Using Reorientation Traversing on a Single-Unknown

Peer Reviewed

Using Reorientation Traversing on a Single-Unknown Station or Multiple-Unknown Stations to Solve the Two-Point Resection (Free Station) Problem Akajiaku C. Chukwuocha ABSTRACT: Traditionally, the two-point resection problem, which is coordinating an unknown station from which lines to two control stations and the included angle are measured without setting up on the control stations (free stationing), is accomplished by solving the triangle formed. There must be only a singleunknown station intervisible with the controls, otherwise the method fails. These limitations are overcome by the new reorientation traversing method by solving the system in a twofold traverse computation. The advantage is successfully coordinating desired single stations or when there is no intervisibility with either or both controls to set up on a few additional stations without setting up on the controls. Field observations were made on a single-new station with intervisibility to the two controls. In another case where the station desired to be coordinated was not intervisible with the two controls, two additional stations were also set up on without setting up on the control stations. A t-distribution test at 99 percent confidence level with a P-value test on the results proved the credibility of the reorientation traversing in solving both cases of the two point resection survey. The reorientation traversing is the only method known for resection survey of multiple-unknown stations in a lone network. KEYWORDS: Two-point resection, reorientation traversing, free station surveys, distance resection, wall stations survey, resected traversing, traverse, accuracy, total station instrument

Introduction

R

esection surveying also referred to as free stationing (Grobler 2016) is the method of survey control extension in which an unknown station is coordinated by taking measurements from the instrument set up over it to some control stations without setting up on the control stations (Chamdra 2005). Generally, there are two types of resection surveys. The first is the case where a point is coordinated by only angles measured at the unknown station between lines to at least three control stations. This method is identified as angular resection (Uren and Price 2006). The resection survey method that requires a minimum of two control points, involves measuring of lines from the station to be coordinated to the two control stations and the angle included by the lines is named the two-point resection survey (Ghilani and Wolf 2012; Smith 2011) because of the requirement of two controls. It is also identified as distance resection (Uren and Price 2006) or free stationing Akajiaku C. Chukwuocha, Department of Surveying and Geoinformatics, Federal University of Technology, Owerri, P.M.B. 1526, Owerri 460001, Imo State, Nigeria. Tel: +2348033398505. E-mail: .

(Uren and Price 2006; Zeiske 2004) or in mining, as wall stations survey (Smith 2011). Major attractions of two-point resection (distance resection) include that, for large projects involving surveying or staking out, the most favorable stations for the instruments may be coordinated by this method. In addition to, when coordinating points under a forest canopy where Global Positioning System (GPS) would not obtain good result the twopoint resections may be used (MacKinnon and Murphy 2011). Two-point resection software that compute the operations are now imbedded in standard total station instruments for computation of the free stations in real time (MacKinnon and Murphy 2011; Zeiske 2004), for example that developed in Zimmerman (1996) (Grobler 2016). The method is also being increasingly employed in tunnel surveys as free stationing in the hanging wall surveys (McCormack 2002). In the traditional two-point resection method illustrated in Figure 1, the total station instrument is set up over the unknown station P only and the internal angle APB, at P is measured together with the distances PA and PB. From Figure 1 the angles BAP and ABP are calculated by the cosine rule. Then the azimuths for lines AP and BP are computed from azimuth of the control line AB and the angles BAP and ABP, respectively. Using the coordinates of the control points A and B and

