Modeling Systematic Errors for the Angle Measurement in a Virtual Surveying Instrument
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Ruei-Shiue Shiu1; Shih-Chung Kang2; Jen-Yu Han, M.ASCE3; and Shang-Hsien Hsieh, M.ASCE4
Abstract: The minimization and elimination of errors caused by instrumental imperfections or human operation is an important topic in surveying education. Nevertheless, despite the clear and definite behaviors of each surveying error, it is usually not easy to demonstrate on a blackboard their actual effects in field surveys. This is because multiple errors not only occur simultaneously, but also interact with one another. This study aims to develop a more effective teaching approach by simulating and visualizing a surveying instrument using computers. The emphasis is on modeling systematic errors that occur in real instruments. Nine kinds of instrumental errors were reconstructed and implemented as a module in SimuSurvey, an existing computer-aided instruction tool for surveying training. Based on the results of a user test, the computer-aided instruction tool with error modules provides a more realistic teaching material and thus can be an effective aid in surveying training. DOI: 10.1061/(ASCE)SU.1943-5428.0000046. © 2011 American Society of Civil Engineers. CE Database subject headings: Surveys; Measuring instruments; Errors; Engineering education; Simulation. Author keywords: Surveying; Instrumental errors; Engineering education; Simulation; Virtual reality; Surveying training.
Introduction Surveying technologies have become indispensable in modern life. They play important roles in the engineering of buildings, highways, railroads, bridges, tunnels, dams, and even urban development (Wolf and Ghilani 2002). Unfortunately, regardless of how carefully observations are made, surveying results always contain errors. Wolf and Chilani (2002) state every observation contains errors in their well-recognized surveying textbook. There are two methods for reducing and eliminating errors. The first is to improve the precision of instruments. A comprehensive review of this can be found in the review paper by Scherer and Lerma (2009). However, high-precision instruments are usually expensive and even then these instruments still have errors. The other method of reducing and eliminating errors is to adopt an appropriate surveying routine. This method essentially relies on the skill of well-trained surveyors. By following the correct surveying procedure, errors can be adjusted to obtain better results. This is an effective method, and therefore proper surveying education is very important. Increasing demands on surveying and spatial information techniques in engineering applications have led more and more schools to provide professional courses for training surveyors. A typical surveying course includes both indoor instruction, which covers surveying-related theories, and outdoor fieldwork, which provides 1
Graduate Student, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan. E-mail:
[email protected] 2 Assistant Professor, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan (corresponding author). E-mail:
[email protected] 3 Assistant Professor, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan. E-mail:
[email protected] 4 Professor, Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan. E-mail:
[email protected] Note. This manuscript was submitted on June 10, 2010; approved on October 14, 2010; published online on July 15, 2011. Discussion period open until January 1, 2012; separate discussions must be submitted for individual papers. This paper is part of the Journal of Surveying Engineering, Vol. 137, No. 3, August 1, 2011. ©ASCE, ISSN 0733-9453/2011/381–90/$25.00.
students with opportunities to familiarize themselves with the proper use of surveying instruments (Noéh 1999). The major drawback of this method of education stems from the constraints imposed because of the availability of physical instruments. Because most schools cannot afford to provide one instrument for each student, students need to share the instrument and take turns practicing. An insufficient number of instruments may reduce students’ learning performance and motivation. Rainy or foggy weather may also impede the learning activities. Furthermore, when surveying errors are considered, the teaching becomes even less effective. Although erratic behaviors (random or systematic) are clear and definite, different types of errors occur simultaneously and interact with each other. Consequently, it is not easy to visualize the instruction approach used in a surveying course. To overcome these problems in surveying education, simulations can be employed. Using simulations in education is a topic that has been studied for years. Many investigators, such as Gredler (1994), Rieber (1996), and Prensky (2001), have studied the applicability and effectiveness of simulations for educational purposes. They not only explained why simulations have great potential to be used in formal education settings, but also provided the theoretical framework for the educational use of simulations. Molenda and Sullivan (2003) pointed out that one of the most important values of the simulations is to provide high interactive feedback, which is very difficult to achieve using traditional teaching methods. Recently, Akilli (2007) summarized the related research in a review paper. It provides further evidence and theoretical background regarding this new approach in education. Some investigators, such as Amory et al. (1999), Noéh (1999), Ghilani (2000), and Muench (2006), started by applying and developing simulations to fulfill their own teaching goals. Among them, several investigators specifically used simulations to enhance surveying education. Edward et al. (2009) use a probabilistic approach to describe and visualize uncertainty and error in spatial data. Sokkia Corporation (2010) provided some videos over the Internet for demonstrating detailed surveying procedures and principles (e.g., setting up a level, theodolite, and total station). Ellis et al. (2006) employed Flash and QuickTime VR to create an interactive JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011 / 81
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multimedia learning environment for leveling surveys. Li et al. (2008) created a virtual reality learning system for surveying practice on a digital terrain model using a virtual total station. These teaching aids can assist instructors in explaining the concepts regarding the spatial relationship between the survey instrument and the targets.
