Section 10

APPENDIX


 

 

 

APPENDIX A

FEDERAL GEODETIC CONTROL COMMITTEE MEMBERSHIP

The Federal Geodetic Control Committee (FGCC), chartered in 1968, assists and advises the Federal Coordinator for Geodetic Control and Related Surveys.  The Federal Coordinator for Geodetic Control is Responsible for Coordinating, planning, and executing national geodetic control surveys and related survey activities of Federal agencies.

The Methodology Subcommittee of FGCC is responsible for revising and updating the Standards and Specifications for Geodetic Control Networks.

MEMBER ORGANIZATIONS:

APPENDIX B

ONE-DIMENSIONAL AND THREE-DIMENSIONAL (ELLIPSOIDAL AND SPHERICAL) ERRORS

Suppose the value m quantifies one of the components of the relative position between two marks, which may be, for example, relative height or the east-west base line component. Then the term “relative accuracy” for m will be defined as the ratio, e/d, where the interval m- to m+ corresponds to the 95% confidence region for m while d equals the distance between two marks and e equals the component error.

For a network of stations surveyed by GPS relative positioning techniques the three components of the relative position can be determined.  The term “relative position accuracy” denotes the relative accuracy of the various components for a representative pair of network marks. Consequently, a GPS network is said to have a relative positioning accuracy of 1 ppm (1:1 000 000) when each component of a representative base line has a relative accuracy of at least 1 ppm.  The concept of relative position accuracy can be applied to networks where relative positions have been determined either by single-dimensional measurement or by three-dimensional space-based measurements (R. Snay, NGS, 1986 personal communications).

Accuracy standards for geometric relative positioning are based on the assumption that errors can be assumed to follow a normal distribution.  Normal distribution applies only to independent random errors, assuming that systematic errors and blunders have been eliminated or reduced sufficiently to permit treatment as random errors.  Although, truly normal error distribution seldom occurs in a sample of observations, it is desirable to assume a normal distribution for ease of computation and understanding.

A three-dimensional error is the error in a quantity defined by three random variables.  The components of a vector base line can be expressed in terms of dX, dY, and dZ.  It is assumed that the spherical standard error (ss) is equal to the linear standard error for the components or ss = sxsy = sz.

A one-sigma spherical standard error (ss) represents 19.9 percent probability.  This compares to a one-sigma linear standard error (sx) which represents 68.3 percent probability.  At the 95 percent probability or confidence level, the spherical accuracy standard is 2.79ss compared to 1.96sx for a linear accuracy standard (Greenwalt and Shultz 1962).

The probability level of 95 percent is consistent with the Standards and Specifications for Geodetic Control Network (FGCC 1984).  One page 1-2 of this document, it is stated “ . . . a safety factor of two . . .” is “. . . incorporated in the standards and specifications.”  Since those accuracy standards were based on one-dimensional errors that exist in such positional data as elevation differences and observed lengths of lines, the factor of two, a 2sx linear accuracy standard, is a probability of confidence level of about 95 percent.

APPENDIX C

CONVERSION OF MINIMUM GEOMETRIC ACCURACIES AT THE 95 PERCENT CONFIDENCE LEVEL FROM FIGURE 4-5 TO MINIMUM “ONE-SIGMA” STANDARD ERRORS

 

The “one-sigma” three- and one-dimensional standard errors are computed by:

 

                             ss = p/2.79    and,    sx = p/1.96

 

where, p  = minimum geometric relative accuracies in (ppm) at the 95 percent confidence level

 

                             ss = “one-sigma” three-dimensional minimum error (ppm)

                             sx = “one-sigma” one-dimensional minimum error (ppm)

 

 

 

Table 10-1:     “One-Sigma” Errors for Corresponding Minimum Geometric Accuracies at the 95 Percent Confidence Level

 

 

RELATIVE ACCURACIES

(95 PERCENT)

MINIMUM GEOMETRIC

“ONE-SIGMA” STANDARD ERRORS

ORDER

CLASS

CONFIDENCE LEVEL

THREE-DIMENSIONAL (ss)

ONE-DIMENSIONAL (sx)

 

 

p

(ppm)

a

(1:a)

 

(ppm)

 

(1:T)

 

(ppm)

 

(1:L)

AA

--

 

0.01

 

1:100 000 000

 

0.0036

 

1:279 000 000

 

0.005

 

1:200 000 000

A

--

 

0.1

 

1:10 000 000

 

0.036

 

1:27 900 000

 

0.05

 

1:20 000 000

B

--

 

1

 

1:1 000 000

 

