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.     

基于自适应前景分割及粒子滤波的人体运动跟踪

提出了在图像序列中用自适应前景分割及粒子滤波对人体的3-D运动轨迹进行跟踪的方法．首先建立了像素点的高斯模型,并结合图像帧间的差分信息以及灰度分布的先验概率等因素完成了图像中人体的自适应分割．根据所得到的分割结果建立了透视投影下的运动平面跟踪模型．根据投影过程的非线性以及图像中噪声分布的未知性,提出了粒子滤波的跟踪方法,并最终得到了人体运动平面的3-D轨迹．实际人体运动图像序列的实验证明,本文方法能有效地跟踪人体运动的3-D轨迹,并反映出在此跟踪问题上粒子滤波比传统的扩展卡尔曼滤波更具优势．     

Kalman filter tracking in a Cherenkov neutrino telescope

The reconstruction of tracks in underwater Cherenkov neutrino telescopes is strongly complicated due to large background counting rate originates from ⁴⁰K beta decay and to the electromagnetic showers accompanying high energy muons together with the effects of light propagation in the water, in particular the photon scattering. These two effects lead to a non-linear problem with a non-Gaussian measurement noise. A method for track reconstruction based on Kalman filter approach in this situation is presented. We use Gaussian Sum Filter algorithm to take into account non-Gaussian process noise. While usual Kalman filter estimators based on linear least-square method are optimal in case all observations are Gaussian distributed, the Gaussian Sum Filter offers a better treatment of non-Gaussian process noise and/or measurement errors when these are modeled by Gaussian mixtures. As an example of the application, the results of muon track reconstruction in NEMO underwater neutrino telescope are presented as well as the comparison of its capability with other standard track reconstruction methods.     

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.     

Study on Posture Estimation Using Delayed Measurements for Mobile Robots

1Introduction Mobilerobotsaredevelopingtowardsintellectualization,whichdependsonthedevelopmentofsensor technologytotheutmostextent.Theinformationfusiontechnologyhasovercomethedrawbackresul tingfromtheapplicationofasingletonsensor.Forthesamereason,inordertoenhancetheposition precisionofthemobilerobot,morethanonesensorisoftenneededtogenerateandmaintainarelia blestateestimation[1].Furthermore,thecomputationcomplexityofdealingwiththesensordatawil oftenbringonsignificanttimedelaysfromtheacquisition…     

基于RFF及GWO-PF的锂电池SOC估计

为了提高锂电池剩余电量估计的准确性,提出一种在线参数辨识与改进粒子滤波算法相结合的锂电池SOC估计方法。针对粒子滤波中的粒子退化问题,引入灰狼算法,利用灰狼算法较强的全局寻优能力优化粒子分布,保证粒子多样性,有效抑制粒子退化现象,提高滤波精度。采用带遗忘因子的递推最小二乘法实时更新模型参数,并与改进粒子滤波算法交替运行,进一步提高SOC的估计精度。实验结果表明,改进算法的平均估计误差始终保持在±0.15%以内,相比扩展卡尔曼滤波与无迹卡尔曼滤波算法,在电池SOC估计上有更高的估计精度与稳定性。     

Bayesian state and parameter estimation of uncertain dynamical systems

The focus of this paper is Bayesian state and parameter estimation using nonlinear models. A recently developed method, the particle filter, is studied that is based on stochastic simulation. Unlike the well-known extended Kalman filter, the particle filter is applicable to highly nonlinear models with non-Gaussian uncertainties. Recently developed techniques that improve the convergence of the particle filter simulations are introduced and discussed. Comparisons between the particle filter and the extended Kalman filter are made using several numerical examples of nonlinear systems. The results indicate that the particle filter provides consistent state and parameter estimates for highly nonlinear models, while the extended Kalman filter does not.     