Instrumental Errors
Error Model in Surveying Simulation
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whether the error models can be used in actual surveying education. The error model must be implemented and integrated with SimuSurvey. A user test must be conducted to evaluate the effectiveness of the error model in surveyor education.
An error model is an important component of a surveying training tool. This study focusus on one of the leading surveying teachingaid tools, SimuSurvey, which was developed by Lu et al. (2007). Kuo et al. (2007a, b) pointed out the benefit of using SimuSurvey in actual surveying courses; because all students can practice assigned tasks virtually on personal computers, their learning performance is better, and the maintenance cost for physical instruments can be reduced. After evaluation, the major drawback of SimuSurvey and other similar virtual surveying training tools are their “idealistic models.” Because the view of SimuSurvey is actually calculated from an ideal model of the instrument, there is no error in the system. In other words, students do not need to follow correct surveying procedure to obtain the correct survey results. This is apparently in contrast to the emphasis of surveying education. To alleviate this problem, it is necessary to develop an error model that can mathematically simulate surveying errors to enable the virtual instrument to provide realistic feedback. Many systematic errors, such as imperfection of the tilting axis and sighting axis, can be eliminated (Anderson and Mikhail 2000). To simulate instrumental errors on computers, a mathematical model that can calculate the readings with errors must be developed. This will allow further development of realistic surveying instruments in a virtual world. Challenge in Surveying Education One of the biggest challenges of surveying education is teaching instrumental errors. Many surveying textbooks, such as Elementary Surveying (Wolf and Ghilani 2002) and Surveying—Theory and Practice (Anderson and Mikhail 2000), include detailed explanations of instrumental errors. These explanations usually present each instrumental imperfection and illustrate how it influences overall survey results. Unfortunately, the textbooks’ explanations are usually made with figures, text, and simplified equations, which very difficult to apply in the development of virtual instruments. One major reason for this is that the explanations for individual errors cannot reflect the overall instrumental error, which is the overall consequence of all the imperfections that exist in the instrument. These individual errors are difficult to apply in the development of virtual instruments. Another reason is that textbooks present the errors mostly through two-dimensional models. Even though these equations are useful for explaining the individual instrumental error on papers, they are too simple for application on the simulation of the behavior of an imperfect instrument in a virtual environment. Therefore, this study evaluates the causes of the errors and develops a mathematical error model that can systematically present the influence of each part of the instrument imperfection and allow programmers to implement the model in a virtual environment. Research Objective and Tasks To improve the simulation of virtual surveying instruments, this study develops a modeling method that can simulate, on a computer, systematic errors caused by the instrumental imperfections. This model must be usable for simulating basic surveying instruments and at the same time be easily implementable on a computer system to support surveyor education. Validation is required for
Instrumental errors are caused by the imperfections in the construction and adjustment of instruments and from the movement of individual parts (Fialovszky 1990; Anderson and Mikhail 2000). These errors are usually persistent and cause systematic bias in the survey. For example, the rotational axes, which are supposed to be perpendicular to one another, may not be perfectly aligned at right angles. Some axes that are supposed to be vertical to the level surface may not be perfectly vertical. The effect of these instrumental errors can be reduced or even eliminated by adopting proper surveying procedures or applying computing corrections. These are important topics in surveying education. This study particularly focuses on modeling the systematic errors in the theodolite, one of the most sophisticated and commonly used instruments in both the field and the classroom. As shown in Fig. 1, five rotational axes—the vertical axis, the tilting axis, the sighting axis, the axis of plate level, and the axis of vertical circle—are present in a theodolite. Nine major instrumental errors may occur because of imperfect relationships among the axes. They are caused by imperfection in any of the following: (1) plate level axis; (2) vertical axis; (3) tilting axis; (4) sighting axis; (5) vertical circle index; (6) tripod centering; (7) tripod leveling; (8) eccentricity of vertical circle; and (9) eccentricity of the horizontal circle. The following section uses the definition of the axis shown in Fig. 1 and uses the horizontal axis to present an axis parallel to the level surface. Simulating Instrumental Errors on a Virtual Environment This study constructs a virtual survey by simulating actual survey scenarios. In this simulation on a virtual environment, as depicted in Fig. 2, the control point, labeled (x0 , y0 , z0 ), presents a known point. The target point, labeled (xt0 , yt0 , zt0 ), presents the coordinates to measure. A survey instrument is set up on a tripod at the control point and aimed at the level rod by a telescope to obtain readings of the horizontal and vertical angles. H T = height of the tripod; d I = distance between the axis of plate level to the tilting axis of instrument; D = distance between the known position and the target position; θv = vertical angle obtained from the vertical circle; θh = horizontal angle obtained from the horizontal circle; and H r = reading of the level rod. In the postcomputing procedure, (xt , yt , zt ) could be obtained from (x0 , y0 , z0 ), θv , θh and the height of instrument, and then (xt0 , yt0 , zt0 ) could be obtained by reducing H r from (xt , yt , zt ). Because of instrumental errors, the height and position of the instrument, the target position that the telescope is aimed at, and the readings of angles should be different from the true values. Instead of using the height of instrument, consider a point, eye position, labeled (xe , ye , ze ) to represent the center of telescope. After instrumental errors are taken into account, the eye position changes from (xe , ye , ze ) to (x0e , y0e , z0e ) and the position of the target changes from (xt , yt , zt ) to (x0t , y0t , z0t ). This study provides a procedure for simulating instrumental errors on computers. The simulation can be divided into three parts: (1) calculating the eye position with errors; (2) calculating the target position with errors; and (3) calculating the reading with errors.
