Non-line-of-sight (NLOS) propagation poses a significant challenge to achieving high-accuracy ultra-wideband (UWB) indoor positioning. To address this issue, this study investigates solutions from two complementary perspectives: NLOS identification and error mitigation. First, an NLOS signal classification model is proposed based on multidimensional statistics of the channel impulse response (CIR). The model incorporates an attention mechanism and an improved snake optimization (ISO) algorithm, achieving significantly enhanced classification accuracy and robustness. Building on this foundation, a UKF–BiLSTM dual-directional mutual calibration framework is proposed to compensate for NLOS errors dynamically. The framework embeds the constant turn rate and velocity (CTRV) motion model within an unscented Kalman filter (UKF) to enhance trajectory modeling. It establishes a bidirectional correction loop with a bidirectional long short-term memory (BiLSTM) network. Through the synergy of physical constraints and data-driven learning, the framework adaptively suppresses NLOS errors. Experimental results demonstrate that the proposed classification model and positioning framework significantly outperform state-of-the-art methods, thereby providing a systematic solution for high-precision and robust UWB positioning in complex indoor environments.