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Theoretical Concept: Using the Reorientation Traversing Technique to Solve the Two-Point Resection (Free Stationing) Problem Reorientation traversing which may also be termed resected traversing is a method of traversing, which may be used to achieve required traverse accuracy even though the field observations omit angular measurements at the takeoff Figure 1. Two-point resection (distance resection) scheme. and closing control stations. It then implies that the reorientation traverse for the single-new stathe azimuths and distances of AP and BP, retion case is the equivalent of the two-point respectively, two sets of the coordinates of the unsection survey because the same quantities are known station are computed and the average taken measured in the field in both cases. (Trimble Navigation Limited Engineering and Figure 2A and B present two different cases in Construction Division 2013; Uren and Price 2006). which a single-point is to be coordinated by traMcCormack (2002) details five different methods ditional traversing from two control stations in of computing the resection. An example of these a closed figure traverse and a link type traverse, methods is the commonly used cosine rule. Each respectively. The traditional traverse begins with of those methods employs the process of solving an instrument set up on the takeoff control stathe resection triangle, which all suffer major tion A, at which a line of known azimuth AB trigonometric limitations experienced in all (Figure 2A) or AA1 (Figure 2B) is referenced for solutions-of-triangles. It is required that for the measurement of the angle to carry over azimuth solution-of-triangles methods, none of the internal control into the new traverse. The traditional ° angles of the triangle should be greater than 135 traverse runs on the unknown point P and then and that the control stations are not close to each ends with the instrument set up on the closing other for some satisfactory coordinate determinacontrol point B with a closing angular sighting on tion (MacKinnon and Murphy 2011; Washington the line of azimuth control BA (Figure 2A) or BB1 State Department of Transportation 2005; Trimble (Figure 2B). The traverse is computed normally Navigation Limited Documentation Group 2001). using the coordinates of the control stations and The triangle shape restrictions and the strict conall the field-observed quantities by computing the dition that the two control stations must be visible coordinates of successive ends of the traverse legs from the unknown station in the traditional twoor by least squares adjustment. point resection procedure are major limitations to If the pairs of points A and B in Figure 2A, A and the surveyors’ aim of coordinating the unknown A1, or B and B1 (Figure 2B) are not intervisible and station by the two-point resection method. Howhence a traverse originating at A and closing at B ever these limitations are mitigated when the reis without takeoff and closing angles then a two orientation traversing method is used. point resection case occurs and the traditional traverse cannot be computed in such a case. The computation of the two point resection in the reorientation traversing method is illustrated in Figure 3. The reorientation traverse is computed in a twofold process. The figure is first computed using the known coordinates of station A, an assumed azimuth of line AP, and the fieldobserved quantities of distance AP (d1), angle APB (f1) at P and the distance PB (d2). The coordinates thus determined for P0 and B0 are in Figure 2. Diagrams illustrating the two methods used in traditional an arbitrarily oriented system, even traversing. though they are in the same map

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Figure 3. Solving the distance resection with reorientation traversing. plane as the published coordinates of A and B. In the preliminary computation the reorientation angle g, may be computed by subtracting the azimuth of the disoriented control line AB0 from the correct azimuth of the control line AB computed from the published coordinates of the control stations. Then g is added to the arbitrary azimuth of AP0 to determine the correct azimuth of AP, which is then used to compute the traverse figure and obtain the coordinates of P. An alternative approach is to compute the base angles BAP (d1) and PBA (d2) from the azimuths of the bordering lines derived from the coordinates of the stations A, P0, and B0, in the arbitrary orientation. An alternative approach is if in this first stage the coordinates of station A is assumed to be (0, 0), and azimuth of line AP assumed to be 180°, then azimuth of line PB will be equal to angle APB (f1) and the coordinates of the three points are as follows:

The full details of the reorientation traversing and how the arising concerns such as in situ checks are taken care of have been fully discussed in Chukwuocha et al. (2017). The aim of this paper is to present reorientation traversing as a credible process for coordinating the unknown station in the twopoint resection (distance resection) situation, without the procedure of solving triangles. The use of the reorientation traversing will allow for the unknown station to be positioned exactly where it is desired without being hampered by bad triangle geometry. In addition with the reorientation traversing method the strict requirement of intervisibility between the unknown point and the controls is not necessary, making room for a special two-point resection scheme in which a new set of controls in a site are established to share internal consistency. Two test case surveys were carried out, the first to validate the method of reorientation traversing in a traditional resection case, and the second to demonstrate the feasibility of the multipleunknown station reorientation traversing to cope with situations of nonintervisibilty between the control stations and the station required to be coordinated. The first was computed both as reorientation traverse (resected traverse) and as a twopoint resection. In each of the two cases a traditional traverse was run to serve as control test.

