Improved pruning algorithm for Gaussian mixture probability hypothesis density filter

With the increment of the number of Gaussian components, the computation cost increases in the Gaussian mixture probability hypothesis density(GM-PHD) filter. Based on the theory of Chen et al, we propose an improved pruning algorithm for the GM-PHD filter, which utilizes not only the Gaussian components’ means and covariance, but their weights as a new criterion to improve the estimate accuracy of the conventional pruning algorithm for tracking very closely proximity targets. Moreover, it solves the end-less while-loop problem without the need of a second merging step. Simulation results show that this improved algorithm is easier to implement and more robust than the formal ones.

A NEW DATA ASSOCIATION ALGORITHM USING PROBABILITY HYPOTHESIS DENSITY FILTER

Probability Hypothesis Density (PHD) filtering approach has shown its advantages in tracking time varying number of targets even when there are noise,clutter and misdetection. For linear Gaussian Mixture (GM) system,PHD filter has a closed form recursion (GMPHD). But PHD filter cannot estimate the trajectories of multi-target because it only provides identity-free estimate of target states. Existing data association methods still remain a big challenge mostly because they are com-putationally expensive. In this paper,we proposed a new data association algorithm using GMPHD filter,which significantly alleviated the heavy computing load and performed multi-target trajectory tracking effectively in the meantime.

Kernel density estimation and marginalized-particle based probability hypothesis density filter for multi-target tracking

In order to improve the performance of the probability hypothesis density(PHD) algorithm based particle filter(PF) in terms of number estimation and states extraction of multiple targets, a new probability hypothesis density filter algorithm based on marginalized particle and kernel density estimation is proposed, which utilizes the idea of marginalized particle filter to enhance the estimating performance of the PHD. The state variables are decomposed into linear and non-linear parts. The particle filter is adopted to predict and estimate the nonlinear states of multi-target after dimensionality reduction, while the Kalman filter is applied to estimate the linear parts under linear Gaussian condition. Embedding the information of the linear states into the estimated nonlinear states helps to reduce the estimating variance and improve the accuracy of target number estimation. The meanshift kernel density estimation, being of the inherent nature of searching peak value via an adaptive gradient ascent iteration, is introduced to cluster particles and extract target states, which is independent of the target number and can converge to the local peak position of the PHD distribution while avoiding the errors due to the inaccuracy in modeling and parameters estimation. Experiments show that the proposed algorithm can obtain higher tracking accuracy when using fewer sampling particles and is of lower computational complexity compared with the PF-PHD.

Cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion

The GM-PHD framework as recursion realization of PHD filter is extensively applied to multitarget tracking system. A new idea of improving the estimation precision of time-varying multi-target in non-linear system is proposed due to the advantage of computation efficiency in this paper. First,a novel cubature Kalman probability hypothesis density filter is designed for single sensor measurement system under the Gaussian mixture framework. Second,the consistency fusion strategy for multi-sensor measurement is proposed through constructing consistency matrix. Furthermore,to take the advantage of consistency fusion strategy,fused measurement is introduced in the update step of cubature Kalman probability hypothesis density filter to replace the single-sensor measurement. Then a cubature Kalman probability hypothesis density filter based on multi-sensor consistency fusion is proposed. Capabilily of the proposed algorithm is illustrated through simulation scenario of multi-sensor multi-target tracking.

Free clustering optimal particle probability hypothesis density(PHD) filter

As to the fact that it is difficult to obtain analytical form of optimal sampling density and tracking performance of standard particle probability hypothesis density(P-PHD) filter would decline when clustering algorithm is used to extract target states,a free clustering optimal P-PHD(FCO-P-PHD) filter is proposed.This method can lead to obtainment of analytical form of optimal sampling density of P-PHD filter and realization of optimal P-PHD filter without use of clustering algorithms in extraction target states.Besides,as sate extraction method in FCO-P-PHD filter is coupled with the process of obtaining analytical form for optimal sampling density,through decoupling process,a new single-sensor free clustering state extraction method is proposed.By combining this method with standard P-PHD filter,FC-P-PHD filter can be obtained,which significantly improves the tracking performance of P-PHD filter.In the end,the effectiveness of proposed algorithms and their advantages over other algorithms are validated through several simulation experiments.

