Three-Dimensional Coordinate Error Correction for Ultra-Wideband Using the GRNN

Ultra-wideband (UWB) positioning systems are prone to significant positioning errors due to multipath effects, non-line-of-sight (NLOS) conditions, and systematic inaccuracies. Most existing UWB coordinate correction methods rely on ranging error modeling, which are often complex and time-consuming, and are mostly focused on two-dimensional (2D) coordinate correction. This study proposes a correction model utilizing neural networks, namely, Generalized Regression Neural Network (GRNN) and Backpropagation Neural Network (BPNN) to directly improve the accuracy of three-dimensional (3D) UWB coordinates. The GRNN- and BPNN-based correction models are evaluated on three real-world datasets from static, dynamic, and NLOS experiments. All three experiments employ UWB for 3D positioning, with reference values obtained via a total station in the static and NLOS experiments, and Real-Time Kinematic (RTK) in the dynamic experiment. Results indicate that the GRNN model achieves substantial improvements in 3D coordinate accuracy. For the limited UWB modules, the corrected 3D coordinates under both static positioning and NLOS conditions achieve millimeter-level accuracy. In dynamic positioning experiments, the corrected errors in the X, Y, and Z axes are all within 5cm, with respective improvements of 79.55%, 70.45%, and 96.26%, compared to pre-correction levels, achieving centimeter-level accuracy in dynamic 3D positioning. The GRNN-based model demonstrates superior correction performance compared to the BPNN-based model, the Long Short-Term Memory (LSTM)-based model, and the commonly used traditional method, the Particle Filter (PF). Furthermore, the positioning errors and fluctuations can be significantly reduced when anchors are not placed on a single horizontal plane. Accordingly, introducing height differences among anchors is recommended to enhance the accuracy of 3D UWB positioning.