扩展容积卡尔曼滤波定位技术研究

为提高被动定位技术的精度与环境适应性,本文提出运用一种新的非线性滤波方法—扩展容积卡尔曼滤波算法进行多角度传感器目标定位;它首先利用EMD(经验模态分解)算法对目标的量测噪声协方差矩阵进行估计;然后,将过程噪声协方差和量测噪声协方差融入循环过程;同时,为保持算法的稳定性和正定性,利用求平方根的形式对算法改进。通过对扩展容积卡尔曼滤波与UKF(不敏卡尔曼滤波)算法跟踪目标的结果进行比较,在运算复杂度与UKF相当的前提下,扩展容积卡尔曼滤波算法不仅可以对未知量测噪声情况下的目标进行跟踪,而且显著提高了被动定位的精度。     

一种新的自适应非线性卡尔曼滤波算法

为避免由于系统噪声统计特性不准确所导致的滤波性能下降问题,改进了一种基于新息的系统噪声方差调整方法,并将其与扩展卡尔曼滤波、Unscented 卡尔曼滤波和差分滤波相结合,形成自适应非线性卡尔曼滤波.将此方法应用到非线性测量光电跟踪系统中,并与采用基本非线性卡尔曼滤波进行性能对比.仿真实验结果证明该方法可以实时调整系统噪声方差,有效地避免由于系统噪声统计特性不准确所带来的滤波性能下降的问题,而且其性能明显优于基本非线性卡尔曼滤波.     

Neural filtering of colored noise based on Kalman filter structure

In this paper, adaptive filtering approaches of colored noise based on the Kalman filter structure using neural networks are proposed, which need not extend the dimensions of the filter. The colored measurement noise is first modeled from a Gaussian white noise through a shaping filter. The Kalman filtering model of colored noise is then built by adopting an equivalent observation equation, which can avoid the dimension extension and complicated computations. An observation correlation-based algorithm is suggested to estimate the variance of the measurement noise by use of a single layer neural network. The Kalman gain can be obtained when a perfect knowledge of the plant model and noise variances is given. However, in some cases, the difficulties of the correlative method and the Kalman filter equations are the amount of computations and memory requirements. A neural estimator based on the Kalman filter structure is also analyzed as an alternative in this paper. The Kalman gain is replaced by a feedforward neural network whose weight adjustment permits minimization of the estimation error. The estimator has the capability of estimating the states of the plant in a stochastic environment without knowledge of noise statistics. If the noise of the plant is white and Gaussian and its statistics are well known, the neural estimator and the Kalman filter produce equally good results. The neural filtering approaches of colored noise based on the Kalman filter structure are applied to restore the cephalometric images of stomatology. Several experimental results demonstrate the feasibility and good performances of the approaches.     

Estimation Performance for the Cubature Particle Filter under Nonlinear/Non-Gaussian Environments

This paper evaluates the state estimation performance for processing nonlinear/non-Gaussian systems using the cubature particle filter (CPF), which is an estimation algorithm that combines the cubature Kalman filter (CKF) and the particle filter (PF). The CPF is essentially a realization of PF where the third-degree cubature rule based on numerical integration method is adopted to approximate the proposal distribution. It is beneficial where the CKF is used to generate the importance density function in the PF framework for effectively resolving the nonlinear/non-Gaussian problems. Based on the spherical-radial transformation to generate an even number of equally weighted cubature points, the CKF uses cubature points with the same weights through the spherical-radial integration rule and employs an analytical probability density function (pdf) to capture the mean and covariance of the posterior distribution using the total probability theorem and subsequently uses the measurement to update with Bayes’ rule. It is capable of acquiring a maximum a posteriori probability estimate of the nonlinear system, and thus the importance density function can be used to approximate the true posterior density distribution. In Bayesian filtering, the nonlinear filter performs well when all conditional densities are assumed Gaussian. When applied to the nonlinear/non-Gaussian distribution systems, the CPF algorithm can remarkably improve the estimation accuracy as compared to the other particle filter-based approaches, such as the extended particle filter (EPF), and unscented particle filter (UPF), and also the Kalman filter (KF)-type approaches, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF) and CKF. Two illustrative examples are presented showing that the CPF achieves better performance as compared to the other approaches.     