0.36

 

1:2 790 000

 

0.5

 

1:2 000 000

1

--

 

10

 

1:100 000

 

3.58

 

1:279 000

 

5

 

1:200 000

2

I

 

20

 

1:50 000

 

7.17

 

1:140 000

 

10

 

1:100 000

2

II

 

50

 

1:20 000

 

17.9

 

1:56 000

 

25

 

1:40 000

3

I

 

100

 

1:10 000

 

35.8

 

1:28 000

 

50

 

1:20 000

5-11-88

APPENDIX D

EXPECTED MINIMUM/MAXIMUM ANTENNA SETUP ERRORS

 

k = the repeatable setup error in (CM) for any component (horizontal and vertical) at the 95 percent confidence level

 

k = 0.1pd (b),    where,  kmin = 0.3 CM and kmax = 10 CM

 

NOTE: The value for kmin is based on current estimates for expected setup errors when the antenna is set on a tripod at a total height of less than 5 M.  When the antenna is set on a mast or tower where the height is greater than 5 M, the estimated minimum value for k may be greater than 0.3 CM.  On the other hand, if the antenna is mounted on a fixed or permanently installed stand, than kmin should be less than 0.1 CM.

 

The value for kmax is the expected largest value for the setup error; in practice, it should be much smaller than 10 CM, typically less than 1 CM.

p = minimum geometric accuracy standard in parts-per-million (ppm).

 

d = distance between any two stations of a survey (KM).

 

b = 0.05 = critical region factor for the 95 percent confidence level (1.00 - 0.95 = 0.05).

 

To convert setup error at the 95 percent confidence level to standard error (one-sigma), divide K by:  1.96 for ¢linear¢ standard error, or 2.79 for ¢spherical¢ standard error.

 

Table 10-2:     Setup Errors (K) in Centimeters at 95 Percent Confidence Level

ORDER

p

d = DISTANCE BETWEEN STATIONS (KM)

 

(ppm)

0.01

0.05

0.1

0.5

1

5

10

50

100

500

1000

 

AA

 

0.01

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

A

 

0.1

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

B

 

1

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.5

 

2.5

 

5

 

1

 

10

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.5

 

2.5

 

5

 

(10)

 

(10)

 

2-I

 

20

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

0.5

 

1.0

 

5

 

(10)

 

(10)

 

(10)

 

2-II

 

50

 

0.3

 

0.3

 

0.3

 

0.3

 

0.3

 

1.2

 

2.5

 

(10)

 

(10)

 

(10)

 

(10)

 

3-I

 

100

 

0.3

 

0.3

 

0.3

 

0.3

 

0.5

 

2.5

 

   5

 

(10)

 

(10)

 

(10)

 

(10)

8-01-89

APPENDIX E

ELEVATION DIFFERENCE ACCURACY STANDARDS FOR GEOMETRIC RELATIVE POSITIONING TECHNIQUES

An elevation difference accuracy is the minimum allowable error at the 95 percent confidence level.  For simplicity and ease of computations, elevation differences (dH) are assumed to be equal to orthometric height differences.

The height differences determined from space survey systems, such as GPS satellite surveying techniques, are with respect to a reference ellipsoid.  These ellipsoid (geodetic) height differences (dh) can be converted to elevation differences (dh) by the relationship:

 

(dh) = (dH) - (dN)

 

where (dN) is the geoid height difference.

 

With accurate estimates for (dN) and adequate connections by GPS relative positioning techniques to network control points tied to National Geodetic Vertical Datum, elevations can be determine for stations with unknown or poorly known values.

 

NOTE:  If GPS ellipsoid height differences are being measured for the purpose of monitoring the change in height between stations, then it is not necessary to have any accurate information on the shape of the geoid.  Thus, the accuracy of the height difference depends only on the accuracy of the GPS ellipsoid height differences.

 

The accuracy of the GPS derived elevations for points in a survey will depend on three factors:  (1) accuracy of the GPS ellipsoid height differences, (2) accuracy of the elevations for the network control, and (3) accuracy of the geoid height difference estimates.

In Table 10-3, elevation difference accuracy standards at the 95 percent confidence level are proposed.  The order/class correspond to the proposed geometric relative position accuracy standards.  At the high orders, the error is dominated by the accuracy for the (dN) values, whereas, for the lower orders, the major source of error is in the ellipsoid height differences.

 

NOTE:  In developing these standards, it is assumed that errors or inconsistencies in the vertical network control are negligible.  Of course, this may not be true in many cases.

