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.     

改进的概率假设密度滤波多目标检测前跟踪算法

基于概率假设密度滤波(Probability Hypothesis Density,PHD)的检测前跟踪(Track before detect,TBD)技术可以有效解决未知目标数的弱小点目标检测前跟踪问题.文章针对现有PHD-TBD算法存在目标数估计不准、目标发现延时较久的问题进行研究.从标准PHD滤波出发,更为合理地推导出PHD-TBD算法的粒子权重更新计算表达式,实现对目标数的准确估计;同时利用贝叶斯滤波理论,推导出基于量测的新生粒子概率密度采样函数,完成对目标的快速发现.仿真实验表明,与现有的PHD-TBD相比,改进算法能够适应目标扩散情况,准确估计目标数目,并实现对目标的快速发现和位置准确估计.     

图像目标检测前跟踪的广义多伯努利滤波算法

针对目标影响区域重叠时的图像目标检测前跟踪问题,推导了基于多伯努利滤波器的多目标联合检测与跟踪算法.在分析多个目标叠加条件下观测似然函数的基础上,利用预测得到的目标状态对观测似然函数进行估计,从而消除目标叠加对观测更新带来的影响.该方法在目标预测与跟踪阶段皆保持了目标状态的多伯努利分布特性,是较为严格意义上的多伯努利多目标滤波器,可应用于一般图像观测条件下(目标重叠或非重叠)的目标检测前跟踪.给出了该算法的实现步骤,并通过加标签的方法,更准确地实现目标轨迹提取和虚假目标剔除,最后通过计算机仿真实验验证了所提算法的有效性.     

基于序贯蒙特卡罗滤波的MIMO快时变信道跟踪

高数据传输速率以及终端的高速移动,导致无线通信信道具有时间选择性与频率选择性两个特征.本文主要研究了基于训练序列的多输入多输出（MIMO）时变频率选择性衰落信道的估计与跟踪问题.首先,根据时变无线信道的动态性,将信道冲击响应近似看作一个低阶的自回归矢量过程（AR）,以便于进行时变信道的跟踪.接着在此模型的基础上,利用序贯蒙特卡罗滤波对MIMO通信系统中的双选择性信道进行了跟踪;跟踪过程中需要与信号检测交替进行,即在状态变量的预测和新息修正的中间要进行一次码元的检测,所采用的方法是极大似然序列检测,最后与扩展卡尔曼滤波作了比较.仿真结果表明,在信道噪声是非高斯的情形下,序贯蒙特卡罗滤波的跟踪性能更优越于扩展卡尔曼滤波.     

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.     

Direct, prediction- and smoothing-based Kalman and particle filter algorithms

We address the recursive computation of the filtering probability density function (pdf) p_n|n in a hidden Markov chain (HMC) model. We first observe that the classical path p_n−1|n−1→p_n|n−1→p_n|n is not the only possible one that enables to compute p_n|n recursively, and we explore the direct, prediction-based (P-based) and smoothing-based (S-based) recursive loops for computing p_n|n. We next propose a common methodology for computing these equations in practice. Since each path can be decomposed into an updating step and a propagation step, in the linear Gaussian case these two steps are implemented by Gaussian transforms, and in the general case by elementary simulation techniques. By proceeding this way we routinely obtain in parallel, for each filtering path, one set of Kalman filter (KF) equations and one generic sequential Monte Carlo (SMC) algorithm. Finally we classify in a common framework four KF (two of which are original), which themselves can be associated to four generic SMC algorithms (two of which are original). We finally compare our algorithms via simulations. S-based filters behave better than P-based ones, and within each class of filters better results are obtained when updating precedes propagation.     

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.     

