The Method of Differential Measurement of Astronomical Refraction and Results of Trial Observations

Because of the influence of atmospheric refraction the astronomical observations of the objects with the angles of elevation below 15° are generally avoided, but for the sake of the complete theoretical research the atmospheric refraction under the condition of lower angles of elevation is still worthy to be analyzed and explored. Especially for some engineering applications the objects with low angles of elevation must be observed sometimes. A new idea for determining atmospheric refraction by utilizing the differential method is proposed. A series of observations of the starry sky at different heights are carried out and by starting from the zenith with a telescope with larger field of view, the derivatives of various orders of atmospheric refraction function at different zenith distances are calculated and finally the actually observed values of atmospheric refraction can be found via numerical integration. The method does not depend upon the strict local parameters and complex precise observational instrumentation, and the observational principle is relatively simple. By the end of 2007 a simply constructed telescope with a larger field of view at Xinglong Observing Station was employed to carry out trial observations. The values of atmospheric refraction at the true zenith distances of 44.8° to 87.5° were obtained from the practical observations based on the differential method, and the feasibility of the method of differential measurement of atmospheric refraction was preliminarily justified. Being limited by the observational conditions, the accuracy of the observed result was limited, the maximal accidental error was about 6” and there existed certain systematic errors. The value of the difference between the result obtained at the zenith distance of 84° and that given in the Pulkovo atmospheric refraction table was about 15”. How to eliminate the cumulative error introduced due to the integration model error is the key problem which needs to be solved in future.     

测定天文大气折射和建立电磁波折射延迟实测模型(Ⅵ)-瞬时大气折射值和折射率差的取得

根据测定天文大气折射的原理,叙述了利用相应的观测值获得瞬时大气折射测定值和建立大气折射实测模型的途径,并从各种测定值与最后结果之间的关系,指出了这里对数据处理的要求;文章介绍了对测定值进行波长改正和建立折射延迟实测模型的处理方法,分析了改正模型对天文大气折射测定值的分布要求,给出了观测数据随天顶距的增大而加密的分布模型。     

提高中性大气折射延迟改正精度的可能途径

针对空间大地测量技术对中性大气折射延迟改正精度的要求,阐述了折射延迟改正值应随测站和随方位而异的必要性．指出,在尚不能直接测定天文大气折射值的情况下,现有的各种改正模型对大气分布模型的依赖性,不能达到预期的精度和降低观测的截止角．根据云南天文台低纬子午环的特殊结构,和测定大气折射的实践,提出了提高折射延迟改正精度的新方法,即：利用各观测站不同方位从天顶附近直到低地平高度角的天文大气折射实测数据,求解得到折射率差和映射函数的参数,从而建立随测站和随方位而异的大气折射延迟改正模型．这一新方法的实施,将能在不需采用大气分布模型的情况下,把天顶延迟的改正精度提高到1 mm以内,低地平高度角的折射延迟改正精度提高到厘米级,并且把截止高度角压缩到5°以内．     

On Astronomical Atmospheric Refraction

Through a comparison between the series expression and mapping function expression of the astronomical refraction, we believe that, as far as a specific atmospheric refraction model is concerned, the computational accuracy is not lower in the former than in the latter, and that the convergence is poorer in the theoretically derived series expression, because of the different approximations made. From an analysis of the method of generating function of the atmospheric refraction mapping function it is considered that this kind of method can not embody the characteristics of geophysics and atmospheric physics. It is pointed out from the comparison that the atmospheric refraction model which is constructed by adopting the specific atmospheric distribution of a certain place does not apply to all other places and cannot be used to evaluate the other atmospheric refraction models. For improving the correction accuracy the key lies in the adoption of an effective method by which the instantaneous refraction values at different positions are directly determined to construct a local, position-dependent model of atmospheric refraction observation.     

