SURPAC
Surveying
Software
The
SURPAC Least
Squares Module Applications 
Single Point Fixing (Resections, Intersections and
Trilaterations)
[This application is Included in SURPAC "Lite"]

The mathematical principle of this programme is the rigorous Least Squares adjustment
by the variation of coordinates. The "Schreiber's Elimination" technique is
used to minimize the variancecovariance matrix.


This
programme will handle any type of single Point fix using any combination of
Triangulation and/or Trilateration, as well as a Height determination for
the Free point, such as :

Point Trilateration [Y, X], or [E, N] 

Point Resection [Y, X], or [E, N] 

Point Resection [Y, X, Z], or [E, N, H] 

Point Resection [Z], or [H] 

Point Intersection [Y, X], or [E, N] 

Point Intersection [Y, X, Z], or [E, N, H] 

Point Intersection [Z], or [H] 


The
current Coordinate File is used to extract the coordinates of the User
defined Fixed Points used in the
determination of the [Y, X] (or
[E, N] ) coordinates (and/or the Height, if required), of the new Point.


The
Observation data (Horizontal angles, Distances, Vertical angles, Target
heights and Instrument heights) are extracted from a User defined General
Observation File.




For
a Trilateration calculation, the programme will use any combination of
Forward and/or Backward measured Distances to compute the new Point. The
minimum number of distances is 3. The programme will search through the
General Observation File , or defined portion of the File and extract all
measured lines to and/or from, the new Point. All Distances will then be
reduced and used to carry out a simultaneous Least Squares fix and
adjustment of the Point’s [Y, X] (or [E, N]) ordinates.








The
output, of a calculation consists of :

the
final coordinates of the new Point,


the
orientation correction, in the case of a resection,


a
comparison of observed quantities with final quantities and a list of
observational residuals,


the
standard deviation of unit weight for the observation set,


the
standard errorellipse parameters,


a
list of [Y, X] (or [E, N] )
ordinate axis cuts for each ray,


a
list of input data for the height fix (if required) and the computed height
differences along with their adjustments and final values.


Planimetric
Control Network Adjustment [Y, X] or [E, N]

The mathematical principle of the
Programme is the method of rigorous leastsquares adjustment by means of the
parametric adjustment, or variation of coordinates, technique.


This
principle is, however, modified by employing techniques, such as the
Schreiber's Elimination technique, which optimize the use of computer space
and time, whilst still maintaining the rigorous nature of the fundamental
principle.


The
Programme is composed of five subroutines, carrying out the following
stages :


The
creation of the Network File by automatic observation data compilation from
a User
defined SURPAC Observation File.
The
programme is able to handle up to 8 Arcs (or faces) of observations for each
Setup point. Each arc may include up to
50 sighted points. The
Multiple Arcs are abstracted and combined in an Abstract Sheet, showing all
observed data as well as the Mean and the Standard Deviation. These meaned
values are used for the Network adjustment.

The
extraction of the Coordinates of the defined Fixed points in the Network
from the current Coordinate file.
The provisional Coordinates of
the Free Points are calculated using the Fixed Points and the network
observational data.

The main "number crunching
stage", in which the leastsquares adjustment is carried out.
The
[AtWA] and
[AtWF] matrices are
determined directly from the observations and from the coordinates of the
Fixed points . All the orientation unknowns are eliminated using the Schreiber
technique, and the upper triangle of the
[AtWA] is compressed into
a vector.
The "Modified
Bordering" technique is used to invert the compressed form of the
[AtWA] matrix, and the vector of corrections X
is calculated from X = 
[AtWA]1 * [AtWF]. In most cases, only a single
iteration is necessary as the provisional coordinates provide good
approximates to the final values.

The
final adjustments to the provisional coordinates are computed and applied
to the provisional values. The standard error ellipse parameters for all
unknown points are computed using the standard deviation of unit weight.

This is the output stage for the
observations giving a full listing of observed directions, tT corrections,
plane equivalent directions, the oriented directions, the adjustments and then
the final directions.
Distances
are treated in a similar manner, with the listing displaying measured
horizontal distances, the projection corrections, where applicable, the
plane projection distances, the adjustments and then the adjustments and
then the final distances. The
printout finally displays the adjusted coordinate values for the Free
Points, with their associated standard error ellipse parameters.
From
the screen display of the Network output, it is possible to call for a Plot
of the Network, showing all Points, observed an measured quantities and the
error ellipses.

This
programme can be used for the computation and adjustment of survey control
networks of almost any configuration, for example, Traversing,
Triangulation, Trilateration and Triangulateration (mixed) networks.


The individual configuration of
a network is immaterial to the Programme, as long as redundant observations
exist for each of the Free Points in the network. The strengths, and/or
weaknesses, of the network will become apparent from an examination of the
resultant error ellipse parameters.


