Improving transient performance in computationally simple gyro-corrected satellite attitude determination

Abstract

This article extends a previously presented Kalman-like filter for fusing gyro measurements with attitude measurements obtained from external sensors such as star-trackers, magnetometers, and sun-sensors. The simplicity of this approach is useful for applications such as micro/nano-satellites where computational power is limited. The previously presented filter uses constant filter gains. It was shown that by appropriately choosing the constant gains, near-optimal steady-state performance is obtained. A drawback of using constant gains is that optimal transient filter performance is lost, meaning that convergence is slower. In this article, a computationally simple analytical approximation to the transient part of the Kalman filter gain is derived, allowing the transient performance to be recovered. The transient approximation of the gain is then applied for a predetermined fixed period of time, after which the gain is switched to the previously presented constant steady-state Kalman gain. A simple expression for a suitable time to switch from transient to steady-state filter operation is derived. Simulation results demonstrate the efficacy of this approach.