CN103092814B - A data measurement method of least squares adjustment General - Google Patents

A data measurement method of least squares adjustment General Download PDF

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CN103092814B
CN103092814B CN 201310020835 CN201310020835A CN103092814B CN 103092814 B CN103092814 B CN 103092814B CN 201310020835 CN201310020835 CN 201310020835 CN 201310020835 A CN201310020835 A CN 201310020835A CN 103092814 B CN103092814 B CN 103092814B
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data
parameters
adjustment
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CN103092814A (en )
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郑茂腾
张永军
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武汉大学
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Abstract

一种测量数据通用最小二乘平差方法,无需先验数学模型,可以进行任何数学模型及任何数据的最小二乘平差,同时还可以将多源数据联合起来进行最小二乘平差处理。 A data common least squares adjustment method for measuring, without prior mathematical model, may be any mathematical model and least squares adjustment of any data, but also can combine the data from multiple sources for least-squares adjustment process. 只需输入数学模型并输入数据,本发明构建平差模型并进行最小二乘平差处理,快速取得测量平差误差处理结果。 Simply enter the mathematical model and the input data, the present invention is constructed adjustment model and least squares adjustment process, adjustment measurement error quickly obtain the processing result. 应用本发明可以有效提高实验室算法研究以及测量数据处理的效率,充分利用多种传感器硬件资源,节省数据处理软件资源。 Application of the present invention can effectively improve the efficiency of research laboratories, and the measurement data processing algorithm, the full use of the hardware resources of various sensors, saving resources data processing software.

Description

一种测量数据通用最小二乘平差方法 A data measurement method of least squares adjustment General

技术领域 FIELD

[0001] 本发明属于测绘科学与技术领域,涉及一种无需先验数学模型的通用最小二乘平差方法,可应用于各类需要进行最小二乘平差的数据处理以及科学研究的行业。 [0001] The present invention belongs to the field of science and technology mapping, relates to a universal method of least squares adjustment without prior mathematical model can be applied to various needs of the least-squares adjustment of the data processing industry and scientific research. 主要包括测绘工程,测量平差,遥感数据处理,计算机视觉,各类数学相关行业的算法研究等。 Including mapping, surveying adjustment, remote sensing data processing, computer vision, research and other kinds of mathematical algorithms related industries.

背景技术 Background technique

[0002] 测量时,需要对大量测量数据进行误差分析及处理,最小二乘平差是常用的测量平差误差处理手段,但是根据测量数据类型不同,测量平差采用的数学模型则不同,如GPS测量中的距离方程,水准测量中的高差方程,遥感数据处理中的共线方程,有理函数方程,SAR构像方程等。 [0002] When the measurement requires a large amount of measurement data processing and error analysis, least squares adjustment is a common error difference measurement processing means, but according to the different types of measurement data, the measurement adjustment mathematical model used is different, as GPS measurements from the equation, the equation height leveling the collinear equation processing remote sensing data, rational function equation, SAR imaging equation like. 不同的数据类型需要用不同的数学方程来进行最小二乘平差处理。 Different types of data needed to perform a different mathematical equations least squares adjustment process. 而目前绝大部分测量平差软件都是针对指定数据类型而定制的,若有新的传感器产生新的数据类型,则需要重新构建最小二乘平差模型,重新编写相关的数据处理软件,耗费大量人力物力财力。 At present, the vast majority of survey adjustment software is customized for a given type of data, if the new sensor produces a new data type, you need to rebuild a least squares adjustment model, re-write the relevant data processing software, consuming a lot of manpower and material resources. 另外随着新型传感器的不断出现,各种传感器数据的联合处理逐渐成为研究热点,传统的针对数据类型而制定的平差软件不能够满足多源数据联合处理的要求,同样也需要重新制定相关的平差程序来处理特定的多源数据。 Also with the continual emergence of new sensors, a variety of joint processing of sensor data is becoming a hot research, and the development of traditional data types for adjustment software does not meet the requirements of multi-source Data Processing, also we need to re-enact the relevant adjustment program to process a particular multi-source data.

发明内容 SUMMARY

[0003] 本发明的目的是提供一种无需先验数学模型的测量数据通用最小二乘平差方法,以满足各类测量数据的平差处理以及多源测量数据联合平差处理的需求。 [0003] The object of the present invention is to provide a mathematical model of the measurement data prior general least squares adjustment method does not need to meet various types of adjustment processing of the measurement data and the measurement data combined multi-source processing needs adjustment.

