Kalman filter estimation of attitude and gyro bias with the QUEST observation model

The loss function for the Wahba attitude estimation problem employs unit vector observations with scalar weights. It is usually associated with the QUEST observation model, where the actual sensor noise is assumed the same for all components of the observed vector, regardless of the position in the field of view. The QUEST model has the great advantage of being sensor-independent except for the scalar parameter that characterizes the sensor errors. Although efficient algorithms for solving the Wahba problem exist, extending these algorithms to estimate gyro biases or sensor alignments has had mixed success. However, it is straightforward to estimate bias and alignment parameters with a Kalman filter. This paper investigates the use of an extended Kalman filter for the attitude and gyro bias that incorporates the QUEST observation model, to be referred to as the Unit Vector Filter (UVF). The UVF results are compared with those from a more conventional filter, the Real-Time Sequential Filter (RTSF), for which the residual is the two-dimensional projection of the unit vector onto the plane perpendicular to the sensor boresight. The RTSF is similar in design to that used by Multimission Modular Spacecraft for onboard attitude determination. An apparent obstacle to the use of unit vectors as measurements is their singular noise covariance matrix. Shuster has shown that this problem should not affect filter performance. The UVF and RTSF are tested using actual flight data from the Extreme Ultraviolet Explorer (EUVE). It is found that these filters generate nearly identical attitude and gyro bias estimates, thus validating the use of unit vectors and the QUEST noise model.