Evaluation of Redshift Determination Methods for Spectral Redshift Navigation: Cross Correlation vs. Density Estimation

Spectral redshift navigation (SRN) is an emerging navigation method for deep space exploration, where the redshifts of spectral signal are taken as the measurements in Kalman filtering to achieve the estimation of navigation parameters. However, the current works on redshift determination are isolated from those on SRN, which have been assigned to the area of astronomical spectral analysis and that of deep space navigation, respectively. This article aims to bridge the gap between these two research areas and constructively answer the question how the redshift determination affect the SRN performance. To be specific, the cross correlation method and the density estimation method, which attach, respectively, to the prestigious complete spectrum matching (CSM) and spectral line matching (SLM) architectures, are carried out as representative redshift determination instances for SRN to show the details. First, a spectral preprocessing technique based on wavelet transform is developed to facilitate the redshift determination procedure. Then within a designed performance evaluation framework, the redshift estimation accuracy and time consumption of the cross correlation and density estimation methods are comparatively analyzed with the spectral data from global astrometric interferometer for astrophysics (GAIAs) mission. On these basis, the navigation accuracy and computation efficiency of the above two redshift determination methods are creatively evaluated for SRN with a Mars exploration mission from the perspective of navigation solution. Experimental results demonstrate that the cross correlation method is with a higher navigation accuracy than the density estimation method, while the latter shows more advantages in terms of computation efficiency. The detailed performance evaluation also offers a guidance for the selection of redshift determination strategy in SRN applications.