Performance evaluation of the simpli¯ed spherical harmonics approximation for cone-beam X-ray luminescence computed tomography imaging

As an emerging molecular imaging modality,cone-beam X-ray luminescence computed tomog-raphy(CB-XLCT)uses X-ray-excitable probes to produce near-infrared(NIR)luminescence and then reconst ructs three-dimensional(3D)distribution of the probes from surface measurements.A proper photon-transportation model is critical to accuracy of XLCT.Here,we presented a systematic comparison between the common-used Monte Carlo model and simplified spherical harmonics(SPN).The performance of the two methods was evaluated over several main spec-trums using a known XLCT material.We designed both a global measurement based on the cosine similarity and a locally-averaged relative error,to quantitatively assess these methods.The results show that the SP_(3) could reach a good balance between the modeling accuracy and computational efficiency for all of the tested emission spectrums.Besides,the SP_(1)(which is equivalent to the difusion equation(DE))can be a reasonable alternative model for emission wavelength over 692nm.In vivo experiment further demonstrates the reconstruction perfor-mance of the SP:and DE.This study would provide a valuable guidance for modeling the photon-transportation in CB-XLCT.

Establishment of European Regional Ionosphere Model Based on Spherical Harmonic Functions

In order to study the temporal and spatial variation characteristics of the regional ionosphere and the modeling accuracy,the experiment is based on the spherical harmonic function model,using the GPS,Glonass,and Galileo dual-frequency observation data from the 305th-334th day of the European CORS network in 2019 to establish a global ionospheric model.By analyzing and evaluating the accuracy of the global ionospheric puncture points,VTEC,and comparing code products,the test results showed that the GPS system has the most dense puncture electricity distribution,the Glonass system is the second,and the Galileo system is the weakest.The values of ionospheric VTEC calculated by GPS,Glonass and Galileo are slightly different,but in terms of trends,they are the same as those of ESA,JPL and UPC.GPS data has the highest accuracy in global ionospheric modeling.GPS,Glonass and Galileo have the same trend,but Glonass data is unstable and fluctuates greatly.

Simulation for MSS-2 low-perigee elliptical orbit satellites:an example of lithospheric magnetic field modelling

A future constellation of at least four geomagnetic satellites(designated Macao Scientific Satellite-1(MSS-1)and Macao Scientific Satellite-2(MSS-2))was recently proposed,to continue high-quality geomagnetic observations in the post-Swarm period,focusing especially on collecting data that will provide a global,three-dimensional survey of the geomagnetic field.In this paper,we present a simulation of two years of orbits(2020.01.01-2022.01.01)of two satellites(tentatively denoted as MSS-2)that are constellated in elliptical(200×5,300 km)low-perigee orbits.By comparing error variances of Gauss coefficients,we investigate the sensitivity of lithospheric magnetic field modelling to data collected from various satellite orbits,including a near circular reference orbit of 300×350km,and elliptical orbit of 180×5,300 km,220×5,300 km,200×3,000 km and 200×1,500 km.We find that in two years the two MSS-2 satellites can collect 35,000 observations at altitude below 250 km,data that will be useful in advancing the quality of lithospheric magnetic field modelling;this number of observations reflects the fact that only 4.5%of the flight time of these satellites will be below250 km(just 6.4%of their flight time below 300 km).By combining observations from the MSS-2 satellites’elliptical orbits of 200×5,300km with observations from a circular reference orbit,the variance of the geomagnetic model can be reduced by a factor of 285 at spherical harmonic degree n=200 and by a factor of 1,300 at n=250.The planned lower perigee of their orbits allows the new satellites to collect data at unprecedentedly lower altitudes,thus dramatically improving the spatial resolution of satellite-derived lithospheric field models,(up to 80%at n=150).In addition,lowering the apogee increases the time interval during which the satellites fly at near-Earth altitudes,thus improving the model predictions at all spherical harmonic degrees(around 52%-62%at n=150).The upper limit of the expected improvement to the field model at the orbital apogee is not as good as at the perigee.However,data from the MSS-1 orbit can help fill the gap between data from the MSS-2 orbits and from the circular reference orbit for the low-degree part of the model.The feasibility of even lower-altitude flight requires further discussion with satellite engineers.