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Fig. 1. Typical structure of a theodolite: (a) a view of vertical circle and horizontal circle; (b) front view when θv = 90°
Fig. 2. Simulation of the virtual survey scenario
Error Modeling This section first presents an overview of all the axes inside an instrument and their relationships by using homogeneous transformation matrices. Then the model is followed (with instrumental errors) to derive the equations to compute the actual position of the surveyor’s eyes and the actual target position. Finally, the equations that simulate the errors in the reading system in the instrument are also presented. Overview of Error Modeling This study categorizes the nine instrumental errors into three groups. The first group consists of errors that influence the calculation of actual eye position. This group includes (1) plate level axis; (2) vertical axis; (3) imperfection from tripod centering; and (4) tripod leveling. The second group consists of errors that influence the calculation from the eye position to the target
position. This group includes (5) imperfect tilting axis; and (6) sighting axis. The third group consists of errors in the reading system. This group includes imperfections in (7) the initial index of vertical circle; (8) eccentricity of the vertical circle and (9) eccentricity of the horizontal circle. Fig. 3 shows the geometrical relationships of the axes inside a virtual instrument modeling with errors: θZZ = angle between the direction perpendicular to tilting axis and the sighting axis of instrument projected on the x-y plane; θHH = angle between the direction perpendicular to the vertical axis of instrument and the tilting axis of instrument projected on the x-z plane; θVZ = angle from the direction perpendicular to the plate level axis to the vertical axis of instrument vector projection on the x-z plane; θSZ = angle between vertical direction (z-axis) and the normal vector of the plate level plane projected on the x-z plane; and θSV = angle from the horizontal direction (y-axis) to the normal vector of plate level plane projected on the x-y plane. JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011 / 83
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Fig. 3. Overview of axes with errors in theodolite
Eye Calculation
Et = homogeneous transformation matrix to transform the control point to the center of the bottom of the instrument; E v = homogeneous transformation matrix to transform the coordinate of center of bottom of the instrument to X v (as shown in Fig. 3), which represents the intersection of the plate level axis and the imaginary line between the center of the bottom of the instrument and the center of the telescope; and Es = homogeneous transformation matrix to transform X v to the eye position, X e .
As shown in Figs. 2 and 3, the actual eye position is located at the intersection of the tilting axis and the sighting axis of instrument. It can be calculated by using a series of homogeneous transformation matrices from the control point (which is a known point) to the eye position. Overall Calculation of Eye Position Four instrumental errors must be considered for calculating actual eye positions. These include the error of tripod centering, the error of tripod leveling, the error of plate level axis, and the error of vertical axis. The overall calculation of eye position can be presented as X 0e ¼ Es Ev E t X 0
Deriving Transformation Matrix Et Et is a homogeneous transformation matrix to transform the coordinate of the control point, X 0 , to the bottom center of the instrument, X c (shown in Fig. 3). It includes the errors from tripod centering and leveling. Fig. 4 illustrates the scenario in which a tripod is not perfectly centered and the leveling problem in the tripod. N T is the normal vector of the tripod platform. From the figures, E t can be derived using
ð1Þ
where X 0e ¼ ½x0e y0e z0e 1T , the eye position with errors; X 0 ¼ ½x0 y0 z0 1T are the coordinates of the known position in surveying;
2
cos θLZ · cos θLV 6 sin θLZ · cos θLV Et ¼ 6 4 sin θLV 0
sin θLZ cos θLZ 0 0
cos θLZ · sin θLV sin θLZ · sin θLV cos θLV 0
where θLV = angle from the vertical direction (z-axis) to the N T vector projection on the x-z plane; θLZ = angle from the horizontal direction (y-axis) to the N T vector projection on the x-y plane; H T = distance from the top of the peg to the center of the tripod; θCV = angle from the vertical direction (z-axis) on the control point (known point) to the imaginary line from the control point to the center of the tripod platform, projected to the x-z plane; and θCZ = angle from the horizontal direction (y-axis) to the imaginary line from the control point to the center of the tripod platform, projected to the x-z plane.