被动定向浮标阵卡尔曼滤波目标跟踪研究

文章研究利用被动定向浮标阵定位跟踪水下机动目标的方法,基于卡尔曼滤波(Kalman Filter, KF)原理提出一种定位跟踪滤波器的具体实现方法。该方法能够整合多枚浮标现在及过去有误差的测量数据,提高定位精度,同时连续输出水下目标运动参数估计从而锁定目标运动轨迹。该方法实现的关键在于建立水下目标与浮标阵的数学迭代运算模型,包括状态空间的动态与观测过程。由于被动定向浮标阵目标跟踪是一个非线性估计问题,而卡尔曼滤波器是线性的,因此文章设计了近似的线性观测方程以利用卡尔曼滤波来解决这个问题。通过计算机仿真研究该滤波器的跟踪效果并与最小二乘法进行比较,估计精度明显高于最小二乘法。同时通过仿真验证该滤波器可以自适应跟踪目标的非稳态运动过程。该方法在工程实践上具有一定应用前景与指导意义。     

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

This paper investigates the minimum error entropy based extended Kalman filter (MEEKF) for multipath parameter estimation of the Global Positioning System (GPS). The extended Kalman filter (EKF) is designed to give a preliminary estimation of the state. The scheme is designed by introducing an additional term, which is tuned according to the higher order moment of the estimation error. The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step. According to the stochastic information gradient method, an optimal filer gain matrix is obtained. The mean square error criterion is limited to the assumption of linearity and Gaussianity. However, non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases. Most of the existing multipath estimation algorithms are usually designed for Gaussian noise. The I (in-phase) and Q (quadrature) accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude, code delay, phase, and carrier Doppler. One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion. The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual. Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.     

Variational Bayesian Based IMM Robust GPS Navigation Filter

This paper investigates the navigational performance of Global Positioning System (GPS) using the variational Bayesian (VB) based robust filter with interacting multiple model (IMM) adaptation as the navigation processor. The performance of the state estimation for GPS navigation processing using the family of Kalman filter (KF) may be degraded due to the fact that in practical situations the statistics of measurement noise might change. In the proposed algorithm, the adaptivity is achieved by estimating the time-varying noise covariance matrices based on VB learning using the probabilistic approach, where in each update step, both the system state and time-varying measurement noise were recognized as random variables to be estimated. The estimation is iterated recursively at each time to approximate the real joint posterior distribution of state using the VB learning. One of the two major classical adaptive Kalman filter (AKF) approaches that have been proposed for tuning the noise covariance matrices is the multiple model adaptive estimate (MMAE). The IMM algorithm uses two or more filters to process in parallel, where each filter corresponds to a different dynamic or measurement model. The robust Huber's M-estimation-based extended Kalman filter (HEKF) algorithm integrates both merits of the Huber M-estimation methodology and EKF. The robustness is enhanced by modifying the filter update based on Huber's M-estimation method in the filtering framework. The proposed algorithm, referred to as the interactive multi-model based variational Bayesian HEKF (IMM-VBHEKF), provides an effective way for effectively handling the errors with time-varying and outlying property of non-Gaussian interference errors, such as the multipath effect. Illustrative examples are given to demonstrate the navigation performance enhancement in terms of adaptivity and robustness at the expense of acceptable additional execution time.     

水声传感器网络中时钟漂移率跟踪方法

时钟同步是水声无线网各个节点协同观测的关键技术。该文针对水下节点长时时钟漂移率受周围环境影响产生变化的问题,提出一种适用于水下传感网络的时钟漂移率跟踪方法。该方法使用多模型描述时钟漂移率的变化,在使用现有高时延时间同步(TimeSynchronizationforHighLatency,TSHL)水声网络授时协议和轻量级高时延授时(Tri-message)算法计算获得时钟漂移率的基础上,使用交互式多模型卡尔曼(Kalman)滤波对变时钟状态向量进行跟踪和估计,并在滤波过程中采用Sage-Husa自适应方法动态调整滤波参数,提高算法估计的准确性。仿真结果表明,使用提出的跟踪方法,时钟漂移率估计均方误差可从3.0×10-9降低到5×10-10,算法性能优于现有授时方法。     

