基于Kalman滤波的实时电离层产品综合及精度分析

为了进一步研究实时全球电离层图(RT-GIM)产品在全球卫星导航系统(GNSS)实时精密定位、实时空间天气监测等领域中的应用,提出一种卡尔曼(Kalman)滤波结合球谐函数模型的实时电离层产品综合方法:对中国科学院(CAS)、武汉大学(WHU)以及国际GNSS服务组织(IGS)综合RT-GIM产品精度和可用性进行评估;并综合所评估的实时状态空间表述(SSR)数据流产品及欧洲定轨中心(CODE)电离层预报产品,分别生成实时综合产品(KRT-GIM)及预报综合产品(KPR-GIM)。实验结果表明,KRT-GIM可有效避免单一实时电离层产品数据流中断影响,与CAS RTGIM产品相比,综合后重建的垂直总电子含量(VTEC)估值精度平均绝对误差和均方根误差分别降低0.29个和0.38个总电子含量单位(TECU);与IGS RT-GIM相比,KRT-GIM在太阳活动活跃期实时单频精密单点定位的平面和高程方向定位精度分别提升13.9%和7.7%;在太阳活动平静期,KPR-GIM产品与IGS RT-GIM产品的精度较为接近,可用于实时数据流全部中断时为实时用户提供电离层产品连续服务。

基于VMD-Kalman-GM组合模型的滑坡位移预测

滑坡位移的预测与分析能为滑坡灾害的预警提供重要数据支持作用,针对受降雨影响存在波动发展的滑坡位移序列,为了提高降雨对滑坡位移影响的预测效果,文章建立了一种变分模态分解(VMD)算法和卡尔曼滤波(Kalman)、改进灰色模型(GM)组合预测的方法,文章基于变分模态分解算法将滑坡地表监测位移序列分解不同频率分量,经过时序组合得到波动值和趋势值,在确定波动值与降雨数值时滞相关性的条件下,提出了一种考虑降雨数值的变化趋势的卡尔曼滤波预测模型,建立降雨时间滞后影响下的卡尔曼滤波预测模型,利用该模型进行滑坡位移波动值的动态预测,同时建立动态灰色预测模型预测趋势值,最后波动值和趋势值合成得到滑坡预测数值,建立了VMD-Kalman-GM组合预测模型。以中国三峡库区八字门滑坡监测数据为例,将预测结果与实测值进行比较,验证了该方法的可行性和准确性,为滑坡位移的预测提供了一种新的方法。

基于Kalman滤波的组合预测模型在建筑物变形监测中的应用

根据建筑物沉降监测数据的特点,结合Kalman滤波算法、BP神经网络模型以及AR自回归模型在数据降噪、数据预测中的优势,提出并构建了一种新的基于Kalman滤波的BP-AR沉降预测模型。该组合预测模型实现建筑物变形预测的主要步骤为:首先,通过Kalman滤波算法对原始观测数据进行降噪,消除随机噪声误差对观测数据的影响;其次,通过BP神经网络模型对降噪后序列进行建模与预测;最后使用AR模型对预测残差进行建模与预测。通过实际建筑物沉降监测数据对本文提出的组合预测模型进行验证,结果表明相较于BP神经网络模型与BP-AR模型,本文提出的组合预测模型的预测精度更高,有效降低了噪声影响,具有较高的优越性。

Multiple Kalman filters model with shaping filter GPS real-time deformation analysis

In order to detect the deformation in real-time of the GPS time series and improve its reliability, the multiple Kalman filters model with shaping filter was proposed. Two problems were solved: firstly, because the GPS real-time deformation series with a high sampling rate contain coloured noise, the multiple Kalman filter model requires the white noise, and the multiple Kalman filters model is augmented by a shaping filter in order to reduce the colored noise; secondly, the multiple Kalman filters model with shaping filter can detect the deformation epoch in real-time and improve the quality of GPS measurements for the real-time deformation applications. Based on the comparisons of the applications in different GPS time series with different models, the advantages of the proposed model were illustrated. The proposed model can reduce the colored noise, detect the smaller changes, and improve the precision of the detected deformation epoch.

