利用半参数模型精化二次曲面GPS高程异常拟合模型

针对利用多项式建立的GPS高程拟合模型不能很好地拟合高程异常变化趋势面的问题,提出了在常规最小二乘多项式模型的基础上,引入一个非参数模型补偿项,并参考重力测量中最小二乘配置模型方法,建立高程异常趋势面的半参数拟合模型。以小区域GPS采集数据为例,并分别运用两种模型进行拟合与推估,结果表明,基于半参数模型的高程异常拟合与推估效果更好。     

拟合推估两步极小解法

在回顾了最小二乘拟合推估的“综合极小”解法（正常拟合推估）后，分析了正常拟合推估存在的问题。考虑到随机场信号不一定完全表现为随机性，其中可能含有趋势性，顾而提出了拟合推估的“两步极小”解法，即将随机场分成趋势性部分和随机性部分，对趋势性部分采用函数拟合，对随机性部分采用协方差函数拟合。给出了“分两步极小”拟合推估的2种解法。计算表明，两步极小解法能部分地改善拟合推估的精度。     

基于自适应拟合推估的最小二乘配置改进模型在地壳形变分析中的应用研究

系统论述在地壳形变场的构建过程中,以最小二乘配置模型作为基础结合自适应拟合推估法对模型加以改进的方法.通过建立自适应因子对信号向量与观测向量间的先验权比进行调整,以提高对形变量推估的准确性,防止并克服由于协方差函数选择不合理所产生的系统偏差.以川滇菱形块体GPS速度场作为实例进行对比分析,结果显示,基于最小二乘配置的自适应拟合推估模型能够更为准确地反映区域形变特征.     

多种地图坐标系统的转换方法及比较

为了统一获取不同坐标系下的地图产品,通常需要进行坐标系统的转换.通过对仿射变换(或相似变换)、最小二乘拟合推估和最小曲率格网三种常用的坐标转换方法的对比,并结合实例的具体分析,得出最小曲率格网与自适应拟合推估法均能较好地控制局部形变的影响,具有较高的拟合精度的结论.     

最小二乘配置法在GPS高程异常推估中的应用

简述了最小二乘配置法的基本原理,并在水准联测点不多的情况下,直接采用平方根函数作为各随机参数间的协方差函数用于推估GPS高程异常值。由于最小二乘配置法的函数模型中同时考虑了非随机变量和随机变量,使得高程异常值的推估精度更高。实例分析也证明了此模型在精度上优于传统的平面拟合模型和协方差推估模型。残差分析表明此方法更适合于同时存在内插和外推高程异常值的情况。     

拟合推估在GPS高程解算中的应用

函数模型逼近和统计模型逼近是大地测量平差中两种重要的方法。前者对趋势性和规律性变化能数的求解较为理想，而后者对随机变化参数的逼近比较合适，首先叙述和分析了目前在GPS高程异常解算中的几种方法的原理及优缺点，然后对最小二乘拟合推估在逼近未知点高程异常方面的应用进行了讨论，并介绍了拟合推估的一种新解法。     

非线性拟合推估

首先讨论了非线性系统的拟合推估线性化算法、迭代算法和顾及二次项的非线性算法,推导了相应计算公式。证明了非线性拟合推估理论是线性拟合推估理论的拓展,线性拟合推估是非线性拟合推估的一个特例。     

基于最小二乘配置法的沿海高程异常模型建立研究

陆海统一高程基准的关键是高程异常模型的建立,本文采用既考虑函数模型中非随机变量同时考虑随机部分的最小二乘配置法进行高程异常的拟合推估,建立区域高程异常模型,并与常用方法进行比较分析.以江苏沿海高程异常模型建立为例,研究得出不同拟合方法的拟合精度和残差图各有特点,最小二乘配置法的外部符合精度最高.     

单位权方差公式的统一推证

本文从二次型的期望公式出发，推导了经典最小二乘平差、最小二乘滤波、最小二乘推估和最小二乘配置的验后单位权方差的估计公式。     

P20 一般性问题

CH20022751 拟合推估新解之一——两步解法/周江文(中国科学院测量与地球物理研究所)∥测绘学报.—2002,31(3).—189～191 拟合推估的一般模式,通常用双拟合法则(2)求解,它有一定的缺陷。提出一种解法,分为2步:(1)将Y项并入△,在单拟合下求X的优估值X;(2)把X项纳入L,Y作确定未知量,也在单拟合下求其估值Y。参4 CH20022752 拟合推估两步极小解法/杨元喜,刘念∥测绘学报.—2002,31(3).—192～195 在回顾了最小二乘拟合推估的“综合极小”解法(正常拟合推估)后,分析了正常拟合推估存在的问题。考虑到随机场信号不一定完全表现为随机性,其中可能含有趋势     

移动配置法在高程异常拟合中的应用

本文将最小二乘配置理论引入到高程异常移动曲面拟合模型中(移动配置法),采用格网内插法解决了配置理论中的难点—协方差函数确定的问题。通过实验,验证了移动配置法的优越性。     

Marine gravity and geoid determination by optimal combination of satellite altimetry and shipborne gravimetry data

