坐标转换中英文翻译—外文翻译毕业论文.doc

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1、本科毕业设计（论文）中英文对照翻译院（系部） 专业名称 年级班级 学生姓名 指导老师 XXX年X月XAbstractStudies on quality evaluation of coordinate transformation have not yet to comprehensively investigate the simulation ability and reliability of a transformation. This paper presents a comprehensive quality evaluation system (QES) for coordin

2、ate transformation that includes the testing of reliability and simulation ability. The proposed QES was used to test and evaluate transformations using typical common point distributions and transform models. Both the transformation model and distribution of common points are factors in the effecti

3、veness of a transformation. The performances of typical common point distributions and transform models are demonstrated using the proposed QES.Keywords：coordinate transformation; QES; reliability; simulation reliability; common point distribution; transform modelI. INTRODUCTIONInformation about com

4、mon points consists of signals. However, noise caused by inadequacies in the precision of surveying techniques, by shortcomings in computational models, and by variations due to crustal movements, etc. also become incorporated. This noise can show systematic or random characteristics, or can even ap

5、pear at some points as gross errors. During computations, random errors can be exposed as residuals, while systematic errors can be simulated by suitable transformation models. In contrast, gross errors are absorbed in parameters that result in remarkable distortion of the transformation. For this r

6、eason, an optimal transformation must have the ability to simulate signals and systematic errors (simulation ability) and also to detect and defend against gross errors (reliability). Precision is generally considered to be a unique indicator that reflects the quality of a transformation (Wells and

7、Vanicek 1975; Appelbaum1982; Featherstone et al. 1999). Chen et al. (2005) proposed a number of simulation indicators for evaluation of the performance of a transformation. You et al. (2006) used least-squares collocation to eliminate noise from common points, but found that the resulting isotropica

8、l covariance was often not correct. Hakan et al. (2006) investigated the effect of common point distribution on reliability of a data transformation. They established that the redundancy numbers in data transformation were determined by the distribution of common points in the area that they bounded

9、. Gui et al (2007) presented a Bayesian approach that allowed gross error detection when prior information of the unknown parameters was available. However, these existing reports on evaluation of the quality of coordinate transformation did not comprehensively investigate either the simulation abil

10、ity or the reliability of thetransformation being studied.The objectives of this paper were therefore: (1) tointroduce a comprehensive quality evaluation system (QES) for coordinate transformation that would include tests of simulation ability and reliability; (2) to analyze the effects of common po

11、int distribution and the transformation model on simulation ability and reliability; and (3) to investigate performance of typical common point distributions and transformation models using the proposed QES. Section 2 provides an introduction to the QES that is proposed for coordinate transformation

12、. Transformations with typical common point distributions and transform models are then tested and evaluated in section 3. Lastly,section 4 presents conclusions.II. THE PROPOSED METHODFig.1. Flowchart of proposed QES.Fig. 1 shows the flowchart for the proposed QES. In this paper, both the distributi

13、on of common points and the transformation are considered to be the determining factors, while reliability and simulation ability are the main indicators used for evaluation. If performances of candidate distributions and models are both able to satisfy certain chosen criteria, then an “optimum” tra

14、nsformation appears. Otherwise, other candidates are introduced for testing performances of the indicators. Thus, Fig. 1is also the flowchart that leads to an “optimum” transformation. When reliability is taken into consideration , the investigation of simulation ability proves both feasible and val

15、uable. The reliability indicators consist of redundant observation components (ROC) and internal and external reliabilities (Li and Yuan 2002), while the simulated indicators consist of precision, extensibility, and uniqueness.A. Reliability Indicators1) Redundant Observation ComponentsThe general l

16、inearized Gauss-Markov model is expressed as follows: (1)Here, l is the vector of observations, V is the vector of residuals, A is the linearized design matrix, and is the approximation of unknown parameters. Its normal equation is as follows: (2)Here, . Then: (3)Eq.3 describes the relationship betw

17、een residuals and the input errors. Residuals depend on the matrix, which is decided by the design matrix A and the weight matrix P. This represents the geometrical condition of an adjustment, termed the reliability matrix, because it reflects the effect of input errors on residuals. Since the relia

18、bility matrix is independent of observations, the adjustment can be designed and tested prior to field observation. The trace of is equal to the redundant observation number r, so its ith diagonal element is considered to be the ith redundant observation component, as follows: , . (4)In general, .2)

19、 Internal ReliabilityThe internal reliability refers to the marginal detecTable gross errorwith significance level and power function , as follows: , (5)Where is the non-centrality parameter of normal distribution caused by gross error. reflects the ability to detect gross error in certain observati

20、ons. A smaller inner reliability will lead to the detection of more gross errors. If the precision component is removed from Eq. 5, then a pure scale of inner reliability is presented as the controllable value, as follows: (6)This controllable value indicates how many times larger a gross error in a

21、 certain observation must be, compared to its standard deviation, so that can it be detected at least with confidence level 0 and the power of tests 0 . This value is independent of the observation unit.3) External ReliabilityExternal reliability reflects the effects of undetected gross errors on ad

22、justment (including all unknown coefficients , etc.). Given that there is just one gross error and that all of the observations are uncorrelated, the effect vector of undetected gross errors in certain observations on unknowns can be deduced from Eq. 2. Its module is as follows: (7)There are many th

23、eoretical methods, but in practice, the data snooping method presented by Baarda (1976) is often successively used to detect gross errors and to find dubiTable observations. Its generalized model is as follows: (8)and ;where is the standardized residual. When , it will be compared with, which decide