3 H T · sin θCV · sin θCZ H T · sin θCV · cos θCZ 7 7 5 HT 1
ð2Þ
Deriving Transformation Matrix Ev Ev is a homogeneous transformation matrix to transform the coordinate of the bottom center of the instrument to X v , which represents the intersection of plate level axis and the imaginary line between the center of the bottom of the instrument and the center of the telescope. Fig. 5 illustrates the case of an instrument with an imperfect vertical axis. N v is the vertical axis of instrument, the imaginary line passing through the center of the bottom of the instrument and the center of the telescope. Because of the imperfection in the instrument, N v may not be parallel to the vertical direction. By analyzing the spatial geometry, E v can be derived as
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2
cosðθVZ þ θh Þ · cos θVV 6 sinðθVZ þ θh Þ · cos θVV Ev ¼ 6 4 sin θVV 0
sinðθVZ þ θh Þ cosðθVZ þ θh Þ · sin θVV cosðθVZ þ θh Þ sinðθVZ þ θh Þ · sin θVV 0 cos θVV 0 0
3 0 07 7 ds 5 1
ð3Þ
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where d S = distance from the center of the bottom of the instrument to the plate level axis; θh = horizontal angle; θVV = angle from the vertical direction (z-axis) to N v vector projection to the x-z plane; and θVZ = angle from the horizontal direction (y-axis) to the N v vector projected on the x-y plane. Deriving Transformation Matrix Es E s is a homogeneous transformation matrix to transform the coordinates of X v (shown in Fig. 3) to the eye position, X e . Fig. 6 illustrates an instrument with an imperfect plate level axis. N S is the normal vector of the plate. It is also a horizontal rotational axis for the upper part of the instrument. It includes the error from the level axis of instrument. From the schematic shown in Fig. 6(c), Es can be derived as 2 3 cos θSZ · cos θSV sin θSZ cos θSZ · sin θSV d I · cos θSZ · sin θSV 6 sin θSZ · cos θSV cos θSZ sin θSZ · sin θSV d I · sin θSZ · sin θSV 7 7 ð4Þ Es ¼ 6 4 5 sin θSV 0 cos θSV d I · cos θSV 0 0 0 1
where d I (shown in Fig. 5) = distance from the level axis to the tilting axis of the instrument; θSV = angle from the vertical direction to the N S vector projected on the x-z plane; and θSZ = angle from the horizontal direction (y-axis) to the N S vector projected on the x-y plane.
point and X 0t as the target position with error included. When calculating X 0t , two instrumental errors are specifically considered: the angular error of the tilting axis and the angular error of the sighting axis. By analyzing geometrical relationship between the axes in Fig. 3, the following equation can be derived to find the target position:
Target Calculation The target position represents the observation point aimed by a telescope of an instrument. Because of the errors in the instrument, the target position obtained from a real instrument is not exactly the point obtained from the “perfect” instrument in the virtual environment. This section focuses on presenting the procedure of calculating target position taking errors into consideration. Calculation of Target Position To calculate the real target position, Fig. 3 must be reviewed because it illustrates the major axes in a theodolite. As mentioned previously, X e is the ideal eye position that is located at the intersection of the vertical axis and tilting axis. X 0e is the real eye position located at the intersection of the vertical axis with error and the tilting axis with error. To find the target position, the coordinates of the target position must be calculated from the eye position. This includes coordinate translation by using the horizontal angle of the instrument, vertical angle of the instrument, and the distance between the control point and the target. Here two points are defined, X t as the ideal target
2
cosðθh þ θHH Þ 6 sinðθh þ θHH Þ Eh ¼ 6 4 0 0
X 0t ¼ Eh Ez X 0e