. Satellite altimetry derived geoid heights and marine gravity anomalies can be combined to determine a detailed gravity field over the oceans using the least-squares collocation method and spectral combination techniques. Least-squares collocation, least-squares adjustment in the frequency domain and input-output system theory are employed to determine the gravity field (both geoid and anomalies) and its errors. This paper intercompares these three techniques using simulated data. Simulation studies show that best results are obtained by the input-output system theory among the three prediction methods. The least-squares collocation method gives results which are very close to but a little bit worse than those obtained using input-output system theory. This slightly poorer performance of the least-squares collocation method can be explained by the fact that it uses isotropic structured covariance (thus approximate signal PSD information) while the system theory method uses detailed signal PSD information. The method of least-squares adjustment in the frequency domain gives the poorest results among these three methods because it uses less information than the other two methods (it ignores the signal PSDs). The computations also show that the least-squares collocation and input-output system theory methods are not as sensitive to noise levels as the least-squares adjustment in the frequency domain method is. Received 19 January 1996; Accepted 17 July 1996     

配置法在局部大地水准面精化中的实例研究

从最小二乘配置方法的基本原理出发,以我国某地区范围内1km分辨率的大地水准面高模型数据为例,根据实用公式计算了试验区大地水准面高的协方差值后,采用多项式函数模型和高斯函数模型分别拟合了该地区大地水准面高的局部协方差函数,并对试验区内18个检核点做了推估计算。根据推估值(Nfit)与实测值(NGPSL)的比较分析表明,虽然多项式协方差函数模型略优于高斯协方差函数模型,但它们都能以厘米级的精度拟合局部大地水准面,这表明了配置法用于精化厘米级大地水准面的有效性。     

基于多面核函数配置型模型的参数估计

针对同时出现非随机参数、已测点和未测点信号的配置型模型精确建立协方差函数的困难，在研究和应用最小二乘配置和多面函数拟合法的基础上，将两法综合，提出了多面核函数配置法，导出了这种平差方法的解算公式。并与最小二乘配置、多面函数拟合作了比较分析。     

卫星重力径向梯度数据的最小二乘配置调和分析

本文深入研究了利用卫星重力梯度径向分量确定地球引力场位系数的最小二乘配置(LSC)调和分析方法。首先论述了最小二乘配置法的原理,推导了扰动引力梯度观测量与球谐系数之间的协方差和自协方差矩阵,在扰动引力梯度观测数据为等经差规则网格数据的情况下,引力位与扰动引力梯度之间的协方差矩阵具有分块Toeplitz循环阵的结构,有效的利用FFT变换技术将其降阶;研究利用截断奇异值分解法（TSVD）解决协方差阵的病态性问题;最后得到了引力梯度径向分量的最小二乘配置调和分析的完整计算公式。模拟试算结果表明,基于TSVD的最小二乘配置调和分析方法,能够以较高的精度还原全球重力场,验证了本文算法的有效性和实用性。     

The combination of GNSS-levelling data and gravimetric (quasi-) geoid heights in the presence of noise

We propose a methodology for the combination of a gravimetric (quasi-) geoid with GNSS-levelling data in the presence of noise with correlations and/or spatially varying noise variances. It comprises two steps: first, a gravimetric (quasi-) geoid is computed using the available gravity data, which, in a second step, is improved using ellipsoidal heights at benchmarks provided by GNSS once they have become available. The methodology is an alternative to the integrated processing of all available data using least-squares techniques or least-squares collocation. Unlike the corrector-surface approach, the pursued approach guarantees that the corrections applied to the gravimetric (quasi-) geoid are consistent with the gravity anomaly data set. The methodology is applied to a data set comprising 109 gravimetric quasi-geoid heights, ellipsoidal heights and normal heights at benchmarks in Switzerland. Each data set is complemented by a full noise covariance matrix. We show that when neglecting noise correlations and/or spatially varying noise variances, errors up to 10% of the differences between geometric and gravimetric quasi-geoid heights are introduced. This suggests that if high-quality ellipsoidal heights at benchmarks are available and are used to compute an improved (quasi-) geoid, noise covariance matrices referring to the same datum should be used in the data processing whenever they are available. We compare the methodology with the corrector-surface approach using various corrector surface models. We show that the commonly used corrector surfaces fail to model the more complicated spatial patterns of differences between geometric and gravimetric quasi-geoid heights present in the data set. More flexible parametric models such as radial basis function approximations or minimum-curvature harmonic splines perform better. We also compare the proposed method with generalized least-squares collocation, which comprises a deterministic trend model, a random signal component and a random correlated noise component. Trend model parameters and signal covariance function parameters are estimated iteratively from the data using non-linear least-squares techniques. We show that the performance of generalized least-squares collocation is better than the performance of corrector surfaces, but the differences with respect to the proposed method are still significant.     

Non-stationary covariance function modelling in 2D least-squares collocation

Standard least-squares collocation (LSC) assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing of, e.g., the gravity field in mountains and under-smoothing in great plains. We introduce the kernel convolution method from spatial statistics for non-stationary covariance structures, and demonstrate its advantage for dealing with non-stationarity in geodetic data. We then compared stationary and non- stationary covariance functions in 2D LSC to the empirical example of gravity anomaly interpolation near the Darling Fault, Western Australia, where the field is anisotropic and non-stationary. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation against data not used in the interpolation, demonstrating that the use of non-stationary covariance functions can improve upon standard (stationary) LSC.     

拟合推估新用——新逼近模式

作为拟合推估的新用之一，提出一种带有随机量的新逼近模式，将拟合推估的通行算法，去短取长，藉以推得良好的插值。