An absolute distance measurement sensor based on self-mixing interferometry (SMI) is suitable for application in aerospace due to its small size and light weight. However, an SMI signal with a high sampling rate places a burden on sampling devices and other onboard sources. SMI distance measurement using compressed sensing (CS) is proposed in this work to relieve this burden. The SMI signal was sampled via a measurement matrix at a sampling rate lower than Nyquist’s law and then recovered by the greedy pursuit algorithm. The recovery algorithm was improved to increase its robustness and iteration speed. On a distance measuring system with a measurement error of 60 µm, the difference between raw data with 1800 points and CS recovered data with 300 points was within 0.15 µm, demonstrating the feasibility of SMI distance measurement using CS.

Long-term monitoring of satellite microvibrations generates a significant amount of data streams, placing strain on satellites with limited transmission capacity. To relieve this transmission strain, a dynamic compressed sensing (CS) framework is proposed for satellite microvibration measurements. Microvibration streams are measured block by block and then reconstructed by a dynamic recovery algorithm. The recovery solution of one block can be used as a priori knowledge for the next block, allowing for faster updates. However, the existing dynamic recovery algorithms are only applicable to the real domain and cannot be applied to the microvibrations projected on a Fourier basis in the complex domain. In light of this, the dynamic homotopy algorithm is expanded to the complex domain to deal with microvibration signals that are sparse on the Fourier basis. In comparison to the traditional uniform sampling methods, the experimental results show that the dynamic CS with the expanded recovery algorithm can achieve a maximum root-mean-square acceleration (Grms) deviation of 4% in power spectrum density (PSD) with 1/5 sampling points. Compared with recovery algorithms applicable to fixed measurements, the dynamic algorithm can achieve comparable accuracy in about 1/3 of computation time. The experimental results demonstrate the feasibility of satellite microvibrations measurement using dynamic CS.