乘性噪声模型的平差方法研究及其应用

Geodetic adjustment has been based on additive noise model, in which error or noise characteristics of geodetic measurements are assumed to have nothing to do with the parameters to be estimated. However, electromagnetic-wave-based geodetic measurements have been shown to be of multiplicative noise nature. In other words, the stronger a signal to be measured, the noisier the collected data. Although a multiplicative noise model has been substantially investigated in statistics and applied to many areas of science and engineering, almost nothing has been done in geodesy. We will start systematically investiagting theory and methods of multiplicative noise from statistical and numerical points of view and apply these theory and methods to process and interpret earth observation and/or geodetic data. More precisely, this research project will focus on the following scientific issues:(1) We will complement the traditional, additive-noise-based geodetic adjustment theory with multiplicative and mixed additive-multiplicative noise models. We will compare four estimation methods, i.e. quasi-likelihood, the least squares (LS) method, the weighted LS method and the bias-corrected weighted LS method numerically, conduct bias analysis and provide the corresponding formulae for error assessment. Particular attention will be paid to the adjusted quantities and the correction to the measurements, since these quantities are of peculiar interest in geodesy; (2) Current statistical estimation theory and methods assume that the noises in a multiplicative noise model are independent. We will extend these theory and methods to the case of correlated multiplicative noises, and further to the case of mixed additive-multiplicative noise models. All the corresponding estimators for these latter two cases will be fully derived. We will also conduct bias analysis on these estimators and derive their variance-covariance matrices. By removing the corresponding biases from the weighted LS estimator, we will construct the bias-corrected weighted LS estimator for the correlated multiplicative noise and mixed additiove-multiplicative noise models; (3) We will be based on the theory of hypothesis testing to work out a geodetic reliability theory for multiplicative noise models; and finally, (4) We will apply the theory and methods developed in this research project to process geodetic data such as GPS,EDM and SAR.

加性噪声模型是所有测量平差理论的基础。以电磁波为手段获取的大地测量数据表现为乘性噪声特性，乘性噪声大小与信号强度成正比。乘性噪声模型在统计学和其他工程领域已有大量理论研究和应用，但其在大地测量相关领域的研究几乎一片空白。本研究项目拟对大地测量中的乘性噪声平差理论开展系统研究。主要研究内容包括：1）研究最小二乘、加权最小二乘、偏差改正最小二乘和拟似然准则下的乘性噪声平差方法，通过模拟分析比较四种方法在大地测量数据处理中的可行性和适用特点；2）给出相应的参数估计、观测值平差量，观测值改正数以及单位权方差的计算式，并对其进行偏差和精度分析；3）把现有的独立乘性噪声模型的统计估计理论扩展至相关乘性噪声模型，深化乘性噪声模型的平差方法；4）依据假设检验理论建立乘性噪声模型的可靠性理论，构建乘性噪声模型下的测量平差软件系统，应用于大地测量的GPS，EDM和SAR等的数据处理。

迄今为止，几乎所有的测量平差理论都是建立的加性噪声模型基础上，但是，以电磁波为手段获取的大地测量数据，则表现为乘性噪声特性，乘性噪声的大小与信号强度成正比。其在统计学和其他工程领域已有大量理论研究和应用，但在大地测量相关领域的研究几乎一片空白。本项目对大地测量中的乘性噪声平差理论展开系统研究。.主要研究成果包括:[1]把偏差改正最小二乘法扩展至混合加乘性噪声的大地测量观测值模型,研究了最小二乘法、加权最小二乘法、偏差改正最小二乘法和拟似然准则下的混合加乘性噪声大地测量观测值的平差理论与方法，通过模拟分析，比较了四种方法在大地测量数据处理中的特点；[2]给出了相应的参数估计、观测值平差量，观测值改正数以及单位权方差的计算式，并对其进行偏差和精度分析；[3]构建乘性噪声模型下的测量平差软件系统，应用于大地测量的数据处理,利用模拟LiDAR的数据进行滑坡灾害评估。主要研究成果全部发表于国际一流的大地测量SCI学术刊物,填补平差理论研究方面的空白,对大地测量数据处理具有重要理论和实际意义。