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为了丰富SLR数据处理研究体系,完善标准点算法框架,研究者对SLR数据识别与滤波开展了充分的探讨与摸索。作为SLR数据处理面临的主要难题,数据的有效识别与滤波可提高SLR数据精度,改善算法运行效率,对生成高质量SLR数据产品具有重要意义。随着SLR数据建模与统计方法的不断完善,不同的SLR数据识别与滤波方法应用在数据处理过程中,主要包括:人工的屏幕处理法、直方图法、图像处理算法、卫星形状效应滤波算法等。
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人工屏幕处理技术是最原始的SLR回波信号提取方式。随着激光发射频率的提升,SLR回波数据量大幅度增长,噪声也随之增加。尽管SLR系统中采用多种滤波技术,如空间滤波、光谱滤波、时间滤波等技术抑制噪声,但仍无法解决白天或天气恶劣情况下系统低信噪比的问题[22-23]。为了解决上述问题,SLR测站多采用人工屏幕处理方法,利用数据坐标转换、翻转拉直等手段,人工地将明显的离群值剔除。该方法可快速识别包含大量噪声的微弱回波,适合各种类型数据的初步筛选。作为标准点算法的补充,屏幕处理法在中国科学院上海天文台、中国科学院长春人造卫星观测站(下面简称长春人卫站)、Zimmer-wald站等SLR台站都取得了不错的效果[24-26]。图4示出长春站SLR的屏幕处理结果。
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直方图法诞生于SLR发展早期,克服了人工屏幕处理法对研究人员经验的依赖性,是一种高效、简便的数据处理手段。直方图法基于回波信号的时间相关性,对SLR原始数据换算并统计距离的累加值,通过分析SLR回波的统计特征设定距离窗的大小、框间隔以及回波阈值,实现卫星回波的有效提取。当直方图中某一时间区域内的数据量超过设定阈值,则认为在该区间内存在SLR有效的回波数据[27]。典型的直方图法包括Graz快速回波辨识算法、SLR2000系统的相关检测算法、N/M算法等。表1为常见直方图法的优缺点。
表 1 常见直方图法优缺点
Table 1. Advantage and disadvantage of various histogram methods
Name Advantage Disadvantage 1 Graz echo identfying algorithm Human machine interface, simple to operate Low detection rates for high-orbit sateliltes 2 SLR2000 correlation algorithm Highly flexible and efficient for dealing
massive observation dataSensitive to the range window and low automation 3 N/M algorithm More adaptive, especially for low S/N ratio Complicated calculation and poor real-time performance 随着激光测距理论研究的不断完善,以直方图方法为基础衍生出了多种适用不同SLR系统的数据处理方法。1994年,针对单光子量级的LLR (Lunar Laser Ranging,LLR)与SLR系统,Ricklefs与Shelus等人以探测器响应的泊松过程为设计思想,提出了泊松滤波算法[28]。
在SLR过程中,背景噪声在距离内呈随机分布,而回波光子理论上服从以下分布:
$$p(k) = \frac{{N_s^k}}{{k!}}\exp ( - {N_s})$$ (1) 式中:
$ {N_s} = \dfrac{{{E_{rec}}}}{{hv}}$ 。泊松滤波算法从SLR回波光子数统计分布规律出发,利用矩形窗口对短时间间隔内的SLR数据进行斜率扫描,并对扫描结果进行直方图统计。当单位时间间隔内统计的回波点数超过阈值且符合泊松过程时,则判定该区域内存在有效回波数据。该方法不依赖高精度预报与趋势函数,可快速提取SLR的有效回波,且不会造成数据损失,是目前高精度SLR回波数据处理方法的代表之一。图5为泊松滤波原理示意图。
图 5 不同数据处理算法产生的SLR数据。(a)直方图法;(b)泊松滤波算法
Figure 5. SLR data generated by various data processing algorithm. (a) Histogram method; (b) Possion filtering method
泊松滤波算法是一种统计滤波算法,对SLR回波量级有着极高的要求。当激光脉冲强度改变或天气变化时,回波数据强度及分布也随之变化,直接影响数据处理结果。2016年,Rodriguez与Appleby等人提出了一种改进的泊松滤波方法[29]。该算法基于SLR单光子及多光子探测机制的分析,利用多光子探测方程评估在该时间间隔内探测器响应时的光子数,将不符合单光子探测的观测数据与噪声同时滤除,有效提高了SLR观测数据的质量。表2为泊松统计滤波算法计算不同卫星的处理结果。
表 2 泊松滤波、后处理算法产生的SLR数据
Table 2. SLR data generated by post-treatment and Possion filtering
Number Satellite Echo points by
post-treatmentEcho points by
Possion filteringObservation