Monte Carlo-based filtering for fatigue crack growth estimation

The lifetime prediction of industrial and structural components is a recognized valuable task for operating safely and managing with profit the production of industrial plants. One way to address this prognostic challenge is by implementing model-based estimation methods for inferring the life evolution of a component on the basis of a sequence of noisy measurements related to its state. In practice, the non-linearity of the state evolution and/or the non-Gaussianity of the associated noise may lead to inaccurate prognostic estimations even with advanced approaches, such as the Kalman, Gaussian-sum and grid-based filters. An alternative approach which seems to offer significant potential of successful application is one which makes use of Monte Carlo-based estimation methods, also called particle filters. The present paper demonstrates such potential on a problem of crack propagation under uncertain monitoring conditions. The crack growth process, taken from literature, is described by a non-linear model affected by non-additive noises. To the authors’ best knowledge, this is the first time that (i) a particle filtering technique is applied to a structural prognostic problem and (ii) the filter is modified so as to estimate the distribution of the component’s remaining lifetime on the basis of observations taken at predefined inspection times.     

Huber-based unscented filtering and its application to vision-based relative navigation

A new algorithm called Huber-based unscented filtering (UF) is derived and applied to estimate the precise relative position, velocity and attitude of two unmanned aerial vehicles in the formation flight. The relative states are estimated using line-of-sight measurements between the vehicles along with acceleration and angular rate measurements of the follower. By making use of the Huber technique to modify the measurement update equations of standard UF, the new filtering could exhibit robustness with respect to deviations from the commonly assumed Gaussian error probability, for which the standard unscented filtering would exhibit severe degradation in estimation accuracy. Furthermore, contrast to standard extended Kalman filtering, more accurate estimation and faster convergence could be achieved from inaccurate initial conditions. During filter design, the global attitude parameterisation is given by a quaternion, whereas a generalised three-dimensional attitude representation is used to define the local attitude error. A multiplicative quaternion-error approach is used to guarantee that quaternion normalisation is maintained in the filter. Simulation results are shown to compare the performance of the new filter with standard UF and standard extended Kalman filtering for non-Gaussian case.     

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.     

Kalman filter-based force estimation in a clamped plate using reduced order model and noisy measurements

Deterministic techniques are available for force estimation in dynamic systems in time, frequency, and modal domain. But, these techniques are susceptible to measurement noise and require an accurate model of the system, hence, are not suitable for precise force estimation. Some combined deterministic-stochastic approaches are available in the literature for unknown input force estimations, where force estimations are performed by considering the model uncertainty and measurement noise. In the present work, one such technique is extended by incorporating reduced-order model to estimate forces in of plate structures. Kalman filter and a recursive least-squares (KF-RLSE)-based technique which uses displacement and/or velocity measurements for force estimation is used in the present work with a reduced-order model. Time-varying unknown forces acting at single/multiple locations are reconstructed using the measured responses from the plate. Numerical simulation followed by experimental verification is presented. The effect of error in model parameters on the force estimation is presented, and robustness of the input estimation technique is tested for different levels of measurement noise.     

Stochastic structural system identification

This paper presents a new scheme for the estimation of the mean values of parameters in multi-degree-of-freedom structural systems. It is based on a combination of a differential operator transform of the measured data with the extended Kalman filter method. The proposed method can deal with a wide variety of estimation problems including those which are of the non-linear-in-the parameter type. On combining this method with a technique for estimating the variance of the parameters, discussed detailly in part two of this paper, a complete stochastic structural system identification technique can be formulated. Results from simulation studies indicate that the new method can yield reliable estimates of the system parameters even when the noise level in the measurement records is significant.     

小波变换与卡尔曼滤波结合的RLG降噪方法

针对激光陀螺随机游走噪声其非平稳和非正态分布的特性,提出了基于小波变换的卡尔曼滤波的RLG降噪方法,该方法既具有小波变换对自相似过程的去相关作用和多分辨分析的功能,同时又保持了卡尔曼滤波器对未知信号的线性无偏最小方差估计的特点,实现了激光陀螺随机游走噪声的实时多尺度分解和最优估计。实测激光陀螺零偏信号去噪的结果表明,基于小波变换的卡尔曼滤波器使随机游走噪声的标准差降低了10.3%,降噪效果优于传统的卡尔曼滤波器。     

A New Optimized Algorithm with Nonlinear Filter for Ultra-Tightly Coupled Integrated Navigation System of Land Vehicle