Materials and Methods Field Survey The field surveys were carried out at Federal University of Technology Owerri, South East Nigeria, shown in the May 2017 Google Earth image in Figure 4 (Google Earth Pro 7.1, 2013). Two control stations, FUTOG 004 near the Senate Building area of the University and FUTOG 005

Coordinates of P1 ðx; yÞ 5 P1 ð0; 0Þ

(1)

Coordinates of P2 ðx; yÞ 5 P2 ðd1 $sin 180° ; d1 $cos 180° Þ 5 P2 ð0; 2 d1 Þ

(2)

Coordinates of P3 ðx; yÞ 5 P3 ðd1 $sin 180° + d2 $sind2 ; d1 $cos 180° + d2 $cos$d2 Þ 5 P3 ðd2 $sind2 ; d2 $cosd2 2 d1 Þ

(3)

It can be shown that: BAPðd1 Þ 5 180° 2 arctanððd2 $sind2 Þ=ðd2 $cosd2 2 d1 ÞÞ

(4)

PBAðd3 Þ 5 arctanðð 2 d2 $sind2 Þ=ðd2 $cosd2 2 d1 ÞÞÞ 2 arctanðð 2 d2 $sind2 Þ=ðd2 $cosd2 2 d1 ÞÞ

(5)

These base angles are then used with the correct azimuth of control line AB, obtained from the published coordinates of control stations A and B to compute the figure as a traverse.

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near the University’s Business Consultancy Block area were coordinated by global navigation satellite systems (GNSS) surveys using dual frequency GNSS receivers in fast static mode.

47

Figure 4. May 2017 Google Earth Image Showing the Site of the Traverses. The GNSS data were processed in the fixed solution mode and adjusted using Trimble Business CenterÔ GNSS software (Trimble Engineering and Construction Group 2011). The coordinates were then transformed into the projected Nigerian (modified) Transverse Mercator map system. The results are presented in Table 1. The traverse field observations were made using a 20 total station on two reflector targets. Apart from the general atmospheric correction factors set for the electronic distance meter of the total station, distance measurement was set on refinement mode of average of three readings. Field observation of angles and distances were by the forced centering method. Angular observation acceptance criteria were set to ensure that the standard error was not more than 50. Angles were estimated by an average of a minimum of 15 zeroes on both faces. Grid distances on the Nigerian Transverse Mercator map projection system were determined from the mean of face left and face right at back sight and fore sight measurements, with a minimum of 75 readings.

For the control test traditional traverse, control station angles were observed at FUTOG 004 and FUTOG 005 in each of the cases. Figure 5 presents the scheme of the observation of the traditional two-point resection and the labels used in the computation. Table 2 presents the final estimates of the observations used in the computations.

Reorientation Traverse Computation of the Coordinates of the Single-New Station and the Three New Station Cases The reorientation traverse computation was used to determine the coordinates of the single-new station and the three new station cases. In the single-new station case and in the three new station case, the angles at the two control stations were indirectly determined in the preliminary reorientation traverse stage in line with Chukwuocha (2017) using the azimuths of the adjoining lines in the arbitrarily oriented scheme, in which from Figure 3,

Easting X (m)

sX (m)

Northing Y (m)

sY (m)

Elevation Z (m)

sZ (m)

FUTO SVG 004

502,633.768

0.005

154,106.624

0.004

56.530

0.014

FUTO SVG 005

503,759.630

0.005

153,583.508

0.004

55.225

0.013

Point ID

Table 1. GNSS-derived coordinates of the control stations.

