Positioning Error Analysis of Least Squares Method for Wireless Sensor Networks

Wireless sensor networks (WSN) is widely used for indoor positioning and navigation of mobile robots. Least squares method (LSM) is the most common and simple method for position calculation, and various optimization algorithms were designed elaborately for reducing localization error. Unlike other localization papers which focus on designing elaborate localization algorithms, this paper takes a different perspective, focusing on the error propagation problem, addressing questions such as where the localization error comes from and how it propagates. Based on the theory of variance and covariance, a novel simplified error propagation algorithm is proposed to analyse the localization error for triangulation method. This algorithm exactly shows influence of ranging errors and network structure on positioning. Finally, a simulation test in Matlab is carried out to verify the validity of the proposed algorithm, and it is shown that the algorithm significantly simplifies the calulation of the positioning error. The work of this paper can be used for multi-sensor fusion where an accurate error model is required. Besides, error estimation is also useful for error control by optimizing the structure of WSN.