实测大气折射值的新方法

简单评述了现有各种版本的大气折射表所依据的理论基础和编制方法，指出了实测大气折射值、建立随地形而异的实测大气折射模型的必要性和应具备的基本条件；在分析了长期以来不能直接测定大气折射值的原因后，介绍了一种在不同方向精确测定大气折射值和建立观测点大气折射模型的新方法，以及所依赖的观测仪器具备的特性，最后给出了用实测数据建立的本地大气折射模型。     

A Possible Means of Improving the Accuracy of Refraction Delay Correction of Neutral Atmosphere

The space geodetic technology requires an accurate model of correction of refraction delay by the neutral atmosphere that varies from one observing station to another, and from one azimuth to the next. It is pointed out that under the present condition the astronomical refraction can not yet be directly determined, any correction model because of its high dependence on the assumed atmospheric distribution, is incapable of achieving the required accuracy or of improving the cut-off altitude. In this paper, based on the special properties of the lower latitude meridian circle at Yunnan Observatory and our experience of determining atmospheric refraction therewith, a new method is proposed for improving the accuracy of refraction delay correction. Namely, the measured data of astronomical refraction of an observing station from near zenith to low altitudes in different azimuths are used to evaluate the refractivities and the parameters of the mapping functions, thereby establishing a model of atmospheric refraction delay correction that varies with the observing station and the azimuth. Since it is unnecessary for the new method to adopt any atmospheric distribution model, application of this new method will improve correction accuracy of refraction delay to better than 1mm at zenith and to centimeters at low altitudes, and improve the cut-off altitude to below 5 degrees.     

测定天文大气折射和建立电磁波折射延迟实测模型(Ⅰ)-观测原理和可行性

简述了天文大气折射和电磁波中性大气折射延迟的成因,以及不同观测站、不同方位的折射值存在差异的事实;根据测定瞬时天文大气折射、建立本地实测模型的观测原理和要求,分析了长期以来不能直接测定天文大气折射的几个主要障碍,介绍了现已具备的排除这些障碍的必要条件,为建立天文大气折射实测模型,和随观测站、随方位而异的电磁波折射延迟改正模型提供了保证。     

测定天文大气折射和建立电磁波折射延迟实测模型(Ⅳ)-瞬时天文纬度测定值

根据测定天文大气折射的原理,以及建立电磁波折射延迟改正模型的需要,叙述了对瞬时天文纬度测定值的严格要求;分析了经典测量仪器和空间大地测量技术所得的瞬时纬度测定值在这里不适用的原因;提出采用子午方向以外的各给定方位的时角测定值与计算值之差,解算瞬时纬度测定值的新方法,以避免大气折射修正值残差的影响;文章对观测数据的处理提出了特殊要求,并论述了所拟专用测量仪器对实施这一方法的可行性。     

研究大气反常折射的迫切性

就地球大气对天体测量观测的影响作了分类，介绍了对各类影响的传统处理方法，也介绍了低纬子午环的分别对待方法，特别强调了短周期的和不规则的反常折射影响对提高观测精度的限制，并提出了测定这些影响的可能途径。     

大气折射母函数方法、大气折射解析解和映射函数

回顾了作为实用天文学和大地测量学中基本研究课题之一的大气折射映射函数研究的进展。介绍了近几年上海天文台发展的大气折射母函数方法 ,以及由此导出的大气折射解析解。对如今广泛地应用在空间测量技术中的几种映射函数做出评述 ;分析了NMF模型的优点和不足之处。介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天文大气折射的映射函数方法。利用VLBI实验中高度截止角与基线长度重复率的关系、探空气球 (radiosonde)观测资料、PRARE资料比较了各种映射函数的结果。特别指出了映射函数方法对天文大气折射和光学波段测距精度的改进。讨论了大气折射计算中的主要误差源。     

