Ultra-wideband (UWB) sensors have been widely applied to indoor positioning. The indoor positioning of UWB sensors usually refers to the positioning of the mobile node that interacts with the anchors through radio for calculating the distance between the mobile node and each of the surrounding anchors. The positioning accuracy of the mobile node is affected by the installation positions of surrounding anchors. A mathematical model was proposed in this paper to respectively analyze the mobile node's 2-dimensional (2D) and 3-dimensional (3D) positioning errors. The factors influencing the mobile node's positioning errors were explored through the mathematical models. The best installation positions of surrounding anchors were obtained based on the mathematical models. The mobile node's 2D and 3D positioning errors were reduced based on the anchor positions derived from the mathematical model. Both computer simulations and practical experiments were implemented to justify the results obtained in the mathematical models.
Keywords: Gaussian distribution; UWB; distance measurement; positioning accuracy; time of flight.