Calibration of Gyros with Temperature Dependent Scale Factors

The general problem of gyro calibration can be stated as the estimation of the scale factors, misalignments, and drift-rate biases of the gyro using the on-orbit sensor measurements. These gyro parameters have been traditionally treated as temperature-independent in the operational flight dynamics ground systems at NASA Goddard Space Flight Center (GSFC), a scenario which has been successfully applied in the gyro calibration of a large number of missions. A significant departure from this is the Microwave Anisotropy Probe (MAP) mission where, due to the high thermal variations expected during the mission phase, it is necessary to model the scale factors as functions of temperature. This paper addresses the issue of gyro calibration for the MAP gyro model using a manufacturer-supplied model of the variation of scale factors with temperature. The problem is formulated as a least squares problem and solved using the Levenberg-Marquardt algorithm in the MATLAB(R) library function NLSQ. The algorithm was tested on simulated data with Gaussian noise for the quaternions as well as the gyro rates and was found to consistently converge close to the true values. Significant improvement in accuracy was noticed due to the estimation of the temperature-dependent scale factors as against constant scale factors.