Estimation of a Spacecraft's Attitude Dynamics Parameters by Using Flight Data

Abstract

An algorithm that uses flight data to estimate the parameters in an attitude dynamics model of a spacecraft has been developed. The new algorithm’s estimates can enhance the fidelity of Euler equation models that are used to implement attitude determination and control functions. The algorithm’s estimation equation is an integrated version of Euler’s equation expressed in inertial coordinates. It uses three-axis attitude data and three-axis rategyro data to yield a set of linear equations in the unknown dynamics parameters, which include moments and products of inertia and scale factors, alignments, and biases for all reaction wheels and magnetic torque rods. The estimation problem statement includes the statistics of unmodeled torques and sensor errors, and it incorporates a scalar quadratic constraint to overcome the unobservability of the parameters’ overall scaling. The sensor errors enter the model equation in a multiplicative fashion, which yields a total least-squares problem. The solution algorithm employs a guarded Newton iteration and recursive factorizations that deal efficiently with the problem’s dynamic structure. The algorithm has been applied to the Wilkinson Microwave Anisotropy Probe spacecraft, and the resulting parameter estimates reduce torque modeling errors by a factor of 5‐7.