arc length/s1 Ajisai 430 159 171.25 2 Jason-1 600 298 349.75 3 Stella 347 119 268.57 4 BE-C 723 372 316.87 5 ERS-1 284 97 144.50 2014年,Clarke等人发现在低信噪比情况下,经过泊松滤波处理后的SLR数据中仍存在一些与有效数据无法分离的背景噪声。为此,Clarke等人设计了一种噪声抑制算法,通过统计、比较背景噪声密度与原始数据密度,实现有效信号的筛选。当回波数据密度结果大于背景噪声密度时,则认为该区域内包含有效回波数据,并依据背景噪声密度随机剔除该区域内的数据点,进而获取SLR的有效回波。噪声抑制算法有效提升了回波点数据量及标准点精度,并减小了不同测站的数据结果差异[30]。
作为直方图法的另一典型代表,样条差值法常应用于自转周期性明显、回波数据曲线波动较大的卫星数据处理[31]。样条差值法是基于细分的统计算法,即将整个观测弧段分成细小的子弧段,然后分别在这些小的时间间隔内应用切比雪夫多项式对观测数据进行拟合,最后在时间间隔的边界点进行多项式匹配。该算法通过低阶多项式拟合,可有效提高数据处理精度,提供更好的标准偏差。图6为利用样条差值法处理的Topex卫星观测数据结果图。
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图像工程技术的出现为SLR数据处理带来了新的契机。以时间相关光子计数为基础的SLR系统在测距过程中出现了大量的噪声点。这些噪声点将呈现无规则的弥散分布,与卫星返回的有效光子呈交替存在。回波光子点云相对密集,而噪声点数据比较分散。为此,2011年雁雨等人提出一种基于点云曲线识别的SLR数据处理算法[32]。该算法将SLR数据视为点云数据,将数据分布网格化后,利用计算机视觉技术、遗传算法等方法确定点云的有效区域,再结合多项式拟合方法剔除离群点,多次迭代最终得到有效数据。
为了进一步改善激光测距数据处理中信号提取困难以及自动化程度不高的现状,2014年李熙提出一种基于二值图像的SLR数据处理方法[33]。将原始数据文件映射为二值图像,再利用区域处理方法将像素点分割,通过图片降噪的方法提取有效数据区域,最后做逆变换求解有效数据。结果表明,二值化方法充分考虑了信号点间的关系,在SLR自动数据处理方面有很好的效果,有效减少了人为误差。然而,该方法鲁棒性较差,在回波率较低时,数据处理结果并不理想。
随着人工智能技术的发展,机器视觉广泛应用于海量数据识别、信息深度挖掘以及图像轮廓提取等方面。2019年,Lixue等人基于深度卷积神经网络模型,利用DeepLabcut工具对SLR回波图像进行有效信号数字标记[34]。然而,由于SLR回波数据呈一维分布,无法在二维图像或视频中看到其回波特征,Deep Labcut无法有效区分SLR回波图像的有效信号点及噪声点。当回波图像帧数较少时,有效信号识别率仅为4%,不能满足高精度SLR数据处理的需求。
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作为影响SLR回波数据精度的最主要因素,卫星质心修正(Centre-of-Mass correction, CoM)误差是由角反射器的卫星形状效应引起的系统误差,其误差范围在10 mm以上[35]。在SLR过程中,卫星表面布满角反射器,发射光束中的同一波阵面的光子到达角反射器的时间不同,不同平面角反射器反射回波有先后之分,最前面的角反射器回波最早,两边的反射器回波较晚,不同的反射回波混叠在一起,导致回波波形的展宽和畸变,严重影响了系统的精度与稳定性[36]。图7为卫星形状效应示意图。
1976年,NASA在对Lageos角反射器阵列进行研究时发现,入射在球形卫星不同角反射器上的激光回波时刻存在明显差异[35]。由于当时技术水平的限制,由卫星形状效应引起的测距误差被其他误差如激光脉宽、探测器响应、大气误差等因素所掩盖,并没有得到重视。随着高重频SLR技术日益成熟,系统的回波点数大幅度增长,由卫星形状效应引起的回波分布的非对称性从噪声中显现出来。1994年,Neubert提出卷积方法,对卫星形状效应进行建模分析,计算了不同球形卫星的CoM值[37];2001年,范建兴等人通过概率密度函数建立了CoM模型,模拟了SLR回波波形[38];2003年,Toshimichi Otsubo等人分析了测站参数对CoM值的影响,讨论了SLR实际回波与理论模型函数的差异[39];2008年,Graz站基于卫星形状效应,提出了前沿切割算法以减小或消除卫星形状效应对SLR数据质量的影响[40](图8)。结果表明,当只选取Lageos有效数据前沿10%数据进行多项式拟合剔除异常值时,可大幅度提高SLR回波数据质量。2018年,Wilkinson与Rodriguez等人利用前沿切割算法对Herstmonceux测站Lageos-1、Lageos-2原始观测数据(2015~2018年)进行数据处理,验证了该算法可有效改善数据精度,但由于Lageos-1、Lageos-2卫星轨道不同,在相同切割位置时数据处理结果存在一定差异,其稳健性并不理想[41]。
为进一步减小或消除卫星形状效应,2016年,Graz站提出了零势效应算法[42]。该算法利用信号处理方法从SLR数据中提取Ajisai的旋转频率,通过建立Ajisai卫星的运动模型筛选Ajisai的有效回波。最后,综合分析Ajsai卫星角反射器的结构参数与分布,只保留测距站最近的角反射器回波数据。这一方法成功地将Aisai标准点精度从15.44 mm提升至3.05 mm,大幅度提高了Ajisai回波数据质量。
2018年,Riepl等人基于卫星形状效应提出了一种基于最优维纳滤波的去卷积算法[43]。利用维纳滤波算法平滑SLR数据分布曲线,根据卫星形状效应模型对SLR数据进行反卷积,并生成了标准点数据。同时,对Wettzell站的Lageos、Ajisai、Etalon等SLR原始数据进行处理。结果表明,维纳滤波算法明显优于2倍中误差的标准点算法。