 

Table 10-3:     Elevation Difference Accuracy Standards for Geometric Relative Positioning Techniques

(95 PERCENT CONFIDENCE LEVEL)

 

 

ORDER

 

 

CLASS

MINIMUM ELEVATION DIFFERENCE ACCURACY STANDARD

 

(FROM TABLE 4-4)

MINIMUM GEOMETRIC RELATIVE POSITION ACCURACY STANDARD

MINIMUM GEOID HEIGHT DIFFERENCE ACCURACY STANDARD

 

 

pH

(ppm)

 

1:e

p

(ppm)

pN

(ppm)

 

1:n

AA

--

 

2

 

1:500 000

 

0.1

 

2

 

1:500 000

A

--

 

2

 

1:500 000

 

0.1

 

2

 

1:500 000

B

--

 

5

 

1:200 000

 

1

 

5

 

1:200 000

1

--

 

15

 

1:67 000

 

10

 

10

 

1:100 000

2

I

 

20

 

1:50 000

 

20

 

10

 

1:100 000

2

II

 

50

 

1:20 000

 

50

 

20

 

1:50 000

3

I

 

100

 

1:10 000

 

100

 

40

 

1:50 000

Note:

THESE ELEVATION DIFFERENCE ACCURACY STANDARDS ARE TO BE USED ONLY FOR ELEVATION DIFFERENCES DETERMINED INDIRECTLY FROM ELLIPSOID HEIGHT DIFFERENCE MEASUREMENTS.

 

FOR DIRECT VERTICAL MEASUREMENT TECHNIQUES SUCH AS DIFFERENTIAL OR TRIGONOMETRIC LEVELING, USE ONLY THE ACCURACY STANDARDS GIVEN IN THE FGCC 1984 DOCUMENT, SECTION 2.2, PAGES 2-2 AND 2-3.                                                                                                        5-11-88

APPENDIX F

PLANNING THE GPS SURVEY OBSERVING SCHEDULE

 

r  =  The number of GPS receivers used for each observing session

 

n  =  Minimum number of independent occupations per each station of a project

 

NOTE: when r = 2, n will always be 2 or greater.

when, r > 2, then n = 1, 2, 3, or more occupations.

 

m =  Total stations for the project (existing and new)

 

s  =  Number of observing sessions scheduled for the project

 

d =  Average number of observing sessions scheduled per observing day (e.g. 1 per day, 2 per day, 2.5 per day, etc.)

 

NOTE: Depends on required observing span, satellite availability, and transportation requirements.

 

x  =  Number of observing days, where x = s/d

 

y  =  Number of observing days scheduled per week, generally 5 to 7.

 

w  =  Number of workweeks, where w = x/y = s/(džy)

 

p  =  Production factor (based on historical evidence of reliability; ratio of proposed observing sessions for a project versus final number of observed sessions)

 

p = f/i,

 

where:  f = final number of observing sessions required to complete the project

 

i = Proposed (initial) number of observing sessions scheduled for the project,

 

where:         i = (mžn)/r

 

FORMULAS:

 

s = (mžn)/r + (mžn) (p-1)/r + kžm

 

where, k is a safety factor:      k = 0.1 for local projects; within 100 KM radius.

k = 0.2 for all other projects

 

x = estimated number of observing days for a project:  x = s/d

 

w = estimated number of work-weeks for a project:      w = x/y

 

v = estimated total vectors for a project:                      v = ržs (r-1)/2

 

b = estimated independent vectors for a project:            b = (r-1)s

 

EXAMPLE:

 

If                                  n =  1.75          independent occupations per station

                                    m =  50            total stations for project

                                    y =   5  observing days per week

                                    k =   0.2           safety factor

                                    r =   4   number of GPS receivers per observing session

                                    d =   2.5           average observing sessions per day

                                    p =   1.1           production factor

 

Then                            s =    22 + 3 + 10 = 35 observing sessions

                                    x =    14 observing days

                                    w =    2.8 workweeks

                                    b =    105 independent vectors

 

COMMENTS:

 

In the equation to compute the number of observing sessions (s), if there were no sessions lost due to receiver malfunctions, and no additional sessions required to cover such factors as human error and irregular network configuration, then

 

s = (mžn)/r

 

However, the second part of the equation for computing “s” is to allow for additional sessions to offset scheduled sessions that may be lost due to equipment breakdown.

 

The third part of the equation, k(m), allows for additional sessions that may be required due to human error, irregular network configuration, etc.

