Solving Control Reference Azimuth Problems of ...

Peer Reviewed

Solving Control Reference Azimuth Problems of Traversing Using Reorientation Traversing Akajiaku C. Chukwuocha, Elochukwu C. Moka, Victus N. Uzodimma, and Matthew N. Ono ABSTRACT: Planned traverse surveys encounter setbacks when control stations are orphaned without any intervisible neighbor. This matter is made more difficult if use of Global Navigation Satellite Systems or astronomic observations are not feasible especially in built-up areas or under canopies. A control azimuth problem exists in any such cases where there are only single control stations at one or both ends of a traverse scheme. The technique of “reorientation traversing” is a simple, time- and cost-saving technique that may be used to control the orientation of traverses between reliable control stations. The reorientation traverse begins and ends with setups on the point next after and last before the initial and closing control stations, respectively, sighting to the control stations but without setting up on the control stations. The rest of the traverse is run normally. A traverse run between two nonintervisible control stations, connecting five new stations over about 1.8 km was computed using the reorientation traverse technique and also with the traditional traverse technique. The linear accuracy results were 1/176,000 and 1/101,400, respectively, showing the feasibility of the new method. Some field exercises have shown that under certain conditions the reorientation traversing would give superior results compared to the traditional traversing. KEYWORDS: Traversing, reorientation traversing, azimuths, control stations, Global Navigation Survey Systems (GNSS)

T

Introduction

he development of the Global Navigation Satellite Systems (GNSS) has improved the quality of establishment of survey controls. It may no longer be necessary to run long traverses to bring in control from distant control stations because GNSS provides for those levels of control establishment. However, today, traverses provide better results in densifying project control between GNSS control points within shorter distances (New South Wales Government Surveyor General 2014; Sass 2013; Surveys Division, Arkansas Highway and Transportation Department 2013; The Division of Plats and Surveys, Maryland State Highway Administration 2001).

Akajiaku C. Chukwuocha, Department of Surveying and Geoinformatics, Federal University of Technology, Owerri, Nigeria. Tel: +2348033398505. E-mail: . Elochukwu C. Moka and Victus N. Uzodimma, Department of Geoinformatics and Surveying, University of Nigeria, Nsukka, Nigeria. Tel: +2347065483464 and +2348060514002. E-mails: and . Matthew N. Ono, Department of Surveying and Geoinformatics, Nnamdi Azikiwe University, Awka, Nigeria. Tel: +2348067751296. E-mail: .

Traversing from old classical controls, which have lost intervisibility with their adjoining stations due to construction works or reforestation (Hamilton 1997) or where the adjoining control stations have been destroyed, pose problems of control azimuths for the takeoff and for the closing of traverses. The “reorientation traversing” technique will be useful in these orphaned control conditions in built-up areas, under canopies, in factories, tunnels, or other conditions adverse to the use of GNSS or astronomic azimuth observations, or even when time and other resources required for the GNSS or astronomic surveys are not available. Additionally, use of relatively very short GNSS survey legs for control of traverses may not provide for accurate azimuths needed for control traverses. The limitation of the GNSS in providing accurate azimuths over short legs especially predominant in urban areas has been noted, for instance, in Hamilton (1997), Londe (2002), and government guides. A number of guides show that it will take establishing GNSS points at over 500-m distance apart to achieve a control of the accuracy of 2000 or less and these distances are not often available in built-up areas, coupled with the fact of GNSS multipath errors (Government of New South Wales 2012; New South Wales Government

Surveying and Land Information Science, Vol. 76, No. 1, 2017, pp. 23-37

Surveyor General 2014; U.S. Department of Agriculture/Forest Service and U.S. Department of Interior/Bureau of Land Management 2001). The scenarios of unavailability of suitable takeoff and closing azimuths for control surveys in Nigeria led to this study. A few control survey campaigns were carried out over Owerri after it was made capital of Imo State. One of such is the Owerri Cadastral Survey (OCS) series, which was completed in 1983 in three accuracy levels in the Universal Transverse Mercator zone 32N projection map coordinate system (Danz Surveys and Consultants 1983). As Owerri grows in urbanization, the OCS beacons are being destroyed and new building constructions obstruct intervisibility between one beacon and another leaving some of those remaining without intervisible control stations for reference orientation control azimuths. In many cases when intervisibility between control points is unavailable and GNSS survey is not feasible for any reason, the option left is that a new set of traverse will have to be run from another suitable control set some distance away to establish new set of controls to provide intervisibility between control stations. Sometimes it is at the point of executing planned surveys that the discovery that control stations planned to be used in the survey exercise have lost intervisibility is made. In some cases, deadlines may already have been set and more so the cost of setting up a new set of controls may be an added complication to the matter. Reorientation traversing method being presented here is a simple, timeand cost-saving option, which does not require additional field procedures or equipment and provides accountable and repeatable procedure to determine coordinates of new control stations at required accuracies. A dysfunctional use of the method being presented in this paper is hinted at in Hamilton (1997). It reports that surveyors in the eastern part of the United States used this method without checking their traverses. They assumed an azimuth for traverse starting leg, then rotated the entire traverse to fit the ending coordinates. And because they did not check their traverses, they sometimes included blunders in the network. This paper includes the necessary checks so that any unacceptable traverse can be recognized. It further provides for the adjustment of the traverse. A proper but a slightly more complex use of the method being proposed was found described for tunneling for use in orienting a traverse between two shaft points that are not intervisible. In using

