Wireless sensor networks often use a distributed configuration and rely on self-organizing mechanisms to integrate local information into a global context. This paper considers the 3-hop path as the basic component of a multi-hop path; the 3-hop path has two types of planar topological structures,‘S’-shaped and ‘U’-shaped. This paper provides a deduction of all possible topological structures when a 4-hop structure is merged into a 3-hop structure. Additionally, it offers an iterative method for determining the overall direct distance between the start and end points of an n-hop path along a polyline, given that each node is aware of the distances to nearby nodes.

Euler's four-point formula is utilized in the proposed method to perform two key functions: identifying whether a 3-hop path is ‘U’-shaped or ‘S’-shaped and calculating the straight-line distance within a virtual quadrilateral. The above method is combined with the distance vector routing (DV-Hop) algorithm, and the resulting algorithm is called Path's Straight Distance DV-Hop (PSDDV-Hop).

PSDDV-Hop significantly increases the accuracy of localization by eliminating the polyline bending errors in the distance estimation for an n-hop path. Several issues related to the implementation of PSDDV-Hop are analyzed, and corresponding solutions are provided, including a method of estimating the straight-line distance within no more than 3-hop and the replacement of nonlinear distance–area functions with linear fitting to reduce complexity and compensate for estimation bias. Two distinct strategies for setting the communication radius are introduced to accommodate diverse scenarios. Ultimately, the experiments confirm that PSDDV-Hop provides greater accuracy in localization across diverse network configurations.