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 tech-nique 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 mul-tiple maneuvering targets with abrupt changing parameters in a more robust manner, compared to the multi-model approaches.     

Sequential Monte Carlo methods for multitarget filtering with random finite sets

Random finite sets (RFSs) are natural representations of multitarget states and observations that allow multisensor multitarget filtering to fit in the unifying random set framework for data fusion. Although the foundation has been established in the form of finite set statistics (FISST), its relationship to conventional probability is not clear. Furthermore, optimal Bayesian multitarget filtering is not yet practical due to the inherent computational hurdle. Even the probability hypothesis density (PHD) filter, which propagates only the first moment (or PHD) instead of the full multitarget posterior, still involves multiple integrals with no closed forms in general. This article establishes the relationship between FISST and conventional probability that leads to the development of a sequential Monte Carlo (SMC) multitarget filter. In addition, an SMC implementation of the PHD filter is proposed and demonstrated on a number of simulated scenarios. Both of the proposed filters are suitable for problems involving nonlinear nonGaussian dynamics. Convergence results for these filters are also established.     

Variational Bayesian labeled multi-Bernoulli filter with unknown sensor noise statistics

It is difficult to build accurate model for measurement noise covariance in complex back-grounds. For the scenarios of unknown sensor noise variances, an adaptive multi-target tracking algorithm based on labeled random finite set and variational Bayesian (VB) approximation is pro-posed. The variational approximation technique is introduced to the labeled multi-Bernoulli (LMB) filter to jointly estimate the states of targets and sensor noise variances. Simulation results show that the proposed method can give unbiased estimation of cardinality and has better performance than the VB probability hypothesis density (VB-PHD) filter and the VB cardinality balanced multi-target multi-Bernoulli (VB-CBMeMBer) filter in harsh situations. The simulations also confirm the robustness of the proposed method against the time-varying noise variances. The computational complexity of proposed method is higher than the VB-PHD and VB-CBMeMBer in extreme cases, while the mean execution times of the three methods are close when targets are well separated.     

未知测量噪声分布下的多目标跟踪算法

 粒子概率假设密度滤波(SMC-PHDF)在进行粒子更新时需要知道测量噪声的概率分布以计算似然函数,这使得SMC-PHDF依赖于测量噪声的概率模型。针对这一点不足,提出一种未知测量噪声分布下的多目标跟踪算法——基于风险评估的概率假设密度滤波(RE-PHDF)。该算法在SMC-PHDF进行概率假设密度(PHD)粒子更新时采用风险函数计算每个PHD粒子的风险值,并通过一个风险评估函数评估每个PHD粒子,然后用评估后的结果更新粒子的权值。由于粒子更新时避免了在多维测量空间中计算似然函数,算法不仅不依赖于测量噪声的概率分布,还可以节省大量计算时间。仿真结果表明：和SMC-PHDF相比,RE-PHDF在未知的复杂测量噪声环境下具有更高的鲁棒性和稳定性;同时,在两种算法跟踪精度接近的情况下,所提算法节省了50%的运行时间。     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.     

Track labeling and PHD filter for multitarget tracking

Multiple target tracking requires data association that operates in conjunction with filtering. When multiple targets are closely spaced, the conventional approaches (as, e.g., MHT/assignment) may not give satisfactory results. This is mainly because of the difficulty in deciding what the number of targets is. Recently, the probability hypothesis density (PHD) filter has been proposed and particle filtering techniques have been developed to implement the PHD filter. In the particle PHD filter, the track labeling problem is not considered, i.e., the PHD is obtained only for a frame at a time, and it is very difficult to perform the multipeak extraction, particularly in high clutter environments. A track labeling method combined with the PHD approach, as well as considering the finite resolution, is proposed here for multitarget tracking, i.e., we keep a separate tracker for each target, use the PHD in the resolution cell to get the estimated number and locations of the targets at each time step, and then perform the track labeling ("peak-to-track" association), whose results can provide information for PHD peak extraction at the next time step. Besides, by keeping a separate tracker for each target, our approach provides more information than the standard particle PHD filter. For example, in group target tracking, if we are interested in the motion of a specific target, we can track this target, which is not possible for the standard particle PHD filter, since the standard particle PHD filter does not keep track labels. Using our approach, multitarget tracking can be performed with automatic track initiation, maintenance, spawning, merging, and termination     

