Accurate localization is a key technology enabling the intelligent and autonomous of mobile devices. Maintaining high-precision positioning capabilities, particularly in Global Positioning System (GPS)-denied environments, has emerged as a critical challenge for autonomous navigation systems. To address the performance degradation of positioning systems in GPS-denied environments, we develop an ultra-wideband (UWB)-based localization system. To improve positioning accuracy, a dual adaptive variational Bayesian cubature Kalman filter (A-VBCKF) is proposed. By introducing a dual adaptive update mechanism into the variational Bayesian framework, the proposed method achieves real-time adaptation of both process and measurement noise covariances, which smooths UWB ranging measurements and significantly reduces ranging errors. Furthermore, a minimum bias criterion shrinkage estimation (MBCSE) method is introduced to estimate the terminal coordinates based on the two-stage weighted least squares (TWLS) method. By incorporating the concept of shrinkage estimation, this method strikes an optimal balance between minimizing estimation bias and variance, thereby yielding more precise positioning results. A localization system was built using UWB P440 modules, and static and dynamic positioning experiments were conducted on a mobile platform. The results show that integrating the A-VBCKF algorithm with the MBCSE method significantly reduces positioning errors. The proposed A-VBCKF-MBCSE algorithm achieves positioning accuracy improvements of 51.6%, 40%, and 23.6% along the x-, y- and z-axes, respectively. Moreover, the dynamic trajectory estimated by the proposed method agrees more closely with the ground-truth path. The experimental results demonstrate that the proposed method effectively improves localization accuracy and provides a viable solution for high-precision positioning in GPS-denied environments.