Application of the Least Squares-Adaptive Vector Projection Iteration Algorithm to Ultra-Wideband Positioning

Ultra-Wideband (UWB) technology is widely used in indoor positioning due to its high accuracy and strong resistance to interference. However, practical UWB positioning systems still encounter challenges such as random errors and asymmetric base station topology, which significantly affect positioning accuracy. To address these issues, this article proposes an adaptive vector projection iteration algorithm based on the least squares method (LS-AVPI). First, the sparrow search algorithm (SSA) is employed to identify optimal parameters, with the fitness function based on an error suppression model established through vector projection angles and iterative concepts. The optimal parameters obtained from the SSA are then used to train a convolutional neural network (CNN) for accurate prediction of unknown data. Finally, the predicted parameters are input into the error suppression model to solve for the final position. Experimental results demonstrate that the LS-AVPI algorithm significantly outperforms the constrained weighted, the iterative, the standard, and the two-step weighted least squares (LS) methods, with accuracy improvements of 57.3%, 62.7%, 65.7%, and 54.8%, respectively. This study not only effectively improves UWB positioning accuracy but also provides a new technical approach for achieving high-precision positioning in complex environments, offering significant theoretical and practical value.