Modeling and Filtering Colored Noise of a Star Tracker

Abstract

This paper presents an attitude error model of a star tracker, which is induced from the optical system errors, and proposes an attitude Kalman filter considering the star tracker errors. Though it can be calibrated before and after launches, it is impossible to obtain error-free star tracker parameters in practice, which generates non-white noise errors in the star tracker outputs. Moreover, star tracker error models are usually a business secret for the manufacturers, so it is hard to estimate them online on the spacecraft bus. We model the attitude bias caused by the error of the optical parameters as colored noise using the camera model parameters and their covariance. A recursive form of the colored noise is derived based on a vector autoregressive model, and a colored noise Kalman filter is proposed to estimate the attitude error along with the spacecraft attitude and gyro bias. The proposed method only needs three additional states to be estimated and does not contain sensitive information for a star tracker manufacturer, which can ease the burden of its applications. The simulations illustrate the stability and reliability of the proposed algorithm.