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this method for aligning tunnels, the need of determining the radius of the earth as necessary for accurate determination of coordinates of the tunnel points complicates the process. This paper is proposing a more simplified approach for surface control densification. It is noted that this method being proposed can provide accuracy of better than 20 sec in orientation if the accuracy and survey methodology of the connecting surveys are properly designed (Davis et al. 1981, pp. 956-57; Veres 2013). The range of better than 20-sec azimuth accuracy achievable by this method recommends it to be used in places where traverses to be run have problems of takeoff or closing azimuth orientation or both. It is acknowledged that using GNSS to establish survey controls in the ranges of 300-m length, the GNSS networks are degraded and often 20-sec azimuth accuracy can hardly be achieved along those lines. This happens in urban areas where it may be difficult to find an unencumbered length and where buildings obstruct satellite signals. This paper names the process and demonstrates the mathematical correctness of the technique by using the reorientation of a wrongly aligned figure to its proper alignment as will be shown later. This paper being presented for the application of the method in establishing lower-order control traverses between global positioning system (GPS) control points at relatively long distances apart. This paper for instance goes further with practical field traverses to compare and list the derived coordinates and linear accuracies achievable between reorientation traversing and traditional traversing. The reorientation traversing being proposed recommends itself for use in traversing between GNSS control stations as it eliminates the azimuth problem. Similar to traditional traversing techniques, the reorientation traversing method accumulates errors propagated from angles and distances measured in the traverse. Keeping the stations few and observations highly accurate will enhance the accuracy of reorientation traversing.

Theoretical Background The field observations in the reorientation traversing technique are made exactly in the same manner as are made in the traditional traversing method. The difference is in the initial and final orientation of the traverse. In the traditional traverse method, the initial angle is normally measured from a known control station with a

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backsight to a known reference azimuth line and a foresight to the first leg of the new traverse. Additionally, the closing angle is normally measured from a closing control station with a backsight to the last leg of the new traverse scheme and foresight to a known azimuth control line. The observation of these two angles is not required in the reorientation traversing method.

Traditional Traversing Normally controlled theodolite or total station traverses are run beginning from a pair of control stations such as A and A1 in Figure 1 to subsequent stations, such as C, D, and E, whose positions are to be determined. The traverse closes also on another pair of control stations such as B and B1. In certain accuracy classes of traverses, the closing pair of control stations could as well be the starting pair. However, in most control densification traverses, the closing pair is at a spatially displaced position from the starting pair as shown in Figure 1. With reference to Figure 1, a theodolite or total station traverse begins with the instrument set up on a survey control station such as A where the angle measurement begins with a backsight to a control reference azimuth line, normally marked at the other end by another survey control station A1. Subsequent measurements of distances along the legs between consecutive stations and measurement of angles between successive traverse legs are carried out to meet required accuracy. The traverse is also concluded following this stated traverse procedure with another instrument set up on the closing control station B and an ending foresight on a control reference azimuth line,

normally marked at the posterior end by another control survey station B1 (Oregon Department of Transportation Geometronics Unit 2000). In all normally controlled traverses, the control station at which the instrument is set up at the beginning of the traverse say A shown in Figure 1 provides the takeoff coordinates, while the line connecting the instrument station to the reference azimuth control station A – A1 provides azimuth orientation for the traverse. The traverse coordinate check control is provided by the control station at which the instrument is set up at the end of the traverse, B. The line linking the closing instrument setup control station at the end of the traverse and its posterior reference control station B – B1 provides the check on the orientation of the traverse. The coordinates of these pairs of control stations used for the takeoff and closing of traverses must be known to the required accuracy in the reference frame in which the survey is conducted (U.S. Army Corps of Engineers 2007). There are a number of methods for adjusting traverses. The Compass Rule is a simple method and is most commonly employed for engineering, construction, and boundary surveys. It is recognized as the accepted adjustment method in some state’s minimum technical standards (U.S. Army Corps of Engineers 2007). More commonly, errors in the measured angles are distributed either on the basis of equal weights or if the variance of each angle was determined that might be used in applying weights in distributing the errors in the angular observations. The lengths are then used with the derived azimuths in computing the provisional coordinates of subsequent stations such as C, D, and E shown in Figure 1 including the computation of a new coordinate set for control station B. The new coordinates of B are checked against the originally published coordinates to determine the error in the newly computed values of B, which is an indicator of the accuracy of the traverse. They may be used in making some adjustments in the computed values of the coordinates of the new traverse stations (Uren and Price 2006, pp. 219-29).

Reorientation Traversing

Figure 1. Traditional method of coordinating points by traversing.

