Horizontal Adjustment

Instrumentation
Leica SR399 dual frequency GPS receivers were used to provide horizontal control for most of the horizontal points. In cases where there were obstructions making GPS observations impossible, a Leica 905L electronic total station was used to tie in the obstructed point to GPS points set in close proximity.

Overall Network Control
The overall control network contains points of known position and elevations. These points surround the City to provide an appropriate geometry to perform a rapid static survey of the City’s interior points.

The data supplied to the City will be in NAD 83 Illinois East Zone (1201) State Plane Coordinates. However, it was known that NGS is performing the adjustment for the Illinois HARN network. The results of this adjustment have not been published at the time of this report, but it is known which points NGS observed for the survey. Three future HARN points that surround the City were chosen as control for the project. A readjustment will be made for the entire network, and the new data will be supplied to the City in the HARN coordinate system when the HARN information is published on these points.

Until the results of the HARN are published, NAD 83 State Plane Coordinates will be used. Consequently, current NGS points will need to be used. Of the three HARN points, two are currently NGS points. ZAU B is an Order A point, and SALT 2 is a Third Order point. SEMINARY 2 and the section corner SE 7-39-9 are First Order points and are within the City limits. These two points served as the primary reference stations for the rapid static survey for the interior points.
Vertical information for the overall network was not critical because local DuPage County benchmarks would be used and a local vertical model developed. However, two control points did have NGS published vertical information. ZAU B was listed as a Second Order benchmark and 807 OFFSET was leveled from the First Order benchmark 807 in Bartlett.

Two more points were included in the overall network (WC100 and WC430). These points are interior to the City and served as primary reference stations for the rapid static survey.
The adjustment revealed that published coordinates of ZAU B did not agree with SE 7-39-9 and SEMINARY 2 by over a foot. It was also discovered that the published coordinates of SE 7-39-9 and SEMINARY 2 did not agree in easting by 9cm. As a result, additional NGS control points were added to determine what NGS point to use to determine horizontal coordinates. The NGS points DEGNAN, FAA 06C A, and PLAPORT, which are all First Order points, were tied directly to SEMINARY 2 using GPS.

Rapid Static Network
The rapid static network would relate all of the interior City points to each other. These interior points also included the four primary reference stations, which are part of the overall control network.

Within the rapid static network, it was decided that each West Chicago point would have two GPS vectors from different references in order to determine a position. It was also attempted that the two GPS vectors would be near orthogonal to ensure uniform precision in position in all directions.
The rapid static network would generally resemble a grid of approximately one mile spacing. The reference GPS receiver would be placed on the section corner and GPS vectors would be observed to adjacent section corners and quarter corners. In the process of observing adjacent corners, the grid network design would also contain cross-bracing.

The four primary references of the overall control network would also be included in the grid structure of the rapid static network. This would ensure that all West Chicago points were accurately surveyed to points that will become part of the future HARN network.

Terrestrial Side shots
Terrestrial surveying was required when GPS use was not feasible. There were several West Chicago points that were in areas that caused obstructions to GPS observations, e.g. buildings and trees. Offset points were then required and were surveyed using GPS. Generally, two offset points were used to survey each West Chicago point that could not be surveyed using GPS. These two offset points were inter-visible to provide the occupying point and back sight for terrestrial surveying.

A Leica 905L electronic total station was used for the terrestrial surveying. A prism / tribrach / tripod setup was used for each back sight, except for the points located on bridge structures which were hand-held using a prism pole. Each setup observed three independent angles and six distances for each point. The data was recorded in a Sokkia SDR33 electronic field book.

There are a total of three points that have not been surveyed at the time of this report. This is due to temporary obstructions at the time of survey. These points are WC30, WC35, and WC110. These points will be surveyed at a later time when section corner reestablishment work will be performed.

Adjustment
The final adjustment consists of the GPS observations of the overall control network, the GPS observations of the rapid static survey, the terrestrial observations to the points unobservable by GPS, and the results of the leveling adjustment. All of this data was adjusted simultaneously by a least squares program STAR*NET-GPS by STARPLUS SOFTWARE, INC. to provide the final coordinates.

A least squares adjustment is based on using more observations than necessary to calculate a solution. More observations are used for two purposes: to provide redundancy to detect blunders, and to arrive at a more accurate result. A least squares adjustment applies a residual (or correction) to all redundant observations to make them “fit” together to give a unique solution. There can be an infinite number of combinations of residuals applied to redundant observations to provide any unique solution. The least squares adjustment will find a combination of residuals in which the sum of the squares of all residuals will be at a minimum in order to provide a unique solution.

This minimum sum of the squares of residuals, or least squares, is further refined to take into account that some observations are more accurate than others. For instance, one would expect the residual of a distance measured with a precision of 0.01 feet will be smaller than the residual of a distance measured with a precision of 1 foot. Hence, least squares will take into account the precision, or standard error, and residuals of all of the observations and find the minimum sum of squares of the “standard residuals.” A standard residual is simply the residual divided by the standard error of the observation. The selection of assigning a standard error to an observation is the weighing of observations.

Prior to the final adjustment, two smaller adjustments were made to determine the weight of observations that is required for a least squares adjustment. An adjustment was made that included only the overall control. Then an adjustment was made which included all of the GPS observations. A final adjustment was made to include all observations and leveling results.

