PHD filter based track-before-detect for MIMO radars

In this paper a Probability Hypothesis Density (PHD) filter based track-before-detect (TBD) algorithm is proposed for Multiple-Input-Multiple-Output (MIMO) radars. The PHD filter, which propagates only the first-order statistical moment of the full target posterior, is a computationally efficient solution to multitarget tracking problems with varying number of targets. The proposed algorithm avoids any assumption on the maximum number of targets as a result of estimating the number of targets together with target states. With widely separated transmitter and receiver pairs, the algorithm utilizes the Radar Cross Section (RCS) diversity as a result of target illumination from ideally uncorrelated aspects. Furthermore, a multiple sensor TBD is proposed in order to process the received signals from different transmitter-receiver pairs in the MIMO radar system. In this model, the target observability to the sensor as a result of target RCS diversity is taken in to consideration in the likelihood calculation. In order to quantify the performance of the proposed algorithm, the Posterior Cramer-Rao Lower Bound (PCRLB) for widely separated MIMO radars is also derived. Simulation results show that the new algorithm meets the PCRLB and provides better results compared with standard Maximum Likelihood (ML) based localizations.     

Convergence Analysis of the Gaussian Mixture PHD Filter

The Gaussian mixture probability hypothesis density (PHD) filter was proposed recently for jointly estimating the time-varying number of targets and their states from a sequence of sets of observations without the need for measurement-to-track data association. It was shown that, under linear-Gaussian assumptions, the posterior intensity at any point in time is a Gaussian mixture. This paper proves uniform convergence of the errors in the algorithm and provides error bounds for the pruning and merging stages. In addition, uniform convergence results for the extended Kalman PHD Filter are given, and the unscented Kalman PHD Filter implementation is discussed     

A novel track maintenance algorithm for PHD/CPHD filter

Probability hypothesis density (PHD) filter and cardinalized PHD (CPHD) filter have proved to be promising algorithms for tracking an unknown number of targets in real time. However, they do not provide the identities of the individual estimated targets, so the target tracks cannot be obtained. To solve this problem, we propose a new track maintenance algorithm based on the cross entropy (CE) technique. Firstly, the particle filter PHD (PF-PHD) algorithm is used to estimate the target states and the target number. Then, the results of the estimation are used as vertexes to construct a connectivity graph with associated weights, and the CE technique is employed as a global optimization scheme to calculate the optimal feasible associated events. Furthermore, due to the advantages of the CPHD filter and the Rao-Blackwellized particle filter (RBPF), we propose another track maintenance algorithm based on the CE technique, named the RBPF–CPHD tracker, which can further improve the track maintenance performance due to the more accurate state estimates and their number estimates. Simulation results show that the proposed algorithms can effectively achieve the track continuity, with stronger robustness and greater anti-jamming capability.     

Convergence index filter for vector fields

This paper proposes a unique fitter called an iris filter, which evaluates the degree of convergence of the gradient vectors within its region of support toward a pixel of interest. The degree of convergence is related to the distribution of the directions of the gradient vectors and not to their magnitudes. The convergence index of a gradient vector at a given pixel is defined as the cosine of its orientation with respect to the line connecting the pixel and the pixel of interest. The output of the iris filter is the average of the convergence indices within its region of support and lies within the range [-1,1]. The region of support of the iris filter changes so that the degree of convergence of the gradient vectors in it becomes a maximum, i.e., the size and shape of the region of support at each pixel of interest changes adaptively according to the distribution pattern of the gradient vectors around it. Theoretical analysis using models of a rounded convex region and a semi-cylindrical one is given. These show that rounded convex regions are generally enhanced, even if the contrast to their background is weak and also that elongated objects are suppressed. The filter output is 1/pi at the boundaries of rounded convex regions and semi-cylindrical ones. This value does not depend on the contrast to their background. This indicates that boundaries of rounded or slender objects, with weak contrast to their background, are enhanced by the iris filter and that the absolute value of 1/pi can be used to detect the boundaries of these objects. These theoretical characteristics are confirmed by experiments using X-ray images.     

Localization of multiple emitters based on the sequential PHD filter

The localization of multiple emitters from passive angle measurements is a widely investigated problem. Traditionally, the central problem of state estimation for multiple targets by multiple passive sensors is data association. Mathematically, the formulation of the data association problem leads to a generalization of an S-dimensional (S-D) assignment problem. Unfortunately, the complexity of solving an S-D assignment problem for S≥3 is NP hard. A practical solution is to solve the multidimensional assignment problem using multistage Lagrangian relaxation. However, the computational requirements of it explode with the number of sensors. Additionally, it cannot give satisfactory results in dense clutter environment. In this paper, the sequential probability hypothesis density (PHD) filter using passive sensors in two different manners for localization of multiple emitters is introduced. Simulation results show that the sequential PHD filter can achieve better performance with smaller computational complexity than the method based on S-D assignment programming in dense clutter environment.     