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The determined control station angles completed the required components for the computation of the reorientation traverse. However, those two control station angles were measured for the control experiment traditional traversing. The quantities used in the computations are presented in Table 2. The reorientation traversing was carried out on a resection case referenced by sighting to the two control stations, FUTOG 004 and FUTOG 005, with three unknown stations. The traditional cosine Figure 5. Field-observed quantities of the traditional distance resection case. rule approach to solving for the base angles in the traditional trig 5 correct azimuth of control line AB angular two-point resection case is not feasible (6) here because the figure is five-sided. The re2 arbitrary azimuth of control line AB0 orientation traverse of the three unknown station d1 5 azimuth of initial traverse leg AP0 case started with an instrument set up on the first (7) 0 unknown station P2 with a back sight to the rear 2 azimuth of control line AB control station, FUTOG 004, to observe the distance d2 5 azimuth of initial traverse leg P0 B and the angle at the new station P2, to the second (8) 0 unknown station of the traverse P3. All the un2 azimuth of control line B A known stations were traversed on until the last setup on the unknown station P4; the angle was The reorientation angle g, determined in the observed with a sight to the forward control station, reorientation procedure was then added to the FUTOG 005, and the distance of this last leg was also arbitrary azimuth of the initial traverse leg to measured. obtain the corrected azimuth of the initial leg of The results of the diverse computations of the the traverse line. The indirectly determined antwo cases, the single-unknown point and threegles at the control stations d1 and d2 were used unknown point cases by the methods of solutiontogether with the other field-observed quantities of-triangles (traditional two-point resection) and in the least squares adjustment using Adjust those from the reorientation and traditional trasoftware (Ghilani 2010) for determination of the versing methods using the Bowditch traverse coordinates of the unknown station. In the case of computation and the least squares adjustment are the traditional traversing the field-observed presented in Table 3. The least squares adjustquantities from the field traverse were used for ment method was also used to compute the rethe least squares adjustment procedure to deorientation traverse and the traditional traverse of termine the coordinates of FUTOG 006. The the three new station case. resulting coordinates of FUTOG 006 in all the cases are presented in Table 3. Statistical Tests of the Quality of Coordinates Determined by the Reorientation Traversing The comparison to establish if there are any The Reorientation and Traditional statistical differences between the coordinates Traverses of the Three-Unknown Station resulting from the reorientation traversing and Case those of the traditional traversing, which was used Figure 6 presents the reorientation traverse as the standard experiment control was carried scheme of the three unknown station case of this out in a t-distribution test. The t-distribution test is research. applied to testing if the sample mean is either staThe angles at the control stations, FUTOG 004, tistically greater or less than the population mean. d1 and FUTOG 005, d2 were determined indirectly The t-distribution single-tail test is applied in such in the preliminary reorientation traverse comtests where the null hypothesis is set to find if the putation as expressed in equations (7) and (8). sample mean is statistically greater or less than the

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The Single-New Station Case Instr. Station