Computation and analysis Computation and analysis of the geomagnetic field model in China and its adjacent area for 2003

Based on the geomagnetic data at 135 stations and 35 observatories in China in 2003, the Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area for 2003 were established. In the model calculation, the truncation order of the model and the influences of the boundary restriction on the model calculation were carefully analyzed. The results show that the geomagnetic data used are precise and reliable, and the selection of the truncation order is reasonable. The Taylor polynomial model and the spherical cap harmonic model in China and its adjacent area established in this paper are consistent very well.

Evaluation of regional ionospheric grid model over China from dense GPS observations

The current global or regional ionospheric models have been established for monitoring the ionospheric variations. However, the spatial and temporal resolutions are not enough to describe total electron content（TEC） variations in small scales for China. In this paper, a regional ionospheric grid model（RIGM） with high spatial-temporal resolution（0.5 0.5 and 10-min interval） in China and surrounding areas is established based on spherical harmonics expansion from dense GPS measurements provided by Crustal Movement Observation Network of China（CMONOC） and the International GNSS Service（IGS）. The correlation coefficient between the estimated TEC from GPS and the ionosonde measurements is 0.97, and the root mean square（RMS） with respect to Center for Orbit Determination in Europe（CODE） Global Ionosphere Maps（GIMs） is 4.87 TECU. In addition, the impact of different spherical harmonics orders and degrees on TEC estimations are evaluated and the degree/order 6 is better. Moreover, effective ionospheric shell heights from300 km to 700 km are further assessed and the result indicates that 550 km is the most suitable for regional ionospheric modeling in China at solar maximum.

Ionospheric time delay corrections based on the extended single layer model over low latitude region

Ionospheric delay error is considered to be one of the most prominent factors impacting the Global Navigation Satellite Systems(GNSS) positioning and navigation accuracies. Due to dispersive nature and anisotropic of the ionosphere above certain regions, the positioning accuracy is seriously affected when using a precision-limited model. In this paper, an attempt has been taken to estimate ionosphere-delays based on Planar Fit(PF) and Spherical Harmonic Function(SHF) models by applying the commonly used single layer Model(SLM) and an extended single layer model(ESLM) which has been explored sparsely over the region. The results show that ESLM of PF and SHF techniques performed better in estimating ionospheric delay compared to the existing SLM model. Although the performance of the ESLM approach is almost comparable to the SLM results during the quiet ionospheric conditions, the ESLM-PF and ESLMSHF models led to respective improvements of 4.66% and 7.14% over the classically used SLM model under the disturbed ionospheric conditions. In view of the uneven variability of equatorial/low latitude ionosphere above the Indian subcontinental region, the suitability of ESLM-PF and ESLM-SHF models has been emphasized and suggested for assessing its completeness and reliableness across other parts of the globe. The output of this work may be useful for high precession GNSS positioning through mitigating the ionospheric delays under quiet as well as varied ionospheric conditions across the low/equatorial latitude regions.

中国及邻区高分辨率三维岩石圈磁场修正球冠谐模型(CUG_CLMFM3Dv1)

日益完善的大区域地面航磁调查与卫星磁测给建立高精度与高分辨率的地磁场模型带来了新的契机,同时也对地磁场建模技术提出了更高的要求.本文基于修正球冠谐分析方法,利用全球岩石圈磁力异常汇编网格WDMAMv2中提取的近地表总磁场强度异常数据与CHAMP卫星近十年的矢量测量数据,联合构建了中国及邻区高分辨率三维岩石圈磁场的修正球冠谐模型.该区域岩石圈磁场模型的分辨率可达球谐3500阶/次,进而基于该模型正演计算了研究区域不同高度的矢量数据.将区域模型与高分辨率的球谐模型分别在空间域与频率域进行对比,结果显示区域模型中的高频成份更加丰富,所描绘出的磁异常的形态和幅值更加接近原始建模数据,且在由低分辨率球谐模型补空的区域更加平滑.该应用案例证明,联合可靠的近地面标量与卫星矢量磁测数据,基于修正球冠谐分析方法,有能力构建出高精度与高分辨率的区域三维岩石圈磁场模型.