A Robust Asynchrophasor in PMU Using Second-Order Kalman Filter

Phasor Measurement Units (PMUs) provide Global Positioning System (GPS) time-stamped synchronized measurements of voltage and current with the phase angle of the system at certain points along with the grid system. Those synchronized data measurements are extracted in the form of amplitude and phase from various locations of the power grid to monitor and control the power system condition. A PMU device is a crucial part of the power equipment in terms of the cost and operative point of view. However, such ongoing development and improvement to PMUs’ principal work are essential to the network operators to enhance the grid quality and the operating expenses. This paper introduces a proposed method that led to low-cost and less complex techniques to optimize the performance of PMU using Second-Order Kalman Filter. It is based on the Asyncrhophasor technique resulting in a phase error minimization when receiving the signal from an access point or from the main access point. The MATLAB model has been created to implement the proposed method in the presence of Gaussian and non-Gaussian. The results have shown the proposed method which is Second-Order Kalman Filter outperforms the existing model. The results were tested using Mean Square Error (MSE). The proposed Second-Order Kalman Filter method has been replaced with a synchronization unit into the PMU structure to clarify the significance of the proposed new PMU.     

基于高斯粒子滤波的当前统计模型跟踪算法

对于非线性系统估计问题,高斯粒子滤波器可以获得近似最优解,与粒子滤波器相比其优点是不需要重采样步骤和不存在粒子退化现象.采用高斯粒子滤波代替当前模型自适应跟踪算法中的卡尔曼滤波,将高斯粒子滤波与当前统计模型的优点相结合,提出了一种新的当前统计模型自适应跟踪算法,用于非线性非高斯系统的机动目标跟踪.MonteCarlo仿真表明,该算法跟踪精度优于标准的交互多模型算法和当前统计模型自适应跟踪算法,实时性好于交互多模型粒子滤波算法.     

An extended complex Kalman filter for frequency measurement ofdistorted signals

The design of an extended complex Kalman filter for the measurement of power system frequency has been presented in this paper. The design principles and the validity of the model have been outlined. A complex model has been developed to track a distorted signal that belongs to a power system. The model inherently takes care of the frequency measurement along with the amplitude and phase of the signals. The theory has been applied to standard test signals representing the worst-case measurement and network conditions in a typical power system. The proposed algorithm is suitable for real-time applications where the measurement noise and other disturbances are high. The complex quantities can be conveniently handled using a floating point processor. Comparison of the results of the proposed method with those obtained from a real extended Kalman filter reveals the superior performance of the former method     

Importance sampling for reliability assessment of dynamic systems under general random process excitation

This paper develops a reliability assessment method for dynamic systems subjected to a general random process excitation. Safety assessment using direct Monte Carlo simulation is computationally expensive, particularly when estimating low probabilities of failure. The Girsanov transformation-based reliability assessment method is a computationally efficient approach intended for dynamic systems driven by Gaussian white noise, and this approach can be extended to random process inputs that can be represented as transformations of Gaussian white noise. In practice, dynamic systems may be subjected to inputs that may be better modeled as non-Gaussian and/or non-stationary random processes, which are not easily transformable to Gaussian white noise. We propose a computationally efficient scheme, based on importance sampling, which can be implemented directly on a general class of random processes — both Gaussian and non-Gaussian, and stationary and non-stationary. We demonstrate that this approach is in fact equivalent to Girsanov transformation when the uncertain inputs are Gaussian white noise processes. The proposed approach is demonstrated on a linear dynamic system driven by Gaussian white noise and Brownian bridge processes, a multi-physics aero-thermo-elastic model of a flexible panel subjected to hypersonic flow, and a nonlinear building frame subjected to non-stationary non-Gaussian random process excitation.     

水声传感器网络移动节点定位技术

针对水声传感器网络的移动节点定位问题,首先研究了基于距离测量值的多边定位方法(Multilateral Localization,ML);然后利用节点运动信息,提出采用扩展卡尔曼滤波(Extended Kalman Filter,EKF)进行跟踪的方法;最后针对水下移动节点的测量值不同步问题,提出了修正扩展卡尔曼滤波(Modified Extend Kalman Filter,MEKF)以改进EKF的精度。仿真分析结果表明,MEKF的定位精度要好于EKF,而EKF和MEKF由于其用到了节点的运动信息,因此其定位精度要远好于ML。     

Particle Filtering for State Estimation in Nonlinear Industrial Systems

State estimation is a major problem in industrial systems, particularly in industrial robotics. To this end, Gaussian and nonparametric filters have been developed. In this paper, the extended Kalman filter, which assumes Gaussian measurement noise, is compared with the particle filter, which does not make any assumption on the measurement noise distribution. As a case study, the estimation of the state vector of an industrial robot is used when measurements are available from an accelerometer that was mounted on the end effector of the robotic manipulator and from the encoders of the joints' motors. It is shown that, in this kind of sensor fusion problem, the particle filter outperforms the extended Kalman filter, at the cost of more demanding computations.     