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When intervisibility between survey control stations at the starting and ending of a traverse are lost it is actually the azimuths needed to take off and close up the traverses in an accountable way for quality assurance that are lost. Urban areas are most susceptible to loss or lack of control azimuths. Construction by heavy machinery,

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Figure 2. Field observation scheme of the reorientation traversing technique. which uproots survey beacons, happens mostly in urban areas. Buildings, which may stand between two previously intervisible survey control stations, are erected mostly in urban areas. The long distances between normal GNSS network stations are too far apart for optical intervisibility. Short-

ening those distances degrades the quality of the networks. GNSS operations are also limited in cities due to the blocking of satellite signals by high-rise buildings. Additionally, it is sometimes challenging to find suitable locations for intervisible reference positions to be controlled by GNSS for control traverses in urban areas. The reorientation traversing technique only requires two control stations, one at each end of the traverse, instead of the traditional requirement of two controls at each end of the traverse. In this method, the traverse begins with an instrument set up at the first point to be coordinated in the traverse, namely C in Figure 2. A backsight is taken to the first control point, A and the distance to that point AC, and angle ACD to the next traverse line, are measured. The traverse is run normally from that point until instrument set up at the last station to be coordinated, which is station E in this case (see Figure 2), and distance EB, from E to the end control point is measured.

Computation of the Reorientation Traverse

The observation of the reorientation traverse is different from the traditional traverse in the sense that the reorientation traverse scheme misses the usual initial angle at the takeoff control station between the orientation azimuth control line and the first leg of the traverse, angle A1AC in Figure 1. It may also miss the closing angle at the closing control station between the last leg of the traverse and an orientation azimuth control line EBB1 in Figure 1. The initial orientation angle would give azimuth orientation to the new traverse from the control line of known azimuth. The angle at the closing control station is used to link the traverse to a closing orientation azimuth control line to compare the calculated value with the published value by which the angles observed in the traverse would be checked. The reorientation traverse is computed in two stages. In the first stage, an arbitrary azimuth is given to the first leg of the traverse as observed in the scheme, AC in Figure 3. The scheme for the computation of the reorientation traverse. Figure 3. Based on this initially

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assumed azimuth, the observed angles are used to compute values for the azimuths of the subsequent legs of the traverse. The azimuth of a succeeding leg is computed from the azimuth of the preceding leg and the observed angle at the station joining the two legs just as it is done in traditional traversing. The entire traverse is then computed to get values for the coordinates of B0 in this arbitrary orientation of the traverse. The plot of the first part of the computation of the reorientation traverse is as shown in Figure 3, in which the traverse shown in dashed lines swings away from its proper orientation pivoted at the initial control point A. The assumed azimuth of line AC, t, causes the orientation to be in error along AC0 . The bearings of all the traverse lines are disorientated by this same error in AC0 , causing the computed position of B at this stage to be displaced to B0 . The line AB0 disorients from its correct control orientation AB by g, the gross error in the assumed azimuth with which the traverse is computed at this stage. To determine g, the gross error in the assumed azimuth of AC, the disoriented arbitrary azimuth of the initial line along AC0 is subtracted from the correct azimuth of the initial line AC. It can be seen from Figure 3 that geometrically the traverse figure ACDEBA is the same figure in shape and size as AC0 D0 E0 B0 A. So that: Angle BAC ¼ angle B0 AC0 ; which are the corresponding angles of the same figure ð2:1Þ angle BAB0 ¼ BAC þ CAB0

ð2:2Þ

angle CAC0 ¼ B0 AC0 þ CAB0

ð2:3Þ

0

0

Since from (2.1) BAC = B AC , therefore from (2.2) and (2.3), angle BAB0 ¼ angle CAC0

ð2:4Þ

Angle CAC0 = BAB0 = g, the reorientation angle of the arbitrarily oriented traverse determined from azimuth of line AC minus azimuth of line AC0 . When this vector quantity is applied to the azimuth, AC0 the correct azimuth of AC is recovered. However, this recovered azimuth is encumbered with propagated errors from the observed angles and distances in the traverse measurements. Reorientation angle, g = Correct control azimuth C – arbitrary control azimuth, A g ¼CA

ð2:5Þ

Therefore, the corrected azimuth of initial line of reorientation traverse T, is given by the arbitrary

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azimuth of initial line of the reorientation traverse, t plus the reorientation angle g. T ¼t þg

ð2:6Þ

From Figure 3, it is seen that g is a negative value since g is rotated counterclockwise to make AC0 coincide with AC. At this point, the second stage of the computation of the reorientation traverse method would be carried out using T, the determined azimuth of initial line AC as initial bearing of the first leg of the traverse, this is the only quantity taken from the first stage of the computation. The second stage of the computation is carried out purely as in the traditional traverse case. The known coordinates of control station A are used as takeoff coordinates and the recovered azimuth of line AC is the takeoff azimuth. The traverse is then computed entirely afresh using the quantities measured in the traversing. It is to be noted that the angular misclosure of the traverse is not determined and hence the angular misclosure is not distributed directly. However, the angular misclosure is distributed indirectly as part of the system of the linear misclosure. It is not expected that the computed coordinates of B will coincide with the published coordinates. The positional errors of the takeoff and closing control stations A and B and the errors in the measured angles and distances will have propagated into the computed coordinates of B. The linear accuracy of the traverse is determined using the length of the misclosure in the Northings and Eastings of the control station B over the total length of the traverse. If the traverse does not meet the required standards it would then be rejected. However, with the advancements in measurement science, the required accuracy of the traverse would be used to determine the refinement of equipment (Uren and Price 2006, p. 219) and methods of traverse observations in order to meet required accuracy (Anzilic Committee on Surveying and Mapping 2014), except for in situ errors of the control stations. Thereafter the errors may be distributed using any of the traditional traverse adjustment procedures suitable, such as the Compass rule, Crandall rule or Transit rule (Oregon Department of Transportation Geometronics Unit 2000). The final coordinates of the new stations are thus determined. The finally adjusted traverse of Figure 3 has inherent in the coordinates of consecutive stations the azimuths of the lines AC, CD, Delaware and so on. When computation of final coordinates of the new control stations is completed any of the new traverse stations and lines may

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then be used as reference to control other sets of equivalent or lower-order traverses.