24、s whether it will be detected as a gross error.4) PrecisionPrecision indicates the difference between the transformed coordinates from one reference system and the known coordinates in another reference system. The residuals between the transformed and the known coordinates are generally considered

25、to represent precision. Mathematical expectation and standard deviation have been widely used in statistics to express precision of a calculation, shown as follows: (9) (10)where xi represents transformed coordinates, Xi represents known coordinates, n is the number of common points; is mathematical

26、 expectation and std is standard deviation. However, this does not provide the distribution of residuals. A random selection of 75% of all available data is used to generate a transformation model, while the other 25% are used to test the model (Wu Chen et al. 2005). The residuals from both data set

27、s are used to quantify the precision of the transformation. If all common points available are used to generate the model, without leaving data for testing the model, the result will only show how well the model fits the existing data. The precision of the transformation may be misleading, resulting

28、 in no clear indication of how well the transformation will perform with independent data.5) ExtensibilityExtensibility requires that the transformation model obtained from a given distribution of common points will be applicable beyond the boundaries of the distribution, within certain precision li

29、mits. If the transformation precision with the surrounding points is comparable to that obtained for the points used to generate the model, this transformation is extensible. Extensibility is important to a transformation. If no data are available outside the distribution for generating correspondin

30、g transformation parameters, a number of common points in the interior of the distribution need to be selected to generate these parameters. Prediction or checking transformations beyond the boundaries of the distribution is done in a similar manner.6) UniquenessUniqueness requires: (1) that each po

31、int in coordinate system 1 transforms to a single unique coordinate in system 2; (2) that different transformations used in different regions agree at the boundary of adjoining regions.B. Simulation IndicatorsWhen the reliability is taken into consideration for data transformation, the issue becomes

32、 a matter of distortions rather than of gross errors. The investigation of its simulation ability becomes both feasible and valuable.III. EXPERIMENTS AND DISCUSSIONSA. Data and MethodsIn this study, a total of 30 GCPs in the city of Anyang China, with coordinates in both the WGS 84 and Xian 80 coord

33、inate system (as shown in Fig. 2a), are used to provide several typical common point distributions. Coordinates of the GCPs in WGS 84 are obtained by tertiary GPS control surveying. UTMs are used to transform these into a plane coordinate system. Coordinates of the GCPs in Xian 80 are obtained by tr

34、iangular surveying. The 15 GCPs in the lower right of Fig. 2a are selected as a new distribution of common points in a smaller area (as shown in Fig. 2b). Some GCPs are so close to each other that they cannot be distinguished easily in either of the small-scale maps shown in Fig. 2a and Fig. 2b.Typi

35、cal transformation models used in these types of experiments have included analytic transformation, plane similarity transformation, and polynomial transformation. In analytic transformation, the coordinates in the plane system must first be transformed into a geodetic coordinate system, and then in

36、to a rectangular space coordinate system. The parameters of a 3D transformation model between two rectangular space coordinate systems are then generated by common points transformed from Xian 80 and WGS 84. In the current paper, we use Molodenski transformation with 3 parameters and Helmert transfo

37、rmation with 7 parameters as 3D transformation models. Given that the coordinate in the source system is, and the transformed coordinate in the target system is, the Molodenski transformation and Helmert transformation are shown as Eq.11 and Eq.12, respectively: (11) (12)Here, dX dY dZT is the trans

38、lation vector between the origins of the two systems, M is relative scale factor between two systems, and RX, RY, RZ are the rotation parameters from the source system to the target system. Plane similarity transformation and quadratic polynomial transformation can be implemented when both systems a

39、re plane coordinate systems. Given that the coordinates in source system areXS YS ZS, and the transformed coordinates in the target system are XTYTT, plane similarity transformation and polynomial transformation are shown as in Eq.13 and Eq.14,respectively. (13)where is the rotation angle between tw

40、o systems,is the coordinate of the origin of the source system in the target system, and dS represents the increment of scale between the two systems, as follows: , (14)Here, are parameters of polynomial transformation.In Fig.3a, the distributions of ROCs and internal reliabilities are maintained ev

41、enly, with no sudden disruptions. Although the distribution of external reliabilities becomes somewhat steeper, the actual values remain small. In Fig.3b, the distributions of all reliability indicators become steeper; but they all still maintain arelatively small value. In Fig.3c, distributions of

42、all reliability indicators are the steepest; in particular, the external reliabilities at some points are much greater than are others. In other words, it becomes more difficult to detect and to eliminate gross errors, and more errors may be absorbed within the parameters at these points. The effect

43、s of different transformation models on reliability of a transformation clearly indicate that rigorous analytical transformation provides better reliability. Fig. 4 follows similar rules. However, distributions of reliability indicators in each pane are now all worse than B. Testing Reliability Figu

44、res 3 and 4 show the effects of common point distribution and transformation models on the reliability of a coordinate transform. To conserve the number of pages, only experiments on more typical models such as the Helmert transformation, plane similarity transformation, and quadratic polynomial tra

45、nsformation, are shown and compared below. In the Figures, the ROC, internal reliability, and external reliability are calculated and shown as bars at each point, given significance level, power function , and the non-centrality parameter . Fig.4. Reliability indicators generated by typical transfor

46、mation models with common points shown in Fig.2bare those in the corresponding panes in Fig.3. Comparing Fig.1a and Fig.1b, the number of common points in Fig.2b becomes fewer and the distribution of common points also becomes more uneven. Fig.3 and Fig.4 show that the redundancy numbers and distribution of common points are key factors that impinge on reliability indicators. Adistribution of common points that provides high redundancy numbers therefore leads to reli