<p>In response to challenges in quadruped robot motion measurement, including insufficient feature detection robustness, large matching errors, and significant vibration interference, this study develops a high-precision measurement methodology tailored to dynamic scenarios. First, a circular target recognition and polar-angle feature modeling method based on geometric constraints is proposed: by exploiting the circle’s center and radius parameters for robust detection and mapping geometric information into polar-angle space, the approach enhances the discernibility and stability of feature points under dynamic imaging conditions. Second, a state-space-driven polar-angle feature matching method is introduced, in which the polar-angle and radial parameters of feature points are modeled as the states of a dynamic system; temporal recursion is employed to predict inter-frame continuity and enforce consistency constraints, significantly reducing mismatches in dynamic scenarios. Third, a high-frequency vibration state modeling and error compensation mechanism is established, quantitatively revealing the coupling between vibration parameters and feature-point offsets, while a “vibration recognition–state filtering–dynamic compensation” strategy effectively suppresses error accumulation. Experimental results indicate that the proposed method achieves high matching accuracy and measurement precision under suspended conditions, whereas performance under ground locomotion is used to assess robustness and adaptability in the presence of non-ideal factors. The proposed methodology thus provides a reliable technical pathway for high-precision perception and robust measurement of quadruped robot motion states.</p>