Applications Of Nonlinear Bayesian Filtering Algorithms To Spacecraft Attitude Determination

This thesis discusses how to choose an appropriate solution to some state filtering problem from lots of nonlinear filtering algorithms, which in general can be described in a unified way from the recursive Bayesian estimation. First, many filters using local model approximations are systematically investigated, such as the extended Kalman filter (EKF), the iterated extended Kalman filter (IEKF), the second-ordered extended Kalman filter, the unscented Kalman filter (UKF). Secondly, three filtering algorithms using global approximations, i.e., the approximate grid-point filtering algorithm, the Gaussian sum filtering algorithm, and the particle filtering algorithm are investigated. Especially for the last one, the thesis completely introduces its basis and development. Also, the thesis discusses and solves the difficulties in expanding the nonlinear state filtering algorithms into parameter learning. For the lack of process noise, the parameter estimation might converge in a very slow rate or all but one initial parameter particles will have negligible weights after a few iterations. Artificial process noises are introduced to deal with these problems. On the other hand they might cause"loss of information". The thesis studies the tricks to use the artificial noise and introduces a shrinkage modification of kernel smoothing to an auxiliary parameter particle filter. In addition, the thesis discusses and solves the difficulties in expanding the nonlinear state filtering algorithms into state estimation combined with parameter learning. There are two common estimation schemes, i.e. the augmented-state scheme and the dual filter scheme. The augmented-state estimation scheme is simple, but possibly suffering from various high-dimensional computing problems. In fact the state/parameter combined filtering problem can be decomposed into a state filtering sub-problem and a parameter learning sub-problem by using the marginalized Bayesian estimation. However the dual filter estimation scheme is an approximation of the augmented-state posterior density estimation. The thesis completely reviews and systematically investigates the applications of the two schemes to various nonlinear filtering algorithms.The thesis studies the applications of nonlinear filtering algorithms to several state filtering problems, parameter learning problems, and combined estimation problems in the field of spacecraft attitude determination. In this thesis the scope of spacecraft attitude determination has been extended to also include attitude sensor calibration, inertia matrix estimation, attitude determination combined with sensor calibration or inertia matrix estimation, and so on. Considering a low-Earth-satellite with a three-axis magnetometer (with a three-axis gyro or not), the thesis systematically investigates the applications of nonlinear filtering algorithms to these estimation problems respectively. Some contributions are made: 1) a complete geomagnetic field vector observation model has been derived again and modified to include two extra factors: nominal mounting matrix of magnetometer and orbit determination error. The model has been used for attitude determination and three-axis magnetometer calibration for the first time. 2) a iterative observation update approach has been used to improve the performances of the recently proposed EKF and UKF algorithms for a three-axis magnetometer scalar calibration. Three iterative filters, i.e., a IEKF filter, a iterative UKF (IUKF) filter, and a iterative sigma point filter (ISPF) have been proposed. Furthermore, a particle filter has been proposed to calibrate the magnetometer observations by using the general parameter auxiliary particle filter. 3) the augmented-state estimation scheme and the dual filter estimation scheme have been used to solve the gyro-equipped attitude determination problem, the gyro-based/gyroless attitude determination and three-axis magnetometer calibration problem, and the gyroless attitude determination and inertia matrix estimation problem. Some recently proposed algorithms have been modified and some new filters have been given, such as: i) a modified dual particle filter and a hybrid filter for gyro-equipped spacecraft global attitude determination. Both filters use a same quaternion particle filter, but use a different bias estimator. ii) an augmented UKF filter and two (decoupled/coupled) dual UKF filters respectively for gyro-based/gyroless attitude determination and three-axis magnetometer calibration. iii) a modified augmented UKF filter and a modified dual UKF filter for gyroless attitude determination and inertia matrix estimation. Various computer-based simulations have been used to test the validities of the modified or proposed nonlinear filters and to compare them to some classical filters.