Accounting for the Checks for Errors That Could Go Undetected in Reorientation Traversing Some critics may imagine that the reorientation traversing method discards the two angles at the takeoff and closing control stations. However, in the reorientation traversing method, no angle is lost. The two angles that are not measured in the field are accounted for using the reorientation traversing geometry technique. This method does have its own error implications. Since the reorientation angle is determined using measured angles and distances that are unadjusted, errors from the measurements will be propagated into the derivation. It is thought that every time the error introduced by error propagation of the reorientation traversing process is smaller than the errors introduced by the measurement of the two angles at the station angles, the reorientation traverse will give better results and vice versa. In a case where one of the control station angles is measured, the angular misclosure can be distributed before the stage in which the final coordinates of the traverse stations are computed. In Situ Checks, Errors in Control Stations, and Errors in Measurements In the traditional theodolite or total station traverse, angular and distance in situ checks are carried out to confirm the suitability of the controls from which the traverses are to take off from and close on prior to the traversing proper. Control stations may have suffered some movements due to settlement of the beacon or some anthropogenic activities or may have some significant errors in their published coordinates, which may affect the calculated linear accuracy of a new traverse that depends on it. If a set of three control beacons are available at the beginning of the traverse as A1, A, and B in Figure 4, the angle at A between the two lines formed from that station to the two other stations A1 and B and the distances d1 and d2 are measured. The field measured angle and distances are expected to agree with those same quantities computed from the published coordinates of the control stations within allowable limits. If the control stations fail the in situ check another set of controls will have to be used for the traverse.

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Figure 4. In situ checks. At face value, as its name states, in situ checks are to confirm that the control beacons have been unmoved since they were coordinated, so that the published coordinates are still in usable consistency with the actual physical positions of the beacons. However in situ checks may also reveal the level of errors laden in the control stations after the adjustments that produced their final coordinates. It may be feared that since reorientation traversing begins only on one control station and ends on another, it is not possible to carry out the in situ checks and that the in situ errors in the controls will go undetected. First, the standards have allowed for traverses to be run on stations where in situ checks cannot be carried out. The provision that astronomic azimuth be carried out at control stations that lack reference orientation marks is such a case. In situ state of control stations show up in the accuracy of the traverses. It is a well-known fact that linear accuracy of traverses depend on both the accuracy of determination of the traverse observables as well as on the degree of consistency of the field position of the control stations with their published positions (Federal Geodetic Control Committee 1984). Some implications of different effects of errors on linear accuracy are illustrated hereunder. In Figure 5A, the published coordinates of two control points is A1 and B1 displaced by –0.1 m and +0.1 m, respectively, in the line of the traverse from their true positions, A and B. The control stations therefore introduce a combined linear error of 0.2 m in the traverse. Assuming the field observations introduce no errors, the traverse will still reveal a linear error of 0.2 m. If the planar distance between the two control stations is 1,000 m, the linear accuracy of the traverse will be 0.2/1,000 = 1/5,000.

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Figure 5. (A) Effects of in situ errors along line in traverse accuracy and (B) in situ errors plus measurement errors along line in traverse accuracy.

If, however, the traverse measurements introduce a linear error of 0.2 m, along the direction AB as is illustrated in Figure 5B, the combined effect of the measurement error with the in situ error is 0.4 m and the linear accuracy of the traverse will be 0.4/1,000 = 1/2,500. The point here is that the effect of the error in the positions of the control stations will show up in the linear accuracy of the traverse. Even when the errors in the positions of the controls are not along the line of the immediate traverse leg, they then introduce both linear and angular errors. Figure 6 is used to demonstrate that angular errors, whether in the control stations or in the field measured quantities, will also show up in a linear displacement. Figure 6 illustrates that if d1 (angle CAB1) is measured instead of d (angle CAB), an angular error equivalent to d1 – d is incurred. This error is not only visible in the measured angle but also in the positional displacement of the computed end point B1 from the published coordinate B which is as d1, equal to BB1. With this understanding, it is clear that the linear accuracy of the traverse will reveal the effects of the combined errors in the positions of the control stations coupled with the errors in field-measured angles and distances, so that they will not go undetected. As in the traditional traverses, reorientation traverses may be rejected if

they do not meet the required survey standards. Specific standards may in the future be worked out for this kind of traverse.

