An analytical model of zenith radiance under different atmosphere and earth-surface conditions for JHKs bands

The application of star sensor navigation to aircraft and ships is a significant development direction. Due to the intense sky background radiation in the daytime, it is difficult for a visible-light camera to detect stars effectively in near-earth space, the development of a short-wavelength infrared (SWIR, especial for JHKs bands) detector provides the possibility for it. However, in the system design, simulation verification, and software integration of star sensor based on SWIR, a mass of sky background data of JHKs bands under different atmosphere and earthsurface conditions is needed as input. Although the existing atmospheric radiative transfer software can generate large amounts of discrete sky background data in some directions, it has a complicated operation, low efficiency, and time-consuming disadvantage, which is challenging to meet the real-time application in engineering. To use the sky background radiation data more efficiently and conveniently, an analytical model of zenith radiance for JHKs bands is urgent to build. Zenith radiance reference data are generated by libRadtran. Atmospheric absorption function and atmospheric scattering function are used to construct the analytical model of zenith radiance. The Levenberg-Marquardt (L-M) method is used to solve the parameters of the analytical model of zenith radiance. The Adaptive Moment Estimation (Adam) method is used to optimize the parameters of the analytical model of zenith radiance. The mean relative error between the zenith radiance's analytical function value and the zenith radiance's reference data is calculated to evaluate the accuracy of the constructed analytical model of zenith radiance. The results show that the mean relative errors are no greater than 2.54%, 2.15%, 2.26%; the root mean square errors are no greater than 1.0414, 0.2462, 0.0642; the correlation coefficients are no less than 0.9985, 0.9976, 0.9979 for all combination of cases corresponding to JHKs bands. It indicates that zenith radiance's analytical model constructed is exact and can provide a useful reference for the star sensor's demonstration design and application assessment based on SWIR technology.

Automated summary

The study establishes an analytical model of zenith radiance for JHKs bands, using atmospheric absorption and scattering functions to construct the model parameters, and employing the Levenberg-Marquardt (L-M) method and Adaptive Moment Estimation (Adam) method for parameter solving and optimization. The accuracy of the constructed analytical model is evaluated by calculating the mean relative error between the model value and reference data.