[0004] 本发明的技术方案为一种测量数据通用最小二乘平差方法,包括以下步骤: [0004] aspect of the present invention is a general least-squares adjustment method of measurement data, comprising the steps of:

[0005] 步骤1,输入包含多个模型的数学模型文件和对应的观测值数据文件、辅助数据文件,所述数学模型文件包含每个模型的观测方程公式以及公式所涉及各类参数的对应关系,所述参数包括未知参数和已知参数,所述已知参数包括观测值;所述观测值数据文件包含每个模型平差所需观测值数据,所述辅助数据文件包含记录每个模型中参数之间对应关系的辅助数据; [0005] Step 1, an input file comprising a plurality of models of the mathematical model and the corresponding case data file, auxiliary data files, the file containing the mathematical model equations and observation equations corresponding relationship model formula for each of the various parameters involved the parameters include known parameters and unknown parameters, including observations of the known parameters; the observations data file contains the required data for each observation value adjustment model, the auxiliary data file contains records each model correspondence relation between the parameters of the auxiliary data;

[0006] 步骤2,对每个模型,解析观测方程公式,统计各类参数,求未知参数一阶导数,构建最小二乘平差模型,输出包含所有最小二乘平差模型的平差模型文件; [0006] Step 2, for each model, analytical formulas observation equation, various parameters statistics, find the first derivative of unknown parameters, constructs a least squares adjustment model, output adjustment model comprising all the least-squares adjustment model file;

[0007] 步骤3,读取步骤2所得平差模型文件和相应观测值数据文件和辅助数据文件; [0007] Step 3, the reading step 2 and the resulting adjustment model files corresponding observations auxiliary data files and data file;

[0008] 步骤4,平差数据预处理,包括连接平差模型文件中的所有最小二乘平差模型,绑定观测值数据、辅助数据与最小二乘平差模型,分析得到需要消去的未知参数,对各模型观测值排序; [0008] Step 4, pre-adjustment data, least squares adjustment model including all files connected to adjustment model, binding observed value data, the auxiliary data with least squares adjustment model, to give the desired analysis erasing unknown parameters, ordering value for each observation model;

[0009] 步骤5,逐点构建误差方程,逐点法化得到法方程,并逐点消去未知参数; [0009] Step 5, constructed point by point error equation, point by point of the obtained normal equation, and point by point to eliminate the unknown parameter;

[0010] 步骤6,求解法方程,获取未知参数改正数,回代计算各消去未知参数的改正数,更新各未知参数数值,并计算观测值权; [0010] Step 6, the equation solving method, corrections obtaining unknown parameters, eliminate back substitution corrections calculated for each of the unknown parameters, update each unknown parameter values, and calculates the weight value observed;

[0011] 步骤7,若未知参数改正数绝对值最大值小于指定阈值,则退出并转到步骤8,否则转到步骤4 ; [0011] Step 7, if the absolute value of the maximum number of unknown parameters correction less than a specified threshold value, the exit and go to step 8, otherwise go to step 4;

[0012] 步骤8,输出联合平差精度报告,包括各未知参数数值、平差系统中误差、各未知参数中误差以及观测值残差。 [0012] Step 8, the output adjustment precision joint report, including the error of each unknown parameter values, adjustment system, each of the unknown parameters and an observation error residuals.

[0013] 而且,步骤4所述连接多个最小二乘平差模型,包括读取各最小二乘平差模型参数并排序,合并最小二乘平差模型的各类参数。 [0013] Further, the step 4 is connected to a plurality of least-squares adjustment model, including the model parameters of the least squares adjustment reading and sorting, merging various parameters of the least-squares adjustment model.

[0014] 而且,步骤4所述绑定数据与最小二乘平差模型,包括各最小二乘平差模型从观测值数据以及辅助数据文件中自动识别对应的参数并获取参数的值。 [0014] Further, step 4 binding data with least squares adjustment model, including the model of a least squares adjustment automatically identifying the corresponding parameter value from the observed data and the auxiliary data file and obtain the parameter values.

