Estimation of Polygons and Areas

Abstract.  In forestry the problem of estimating areas is central. This paper addresses area estimation through fitting of a polygon to observed coordinate data. Coordinates of corners and points along the sides of a simple closed polygon are measured with independent random errors. This paper focuses on procedures to adjust the coordinates for estimation of the polygon and its area. Different new techniques that consider different amounts of prior information are described and compared. The different techniques use restricted least squares, maximum likelihood and the expectation maximization algorithm. In a simulation study it is shown that the root mean square errors of the estimates are decreased when coordinates are adjusted before estimation. Minor further improvement is achieved by using prior information about the order and the distribution of the points along the sides of the polygon. This paper has its origin in forestry but there are also other applications.