where X 0t ¼ ½x0t y0t z0t 1T = target position with error considerations; X 0e ¼ ½x0e y0e z0e 1T = eye position with error considerations; and Eh is a homogeneous transformation matrix that represents the rotation of the telescope about the imperfect tilting axis. It includes the error caused by the mismatch between the tilting axis of instrument and the ideal tilting axis. E z = homogeneous transformation matrix that represents the rotation of the telescope about the imperfect vertical axis. This includes the error caused by the imperfect perpendicular alignment of the sighting axis to the tilting axis. Deriving Transformation Matrix Eh Eh is a homogeneous transformation matrix for rotating the telescope about the imperfect tilting axis. Fig. 7 illustrates the tilting axis error in different configurations. Figs. 7(a) and 7(b) illustrate the front view and top view, respectively, when the telescope is pointed vertically upward (zenith = 0°). Fig. 7(c) illustrates the front view of another configuration in which the telescope is horizontal (zenith = 90°).Geometrical analysis results in Eq. (6):
sinðθh þ θHH Þ · cos θHV cosðθh þ θHH Þ · cos θHV sin θHV 0
where θHV = angle from the ideal tilting axis to the imperfect tilting axis projection to the y-z plane; and θHH = angle from the ideal tilting axis to the imperfect tilting axis projection on the x-y plane. Deriving Transformation Matrix Ez E z is a homogeneous transformation matrix representing the rotation of the telescope about the titling axis and the translation from
ð5Þ
sinðθh þ θHH Þ · sin θHV cosðθh þ θHH Þ · sin θHV cos θHV 0
3 0 07 7 05 1
ð6Þ
the imperfect eye point to the imperfect target point. Fig. 8 illustrates configurations of the instrument with sighting axis errors from the front view and top view. Figs. 8(a) and 8(b) illustrate the front view and top view of the instrument, respectively. The telescope is pointed vertically upward (i.e., zenith distance is 0°) in the figures. Fig. 8(c) illustrates two possible configurations, i.e., zenith distance is 90° or 270°. E z can be presented as JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011 / 85
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instrument, the errors caused by the imperfect reading system in an actual instrument must be added. This study models the following errors: the vertical circle index error, eccentricities of the vertical, and horizontal circle.
Implementation
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The error models developed in this study were implemented on a computer-based surveyor training tool, SimuSurvey (Lu et al. 2007). The implementation details, including dataflow of the system and the user interface, are described in the following sections. Fig. 4. Error caused by failure to center the tripod on the peg: (a) front view; (b) top view
2
cos θZ 6 0 Ez ¼ 6 4 sin θZ 0
0 1 0 0
sin θZ 0 cos θZ 0
3 D0 · cos θZZ · cos θZ 7 D0 · sin θZZ 7 0 D · sin θZZ · cos θZ 5 1
ð7Þ
where θZ = zenith distance; θZZ = angle from the axis perpendicular to the horizontal axis to the sighting axis; and D0 = horizontal distance between the target and the control point with distance measurement error. Reading Calculation Because of imperfections in the reading system, the surveyor is unable to obtain the ideal readings from the instrument. To calculate the real readings (the readings including errors) from a virtual
Brief Introduction to SimuSurvey SimuSurvey was implemented using the OpenGL library (Shreiner 2005) and C# (Liberty 2006) and designed for use in surveying training through a computer-generated virtual environment. SimuSurvey provides five major simulators to support various training activities, including a level simulator, a theodolite simulator, an accessory simulator, a total station simulator, and a tangible controller. The modules provided by SimuSurvey include (1) the visualization module, which visualizes the survey instrument and measurement poles involved in an assigned survey task; (2) the manipulation module, which simulates the control interface of real surveying instruments and provides real-time interaction with users; (3) the calculation module, which calculates the ideal point and ideal reading during the surveying task; (4) the operation recording module, which records the operation of users for display and analysis; and (5) the learning activity module for students to practice surveying tasks in a simulated environment.