THE PROBABILITY HYPOTHESIS DENSITY FILTER WITH EVIDENCE FUSION

The original Probability Hypothesis Density (PHD) filter is a tractable algorithm for Multi-Target Tracking (MTT) in Random Finite Set (RFS) frameworks. In this paper,we introduce a novel Evidence PHD (E-PHD) filter which combines the Dempster-Shafer (DS) evidence theory. The proposed filter can deal with the uncertain information,thus it forms target track. We mainly discusses the E-PHD filter under the condition of linear Gaussian. Research shows that the E-PHD filter has an analytic form of Evidence Gaussian Mixture PHD (E-GMPHD). The final experiment shows that the proposed E-GMPHD filter can derive the target identity,state,and number effectively.

Robust Frequency Estimation Under Additive Symmetric α-Stable Gaussian Mixture Noise

Here the estimating problem of a single sinusoidal signal in the additive symmetricα-stable Gaussian(ASαSG)noise is investigated.The ASαSG noise here is expressed as the additive of a Gaussian noise and a symmetricα-stable distributed variable.As the probability density function(PDF)of the ASαSG is complicated,traditional estimators cannot provide optimum estimates.Based on the Metropolis-Hastings(M-H)sampling scheme,a robust frequency estimator is proposed for ASαSG noise.Moreover,to accelerate the convergence rate of the developed algorithm,a new criterion of reconstructing the proposal covar-iance is derived,whose main idea is updating the proposal variance using several previous samples drawn in each iteration.The approximation PDF of the ASαSG noise,which is referred to the weighted sum of a Voigt function and a Gaussian PDF,is also employed to reduce the computational complexity.The computer simulations show that the performance of our method is better than the maximum likelihood and the lp-norm estimators.

MULTITARGET STATE AND TRACK ESTIMATION FOR THE PROBABILITY HYPOTHESES DENSITY FILTER

The particle Probability Hypotheses Density (particle-PHD) filter is a tractable approach for Random Finite Set (RFS) Bayes estimation, but the particle-PHD filter can not directly derive the target track. Most existing approaches combine the data association step to solve this problem. This paper proposes an algorithm which does not need the association step. Our basic ideal is based on the clustering algorithm of Finite Mixture Models (FMM). The intensity distribution is first derived by the particle-PHD filter, and then the clustering algorithm is applied to estimate the multitarget states and tracks jointly. The clustering process includes two steps: the prediction and update. The key to the proposed algorithm is to use the prediction as the initial points and the convergent points as the es- timates. Besides, Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC) ap- proaches are used for the FMM parameter estimation.

Adaptive Linear Filtering Design with Minimum Symbol Error Probability Criterion

Adaptive digital filtering has traditionally been developed based on the minimum mean square error （MMSE） criterion and has found ever-increasing applications in communications. This paper presents an alternative adaptive filtering design based on the minimum symbol error rate （MSER） criterion for communication applications. It is shown that the MSER filtering is smarter, as it exploits the non-Gaussian distribution of filter output effectively. Consequently, it provides significant performance gain in terms of smaller symbol error over the MMSE approach. Adopting Parzen window or kernel density estimation for a probability density function, a block-data gradient adaptive MSER algorithm is derived. A stochastic gradient adaptive MSER algorithm, referred to as the least symbol error rate, is further developed for sample-by-sample adaptive implementation of the MSER filtering. Two applications, involving single-user channel equalization and beamforming assisted receiver, are included to demonstrate the effectiveness and generality of the proposed adaptive MSER filtering approach.

计算高效的分布式多传感器PHD融合方法

基于广义协方差交集(GCI)融合理论,提出一种计算高效的分布式多传感器多目标跟踪算法,其中概率假设密度(PHD)滤波器在每个传感器节点运行,进行滤波处理。GCI用于融合多个PHD时,融合密度包括大量融合假设,这些假设随着高斯分量的数量增加呈指数增长。因此,GCI融合在实际运行中往往难以计算。为了提高多传感器融合的运算效率,文中通过距离度量将高斯分量聚类,然后进行孤立。距离度量可计算出目标融合后的密度权重,丢弃权重可忽略不计的融合假设,就能够构建简化的近似密度函数。分析表明,所提出的融合算法相较于传统的GCI融合算法,计算效率能够呈倍数提升。在先后出现12个目标的仿真场景中,通过实验验证了所提融合算法的有效性。