Cellular automaton and Kalman filter based track search in the HERA-B pattern tracker

The paper describes track reconstruction package OTR/ITR-CATS developed for the Pattern Tracker of the HERA-B experiment. This package employs a combined approach for track reconstruction based on the use of a cellular automaton for track searching and the Kalman filter techniques for track fitting. A similar reconstruction strategy is already successfully applied to the Vertex Detector System (VDS) (Nucl. Instr. and Meth. A 489 (2002) 389). However, hit efficiencies and resolutions of the Pattern Tracker lower than those of the VDS require much more delicate implementation of the method.

The package developed has been tested on simulated data. The results of the tests regarding reconstruction efficiency, accuracy of estimates and computing time are presented.     

一种信标水声定位的改进扩展卡尔曼滤波算法

水声测距误差通常偏离高斯分布,纯距离扩展卡尔曼滤波(Extended Kalman Filter,EKF)定位跟踪算法误差较大。在将测距噪声分为高斯分量和非高斯缓变分量的基础上,提出了一种改进的扩展卡尔曼滤波EKF算法(Improved Extended Kalman Filter,IEKF)和初值选取方法。利用仿真实验和湖试对IEKF算法进行了验证,结果表明IEKF算法能够对测距偏差进行跟踪补偿,定位精度明显优于常规EKF算法。     

采用矢量阵测量的水中宽带近场声全息技术研究

基于声强测量的宽带声全息技术(BAH IM)是由近场声全息(NAH)领域脱颖而出的一项技术,它由全息面上互相垂直的两个切向声强分量计算出全息面上的复声压相位,得到全息面上复声压,再进行NAH处理。针对水中圆柱体的噪声源识别问题,给出了该方法在柱体中运用的基本原理,利用所编制的程序进行了仿真验证,最后,采用矢量阵进行了水中近场声全息测量实验,验证了该方法的可行性和准确性,实验结果表明柱面内BAH IM技术在水中柱形声源内辐射声场的重建噪声源识别和定位中有着明显的优势。     

环境激励下基于奇异谱互熵的结构损伤诊断方法

环境激励下的结构响应是一个随机过程,结构发生破损时其响应将随之变化,因而可将描述随机过程特性的参数作为评判结构状况的指标。熵是测量随机过程不确定性的一个比较方便的方法,能够用于高斯及非高斯分布的情况。在相空间重构与奇异值分解的基础上建立了奇异谱互熵的概念,提出了一种环境激励下用奇异谱互熵诊断结构损伤的方法。以ASCE学会提出的基准结构为对象进行研究,利用NExT技术获得响应,采用伪邻近法确定相空间的嵌入维数,讨论了不同工况及噪声对诊断结果的影响,分析结果验证了该方法的有效性和鲁棒性。     

基于卡尔曼滤波的STFT域回声抵消算法

提出了一种低复杂度的短时傅里叶变换域卡尔曼滤波算法来解决声学回声抵消问题。首先在短时傅里叶变换域建立了基于频域卷积传递函数的观测方程,并利用一阶马尔科夫模型对频域回声路径进行建模,给出了精确的卡尔曼滤波方程,并讨论了过程噪声和观测噪声的估计问题。为降低算法计算复杂度,提出了低复杂度卡尔曼滤波算法。另外,在更新滤波器时加入远端信号邻近频点的信息来进一步提高回声抵消性能。实验结果表明,所提算法对近端干扰不敏感,不需要额外的双端对讲检测算法,且比传统的频域自适应滤波算法具有更快的收敛速度。     

Infrared species tomography of a transient flow field using Kalman filtering

In infrared species tomography, the unknown concentration distribution of a species is inferred from the attenuation of multiple collimated light beams shone through the measurement field. The resulting set of linear equations is rank-deficient, so prior assumptions about the smoothness and nonnegativity of the distribution must be imposed to recover a solution. This paper describes how the Kalman filter can be used to incorporate additional information about the time evolution of the distribution into the reconstruction. Results show that, although performing a series of static reconstructions is more accurate at low levels of measurement noise, the Kalman filter becomes advantageous when the measurements are corrupted with high levels of noise. The Kalman filter also enables signal multiplexing, which can help achieve the high sampling rates needed to resolve turbulent flow phenomena.