Materials and Methods To test this method, two stations OCS 217S and OCS 214S separated by a distance of 1.8 km and which were not intervisible were chosen to be used for reorientation traverse method of control establishment. The equipment used for this research were a Kolida 200 total station (theodolite) – KTS 442L (S/N K56977), two reflectors, and other accessories. The reflectors were calibrated to determine the reflector constant. The weather factors such as the atmospheric temperature, humidity, and atmospheric pressure were set for the total station. Additionally, the distance scale factor of 9 ppm was set for total station with the distance measurement refinement set to average of three readings. Distances were recorded in the horizontal mode. To minimize in situ errors in control station OCS 217S with a corresponding azimuth reference station (GPS 002) P1, and control station OCS 214S with its own azimuth reference station (GPS 001) P7, were coordinated in the Nigerian Transverse Mercator (NTM) projection system using GNSS dual-frequency receivers.

Reorientation Traverse Field Survey

Figure 6. Angular errors with effects on the linear accuracy of the traverse.

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OCS 214S and OCS 217S were nonintervisible control stations in the OCS Secondary Order series. Figure 7 illustrates how the reorientation traverse was run. The reorientation traverse was run beginning with the total station setup on P2, which is a station to be coordinated in the traverse exercise. At P2 with a backsight to control

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bob threads of the tribrach set up on tripods over the ground stations. For a control of the experiment, the reorientation traverse run above was also to be computed in the traditional traverse manner. Figure 8 illustrates the fitting of the two end control azimuth angles at control stations OCS 217S and OCS 214S missing in the reorientation traverse to create the traditional traverse scheme. The control azimuth angles at OCS 217S backsighting (GPS 002) P1 and forward sighting P2 and angle at OCS 214S with backsight to P6 and forward sight Figure 7. Reorientation traverse run from OCS 217S to OCS 214S. to (GPS 001) P7 were observed to be used together with the quantities measured in the reorientation traverse. This coustation OCS 217S, the angle was measured to P3. pling of the orientation angles at OCS 217S and All traverse angles P2, P3, P4, P5, and P6 OCS 214S were used in the traditional traverse were measured as shown in Figure 7. All legs of computation for comparison. Table 1 shows the the reorientation traverse beginning with OCS final estimates of the field observations. 217S – P2, P2 – P3, P3 – P4, P4 – P5, P5 – P6, and P6 – OCS 214S were measured using the total station EDM. The angles in this exercise were each measured Results and Discussions 20 times so that an estimate of the standard deviation of angular determination could be After the field observations and the office estimaobtained for these analyses. Angular observation tion of the final observed quantities, the comacceptance criteria were set to reject any fringe 00 putations for coordinates of the reorientation angular values that were up to 2 from the angle traverse stations were carried out in the two deduction next to the mean and minimum numstages. The preliminary computation of the reoriber of angular observations to be used in each set entation traverse was carried in Table 2. It shows was not to be less than 15 observed on both faces the computations carried out using the correct and in different zeroes. Each theodolite pointing coordinates of OCS 217S and an arbitrary aziin the traverse was made by bisecting the plumb muth of 300 000 00.000 for the traverse leg OCS 217S to P2. The entire traverse was computed in this arbitrary orientation. The correct coordinates of the pivot station OCS 217S and the arbitrary coordinates of OCS 214S determined in this first stage of the reorientation traverse computation were used in computing the arbitrary azimuth of the line OCS 217S – OCS 214S in the arbitrary orientation. The determined arbitrary azimuth of OCS 217S to OCS 214S was 270 200 51.900 . The correct azimuth of OCS 217S to OCS 214S computed from the published coordinates of the control stations was 309 130 17.300 . From equation (2.5) Figure 8. Traditional traverse run from OCS 217S to OCS 214S. g=C–A

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GPS 001 (PA7) 220.397

0.0027

80

T ¼t þg

Table 1. The result of the fieldwork on the traditional and reorientation traverses.

19 1.50 PA6

PA6

OCS 214S 80 0.0028 308.295 19 1.80

OCS 214S

165 44 29.00

00 0 o

PA5

PA6

176 47 21.32

00 0 o

PA5 79

78 0.0031

0.0021 230.102

800.992 19 1.69

18 1.53 161 01 19.08

180o 180 49.3900 PA5

PA4 PA3

PA4

PA4 78 0.0018 159.103 18 1.57

00 0 o

158 08 55.65 PA3 PA2

80 0.0011 107.893 19 1.30

00 0

183o 330 02.2400 OCS 217S

PA2

146o 560 07.5300

o

PA3

Station To PA2 40 0.0005 134.531 1.59

Horizontal Angle Station

OCS 217S

Back Sight

GPS 002 (PA1)

18

Number of Distance Observations Standard Deviation (m) Grid Distance (m) Number of Angular Observations Standard Deviation (”) Vol. 76, No. 1

(the reorientation angle, g = Correct control azimuth C, – arbitrary control azimuth, A) Hence g = 309 130 17.300 – 270 200 51.900 = 38 520 25.400 . From equation (2.6)