一种基于红外图像的小目标跟踪置前检测算法

为在低信噪比、强杂波的环境下提取目标，人们提出了跟踪置前检测(TbD)的小目标检测方法。讨论了红外图像杂波剔除和用最优非线性滤波器跟踪置前检测的算法，给出了算法模型和基本步骤，利用这种算法可有效地进行杂波抑制和对小目标跟踪置前检测。     

MIMO系统的改进序贯蒙特卡罗迭代检测算法

为了得到最优的MIMO迭代接收机,需要精确计算软输入软输出检测器输出的外信息,但精确计算的复杂度随调制阶数和天线数指数增长,不适合多天线高阶调制的情况。该文首先将外信息的估计归结为一个目标集合的选取,并提出通过序贯蒙特卡罗抽样方法获取目标集合。但是研究表明传统抽样方法不能有效获得合适的集合;因此一种改进的序贯蒙特卡罗抽样方法被提出,用于解决有限元离散概率空间的样本近似。最终,基于改进序贯蒙特卡罗抽样的外信息近似计算应用于迭代检测算法中。分析表明,该文提出的迭代检测算法的复杂度和抽取的样本数量呈线性比例;而仿真结果证明,较少的样本就可以取得逼近最优的误码率性能。     

基于改进概率假设密度的多目标跟踪算法

经典序贯蒙特卡罗概率假设密度(Sequential Mote Carlo Probability Hypothesis Density, SMC-PHD)滤波中, 将目标状态转移密度函数做为建议密度函数, 没有利用当前观测信息, 导致大部分预测粒子状态偏离目标真实状态, 粒子退化严重.针对上述问题, 提出利用均方根容积卡尔曼滤波产生建议密度函数, 对其进行采样得到预测粒子状态, 该方法有严格理论基础, 能有效减轻SMC-PHD滤波中的粒子退化, 且适用性很强.仿真实验对比了该算法、经典SMC-PHD和基于无迹卡尔曼的SMC-PHD算法的跟踪性能, 验证了该方法无论对势估计还是对目标状态估计的精度都优于其他两种算法.     

基于序贯蒙特卡罗算法的多天线快时变信道的盲跟踪

针对通信系统时变信道采用蒙特卡罗算法进行盲信道跟踪,并将该盲跟踪算法用于多天线信道及空时分组编码的情况,在相同的系统条件下与卡尔曼滤波跟踪算法进行了性能比较,并讨论了系统存在载波频偏情况下的跟踪性能。仿真结果表明,序贯蒙特卡罗算法可以对时变信道进行很好的跟踪。     

Detection-guided multi-target Bayesian filter

Multi-target Bayesian filter in the framework of finite set statistics (FISST) and its approximations, including probability hypothesis density (PHD) filter and cardinalized probability hypothesis density (CPHD) filter, are elegant methods for multi-target tracking by jointly estimating the number of targets and their states from a sequence of noisy and cluttered observation sets. PHD filter and CPHD filter can deal with the tracking scenario involving the surviving targets, the spawned targets, and the spontaneous births. One of the limitations of PHD and CPHD filter is that it is assumed that intensities of spontaneous birth targets are known at the initialization stage. To address the problem, a track initiation technique is proposed to detect the position unknown birth targets and is hybridized with PHD and CPHD filter. Once new targets are detected, the position estimates are employed to form intensities of spontaneous births for starting PHD and CPHD filter. Simulation results demonstrate that the proposed tracker can adaptively and efficiently track multiple targets especially in scenarios with birth targets of unknown position, which the PHD and CPHD filter are unable to do on their own.     

平坦衰落MIMO信道的序列蒙特卡罗双层迭代检测

针对平坦衰落MIMO信道,该文在传统采样检测技术仅依靠时间或空间样本的基础上,提出一种基于序列蒙特卡罗的空时双层迭代采样检测算法。算法将符号的后验概率计算分解为多维的空时双层积分,利用序列蒙特卡罗技术在空间和时间维度上抽取样本,通过加权样本累加得到多维积分的解;同时利用时间样本对信道进行联合估计。仿真结果表明算法可以逼近理想条件下的最优性能,并具有较低的计算复杂度。     

非频率选择性衰落MIMO信道上基于序列蒙特卡罗的数字调制识别方法

该文针对非频率选择性衰落多输入多输出(MIMO)信道提出了一种基于序列蒙特卡罗(SMC)方法的幅度-相位调制方式识别方法。首先将MIMO系统等效为一个动态状态空间模型,然后利用序列重要性采样和模式转移步骤估计每根发送天线采用的各种可能调制方式的概率,最后利用各个信道上发送符号的不相关性在长为N的观测信道上进行噪声平均。该方法能够在识别数字调制方式的同时估计发送数据符号。其复杂度是信道观测长度、发送天线数、采样大小、调制星座大小的线性函数。仿真结果表明提出的数字调制识别方法在各种调制星座上具有良好的性能。     