一种基于多模型高斯逆Wishart PHD滤波器的空间邻近目标跟踪方法

将空间邻近目标(Closely Spaced Objects,CSOs)整体建模为扩展目标(Extended Target,ET),用随机矢量和随机矩阵分别描述CSOs质心运动和扩散状态,并采用高斯逆Wishart(Gaussian inverse Wishart,GIW)概率假设密度(Probability Hypothesis Density,PHD)滤波器实现杂波和漏检条件下CSOs的稳定跟踪.修正了原GIW-PHD滤波器量测模型和形状估计的缺陷,给出新的递推表达式,并在此基础上提出一种多(形变)模型GIW-PHD滤波器,以适应CSOs分裂和融合引起的形状变化.仿真结果表明,所提算法能够有效跟踪CSOs,状态估计比原GIW-PHD更加准确,对CSOs的变化更加敏感.     

A new multiple extended target tracking algorithm using PHD filter

A new multiple extended target tracking algorithm using the probability hypothesis density (PHD) filter is proposed in our study, to solve problems on tracking performance degradation of the extended target PHD (ET-PHD) filter under the nonlinear conditions and its intolerable computational requirement. It is noted that with the current Gaussian mixture implement of ET-PHD filter satisfying tracking performance could only be obtained under linear and Gaussian conditions. To extend the application of ET-PHD filter for nonlinear models, our study has derived a particle implement of ET-PHD (ET-P-PHD) filter. Our study finds that the main factors influencing the computational complexity of the ET-P-PHD filter are the partition number of measurement set and the calculation of non-negative coefficients of cells in partitions. With the pretreatment of measurements and application of a new K-means clustering based measurement set partition method, we have successfully decreased the partition number. In addition, a gating method for target state space, which is based on likelihood relationship between target state and measurement, is proposed to simplify the calculation of non-negative coefficients. Simulation results show that the algorithms proposed by our study could satisfyingly deal with multiple extended target tracking issues under nonlinear conditions, and lead to significantly lower computational complexity with tiny effect on tracking performance.     

Gaussian mixture PHD filter for jump Markov models based on best-fitting Gaussian approximation

A new Gaussian mixture probability hypothesis density (PHD) filter is developed for tracking multiple maneuvering targets that follow jump Markov models. This approach is based on the best-fitting Gaussian approximation which has been shown to be an accurate predictor of the interacting multiple model (IMM) performance. Compared with the existing Gaussian mixture multiple model PHD filter without interacting, simulations show that the proposed filter achieves better results with much less computational expense.     

Distributed multi-sensor particle filter for bearings-only tracking

In this article, the classical bearings-only tracking (BOT) problem for a single target is addressed, which belongs to the general class of non-linear filtering problems. Due to the fact that the radial distance observability of the target is poor, the algorithm-based sequential Monte-Carlo (particle filtering, PF) methods generally show instability and filter divergence. A new stable distributed multi-sensor PF method is proposed for BOT. The sensors process their measurements at their sites using a hierarchical PF approach, which transforms the BOT problem from Cartesian coordinate to the logarithmic polar coordinate and separates the observable components from the unobservable components of the target. In the fusion centre, the target state can be estimated by utilising the multi-sensor optimal information fusion rule. Furthermore, the computation of a theoretical Cramer–Rao lower bound is given for the multi-sensor BOT problem. Simulation results illustrate that the proposed tracking method can provide better performances than the traditional PF method.     

一种导向粒子滤波跟踪算法

粒子滤波算法在运动目标跟踪方面有着广泛的使用,粒子滤波中的重采样是解决粒子退化的一种重要方法,但是重采样会导致粒子的多样性的丧失。针对这个问题,改进粒子滤波算法,改进过程中结合了导向滤波的基本思想,因此将这种方法称为导向粒子滤波跟踪算法。导向滤波是近几年提出的一种新的滤波方式,与传统滤波相比,它在滤波的时候会引入一幅指导图像,鉴于这个思想,我们在进行粒子滤波的时候,引入一种导向粒子作为一个指导量,来保留一些目标图像上的信息。实验证明了这种算法可以更好地对目标进行定位跟踪。     

自适应差分演化粒子滤波器

针对非线性、非高斯系统中的粒子滤波算法存在粒子权值退化和重采样后引起样本枯竭问题,提出一种自适应差分演化粒子滤波算法。用一种自适应参数控制策略对差分演化算法的参数进行控制,并以此代替粒子滤波中的重采样算法。通过对状态更新后的粒子做自适应差分变异、自适应杂交和选择等优化操作,利用权值大小选出下一时刻的粒子集合。实验表明,该算法能有效缓解粒子权值退化和样本枯竭问题,缩短算法运行时间,提高估计精度,同一般的差分演化粒子滤波算法相比,状态估计的精度更高。     

An improved Bernoulli particle filter for single target tracking

Single target tracking is widely applied in the current surveillance systems. The Bernoulli filter can complete the task of single target tracking using available measurements. However, the existing Bernoulli filters have estimation bias during the whole tracking process. Therefore, we present an improved Bernoulli filter and its particle implementation in this paper. Employed the weight optimization strategy, the under-estimated number of target is corrected by enlarging the maximal measurement-updated weight of sampling particle. In addition, the track identification strategy is applied to optimize number of the required particles and extract the actual target. Combined with the unscented transform for the complicated dynamic models, the nonlinear motion state of maneuvering target is effectively estimated. Besides, we extend the proposed filter in unknown clutter environment and estimate the mean clutter rate, which has significant application meaning owing to avoiding the assumption of the given detection profile. Finally, the numerical simulations demonstrate the tracking advantages with the promising results in comparison to the standard Bernoulli filter.     

