problems maintaining your spatial reference system - adjustit

Problems Maintaining Your Spatial Reference System? - adjustIT: we-do-IT

Justin Eldridge, Richard Homburg, Tim Patchett and Dr. Walter Hesse

we-do-IT Pty Ltd

Smallworld ‘98 International Conference

Abstract Optimising, maintaining and updating spatial reference systems, in particular Digital Cadastral Data Bases (DCDB’s), has been an ongoing challenge for the GIS User Community. This paper details a technique which accommodates spatial quality improvements while maintaining the relationships that exist, for example, between a utility network and the spatial reference system. The method can also be used to cope with incremental updates of the spatial reference system. The paper details the theory behind the technique and presents adjustIT, a Smallworld GIS implementation of the methodology. Practical applications of adjustIT are described with particular reference to the requirements of utilities in maintaining their networks while accommodating incremental changes to the DCDB upon which their assets are referenced. Introduction Updating Digital Cadastral Data Bases (DCDB’s) presents challenges for both the custodian and the end user of the information. The custodian has the task of merging heterogeneous data sets which at present vary widely in accuracy. The customer while requiring the latest information must also maintain the association of their assets to the cadastre which will shift as more recent information of greater accuracy is added to the DCDB. These demands on the custodian and the end user are further compounded by the dynamic nature of the DCDB. This paper initially gives a brief overview of the development of the DCDB in Victoria Australia. A methodology to tackle the problems mentioned above is then presented and a software package called adjustIT implemented in the Smallworld GIS environment is introduced. Historical Background and Current Practices The DCDB in Victoria as in most other states of Australia was digitised from available paper cadastral maps. Cadastral maps in Victoria have no legal status and are not part of the subdivision and land titling process. As a result when the requirement for a DCDB eventuated there was no complete cadastral map on which it could be based. To compensate the best available cadastral survey plans were collated and, using additional control surveys, linked to a topographic base map. The newly created cadastral base map was then digitised to form the basis of the DCDB. The quality of paper source maps and subsequent rubber sheeting of these maps resulted in large accuracy variations across the state. The source maps are generally accepted to be accurate to 1mm at map scale (Effenberg et al, 1997). The scale in urban areas ranged from 1:250 to 1:5000 while in rural areas the source maps were up to 1:25000 (Effenberg et al, 1997). The accuracy of the paper cadastral map base therefore varied between 0.5 to 5 metres in urban areas and generally up to 25 metres in rural areas although inaccuracies of +100 metres have been reported. The accuracy was further degraded as the paper maps were digitised. Geometric attributes such as parallelism of lot boundaries, straightness of road alignments, right

Copyright 1998. we-do-IT Pty Ltd. All rights reserved.


angles, areas, bearings and distances were generally not maintained through the digitising process. If this information could be recovered through ‘spatial data mining’, improvements in spatial accuracy could be made. The initial capture phase is now complete and the ongoing maintenance and improvement of the DCDB has become an important issue. At present new information regardless of its accuracy is distorted to fit in with the surrounding area. A method that will take into account the relative accuracy of the old and new information is required. This method must also allow for users of the DCDB to identify changes easily and adjust their related information accordingly. Currently the DCDB has only ‘spaghetti’ or ‘dumb’ line work. Unique Feature Identification (UFI) codes are planned to be implemented. The lack of UFI codes is one of the main reasons new information is distorted as there is no way to keep track of individual nodes. UFI will also allow topology to be incorporated into the DCDB. Essentially a technique is required that;

• can integrate data sets of differing accuracies, • is based on sound mathematical principles and • can allow relationships between customer information and the DCDB to be

defined and maintained throughout the update process. A program called adjustIT implemented in the Smallworld GIS suite achieves the above requirements through applying standard surveying adjustment techniques via a user friendly graphical interface. AdjustIT - an Overview The methodology presented here is largely based on that presented in Hesse, Benwell and Williamson (1990) and Hesse and Williamson (1993). The technique is based on a mathematical adjustment of points within a selected area based on a set of constraints. The constraints are manually or automatically specified by the user and are given a weight which controls the strength of each constraint. An example of a constraint that a utility company would apply is the offset of a utility line from the cadastral boundary. Once this constraint is specified it is always maintained unless it is removed. If the cadastre is shifted, as a result of the addition of more accurate information, the constraint will ensure that the utility line maintains its relative position to the cadastral boundary. A more rigorous method for updating the DCDB can also be achieved using a constraint based approach. As new information is supplied constraints are set and given weights based on the accuracy of the data. The cadastre surrounding the area to be updated also has constraints specified and weights assigned according to the