[0015] 而且,步骤6所述回代计算各消去未知参数的改正数,实现方式为根据每个与该未知参数相关的观测值的法方程系数矩阵、常数项以及总的法方程回代计算各未知参数的改正数值。 [0015] Further, the calculation step 6 for each back substitution corrections eliminate the unknown parameters, implementations according to the equation coefficient matrix for each observation is related to the unknown parameters, the constant term and the total back substitution method calculates equation correction values ​​for each of the unknown parameters.

[0016] 本发明的优点是不依赖于数据,不依赖于数学模型,可以对不同数据采用不同模型进行最小二乘平差处理,而且可以将多种传感器获取的数据进行联合处理。 Data [0016] The advantage of the present invention is not dependent on the data, does not rely on the mathematical model, different data can be processed using the least-squares adjustment of different models, can be acquired and various sensors for joint processing. 用户只需要输入对应数学模型的公式,例如共线方程,并指定未知参数以及已知参数,并按照指定格式输入对应的数据文件,即可进行最小二乘平差。 Users only need to enter a formula corresponding to the mathematical model, for example, co-linear equation, and specify the parameters and the unknown parameters are known, and enter the corresponding data file in the specified format, to perform least squares adjustment. 该方法支持多模型联合最小二乘平差,因此可以方便的进行多源数据联合处理,充分有效的利用现有资源。 The method supports multiple model joint least-squares adjustment, and therefore can easily be combined multi-source data processing, full and effective use of available resources. 另外,本方法还可以用观测数据来拟合各类数学函数以及几何变换函数,包括仿射变换模型,空间相似变换模型,有理函数模型,N阶多项式模型,样条内插曲线模型等等。 Further, the method can also be used to fit the observed data and the various types of geometric transformation function mathematical functions, including affine transformation model, similarity transformation model space, rational function model, N order polynomial model, spline interpolation curve model and the like. 应用本发明可以有效提高实验室算法研究以及测量数据处理效率,高效地进行测量平差误差处理,充分利用多种传感器硬件资源,节省数据处理软件资源。 Application of the present invention can effectively improve the research laboratory measurement algorithm and data processing efficiency, efficiently perform the measurement error adjustment process, make full use of hardware resources of various sensors, saving resources data processing software.

附图说明 BRIEF DESCRIPTION

[0017] 图1是本发明实施例的流程图。 [0017] FIG. 1 is a flowchart of an embodiment of the present invention.

具体实施方式 detailed description

[0018] 具体实施时,本发明技术方案采用计算机软件方式实现自动运行流程。 [0018] During specific embodiments, the present invention adopts the technical solution manner automatic operation of computer software processes. 以下结合附图和实施例详细说明本发明技术方案。 The following detailed description and the accompanying drawings aspect of the invention embodiments.

[0019] 参见图1,本发明无需先验数学模型的通用最小二乘平差方法,输入数据为数学模型文件(或者直接输入平差模型文件则不需要执行步骤2),观测值数据文件,辅助数据文件,输出数据为最小二乘平差精度报告。 [0019] Referring to Figure 1, the present invention does not require a priori general mathematical model of least squares adjustment method, the mathematical model for the input data file (or directly into the model file is not required adjustment step 2), the observed value of the data file, auxiliary data file, the output data for the least-squares adjustment accuracy of the report. 实施例的具体实现流程包括以下步骤: Specific implementation process embodiment comprises the steps of:

[0020] 步骤1,输入包含多个模型的数学模型文件和对应的观测值数据文件、辅助数据文件,所述数学模型文件包含每个模型的观测方程公式以及公式所涉及各类参数的对应关系,所述参数包括未知参数和已知参数,所述已知参数包括观测值;所述观测值数据文件包含每个模型平差所需观测值数据,所述辅助数据文件参数包含记录每个模型中参数之间对应关系的辅助数据。 [0020] Step 1, an input file comprising a plurality of models of the mathematical model and the corresponding case data file, auxiliary data files, the file containing the mathematical model equations and observation equations corresponding relationship model formula for each of the various parameters involved the parameters include known parameters and unknown parameters, including observations of the known parameters; the observations data file contains the required data for each observation value adjustment model, the auxiliary data file contains a record for each model parameter auxiliary data correspondence relationship between the parameters.

