GPS-Based Attitude Determination for a Spinning Rocket

An algorithm is developed for determining the attitude of a spinning sounding rocket. This algorithm is able to track global positioning system (GPS) signals with intermittent availability but with enough accuracy to yield phase observables for the precise, three-axis attitude determination of a nutating rocket. Raw, single-frequency GPS RF front-end data are processed by several filters to accomplish this task. First, a Levenberg-Marquardt algorithm (LMA) estimates GPS observables for multiple satellites by performing a least-squares fit to the accumulation outputs of a bank of correlators. These observables are then used as measurements in a Rauch-Tung-Striebel smoother that optimizes estimates of carrier phase, Doppler shift, and code phase. Finally, attitude determination is carried out by another batch filter that uses the single-differenced optimized carrier phase estimates between two antennas and an Euler dynamics model for the torque-free attitude motion of the spinning rocket. This second batch filter implements a combination of a substantially modified form of the LMA and the least-squares ambiguity decorrelation adjustment (LAMBDA) method. This design enables it to deal with integer ambiguities that change over long data gaps between times of carrier phase availability. The algorithm presented in this paper is applied to recorded RF data from a spinning sounding rocket mission to produce attitude quaternion and spin-rate estimates using a pair of antennas separated by a 0.3-m baseline. These results are confirmed by another set of quaternions and spin-rate vectors independently estimated from magnetometer and horizon crossing indicator data. Attitude precision on the order of several degrees has been demonstrated.