交互多模型PHD滤波跟踪多目标方法

在机动多目标跟踪问题中,目标数未知或随时间而变化,概率假设密度（PHD）滤波可以在每一时间步估计多目标状态和目标数,但单模型方法不能给出精确的估计。提出了一种交互多模型PHD滤波方法,建立多模型描述多目标运动方式,利用PHD滤波结合多模型跟踪目标运动轨迹。同时,给出了多传感器交互多模型PHD滤波方法,以提高目标跟踪精度。     

Hierarchical adaptive Kalman filtering for interplanetary orbitdetermination

A modular and flexible approach to adaptive Kalman filtering has recently been introduced using the framework of a mixture-of-experts regulated by a gating network. Each expert is a Kalman filter modeled with a different realization of the unknown system parameters. The unknown or uncertain parameters can include elements of the state transition matrix, observation mapping matrix, process noise covariance matrix, and measurement noise covariance matrix. The gating network performs on-line adaptation of the weights given to individual filters based on performance. The mixture-of-experts approach is extended here to a hierarchical architecture which involves multiple levels of gating. The proposed architecture provides a multilevel hypothesis testing capability. The utility of the hierarchical architecture is illustrated via the problem of interplanetary navigation (Mars Pathfinder) using simulated radiometric data. It serves as a useful tool for assisting navigation teams in the process of selecting the parameters of the navigational filter over various operating regimes. It is shown that the scheme has the capability of detecting changes in the system parameters and switching filters appropriately for optimal performance. Furthermore, the expectation-maximization (EM) algorithm is shown to be applicable in the proposed framework     

Novel data association schemes for the probability hypothesis density filter

The probability hypothesis density (PHD) filter is a practical alternative to the optimal Bayesian multi-target Alter based on finite set statistics. It propagates the PHD function, a first-order moment of the full multi-target posterior density. The peaks of the PHD function give estimates of target states. However, the PHD filter keeps no record of target identities and hence does not produce track-valued estimates of individual targets. We propose two different schemes according to which PHD filter can provide track-valued estimates of individual targets. Both schemes use the probabilistic data-association functionality albeit in different ways. In the first scheme, the outputs of the PHD filter are partitioned into tracks by performing track-to-estimate association. The second scheme uses the PHD filter as a clutter filter to eliminate some of the clutter from the measurement set before it is subjected to existing data association techniques. In both schemes, the PHD filter effectively reduces the size of the data that would be subject to data association. We consider the use of multiple hypothesis tracking (MHT) for the purpose of data association. The performance of the proposed schemes are discussed and compared with that of MHT.     

一种基于冗余测量的自适应卡尔曼滤波算法

针对目前自适应滤波算法的不足,在测量系统量测噪声方差未知的情况下,设计了一种基于冗余测量的自适应卡尔曼滤波(RMAKF)算法。通过对系统冗余测量值的一阶、二阶差分序列进行有效的统计分析,可以准确估计系统量测噪声统计特性,进而在滤波过程中自适应调节噪声方差阵R,提高滤波精度。以全球定位系统/惯性导航系统(GPS/INS)松组合导航系统为对象进行了仿真实验,结果表明该算法在测量系统噪声特性未知或发生改变时,可对其进行准确估计,在采用低精度惯性器件情况下,滤波结果较其他主要自适应卡尔曼滤波算法有较明显的改进。     