(the corrected azimuth of initial line of reorientation traverse T, [Azimuth of OCS 217S to P2] is given by the arbitrary azimuth of initial line of the reorientation traverse, t plus the reorientation angle g) where t = 300 000 00.000 and g = 38 520 25.400 . Giving T = 300 000 00.000 + 38 520 25.400 = 338 520 25.400 . The newly determined corrected azimuth of the initial line of the reorientation traverse was then used in computing the traverse afresh to then determine the correct coordinates of the traverse stations. Table 3 shows the final computation of coordinates in the reorientation traverse. For a check, the positions of takeoff controls GPS 002 (P1) and OCS 217S and closing line OCS 214S and GPS 001 (P7) specified in the NTM (Modified) map projection system, which were coordinated using GNSS were used in computing the traverse in the traditional manner using the same observations used in the reorientation traverse case. The accuracy and coordinates determined were later compared to those from the reorientation traverse. Table 4 shows the traditional computation of the same traverse. Table 5 shows the accuracies and coordinates of the traverse computed using the reorientation traverse method and that by the traditional traverse computation method. The results show a very fair comparison and very strong similarities between the two methods and give good reasons for the use of the reorientation traverse method where it is necessary. The accuracies and coordinates compare quite fairly. The accuracy of the reorientation traverse was 1/176,000 while that of the traditional traverse method was 1/101,400.

Conclusions and Recommendations Conclusions The study has established the viability of reorientation traversing method for use in cases where orientation azimuths are not available for the

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Station From

Back Azimuth Observed Angle Forward Azimuth 

OCS 217S 300

0

Horizontal Distance

Delta Northing (m)

Delta Easting (m)

Northing (m)

Easting (m)

Station To

167529.435

514412.851

OCS 217S

00

00

00.0

183

33

02.2

303

33

02.2

158

08

55.6

281

41

57.8

161

01

19.1

262

43

16.9

180

18

49.4

263

02

6.3

107.893

53.9465

93.4381

167583.382

514319.413

P2

159.103

87.93199

–132.596

167671.313

514186.817

P3

230.102

46.65936

–225.322

167717.973

513961.495

P4

800.992

–101.482

–794.537

167616.491

513166.958

P5

308.295

–37.3843

–306.02

167579.107

512860.938

P6

220.396

–38.9366

–216.929

167540.17

512644.008

OCS 214 S

120 PA2

123 PA3

101 PA4

082 PA5

083 PA6

176

47

21.3

259

49

27.6

Computation of Reorientation Angle (g), and Corrected initial azimuth Arbitrary Azimuth OCS 217S to OCS 214S 270

20

51.8

Delta Northing (m)

Delta Easting (m)

167529.435

514412.851

OCS 217S

10.73535

–1768.84

167540.17

512644.008

OCS 214 S

Correct Azimuth OCS 217S to OCS 214S 309

13

17.3

Delta Northing (m)

Delta Easting (m)

167529.435

514412.851

OCS 217S

1118.501

–1370.37

168647.936

513042.482

OCS 214S

REORIENTATION ANGLE (GROSS ERROR) IN INITIAL TRAVERSE AZIMUTH (g) = Correct Azimuth minus Arbitrary Azimuth (OCS 217S to OCS 214S) 309 130 17.300 – 270 200 51.900 = 38 520 25.400 CORRECTED INITIAL TRAVERSE LEG AZIMUTH = Arbitrary Azimuth of Initial Traverse Leg (OCS 217S to OCS 214S) plus the Reorientation Angle (g) 300 000 0000 + 38 520 25.400 = 338 520 25.400

TABLE 2. The preliminary computation of the reorientation traversing.

takeoff of and/or closing of traverses. Field traverse measurements were carried out on traverse stations between two nonintervisible control stations, OCS 217S and OCS 214S about 1.8 km apart. The traverse and computation were carried out using the reorientation traverse method. The traditional traverse method was also applied to provide a check on the new method being introduced. The accuracies and coordinates resulting from the two methods were compared and showed very strong similarities.

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The reorientation traversing method is applicable in cases where there is no reliable azimuth reference control line. It will also be useful when either due to time available or the environmental condition or even cost it is not feasible to use other methods to establish a reference azimuth control line. A reorientation traverse may be planned to run with a control station at each end of a traverse route. The method can also be applied in difficult woods or built-up areas where availability of orientation azimuth control lines

Surveying and Land Information Science

Vol. 76, No. 1

33

298

41

52.0

220.396

1826.781

Linear Accuracy: 1/176,000

105.833

-193.323

-261.709

168542.103

168647.936

0.007

21.3

162.955

168647.929

47

31.0

176

54

1606.385

168379.146

121

301

308.295

-682.262

0.006

49.4

419.650

168542.096

18

42.0

1298.090

167959.494

0.003

167959.491

167781.754

0.002

167781.752

167630.077

513042.482

-0.008

513042.490

513235.806

-0.007

513235.813

513497.516

-0.005

513497.521

514179.783

-0.001

514179.784

514325.920

0.000

514325.920

514373.963

0.000

0.001

180

35

800.992

-146.136

-48.044

-38.887

514373.964

167630.076

121

301

19.1

177.739

151.676

100.641

514412.851

Easting (m)

167529.435

Northing (m)

0.005

01

497.098

266.996

107.893

1370.369

Delta Easting (m)

161

230.102

159.103

107.893

-1118.5

Delta Northing (m)

168379.141

23.2

55.6

27.6

27.6

02.2

25.4

25.4

"

Cumulative Distance (m)

140

34

08

158

320

25

162

33

183

25

52

158

342

52

'

338



Grid Distance (m)

TABLE 3. Final reorientation traverse computation.

