Simultaneous Estimation of Respective Observation Refraction and Terrestrial Star Sensor Attitude Error

Stellar light atmospheric refraction (SLAR), which is the deviation of light direction before and after passing through the atmosphere, is a nonnegligible factor that hinders terrestrial star sensors (TSSs) from performing high-precision attitude measurement. To meet the TSS requirements for autonomous and accurate SLAR estimation and correction, a simultaneous estimation method of observation refraction and attitude error is proposed in this article. First, a stellar light refraction and imaging model is established, and the spatial geometric relationship between the observation star vector, reference star vector, and modified reference star vector is clarified. Considering the refraction plane principle and the random directional noise, this model presents the problem of refraction correction of stellar light as a variable estimation problem, so no meteorological sensors and prior attitude are required. After the coarse attitude estimation of the TSS, the value of refraction corresponding to each star is separately modeled as an independent variable to be estimated, and the Euler angles of the attitude error are taken as the variables to be estimated simultaneously. Thus, the complex nonconvex optimization problem is transformed into a linear least-squares problem to estimate SLAR and measure the refined attitude of the TSS. A numerical simulation and a night sky experiment both demonstrated the validity and reliability of the proposed method. When the zenith distance of boresight was approximately 20°, the means of average reprojection error (ARE) and average angular distance error (AADE) for the tested star sensor decreased from
${28.73^{\prime \prime }}$
to
${3.31^{\prime \prime }}$
and from
${38.55^{\prime \prime }}$
to
${2.95^{\prime \prime }}$
, before and after correction, respectively.