Investigation of the different weight models in Kalman filter:A case study of GNSS monitoring results

During geodetic monitoring with GNSS technology one of important steps is the correct processing and analysis of the measured displacements. We used the processing method of Kalman filter smoothing algorithm, which allows to evaluate not only displacements, but also the speed, acceleration, and other characteristics of the deformation model. One of the important issues is the calculation of the obser- vations weight matrix in the Kalman filter. Recurrence algorithm of Kalman filtering can calculate and specify the weights during processing. However, the weights obtained in such way do not always exactly correspond to the actual observation accuracy. We established the observations weights based on the accuracy of baseline measurements. In the presented study, we offered and investigated different models of establishing the accuracy of the baselines. The offered models and the processing of the measured displacements were tested on an experimentally geodetic GNSS network. The research results show that despite of different weight models, changing weights up to 2 times do not change Kalman filtering ac- curacy extremely. The significant improvements for Kalman filtering accuracy for baselines shorter than 10 km were not got. Therefore, for typical GNSS monitoring networks with baseline range 10-15 km, we recommend to use any kind of models. The compulsory condition for getting correct and reliable results is checking results on blunders. For baselines, which are longer than 15 km we propose to use weight model which include baseline standard deviation from network adjustment and corrections for baseline length and its accuracy.

Kalman Filter for Generalized 2-D Roesser Models

The design problem of the state filter for the generalized stochastic 2-D Roesser models, which appears when both the state and measurement are simultaneously subjected to the interference from white noise, is discussed. The well-known Kalman filter design is extended to the generalized 2-D Roesser models. Based on the method of “scanning line by line”,the filtering problem of generalized 2-D Roesser models with mode-energy reconstruction is solved. The formula of the optimal filtering, which minimizes the variance of the estimation error of the state vectors, is derived. The validity of the designed filter is verified by the calculation steps and the examples are introduced.

A Framework of Finite-model Kalman Filter with Case Study： MVDP-FMKF Algorithm

然而，过滤技术的 Kalman 广泛地在许多应用被使用了为线性 Gaussian 系统的标准 Kalman 过滤器不能通常工作很好或甚至面对大模型无常分叉。在实际应用程序，有高费用的实验的大数字是昂贵的或对甚至不可能获得一个准确系统模型。在有限模型的适应控制上由我们的以前的开创的工作激发了，过滤的有限模型的 Kalman 的一个框架在这份报纸被介绍。这个框架想那大模型无常可以被能与对方很不同的已知的模型的一个有限集合限制。而且，在集合的已知的模型的数字能灵活地被选择以便换句话说，不明确的模型可以被已知的模型之一总是接近大模型无常被已知的模型的凸的壳盖住。在介绍框架以内根据经由最小化的向量距离原则的适应切换的想法，一个简单有限模型的 Kalman 过滤器， MVDP-FMKF，被广泛的模拟算术地提出并且说明。MEMS 回转仪飘移的一个实验验证了建议算法的有效性，显示有限模型的 Kalman 过滤器的机制在 Kalman 过滤器的实际应用有用、有效，特别在惯性的航行系统。

Assimilation of Remote Sensing and Crop Model for LAI Estimation Based on Ensemble Kalman Filter

Data assimilation in agricultural remote sensing research is of great significance to integrate with remote sensing observations and model simulations for parameters estimation. The present investigation not only designed and realized the Ensemble Kalman Filtering algorithm （EnKF） assimilation by combing the crop growth model （CERES-Wheat） with remote sensing data, but also optimized and updated the key parameters （LAI） of winter wheat by using remote sensing data. Results showed that the assimilation LAI and the observation ones agreed with each other, and the R2 reached 0.8315. So assimilation remote sensing and crop model could provide reference data for the agricultural production.