异常值和未知观测噪声鲁棒的非线性滤波器

针对含异常观测值的非线性系统滤波问题,以Huber损失函数替代推导滤波器最大后验准则中观测误差的l₂范数,构造出了一种新的优化准则函数,从而给出了一种对异常值鲁棒的非线性后验线性化滤波器。分析表明：由于Huber损失函数兼具l₁和l₂范数的性质,从而使得由这个新准则推导出的滤波器,不仅具有l₂范数的低误差拟合性,也具备l₁范数对异常值的鲁棒性。而当观测噪声的分布未知时,通过引入箱线图法检测异常值,并对噪声统计分布的参数进行估计,进一步提出了对异常值和未知观测噪声分布鲁棒的非线性后验线性化滤波器。仿真实验验证了分析结果的有效性,并表明本文算法的性能优于现有文献报道的非线性滤波算法。     

Multiple-Model Probability Hypothesis Density Filter for Tracking Maneuvering Targets

Tracking multiple targets with uncertain target dynamics is a difficult problem, especially with nonlinear state and/or measurement equations. With multiple targets, representing the full posterior distribution over target states is not practical. The problem becomes even more complicated when the number of targets varies, in which case the dimensionality of the state space itself becomes a discrete random variable. The probability hypothesis density (PHD) filter, which propagates only the first-order statistical moment (the PHD) of the full target posterior, has been shown to be a computationally efficient solution to multitarget tracking problems with a varying number of targets. The integral of PHD in any region of the state space gives the expected number of targets in that region. With maneuvering targets, detecting and tracking the changes in the target motion model also become important. The target dynamic model uncertainty can be resolved by assuming multiple models for possible motion modes and then combining the mode-dependent estimates in a manner similar to the one used in the interacting multiple model (IMM) estimator. This paper propose a multiple-model implementation of the PHD filter, which approximates the PHD by a set of weighted random samples propagated over time using sequential Monte Carlo (SMC) methods. The resulting filter can handle nonlinear, non-Gaussian dynamics with uncertain model parameters in multisensor-multitarget tracking scenarios. Simulation results are presented to show the effectiveness of the proposed filter over single-model PHD filters.     

Convolution Particle Filter for Parameter Estimation in General State-Space Models

The state-space modeling of partially observed dynamical systems generally requires estimates of unknown parameters. The dynamic state vector together with the static parameter vector can be considered as an augmented state vector. Classical filtering methods, such as the extended Kalman filter (EKF) and the bootstrap particle filter (PF), fail to estimate the augmented state vector. For these classical filters to handle the augmented state vector, a dynamic noise term should be artificially added to the parameter components or to the deterministic component of the dynamical system. However, this approach degrades the estimation performance of the filters. We propose a variant of the PF based on convolution kernel approximation techniques. This approach is tested on a simulated case study.     

无迹增量滤波方法

提出无迹增量滤波(UIF)的概念,建立一般无迹增量滤波模型及其分析方法,并对具有加性噪声的无迹增量滤波进行了详细讨论,给出其递推算法.在工程实际中,由于环境因素的影响、测量设备的不稳定性、模型和参数的选取不当等原因往往带来未知的系统误差.在这种情况下,传统的无迹Kalman滤波方法(UKF)在递推过程中会产生较大误差,甚至导致发散.提出的无迹增量滤波方法能够成功消除这种未知的系统误差,提高滤波的精度.该方法计算简单,便于工程应用.      

Adaptive cubature Kalman filter with the estimation of correlation between multiplicative noise and additive measurement noise

Mobile robots are often subject to multiplicative noise in the target tracking tasks, where the multiplicative measurement noise is correlated with additive measurement noise. In this paper,first, a correlation multiplicative measurement noise model is established. It is able to more accurately represent the measurement error caused by the distance sensor dependence state. Then, the estimated performance mismatch problem of Cubature Kalman Filter(CKF) under multiplicative noise is analyzed. An i...     

