英文平差试题.docx

武汉大学测绘学院2013-2014学年度第一学期期末考试误差理论与测量平差基础（双语）课程试卷A出题者 吴云 审核人班级 学号 姓名 1. Fill the following blanks1.1 is defined as the degree of conformity among a set of observations, which is qualified by “variance”, and is considered as the degree of closeness to the true value, which is qualified by “MSE”1.2 According to properties of errors, errors are categorized into mistakes (gross), and .1.3 The mathematical model of adjustment includes model and model, on which the adjustment is applied.1.4 If the functional model is and the observations in are weighted by matrix , the least squares principle is stated by . To enforce this criterion and at the same time have constraint, we should get function minimum.1.5 In order to verify the precision of a theodolite, an angle of was measured 6 times and the observations are presented as below. The standard error of the theodolite is . Given confidence level of 95.5%, corresponding to the confidence level, the confidence interval is .1.6 given the observations with the covariance matrix and , the cofactor of . the unit-weight standard error is and the weight matrix is , in which the weight is and is .1.7 Given coordinate of point A, in order to determine the position of point P (figure1). The angle and the distance of AP were measured with standard deviations of and respectively. If , the positional error of point P is ; the angle should be repeatedly measured at least of resulting in the positional error less than. Figure 1(32)2 Solve the following problem (50 points)2.1 The figure depicts a simplified problem of intersection in a plane. The thee points A, B, and C are perfectly know control with X Y coordinates shown in table 1. An unknown point P is to be determined such that its X coordinate is the same as that for point C (that is, angle BCP is perfectly known to be 90 degree). The observations are the two angle shown in the figure, and where and are uncorrelated and of equal weight. In order to estimate the position of point P, (1) build the functional model and stochastic model; (2)compute the position of point P. (if an approximate value is needed use ) (10)Point XYA19.322.00B2.002.00C2.0019.322.2 the figure shows a rectangle areas. The observations, which are uncorrelated of equal precision of 1cm, are (1) Compute the Least Squares estimates the areas of rectangle ABEF and BCDE;(2) Compute the variances of the above estimates by using the prior precision;(3) If constrain the area of rectangle ABEF be 3 time of rectangle BCDE, write the functional model with the constraint and give the normal equation. (18)2.3 (15 points）If is adjusted coordinates of point P and given the normal equation (a) Calculate the standard error ellipse for point P ( the orientation and semi- axes of the standard error ellipse ); (b) Calculate the positional variance of estimated point P, ; (c) Given a control station A, and , calculate .2.4 (12 points) Given the observation equations and cofactor of observations , (1) Estimate by least square adjustment; (2) Calculate the posterior reference