The following explanations should be
used in conjunction with the report at the end of the explanatory
text. The report is shown in a tabbed window.
Project Settings
The first section of the report
displays the project settings at the time the project was
processed.
Tolerances
The second section of the report
displays warning and error messages generated during the
preprocessing of the raw data. The primary messages displayed will
be warnings when multiple angles, horizontal distances, and
vertical differences exceed the tolerance settings as set in the
project settings. The low and high measurement and the difference
are displayed. It is prudent to pay attention to any messages
generated in this section of the report. Some warnings may be
innocuous but it is prudent to check and understand all warning
messages.
The next four sections list the reduced and averaged, but unadjusted measurements that make up the network. Multiple measurements of the same angle or distance are averaged to a single measurement. The standard error of multiple averaged measurements is less than the standard error of a single measurement. When multiple measurements are used, the standard error for the averaged measurement will be computed using the average of the mean formula.
The first of the four sections lists the control coordinates used in the network adjustment. These coordinates could have been read from the .CGR raw data file, or from the .CRD or .NEZ supplemental coordinate file. Notice that the standard errors for the control points are displayed.
The second of the four measurement
sections shows the control reference azimuths and azimuth standard
errors used in the adjustment. Azimuths are defined in the .CGR or
RW5 files (Add->Reference Azimuth).
The third of the four measurement sections shows the distances and distance standard errors used in the adjustment. These distances are horizontal distances computed from all slope distance and vertical angles for that distance, including all foresight and backsight distances. The standard error settings used to calculate the final distance standard error include the distance standard error, the PPM standard error, the target centering standard error and the instrument centering standard errors. The techniques and formulas used to calculate the final distance standard error are found in section 6.12 of the textbook "Adjustment Computations, Statistics and Least Squares in Surveying and GIS", by Paul Wolf and Charles Ghilani.
The fourth of the four measurement
sections shows the angles and angle standard errors used in the
adjustment. These angles are the averaged angle value for all the
multiple angles collected. The standard error settings used to
calculate the final angle standard error include the pointing
standard error, the reading standard error, the target centering
standard error and the instrument centering standard errors. The
techniques and formulas used to calculate the final angle standard
error are found in section 6.2 of the textbook "Adjustment
Computations, Statistics and Least Squares in Surveying and GIS",
by Paul Wolf and Charles Ghilani.
If you have a traverse closure
file selected, there will be a fifth section in the Unadjusted
Observations section which shows the error of closure
report.
If the adjustment of the network
converges the next section displays a list of the final adjusted
coordinates and the computed standard X, Y standard error. An
interpretation of the meaning of the X, Y standard error, is that
there is a 68% probability that the adjusted X, Y is within plus or
minus the standard error of the X, Y of its true value.
Also shown are the Delta N, Delta E
and Delta EL values of the non-fixed control points (how much the
control points moved).
The next section displays the error ellipses for the adjusted coordinates. The error ellipse is a truer representation of the error of the point than the X, Y standard error. The error ellipses are calculated to the confidence interval as defined in the settings screen. In this report the error ellipse axis is larger than the X, Y standard errors since the error ellipses in this report are calculated at a 95% probability level as set in the Settings screens. The maximum error axis direction is along the axis of the semi-major axis. The direction of the minimum error axis direction is along the semi-minor axis and is perpendicular to the semi-major axis. If a point is located from a variety of stations, you will most likely see that the error ellipse will approach a circle, which is the strongest geometric shape.
The next three sections list the adjusted horizontal distance, horizontal angle, and azimuth measurements. In addition to the adjusted measurement the, residual, the standard residual and the standard deviation of the adjusted measurement is displayed.
The residual is defined as the difference between the unadjusted measurement and the adjusted measurement. The residual is one of the most useful and intuitive measures displayed in the report. Large residuals in relation to the standards of the survey are indications of problems with the data.
The standard residual is the a priori standard error divided by the residual of a measurement. The a priori standard errors are the standard errors of the measurements as displayed in the unadjusted measurement section. A standard residual of 1 indicates that the adjustment applied to the measurement is consistent with the expected adjustment to the measurement. One or a few measurements having high standard residuals, in relation to the rest of the standard residuals, may be an indication of a blunder in the survey. When all standard residuals are consistently large there is likely an inconsistency in the a priori standard errors and the adjustments being made to the measurements. In other words the standard errors defined for the project are too small, in relation to the survey methods used.
