An Mme-based Attitude Estimator Using Vector Observations

In this paper, an optimal batch estimator and filter based on the Minimum Model Error (MME) approach is developed for three-axis stabilized spacecraft. Three different MME algorithms are developed. The first algorithm estimates the attitude of a spacecraft using rate measurements. The second algorithm estimates the attitude without using rate measurements. The absence of rate data may be a result of intentional design or from unexpected failure of existing gyros. The third algorithm determines input-torque modeling error trajectories. All of the algorithms developed in this paper use attitude sensors (e.g., three-axis magnetometers, sun sensors, star trackers, etc). Results using these new algorithms indicate that an MME-based approach accurately estimates the attitude, rate, and input torque trajectories of an actual spacecraft. Introduction The attitude of a spacecraft can be determined by either deterministic methods or by utilizing algorithms which combine dynamic models with sensor data. Three-axis deterministic methods, such as TRIAD [1], QUEST [2], and FOAM [3], require at least two simultaneous vector measurements 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 more than two measurements. This is accomplished by minimizing a quadratic loss function first posed by Wahba [4]. However, all deterministic methods fail when only one vector measurement is available, (e.g., magnetometer data only). Estimation algorithms utilize dynamic models, and subsequently can (in theory) estimate the attitude of a spacecraft using measurements of a single reference 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 sensor co-alignment. The most commonly used technique for attitude estimation is the Kalman filter [5]. The Kalman filter utilizes state-space representations to both estimate plant dynamics and also filter noisy data. Errors in the dynamical model and measurement process are assumed to be modeled by a zero-mean Gaussian process with known covariance. The optimality criterion in the Kalman filter minimizes the trace error covariance between estimated responses and model responses. In theory, the Kalman filter does not require actual measurements to satisfy this optimality criterion; however, in actual practice measurements are often used to properly “tune” the filter estimates. Smoothing algorithms further refine state estimates by utilizing both a “forward filter” and a “backward filter” (see e.g., Gelb [6]). An advantage of smoothing algorithms is that the error covariance is always less or equal to either the forward or backward filter alone. A disadvantage of smoothing algorithms is that they cannot be implemented in sequential (real-time) estimation. In order for the Kalman filter to be truly optimal, both the measurement error process and model error process must be random Gaussian processes with known covariance. In most circumstances,