Rao-Blackwellized粒子概率假设密度滤波算法

针对多目标跟踪（MTT）,提出一种新的基于随机集的滤波算法,称为Rao-Blackwellized粒子概率假设密度滤波算法（RBP-PHDF）。算法运用Rao-Blackwellized思想,通过挖掘分析“混合线性/非线性模型”的结构,采用序列蒙特卡罗（SMC）方法预测与估计概率假设密度（PHD）迭代式中各个目标的非线性状态,并利用非线性状态粒子中包含的信息,使用卡尔曼滤波器（KF）对线性状态进行预测与估计。以更好地估计PHD进而提高各目标状态估计精度。分析与MTT仿真的结果表明,在相同的仿真条件下,与现有序列蒙特卡罗概率假设密度滤波算法（SMC-PHDF）相比,RBP-PHDF在降低粒子维数、减少计算量的同时,有效提升了估计精度。     

Multitarget Bayes filtering via first-order multitarget moments

The theoretically optimal approach to multisensor-multitarget detection, tracking, and identification is a suitable generalization of the recursive Bayes nonlinear filter. Even in single-target problems, this optimal filter is so computationally challenging that it must usually be approximated. Consequently, multitarget Bayes filtering will never be of practical interest without the development of drastic but principled approximation strategies. In single-target problems, the computationally fastest approximate filtering approach is the constant-gain Kalman filter. This filter propagates a first-order statistical moment - the posterior expectation - in the place of the posterior distribution. The purpose of this paper is to propose an analogous strategy for multitarget systems: propagation of a first-order statistical moment of the multitarget posterior. This moment, the probability hypothesis density (PHD), is the function whose integral in any region of state space is the expected number of targets in that region. We derive recursive Bayes filter equations for the PHD that account for multiple sensors, nonconstant probability of detection, Poisson false alarms, and appearance, spawning, and disappearance of targets. We also show that the PHD is a best-fit approximation of the multitarget posterior in an information-theoretic sense.     

增量粒子滤波方法

提出增量粒子滤波的概念,建立增量粒子滤波模型及其分析方法,给出其算法.对于工程实际中存在的由未知系统误差的影响而无法精确建立量测似然函数的这一问题,提出增量粒子滤波方法,通过对带有未知系统误差的量测数据进行校正,获得精确的量测似然函数,建立精确的增量粒子滤波模型,从而消除这种未知系统误差的影响,减少重采样的次数,较好地保存了粒子的多样性,提高非线性滤波的精度.模拟仿真中,重采样的次数减少41.7%,滤波误差均值和均方根误差分别降低了45.3%和70.1%,有效地改善了滤波的效果.      

新生目标强度未知的双门限粒子PHD滤波器

传统粒子概率假设密度(PHD)滤波器假定新生目标强度已知,当新生目标在整个观测区域随机出现时不再适用。为解决新生目标强度未知时的多目标跟踪问题,提出了一种基于量测信息的双门限粒子PHD(PHD-DT)滤波器。首先基于似然函数设定门限对存活目标量测进行粗提取,利用上一时刻的目标估计值构建圆形波门进行精细提取,并对门限设定方法进行分析,然后根据提取结果对目标PHD进行分解,得到存活目标和新生目标的PHD预测及更新表达式,最后给出了滤波器的实现方法并同基于量测驱动的PHD(PHD-M)滤波器和Logic+联合概率数据互联(JPDA)方法进行了仿真对比。仿真结果表明,在新生目标强度未知时,PHD-DT可有效避免Logic+JPDA在杂波背景下因航迹起始错误带来的估计误差,并较好地解决了PHD-M的目标数目过估问题,多目标估计性能更优,且杂波越强性能优势越明显。     

自适应扩展增量 Kalman 滤波方法

基于扩展增量Kalman滤波方法(EIKF)和自适应增量Kalman滤波(AIKF),建立自适应扩展增量Kalman(AEIKF)模型及其分析方法,给出递推算法.在许多实际情况(如深空探测),由于环境因素的影响、测量设备的不稳定性等原因,量测方程往往存在未知的系统误差,并且模型参数也具有不确定性,结果导致较大的Kalman滤波误差,影响滤波的收敛性.提出的AEIKF方法能够成功消除这种未知的系统误差,并能够实时估计变化的噪声统计量,提高Kalman滤波精度.该方法计算简单,便于工程应用.