毕业论文坐标转换中英文翻译

本科毕业设计（论文）

中英文对照翻译

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XXX年X月X

Abstract

Studies 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 coordinate 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 effectiveness 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 model

. INTRODUCTION

Information about common 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 appear 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 reason, 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 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 isotropical 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. 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 ability 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 point 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. 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 METHOD

Fig.1. Flowchart of proposed QES.

Fig. 1 shows the flowchart for the proposed QES. In this paper, both the distribution 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” transformation 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 valuable. 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 Indicators

1) Redundant Observation Components

The general linearized 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 between 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 reliability 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) Internal Reliability

The 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 observations. 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 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 Reliability

External reliability reflects the effects of undetected gross errors on adjustment (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 theoretical 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 decides whether it will be detected as a gross error.

4) Precision

Precision 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 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 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 sets 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 in no clear indication of how well the transformation will perform with independent data.

5) Extensibility

Extensibility 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 limits. 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 corresponding 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) Uniqueness

Uniqueness requires: (1) that each point 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 Indicators

When the reliability is taken into consideration for data transformation, the issue becomes a matter of distortions rather than of gross errors. The investigation of its simulation ability becomes both feasible and valuable.

III. EXPERIMENTS AND DISCUSSIONS

A. Data and Methods

In this study, a total of 30 GCPs in the city of Anyang China, with coordinates in both the WGS 84 and Xi’an 80 coordinate 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 Xi’an 80 are obtained by triangular 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.

Typical 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 into 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 Xi’an 80 and WGS 84. In the current paper, we use Molodenski transformation with 3 parameters and Helmert transformation 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:

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