基于椭圆随机超曲面模型CPHD滤波器的多扩展目标跟踪算法

复杂场景下多扩展目标跟踪在自动驾驶、目标识别等领域具有很高的应用价值。文中提出了一种基于椭圆随机超曲面模型(ERHM)的势概率假设密度(CPHD)滤波器。首先,基于有限集统计理论,利用CPHD滤波器建立多扩展目标的贝叶斯滤波框架;然后,采用ERHM描述扩展目标的量测源分布,并利用无迹变换嵌入CPHD滤波流程;最后,仿真实验结果表明,ERHM-CPHD滤波器对椭圆扩展目标的跟踪性能优于传统的伽马高斯逆威沙特CPHD滤波器,在杂波密度较高、目标新生的位置比较确定的场景或者扩展目标数目较多时,对扩展目标的参数估计更为准确。所提方法在高分辨率雷达多目标跟踪方面具备很好的运用前景。

基于高斯混合模型的物流非高斯随机振动损伤分析

针对公路运输环境中的振动信号具有明显的非高斯性,提出一种非高斯随机振动疲劳损伤分析方法。为了描述振动信号的幅值概率密度分布,采用移动加速度均方根来代表该段信号的振动强度,并引入高斯混合模型对加速度均方根值进行描述。在此基础上结合Tovo-Benasciutti方法和Dirlik方法推导出非高斯宽带频域疲劳损伤计算方法。最后,以雨流计数法作为参考,对不同峭度的实测振动信号进行疲劳损伤分析,结果表明,与传统频域疲劳损伤计算方法相比较,提出的非高斯疲劳损伤方法具有更高的计算精度。该研究对于运输包装件的随机振动加速试验设计有实际意义。

一种改进的GM-C-CPHD空间多目标跟踪算法

随着空间目标的数目急剧上升,提高空间多目标跟踪精度成为必然要求,但空间多目标跟踪存在轨道动力学模型不完善的问题。针对该问题,提出一种改进的高斯混合势概率假设密度滤波(GM-C-CPHD)算法。通过在轨道动力学模型中考虑一个不确定性模型参数,即面质比参数(AMR),基于协方差传递面质比参数对位置、速度状态估计的影响,提高空间目标跟踪精度。仿真分析表明:相对于GM-CPHD滤波器,目标数量的跟踪和状态估计性能均有所提高,具有良好的应用前景。

Probability hypothesis density filter with adaptive parameter estimation for tracking multiple maneuvering targets

The probability hypothesis density(PHD) filter has been recognized as a promising technique for tracking an unknown number of targets. The performance of the PHD filter, however, is sensitive to the available knowledge on model parameters such as the measurement noise variance and those associated with the changes in the maneuvering target trajectories. If these parameters are unknown in advance, the tracking performance may degrade greatly. To address this aspect, this paper proposes to incorporate the adaptive parameter estimation(APE) method in the PHD filter so that the model parameters, which may be static and/or time-varying, can be estimated jointly with target states. The resulting APE-PHD algorithm is implemented using the particle filter(PF), which leads to the PF-APE-PHD filter. Simulations show that the newly proposed algorithm can correctly identify the unknown measurement noise variances, and it is capable of tracking multiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.

Fast density peak-based clustering algorithm for multiple extended target tracking

The key challenge of the extended target probability hypothesis density (ET-PHD) filter is to reduce the computational complexity by using a subset to approximate the full set of partitions. In this paper, the influence for the tracking results of different partitions is analyzed, and the form of the most informative partition is obtained. Then, a fast density peak-based clustering (FDPC) partitioning algorithm is applied to the measurement set partitioning. Since only one partition of the measurement set is used, the ET-PHD filter based on FDPC partitioning has lower computational complexity than the other ET-PHD filters. As FDPC partitioning is able to remove the spatially close clutter-generated measurements, the ET-PHD filter based on FDPC partitioning has good tracking performance in the scenario with more clutter-generated measurements. The simulation results show that the proposed algorithm can get the most informative partition and obviously reduce computational burden without losing tracking performance. As the number of clutter-generated measurements increased, the ET-PHD filter based on FDPC partitioning has better tracking performance than other ET-PHD filters. The FDPC algorithm will play an important role in the engineering realization of the multiple extended target tracking filter.