A Virtual Puncture Surgery System Based on Multi-Layer Soft Tissue and Force Mesh

Puncture is a common operation in surgery,which involves all kinds of tissue materials with different geometry and mechanical properties.As a new cross-disciplinary research area,Virtual Surgery(VS)makes simulation of soft tissue in puncture operation possible in virtual environment.In this paper,we introduce a VS-based puncture system composed by three-layer soft tissue,simulated with spherical harmonic function(SHF),which is covered with a force mesh,constructed by mass spring model(MSM).The two models are combined together with a parameter of SHF named surface radius,which provides MSM with real-time deformation data needed in force calculation.Meanwhile,force calculation,divided into the surface spring force and the puncture damping force,makes the force presentation better accord to the corresponding tissue characteristics.Moreover,a deformation resumption algorithm is leveraged to simulate the resumption phenomenon of the broken tissue surface.In evaluation experiment,several residents are invited to grades our model along with other four mainstream soft tissue models in terms of 7 different indicators.After the evaluation,the scores are analyzed by a comprehensive weighted grading method.Experiment results show that the proposed model has better performance during puncture operation than other models,and can well simulate surface resumption phenomenon when tissue surface is broken.

WHU-Grace01s:A new temporal gravity field model recovered from GRACE KBRR data alone

A new temporal gravity field model called WHU-Grace01s solely recovered from Gravity Recovery and Climate Experiment （GRACE） K-Band Range Rate （KBRR） data based on dynamic integral approach is presented in this paper. After meticulously preprocessing of the GRACE KBRR data, the root mean square of its post residuals is about 0.2 micrometers per second, and seventy-two monthly temporal solutions truncated to degree and order 60 are computed for the period from January 2003 to December 2008. After applying the combi- nation filter in WHU-Grace01s, the global temporal signals show obvious periodical change rules in the large-scale fiver basins. In terms of the degree variance, our solution is smaller at high degrees, and shows a good consistency at the rest of degrees with the Release 05 models from Center for Space Research （CSR）, GeoForschungsZentrum Potsdam （GFZ） and Jet Pro- pulsion Laboratory 0PL）. Compared with other published models in terms of equivalent water height distribution, our solution is consistent with those published by CSR, GFZ, JPL, Delft institute of Earth Observation and Space system （DEOS）, Tongji University （Tongji）, Institute of Theoretical Geodesy （ITG）, Astronomical Institute in University of Bern （AIUB） and Groupe de Recherche de Geodesie Spatiale （GRGS}, which indicates that the accuracy of WHU-Grace01s has a good consistency with the previously published GRACE solutions.

超高阶全球地形球谐系数模型的构建方法与实现

针对10800阶地形球谐系数模型构建的计算精度、计算稳定性及超大规模运算量等问题,本文首先通过比较分析矩形离散积分方法、Gauss-Legendre积分方法和Driscoll/Healy积分方法,验证了Driscoll/Healy积分方法具有更高的计算精度。然后,给出了改进的Belikov公式,将完全正常化缔和勒让德函数在全球范围内以优于10^(-12)精度高效、稳定递推至10800阶;提出了联合FFT和基于OpenMP的多核并行方法求解超高阶球谐系数的优化策略,显著提高了球谐系数模型构建的计算效率。最后,利用Earth2014_TBI与全球海底地形模型STO_IEU2020格网数据建立了全球10800阶地形球谐系数模型sph.10800_IEU,总体精度与Earth2014_TBI2014.shc相当,在试验海域的相对精度略优于模型Earth2014_TBI2014.shc。

基于球谐模型与多传感器融合的高精度重力扰动补偿方法

随着对高精度长航时惯导系统性能要求的提升,重力扰动已成为惯导系统的主要误差源,能否对其进行有效补偿是提升导航精度的关键因素。传统基于球谐模型的补偿方法无法反映地球重力场的细节信息,对中短波重力扰动分量补偿效果不佳;传统状态估计法中马尔科夫状态模型对长波重力扰动分量描述精度较差,因此对长波分量的补偿效果不佳。以上方法均无法对波段较宽的实际重力扰动进行精确补偿,针对这一问题,本文设计了一种综合利用球谐模型与多传感器信息融合的高精度重力扰动补偿方法。该方法一方面利用低阶球谐模型对长波重力扰动分量计算精度较高的特点,对长波分量进行补偿;另一方面利用捷联惯导/激光多普勒测速/气压高度计构成完全自主的组合导航系统,将残余的中短波重力扰动分量建立为高精度的马尔科夫模型,从而实现对中短波分量的状态估计与补偿。仿真结果表明,所提出的重力扰动补偿方法可有效改善重力扰动估计效果,进而实现高精度的重力扰动补偿,具有较高的导航精度。