High-speed parallel particle filter for PCMA signal blind separation

The paper proposes an improved high-speed parallel particle filter algorithm for the blind separation of PCMA-signals by utilizing particle filter’s characteristics of parallelism with the help of a cluster computer system built by using the Matlab distributed computing server and Matlab parallel computing toolbox. The simulation results show that the parallel algorithm can perform the PCMA-signal blind separation quickly and effectively. Further, it can greatly decrease the time of the separation, without reducing the performance of the algorithm, and improve the real-time application of system.     

基于粒子滤波的机载目标跟踪系统设计

基于微小型机载成像跟踪系统设计思想及需求,设计并实现了以高性能的DSP芯片TMS320-DM642为核心处理器,结合可编程逻辑器件CPLD和FPGA的实时图像跟踪处理平台。平台采用基于粒子滤波的目标跟踪算法,实现对目标的实时跟踪。采用卡尔曼滤波器,提高了粒子的利用效率,在改进了算法实时性的同时解决了图像跟踪系统的延时性问题,提高了跟踪系统的稳定性。算法仿真结果表明,与传统相关匹配算法相比,基于粒子滤波的跟踪算法具有更好的鲁棒性和实时性,能满足机载成像跟踪系统实时图像跟踪的要求。     

Asynchronous particle filter for tracking using non-synchronous sensor networks

This paper deals with the problem of tracking using a sensor network when the sensors are not synchronised. We propose a new algorithm called the asynchronous particle filter that, with much less computational burden than the traditional particle filter, has a slightly poorer performance. Thus, it is a good solution to real-time applications with non-synchronised sensors when high performance is required. The low computational burden of the method lies in the fact that we do not predict and update the state every time a measurement is collected. Its high performance is due to the fact that we account for the time instant at which each measurement was taken.     

Robust observation model for visual tracking in particle filter

A robust observation model for visual tracking is proposed in this paper. The model consists of three appearance models: fixed appearance model, adaptive appearance model, and two-frame appearance model. The three appearance models are used, respectively, for catching unchanged components, slow changes, and rapid changes in object appearance. During tracking, the robust observation model is incorporated in a particle filter, and the particle filter can automatically select proper appearance models to track object according to the current tracking situation. Occlusion analysis is implemented using the M-estimation technique. Experimental results demonstrate that the proposed algorithm can track objects well under many challenging tracking situations.     

Convergence analysis of the adaptive lattice filter for a mixed Gaussian input sequence

The convergence performance of the adaptive lattice filter (ALF) using the stochastic gradient algorithm is measured by the convergence speed and estimated error variance of the PARCOR coefficient. The convergence properties of the ALF are analysed when the filter input has a Gaussian mixture distribution. First, theoretical expressions for the convergence rate and asymptotic error variance of the PARCOR coefficient are derived, and then the theoretical expressions are compared for single and mixed Gaussian input sequences. It is shown that the convergence performance of the ALF improves as the distribution of the input signal approaches a single Gaussian distribution.     

Dynamic multi-cue tracking using particle filter

We consider the problem of decomposing audio into components that have different time frequency characteristics. For this, we model the components using different transforms and mixed norms applied on the transform domain coefficients. We formulate the problem as a search for a saddle point and derive algorithms through a primal-dual framework. We also discuss how to modify the primal-dual algorithms in order to derive a simpler heuristic scheme.     

基于量子遗传粒子滤波的WSN目标跟踪算法

粒子滤波器是解决非线性非高斯运动跟踪的一种有效方法,很适合于无线传感器网络的目标跟踪.但是粒子滤波算法存在严重的退化现象.常规的重采样方法虽可解决退化问题,但容易导致粒子耗尽.本文针对此问题,将量子遗传算法引入粒子滤波,提出了基于量子遗传粒子滤波的无线传感器网络目标跟踪算法.通过量子遗传算法的编码方式增加粒子集的多样性...     

基于粒子滤波技术的抗多径测向方法

针对空间相干信号源的测向困难问题,提出了一种基于"粒子"滤波的处理方法,从概率角度进行相干波的DOA估计,用后验权值内插法避开再采样枯竭困扰,改善了滤波性能.只需极少的几次快拍完成对瞬间相干信号的测向,仿真表明该方法是可行的.