共查询到18条相似文献,搜索用时 281 毫秒
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根据反对称矩阵和罗德里格矩阵的性质,针对线性转换模型线性化复杂、计算量大和误差大等缺点,通过采用反对称矩阵中的三个独立参数来代替旋转矩阵中的九个相关参数,推导出了基于罗德里格矩阵的坐标转换模型。相对于其他的一些线性转换模型,该模型简单且便于计算,其较高的计算精度也通过将基于罗德里格矩阵的坐标转换模型应用于盾构姿态测量中而得到了验证。 相似文献
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罗德里格矩阵在三维坐标转换严密解算中的应用 总被引:6,自引:0,他引:6
利用反对称矩阵和罗德里格矩阵的性质,把传统的三个旋转角参数用反对称矩阵的三个独立元素代替,推导了用三个公共点计算任意旋转角情况下的7个参数的直接计算公式,井建立了相应的平差模型。 相似文献
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3维坐标转换参数直接计算的严密公式 总被引:19,自引:0,他引:19
首先对坐标转换的物理意义进行解释,又把传统3个旋转角参数用反对称矩阵的3个元素代替,推出用3个和4个公共点直接计算转换参数的严密公式,在此基础上推导出严密的线性化公式。由于不用进行三角函数计算,只用简单加减乘除,也不用迭代计算,所以该模型计算速度快。 相似文献
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利用反对称矩阵和罗德里格矩阵的性质,把传统旋转角参数用反对称矩阵的3个独立元素代替,推导了用三个公共点坐标计算7个参数的公式,并建立了相应的平差模型.并通过实测数据,验证了该方法的可行性. 相似文献
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三维坐标转换一直是测量领域的一个重要内容。针对现有算法普遍存在的不适用大旋角转换、计算繁杂等缺点,从旋转矩阵的表达方式入手,提出了一种基于罗德里格矩阵的三维坐标转换方法。算例分析表明,文中方法无需线性化,计算简便,且能适用大旋角转换。 相似文献
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针对三维坐标转换模型参数估计的核心是旋转矩阵的表示方法这一客观事实,该文通过对现有三维坐标转换模型中不同旋转矩阵的表示方法进行研究,依据任何一个方阵都可以惟一地分解为一个对称矩阵与一个反对称矩阵之和的矩阵理论,提出了一种使用反对称矩阵表示旋转矩阵的新方法,并详细推导了基于布尔莎模型的三维坐标转换算法——平方根矩阵法;最后,根据文献算例对该方法进行实验分析。实验结果表明,该算法适用于大旋转角,且相较于方向余弦法、罗德里格矩阵法和单位四元数法具有计算收敛速度快、精确度高的优点。 相似文献
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基于布尔莎空间坐标转换的自检校误差模型,旋转参数的线性化要顾及角度的象限问题,计算过程繁琐且计算量大,而罗德里格矩阵的应用能有效地提高自检校误差模型的效率和精度.本文对新自检校误差模型进行了详细推导,并提出了新模型有效性评定的方法.通过0.5″级全站仪和三维激光扫描仪同步采集数据,分别利用两种模型进行数据处理和对比,确定新自检校误差模型的实用性,验证了基于罗德里格矩阵的自检校误差模型的可行性. 相似文献
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Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: the traditional ? rotation angles θ, φ, ψ are substituted with a,b,c which are three respective values in the anti-symmetrical or Lodrigues matrix; ? directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ? a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick. 相似文献
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YAO Jili XU Yufei XIAO Wei 《地球空间信息科学学报》2007,10(3):173-176
Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick. 相似文献
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针对求解7参数的过程中,经典的线性化最小二乘法因需线性化、迭代及初值以及存在算法耗时出现不收敛现象的问题,该文对无须迭代的7参数坐标变换公式进行了研究。为避免各类参数间的相关性,采用消去法并按照依次求解旋转参数、比例系数和平移参数的顺序解得坐标变换参数。先利用最小二乘法求解旋转参数,然后通过构建目标函数的方式求解比例系数与平移参数,最终得到无须线性化、无须迭代、无须初值的,可用于大旋转角的7参数坐标变换公式。与线性化最小二乘方法进行相比,该方法具有相当的精度及更高的运算效率,可在一定程度上丰富坐标变换理论。 相似文献
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The weighted Procrustes algorithm is presented as a very effective tool for solving the three-dimensional datum transformation
problem. In particular, the weighted Procrustes algorithm does not require any initial datum parameters for linearization
or any iteration procedure. As a closed-form algorithm it only requires the values of Cartesian coordinates in both systems
of reference. Where there is some prior information about the variance–covariance matrix of the two sets of Cartesian coordinates,
also called pseudo-observations, the weighted Procrustes algorithm is able to incorporate such a quality property of the input
data by means of a proper choice of weight matrix. Such a choice is based on a properly designed criterion matrix which is
discussed in detail. Thanks to the weighted Procrustes algorithm, the problem of incorporating the stochasticity measures
of both systems of coordinates involved in the seven parameter datum transformation problem [conformal group ℂ7(3)] which is free of linearization and any iterative procedure can be considered to be solved. Illustrative examples are
given.
Received: 7 January 2002 / Accepted: 9 September 2002
Correspondence to: E. W. Grafarend 相似文献
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三维坐标转换参数求解的一种直接搜索法 总被引:1,自引:0,他引:1
采取了两步措施简化三维坐标转换非线性模型:①旋转矩阵的3个旋转角用一个反对称矩阵的3个独立元素代替,将旋转矩阵由反对称矩阵构成Lodrigues矩阵;②将坐标转换7参数模型变换成基线向量模型,消去平移3参数.然后,采用遗传算法与模式搜索法相结合的一种直接搜索法求解参数.算例表明,该算法是可行的.最后,从坐标转换精度的角度时基线向量模型原点与公共点的选取进行了分析,结论是原点选取的点的精度相对较高时坐标转换精度相对较高,公共点的选取以3~5个精度高的点为宜. 相似文献
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A Quaternion-based Geodetic Datum Transformation Algorithm 总被引:1,自引:1,他引:1
This paper briefly introduces quaternions to represent rotation parameters and then derives the formulae to compute quaternion, translation and scale parameters in the Bursa–Wolf geodetic datum transformation model from two sets of co-located 3D coordinates. The main advantage of this representation is that linearization and iteration are not needed for the computation of the datum transformation parameters. We further extend the formulae to compute quaternion-based datum transformation parameters under constraints such as the distance between two fixed stations, and develop the corresponding iteration algorithm. Finally, two numerical case studies are presented to demonstrate the applications of the derived formulae. 相似文献