Localization error propagation model of range-based least squares method for wireless sensor networks

Abstract

Abstract In recent years, Wireless Sensor Networks (WSNs) have seen increasing application in GPS-Denied environments, such as indoor localization and mobile robot navigation. Among various positioning algorithms, the Least Squares Method is widely used for its simplicity and robustness. While numerous optimization algorithms have been developed to reduce localization error, comprehensive studies on the sources and propagation of positioning errors remain limited.This paper focuses on the error propagation mechanisms in range-based WSN localization. It conducts an in-depth analysis of the primary sources of positioning error, including ranging errors, anchor node position errors, and the influence of network topology on error propagation. A novel, simplified error propagation model based on covariance theory is proposed to quantitatively estimate the cumulative impact of these errors on localization accuracy.To evaluate the accuracy and practicality of the proposed algorithm, comprehensive assessments were carried out through both MATLAB simulations and physical experiments in representative indoor environments. The results show that the average discrepancy between the estimated and actual positioning errors remains within a few centimeters, demonstrating strong predictive capability. Furthermore, the Geometric Dilution of Precision is introduced to assess the influence of base station configurations. The experimental results further confirm that the proposed algorithm maintains strong robustness even in suboptimal geometric configurations of the network. In conclusion, the error propagation model proposed in this study not only significantly simplifies the theoretical computation of localization errors but also offers high accuracy in error estimation, making it particularly suitable for multi-sensor fusion scenarios that require precise error modeling. It also provides new insights and quantitative tools for optimizing WSN structures and improving overall localization performance.