天文实测蒙气差的研究

建立在子午—卯酉交替观测原理基础上的低纬子午环（ＬｏｗＬａｔｉ－ｔｕｄｅＭｅｒｉｄｉａｎＣｉｒｃｌｅ）即将出厂投入调试及试运行阶段，进一步研究天文蒙气差修正将是低纬子午环进行高精度观测的重要保证之一。作为对天文蒙气差修正的初步研究，本文首先分析了影响天文蒙气差的主要气象因素，对蒙气差随各种条件的变化情况进行了讨论；在此基础上，推算了大气平面平行层模型以及同心球层模型下的蒙气差值，论述了蒙气差表的编制方法，进而对各种蒙气差理论公式计算所得的修正值进行了分析比较；针对理论计算蒙气差值精度的不足，本文着重阐述了利用低纬子午环（ＬＬＭＣ）进行大气蒙气差实测的方法、原理，较为详尽的说明传统的方法不能满足实测大气折射的要求，而低纬子午环由于自身一些新的特点，能够满足Ｔｅｌｅｋｉ所提出的四个要求；在此基础上推导了相应的计算公式并进一步探讨了实测大气等密度倾斜的方法，最后给出了相应的精度估计，就如何建立一个适合于观测点的实用的实测大气模型进行了探讨     

Research on the Method of Orbit Determination Based on the Self-adaptive Stable Least p-norm Estimate

The traditional least square estimation (LSE) method for orbit determination will not be optimal if the error of observational data does not obey the Gaussian distribution. In order to solve this problem, the least p-norm (Lp) estimation method is presented in this paper to deal with the non-Gaussian distribution cases. We show that a suitable selection of parameter p may guarantee a reasonable orbit determination result. The character of Lp estimation is analyzed. It is shown that the traditional Lp estimation method is not a robust method. And a stable Lp estimating based on data depth weighting is put forward to deal with the model error and outlier. In the orbit determination process, the outlier of observational data and coarse model error can be quantitatively described by their weights. The farther is the data from the data center, the smaller is the value of data depth and the smaller is the weighted value accordingly. The result of the new Lp method is stabler than that of the traditional Lp estimation and the breakdown point could be up to 1/2. In addition, the orbit parameter is adaptively estimated by residual analysis and matrix estimation method, and the estimation efficiency is enhanced. Finally, by taking the Space-based Space Surveillance System as an example and performing simulation experiments, we show that if there are system error or abnormal value in the observational data or system error in satellite dynamical model and space-based observation platform, LSE will not be optimal even though the observational data obeys the Gaussian distribution, and the orbit determination precision by the self-adaptive robust Lp estimation method is much better than that by the traditional LSE method.     

对流层大气折射延迟改正：（Ⅱ）：当前主要研究方向和进展

在文献「１」，综述了对流层大气折射延迟改正的基本概念和研究方法。本文中，介绍了在此领域中的主要研究方向的动态，以及一些最新成果。同时，还评述和分析了这些研究工作的主要特色和将来的发展方向。在本文的第８节，简要地介绍了作者在大气折射研究中的最新进展－大气折射母函数方法。     

中性大气折射映射函数和大气折射母函数方法

回顾了作为实用天文学和大地测量学中基本研究课题之一的大气折射函数研究的最新进展;介绍了近几年发展的大气折射母函数方法。对如今广泛地应用在空间测量技术中的几种映射函数,如ＣｆＡ２．２、ＭＴＴ等模型作出评述;特别分析了ＮＭＦ模型的优点和不足之处。还介绍了由大气折射母函数方法引出的大气延迟新连分式映射函数和天文大气折射的映射函数方法,利用ＶＬＢＩ实验中高度截止角与基线长变化的关系和探空气球（ｒａｄｉｏｓ     

Comparative evolution of Jupiter and Saturn

We present evolutionary sequences for Jupiter and Saturn, based on new non-gray model atmospheres, which take into account the evolution of the solar luminosity and partitioning of dense components to deeper layers. The results are used to set limits on the extent to which possible interior phase separation of hydrogen and helium may have progressed in the two planets. When combined with static models constrained by the gravity field, our evolutionary calculations constrain the helium mass fraction in Jupiter to be between 0.20 and 0.27, relative to total hydrogen and helium. This is consistent with the Galileo determination. The helium mass fraction in Saturn’s atmosphere lies between 0.11 and 0.21, higher than the Voyager determination. Based on the discrepancy between the Galileo and Voyager results for Jupiter, and our models, we predict that revised observational results for Saturn will yield a higher atmospheric helium mass fraction relative to the Voyager value.     