Fig. 5. Error caused by the mismatch between the vertical axis of instrument and vertical direction (z-axis); (a) front view; (b) top view; (c) schematic view
Fig. 6. Error caused by the level axis not being perpendicular to the vertical direction (z-axis): (a) front view; (b) top view; (c) schematic view 86 / JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011
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Fig. 7. Error caused by the horizontal axis (tilting axis) not being perpendicular to the vertical axis of instrument: (a) front view when zenith = 0°; (b) top view when zenith = 0°; (c) top view when zenith = 90°
Fig. 8. Error caused by the sighting axis not being perpendicular to the tilting axis of instrument: (a) front view when zenith distance = 0°; (b) top view when zenith distance = 0°; (c) top view when zenith distance = 90° or 270°
Previous papers (Kuo et al. 2007a, b; Lu et al. 2009) explain the technical details and the application of SimuSurvey in a real surveying class. One of its major drawbacks pointed out in previous studies is the lack of reasonable simulation for instrumental errors, which is a critical topic in a surveying training course. Dataflow of the Error Simulation Module The mathematical error models [i.e., Eqs. (1)–(7)] were implemented as a module in SimuSurvey. Fig. 9 shows the dataflow of SimuSurvey with the error module. The dataflow in the original SimuSurvey (without error considerations) is depicted on the left. The control point (x0 , y0 , z0 ) is a known position during surveying, and it is the major input when a user manipulates the virtual instrument. The eye position (xe , ye , ze ) is calculated by using the calculation module in SimuSurvey. After the eye position is calculated, the system allows users to manipulate the virtual instrument through the manipulation module. The users adjust θv and θh in the system during this process. The system then calculates the target position (xt , yt , zt ) in real time, and then the visualization module visualizes the view of the telescope. The users finally obtain the values of θv and θh . With the error module added, the dataflow is different (shown as the solid-line dataflow in Fig. 9). Three submodules—eye calculation, target calculation, and reading calculation—are included in the error module. The eye calculation module calculates the eye position from the control point, (x0 , y0 , z0 ) to the actual eye position (x0e , y0e , z0e ) using Eq. (1). Related instrumental errors are considered during the processes. The users may also adjust θv and θh by using the manipulation module, and then the system sends the parameters to the target calculation submodule. The actual target position (x0t , y0t , z0t ) can be calculated using Eq. (5). After calculation of the eye
Fig. 9. Dataflow of SimuSurvey with error considerations
position and target position with error consideration, the visualization module visualizes the view of telescope with error considerations. Finally, the reading calculation module factors in the reading errors. The actual readings θ0v and θ0h are then displayed in the system. Although users may not notice the differences between the original and revised dataflow in terms of the manipulation processes, the instrumental errors have been considered implicitly as an actual instrument. JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011 / 87
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Fig. 10. User interface of SimuSurvey with error considerations
User Interface of SimuSurvey with the Error Module
Background of the Testers
After the development of the error module, three additional interfaces were also developed to leverage the use of the error module in surveying training. The first interface is the interactive interface for error configuration. As shown in Fig. 10(a), this interface displays a three-dimensional (3D) instrument with major axes and an input panel for customizing the errors in the virtual instrument. This interface allows the user to modify the parameters associated with instrumental errors and obtain real-time visual feedback in the 3D instrument. This can enhance the student’s understanding of the effects of the errors in the motion of the instrument. The second interface is designed to allow users to define multiple instruments in a virtual environment, as shown in Fig. 10(b). This will facilitate teaching activities by allowing the comparison of instruments with different error configurations. The third interface is the optional ideal view of the telescope, as shown in Figs. 10(c) and 10(g). This allows viewing the telescope with and without the error considerations. Figs. 10(d) and 10(h) show the different interface of the detail control for users. A representation of the side and top views of the virtual instrument are shown in Figs. 10(e) and 10(f).
Thirty undergraduate students who were taking surveying courses were included in the study. All the students learned the concepts of instrumental errors in the class. Instructors had explained the related concepts and the cause and effect of the errors using textbooks. In addition, all the students were also experienced users of the original SimuSurvey (without error considerations). They were already familiar with the manipulation of the virtual instrument in SimuSurvey using the mouse and keyboard. Procedure of User Testing
User Test
The user test was composed of a pretest, a 1 h learning session, and a posttest. The purpose of the pretest was to obtain the baseline of the testers’ knowledge about the concepts of instrumental errors. The learning session was a self-learning task. Testers were instructed to follow a specific procedure to manipulate SimuSurvey. This procedure was designed to allow the testers to explore, observe, and naturally learn the cause and effect relationship between the imperfection of the instrument and the surveying results. The posttest measured the testers’ learning performance during the learning session. At the end of the user test, the results of the pretest and posttest were statistically compared to determine whether the new version of SimuSurvey enhanced testers’ understanding of surveying errors.
A user test was conducted to validate the feasibility and practicality of SimuSurvey with error considerations for surveying training. The objective was to find out whether the error module in SimuSurvey can enhance students’ understanding of topics related to instrumental errors.