[0021] 具体实施时,可以直接输入包含多个模型的数学模型文件和对应的观测值数据文件、辅助数据文件。 [0021] In particular implementation, the mathematical model may be input file and the corresponding case data file, a data file containing a plurality of auxiliary models directly. 用户也可以文件或以命令行形式输入数学模型公式,并指定相关的未知参数以及已知参数,并按照预先指定的格式,组织对应的观测值数据文件。 The user may also be a file or a command line input mathematical expression model, and specifying the associated parameters and the unknown parameters are known, and in accordance with pre-specified format, organization observed value corresponding to the data file. 一般输入传感器成像或者感应的数学模型文件,也可以输入各类数学函数以及几何变换函数的数学模型文件,所述数学模型文件包含观测方程公式以及相关未知参数、已知参数。 General mathematical model input document or an imaging sensor sensing can also enter all kinds of mathematical functions and geometric transformation function of a mathematical model file, the file containing the mathematical model equation and an observation equation related to unknown parameters, known parameters. 具体来说,数学模型文件对每个模型进行描述,包括模型中涉及的观测值的观测方程公式,未知参数以及已知参数。 Specifically, the mathematical model description file for each model, the observed values ​​including observation equations involved in the model formula, known parameters and unknown parameters. 各参数之间可能有数学关系,因此,一般还包括相关已知参数和未知参数之间的相互关系方程公式。 There may be a mathematical relationship between the parameters, thus, typically it includes the relationship between the equation equation related known parameters and unknown parameters.

[0022] 步骤2,对每个模型,解析观测方程公式,统计各类参数,求未知参数一阶导数,构建最小二乘平差模型,输出包含所有最小二乘平差模型的平差模型文件。 [0022] Step 2, for each model, analytical formulas observation equation, various parameters statistics, find the first derivative of unknown parameters, constructs a least squares adjustment model, output adjustment model comprising all the least-squares adjustment model file. 具体实施时,本领域技术人员可设计通过软件流程自动构建最小二乘平差模型,包括自动解析用户输入的数学模型公式,自动求一阶偏导数以便线性化输入的公式,构建最小二乘平差模型。 During specific embodiments, those skilled in the art may be designed to automatically build a least squares adjustment process model by software, including automatic analytical mathematical model formula entered by the user, the automatic evaluation of the first partial derivatives to a linear equation of input construct The least squares difference model.

[0023] 实施例具体实现方法是:用户输入模型文件后,软件程序智能解析文件中每个观测方程公式以及相关的未知参数和已知参数,对未知参数进行求导工作,从而线性化误差方程,最终构建出最小二乘平差模型,并以文件形式将多个最小二乘平差模型存储输出为平差模型文件。 [0023] Example specific method is: after the user input model file, an observation equation formula Intelligent Analytical software program and associated files each known parameters and unknown parameters, the unknown parameters derivative work, whereby linear error equation , final construct least-squares adjustment model, and the form of a file storing a plurality of least-squares adjustment model output adjustment model file. 这种平差模型文件是经过对数学模型文件进行处理后,得到的记录最小二乘平差模型信息的文件,包含各未知参数一阶导数以及各未知参数的分组统计信息等。 This document is post-adjustment model for the mathematical model file processing pass, file record least squares adjustment obtained model information, statistics on each packet contains a first derivative of the unknown parameter as well as unknown parameters, and the like.

[0024] 本发明涉及的最小二乘平差原理即对观测值根据观测方程构建误差方程,如式 [0024] The principles of the present invention relates to a least-squares adjustment, i.e., the observation value of Error equation, the observation equation in accordance with the formula

(I),并计算该组误差方程最小二乘解,如式(2)。 (The I), and calculates the set of equations the least squares error solution of formula (2).

[0025] V = Ax-L (I) [0025] V = Ax-L (I)

[0026] AtPAx = AtPL (2) [0026] AtPAx = AtPL (2)

[0027] X = (AtPA) 1IAtPL (3)其中,V表示观测值改正数向量,A表示误差方程设计矩阵,X表示误差方程未知参数向量,L表示常数项向量,P为观测值权矩阵。 [0027] X = (AtPA) 1IAtPL (3) wherein, V represents the observed value corrections vector, A denotes an error equation design matrix, X is the unknown parameter vector error equation, L represents a constant term vector, P is the observed value of the weight matrix.

[0028] 步骤3,读取步骤2所得平差模型文件和相应观测值数据文件和辅助数据文件,开始最小二乘平差。 [0028] Step 3, the reading step 2 and the resulting adjustment model files corresponding observations auxiliary data files and data files, start least squares adjustment.

