The difficulty in precisely extracting single-fault signatures from hydraulic pump composite faults, which stems from structural complexity and coupled multi-source vibrations, is tackled herein via a new diagnostic technique based on underdetermined blind source separation (UBSS). Utilizing sparse component analysis (SCA), the proposed method achieves blind source separation without relying on prior knowledge or multiple sensors. However, conventional SCA-based approaches are limited by their reliance on a predefined number of sources and their high sensitivity to noise. To overcome these limitations, an adaptive source number estimation strategy is proposed by integrating information–theoretic criteria into density peak clustering (DPC), enabling automatic source number determination with negligible additional computation. To facilitate this process, the short-time Fourier transform (STFT) is first employed to convert the vibration signals into the frequency domain. The resulting time–frequency points are then clustered using the integrated DPC–Bayesian Information Criterion (BIC) scheme, which jointly estimates both the number of sources and the mixing matrix. Finally, the original source signals are reconstructed through the minimum L1-norm optimization method. Simulation and experimental studies, including hydraulic pump composite fault experiments, verify that the proposed method can accurately separate mixed vibration signals and identify distinct fault components even under low signal-to-noise ratio (SNR) conditions. The results demonstrate the method’s superior separation accuracy, noise robustness, and adaptability compared with existing algorithms.

To suppress pedestrian positioning drift, a velocity constraint commonly known as zero-velocity update (ZUPT) is widely used. However, it cannot correct the error in the non-zero velocity interval (non-ZVI) or observe heading errors. In addition, the positioning accuracy will be further affected when a velocity error occurs in the ZVI (e.g., foot tremble). In this study, the foot, ankle, and shank were regarded as a triangular structure. Consequently, an angle constraint was established by utilizing the sum of the internal angles. Moreover, in contrast to the traditional ZUPT algorithm, a velocity constraint method combined with Coriolis theorem was constructed. Magnetometer measurements were used to correct heading. Three groups of experiments with different trajectories were carried out. The ZUPT method of the single inertial measurement unit (IMU) and the distance constraint method of dual IMUs were employed for comparisons. The experimental results showed that the proposed method had high accuracy in positioning. Furthermore, the constraints built by the lower limb structure were applied to the whole gait cycle (ZVI and non-ZVI).