Lateral resection in three dimensions

An equation is developed to obtain the azimuths to the known observed points in space, thus reducing the solution to one of intersection.     

Geodetic applications of conformal transformations in three dimensions by M. Hotine

Sans résumé

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Geodetic applications of conformal transformations in three dimensions by M. Hotine

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The online version of the original article can be found at     

利用三颗导航卫星进行二维定位的解算模型及其仿真解算

给出了用户接收机只收到三颗导航卫星信号时的二维定位解算模型及其解算方法，重点介绍了解算方法中接收机概略坐标的求法及利用得到的概略坐标求解接收机位置和钟差，并做了仿真解算。从卫星和接收机不同位置的很多次仿真解算结果表明，接收机位置和钟差能够极收收敛，通常迭代两次就能得到非常好的结果，完全适合工程应用。     

高斯投影公式的机助推导

随着GPS应用的普及,高斯投影在测量中出现的机会越来越多。许多文献上都给出了推导过程,这个推导过程的运算量是非常大的,而且计算精度难于提高。经过研究,一种易于编程的递推公式被发现,虽然这个公式在计算量上没有减少,但是可以较好地解决精度问题。     

网平差中确定必要观测数的统一公式

在测量平差中,为使确定必要观测数更加简单,针对常见的四类控制网分别总结出公式,通过概括,构建了适用于多种网型及各种观测条件下确定必要观测数的统一公式。     

基于条件方程的方差分量估计公式

著名的Helmert方差分量估计公式是基于间接观测平差模型导出的。基于条件观测平差模型导出了方差分量估计公式并给出了实际应用范例,且对两种模型的方差分量估计公式的等价性进行了理论证明。算例表明,文中的估计公式能正确地估计出各类观测值的方差因子。     

Two deterministic and three stochastic modifications of Stokes’s formula: a case study for the Baltic countries

In regional gravimetric geoid determination, it is customary to use the modified Stokes formula that combines local terrestrial data with a global geopotential model. This study compares two deterministic and three stochastic modification methods for computing a regional geoid over the Baltic countries. The final selection of the best modification method is made by means of two accuracy estimates: the expected global mean square error of the geoid estimator, and the statistics of the post-fit residuals between the computed geoid models and precise GPS-levelling data. Numerical results show that the modification methods tested do not provide substantially different results, although the stochastic approaches appear formally better in the selected study area. The 2.8–5.3 cm (RMS) post-fit residuals to the GPS-levelling points indicate the suitability of the new geoid model for many practical applications. Moreover, the numerical comparisons reveal a one-dimensional offset between the regional vertical datum and the geoid models based upon the new GRACE-only geopotential model GGM01s. This gives an impression of a greater reliability of the new model compared to the earlier, EGM96-based and somewhat tilted regional geoid models for the same study area.     

Helmert方差分量估计严密公式与简化公式等价性的证明

在分析了Helmert方差分量估计严密公式与简化公式迭代收敛结果一些统计性质的基础上,导出了关于收敛结果共同的求解方程,从理论上证明了两种结果的等价性,为使用简化公式提供了依据。     

由空间直角坐标计算大地坐标的简便公式

对大地测量教科书中给出的空间三维直角坐标与大地坐标的转换公式进行了大量的计算与分析，总结得出一组由空间直角坐标计算大地坐标的简便公式。     

The IAG approach to the atmospheric geoid correction in Stokes' formula and a new strategy

The well-known International Association of Geodesy (IAG) approach to the atmospheric geoid correction in connection with Stokes' integral formula leads to a very significant bias, of the order of 3.2 m, if Stokes' integral is truncated to a limited region around the computation point. The derived truncation error can be used to correct old results. For future applications a new strategy is recommended, where the total atmospheric geoid correction is estimated as the sum of the direct and indirect effects. This strategy implies computational gains as it avoids the correction of direct effect for each gravity observation, and it does not suffer from the truncation bias mentioned above. It can also easily be used to add the atmospheric correction to old geoid estimates, where this correction was omitted. In contrast to the terrain correction, it is shown that the atmospheric geoid correction is mainly of order H of terrain elevation, while the term of order H ² is within a few millimetres. Received: 20 May 1998 / Accepted: 19 April 1999     