Blind channel and symbol joint estimation in cooperative MIMO for wireless sensor network

In this paper,application of Sequential Quasi Monte Carlo（SQMC）to blind channel and symbol joint estimation in cooperative Multiple-Input Multiple-Output（MIMO）system is proposed,which does not need to transmit training symbol and can save the power and channel bandwidth.Additionally,an improved version of SQMC algorithm by taking advantage of current received signal is discussed.Simulation results show that the SQMC method outperforms the Sequential Monte Carlo （SMC）methods,and the incorporation of current received signal improves the performance of the SQMC obviously.     

Penalized Gaussian mixture probability hypothesis density filter for multiple target tracking

Bayesian multi-target filter develops a theoretical framework for estimating the full multi-target posterior which is intractable in practice. The probability hypothesis density (PHD) is a practical solution for Bayesian multi-target filter which propagates the first order moment of the multi-target posterior instead of the full version. Recently, the Gaussian Mixture PHD (GM-PHD) has been proposed as an implementation of the PHD filter which provides a close form solution. The performance of this filter degrades when targets are moving near each other such as crossing targets. In this paper, we propose a novel approach called penalized GM-PHD (PGM-PHD) filter to improve this drawback. The simulation results provided for various probabilities of detection, clutter rates, targets velocities and frame rates indicate that the proposed method achieves better performance compared to the GM-PHD filter.     

基于截断修正平滑l0范数的MIMO雷达目标参数估计

在多输入多输出(MIMO)雷达中,针对平滑l0范数(SL0)因感知矩阵的病态性而导致其失效的问题,提出了一种基于截断修正SL0的MIMO雷达目标参数估计方法.该方法在对MIMO雷达感知矩阵进行截断奇异值分解(TSVD)处理的基础上,将保留的奇异值以均值为截断门限,分成较大和较小的两部分,分别采用不同的修正准则进行修正;然后经奇异值分解(SVD)反变换获得非病态感知矩阵,利用该非病态感知矩阵通过SL0算法对MIMO雷达目标参数进行估计,从而显著提高了MIMO雷达目标参数估计的精度和速度.仿真结果验证了该方法的有效性.     

基于序贯蒙特卡罗概率假设密度滤波的多目标检测前跟踪改进算法

实现目标数目未知且可变条件下的多目标检测与跟踪是个极具挑战性的问题,在信噪比较低的情况下更是如此。针对这一问题,该文提出一种基于点扩散模型的多目标检测前跟踪改进算法。该算法在序贯蒙特卡罗概率假设密度(SMC-PHD)滤波框架下实现,通过自适应粒子产生机制完成新生目标在像平面中的初始定位,并根据目标在图像中可能出现的位置对全体粒子集进行有效子集分割和快速权值估算,最后利用动态聚类方法完成多目标状态的准确提取。仿真结果表明,该方法有效改善了多目标检测前跟踪的估计性能,并大大提高了算法执行效率。     

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。     

Practical development of the second-order extended Kalman filter for very long range radar tracking

This paper improves the second-order extended Kalman filter (SOF) by accounting the correlation of the first and second-order terms (FSOT) in the measurement Taylor approximation—a matrix assumed to be zero in the conventional SOF. The goal is to achieve consistent estimation results for very long range radar tracking, whereas this correlation term becomes non-negligible. Remarkably, the range element of the correlation term is so significant that it is several times larger than the range variance of the second-order term (SOT) and four orders of magnitude larger than the variance of the range measurement. In the absence of a closed form expression, the correlation of interest is approximated by scaling the variance of SOT using a design parameter. Improved performance of the new method is shown in simulated tests when the parameter is tuned up using the off-line Monte-Carlo averaging. The proposed SOF can process measurements in either the range-direction-sine (r-u-v) coordinates or the spherical (r-a-e) coordinates.