Raymond J. Hintz D
epartment of Surveying Engineering,
University of Maine
Orono, Maine 04469

Kurt Wurm
Bureau of Land Management,
Division of Cadastral Surveys
Billings, Montana

Jerry L. Wahl
Bureau of Land Management,
Cadastral Survey,
Eastern States, Springfield, VA 22153

Dennis McKay
Bureau of Land Management,
Division of Cadastral Surveys
Phoenix, Arizona


The Bureau of Land Management is responsible for the collection and maintenance of the Geographic Coordinate Data Base (GCDB). This is collection of all survey and coordinate records in the U.S. Public Land Survey System (PLSS), placing error estimates on these records, producing coordinates and error estimates on those coordinates for all corners, subdivision to the quarter-quarter section level using the rules of the Manual of Surveying Instructions, 1973, and generation of the parcels created by this process.

One of the more unique things about the PLSS is that it is a continuous network of survey information where very few geodetic coordinates from field surveys are known. The data is also highly redundant in nature.

A least squares approach to analysis of this data is very suitable due to its redundant nature and differing error estimates from the varying quality of the surveys. The problem is the amount of nature makes a simultaneous adjustment of contiguous data near impossible.

A regional approach to coordinate generation, and error estimates of those coordinates, has resolved these problems. The process produces seamless coordinates efficiently, resolves reliabilities (error ellipses) independent of the coordinate production, and lends itself to maintenance operations where newer survey data will be added to GCDB and will result in better coordinates. This regional approach will be fully discussed and demonstrated.


The GCDB is produced from all available survey records (distances and bearings) and any geodetic coordinates which exist for corners in the U.S.P.L.S. The former is derived from boundary surveys (original, dependent retracement, subdivision, etc.). The latter can come from digitizing of corner information on maps (primarily U.S.G.S. quadrangle maps) or as derived from field surveys (conventional survey and G.P.S.). Note many of today's land surveys often produce both geodetic coordinates and survey record information, the latter being derived directly from the coordinates. The original surveys were usually not tied to geodetic control as they often preceded these kinds of surveys in time. Fortunately, these surveys all had a link to geodetic orientation via astronomic observation, and resulted in astronomically referenced mean bearings and ground distances on plats. Likewise, subsequent boundary surveys do not necessarily require a tie to geodetic control but hopefully provide more reliable bearings and distances between survey corners due to the better instrumentation surveyors now utilize.

The redundant nature of record data in the U.S.P.L.S. enables least squares analysis to be a suitable choice for coordinate generation and validation of the quality of the input data. The ability that least squares analysis provides in error estimation (weighting) of the input data is very critical. As an example, the record data of an 1850 original survey normally will have larger error estimates than a 1975 dependent resurvey in the same area. The 1850 original survey could have varying error estimates in its data - meander lines were generally surveyed less precisely than section lines. The GCDB operator is in charge of assigning logical error estimates to record data based on date of survey, techniques used, terrain, and the inferred knowledge of the quality of that particular surveyor's work.

Likewise, digitized coordinates cannot be treated as perfect. They are only as good as the map compiler's abilities in locating the corner position. It may have been targeted and thus easily identified, or in other cases a road intersection may have been assumed to be a section corner. That map information is then digitized by a GCDB operator in a process which obviously contains error. Coordinates are thus assigned logical error estimates and allowed to be treated as an observation in the least squares process. Coordinates derived from field survey processes will obviously be assigned error estimates of several times smaller magnitude than the digitized coordinates.

In least squares analysis of a particular field survey the amount of data is quite finite - it is basically a function of the size and purpose of the job. A state-wide high precision GPS survey is a finite amount of data which in the end is processed by least squares. The state boundary is the limits of the job, and its purpose is improvement of the quality of their coordinates. NAD 83 was a re-processing of information to improve coordinate quality over NAD 27. The limits of the job were the ends of the control networks.

GCDB is confronted by the particulars of data as identified. In an abstract sense, the boundaries of the GCDB data are the boundary of the U.S.P.L.S. system. In a practical sense, BLM GCDB state offices manage their own state GCDB data sets, and thus the bounds are the state boundaries which they manage. On the other hand, Montana and Wyoming would obviously desire that their common boundary's corners have the same coordinates. The least squares processing of even one state's GCDB would be larger than the NAD 83 adjustment of approximately 250,000 stations. Further complicating this issue is most GCDB processing is now PC based.

The second complexity is that the quality of GCDB needs to improve over time. An example is an area where a recent survey results in survey quality coordinates and better quality measurements between corners. This data needs to be efficiently integrated into GCDB to improve coordinates in that area.