Probability Distribution of the Hull Motion and Mooring Line Tension of Two Floating Systems

The statistical and distribution characteristics of the responses of a floater and its mooring lines are essential in designing floating/mooring systems.In general,the dynamic responses of offshore structures obey a Gaussian distribution,assuming that the structural system,and sea loads are linear or weakly nonlinear.However,mooring systems and wave loads are considerably nonlinear,and the dynamic responses of hull/mooring systems are non-Gaussian.In this study,the dynamic responses of two types of floaters,semi-submersible and spar platforms,and their mooring lines are computed using coupled dynamic analysis in the time domain.Herein,the statistical characteristics and distributions of the hull motion and mooring line tension are discussed and compared.The statistical distributions of the dynamic responses have strong non-Gaussianity and are unreasonably fitted by a Gaussian distribution for the two floating and mooring systems.Then,the effects of water depth,wave parameters,and low-frequency and wave-frequency components on the non-Gaussianity of the hull motion,and mooring line tension are investigated and discussed.A comparison of the statistical distributions of the responses with various probability density functions,including the Gamma,Gaussian,General Extreme Value,Weibull,and Gaussian Mixture Model(GMM)distributions,shows that the GMM distribution is better than the others for characterizing the statistical distributions of the hull motion,and mooring line tension responses.Furthermore,the GMM distribution has the best accuracy of response prediction.

Multiple extended target tracking algorithm based on Gaussian surface matrix

In this paper, we consider the problem of irregular shapes tracking for multiple extended targets by introducing the Gaussian surface matrix（GSM） into the framework of the random finite set（RFS） theory. The Gaussian surface function is constructed first by the measurements, and it is used to define the GSM via a mapping function. We then integrate the GSM with the probability hypothesis density（PHD） filter, the Bayesian recursion formulas of GSM-PHD are derived and the Gaussian mixture implementation is employed to obtain the closed-form solutions. Moreover, the estimated shapes are designed to guide the measurement set sub-partition, which can cope with the problem of the spatially close target tracking. Simulation results show that the proposed algorithm can effectively estimate irregular target shapes and exhibit good robustness in cross extended target tracking.

Convolution Kernels Implementation of Cardinalized Probability Hypothesis Density Filter

The probability hypothesis density （PHD） propagates the posterior intensity in place of the poste- rior probability density of the multi-target state. The cardinalized PHD （CPHD） recursion is a generalization of PHD recursion, which jointly propagates the posterior intensity function and posterior cardinality distribution. A number of sequential Monte Carlo （SMC） implementations of PHD and CPHD filters （also known as SMC- PHD and SMC-CPHD filters, respectively） for general non-linear non-Gaussian models have been proposed. However, these approaches encounter the limitations when the observation variable is analytically unknown or the observation noise is null or too small. In this paper, we propose a convolution kernel approach in the SMC-CPHD filter. The simuIation results show the performance of the proposed filter on several simulated case studies when compared to the SMC-CPHD filter.

A novel SMC-PHD filter based on particle compensation

As a typical implementation of the probability hypothesis density(PHD) filter, sequential Monte Carlo PHD(SMC-PHD) is widely employed in highly nonlinear systems. However, the particle impoverishment problem introduced by the resampling step, together with the high computational burden problem, may lead to performance degradation and restrain the use of SMC-PHD filter in practical applications. In this work, a novel SMC-PHD filter based on particle compensation is proposed to solve above problems. Firstly, according to a comprehensive analysis on the particle impoverishment problem, a new particle generating mechanism is developed to compensate the particles. Then, all the particles are integrated into the SMC-PHD filter framework. Simulation results demonstrate that, in comparison with the SMC-PHD filter, proposed PC-SMC-PHD filter is capable of overcoming the particle impoverishment problem, as well as improving the processing rate for a certain tracking accuracy in different scenarios.

基于GMM-DBC的CSI室内定位算法

针对贝叶斯室内定位技术存在定位精度低及时间复杂度较高的问题,提出了一种基于高斯混合模型和密度聚类(GMM-DBC)的信道状态信息(CSI)定位算法.通过对分模型参数的初次估计构建GMM概率分布模型并进行误差计算;引入确定分模型个数(DSM)策略,结合误差计算结果更新GMM模型参数,减小由模型精度引起的定位误差;基于不同参考点的分布特征,判断参考点间紧密程度,将紧密相连的参考点划为一类,减小搜索范围,降低时间复杂度;根据分簇结果,利用改进的贝叶斯概率算法进行权值计算,得到最终定位结果.实验结果表明:所提算法能较好地提高定位精度,降低时间复杂度.