A general framework for error analysis in measurement-based GIS Part 1: The basic measurement-error model and related concepts

This is the first part of our four-part series of papers which proposes a general framework for error analysis in measurement-based geographical information systems (MBGIS). The purpose of the series is to investigate the fundamental issues involved in measurement error (ME) analysis in MBGIS, and to provide a unified and effective treatment of errors and their propagations in various interrelated GIS and spatial operations. Part 1 deals with the formulation of the basic ME model together with the law of error propagation. Part 2 investigates the classic point-in-polygon problem under ME. Continued onto Part 3 is the analysis of ME in intersections and polygon overlays. In Part 4, error analyses in length and area measurements are made. In the present part, a simple but general model for ME in MBGIS is introduced. An approximate law of error propagation is then formulated. A simple, unified, and effective treatment of error bands for a line segment is made under the name of “covariance-based error band”. A new concept, called “maximal allowable limit”, which guarantees invariance in topology or geometric-property of a polygon under ME is also advanced. To handle errors in indirect measurements, a geodetic model for MBGIS is proposed and its error distribution problem is studied on the basis of the basic ME model as well as the approximate law of error propagation. Simulation experiments all substantiate the effectiveness of the proposed theoretical construct.