Observation Description

Traditional Two-Point Resection Observation

Source

Reorientation Traversing

Traditional Traversing

Observation

Source

Observation

Source

FUTOG 004

Angle at FUTOG 004

016°56046.970

Cosine rule

016°56042.90

Computation

016°56045.20

Field observed

FUTOG 006

Angle at FUTOG 006

136°20029.80

Field observed

136°20029.80

Field observed

136°20029.80

Field observed

FUTOG 005

Angle at FUTOG 005

026°42054.000

Cosine rule

026°42047.30

Computation

026°42054.90

Field observed

FUTOG 004

Line: FUTOG 004 – FUTOG 006

808.421 m

Field observed

808.421 m

Field observed

808.421 m

Field observed

FUTOG 006

Line: FUTOG 006 – FUTOG 005

524.156 m

Field observed

524.156 m

Field observed

524.156 m

Field observed

Instr. Station

Observation Description

The Three-Unknown Stations Case Traditional Two-Point Resection

Reorientation Traversing

Traditional Traversing

Observation

Source

Observation

Source

Observation

Source

FUTOG 004

Angle at FUTOG 004

N/A

N/A

021°01016.30

Computation

021°01014.10

Field observed

P2

Angle at P2

N/A

N/A

166°08026.70

Field observed

166°08026.70

Field observed

P3

Angle at P3

N/A

N/A

174°07004.20

Field observed

174°07004.20

Field observed

P4

Angle at P4

N/A

N/A

153°59015.950

Field observed

153°59015.950

Field observed

FUTOG 005

Angle at FUTOG 005

N/A

N/A

024°43056.90

Computation

024° 44003.60

Field observed

FUTOG 004

Line: FUTOG 004 – P2

N/A

N/A

306.802 m

Field observed

306.802 m

Field observed

P2

Line: P2 – P3

N/A

N/A

236.740 m

Field observed

236.740 m

Field observed

P3

Line: P3 – P4

N/A

N/A

398.066 m

Field observed

398.066 m

Field observed

P4

Line: P4 – FUTOG 005

N/A

N/A

354.843 m

Field observed

354.843 m

Field observed

Table 2. Final field observation estimates.

population mean. In the case being studied, the t-distribution two-tail test is applicable because the null hypothesis is set to see if the sample mean is within a prescribed confidence interval. The statistical tests carried out in this research were between the coordinates determined by the reorientation traversing process as the sample means, against the coordinates resulting from the already established method of traditional traversing as the

50

population mean. The null hypothesis was whether the difference in the two means was equal to zero versus its alternative, of the difference not being equal to zero. The test statistic based on the difference in two means detailed by Ghilani (2010) for the t-distribution test was followed, whereas online calculators provided by GraphPad Software, Inc. (2017) and Stangroom (2017) were used to calculate the P-values of the statistical test.

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51

502,846.697

503,047.284

503,404.453

P2

P3

P4

503,404.433

P4 153,584.049

153,759.803

153,885.547

153,566.488

Northing, Y (m)

153,584.041

153,759.798

153,885.544

153,566.492

Northing, Y (m)

503,404.470

503,047.294

502,846.703

503,235.378

Easting, X (m)

153,584.075

153,759.816

153,885.553

153,566.482

Northing, Y (m)

1/42,700

1/84,000

Linear Accuracy

Traditional Traverse

60.0031

60.0033

60.0027

60.0028

sx

60.0036

60.0032

60.0027

60.0037

sy

Reorientation Traverse

0.0082

0.0080

0.0067

0.0081

r (95%)

503,404.433

503,047.273

502,846.692

503,235.374

Easting, X (m)

153,584.045

153,759.801

153,885.546

153,566.483

N/A

sx

N/A

60.0031

60.0033

60.0027

60.0036

60.0032

60.0027

60.0037

sy

0.0082

0.0080

0.0067

0.0081

r (95%)

153,566.476

Northing, Y (m)

Distance Resection

Traditional Traverse

60.0028

503,235.372

Easting, X (m)

Northing, Y (m)

Results of Traverse Computations by Least Squares Adjustment Method

1/88,800

1/111,100

Linear Accuracy

Table 3. Results of the computation of the different cases.

503,047.272

P3

502,846.691

P2

3

503,235.376

FUTOG 006

1

Easting, X (m)

New Stn Number

Number of New Stations

3

503,235.376

FUTOG 006

1

Easting, X (m)

New Stn Number

Number of New Stations

Reorientation Traverse

Results of Traverse Computations by Bowditch Method

Trad. trav: 0.0076

Reorient. trav: 0.0076

Trad. Trav: 0.0081

Reorient. trav: 0.0081

Local Accuracy

N/A

N/A

Linear Accuracy

Figure 6. Sketch of the three new station reorientation Because both the reorientation and traditional traverses in each of the single-new station case and the three new station case were closed traverses and contained the minimum number of observations, that is, n1 5 n2 , the redundancies; v1 5 v2 5 3, the critical t.005,6 value was 3.707 (Anglia Ruskin University, 2008) for all the traverses. The tests were carried out at the 99 percent confidence level. Table 4 presents the statistical comparison.

