Steepest descent quaternion attitude estimator

Abstract

A new computationally inexpensive attitude determination algorithm based on the minimization of Wahba's loss function is presented in the paper. The estimation problem is converted into quaternion representation and solved with iterative prediction–correction scheme. Unlike Kalman filter approach, an iterative gradient optimization is used to estimate the attitude quaternion and gyroscope bias. Algorithm derivation is shown and its performance is tested. The presented case study assumes configuration with three types of sensors: Sun sensors with full angular coverage, a magnetometer and a MEMS rate gyroscope. Sensor model parameters are selected to mimic a pico or nano class satellite. Orbital environment is simulated with the Bouvier–Lyddane orbit model, the IGRF magnetic field model and geometric properties of the Earth–Sun system. Periodical loss of Sun sensor data due to eclipses is taken into account. Based on the presented case study a proposition of tuning procedure and a brief comment on algorithm stability are given. The tuning approach trades off estimate convergence versus noise rejection property. In a Monte Carlo test the proposed algorithm compares well against an EKF with an attitude error within 0.1 deg in sunlight and 0.4 deg in the eclipse. Finally, a simulation showing a possibility of operating the SDQAE algorithm while sampling each of the sensors at different rate is presented.