# A statistical simulation model for positional error of line features in geographic information systems (GIS)

Xiaohua Tong, Tong Suna, Junyi Fana, Michael Goodchild, Wenzhong Shic

Research output: Contribution to journalArticle

16 Citations (Scopus)

### Abstract

This paper presents a new error band model, the statistical simulation error model, for describing the positional error of line features by incorporating both analytical and simulation methods. In this study, line features include line segments, polylines, and polygons. In existing error models, an infinite number of points on the line segment are considered as the stochastic variables and the error band of a line segment is obtained from the union of all intermediate points on the line segment, while that of a polyline/polygon is obtained from the union of all error bands of the composite line segments. Our proposed error band model, however, regards the entire line feature (line segment/polyline/polygon) as the stochastic variable, instead of the infinite number of points on the line segment. Based solely on the statistical characteristics of the endpoints of the line feature and the predefined confidence level, our proposed error model is created by a simulation method that integrates a population of line segments/polylines/polygons computed from the entire solution set of the error model's defining equation. A comprehensive comparison of the proposed and existing error band models is carried out through both simulated and practical experiments. The experimental results show the following: (1) For line segments, the proposed standard statistically simulated error band matches that of existing error models (for example, the G-band). Further, it is found that a scaled G-band with a specific scale factor (e.g., √X24(σ)) matches the proposed statistically simulated error band with probability (1-α)×100%. (2) For polylines and polygons, if we correlate the errors of all the endpoints of the polyline/polygon, there is a marked difference between the proposed statistically simulated error band and existing error bands. The reason for the difference is explained as follows. The existing error model defines the error band of a polyline/ polygon as the union of all error bands of the composite line segments, thereby only accounting for the correlation between the two endpoints of each composite line segment. However, our proposed error band model considers the entire polyline/polygon as a whole by accounting for the variance-covariance matrix of all vertices of the polyline/polygon when constructing the statistically simulated error band.

Original language English (US) 136-148 13 International Journal of Applied Earth Observation and Geoinformation 21 1 https://doi.org/10.1016/j.jag.2012.08.004 Published - Jan 1 2012 Yes

### Fingerprint

polygon
Geographic information systems
simulation
geographic information system
Composite materials
matrix
Covariance matrix

### Keywords

• Gis
• Line feature
• Positional error
• Probability
• Simulation

### ASJC Scopus subject areas

• Global and Planetary Change
• Earth-Surface Processes
• Computers in Earth Sciences
• Management, Monitoring, Policy and Law

### Cite this

A statistical simulation model for positional error of line features in geographic information systems (GIS). / Tong, Xiaohua; Suna, Tong; Fana, Junyi; Goodchild, Michael; Shic, Wenzhong.

In: International Journal of Applied Earth Observation and Geoinformation, Vol. 21, No. 1, 01.01.2012, p. 136-148.

Research output: Contribution to journalArticle

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abstract = "This paper presents a new error band model, the statistical simulation error model, for describing the positional error of line features by incorporating both analytical and simulation methods. In this study, line features include line segments, polylines, and polygons. In existing error models, an infinite number of points on the line segment are considered as the stochastic variables and the error band of a line segment is obtained from the union of all intermediate points on the line segment, while that of a polyline/polygon is obtained from the union of all error bands of the composite line segments. Our proposed error band model, however, regards the entire line feature (line segment/polyline/polygon) as the stochastic variable, instead of the infinite number of points on the line segment. Based solely on the statistical characteristics of the endpoints of the line feature and the predefined confidence level, our proposed error model is created by a simulation method that integrates a population of line segments/polylines/polygons computed from the entire solution set of the error model's defining equation. A comprehensive comparison of the proposed and existing error band models is carried out through both simulated and practical experiments. The experimental results show the following: (1) For line segments, the proposed standard statistically simulated error band matches that of existing error models (for example, the G-band). Further, it is found that a scaled G-band with a specific scale factor (e.g., √X24(σ)) matches the proposed statistically simulated error band with probability (1-α)×100{\%}. (2) For polylines and polygons, if we correlate the errors of all the endpoints of the polyline/polygon, there is a marked difference between the proposed statistically simulated error band and existing error bands. The reason for the difference is explained as follows. The existing error model defines the error band of a polyline/ polygon as the union of all error bands of the composite line segments, thereby only accounting for the correlation between the two endpoints of each composite line segment. However, our proposed error band model considers the entire polyline/polygon as a whole by accounting for the variance-covariance matrix of all vertices of the polyline/polygon when constructing the statistically simulated error band.",
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