PA6

PA5

PA4

PA3

PA2

OCS 217S

STN FROM

Back Azimuth Observed Angle Forward Azimuth

OCS 214S

PA6

PA5

PA4

PA3

PA2

OCS 217S

Station To

34

Surveying and Land Information Science

25

44

165

284

41

47

176

298

54

301

18

180

1

35

301

161

8

158

33

25

162

320

25

33

342

51

183

56

146

158

55

191

51

55

011

338

'



55.5

29.0

26.0

21.3

5.0

49.4

15.0

19.1

56.0

55.6

1.0

1.0

2.2

58.0

58.0

07.5

51.0

51.0

"

BCK AZ OBS. ANGLE FWD AZ

50.08

42.93

35.77

28.62

21.46

14.31

7.15

“

Correction to the Forward Azimuth

284.446

298.7026

301.9114

301.5957

320.5717

342.421

338.8684

11.93095

Corrected Azimuth (Decimal of Degree)

Table 4. Traditional check computation of the traverse.

OCS 214S

PA6

PA5

PA4

PA3

PA2

OCS 217S

STN FROM

1826.781

1606.385

1298.09

497.098

266.996

107.893

Cumulative Distance (m)

Linear Accuracy: 1/101400

220.396

308.295

800.992

230.102

159.103

107.893

HOR. Distance (m)

31.532

105.848

162.967

419.657

177.735

151.673

100.638

131.625

Delta Northing (m)

-122.401

-193.315

-261.701

-682.258

-146.141

-48.052

-38.897

27.812

Delta Easting (m)

168679.468

168647.936

512920.081

513042.482

-0.005

513042.487

168647.953 -0.017

513235.797

168542.089

-0.004

513235.802

168542.105 -0.016

513497.500

168379.125

-0.003

513497.503

168379.138 -0.013

514179.760

-0.001

514179.761

514325.901

0.000

514325.902

514373.954

0.000

514373.954

514412.851

514385.039

Easting (m)

167959.475

-0.007

167959.481

167781.742

-0.004

167781.746

167630.071

-0.002

167630.073

167529.435

167397.81

Northing (m)

GPS 001

OCS 214S

PA6

PA5

PA4

PA3

PA2

OCS 217S

GPS 002

STN TO

Reorientation Traverse Computation Results

Beacon No.

Traditional Traverse Computation Results

Unadjusted Northing

Unadjusted Easting (m)

Unadjusted Northing

Unadjusted Easting (m)

Correction

Correction

Correction

Correction

Adjusted Northing

Adjusted Easting

Adjusted Northing

Adjusted Easting

167630.076

514373.964

167630.073

514373.954

PA2

0.001

0.000

-0.002

0.000

167630.077

514373.963

167630.071

514373.954

167781.752

514325.920

167781.746

514325.902

0.002

0.000

-0.004

0.000

167781.754

514325.920

167781.742

514325.901

167959.491

514179.784

167959.481

514179.761

0.003

-0.001

-0.007

-0.001

167959.494

514179.783

167959.475

514179.760

PA3

PA4

168379.141

513497.521

168379.138

513497.503

0.005

-0.005

PA5

-0.013

-0.003

168379.146

513497.516

168379.125

513497.500

168542.096

513235.813

168542.105

513235.802

PA6

0.006

-0.007

-0.016

-0.004

168542.103

513235.806

168542.089

513235.797

168647.929

513042.490

168647.953

513042.487

0.007

-0.008

-0.017

-0.005

168647.936

513042.482

167529.435

514412.851

OCS 214S

OCS 217S

168647.936

513042.482

167529.435

514412.851

Linear Accuracy: 1/176,000

Linear Accuracy: 1/101,400

Table 5. Comparison of results of the reorientation and the traditional traversing methods.

are often difficult to meet. It is obvious that reorientation traversing reduces the time the field process would take. The apparent possibility of reduction of observational errors especially when the reorientation traverse is run over fewer stations is a major attraction.

Advantages The advantages of the reorientation traverse approach include the following: 1. Accuracy achievable in the reorientation traverses is at least at the same level as those of the traditional traverses. 2. The time spent on the reorientation traverse method compares better to the options of either reestablishing the lost control points or observing azimuths on the two end points. 3. Even when the two control points are intervisible, the reorientation traverse approach reduces time of running a traverse since the

Vol. 76, No. 1

two end angles do not have to be observed but are recovered mathematically. 4. The total angular errors in the observations may be reduced if the error propagated from the traverse into the two mathematically determined angles at the two control points are kept low. 5. The reorientation traverse method is still useful if the lost reference azimuth is only at one end of the traverse. 6. If accumulation of errors are kept low, the reorientation traversing has chances of being a better option for densification of controls between GNSS control stations.

Limitations The limitations of the reorientation traverse method would include the following: 1. The use of the reorientation traverse approach is limited to traverses that run between

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spatially separated control points. It cannot be applied to traverses that start and end on the same point. The reason is because orientation or reorientation is an azimuth line matter. 2. The reorientation traverse should be used only if the surveyor believes that the two control points have not been moved in their ground position. It will be a waste to run a traverse possibly in kilometers of length, only to discard the result because the accuracy of the traverse failed the required standards. 3. The reorientation angle g, contains an error due to the error propagated into the coordinates of the end control position from the errors in the field observations. These errors will be propagated into that position again during the subsequent computations. However, these errors are distributed during the correction of the traverse. The solution for now is to keep the errors in the field observations very low by adopting excellent field procedures.