APPENDIX G

EXAMPLES OF GPS SURVEYS WITH SUMMARY OF STATISTICS USED TO CLASSIFY THE ORDER OF SURVEY BASED ON THE OBSERVING SCHEME AND DATA COLLECTION PROCEDURES

EXAMPLE 1:

 

 

Observing sessions, total number (A, B, and C)

 

 

3

Receivers observing simultaneously

 

 

3

Stations, total number

 

 

7

Station occupations

 

 

 

Single occupations (no redundancy)

5

 

Two or more occupations, number/percent of all stations

2/29

 

Three or more occupations, number/percent of all stations

 

0/0

Base lines determined:

 

 

 

All (trivial and nontrivial)

9

 

Independent (nontrivial)

 

6

Repeat base lines (N-S/E-W/percent of nontrivial)

 

 

0/0/0

Loop closure analyses:

 

 

 

Valid loops formed?/Number of stations that can’t be included

No/7

 

Loops containing base lines from (2 or)/(3 or more) sessions?

 

0/0

Geometric relative position classification (based on Table 4-7)

 

None


EXAMPLE 2:

 

 

Observing sessions, total number (A, B, C, and D)

 

 

4

Receivers observing simultaneously

 

 

3

Stations, total number

 

 

7

Station occupations:

 

 

 

Single occupations (no redundancy)

2

 

Two or more occupations number/percent of all stations

5/71

 

Three or more occupations number/percent of all stations

 

0/0

Base lines determined:

 

 

 

All (trivial and nontrivial)

12

 

Independent (nontrivial)

 

8

Repeat base lines (N-S/E-W/percent of nontrivial)

 

 

0/0/0

Loop closure analyses:

 

 

 

Valid loops formed?/Number of stations that can’t be included

Yes(a)/0

 

Loops containing base lines from (2 or)/(3 or more) sessions?

 

0/2

Geometric relative position classification (based on Table 4-7)

 

 

Order “2-II”

(a)  Loops formed:

1 -

1(A)3 + 3(B)5 + 5(B)4 + 4(D)2 + 2(D)1

Includes 3 sessions

 

2 -

5(C)7 + 7(C)6 + 6(D)4 = 4(B)5

Includes 3 sessions


EXAMPLE 3:

 

 

Observing sessions, total number (A, B, C, D, and E)

 

 

5

Receivers observing simultaneously

 

 

3

Stations, total number

 

 

7

Station occupations:

 

 

 

Single occupations (no redundancy)

1

 

Two or more occupations, number/percent of all stations

6/86

 

Three or more occupations, number/percent of all stations

 

2/29

Base lines determined:

 

 

 

All (trivial and nontrivial)

15

 

Independent (nontrivial)

 

10

Repeat base lines (N-S/E-W/percent of nontrivial)

 

 

0/1/10

Loop closure analyses:

 

 

 

Valid loops formed?/Number of stations that can’t be included

Yes(a)/0

 

Loops containing base lines from (2 or)/(3 or more) sessions?

 

1/2

Geometric relative position classification (based on Table 4-7)

 

 

Order “1”

a)  Loops formed:

1 -

1(A)3 + 3(E)4 + 4(D)2 + 4(A)1

Includes 3 sessions

 

2 -

3(B)5 + 5(B)4 + 4(E)3

Includes 2 sessions

 

3 -

5(C)7 + 7(C)6 + 6(D)4 + 4(B)5

Includes 3 sessions

 


EXAMPLE 4:

 

 

Observing sessions, total number (A, B, C, D, E, and F)

 

 

6

Receivers observing simultaneously

 

 

3

Stations, total number

 

 

7

Station occupations:

 

 

 

Single occupations (no redundancy)

0

 

Two or more occupations, number/percent of all stations

7/100

 

Three or more occupations, number/percent of all stations

 

3/43

Base lines determined:

 

 

 

All (trivial and nontrivial)

18

 

Independent (nontrivial)

 

12

Repeat base lines (N-S/E-W/percent of nontrivial)

 

 

2/1/25

Loop closure analyses:

 

 

 

Valid loops formed?/Number of stations that can’t be included

Yes(a)/0

 

Loops containing base lines from (2 or)/(3 or more) sessions?

 

0/4

Geometric relative position classification (based on Table 4-7)

 

 

Order “B”

NOTE:

If one additional session was observed where session G would include stations 1, 2 and 5 (or 7), then the survey would be classified with an Order of “A”.

