In the field of ultra-wideband (UWB) indoor localization, traditional backpropagation neural networks (BPNNs) are limited by their susceptibility to local minima, which restricts their ability to achieve global optimization. To overcome this challenge, this paper proposes a novel hybrid algorithm, termed ARO-BP, which integrates the Artificial Rabbit Optimization (ARO) algorithm with a BPNN. The ARO algorithm optimizes the initial weights and thresholds of the BPNN, enabling the model to escape local optima and converge to a global solution. Experiments were conducted in both line-of-sight (LOS) and non-line-of-sight (NLOS) environments using a four-base-station configuration. The results demonstrate that the ARO-BP algorithm significantly outperforms traditional BPNNs. In LOS conditions, the ARO-BP model achieves a localization error of 6.29 cm, representing a 49.48% reduction compared to the 12.45 cm error of the standard BPNN. In NLOS scenarios, the error is further reduced to 9.86 cm (a 46.96% improvement over the 18.59 cm error of the baseline model). Additionally, in dynamic motion scenarios, the trajectory predicted by ARO-BP closely aligns with the ground truth, demonstrating superior stability. These findings validate the robustness and precision of the proposed algorithm, highlighting its potential for real-world applications in complex indoor environments.