Pretest Session Fig. 11 presents (a) an instrument with vertical axis errors; (b) an instrument with sighting axis errors; and (c) an instrument with tilting axis errors. In an ideal case, when a user rotates the telescope by θV , the crosshair of the telescope points to the ideal initial point
Fig. 11. Behaviors of instrumental errors: (a) vertical axis error; (b) sighting axis error; (c) tilting axis error 88 / JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011
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(point A in Fig. 11) and then to the ideal ending point (point a in Fig. 11). But when the instrumental error is considered, the crosshair of the telescope will point to another point A0 at the beginning and a0 in the end. The pretest also included three basic but important questions asked in many surveying textbooks. They are as follows. (1) Which errors can be eliminated by taking the mean of two angular observations? (2) Which errors affect the reading of the horizontal angle? (3) Which errors affect the reading of the vertical angle? Learning Session The testers were separated into 10 groups of three testers each. During the learning session, no instructions were provided except for help with problems in the use of the software. In a 60-min learning session, the testers learned by themselves by manipulating the software and by following the steps described subsequently. The first step was to load a file to import a predefined virtual survey environment. This environment included a virtual theodolite, a level ruler, and a field for surveying. In the second step, testers were asked to aim the crosshair of the telescope toward the top right corner of the level rod and then to record the vertical angle and horizontal angle read from the system. The third step asked testers to rotate the telescope downward to aim at the bottom right corner of the level ruler and to record the vertical angle and the horizontal angle read from the system. The fourth step was to perform the same procedure as the third step and obtained readings from the two corners with the setup of telescope reversed. From the fifth step on, testers were asked to assign individual instrumental errors to the virtual instrument and to observe its behavior to learn about the cause and effect of the errors. The fifth step was to modify the instrumental errors through the interface of the error configuration window [as shown in Fig. 10(a)]. Testers were asked to set the vertical axis error as 30°00’00” (an exaggeration from reality to highlight the effect of the vertical axis error) and repeat Steps 2–4 to obtain four readings with the telescope in the direction position and with the telescope reversed from the two corners. The sixth and seventh steps asked testers to reset the error configuration and assign 00°30’00” to the error of the tilting axis and likewise to the vertical circle index. They also needed to repeat
Steps 2–4 to obtain the readings. Finally, the testers summarized the readings and calculated θV , the actual rotational angle of the telescope between point A and point a. Posttest Session A posttest was conducted after the learning session. The purpose of the posttest was to determine whether testers understand instrumental errors after performing the given task using SimuSurvey in the learning session. The questions in the posttest were equivalent to those in the pretest. After both the pretest and posttest, both tests were graded and their scores were recorded. Results of User Test The results of the pretest and posttest are shown in Fig. 12. It shows that before the learning session, the percentage of correct answers was on average 29.67%. After the learning session, the testers’ percentage of correct answers was 73.33% on average. As shown in the second row of Fig. 12, only one tester answered more than 50% of the questions correctly during the pretest. After completing the learning session, all 30 testers answered more than 50% of these questions correctly. The result shows us that, on average, users who correctly answered less than 20% in the pretest experienced improvement of about 50%. When their correctness-answering rate in the pretest was 40%, the progress was about 41%. Although all the students learned the concepts of instrumental errors in the class, most of them were unable to link the effect of the errors to a real situation. SimuSurvey simulates a virtual instrument with consideration of errors, which cannot be achieved in the real world, to assist the users in understanding the effect of errors. The t-test also shows the statistical significance of the change in the number of correct answers between the pretest and posttest (t0:01ð29Þ ¼ 2:462, p < 0:01). By having students perform a specific task, SimuSurvey can significantly improve the users’ understanding on instrumental errors.
Major Contributions of This Research This research includes three major contributions. First, mathematical error models that can simulate the imperfection of real surveying
Fig. 12. Percentage of correct answers from the pretest and posttest JOURNAL OF SURVEYING ENGINEERING © ASCE / AUGUST 2011 / 89
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instruments on computers were developed and implemented. Homogeneous transformation matrices were used to present the complex spatial geometry relationship in a real instrument. It can not only provide a concise format for presenting spatial information, but also facilitate the implementation of the error model on computers. Additionally, common graphics cards by ATI and NVIDIA are even able to support the acceleration of matrix computations. Second, the error models were implemented as a module and integrated with SimuSurvey, a computer-aided instruction tool specifically developed for surveyor training. For the students, it provided an opportunity to practice correct surveying procedures that are designed to eliminate these errors. For the instructors, it can generate multiple instruments, each with different errors, to facilitate in-class explanations and other teaching activities. Third, a user test was conducted with 30 testers who were taking surveying courses at the time. A virtual instrument that visually provides the realistic feedback to the users can effectively facilitate the learning process. The results validate the effectiveness of the use of virtual instrument tools with error models for surveying training.
Conclusions In this research, an error model was developed to realistically simulate the instrumental errors for surveying education. The error model is presented using multiple matrices. Each matrix presents a single imperfection relationship between the rotational axes in a surveying instrument. The error model was implemented as an error module and integrated into SimuSurvey, an existing virtual surveying training tool. A user test was conducted to validate the effectiveness of the error module. The results reveal a significant improvement on the students’ learning performances, which can be attributed to the successful implementation of realistic surveying instruction tool develop in this study.
