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A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem to the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The original Wahba problem seeks the attitude that fits a set of unit-normalized direction vector measurements. The generalized problem seeks an initial attitude and rate that, when combined with a torque-free rigid-body attitude dynamics model, fit a time series of direction vector measurements. The new algorithm combines an inner analytic solution for the unknown initial attitude quaternion with an outer numerical solution for the unknown initial rate. The inner problem can be cast in a standard Wahba form, and it is solved in closed form using an adaptation of the q method. The outer problem relies in a trust-region implementation of Newton's method in order to ensure global convergence. The global solution is determined by resolving starting from a random set of first guesses of the attitude rate that cover the space of non-aliasing rates. Tests on truth-model simulation data for minor-axis and major-axis spinning spacecraft confirm the new algorithm's ability to achieve global convergence and its estimation accuracy's consistency with its computed estimation error covariance matrix.

A new form of consider covariance analysis suitable for application to square-root information filters with a wide variety of model errors is presented and demonstrated. A special system formulation is employed, and the analysis draws on the algorithms of square-root information filtering to provide generality and compactness. This analysis enables one to investigate the estimation errors that arise when the filter's dynamics model, measurement model, assumed statistics, or some combination of these is incorrect. Such an investigation can improve filter design or characterize an existing filter's true accuracy. Areas of application include incorrect initial state covariance; incorrect, colored, or correlated noise statistics; unestimated states; and erroneous system matrices. Several simple, yet practical, examples are developed, and the consider analysis results for these examples are shown to agree closely with Monte Carlo simulations.

A numerical solution algorithm has been developed to solve a generalization of Wahba's attitude determination problem to the case of unknown attitude and attitude rate. It provides a robust global solution to nonlinear batch attitude and rate estimation problems for spinning spacecraft. The original Wahba problem seeks the attitude that fits a set of unit-normalized direction vector measurements. The generalized problem seeks an initial attitude and rate that, when combined with a torque-free rigid-body attitude dynamics model, fit a time series of direction vector measurements. The new algorithm combines an inner analytic solution for the unknown initial attitude quaternion with an outer numerical solution for the unknown initial rate. The inner problem can be cast in a standard Wahba form, and it is solved in closed form using an adaptation of the q method. The outer problem relies in a trust-region implementation of Newton's method in order to ensure global convergence. The global solution is determined by re-solving starting from a random set of first guesses of the attitude rate that cover the space of non-aliasing rates. Tests on truth-model simulation data for minor-axis and major-axis spinning spacecraft confirm the new algorithm's ability to achieve global convergence and its estimation accuracy's consistency with its computed estimation error covariance matrix.