Attitude estimation for sounding rockets using microelectromechanical system gyros

An attitude determination and in-flight calibration extended Kalman filter and the corresponding smoother have been developed to estimate three-axis attitude of spinning sounding rockets. The attitude determination system uses low-accuracy commercial microelectromechanical system rate gyros, coupled with a three-axis magnetometer and a one-axis sun sensor. Because only postflight analysis is necessary, the improved performance of a smoother is used in the attitude reconstruction because postflight computation allows the use of a noncausal algorithm. Gyro misalignment and scale-factor errors are proportional to the angular rate, and spin-stabilized rockets without a despin unit usually have a large angular velocity in the range of 4-6 cycles per second about the spin axis. Therefore, gyro misalignment and scale-factor errors can have a significant effect on the attitude propagation, which is based on the gyro measurements. In this work, in-flight calibration is carried out, estimating sensor relative misalignments in addition to bias and scale-factor errors. To ensure filter convergence, an initialization algorithm suitable for producing an initial attitude estimate from a vector measurement and a scalar measurement has been developed. The initialization algorithm uses an attitude representation based on the minimum quaternion combined with a search method. The filter and smoother have been tested using a truth-model simulation, and the accuracy is shown to be dependent on the rocket motion. A rich motion time history makes the parameters more observable and thereby the estimates more accurate. Simulation results indicate that an attitude accuracy on the order of 0.5-1 degrees (3 sigma) can be achieved with a low-cost suite of sensors.