Finally, an important component of GCDB has been providing indicators of the reliability of its coordinates. The standard errors of coordinates as derived from the variance-covariance error propagation in the least squares analysis seemed to be the logical indicator of reliability. Unfortunately, this is the most time consuming process in the least squares analysis, and can be avoided if only coordinate production is your desired product (as in NAD 83).

Data Structure of GCDB
and its Limit in Data Analysis

GCDB is organized logically into individual townships of information such as corner type, coordinates, coordinate reliabilities, record data and error estimates, control (including digitized) coordinates and error estimates, rules of subdivision of section, and identified land parcels. Organizing by township enables easy indexing, archiving, and retrieval of information.

In the infancy of GCDB data collection it was originally thought that a township would also be the region which defines the limits of data analysis. To ensure a seamless "connection" to an adjacent township, once a township was completed any adjacent neighboring townships not completed would require fixed coordinates along the common border. As an example, if T12NR18E was completed, to process T12NR19E the coordinates along its west boundary would be held fixed as derived from the adjacent township. While this solves the seamless issue, note the data in T12NR19E was not used in determination of its westerly boundary. This creates systematic error buildup which propagates to larger and larger amounts as more townships are processed. This was identified when the least squares analysis of a township with fixed boundaries from adjacent townships forced residual error into the record measurements and control coordinates in that township which did not really exist. This appeared quickly if the fixed boundaries were allowed to adjust, but then the seamless match between townships disappeared.

Furthermore, fixed boundaries for seamless purposes creates optimistic coordinate standard deviations of corners near the boundary. As an example, a quarter corner one-half mile from a fixed boundary will have small coordinate standard deviations due to its local nature to the fixed positions.

The Concept of Region Analysis
Phase 1

The recognition of this systematic error buildup due to fixed township boundaries resulted in the realization that multi-township least squares analysis (region) was required. The common boundaries would not be held fixed. After a suitable region analysis takes place those coordinates are imported back to the individual township data structure and those township's sections are then subdivided. The entire process of merging townships, performing the least squares analysis, re-populating the individual townships with coordinates and reliabilities, and subdivision could be performed in a batch process.

The most difficult concept of phase 1 was how to ensure townships are merging correctly. On a township boundary a corner has different point identifications in individual townships. This is because the point identification is a function of its location in the township. An additional complication is that the point identification infers how that point controls subdivision. On an E-W line between two townships with conventional closing corners, the closing corners control to the south while the standard corners control to the north. The point identification provided an automated process for identifying how it controls, but it does nothing to lend itself to indication of point match across township lines. Fractional townships can cause a required match of interior township lines to an adjacent township exterior. Offset townships exist where section 31 and 32 in the northerly township may be common to section 2 and 3 in the southerly township. Finally, non- standard lines (meanders, mineral claims, etc.) cross township boundaries but their intersection with the boundary is not always identified by record information to the intersection point.

Due to the systematic error buildup problem, it was not desired to hold an township boundary fixed so absolutely comparing coordinates could not be the mechanism for resolving a common line. The general nature of the boundaries does not enable a point identification rule based system.

The township merge was finally resolved by not basing it upon point identification, and only using coordinates in a relative sense. At the beginning of the merge process, GCDB personnel are asked to input an appropriate coordinate match for the region. The merge process (called FORMLSA) reads a region file consisting of townships and their location on the computer's hard disk. The first township is read in and the township name is attached to the original point identification. When a subsequent township is read in, the bearing and distance (record data) is compared absolutely to existing bearings and distances in the building region. If a match is found, coordinate comparisons are made to see if they are within the user defined tolerance. If no match is found the record data does not yet exist in the building region, and region point identifications are assigned based on the township it is in. If a unique match is found that line already exists in the building region and those points are identified as belonging to more than one township. More than one match results in an error message to the user that the tolerance level needs to be refined. Lines where only one corner is in the region are handled in a similar fashion though that line is a new bearing and distance. A bearing-distance closing to a township line is the best example of this kind of line.

This approach insists that the same bearing and distance for a common line exist in all townships. This is actually a requirement of GCDB, and thus fits nicely into the region concept.

Another point of interest is that some GCDB offices have decided to continue the practice of holding township exteriors fixed in adjacent situations until the region analysis occurs. This means a corner may be unknown in one township, and treated as fixed (very small error estimate) in an adjacent township. Similarly digitized coordinates may be assigned error estimates of 40 ft. in the first township, but then have their adjusted coordinates held fixed in the adjacent process. In the region merging process if a corner is unknown in any township it is treated as unknown in the region. Likewise, if a corner has different "control" coordinate error estimates, the largest error estimates are used.