[0029] 实施例具体实现方法是:分别执行步骤I和2后,读取步骤2根据数学模型文件生成的平差模型文件,或者不执行步骤I和2,直接读取由用户直接输入的平差模型文件,读取相关的且指定格式的数据文件,开始进行最小二乘平差处理。 [0029] Example embodiments specific method is: respectively performing the steps I and 2, 2 and reading step 2 directly reads input directly by the user according to a mathematical model of a flat adjustment model document files generated or does not execute step I difference model file, read the data file associated with a specified format, least squares adjustment process is started.

[0030] 步骤4,平差数据预处理。 [0030] Step 4, adjustment data preprocessing. 平差数据预处理,包括连接平差模型文件中的所有最小二乘平差模型,绑定观测值数据、辅助数据与最小二乘平差模型,分析得到需要消去的未知参数,对各模型观测值排序。 Adjustment data preprocessing, all connected to a least squares adjustment model comprising adjustment model file, binding observed value data, the auxiliary data with least squares adjustment model, to give the desired analysis erasing unknown parameters, for each observation model values ​​are sorted. 具体实施时,本领域技术人员可设计通过软件流程自动执行本步骤。 During specific embodiments, those skilled in the art may be designed to automatically perform the steps of the present process by software. 需要消去的未知参数可能有多组。 Elimination of unknown parameters may need more than one set.

[0031] 实施例具体实现方法是:自动读取各最小二乘平差模型的参数,合并模型的未知参数以及各类参数实现多个最小二乘平差模型自动连接,包括读取各最小二乘平差模型参数并排序,合并最小二乘平差模型的各类参数;各模型从观测值数据文件以及辅助数据文件中自动识别对应的参数并获取该参数的值,实现数据与模型绑定;进行未知参数智能分析,包括分析各未知参数的数量以及相互关系,从而自动确定需要消去未知参数,以便减少法方程系数矩阵的带宽;进行观测值智能排序,对各模型的观测值进行重新排序,与待消去未知参数相关的所有观测值应该连续放在一起,以便于逐组消去这类未知参数。 [0031] Example embodiments are specific method: automatically read a least squares adjustment parameter of each model, the combined model and unknown parameters to achieve various parameters automatically connect a plurality of least-squares adjustment model including two were read minimum and sorted by adjustment model parameters, various parameters merge least-squares adjustment model; automatic identification of each model parameter from observed values ​​corresponding to the data file and the auxiliary data file and acquires the value of the parameter, data and model binding ; be unknown parameters intelligent analysis, including analysis of the number of each of the unknown parameters and the relationship to automatically determine the need to eliminate the unknown parameters, in order to reduce the bandwidth coefficient equation matrix; observation value intelligent sorting, the observation value of each model reorder All observations associated with the elimination of unknown parameters should be continuously together, in order to eliminate the unknown parameters of such a group by group.

[0032] 步骤5,逐点构建误差方程,逐点法化得到法方程,并逐点消去未知参数。 [0032] Step 5, constructed point by point error equation, point by point of the obtained normal equation, and point by point to eliminate the unknown parameters.

[0033] 每完成一组观测值的处理,可以消去一组未知参数。 [0033] each completed processing a set of observed values, a set of unknown parameters can be eliminated. 实施例具体实现方法是按组处理:对待消去的某组未知参数,根据式(I),对与待消去的这组未知参数相关的一组观测值,逐个观测值构建误差方程,计算误差方程的系数矩阵,常数项向量,并对其进行法化处理,即转化成如式(2)所示的法方程,与待消去的这组未知参数相关的一组观测值处理完毕后,立即消去法方程中这组未知参数,然后再同样进行下一组观测值数据的构建误差方程、法方程的工作。 Example particular implementation is processed as a group: treatment of a set of unknown parameters eliminated, according to formula (the I), a set of observed values ​​for the set of unknown parameters to be erased associated, one by one observation value of Error equation, the error equation the coefficient matrix, constant term vector, and subjected to treatment method, i.e. converted into the method as shown in equation (2) after a set of observations to be eliminated in the set of unknown parameters relating to processed immediately erased in this normal equation set of unknown parameters and then operates similarly constructed error equations, normal equations of a next set of observations data.