2019年,长春人卫站刘源等人开展了卫星形状效应的研究,并提出边缘滤波算法[44]。该算法沿承了前沿切割算法的思想,根据不同球形卫星的回波特性对数据进行剪切,选取了回波数据半峰宽内的回波数据,滤除了大量噪声点。与基本滤波算法相比,边缘滤波算法处理的SLR标准点精度约提高20%~50%。
Development review of satellite laser ranging data processing technology
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摘要: 数据处理技术的发展与进步是实现毫米级卫星激光测距(Satellite Laser Ranging,SLR)的重要保障。文中简要回顾了SLR技术的发展历程,阐述了数据处理技术在SLR的实际应用,着重介绍了国内外典型的数据处理算法及其发展脉络。同时,针对大地测量产品的应用需求,分析了目前SLR数据处理算法的适用性、稳定性及存在的问题。最后,针对激光测距的未来发展态势,提出了新一代SLR数据处理方法面临的挑战及可能的解决方案,并对其发展趋势做出展望。Abstract: The development and progress of data processing technology is important to guarantee the realization of millimeter-level satellite laser ranging (Satellite Laser Ranging, SLR). The history and research actuality of SLR technology were reviewed briefly, the practical application of data processing methods in SLR was introduced emphatically, and the typical data processing algorithms and its development at home and abroad were summarized. At the same time, the suitability, stability and technical problems of the existing SLR data processing algorithms were concluded and analyzed in accordance with the applicable demands and features of geodetic data products. Finally, in view of the future development trend of laser ranging, the challenges and possible solutions of the new generation of SLR data processing methods were proposed and its development trend was prospected.
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Key words:
- satellite laser ranging /
- data processing /
- normal point algorithm /
- data quality
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表 1 常见直方图法优缺点
Table 1. Advantage and disadvantage of various histogram methods
Name Advantage Disadvantage 1 Graz echo identfying algorithm Human machine interface, simple to operate Low detection rates for high-orbit sateliltes 2 SLR2000 correlation algorithm Highly flexible and efficient for dealing
massive observation dataSensitive to the range window and low automation 3 N/M algorithm More adaptive, especially for low S/N ratio Complicated calculation and poor real-time performance 表 2 泊松滤波、后处理算法产生的SLR数据
Table 2. SLR data generated by post-treatment and Possion filtering
Number Satellite Echo points by
post-treatmentEcho points by
Possion filteringObservation
arc length/s1 Ajisai 430 159 171.25 2 Jason-1 600 298 349.75 3 Stella 347 119 268.57 4 BE-C 723 372 316.87 5 ERS-1 284 97 144.50 -
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