Results and Discussions The results presented in Table 3 include a compilation of the final coordinates and their accuracy indicators in the two cases. In the first part, the results of the single-unknown station case computed by the cosine rule, reorientation traversing, and the traditional traversing are presented. Next, in the first part are the results of the three-unknown station case computed only by the

Number of New Stations 1

3

traditional traversing and the reorientation traversing methods, using the Bowditch system, are presented. The second part of Table 3 presents the coordinates resulting from the least squares adjustment and their corresponding accuracy indicators for both the singleunknown station and the threeunknown station cases. The corresponding standard deviations and the associated binormal radial errors (for the error circle) at 95 percent confidence level realized in the two cases in the least squares adjustment indicate that the reorientation traversing and the traditional traversing are presented too and appear quite similar. traverse case. The statistical test to find out if the coordinates derived from the reorientation traversing differed from the ones derived from the traditional traversing is a two-tail test; hence, the significance level at 99 percent is 0.01 has 2a 5 0.01, hence a 5 0.005, listed as t0. The result of the statistical tests showed that t of the compared values were less than the critical t0.005,6 value of 3.707 for all the cases. Equally the P-value test of the probability of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P-value is less than (or equal to) a, then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than a, then the null hypothesis is not rejected (Penn State Eberly College of Science 2018). The word “pass” in the statistical test result presented in Table 4 indicates that the test failed to reject that the two means derived by the reorientation method and traditional method were different at a 0.01 level of confidence; thus, there

For X

For Y

For X

For Y

P-Value

P-Value

Station

|DX|

|DY|

s

s

t

t

X

Y

FUTOG 006

0.002

0.005

60.0028

60.0037

1.5972

3.0217

0.2085 (pass)

0.0557 (pass)

P2

0.001

0.001

60.0027

60.0027

1.1111

1.1111

0.3476 (pass)

0.3476 (pass)

P3

0.001

0.002

60.0033

60.0032

0.9091

1.8750

0.4303 (pass)

0.1575 (pass)

P4

0.000

0.004

60.0031

60.0036

0.0000

3.3333

1.000 (pass)

0.0446 (pass)

Table 4. Statistical test of the differences in the coordinates.

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is no reason to believe that there is any statistical difference in the two sets of coordinates. The viability of the reorientation traversing method is therefore obvious.

Conclusions and Recommendations Reorientation traversing procedure successfully coordinated station FUTOG 006 in a single-new point case proving its usefulness in solving the twopoint resection problem. The method demonstrated its additional advantage over the traditional cosine rule solution of the two-point resection procedure by solving the three new stations case in a traverse resected from the controls. The success of solving the three-unknown stations case is important because if the point desired to be coordinated in the resection exercise is not intervisible with any of the control stations or both, reorientation traversing would accomplish the task, which the traditional solution-of-triangle approach to solving the two-point resection method could not. The quality of the results of the reorientation traversing were compared with the traditional traversing method considered to be a standard survey method and the control test and the results for the tested number of new stations shows the reorientation traversing to be as reliable as the traditional traverse when used for the single-new station or the three new station cases. This has implication for providing reliable control extension flexibility compared with the traditional two point resection method. The use of the method of reorientation traversing recommends itself in solving two point resection (distance resection) surveys given the advantages already pointed out and including that multiple stations can be distributed in the site in one network of resected traversing that are adjusted together in a lone system thereby providing internal consistency for further control extension. Further research is needed to determine how many unknown stations can be coordinated with acceptable accuracy in one reorientation traversing network. REFERENCES Anglia Ruskin University. 2008. Numbers Toolkit: t-test. [web.anglia.ac.uk/numbers/biostatistics/t_test/local_ folder/critical_values.html; accessed January 2, 2018].