[0034] 步骤6,求解法方程,获取未知参数改正数,回代计算各消去未知参数的改正数,更新各未知参数数值,并计算观测值权。 [0034] Step 6, the equation solving method, corrections obtaining unknown parameters, eliminate back substitution corrections calculated for each of the unknown parameters, update each unknown parameter values, and calculates the weight observations.

[0035] 实施例具体实现方法是:对步骤5中的法方程系数矩阵AtPA进行求逆工作,并按照式(3)求解未知参数改正数向量。 [0035] Example specific method is: the step of Equation 5, coefficient matrix inversion AtPA work performed, and (3) solve for the unknown parameter vector of corrections in accordance with the formula. 获取未知参数改正数后,所有被消去的未知参数改正数则需要根据各观测值法方程系数矩阵、常数项以及总法方程回代计算,最终求得所有未知参数的改正数,然后据此更新各未知参数数值,并自动重新计算观测值权。 After obtaining unknown parameters corrections, corrections are eliminated all unknown parameters of the need to process each observation value of the coefficient matrix of the equation, the constant term and the total back substitution method to calculate the equation, to obtain the final corrections of all unknown parameters, and then updated accordingly each unknown parameter values, and automatically recalculate the weights observed values.

[0036] 步骤7,判断迭代是否收敛,即若未知参数改正数绝对值最大值小于指定阈值,则退出并转到步骤8,否则转到步骤4。 [0036] Step 7, it is determined whether the iteration converges, that is, if the absolute value of the number of unknown parameters correction less than a specified maximum threshold, the exit and go to step 8, otherwise go to step 4.

[0037] 实施例具体实现方法是:获取所有未知参数改正数中的绝对值最大值,若未知参数改正数绝对值最大值小于指定阈值,则退出迭代并转到步骤8,否则转到步骤4,继续进行迭代计算。 [0037] Example embodiments specific method is: obtaining the maximum absolute value of all corrections unknown parameters, if the number of unknown parameters to correct the absolute value less than a specified maximum threshold value, the iteration is exited and go to step 8, otherwise go to Step 4 continued iterative calculation. 具体实施时,本领域技术人员可根据精度要求等情况自行指定阈值。 During specific embodiments, those skilled in the art may be specified threshold accuracy requirements according to their own situation.

[0038] 步骤8,输出联合平差精度报告。 [0038] Step 8, the output adjustment precision joint report.

[0039] 实施例具体实现方法是:以文件形式输出平差结果,包括平差计算结束后各未知参数的数值,平差系统的中误差,各未知参数中误差以及各观测值残差等,形成联合平差精度报告。 [0039] Example embodiments specific method is: the output adjustment results in a file format, including the error of each unknown parameter values ​​after the adjustment calculation, the adjustment system, each of the unknown parameters in each observation residual error and the like, Combined adjustment accuracy of the report form.

[0040] 本文中所描述的具体实施例仅仅是对本发明精神作举例说明。 Specific Example [0040] described herein is merely illustrative for spirit of the invention. 本发明所属技术领域的技术人员可以对所描述的具体实施例做各种各样的修改或补充或采用类似的方式替代,但并不会偏离本发明的精神或者超越所附权利要求书所定义的范围。 Those skilled in the art of the present invention can be made to the specific embodiments described various modifications or additions, or a similar alternative embodiment, but without departing from the spirit of the invention or exceed defined in the appended claims range.

Claims (4)