Recommendations Surveyors should feel free to work with this method even when traditional traverses that end on two different control stations are run. All that is needed to use the reorientation traverse method is to take out the takeoff and closing angles and to assign an arbitrary azimuth to the initial traverse leg. Further research work needs to be carried out for a clearer explanation of the error implications of the reorientation traversing. There is need, after understanding the error implications to then set standards for the use of the method. Specific standards may in the future be worked out for this kind of traverse to take into consideration the fact that angular and distance errors are only distributed here as linear functions. REFERENCES Anzilic Committee on Surveying and Mapping. 2014. Guideline for conventional traverse surveys: Special Publication 1. V2.1. Intergovernmental Committee on Surveying and Mapping (ICSM), Permanent Committee on Geodesy (PCG), Commonwealth of Australia. [http://www.icsm.gov.au/publications/ sp1/Guideline-for-Conventional-Traverse-Surveys_ v2.1.pdf; accessed August 22, 2015].

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Danz Surveys and Consultants. 1983. A technical report on Owerri township mapping. The Surveyor General’s Office, Imo State, Nigeria. Davis, R.E., F.S. Foote, M. Anderson, and E.M. Mikhail. 1981. Surveying theory and practice, 5th ed. New York, New York: McGraw-Hill. Federal Geodetic Control Committee. 1984. Standards and specifications for geodetic control networks. Rockville, Maryland: National Oceanic and Atmospheric Administration. [http://www.ngs.noaa.gov/FGCS/tech_ pub1984-stds-specs-geodetic-control-networks.htm#3.3; accessed August 21, 2015]. Government of New South Wales. 2012. Surveying and spatial information regulation 2012. Her Excellency, the Governor of New South Wales. [http:// www.lpi.nsw.gov.au/about_lpi/announcements/ 2012/?a=171999; accessed August 19, 2015]. Hamilton, J. 1997. Azimuth in control surveys. [http:// www.terrasurv.com/azimuths.pdf; accessed August 19, 2015]. Londe, M.D. 2002. Standards and guidelines for cadastral surveys using global positioning methods. In: Proceedings of the FIG 22nd International Congress, Washington, D.C. [http://www.wsrn3.org/ CONTENT/Reference/RTK_Standards_FIG.pdf; accessed August 20, 2015]. New South Wales Government Surveyor General. 2014. Global navigation satellite system for cadastral surveys. Surveyor General’s Directions No. 9. [http:// www.lpi.nsw.gov.au/__data/assets/pdf_file/0006/ 25944/sgddir9_Ver2.5_May_2014.pdf; accessed August 20, 2015]. Oregon Department of Transportation Geometronics Unit. 2000. Basic surveying: Theory and practice. In: Proceedings of the Ninth Annual Seminar, Bend, Oregon. [www.oregon.gov-odot-hwy-geometronicsdocs-basicmanual2000_02.pdf; accessed August 26, 2015]. Sass, J. 2013. GNSS or total station?—Selecting the right tool for the job. Machine Control magazine Vol. 3 (1) [http://machinecontrolonline. com/PDF/MachineControlMagazine_Sass-GNSSor TotalStation_Vol3No1.pdf; accessed August 26, 2015]. Surveys Division, Arkansas Highway and Transportation Department. 2013. Requirements and procedures for control, design, and land surveys. [https://www.arkansashighways.com/surveys_ division/manuals/Surveys.pdf; accessed August 26, 2015]. The Division of Plats and Surveys, Maryland State Highway Administration. 2001. Survey field procedures manual. [www.marylandroads.com/ORE/ FieldManual.pdf; accessed August 26, 2015]. Uren, J.F., and W.F. Price. 2006. Surveying for engineers: Traversing and coordinate calculations, 4th ed. Hampshire, United Kingdom: Macmillian. U.S. Department of Agriculture/Forest Service & U.S. Department of Interior/Bureau of Land Management. 2001. Standards and guidelines for cadastral

Surveying and Land Information Science

surveys using global positioning methods. [www .blm.gov/or/gis/geoscience/files/CadGPSstandards2 .pdf; accessed August 16, 2016]. U.S. Army Corps of Engineers. 2007. Control and topographic surveying. Washington, D.C.: U.S Army Corps of Engineers. pp. 20314-1000. [http://www .publications.usace.army.mil/Portals/76/Publications/ EngineerManuals/EM_1110-1-1005.pdf; accessed August 15, 2015].

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Veres, I. 2013.The accurate determination of the orientations in an underground traverse through indirect measurements, recent advances in applied and theoretical mathematics. In: D. Anderson (ed), Proceedings of the 18th WSEAS International Conference on Applied Mathematics (AMATH ’13), Budapest, Hungary, pp. 89-92. [http://www.wseas.us/e-library/ conferences/2013/Budapest/MATH/MATH-12.pdf; accessed August 15, 2015].

m

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