The standard deviation of the measurement means that there is a 68% probability that the adjusted measurement is within plus or minus the standard deviation of the measurement's true value.
Additionally, the root mean square of each measurement type is displayed. The root mean square is defined as the square root of the average of the squares of a set of numbers. Loosely defined, it is as an average residual for that measurement type.
Statistics
The next section displays some statistical measures of the adjustment including the number of iterations needed for the solution to converge, the degrees of freedom of the network, the Error Factor for each type of measurement, the standard error of unit weight, the reference variance and the results of a Chi-square test.
The degree of freedom is an
indication of how many redundant measurements are in the survey.
Degree of freedom is defined as the number of measurements in
excess of the number of measurements necessary to solve the
network. The higher the DOF the more meaningful the statistics
are.
A standard error of unit weight is
shown for each type of measurement. The possible measurement types
are:
Coordinates
(control points - in the 2D/1D model each point counts as 2
measurements (N & E); in the 3D model each point counts as 3
measurements (N, E, & EL)
Elevations (elevation control - from elevation
records in the raw data file)
Azimuths (azimuth control - from reference
azimuth records in the raw data file)
Angles (horizontal angles)
Distances (horizontal in 2D/1D model and
mark-to-mark in 3D model)
VertAngles (mark-to-mark, 3D model only)
GPS Vectors (3D model only)
The total standard error of unit
weight relates to the overall adjustment and not an individual
measurement. A value of one indicates that the results of the
adjustment are consistent with a priori standard errors. The total
standard error of unit weight equals the sum of all the measurement
standard errors of unit weight.
The reference variance is the standard error of unit weight squared.
The chi-square test is a test of the
"goodness" of fit of the adjustment. It is not an absolute test of
the accuracy of the survey. The a priori standard errors which are
defined in the project settings dialog box or with the SE record in
the raw data (.RW5 or .CGR) file are used to determine the weights
of the measurements. These standard errors can also be looked at as
an estimate of how accurately the measurements were made. The
chi-square test merely tests whether the results of the adjusted
measurements are consistent with the a priori standard errors.
Notice that if you change the project standard errors and then
reprocess the survey the results of the chi-square test change,
even though the final adjusted coordinates may change very
little.
If the project passes the Chi Square
test, the expansion factor used to calculate the confidence regions
(error ellipses at say 95% confidence) will be taken from the
normal distribution table. If the project fails the Chi Square
test, the expansion factors will be taken from the F-Distribution
table.
All confidence regions were computed using the following factors:
Variance factor: 1.0000
1-D Expansion Factor: 1.9600
2-D Expansion Factor: 2.4477
Expansion factors for 95.00 confidence regions taken from normal distribution table
The next section displays the computed sideshots of the network. Sideshots are filtered out of the network adjustment as part of the preprocessing process if the 'Enable Sideshots for Error Ellipses' toggle is off. Least squares adjustment requires a lot of computer resources. Sideshots are filtered out to minimize the computer resources needed in a large network adjustment. The sideshots are computed from the final adjusted network points. The results of the side shot computations are the same whether they are reduced as part of the least squares adjustment or from the final adjusted coordinates.
The next part of the report displays the results of the vertical adjustment. In the 2D/1D model the horizontal and the vertical adjustments are separate least squares adjustment processes. As long as there are redundant vertical measurements the vertical component of the network will also be reduced and adjusted using least squares.
The first section displays the
vertical benchmarks used in the vertical adjustment. Next, is
listed the points that will be adjusted as part of the vertical
adjustment. The following section displays the measurements used in
the adjustment. The measurements consist of the vertical elevation
difference between points in vertical adjustment. The lengths
between these points are used to determine the weights in the
vertical adjustment. Longer length lines are weighted less in the
vertical adjustment than shorter length lines.
The next section displays some
statistics about the vertical control: Number of unknown
elevations, number of routes, number of fixed and non-fixed
benchmarks, and degrees of freedom.
The next section displays the
adjusted elevations and the computed standard deviations of the
computed elevations. Following the adjusted elevation section is a
section displaying the final adjusted elevation difference
measurements and their residuals. Finally, the computed side shot
elevations are displayed.