Celestial Spectrum Velocimetry with Non-Linear Fourier Phase Shift and Its CRLB

To solve the problem of the non-linear Fourier phase shift caused by the wavelength shift in the celestial spectrum velocimetry, a celestial spectrum velocimetry method based on non-uniform discrete Fourier transform and compressed sensing is proposed. First, according to the properties of the non-uniform discrete Fourier transform with non-periodic celestial spectra, the non-linear relationship between the spectral wavelength shift and the Fourier phase shift is deduced theoretically. And then, the discrete cosine transform is used to decompose and reconstruct the spectrum to construct the phase dictionary of the non-periodic spectrum. In this dictionary, the spectral wavelength shift has a non-linear relationship with the Fourier phase shift. Finally, the non-uniform Fourier transform matrix is used as the measurement matrix. And the Doppler wavelength shift is estimated by using a non-linear and super-resolution matching algorithm to estimate the velocimetry. Experimental results show that when the spacecraft's velocity is high, the celestial spectrum velocimetry method with non-linear Fourier phase shift (CSV-NFPS) can effectively measure the velocity from the spectrum, and its accuracy approaches the theoretical Cramer-Rao lower bounds (CRLB). Compared with the traditional Taylor method, the CSV-NFPS has an average accuracy improvement of 16.18% and a computational complexity reduction of 25.07%. In short, our method eliminate the non-linear bias in the celestial spectrum velocimetry and reduce a certain computational complexity.