The adjustment of the overall control network was performed to specifically deal with the long vectors that were observed. A weighting scheme was determined in order to ensure that the standard errors used for the adjustment would actually agree with the actual adjustment results. This was verified by performing a Chi-Squared statistical test. The weighting scheme would be modified until it would agree with the adjustment results. For the long baselines of the overall control survey, a weighting scheme of 0.005 m + 1 part per million, the manufacturer specification, was initially used. This was later revised to 0.005m + 0.6 ppm in horizontal and 0.005m + 1.1 ppm in vertical.

Next, the adjustment of all GPS vectors was performed to determine the weighting of the rapid static observations. The weighting scheme used the variance-covariance matrix from the output of processing the vectors. The variance-covariance matrix needs to be scaled in order to ensure that the standard errors used will agree with the adjustment results.
The terrestrial observations were weighted in terms of distance precision and angular precision. The distances were given a standard error of 0.0067 feet + 5 ppm and the directions, the angular observations, were given a standard error of two arc seconds.

The final adjustment incorporated all of the observations and leveling results and all of the standards errors. A minimally constrained adjustment was first performed to ensure that all of the observations agreed with each other. The minimally constrained adjustment used SE 7-39-9 fixed in position and elevation. The results indicated no blunders.

The next step was to use all of the leveling results and published NGS points to determine which additional constraints would be used. It was found that all of the leveling results agreed with the GPS vectors within precision limits. The surrounding NGS points, however, did not correspond to the published information.

The minimally constrained adjustment held the first order point SE 7-39-9 as fixed in position and the coordinates of all the other NGS points were calculated relative to it. The results were somewhat confusing due to the variety of the discrepancies between the published and calculated positions of the NGS points. The following table to summarizes the results of the minimal constrained adjustment.

Changes in position from NGS values
By holding SE 7-39-9 (WC360) Fixed
Change = Calculated – Published

In detail, we see (excluding the two third order points) that the northing of the three NGS points agree quite closely. The eastings, however, do not match. The published coordinate for ZAU B can be disregarded due to the possibility that it may never have been surveyed directly to the local first order points in the area, but only to other order A points around the country. ZAU B’s coordinates can also be ignored due to fact that it is far from West Chicago, while SE 7-39-9 and SEMINARY 2 are within city limits. This leaves a 0.31 foot discrepancy between SE 7-39-9 and SEMINARY 2 that needed to be resolved. The 0.31 foot discrepancy can be distributed throughout the City by holding both SE 7-39-9 and SEMINARY 2 fixed in position. It is then estimated that a relative error of 0.05 feet in easting would be present between all points. The adjustment results show that by holding both points fixed causes several vectors to have excessively high residuals. Therefore, using the NGS published values for the two First Order points is considered unacceptable.
To remedy the two First Order points’ horizontal discrepancy; other First Order points were GPS surveyed. GPS vectors were observed from SEMINARY 2 to the First Order points FAA 06C A, DEGNAN, and PLAPORT.

The result of this additional survey provided several items. The easting of FAA 06C A, DEGNAN, and PLAPORT were consistent with each other. The easting of these three First Order points were within an average of 0.07 feet to SE 7-39-9 and 0.24 feet to SEMINARY 2. These results provide evidence that the published easting of SEMINARY 2 does not agree with surrounding First Order points. However, the northings of the three First Order Points were not consistent with each other.
Past GPS data observed by PEI were included in the adjustment to verify the results of the recent survey concerning the inconsistent northings of the three First Order points. The data included observations to ten additional First Order points in the DuPage County area. Again SE 7-39-9 was held fixed in position for the final adjustment. The deviations of calculated versus published coordinates for First Order Horizontal NGS points have been summarized by the following table.

Changes in position from NGS values
By holding SE 7-39-9 (WC360) fixed
Change = Calculated - Published

It can be seen that SE 7-39-9 is consistent in position with most of the First Order points. Though there are several points that have either an easting or northing that is different by 0.2 to 0.3 feet, it should not be surprising. The distance accuracy standard for First Order points is 1:100,000. A typical distance between two First Order points is around 10 miles. Therefore the expected accuracy of the distance between the First Order points is 0.53 feet. The inconsistencies that have been seen are much less than what can be expected for First Order accuracy and should not be of much source of concern.

Hence, the First Order NGS point SE 7-39-9 (WC360) was held fixed by using the published NGS coordinates to provide a minimal constrained adjustment in horizontal position. The DuPage Benchmarks were all used as constraints based on the leveling adjustment.
The result of the adjustment is a list of points that have horizontal and vertical information. The horizontal information is in NAD 83 Illinois East Zone State Plane Coordinates. The elevations are on the DuPage County Datum. Also, there is a scale factor associated for each point. This is a characteristic of State Plane Coordinates. Due to the map projection qualities of State Plane Coordinates and the variety of elevations for all of the West Chicago points, each point will have its own unique scale factor.

This scale factor is the combined scale factor that takes into account the grid factor and elevation factor. If the combined scale factor is not used when measuring distances, one will never be able to match into the points that have State Plane Coordinates. One will always find that the distance measured between two points will be different than the inversed distance using the State Plane coordinates. This is a very important characteristic of State Plane Coordinates when one is performing terrestrial surveying. The scale factor is applied correctly when using the following equation:

Ground distance * combined scale factor = “State Plane” distance