accuracy of the data. Both the new and the old data will be modified however the amount of modification is governed by the weights assigned. The method can also be applied to increase the accuracy of the DCDB without the need for expensive field surveys. As mentioned earlier when the cadastral maps were digitised geometric attributes in the original data were not preserved. This information can be recovered either by spatial data mining for standard measurements, for example road widths, or from title information. These pseudo observations are entered as constraints with high weights and an adjustment performed. This process helps to rectify the cadastre. Improvements in point standard deviations from 2.5m to 1m from automatically ‘data mined’ constraints in test data sets have been reported (Hesse et. al., 1990). These results are comparable with standard affine and helmert transformations which require the (costly) establishment additional survey control points. AdjustIT - The Constraints Constraints and a corresponding weight are specified interactively by the user or through automatic ‘data mining’ of the data set. At present nine constraint types are implemented in the adjustIT package. Additional constraints can be added provided that the constraint can be expressed as a function of coordinates. The constraints currently implemented are:

• point • fixed point • distance • azimuth • vector components (delta x /y) • parallel • straight and • area

All points referred to in a constraint within the data set to be adjusted are either point constraints or fixed point constraints. Point constraints have the lowest weight while fixed point constraints have the highest weight. All points that form part of a constraint are considered as pseudo observations to avoid matrix singularity, in this situation the adjustment algorithm would fail. (The words constraints, measurements and observations are used interchangeably throughout this paper in order to remain consistent with other texts). All other constraints are expressed as a function of the unknown coordinates. For example the distance constraint:

( ) ( )a bd aX bX aY bY− = − + −

122 2

The unknowns that must be solved for are the coordinates (Xa, Ya) and (Xb, Yb).



The distance constraint can be used to ‘constrain’ the length of a line to be a user specified value within a chosen tolerance. The diagram below illustrates how the different constraints are applied to a typical subdivision. The constraints listed below are far more than is normally required. Constraints are only set when the measurement or attribute (for example orthogonality) is known to exist. The basic point constraints are not listed though they are always created for points referenced in an observation.

12 10

7

4 5

6

3

2

119

1

8

Constraint Stations Value Standard

Deviation Fixed Point 3 100, 5000 0.0001 Fixed Point 8 121.64, 5009.40 0.0001 Parallel (1, 2), (3, 8) NA 30” Parallel (4, 9), (5, 10) NA 30” Parallel (5, 10), (6, 11) NA 30” Parallel (6, 11), (7, 12) NA 30” Distance 4, 5 20.0m 0.01m Distance 5, 6 20.0m 0.01m Distance 6, 7 22.0m 0.01m Distance 5, 10 40.0m 0.01m Distance 7, 12 45.0m 0.01m Angle 5, 4, 9 90 o 30” Angle 6, 5, 10 90 o 30” Angle 4, 9, 10 98 o 30” Bearing 3, 8 85o 35’ 30” Bearing 9, 10 95 o 30” Bearing 10, 11 120 o 30” Bearing 11, 12 92 o 30” Straight 4, 5, 6 NA 10” Straight 5, 6, 7 NA 10”



Straight 6, 7, 8 NA 10” Area 4, 5, 10, 9 800m2 1m2 Area 5, 6, 11, 10 900m2 1m2 Area 6, 7, 12, 11 990m2 1m2

To ease the workload involved in entering a large number of constraints manually, automatic snooping for constraints has been developed. This is analogous to data mining with the spatial context being the only difference. Data mining is used to find relationships and patterns that exist in large data bases that would otherwise be hidden in the vast amounts of data. The screen shot below illustrates the output generated after spatial data mining for bearings in a typical cadastral data set.

Cadastral data sets tend to have a significant number of recurring or common measurements. Road widths, lot frontages, areas and alignments are often maintained throughout a subdivision. By automatically examining the data set and obtaining counts, for example the number of distances that are close to 15.24m (a standard road width in Victoria), and performing statistical significance testing, standard measurement lookup tables can be generated. All measurements in the data set that fall within a statistically determined range of a common measurement are constrained to that value. The user has final control over this process. The automatic snooping of constraints or ‘spatial data mining’ can be used to improve the accuracy of the cadastre through simply snooping for geometric constraints that were lost in the digitising process.



