Observability-enhanced dual-filter design for attitude estimation with minimum observations

Determining spacecraft attitude in real time using only magnetometer data presents a challenging filtering problem. A flexible and computationally efficient method for solving the spacecraft attitude using only an inexpensive and reliable magnetometer would be a useful option for satellite missions, particularly those with modest budgets. The primary challenge is that magnetometers only instantaneously resolve two axes of the spacecraft attitude. Typically, magnetometers are used in conjunction with other sensors to resolve all three axes. However, by using a filter over an adequately long orbit arc, the magnetometer data can yield full attitude, and in near real time. The method presented solves the problem using a two-nested extended Kalman filter as a means to improve convergence. In the first filter, the magnetic field data are filtered to obtain the magnetic field derivative vector, which is combined with the magnetic field vector in the second filter to fully resolve the attitude. As revealed by a literature review and previous research by the author, this method fails to accurately estimate the attitude unless the spacecraft is spin-stabilized with a relatively high angular velocity. To address this limiting restriction, the observability of the problem is examined from an analytical perspective. This study separates the problem into two stages and considers different methods for solving each stage. The first estimates the magnetic field derivative and possibly the angular rates, and then uses this information to calculate the attitude in the second stage. A new dynamic model is developed to estimate angular rates without estimating the attitude quaternion. MATLAB numerical routines are used to solve the complex nonlinear system of equations to yield a deterministic method. Finally, a parametric study analyzes the accuracy and utility of this method for different orbit trajectories and angular rates --Abstract, page iii