测定天文大气折射和建立电磁波折射延迟实测模型(Ⅲ)-专用测量仪器

针对用天文大气折射测定值,建立随观测站和随方位而异的电磁波折射延迟改正模型的高精度要求,提出了新的仪器误差理论,其主要内容是允许仪器误差存在,并看成是不断变化的,采用相应的测量方法作实时的测定和修正,同时消除仪器的各种变形和误差的影响,排除观测数据中的各种系统误差来源,并达到提高单次测定精度目的;文中还针对不同纬度的观测站、多方位、从天顶直到低空的观测需要,给出了仪器总体结构的安排,和采用视频CCD作为接收器的终端设计方案,也给出了各种仪器误差的测定方法和测量装置的设计要求。     

Fourier-component phase accumulation in observation of an object through a turbulent atmosphere: I

We discuss the problem of obtaining a diffraction-limited image when an object is observed through a medium with random inhomogeneities of refraction index. A new method for post-detector signal accumulation over a significantly long sequence of instantaneous images is examined. The effectiveness of the method is illustrated by the example of images obtained by computer simulation.     

关于大气分布模型

简述了大气垂直分布情况和高空探测方法,分析了目前只能采用球对称大气分布模型的原因;论证了随观测站、随方位而异的天文大气折射实测模型和折射延迟改正模型,已经包含了观测站上空大气实际分布的非球对称特性,不必再去寻找或建立随地势而异和随季节而变的大气分布模型,避免了大气分布模型选择不当的影响,从一个方面为提高天文大气折射改正精度和电磁波大气折射延迟改正精度提供了保证。     

The correction of atmospheric dispersion in LAMOST

Atmospheric refraction and dispersion affect the observational quality and efficiency of the Large Sky Area Multi-object Fiber Spectroscopic Telescope (LAMOST). In this paper, by both ZEMAX simulation and numerical calculation, the atmospheric dispersion for LAMOST, which will be installed at the latitude 40°.4 and has a 20 m focal length and F5 focal ratio, are calculated for the 0.75 h before and after the transit time. Various types of dispersion prism to be used for correcting the atmospheric dispersion in LAMOST were calculated and analyzed, from which one was finally adopted. The secondary spectrum of the dispersion prism, the residual dispersion during tracking of the telescope and the installation errors of the dispersion prism are investigated.     

Homogeneous and Heterogeneous Observational Data Weighting Method of Combined Orbit Determination of Near-earth Satellites of Bi-satellite Positioning System and its Applications

In the light of the problem of amalgamation and processing of multisource observational data in the combined orbit determination of near-earth satellites of the bi-satellite positioning system, the optimal weighting method of the improved variance component estimation of the two-step systematic error correction of homogeneous observational data is proposed. Analyses show that the multi-source amalgamation measurement model of the heterogeneous observational data essentially is a multi-structure, multi-parameter non-linear regression model, and the optimal weighting method of the combination of model structure characteristic analysis and variance component estimation of the heterogeneous observational data is established. The realization algorithms of the optimal weighting and the combined orbit determination parameter estimation of the two sorts of observational data are designed, and the simulation experiments of the combined orbit determination are carried out by taking the distances among the two satellites and the backup satellite and the homogeneous observational data and the distance between the two satellites and the heterogeneous observational data of satellite sensor angle measurements as the examples. The results of theoretical analysis and simulation calculation show that for the combined orbit determination of homogeneous observational data, the accuracy of orbit determination obtained by adopting the variance component estimation method of the two-step systematic error correction can be more superior than that obtained by means of the traditional empirical weighting method. For the combined orbit determination of heterogeneous observational data, through the introduction of the weighting factor by which the model structure is characterized the accuracies of the combined orbit determination of the near-earth satellite and geostationary satellite are both improved to a certain extent in comparison with the mean weighting mode.