Once the constraints have been set a standard least squares adjustment is performed. For more information on the least squares adjustment process see Harvey (1993), Gelb (1988) and Eldridge (1997). AdjustIT - The program AdjustIT is implemented in the Smallworld GIS environment using the magik programming language. The user interface allows constraints to be set and weights assigned manually and also provides an automatic constraint snooping option. The program consists of three modules. The low level matrix operations to perform the least squares adjustment are written in ‘C’ to maximise performance. The user interface which allows constraints to be set interactively and the automatic constraint snooper are written in magik. Matrix operations are generally computationally expensive and to speed up the operation sparse matrix techniques have been employed. The entire adjustment process has been programmed in ‘C’ to maximise speed and efficiency and is invoked via the Smallworld Alien Coprocessor (ACP) mechanism. AdjustIT - Performance The least squares adjustment engine written in ‘C’ has been tested extensively. The following graph illustrates the performance of the adjustment engine on a test network with an increasing number of unknowns to be solved.

Performance of adjustIT

0

50

100

150

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00

400012996

800025996

1200038996

1600051996

2000064996

40000129996

60000194996

Number of Unknowns and Number of Constraints Specified

Tim

e El

apse

d (s

ec)

Win 95 P166 32Mb RAM

Win NT P180 98Mb RAM

NOTE 1: The times above only include the actual time for the Least Squares Adjustment engine running as an Alien Coprocessor (ACP) within the Smallworld GIS environment. Allow extra time for the selection and transfer of constraint information to the ACP and for the transfer of adjusted points



back from the ACP and subsequent GIS update. However, the major "bottle-neck" in the process, the actual adjustment engine calculation time, has been overcome. NOTE 2: The small step in the Win95 curve is due to the limited memory on the test machine and the required paging (caching) of adjustment data. The values immediately below the x axis indicate the number of unknowns that were solved for in an adjustment. The second line of values indicate the total number of measurements or constraints used to solve for the unknown station coordinates. The constraints include distance, bearing, angle, vector, parallel and area. Two fixed point constraints were set at either end of the test network. The raw speed of the adjustment engine is quite acceptable with 40,000 unknowns determined in less than 60 seconds using approximately 130,000 constraints. This will continue to improve as hardware and software performance increases. Conclusion The computational overhead traditionally imposed by least squares adjustments has been minimised and can now be used where large amounts of data are involved. The power of least squares with its ability to handle and combine redundant information in an optimal way has been harnessed and applied in adjustIT. AdjustIT has applications wherever spatial constraints must be maintained. The automatic generation of schematics that conform to a set of predefined cartographic constraints is one application while maintenance and updating of DCDB’s has been demonstrated to be another. Finally the ability to specify relationships between cadastral and non cadastral information and maintain these relationships is essential if a changing DCDB is to be accommodated. Updating of DCDB’s should not only improve the completeness of the data but also the spatial accuracy. AdjustIT allows the custodian and the end user of the information to achieve both of these aims. References and Bibliography Ashkenazi, V., 1967, “Solution and Error Analysis of Large Geodetic Networks - Part I, Direct Methods”, Survey Review, Vol. XIX, No. 146 and No. 147, 1968. Benning, W., 1997, “Homogeneous digital maps, derived from rigorous adjustment techniques”, Smallworld International Conference Proceedings 1997, Berlin, pp. A1-A10. Eldridge, J.E., 1997, “Kalman Filtering - Assigning the Precision of Jerk”, Final Year Project, Department of Geomatics, The University of Melbourne. See also http://www.we-do-it.com/papers/kalman/index.htm Gelb A., 1988, “Applied Optimal Estimation”, MIT Press. Harvey B.R., 1993, “Practical Least Squares and Statistics for Surveyors”, The School of Surveying, University of New South Wales. Hesse, W.J., Williamson, I.P., 1990, “A Review of Digital Cadastral Data Bases in Australia and New Zealand”, The Australian Surveyor, Vol. 35, No. 4.



See also http://www.we-do-it.com/papers/dcdb/index.htm Hesse, W.J., Benwell, G.L., Williamson, I.P., 1990, “Optimising, Maintaining and Updating the Spatial Accuracy of Digital Cadastral Data Bases”, The Australian Surveyor, Vol. 35, No. 2. See also http://www.we-do-it.com/papers/optimising/index.htm Hesse, W.J., Williamson, I.P., 1993, “MAGIC revisited: An Object-Oriented Solution to the Cadastral Maintenance Problem”, The Australian Surveyor, Vol. 28, No. 1. See also http://www.we-do-it.com/papers/magic/index.htm Effenberg, W., Williamson, I.P., 1997, “Digital Cadastral Data Bases: The Australian Experience”, Proceedings of AGI 97 Conference, Birmingham, UK. See also http://www.sli.unimelb.edu.au/research/publications/IPW/wolfdcdb.htm


problems maintaining your spatial reference system - adjustit

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