Acknowledgments The authors wish to express gratitude to Cho-Chien Lu of National Taiwan University for developing the original SimuSurvey. Also, thanks to Ms. Suet-Wa Choi of National Taiwan University for providing technical support of the user tests.
References Akilli, G. K. (2007). “Games and simulations: A new approach in education?” Games and simulations in online learning: Research and development frameworks, D. Gibson, C. Aldrich, and M. Prensky, eds., Information Science, Hershey, PA, 1–20. Amory, A., Naicker, K., Vincent, J., and Adams, C. (1999). “The use of computer games as an educational tool: Identification of appropriate game types and game elements.” Br. J. Educ. Technol., 30(4), 311–321.
Anderson, J. M., and Mikhail, E. D. (2000). Survey: Theory and practice, 7th Ed., McGraw-Hill, New York. Edward, S. F., Thomas, K. W., and Kate, B. (2009). “Probabilistic approach for modeling and presenting error in spatial data.” J. Surv. Eng., 135(3), 101–112. Ellis, R. C. T., Dickinson, I., Green, M., and Smith, M. (2006). “The implementation and evaluation of an undergraduate virtual reality surveying application.” Proc., Built Environment Educational Conf. (BEECON 2006), London. Fialovszky, L. (1990). Surveying instruments and their operational principles, Elsevier Science, Budapest, Hungary. Ghilani, C. D. (2000). “The surveying profession and its educational challenge.” Surv. Land Inform. Syst., 60(4), 225–230. Gredler, M. E. (1994). Designing and evaluating games and simulations: A process approach, Gulf Publication, Houston. Kuo, H. L., Kang, S. C., and Lu, C. C. (2007a). “The feasibility study of using a virtual survey instrument in surveyor training.” Proc., Int. Conf. on Engineering Education (ICEE 2007), Coimbra, Portugal. Kuo, H. L., Kang, S. C., Lu, C. C., Hsieh, S. H., and Lin, Y. H. (2007b). “Using virtual instruments to teach surveying courses: Application and assessment.” Computer-Aided Engineering Rep., Dept. of Civil Engineering, National Taiwan Univ., Taipei, Taiwan. Li, C. M., Yeh, I. C., Cheng, S. F., Chiang, T. Y., and Lien, L. C. (2008). “Virtual reality learning system for digital terrain model surveying practice.” J. Prof. Issues Eng. Educ. Pract., 134(4), 335–345. Liberty, J. (2006). Programming C#, 4th Ed., O’Reilly Media, Sebastopol, CA. Lu, C. C., Kang, S. C., and Hsieh, S. H. (2007). “SimuSurvey: A computerbased simulator for survey training.” Proc., CIB 24th W78 Conf.; and 14th EG-ICE Workshop; and 5th ITC@EDU Workshop, Maribor, Slovenia. Lu, C. C., Kang, S. C., Hsieh, S. H., and Shiu, R. S. (2009). “Improvement of a computer-based surveyor-training tool using a user-centered approach.” Adv. Eng. Inform., 23(1), 81–92. Molenda, M., and Sullivan, M. (2003). “Issues and trends in instructional technology: Treading water.” Educational media and technology yearbook, M. A. Fitzgerald, M. Orey, and R. M. Branch, eds., Libraries Unlimited, Englewood, CO, 3–20. Muench, S. T. (2006). “Self-managed learning model for civil engineering continuing training.” J. Prof. Issues Eng. Educ. Pract., 132(3), 209–216. Noéh, F. (1999). “Training for the architecture students in surveying at the Technical University of Budapest.” Period. Polytechnica Civ. Eng., 43(1), 55–61. Prensky, M. (2001). Digital game-based learning, McGraw-Hill, New York. Rieber, L. P. (1996). “Seriously considering play: Design interactive learning environments based on the blending of microwolds.” Educ. Technol. Res. Dev., 44(2), 43–58. Scherer, M., and Lerma, J. L. (2009). “From the conventional total station to the prospective image assisted photogrammetric scanning total station: Comprehensive review.” J. Surv. Eng., 135(4), 173–178. Shreiner, D., Woo, M., Neider, J., and Davis, T. (2005). OpenGL programming guide: The official guide to learning OpenGL, 5th Ed., Addison Wesley, New York. Sokkia Corporation. (2010). “Sokkia’s robotic total station.” 〈http://www .sokkiasrx.net〉 (May 31, 2010). Wolf, P. R., and Ghilani, C. D. (2002). Elementary surveying: An introduction to geomatics, 10th Ed., Prentice-Hall, Upper Saddle River, NJ.
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