 

(a)  Loops formed:

1 -

1(A)3 + 3(E)4 + 4(D)2 + 2(A)1

Includes 3 sessions

 

2 -

3(B)5 + 5(C)7 + 7(C)6 + 6(F)3

Includes 3 sessions

 

3 -

6(D)4 + 4(B)5 + 5(C)7 + 7(F)6

Includes 3 sessions

 

4 -

1(E)3 + 3(B)5 + 5(B)4 + 4(E)2 + 2(A)1

Includes 4 sessions

APPENDIX H

SPECIFICATIONS AND SETTING PROCEDURES FOR
THREE-DIMENSIONAL MONUMENTATION  (May 11, 1988)

1.         Materials required for each marker:

 

a.                  Rod, stainless steel, 1.2 M sections

b.                  Rod, stainless steel, one 100 MM  - 130 MM 

c.                  Studs, stainless steel, 10 MM

d.                  Datum point, stainless steel, 10 MM  bolt

e.                  Spiral (fluted) rod entry point, standard

f.                    NGS logo caps, standard, aluminum

g.                  Pipe, schedule 40 PVC, 130 MM  inside diameter, 600 MM  length

h.                  Pipe, schedule 40 PVC, 25 MM  inside diameter, 900 MM  length

i.                     Caps, schedule 40 PVC, (Slip-on caps centered and drilled to 15 MM 

± 0.002)

j.                     Cement for making concrete

k.                   Cement, PVC solvent

l.                     Loctite (2 oz. bottle)

m.                Grease

n.                  Sand (washed or play)

 

2.         Setting procedures:

 

a.                  The time required to set an average mark using the following procedures is 1 to 2 hours.

b.                  Using the solvent cement formulated specifically for PVC, glue the aluminum logo cap to a 600 MM  section of 130 MM  PVC pipe.  This will allow the glue to set while continuing with the following setting procedures.

c.                  Glue the PVC cap with a drill hole on one end of a 900 MM  section of schedule 40 PVC pipe 25 MM  inside diameter.  Pump the PVC pipe full of grease.  Thoroughly clean the pen end of the pipe with a solvent which will remove the grease.  Then glue another cap with drill hole on the remaining open end.  Set aside while continuing with the next step.

d.                  Using a power auger or post hole digger, drill or dig a hole in the ground

300 - 355 MM  in diameter and 1.0 M deep.

e.                  Attach a standard spiral (fluted) rod entry point to one end of a 1.2 M section of stainless steel rod with the standard 10 MM  stud.  On the opposite end screw on a short 100 - 130 MM  piece of rod which will be used as the impact point for driving the rod.  Drive this section of rod with a reciprocation driver such as Whacker model BHB 25, Pionjar model 120, or another machine with an equivalent driving force.

f.                    Remove the short piece of rod used for driving and screw in a new stud.  Attach another 1.20 M section of rod.  Tighten securely.  Reattach the short piece of rod and drive the new section into the ground.

g.                  Repeat step 6 until the rod refuses to drive further.  The top of the rod should terminate about 76 MM below the ground surface.

h.                  When the desired depth of the rod is reached, cut off the top removing the tapped and threaded portion of the rod leaving the top about 76 MM  below ground surface.  The top of the rod then must be shaped to a smooth rounded (hemispherical) top, using a portable grinding machine to produce a datum point.  The datum point must then be center punched to provide a plumbing (centering) point.

 

NOTE:  For personnel that may not have the proper cutting or grinding equipment to produce the datum point, the following alternative procedure should be used if absolutely necessary.  When the desired depth of the rod is obtained (an even 1.2 M section), thoroughly clean the thread with a solvent to remove any possible remains of grease or oil that may have been used when the rod was tapped.  Coat the threads of the datum point with Loctite and screw the datum point into the rod.  Tighten the point firmly with vise grips to make sure it is secure.  The datum point is a stainless steel 10 MM  bolt with the head precisely machined to 14 MM.

 

i.                     Insert the grease filled 900 MM  section of 25 MM  PVC pipe (sleeve) over the rod.  The rod and datum point should protrude through the sleeve about 76 MM.

j.                     Backfill and pack with sand around the outside of the sleeve to below ground surface.  Place the 130 MM PVC and logo cap over and around the 25 MM  sleeve and rod.  The access cover on the logo cap should be flush with the ground.  The datum point should be about 76 MM below the cover of the logo cap.

k.                   Place concrete around the outside of the 130 MM  PVC and logo cap, up to the top of the logo cover. Trowel the concrete until a smooth neat finish is produced.

l.                     Continue to backfill and pack with sand inside the 130 MM PVC and around the outside of the 25 MM sleeve and rod to about 25 MM below the top of the sleeve.

m.                 Remove all debris and excess dirt to leave the area in the condition it was found.   Make sure all excess grease is removed and the datum point is clean.