Predictive Filtering for Attitude Estimation without Rate Sensors

In this paper, a real-time predictive filter is derived for spacecraft attitude estimation without the utilization of angular rate measurements from gyros. The formulation described in this paper is shown using only attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc.). The new real-time nonlinear filter predicts the required torque modeling error input in order to propagate the spacecraft dynamic model, so that model responses match the measured vector observations. Algorithms are developed which require the output estimates to track either the body measurements from the on-board sensors or the inertial reference trajectories generated from ephemeris data sets. The realtime predictive filter is used to estimate the attitude of the Solar, Anomalous, Magnetospheric Particle Explorer (SAMPEX) spacecraft. Results using this new algorithm indicate that the real-time predictive filter accurately estimates the attitude of an actual spacecraft with the sole use of magnetometer sensor measurements. INTRODUCTION The attitude of a spacecraft can be determined by either deterministic methods or by utilizing algorithms which combine dynamic and/or kinematic models with sensor data. Three-axis deterministic methods, such as TRIAD (algebraic method) [1], QUEST [2], and FOAM [3], require measurements of at least two vectors to determine the attitude (direction-cosine) matrix. An advantage of both the QUEST and FOAM algorithms is that the attitude of a spacecraft can be estimated using measurements of more than two vectors. This is accomplished by minimizing a quadratic loss function first posed by Wahba [4]. However, all deterministic methods fail when only one set of vector measurements is available, (e.g., magnetometer data only). Estimation algorithms utilize dynamic and/or kinematic models and subsequently can (in theory) estimate the attitude of a spacecraft using a time series of measurements of a single vector. Although all spacecraft in use today have at least two on-board attitude sensors, estimation techniques can be used to determine the attitude during anomalous periods, such as solar eclipse and/or vector-measurement co-alignment. The Kalman filter has been proven to be extremely useful for attitude estimation using vector attitude measurements and gyro measurements. The essential feature of the Kalman filter is the utilization of state-space formulations in the system model design. Errors in the dynamic model are treated as “process noise,” since system models are not usually improved or updated during the estimation process. The process noise is essentially used to shift the emphasis from the system model to the measurements. The Kalman filter satisfies an optimality criterion which minimizes the trace of the covariance of the estimate error between the system model responses and the actual measurements.