交互多模自适应容积Kalman滤波算法设计及履带车辆跟踪应用

为满足履带车辆作为机动目标的实时跟踪和对目标速度、航向角的准确估计,针对测量值含有相关乘性噪声,采用新息分析法依据噪声相关系数已知和未知改进容积Kalman滤波算法。考虑到单模型滤波器难以准确地实现机动目标的跟踪,采用交互式多模型算法对履带车辆运动轨迹进行描述,提出一种交互式多模自适应容积Kalman滤波算法。仿真表明交互式多模型自适应容积Kalman滤波算法对车辆机动具有稳定的跟踪效果且乘性噪声得到有效处理。

Kalman融合模型在无人装备关键部件寿命预测中的应用

无人装备一般数量众多、执行任务时间长、环境恶劣,因此剩余使用寿命(RUL)预测尤为重要。综合性能指标序列使用单一模型的预测精度较低,为解决此问题,提出基于Kalman融合模型的RUL预测方法。首先,采用面积最大值法提取无人装备关键部件综合性能指标的退化阶段;其次,利用具有指数特征的GM(1,1)模型、线性支持向量机SVR模型、非线性极端学习机(ELM)模型对综合性能指标进行预测,每种模型可以捕捉综合性能指标的不同特征;最后,通过Kalman框架将3种模型的预测结果以迭代最小二乘的原则进行融合。实验结果显示,Kalman融合模型的预测方法可显著提高对综合性能指标的预测精度,与ELM,SVR和GM(1,1)单一模型相比,拟合精度分别提高了16.96%,1.61%和39.84%,预测精度分别提高了45.06%,38.35%和74.12%。

A numerical storm surge forecast model with Kalman filter

Kalman filter data assimilation technique is incorporated into a standard two-dimensional linear storm surge model. Imperfect model equation and imperfect meteorological forcimg are accounted for by adding noise terms to the momentum equations. The deterministic model output is corrected by using the available tidal gauge station data. The stationary Kalman filter algorithm for the model domain is calculated by an iterative procedure using specified information on the inaccuracies in the momentum e- quations and specified error information for the observations. An application to a real storm surge that occurred in the summer of 1956 in the East China Sea is performed by means of this data assimilation technique. The result shows that Kalman filter is useful for storm surge forecast and hindcast.

A “Dressed” Ensemble Kalman Filter Using the Hybrid Coordinate Ocean Model in the Pacific

The computational cost required by the Ensemble Kalman Filter （EnKF） is much larger than that of some simpler assimilation schemes, such as Optimal Interpolation （OI） or three-dimension variational as- similation （3DVAR）. Ensemble optimal interpolation （EnOI）, a crudely simplified implementation of EnKF, is sometimes used as a substitute in some oceanic applications and requires much less computational time than EnKF. In this paper, to compromise between computational cost and dynamic covariance, we use the idea of ＂dressing＂ a small size dynamical ensemble with a larger number of static ensembles in order to form an approximate dynamic covariance. The term ＂dressing＂ means that a dynamical ensemble seed from model runs is perturbed by adding the anomalies of some static ensembles. This dressing EnKF （DrEnKF for short） scheme is tested in assimilation of real altimetry data in the Pacific using the HYbrid Coordinate Ocean Model （HYCOM） over a four-year period. Ten dynamical ensemble seeds are each dressed by 10 static ensemble members selected from a 100-member static ensemble. Results are compared to two EnKF assimilation runs that use 10 and 100 dynamical ensemble members. Both temperature and salinity fields from the DrEnKF and the EnKF are compared to observations from Argo floats and an OI SST dataset. The results show that the DrEnKF and the 100-member EnKF yield similar root mean square errors （RMSE） at every model level. Error covariance matrices from the DrEnKF and the 100-member EnKF are also compared and show good agreement.

Assimilation of temporal-spatial leaf area index into the CERES-Wheat model with ensemble Kalman filter and uncertainty assessment for improving winter wheat yield estimation

To accurately estimate winter wheat yields and analyze the uncertainty in crop model data assimilations, winter wheat yield estimates were obtained by assimilating measured or remotely sensed leaf area index （LAI） values. The performances of the calibrated crop environment resource synthesis for wheat （CERES-Wheat） model for two different assimilation scenarios were compared by employing ensemble Kalman filter （EnKF）-based strategies. The uncertainty factors of the crop model data assimilation was analyzed by considering the observation errors, assimilation stages and temporal-spatial scales. Overalll the results indicated a better yield estimate performance when the EnKF-based strategy was used to comprehen- sively consider several factors in the initial conditions and observations. When using this strategy, an adjusted coefficients of determination （R2） of 0.84, a root mean square error （RMSE） of 323 kg ha-1, and a relative errors （RE） of 4.15% were obtained at the field plot scale and an R2 of 0.81, an RMSE of 362 kg ha-1, and an RE of 4.52% were obtained at the pixel scale of 30 mx30 m. With increasing observation errors, the accuracy of the yield estimates obviously decreased, but an acceptable estimate was observed when the observation errors were within 20%. Winter wheat yield estimates could be improved significantly by assimilating observations from the middle to the end of the crop growing seasons. With decreasing assimilation frequency and pixel resolution, the accuracy of the crop yield estimates decreased; however, the computation time decreased. It is important to consider reasonable temporal-spatial scales and assimilation stages to obtain tradeoffs between accuracy and computation time, especially in operational systems used for regional crop yield estimates.

