Particle flters for probability hypothesis density flter with the presence of unknown measurement noise covariance

In Bayesian multi-target fltering,knowledge of measurement noise variance is very important.Signifcant mismatches in noise parameters will result in biased estimates.In this paper,a new particle flter for a probability hypothesis density（PHD）flter handling unknown measurement noise variances is proposed.The approach is based on marginalizing the unknown parameters out of the posterior distribution by using variational Bayesian（VB）methods.Moreover,the sequential Monte Carlo method is used to approximate the posterior intensity considering non-linear and non-Gaussian conditions.Unlike other particle flters for this challenging class of PHD flters,the proposed method can adaptively learn the unknown and time-varying noise variances while fltering.Simulation results show that the proposed method improves estimation accuracy in terms of both the number of targets and their states.     

基于标签多伯努利滤波的衍生目标跟踪算法

针对现有随机有限集(RFS)滤波器在低信噪比环境下对衍生目标跟踪性能严重下降的问题,提出了一种基于Delta扩展标签多伯努利(δ-GLMB)滤波器的改进算法。基于随机集理论和伯努利衍生模型,推导了新的预测方程,并采用了假设裁剪及分组手段和多伯努利近似技术以降低算法的计算量。针对假设增多引起的虚警问题,将多帧平滑思想和算法相结合,利用标签信息对新目标进行回溯处理。仿真结果表明,所提算法能对目标数目进行无偏估计,在低探测概率和强杂波环境下性能明显优于概率假设密度(PHD)算法,计算开销在衍生初始阶段增长快于PHD,目标较分散时低于PHD。     

Cardinality compensation method based on information-weighted consensus filter using data clustering for multi-target tracking

In this paper, a cardinality compensation method based on Information-weighted Consensus Filter(ICF) using data clustering is proposed in order to accurately estimate the cardinality of the Cardinalized Probability Hypothesis Density(CPHD) filter. Although the joint propagation of the intensity and the cardinality distribution in the CPHD filter process allows for more reliable estimation of the cardinality(target number) than the PHD filter, tracking loss may occur when noise and clutter are high in the measurements in a practical situation. For that reason, the cardinality compensation process is included in the CPHD filter, which is based on information fusion step using estimated cardinality obtained from the CPHD filter and measured cardinality obtained through data clustering. Here, the ICF is used for information fusion. To verify the performance of the proposed method, simulations were carried out and it was confirmed that the tracking performance of the multi-target was improved because the cardinality was estimated more accurately as compared to the existing techniques.     

Radar Measurement Noise Variance Estimation with Several Targets of Opportunity

A number of methods exist to track a target's uncertain motion through space using inherently inaccurate sensor measurements. A powerful method of adaptive estimation is the interacting multiple model (IMM) estimator. In order to carry out state estimation from the noisy measurements of a sensor, however, the filter should have knowledge of the statistical characteristics of the noise associated with that sensor. The statistical characteristics (accuracies) of real sensors, however, are not always available, in particular for legacy sensors. A method is presented of determining the measurement noise variances of a sensor, assumed to be constant, by using multiple IMM estimators while tracking targets whose motion is not known---targets of opportunity. Combining techniques outlined in [2] and [6], the likelihood functions are obtained for a number of IMM estimators, each with different assumptions on the measurement noise variances. Then a search is carried out over a varying grid of IMMs to bracket the variances of the sensor measurement noises. The end result consists of estimates of the measurement noise variances of the sensor in question.     

Identification Method for RLG Random Errors Based on Allan Variance and Equivalent Theorem

An identification method using Allan variance and equivalent theorem is proposed to identify non-stationary sensor errors mixed out of different simple noises. This method firstly derives the discrete Allan variances of all component noises inherent in noise sources in terms of their different equations; then the variances are used to estimate the parameters of all component noise models; finally, the original errors are represented by the sum of the non-stationary component noise model and the equivalent model mixed out of the stationary and critically stationary component noises. Results of two examples for identification confirm the superiority of this approach regardless of the errors being stationary or not. The comparison of results of real ring laser gyro (RLG) errors processed by various methods shows that the proposed approach is more suited to depict the original noises than common ones.     