不同分析中心电离层TEC产品精度评估

针对不同电离层产品精度存在差异的问题,对国际全球卫星导航系统(GNSS)服务员组织(IGS)、美国喷汽动力实验室(JPL)、欧洲定轨中心(CODE)、国际GNSS监测评估系统(iGMAS)、欧空局欧洲空间运行中心(ESOC)分析中心电离层产品进行精度评估,实验结果表明:在中国地区CODE和ESOG的中心电离层产品电离层格网数据(GIM)时间序列结果表现出高度的一致性;在欧洲地区CODE、ESOG和IGS中心电离层产品GIM的时间序列结果表现出高度的一致性;JPL中心电离层产品在中国地区、欧洲地区VTEC日平均值均最大;iGMAS中心电离层产品在中国地区、欧洲地区电离层VTEC日平均值均最小。IGS、JPL、CODE、i GMAS、ESOC分析中心电离层产品在中国地区VTEC的互差在3.6 TECU内,在欧洲地区VTEC的互差在3.2 TECU内,IGS、JPL、CODE、iGMAS、ESOC分析中心电离层产品在中国地区VTEC值相关系数均大于0.90,在欧洲地区相关系数均大于0.94,均表现出强相关性。

单站区域实时电离层异常改正拟合模型研究

针对传统电离层模型受伪距数据质量制约,局部或某时刻误差较大以及实时性不高的问题,提出一种拟合模型。利用CODE提供数据进行季节性时间序列法(Holt-Winters’)得到预测模型,将其与所求区域内基于接收机的多频载波相位平滑伪距法得到的球谐多级模型进行比较,经异常条件判定,使两种方法的结合可以充分发挥各自优势。对比验证分析模型与传统模型精度结果,结果表明,在所求测站MIZU上空及周边区域内建立模型相比于载波相位平滑法,日测点上空电离层(VTEC)的均方差(RMSE)提高3.992,稳定度提高59.44%;较预测模型法,日VTEC的RMSE提高3.458,稳定度提高53.99%。该方法有效提高预测模型实时性,削弱计算模型的不稳定性,提高电离层模型精度,支撑北斗导航研究。

基于张衡一号卫星数据的中国区域岩石圈磁场球冠谐分析

张衡一号卫星于2018年2月成功发射升空,卫星上搭载有测量地磁场的高精度磁强计,包括标量和矢量磁力仪.本文基于张衡一号卫星2018年3月—2022年5月的标量磁测数据,利用球冠谐分析进行中国区域的岩石圈磁场建模工作.首先选取地磁活动平静时期(Kp≤2o)的夜侧数据,来减少外源场的影响;然后,利用CHAOS-7模型计算值去除主磁场和外源场,得到岩石圈磁异常值,再利用球冠谐分析进行中国区域的地磁场建模,得到最大阶数为53.17(对应地表波长为752 km)的球冠谐模型.该模型可以明显揭示出中国及邻区的主要岩石圈磁异常,包括位于我国塔里木盆地、四川盆地、松辽盆地和境外的贝加尔湖、孟加拉盆地附近的高值磁异常,以及位于青藏高原南部的东西向低值磁异常.为了对模型结果进行进一步分析,将其与Swarm-A卫星数据球冠谐建模结果和CHAOS-7球谐模型结果在不同高度上进行了对比,主要磁异常的分布基本一致,而且在向下延拓到100 km高度时,本文的模型也能够提供比较稳定的结果,但是在幅值和磁异常形态细节上存在一定差异.

