Improved Accuracy of Area Objects in a Geographic Information System Based on Helmert’s Variance Component Estimation Method

Helmert's variance component estimation method based on a least-squares adjustment of condition equations is presented, in which the registered area and the coordinates of a cadastral parcel are assumed to be different and independent types of observations with errors in the cadastral parcel area adjustment. The Helmert method is employed for the estimation of variance components of these two types of observations, thus providing a determination of accurate weights between them. At the same time, inconsistencies between the registered and digitized areas of the parcels are adjusted through a least-squares adjustment. The mathematical models for adjusting the boundaries of the parcel areas are derived, incorporating both the area conditions and geometric conditions. An empirical test is conducted and the results are compared to those obtained from the conventional method, assuming that the digitized coordinates are treated as observations while the registered parcel areas are not. The analysis of the results demonstrates that the least-squares adjustment, when based on Helmert's variance component estimates, refinds the weights of the observations more accurately, improves the accuracy of the adjusted coordinates in parcel digitization, and resolves the inconsistencies between the registered areas and digitized areas of the parcels more rigorously.