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Chamdra, A.M. 2005. Triangulation and trilateration. In: Surveying. New Delhi, India: New Age International (P) Ltd. pp. 166-201. Chukwuocha, A.C. 2017. Case studies of reorientation traversing. Surveying and Land Information Science 76(2): 107-17. Chukwuocha, A.C., E.C. Moka, V.N. Uzodimma, and M.N. Onoh. 2017. Solving control reference azimuth problems of traversing using reorientation traversing. Surveying and Land Information Science Journal 76(1): 23-37. Ghilani, C.D. 2010. Adjustment computations—Spatial data analysis, 5th ed. Hoboken, New Jersey: John Wiley and Sons. pp. 74-76. Ghilani, C.D., and P.R. Wolf. 2012. Elementary surveying: An introduction to geomatics, 13th ed. Boston, Massachusetts: Prentice Hall. pp. 299-303. Google Earth Pro 7.1.2.2041. 2013. May 2017 Google Earth image of the site of the Reorientation Traverses at Federal University of Technology Owerri, Nigeria. 5° 230 19.980N, 6° 590 27.890W. Eye alt 1.70km. SIO, NOAA, U.S. Navy, NGA, GEBCO. DigitalGlobe 2017. [http://www.earth.google.com; accessed 23 December 2017]. GraphPad Software, Inc. 2017. Quick calcs. [https:// www.graphpad.com/quickcalcs/pValue2/; accessed December 25, 2017]. Grobler, H. 2016. Does the underground sidewall station survey method meet MHSA standards? South African Journal of Geomatics 5(2): 175–85. doi: 10.4314/sajg.v5i2.6. [Accessed May 2, 2017]. MacKinnon, T., and J. Murphy. 2011. Total station basics—Introduction and simple guide to using the Leica total station. [http://tmackinnon.com/2005/ PDF/Total-Station-basics–Introduction-to-Usingthe-Leica-Total-Station.pdf; accessed July 14, 2016]. McCormack, B. 2002. Wall stations (reference points): The use of resection to replace underground traversing. In: Proceedings, National Mine Surveying Conference, Darwin, Australia, 8-12 July, 2002. [http://benchmarksoftware.com.au/downloads/ Wall%20Stations.pdf; accessed October 11, 2016]. Penn State Eberly College of Science. 2018. Statistics Online. The Pennsylvania State University. [https:// onlinecourses.science.psu.edu/statprogram/node/ 138]. Smith, F. 2011, Accuracy of wall station surveys. In: Proceedings of the Australian Institute of Mine Surveyors Conference 2011, 17-19 August 2011. Melbourne, Australia. [https://www.minesurveyors. com.au/files/2011Conference/Accuracy_Of_Wall_ Station_Surveys.pdf; accessed October 11, 2016]. Stangroom, J. 2017. Social science statistics. [http:// www.socscistatistics.com/pvalues/tdistribution.aspx; accessed December 25, 2017]. Trimble Engineering and Construction Group. Trimble Business Center 2.50 software. Trimble Navigation Limited. Dayton, Ohio. Trimble Navigation Limited Documentation Group. 2001. Trimble Survey ControllerÔ user guide. Trimble Navigation Limited, Sunnyvale, California. p. 349

53

[https://www.ngs.noaa.gov/corbin/class_description/ controllerv10UserGuide.pdf; accessed January 12, 2017]. Trimble Navigation Limited Engineering & Construction Division. 2013. Resection computations: Trimble AccessÔ software. Trimble Navigation Limited, Dayton, Ohio: [http://geodesy.kz/loaddb/ldname15_3_19. pdf; accessed January 12, 2017]. Uren, J.F., and W.F. Price. 2006. Traversing and coordinate calculations. In: Surveying for engineers, 4th ed. Hampshire, United Kingdom: Macmillan. pp. 183-251.

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Washington State Department of Transportation. 2005. Total Station System (TSS) survey specification. In: Highway surveying manual. pp. 9-5 to 9-7. [http://www. wsdot.wa.gov/publications/manuals/fulltext/M22-97/ highwaysurvey.pdf; accessed February 15, 2017]. Zeiske, K. 2004. Surveying made easy. Heerbrugg, Switzerland: Leica Geosystems AG. p. 33. [https:// www1.aps.anl.gov/files/download/DET/DetectorPool/Beamline-Components/Lecia_Optical_Level/ Surveying_en.pdf; accessed February 15, 2017]. Zimmerman, M. 1996. Free Station (v2.1) FS01_v21 DOC 15/05/96. Leica Geosystems.

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