Optimization of UWB 3D Positioning Coordinates Based on Levenberg-Marquardt Algorithm

This paper proposes a joint optimization method combining the Levenberg-Marquardt (L-M) algorithm and an axis-separated quadratic polynomial error compensation model to address nonlinear errors in ultra-wideband (UWB) three-dimensional positioning. Distance measurements between base stations and tags are obtained using bilateral two-way ranging technology, and a trilateration model is employed to construct a system of nonlinear equations for 3D coordinate determination. To mitigate nonlinear errors between measured and true values, an axis-separated quadratic polynomial model is proposed to independently compensate for errors along each axis, effectively reducing cross-axis interference. Furthermore, the L-M algorithm is adopted to iteratively solve the nonlinear equations, dynamically adjusting the damping factor to balance the rapid convergence of the Gauss-Newton method and the stability of gradient descent. Experimental results demonstrate that after error compensation, the root mean square errors (RMSE) along the X, Y, and Z axes are reduced by 35.7%, 21.9%, and 33.3%, respectively. The L-M algorithm also outperforms traditional methods in convergence speed and positioning accuracy. The combined optimization strategy significantly enhances the precision and robustness of UWB 3D positioning.