碳循环反演大数据模型的探索与分析

本文在分析碳源排放清单(R_(排放))、生物过程模拟植被净生态系统生产力(NEP_(植被))、大气层碳卫星监测CO_(2)浓度(CO_(2月平均浓度))三种反演时空分布数据的基础上,利用LM最优估算法结合球冠谐模型解析碳的基础量值及空间分布关系,通过计算机深度学习,构建基于上述三个模型融合的大数据模型,以期探明工业碳源排放清单CO_(2)较为明晰准确的反演过程和各个环节的数学关系,为有效的消碳提供技术路径支撑。

电离层预报模型研究

当利用无线电电磁波进行远程通信、卫星导航时，传递信号要受到电离层的影响，因此，对电离层中电子含量的研究显得特别重要．虽然国际上有几种电离层的电子含量预报模型，但其预报只能精确到电子含量的50％-60％．本文提出了一种新的电离层电子含量预报方法：即用球谐函数对IGS（国际GPS服务）所给出的离地面450km高的球面上的每一网点的电离层电子含量进行拟合，对不同的时间所得到的拟合系数所形成的时间序列用时间序列分析理论中的ARMA（p，q）模型进行预报，从而实现全球的电离层电子含量预报．利用本方法对2004年和2005年IGS所给电离层电子含量资料在地理框架中做了分析预报，5天内电子含量预报相对精度在90％左右．

基于GPS探测汶川地震电离层TEC的异常

利用球谐模型和中国地壳运动观测网络及IGS（International GNSS Service）基准站的GPS观测数据,分别计算了中国区域及全球电离层电子总含量（Total Electron Content,TEC）,采用了不同的统计分析方法,对汶川震中上空及邻近区域的TEC进行检查.结果发现：震前后一个星期,孕震区上空连续出现电离层异常扰动,其异常形态具有共轭结构,且呈现向磁赤道漂移趋势.

利用球冠谐分析方法和GPS数据建立中国区域电离层TEC模型

利用GPS实测资料建立了中国区域电离层TEC球冠谐分析模型（spherical cap harmonic analysis，SCHA），评估了该模型的精度和有效性。结果表明，该模型有较高的拟合精度，其拟合残差约为±3TECU，且精度在时间和空间上分布较均匀。根据IGS分析中心发布的IONEX全球电离层数据（GIM），内插得到了区域内相应时段的平均电离层电子含量，并利用它对CSHA模型的零阶项系数C0.0所表示的区域平均电离层电子含量进行了检核。结果表明，二者具有较高的一致性和相关性，其谱特征相关系数为0．993。由于SCHA模型较GIM模型利用了更多本区域的GPS观测数据，因此其拟合精度更高，拟合结果与实测数据更一致。对SCHA模型参数的时间序列进行谱分析，结果表明，该模型的模型系数较好地描述了区域电离层TEC的周期性变化特征。

融合BDS/GPS/GLONASS反演全球电离层特性研究

融合BDS/GPS/GLONASS三系统,采用载波相位平滑伪距观测值和球谐函数建立电离层延迟改正模型,并进行全球电离层反演实验。结果表明,电离层延迟格网值与IGS各分析中心最终产品对比,精度均在4TECu以内,均值为0.675TECu。与基准站GNSS实测TEC比较,差值的均值在5TECu以内。对计算得到的频间偏差月综合产品进行外符合精度和稳定性分析表明,GPS精度优于GLONASS,而BDS稳定性较差。

基于3D人脸重建的光照、姿态不变人脸识别

待匹配人脸图像与库存原型图像之间姿态和光照的差异是自动人脸识别的两个主要瓶颈问题,已有的解决方法往往只能单独处理二者之一,而不能同时处理光照和姿态问题.提出了一种对人脸图像中的姿态和光照变化同时进行校正处理的方法,即通过光照不变的3D人脸重建过程,将姿态和光照都校正到预先定义的标准条件下.首先,利用先验的统计变形模型,结合人脸图像上的一些关键点来恢复较为精细的人脸3D形状.基于此重建的3D形状,进而通过球面谐波商图像的方法估计输入图像的光照属性并提取输入图像的光照无关的纹理信息,从而将光照无关的3D人脸完全重构出来,生成输入人脸图像在标准姿态和光照条件下的虚拟视图,用于最终的分类识别,实现了对光照和姿态问题的同时处理.在CMUPIE数据库上的实验结果表明,此方法可以在很大程度上提高现有人脸识别方法对于原型集合(gallery)和测试集合中图像在姿态和光照不一致情况下识别结果的正确性.