Spinning Spacecraft Attitude Estimation Using Markley Variables: Filter Implementation And Results

Attitude estimation is often more difficult for spinning spacecraft than for three-axis stabilized platforms due to the need to follow rapidly-varying state vector elements and the lack of three-axis rate measurements from gyros. The estimation problem simplifies when torques are negligible and nutation has damped out, but the general case requires a sequential filter with dynamics propagation. This paper describes the implementation and test results for an extended Kalman filter for spinning spacecraft attitude and rate estimation based on a novel set of variables suggested in a paper by Markley [AAS93-3301 (referred to hereafter as Markley variables). Markley has demonstrated that the new set of variables provides a superior parameterization for numerical integration of the attitude dynamics for spinning or momentum-biased spacecraft. The advantage is that the Markley variables have fewer rapidly-varying elements than other representations such as the attitude quaternion and rate vector. A filter based on these variables was expected to show improved performance due to the more accurate numerical state propagation. However, for a variety of test cases, it has been found that the new filter, as currently implemented, does not perform significantly better than a quaternion-based filter that was developed and tested in parallel. This paper reviews the mathematical background for a filter based on Markley variables. It also describes some features of the implementation and presents test results. The test cases are based on a mission using magnetometer and Sun sensor data and gyro measurements on two axes normal to the spin axis. The orbit and attitude scenarios and spacecraft parameters are modeled after one of the THEMIS (Time History of Events and Macroscale Interactions during Substorms) probes. Several tests are presented that demonstrate the filter accuracy and convergence properties. The tests include torque-free motion with various nutation angles, large constant-torque attitude slews, sensor misalignments, large initial attitude and rate errors, and cases with low data frequency. It is found that the convergence is rapid, the radius of convergence is large, and the results are reasonably accurate even in the presence of unmodeled perturbations.