GGA-EMD-Based Inversion Method of Spectrum Reflectance Template for Celestial Doppler Difference Navigation

The Doppler difference velocity between the measured solar spectrum and the measured asteroid spectrum is the measurement of the celestial Doppler difference navigation. Due to the absorption effect of the asteroid on the measured asteroid spectrum, the Doppler difference velocity is inevitably affected. In order to solve this problem, considering the fact that the asteroid reflectance is the ratio of the approximation of the asteroid spectrum to that of solar spectrum, we utilize the Gaussian genetic algorithm (GGA) and empirical mode decomposition (EMD) to extract the approximation of celestial spectra and propose an inversion method of celestial spectrum reflectance template based on GGA-EMD. First, the celestial spectrum is decomposed by EMD into the intrinsic mode functions (IMFs). A certain combination of IMFs can embody the spectrum reflectance. Then, we utilize the undetermined spectrum reflectance function and the measured solar spectrum to produce the virtual asteroid spectrum and adopt the Taylor method to estimate the Doppler difference velocity between the measured asteroid spectrum and the virtual one. Finally, to converge fast, we utilize the Gaussian function to optimize the mutation and crossover operations of genetic algorithm (GA) and propose the GGA. Using the Doppler difference velocity errors as the object of the fitness function, the GGA optimizes the combination of IMFs, which is used to construct an optimized celestial spectrum reflectance template. The experiment results show that the inversion method of celestial spectrum reflectance template based on GGA-EMD constructs the spectrum reflectance template effectively and improves the accuracy of the Doppler difference velocity.