非线性非高斯模型的高斯和PHD滤波算法(英文)

A new multi-target filtering algorithm, termed as the Gaussian sum probability hypothesis density （GSPHD） filter, is proposed for nonlinear non-Gaussian tracking models. Provided that the initial prior intensity of the states is Gaussian or can be identified as a Gaussian sum, the analytical results of the algorithm show that the posterior intensity at any subsequent time step remains a Gaussian sum under the assumption that the state noise, the measurement noise, target spawn intensity, new target birth intensity, target survival probability, and detection probability are all Gaussian sums. The analysis also shows that the existing Gaussian mixture probability hypothesis density （GMPHD） filter, which is unsuitable for handling the non-Gaussian noise cases, is no more than a special case of the proposed algorithm, which fills the shortage of incapability of treating non-Gaussian noise. The multi-target tracking simulation results verify the effectiveness of the proposed GSPHD.     

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.     

基于决策不确定性的多目标跟踪传感器管理

针对高杂波、电子干扰环境,在量测驱动的多目标滤波框架下提出了一种基于决策不确定性的传感器管理方法。首先,根据部分可观测马尔科夫决策过程的理论,给出了基于Rényi信息增量的传感器管理一般方法。其次,综合考虑决策过程的信息完整性、信息质量、信息的内涵等因素,在量测驱动的自适应滤波框架下,基于目标运动态势评估多目标决策不确定性水平,并选取最大决策不确定性目标。最后,以最大决策不确定性目标的信息增量最大化为准则进行传感器分配方案的求解。仿真实验表明所提方法能够有效抑制电子干扰、杂波对多目标跟踪及传感器分配的影响,与基于威胁的传感器管理方法相比,所提方法的平均最优子模式分配（OSPA）距离及平均计算时长均显著降低,且在高杂波、电子干扰情形下具有较高的可靠性。     

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。     

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.     

一种用于仿生导航无人机航姿求解的混合滤波方法

针对现有组合导航系统易被干扰欺骗以及姿态求解精度不足的问题，设计了惯性测量单元(IMU)与偏振光传感器组成的航姿参考系统(AHRS)。同时，考虑到传统的姿态求解方法精度不高，提出了一种用于仿生导航无人机航姿求解的混合滤波方法。将Mahony滤波后的姿态值作为系统观测量，再结合扩展卡尔曼滤波(EKF)实现传感器数据的深层融合，以获得高精度的姿态角信息。实验结果表明：在静态环境下采用混合滤波方法求解的姿态值能有效滤除偏振光传感器和加速度计内部噪声干扰，其稳定性明显优于两种方法各自求解时的情况；在动态实验中该方法能有效抑制单独采用Mahony滤波时存在的超调问题，表现出更高的动态解算精度，从而为偏振光组合导航系统提供了更精确的姿态估计信息。     

A practical filter error method for aerodynamic parameter estimation of aircraft in turbulence

It is common for aircraft to encounter atmospheric turbulence in flight tests. Turbulence is usually modeled as stochastic process noise in the flight dynamics equations. In this paper, parameter estimation of nonlinear dynamic system with both process and measurement noise was studied, and a practical filter error method was proposed. The linearized Kalman filter of first-order approximation was used for state estimation, in which the filter gain, along with the system parameters and the initial states, constituted the parameter vector to be estimated. The unknown parameters and measurement noise covariance were estimated alternately by a relaxation iteration method, and the sensitivities of observations to unknown parameters were calculated by finite difference approximation. Some practical aspects of the method application were discussed. The proposed filter error method was validated by the flight simulation data of a research aircraft. Then, the method was applied to the flight tests of a subscale aircraft, and the aerodynamic stability and control derivatives were estimated. All the estimation results were compared with the results of the output error method to demonstrate the effectiveness of the approach. It is shown that the filter error method is superior to the output error method for flight tests in atmospheric turbulence.     

A novel variable-lag probability hypothesis density smoother for multi-target tracking

It is understood that the forward-backward probability hypothesis density (PHD) smoothing algorithms proposed recently can significantly improve state estimation of targets. However, our analyses in this paper show that they cannot give a good cardinality (i.e., the number of targets) estimate. This is because backward smoothing ignores the effect of temporary track drop- ping caused by forward filtering and/or anomalous smoothing resulted from deaths of targets. To cope with such a problem, a novel PHD smoothing algorithm, called the variable-lag PHD smoother, in which a detection process used to identify whether the filtered cardinality varies within the smooth lag is added before backward smoothing, is developed here. The analytical results show that the proposed smoother can almost eliminate the influences of temporary track dropping and anomalous smoothing, while both the cardinality and the state estimations can significantly be improved. Simulation results on two multi-target tracking scenarios verify the effectiveness of the proposed smoother.     

