Attitude Estimation and Optimal Relative Orientation of Redundant Inertial Measurement Units

Navigation systems for human-rated space vehicles are typically required to be two-fault tolerant. This paper presents an optimal relative orientation of multiple orthogonal three-axis inertial measurement units in order to maximize fault detection capabilities. The optimality criterion is the entrywise one norm of the matrix mapping measurement or estimate errors into the fault detection vector. This choice of norm maximizes the projection of each measurement or state error into all components of the fault detection vector. Other matrix norms based on spectral decomposition are shown to be inadequate. A new formulation of the multiplicative extended Kalman filter is derived and used to validate the optimal arrangements. The filter uses measurements from one three-axis gyroscope for model propagation and fuses measurements from additional redundant gyros and a star tracker with Kalman updates. Fault detection and isolation are performed with a Cramer–von Mises goodness-of-fit test using a buffer of stored prefit measurement residuals. It is shown that the faulty gyro axis can be isolated with greater certainty when the optimal arrangement is used.