Median-Distance Geometry: A Low-Tech Method for Measuring Linear Objects

This proof-of-concept study explores a geometric method for estimating the length of vertical, inclined, or horizontal objects using only line-of-sight distance measurements obtained from a single observation point. The approach requires distances from the observer to the two end points of the object, together with two or more intermediate measurements taken at arbitrary positions along its span. These intermediate points do not need to be evenly spaced and may be irregularly or approximately located, reflecting realistic field acquisition conditions. Importantly, the method does not require angular observations, thereby reducing instrumentation complexity and sensitivity to angular measurement errors.When plotted, the set of distance measurements forms a smooth and readily interpretable profile along the object’s extent. Although this profile may be represented by a low-order polynomial for illustrative purposes, the essential geometric insight is contained in its central tendency, expressed by the median distance. This median serves as the key indicator for inferring the object’s true length and can be obtained through straightforward interpretations of the distance profile, without reliance on formal curve-fitting procedures. Such a formulation is particularly attractive in navigation and positioning contexts where robust summary measures are often preferred over fully parameterised models.The technique is flexible with respect to observer placement, which may be located above or below the base of the object of interest, thereby enabling practical use across a wide range of field conditions. Once the median distance and the distances to the two end points are established, a simple geometric model can be applied to estimate the total object length. The approach is equally applicable to linear horizontal features and planar structures and may be envisaged as a complementary measurement strategy within GNSS navigation or mapping frameworks, particularly in situations where angular information is unavailable, degraded, or unreliable.Preliminary field trials demonstrate encouraging performance. Comparisons with total station measurements for conifer trees, electricity poles, and linear fences with spans of 20–25 m yielded average RMSE values of ±0.65 m, ±0.52 m, and ±0.38 m, respectively. These results suggest that the proposed low-tech method offers a practical alternative, or adjunct, to established surveying and GNSS-supported positioning practices, particularly in constrained or opportunistic measurement scenarios.