多目标跟踪的核粒子概率假设密度滤波算法

提出一种新的多目标跟踪算法：核粒子概率假设密度滤波算法(KP-PHDF)。算法的创新点在概率假设密度滤波算法(PHDF)的目标状态提取步骤,以粒子概率假设密度滤波算法为框架,并运用结合了mean-shift算法的核密度估计(KDE)理论进行概率假设密度(PHD)分布的二次估计、提取PHD峰值位置作为目标状态估计值。分析与多目标跟踪(MTT)仿真的结果表明,与现有序列蒙特卡罗概率假设密度滤波算法（SMC-PHDF）相比,在相同仿真条件下新算法的估计精度提高30.5%。     

Modified unscented Kalman filtering and its application in autonomous satellite navigation

In this paper, a modified unscented Kalman filter (UKF) for nonlinear stochastic systems is proposed, and it is applied to autonomous orbit determination for Earth satellites. Based on some standard results about the boundedness of stochastic processes and a new formulation of the unscented transformation (UT), it is demonstrated that the design of the noise covariance matrix plays an important role in enhancing the filter stability. Furthermore, a particular design of the noise covariance matrix is proposed as a modification of the UKF. The modified UKF is less sensitive to the initial error than the usual one. High performance of the modified UKF is illustrated in comparison with the usual one by using the real data obtained from an Earth sensor.     

Vibration signal-based chatter identification for milling of thin-walled structure

In high speed milling aeronautical part, tool condition monitoring(TCM) is very important, because it is prone to get a chatter owing to the low stiffness of thin-walled structures. And the TCM is key technology for automated machining. In this paper, aiming to chatter monitoring in thin-walled structure milling, a variational mode decomposition – energy distribution(VMD-ED)method is proposed to improve the identification accuracy. And a moving average root mean square – mean value(MARMS-MV) ide...     

基于卡尔曼滤波的星敏感器在轨校准方法

根据星敏感器光学镜头以径向畸变为主的特点,采用一阶径向畸变模型,利用摄像机标定中的径向排列约束(RAC),对其外部姿态和内参数进行在轨校准。以采集到的星点的图像坐标和对应导航星在天球坐标系下的赤经、赤纬信息作为滤波器的输入,外部姿态和内参数作为输出,构造相应的状态方程和观测方程,进行两次卡尔曼滤波迭代,结果作为校准参数的最优估计。仿真实验表明:本方法能消除内部参数与外部参数的耦合,校准过程不依赖外部姿态,且状态方程和观测方程均为线性方程,满足卡尔曼滤波迭代的最优条件,能够精确估计出星敏感器内外参数,在星点成像位置噪声标准差为0.05像素时,校准后x、y方向上的平均误差分别为0.044像素和0.049像素。     

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.     

基于量测一致性的分布式多传感器多目标跟踪算法

针对无线传感器网络跟踪多目标过程中传感器能搭载的计算负荷有限,不宜采用复杂算法实现数据处理的问题,提出了一种基于量测一致性的分布式多传感器多目标跟踪算法。算法采用计算相对简易的最近邻域法处理多目标跟踪中的数据互联问题,针对最近邻域法容易受杂波干扰的情况,通过量测的平均一致性迭代来改进算法的性能。仿真结果证明,算法具备有效抑制因误判产生的错误量测对跟踪过程干扰的性能,实现了良好的传感器网络跟踪精度和估计信息一致性。     

自适应增量 Kalman 滤波方法

提出自适应增量Kalman滤波(AIKF)的概念和定义,建立自适应增量Kalman滤波模型及其分析方法,给出主要的计算步骤.传统自适应Kalman滤波(AKF)方法能够对事先未知的系统噪声和量测噪声的统计量进行有效的估计.但是,传统自适应Kalman滤波方法也无法对由于环境因素(如深空探测)的影响、测量设备的不稳定性等原因产生的未知时变测量系统误差进行补偿和校正,从而产生较大的滤波误差,甚至导致发散.提出的自适应增量Kalman滤波方法不但能够对系统噪声和量测噪声的统计量进行估计,而且还能成功消除这种测量系统误差,有效地提高滤波精度.该方法计算简单,便于工程应用.