Real-Time and Highly Accurate Solar Spectrum Velocimetry Using the Mirror NDFT-CS for Doppler Navigation

Abstract

Solar Doppler velocimetry navigation, which utilizes the Doppler frequency shift between the standard solar and measured solar spectra to invert the velocity of the spacecraft, is an emerging and promising celestial autonomous navigation method. However, its accuracy of estimation does not fulfill the requirement of solar Doppler velocimetry navigation. To solve this problem, we developed nonuniform discrete Fourier transform compressive sensing (NDFT-CS) and applied it to solar spectrum velocimetry navigation. Mirror NDFT-CS consists of the mirror Fourier low-frequency measurement matrix, the Doppler frequency-shift dictionary, and the Taylor matching process. Namely, the mirror Fourier low frequencies of the NDFT matrix are used as the measurement matrix. The solar spectra with different Doppler frequency shifts merge to form a Doppler frequency-shift dictionary. Taking the Taylor formula as the objective function, we matched the measured solar spectrum with the dictionary to estimate a Doppler frequency shift. According to the estimated Doppler frequency shift, the velocity of the spacecraft is inverted. Due to the sparsity of solar spectrum signals, the measurement matrix is small, which means a small computational load and high accuracy. Simulation results demonstrate that the solar spectrum velocimetry method using mirror NDFT-CS has high accuracy in real time.