The extended particle filter (EPF) assisted by the Takagi-Sugeno (T-S) fuzzy logic adaptive system (FLAS) is used to design the ultra-tightly coupled GPS/INS (inertial navigation system) integrated navigation, which can maneuver the vehicle environment and the GPS outages scenario. The traditional integrated navigation designs adopt a loosely or tightly coupled architecture, for which the GPS receiver may lose the lock due to the interference/jamming scenarios, high dynamic environments, and the periods of partial GPS shading. An ultra-tight GPS/INS architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The EPF is a particle filter (PF) which uses the extended Kalman filter (EKF) to generate the proposal distribution. The PF depends mostly on the number of particles in order to achieve a better performance during the high dynamic environments and GPS outages. The T-S FLAS is one of these approaches that can prevent the divergence problem of the filter when the precise knowledge on the system models is not available. The results show that the proposed fuzzy adaptive EPF (FAEPF) can effectively improve the navigation estimation accuracy and reduce the computational load as compared with the EPF and the unscented Kalman filter (UKF).     

State estimation of a boiler model using the unscented Kalman filter

The state estimation of a 300 MW drum-type boiler is examined, using an unscented Kalman filter to improve estimation accuracy by preserving the nonlinearities of the boiler equations. The boiler is modelled by a system of differential state equations for the dynamics of the circulation loop and another set of partial differential equations for the heat exchangers such as the superheaters, reheater and economiser. These modelling equations are the results of first principle balance equations, which have a form that is unsuitable for the extended Kalman filter method because of errors between the linear and nonlinear propagation of the boiler states and the difficulties in obtaining the Jacobian of the state model for the propagation of model uncertainties. An unscented Kalman filter is used to circumvent this problem as it treats the system model as a black box. Filtering results from simulated plant data are presented to demonstrate the effectiveness of the filter application.     

基于自适应滤波的锂电池隔膜卷绕系统张力估计

锂电池隔膜卷绕系统的电机转速、放卷辊的卷材卷径和放卷张力等实时信号都带有高斯白噪声,易形成较大的滞后,从而导致控制系统的稳定性和精度降低。现以协方差匹配技术为滤波发散判据,再结合对于指数加权系数的表达式限定记忆滤波的次数,提高噪声初始值的分配权重,来保持滤波的自适应程度,提出一种基于改进型SageHusa自适应滤波估计张力的方法,实现对系统噪声协方差阵与测量噪声协方差阵的自适应变化。实验结果表明,所提出的方法不仅能更准确、稳定地估计出锂电池隔膜卷绕系统放卷张力,还能在一定范围内使其不受给定的噪声协方差阵初值影响,而且有较高的精度和较强的实时性,优于一般的扩展卡尔曼滤波算法。     

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     

一种自适应EPF算法及其在光纤水听器中的应用

基于椭圆拟合的相位生成载波(Phase Generated Carrier,PGC)解调方法是消除非线性因素对光纤水听器PGC解调结果影响的一种有效手段,椭圆曲线参数的最优估计问题是实现该方法的关键。扩展卡尔曼粒子滤波(Extended Kalman Particle Filter,EPF)是解决此类非线性估计问题的一种常用的最优估计算法。但传统的EPF算法在用于常参数过程方程的参数或状态估计问题时,过程噪声的方差通常设置为一个常量,这使得算法难以兼顾收敛速度和估计精度,一定程度上限制了算法的整体性能。为了解决这个问题,文章对现有的EPF进行了改进,提出了一种自适应扩展卡尔曼粒子滤波(Adaptive Extended Kalman Particle Filter,AEPF)算法。模拟仿真和实验结果表明,文中所提出的AEPF算法能根据基于椭圆拟合的PGC解调方法有效地解调出待测声信号,相比EKF算法和EPF算法,AEPF算法的收敛速度和估计精度都得到了提升。此外,文章所提出的AEPF算法也适用于其他具有常参数过程方程的参数或状态估计问题,具有一定的通用性。     

Noise Immunity of High-Precision Low-Temperature Experiments

In the high-precision low-temperature experiments, noise immunity has long been an important issue. We consider the problem of measuring the slowly changing data in the presence of both white noise and sudden, short noise spikes. The Kalman filter is applied to attenuate the white noise and a spike detecting algorithm is applied to remove spikes resulting from the charged particles. Experimental data show that, with the Kalman filter, the RMS of the measurement noise in a 0.5 Hz bandwidth can be attenuated from 4 nK to 0.2 nK in the best case. A simple spike detecting algorithm worked effectively to remove spikes without increasing the random noise level.