  1. 1.一种测量数据通用最小二乘平差方法,包括以下步骤: 步骤1,输入包含多个模型的数学模型文件和对应的观测值数据文件、辅助数据文件,所述数学模型文件包含每个模型的观测方程公式以及公式所涉及各类参数的对应关系,所述参数包括未知参数和已知参数,所述已知参数包括观测值;所述观测值数据文件包含每个模型平差所需观测值数据,所述辅助数据文件包含记录每个模型中参数之间对应关系的辅助数据; 步骤2,对每个模型,解析观测方程公式,统计各类参数,求未知参数一阶导数,构建最小二乘平差模型,输出包含所有最小二乘平差模型的平差模型文件; 步骤3,读取步骤2所得平差模型文件和相应观测值数据文件和辅助数据文件; 步骤4,平差数据预处理,包括连接平差模型文件中的所有最小二乘平差模型,绑定观测值数据、辅助数据 A least squares adjustment method for measuring general data, comprising the following steps: Step 1, the input file comprising a plurality of models of the mathematical model and the corresponding case data file, auxiliary data files, each file containing the mathematical model equation model observation equation, and the equation relates to the correspondence relationship of various parameters, said parameters including known parameters and unknown parameters, including observations of the known parameters; the observations for each data file containing the desired adjustment model observation value data, the auxiliary data file contains the auxiliary data recording correspondence relationship between each of the model parameters; step 2, for each model, analytical formulas observation equation, various parameters statistics, find the first derivative of unknown parameters, Construction of a least squares adjustment model, output adjustment model file containing all of the least-squares adjustment model; step 3, the reading step 2 and the resulting adjustment model files corresponding observations sub data file and the data file; step 4, flat preprocessing the difference data, least squares adjustment model including connecting all adjustment model file, binding observed value data, auxiliary data 最小二乘平差模型,分析得到需要消去的未知参数,对各模型观测值排序; 步骤5,逐点构建误差方程,逐点法化得到法方程,并逐点消去未知参数; 步骤6,求解法方程,获取未知参数改正数,回代计算各消去未知参数的改正数,更新各未知参数数值,并计算观测值权; 步骤7,若未知参数改正数绝对值最大值小于指定阈值,则退出并转到步骤8,否则转到步骤4 ; 步骤8,输出联合平差精度报告,包括各未知参数数值、平差系统中误差、各未知参数中误差以及观测值残差。 A least squares adjustment model to analyze the obtained unknown parameters need to eliminate, for each ordering model observations; Step Error Equation 5, point by point, point by point of the obtained normal equation, and point by point to eliminate the unknown parameters; Step 6, to solve normal equation, obtaining unknown parameters corrections, calculates the number of corrections for each back substitution to eliminate the unknown parameters, update each unknown parameter values, and calculates the weight observations; step 7, if the absolute value of the maximum number of unknown parameters correction less than a specified threshold, then exit and go to step 8, otherwise go to step 4; step 8, the output adjustment precision joint report, including the unknown parameter values, error adjustment system, each of the unknown parameters and an observation error residuals.
  2. 2.根据权利要求1所述测量数据通用最小二乘平差方法,其特征在于:步骤4所述连接所有最小二乘平差模型,包括读取各最小二乘平差模型参数并排序,合并最小二乘平差模型的各类参数。 The measuring method of the least squares adjustment Data General claimed in claim 1, wherein: said step of connecting all four least-squares adjustment model, including the model parameters of the least squares adjustment is read and sorted, merged Various parameters of the least squares adjustment model.
  3. 3.根据权利要求1所述测量数据通用最小二乘平差方法,其特征在于:步骤4所述绑定数据与最小二乘平差模型,包括各最小二乘平差模型从观测值数据文件以及辅助数据文件中自动识别对应的参数并获取参数的值。 The measurement method of the least squares adjustment Data General claimed in claim 1, wherein: the step of binding data with the 4 least-squares adjustment model, including the model data from a least-squares adjustment file observations and the value of the auxiliary data file corresponding to the automatic identification of the parameters and acquisition parameters.
  4. 4.根据权利要求1或2或3所述测量数据通用最小二乘平差方法,其特征在于:步骤6所述回代计算各消去未知参数的改正数,实现方式为根据每个与该未知参数相关的观测值的法方程系数矩阵、常数项以及总的法方程回代计算各未知参数的改正数值。 The measurement data or the general least-squares adjustment method as claimed in claim 1 or 23, wherein: said back-substitution calculation step 6 for each erasure corrections unknown parameters, according to implementation of each of the unknown equation correlation coefficient parameter matrix of observations, and the total constant term equation back substitution method calculates correction values ​​for each unknown parameters.
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CN102620745A (en) * 2012-02-08 2012-08-01 武汉大学 Airborne inertial measurement unite (IMU) collimation axis error calibration method

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Publication number Priority date Publication date Assignee Title
US6167347A (en) * 1998-11-04 2000-12-26 Lin; Ching-Fang Vehicle positioning method and system thereof
US7409290B2 (en) * 2004-04-17 2008-08-05 American Gnc Corporation Positioning and navigation method and system thereof
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CN102620745A (en) * 2012-02-08 2012-08-01 武汉大学 Airborne inertial measurement unite (IMU) collimation axis error calibration method

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