The
size of the control Network being adjusted can vary from a single unknown
point up to a network containing 500 Points, with the maximum number of Free
Points being 499.

Trig Height Network Adjustment [Z] or [H]

The mathematical principle of the Programme is the method of rigorous leastsquares
adjustment.


As for the previous Adjustment programmers, this
principle is modified by employing techniques which optimize the
use of computer space and time, whilst still maintaining the rigorous nature
of the fundamental principle.


The
Programme is composed of five subroutines, carrying out the following
stages :


The
creation of the Network File by automatic observation data compilation from
a User
defined SURPAC Observation File.
The
programme is able to handle up to 8 Arcs (or faces) of observations for each
Setup point. Each arc may include up to 50 sighted points. The Multiple
Arcs are abstracted and combined in an Abstract Sheet, showing all observed
data as well as the Mean and the Standard Deviation. These meaned values are
used for the Network adjustment.
Vertical
angles may be logged with the horizontal plane being assumed to be at 0
degrees, 90 degrees, 180 degrees or 270 degrees. The maximum vertical angle,
therefore, is 45 degrees above or below the horizontal plane.
The
Network File Editor includes an “Active” column, which can be set to Active or
NonActive, for all the data lines displayed and Points in the Network.

The
extraction of the coordinates and heights of the defined Fixed points in
the Network from the current Coordinate file.
The
provisional Heights of the Free Points are calculated using the Fixed Points
and the network observational data. The
programme will compute corrections for the earth's Curvature and for
Refraction.

The
main "number crunching stage", in which the leastsquares adjustment
is carried out.
The
[AtWA] and
[AtWF] matrices are
determined directly from the observations and the heights of the Fixed
points . The upper triangle of the [AtWA]
matrix is compressed into a vector.
The
"Modified Bordering" technique is used to invert the
[AtWA] matrix, and the vector of corrections, X,
is calculated from X = 
[AtWA]1 * [AtWF].

The
final adjustments to the provisional heights are computed and applied to the
provisional values. The standard error parameters for all unknown point
heights are computed using the standard deviation of unit weight.

This
is the output stage for the observations, giving a full listing of observed
vertical Angles, heights of instrument and heights of target, the calculated
height differences, their adjustments and then the final height differences.
The adjusted heights, along with their associated error parameter are also
listed.

This
programme can be used for the computation and adjustment of survey control
height networks of almost any configuration.


The
individual configuration of a network is immaterial to the Programme, as
long as redundant observations exist for each of the Free Points in the
network. The strengths, and/or weaknesses, of the network will become
apparent from an examination of the resultant height error parameters.


The
size of the Height Network being adjusted can vary from a single unknown
point up to a network containing 500 Points, with the maximum number of Free
Points being 499.

Spirit Level Network Adjustment [Z] or [H]

The mathematical principle of the Programme is the method of rigorous leastsquares
adjustment.


This programme also employs optimizing the
use of computer space and time, whilst still maintaining the rigorous nature
of the fundamental principle.


The
Programme is composed of five subroutines, carrying out the following
stages : 

The
creation of the Network File by automatic observation data compilation from
a User
defined SURPAC Level Observation File.
The
Network File Editor includes an “Active” column, which can be set to Active or
NonActive, for all the data lines displayed and Points in the Network.

The
extraction of the heights of the defined Fixed points in the Network, from
the current Coordinate file.
The
provisional Heights of the Free Points are calculated using the Fixed Points
and the measured level data.

The
main "number crunching stage", in which the leastsquares
adjustment is carried out.
The
[AtWA] and
[AtWF] matrices are
determined directly from the level differences and the heights of the
Fixed points . The upper triangle of the [AtWA]
matrix is compressed into a vector.
The
"Modified Bordering" technique is used to invert the
[AtWA] matrix, and the vector of corrections, X,
is calculated from X = 
[AtWA]1 * [AtWF].

The
final adjustments to the provisional heights are computed and applied to the
provisional values. The standard error parameters for all unknown point
heights are computed using the standard deviation of unit weight.

This
is the output stage for the observations, giving a listing of the measured
Height differences, their adjustments and the final Height differences
derived from the adjustment.
The
adjusted heights, along with their associated error parameter are also
listed.

This
programme can
be used for the computation and adjustment of level circuit networks of
almost any configuration. 

The
individual configuration of a network is immaterial to the Programme, as
long as redundant observations exist for each of the Free Points in the
network. The strengths, and/or weaknesses, of the network will become
apparent from an examination of the resultant height error parameters.


The
size of the Height Network being adjusted can vary from a single unknown
point up to a network containing 500 Points, with the maximum number of Free
Points being 499.