Putting the Regional Approach into Production
Phase 2

Phase one of regional analysis provided an acceptable mechanism for merging of townships into regions, and then the dissemination of region least squares produced coordinates into individual township files. It did not identify two production aspects:

  1. A seam still exists between regions. If the edges of the region were not held fixed in an adjacent region one will still have edge mismatch between regions.
  2. Generating coordinate standard deviations for reliability in regions takes an extensive amount of time as the variance- covariance component of least squares is the most mathematically intense component of the process.

The Township Buffer for Coordinate Production

Unless GCDB personnel had the computing power to readjust an entire state every time new data was added, the problem of matching regions still exists just as matching townships used to exist. It is logical a region match will have fairly insignificant problems as the amount of data being analyzed reduces the problem in magnitude. To enhance the region process the buffer concept can be utilized in two ways. Note this process is for coordinate generation only and not reliability generation.

The first procedure is simply where the user is confident that creating a fixed boundary will not cause adverse problems. In forming a region one is allowed to add what are called buffer townships. These buffer township's measurement information is not made part of the region analysis. Instead common bearing-distance information is identified as in phase 1, but only the existing adjusted coordinates from the buffer township are brought in as fixed control. Buffer townships are obviously not imported back to their individual township coordinate files as they were part of a previous region adjustment where you desire not to change any coordinates.

The second procedure is an alternative to the first process where the user is concerned about the effects of the fixed coordinates. To minimize the effect of fixed coordinates this second procedure can be thought of as a double buffer concept. The first buffer consists of townships which are brought in for least squares analysis, but their coordinates will not be imported back into their respective townships as they were part of a previous region analysis. The second buffer is the fixed layer of coordinates as identified in the first procedure. The double buffer still creates a seamless GCDB as coordinates of boundary points to the first buffer retain their coordinates as they previously existed, and not from this regional analysis. The assumption is that these boundary coordinates are shifting insignificantly due to the double buffer, and statistically (from the reliability values) it does not matter which coordinates are assigned to the point.

While not yet in full production, the double buffer allows the user to perform region analysis with overlapping information and still achieve a seamless GCDB.

Kerplunking for Reliabilities

While the term kerplunking may indeed sound relatively un- scientific, it does best describe the developed regional approach for generating coordinate standard deviations which in GCDB terms is a reliability.

The kerplunking concept is basically derived initially from the theory of survey network design using least squares. Network design involves developing approximate coordinates for your proposed survey stations, determining what measurements you intend to make and assigning error estimates to those measurements, then finally using least squares to generate coordinate standard deviations and error ellipses of your survey stations. If you make the intended measurements and have done a good job of error estimation the field survey process will replicate your reliabilities generated from the design process. In terms of GCDB, survey network design proves that reliabilities can be generated as a distinct process from the least squares portion of coordinate generation.

The next assumption in kerplunking is that measurements not in close proximity to a station do not affect the reliability results of that station. In simple terms, making some measurements five miles from a station, and very indirectly connected to that station, do not appreciably improve the reliability of that station's coordinates.

In generating reliabilities you also do not want any artificially fixed coordinates as this will produce artificially small reliabilities in that general area. Kerplunking thus forms a region measurement system similar to region coordinate production without the fixed buffer concept. What is dramatically different is the entire region is not analyzed for reliability generation.

Instead a user defines a distance tolerance around an individual township which is large enough that the user feels measurement data outside of that tolerance will not affect the generated reliabilities of that unique township. The best example is a six mile tolerance. For a particular township the nine surrounding townships will be used in addition to it in generating its reliabilities. Only that middle township's reliabilities get updated. The algorithm then moves to the next township and performs the same task. One distance tolerance is used for an entire region reliability analysis, and thus the reliability generation process is again non-interactive.

The test if a large enough tolerance has been used will be the reliabilities of corners common to two or more townships. Their values of reliability in each township should show no statistical difference. The one township tolerance appears very suitable for region reliability generation and thus nine townships becomes the largest variance-covariance propagation problem.

Of specific interest is that a region for coordinate generation can differ totally from the region as defined for reliability generation. The region for coordinate generation is limited only by the computing speed of the program/computer, and thus how long one desires to wait for the least squares to process. The reliability generation is performed a township at a time with buffering data, and thus in theory could generate a state's worth of data in one process. Of specific importance is the batch nature of the processing. Jobs can be set into operation during off hours with completely updated township information when one returns to work.


The regional approach to least squares coordinate generation and reliability generation has been applied to U.S.P.L.S. data. The process is especially able at accepting new survey information and thus providing an effective mechanism for improvement of coordinates and reliabilities of corner information over time.


This work has been partially funded through the cooperative agreement between USDI-BLM Eastern States and the University of Maine. The authors especially thank cooperative assistance representative Corky Rodine of BLM Eastern States Cadastral Survey.


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