi-Bernoulli (GLMB) multi-scan estimator to track multiple objects in a wide range of tracking scenarios. In the forward filtering stage, we use the GLMB filter to generate a set of labels and the association history between labels and the measurements. In the trajectory-estimating stage, we apply a track management strategy to eliminate tracks with short lifespan compared to a threshold value. Subsequently, we apply the information of trajectories captured from the forward GLMB filtering stage to carry out standard forward filtering and RTS backward smoothing on each estimated trajectory. For the experiment, we implement the tracker with standard GLMB filter, the hybrid track-before-detect (TBD) GLMB filter, and the GLMB filter with objects spawning. The results show improvements in tracking performance for all implemented trackers given negligible extra computational effort compared to standard GLMB filters.

GLMB Tracker with Partial Smoothing.

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 existing Probability Hypothesis Density (PHD) filters with birth intensity estimation only operate on single or two consecutive scan data for multi-target tracking. However, for those targets with low detection probability, it is hard to achieve a satisfactory level of track initiation and maintenance. To overcome the weakness above, we propose a modified PHD filter with adaptive birth intensity estimation. The core of the proposed filter is to define two state sets as the formal set and the temporary set. In the framework of measurement driven estimation, we classify the measurements into three categories depending on whether it is in the neighborhood of the state in above two sets. And the birth states of the formal set and the temporary set are generated by the classified measurements respectively. In addition, if there is no matching measurement for the state in the formal set, duplicate the corresponding state as the birth state of the temporary set. For each state in temporary set, we introduce a forgetting factor and a dynamic detection probability in filter to cope with the rapid decrease of its intensity due to the absence of measurement. If its forgetting factor is over the dead threshold, the state will be deleted from the set. Based on the principles above, we derive the Gaussian-mixture (GM) implementation of the PHD filter proposed in this paper. Experiment results show that, in low detection probability scenario, the modified PHD filter outperforms other PHD filters with birth intensity estimation.

/pdf/the-modified-probability-hypothesis-density-filter-with-3sygyh6yx1.pdf

The Modified Probability Hypothesis Density Filter With Adaptive Birth Intensity Estimation for Multi-Target Tracking in Low Detection Probability

Adaptively modeling the target birth intensity while maintaining the filtering efficiency is a challenging issue in multi-target tracking (MTT). Generally, the target birth probability is predefined as a constant and only the target birth density is considered in existing adaptive birth models, resulting in deteriorated target tracking accuracy, especially in the target appearing cases. In addition, the existing adaptive birth models also give rise to a decline in operation efficiency on account of the extra birth modeling calculations. To properly adapt the real variation of the number of newborn targets and improve the multi-target tracking performance, a novel fast sequential Monte Carlo (SMC) adaptive target birth intensity cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter is proposed in this paper. Through adaptively conducting the target birth probability in a pre-processing step, which incorporates the information of current measurements to correct the pre-setting of the target birth probability, the proposed filter can truly adapt target birth cases and achieve better tracking accuracy. Moreover, the implementation efficiency can be improved significantly by employing a measurement noise-based threshold in the likelihood calculations of the multi-target updating. Simulation results verify the effectiveness of the proposed filter.

https://www.mdpi.com/1424-8220/19/5/1120/pdf

Adaptive Target Birth Intensity Multi-Bernoulli Filter with Noise-Based Threshold.

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.

Gaussian mixture particle flow probability hypothesis density filter

Multiple object tracking faces a challenge of realistically modelling birth background in the premise of keeping the efficiency of filtering. Existing adaptive birth models only pay attention to modeling the birth density, simply assuming the birth probability (BP) constant, resulting inaccurate birth description and deteriorated tracking performance. Moreover, the adaptive birth models incur much heavier computational burden, which greatly limits the real-time capability. The paper gives an efficient adaptive birth intensity cardinality balanced multi-target multi-Bernoulli (CBMeMBer) filter, capable of truly adapting birth as well as effectively achieving good tracking performance via the adaptive calculation of the BP by pre-processing, and reducing the unnecessary likelihood calculations by a measurement noise (MN)-based threshold.

Xiaolong Hu

Papers

Adaptive Target Birth Intensity Multi-Bernoulli Filter with Noise-Based Threshold.

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

σ-threshold Bayes Filter in Unknown Birth Background with Multi-Bernoulli Finite Sets