Marginalized cubature Kalman filtering algorithm based on linear/nonlinear mixed-Gaussian model

Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is reduced.Meanwhile,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.

Updating Geologic Models using Ensemble Kalman Filter for Water Coning Control

This study investigated the feasibility of updating prior uncertain geologic models using Ensemble Kalman filter for controlling water coning problems in horizontal wells. Current downhole data acquisition technol-ogy allows continuous updating of the reservoir models and real-time control of well operations. Ensemble Kalman Filter is a model updating algorithm that permits rapid assimilation of production response for res-ervoir model updating and uncertainty assessment. The effect of the type and amount of production data on the updated geologic models was investigated first through a synthetic reservoir model, and then imple-mented on a laboratory experiment that simulated the production of a horizontal well affected by water con-ing. The worth of periodic model updating for optimized production and oil recovery is demonstrated.

Analysis of SDEs Applied to SEIR Epidemic Models by Extended Kalman Filter Method

A disease transmission model of SEIR type is discussed in a stochastic point of view. We start by formulating the SEIR epidemic model in form of a system of nonlinear differential equations and then change it to a system of nonlinear stochastic differential equations (SDEs). The numerical simulation of the resulting SDEs is done by Euler-Maruyama scheme and the parameters are estimated by adaptive Markov chain Monte Carlo and extended Kalman filter methods. The stochastic results are discussed and it is observed that with the SDE type of modeling, the parameters are also identifiable.

Efficient hemodynamic states stimulation using fNIRS data with the extended Kalman filter and bifurcation analysis of balloon model

This paper introduces a stochastic hemodynamic system to describe the brain neural activity based on the balloon model. A continuous-discrete extended Kalman filter is used to estimate the nonlinear model states. The stability, controllability and observability of the proposed model are described based on the simulation and measurement data analysis. The observability and controllability characteristics are in- troduced as significant factors to validate the preference of different hemodynamic factors to be considered for diagnosis and monitoring in clinical applications. This model also can be efficiently applied in any monitoring and control platform include brain and for study of hemodynamics in brain imaging modalities such as pulse oximetry and functional near infrared spectroscopy. The work is on progress to extend the proposed model to cover more hemodynamic and neural brain signals for real-time in-vivo application.

GNSS/MEMS IMU车载组合导航中IMU比例因子误差的影响分析

从系统状态模型出发,分析比例因子误差对组合导航精度和计算量的影响,同时基于车载运动的特点分析比例因子误差的观测性,提出一种仅保留航向陀螺仪和水平加速度计比例因子误差的降维状态模型。实验结果表明,当比例因子误差大于6×10^(-3)时,增广比例因子误差有助于提高导航精度,但计算量增加约170%;降维模型能够达到高维模型的导航精度,与不增广比例因子误差相比,计算量仅增加约70%。

Kalman滤波算法在海洋钻机中控制信号的优化

海洋钻机由于其应用的特殊性,对控制信号的稳定程度及控制精度有更高的要求。针对海洋钻机电控系统中信号受噪声干扰大的情况,提出一种基于Kalman滤波算法的PID控制信号优化方式,控制过程中信号是多维且非平稳输出,利用Matlab/Simulink软件仿真PID传递函数并整定参数,利用传递控制信号的输出作为Kalman滤波算法线性观测方程的输入,运行正态分布融合模型,建立海洋钻机控制信号的干扰高斯白噪声的模型,对稳定信号及噪声观测值进行加权平均更新迭代计算,以便于获取最小方差估计值,从而得到降噪的信号。实验仿真表明,与传统的PID信号输出相比较,系统具备更强的抗干扰能力和更好的鲁棒性。