Scaling dimensions in spectroscopy of soil and vegetation

The paper revises and clarifies definitions of the term scale and scaling conversions for imaging spectroscopy of soil and vegetation. We demonstrate a new four-dimensional scale concept that includes not only spatial but also the spectral, directional and temporal components. Three scaling remote sensing techniques are reviewed: (1) radiative transfer, (2) spectral (un)mixing, and (3) data fusion. Relevant case studies are given in the context of their up- and/or down-scaling abilities over the soil/vegetation surfaces and a multi-source approach is proposed for their integration.Radiative transfer (RT) models are described to show their capacity for spatial, spectral up-scaling, and directional down-scaling within a heterogeneous environment. Spectral information and spectral derivatives, like vegetation indices (e.g. TCARI/OSAVI), can be scaled and even tested by their means. Radiative transfer of an experimental Norway spruce (Picea abies (L.) Karst.) research plot in the Czech Republic was simulated by the Discrete Anisotropic Radiative Transfer (DART) model to prove relevance of the correct object optical properties scaled up to image data at two different spatial resolutions. Interconnection of the successive modelling levels in vegetation is shown. A future development in measurement and simulation of the leaf directional spectral properties is discussed.We describe linear and/or non-linear spectral mixing techniques and unmixing methods that demonstrate spatial down-scaling. Relevance of proper selection or acquisition of the spectral endmembers using spectral libraries, field measurements, and pure pixels of the hyperspectral image is highlighted. An extensive list of advanced unmixing techniques, a particular example of unmixing a reflective optics system imaging spectrometer (ROSIS) image from Spain, and examples of other mixture applications give insight into the present status of scaling capabilities.Simultaneous spatial and temporal down-scaling by means of a data fusion technique is described. A demonstrative example is given for the moderate resolution imaging spectroradiometer (MODIS) and LANDSAT Thematic Mapper (TM) data from Brazil. Corresponding spectral bands of both sensors were fused via a pyramidal wavelet transform in Fourier space. New spectral and temporal information of the resultant image can be used for thematic classification or qualitative mapping.All three described scaling techniques can be integrated as the relevant methodological steps within a complex multi-source approach. We present this concept of combining numerous optical remote sensing data and methods to generate inputs for ecosystem process models.     

A strict formula for geoid-to-quasigeoid separation

The paper presented by Flury and Rummel (J Geod 83:829–847, 2009) discusses an important topographic correction to the traditional formula for the quasigeoid-to-geoid separation. Nevertheless, as their formula is approximate, the reader may ask for its relation to the strict one (defined as the one consistent with Bruns’s formula and the boundary condition of physical geodesy), which is now derived. Although the result formally differs from that of Flury and Rummel, we show that the two formulas agree to the centimetre level all over the Earth. We also discuss the practical computation of the topographic correction.     

Sonifying data uncertainty with sound dimensions

ABSTRACT

The communication of data uncertainty is a crucial problem in data science, information visualization, and geographic information science (GIScience). Effective ways to communicate the uncertainty of data enables data consumers to interpret the data as intended by the producer, reducing the possibilities of misinterpretation. In this article, we report on an empirical investigation of how sound can be used to convey information about data uncertainty in an intuitive way. To answer the research question How intuitive are sound dimensions to communicate uncertainty? we carry out a cognitive experiment, where participants were asked to interpret the certainty/uncertainty level in two sounds A and B (N = 33). We produce sound stimuli by varying sound dimensions, including loudness, duration, location, pitch, register, attack, decay, rate of change, noise, timbre, clarity, order, and harmony. In the stimuli, both synthetic and natural sounds are used to allow comparison. The experiment results identify three sound dimensions (loudness, order, and clarity) as significantly more intuitive to communicate uncertainty, providing guidelines for sonification and information visualization practitioners.     

A general formula and its inverse formula for gravimetric transformations by use of convolution and deconvolution techniques

A general formula is developed and presented for transformations among geoidal undulation, gravity anomaly, gravity disturbance and other gravimetric quantities. Using a spectral form of the general formula, a criterion has been built in order to classify these transformations into forward and inverse transformations in this paper. Then, the two-dimensional convolution techniques are applied to the general formula to deal with the forward transformation while the two-dimensional deconvolution techniques are employed to treat the inverse transformation and evaluate the inverse general formula. Concepts of convolution and deconvolution are also reviewed in this paper. The stability and edge effect problems related to the deconvolution techniques are investigated using simulated data and numerical tests are done to quantify the stability of the deconvolution techniques for estimated gravity information. Finally, the marine gravity information for the Norwegian-Greenland Sea area has been derived from ERS-1 altimetry data using the deconvolution techniques.     

Taylor expansion of the theoretical gravity formula

A recurrence relation has been derived to obtain the derivatives required for the Taylor expansion of the theoretical gravity formula in powers of latitude. The computations using the relationship derived can provide easily all required derivatives for any reference ellipsoid.