The Analysis and Verification of Unbiased Estimator for Multilateral Positioning

The ranging error model is generally very complicated in actual ranging technologies. This paper gives an analysis of the biased distance substitution and proposes an unbiased multilateral positioning method to revise the biased substitution, making it an unbiased estimate of the squared distance. An unbiased estimate of the multilateral positioning formula is derived to solve the target node coordinates. Through simulation experiments, it is proved that the algorithm can improve the positioning accuracy, and the improvement is more obvious when the error variance is larger. Experiments using SX1280 also show that the ranging conforms to the biased error model, and the accuracy can be improved by using the unbiased estimator. When the actual experimental error standard deviation is 0.16 m, the accuracy can be improved by 0.15 m.