Research On Robust Adaptive Filter Algorithms And Their Applications To Flight Vehicle Technology

There are some flaws including the low estimation accuracy, the slow convergence rate, non-robust to modeling and approximation errors, and sensitive to non-Gaussian measurement errors/noises and the large initial state errors in spacecraft attitude estimation, relative navigation for spacecraft formation flying and target tracking problems using standard Kalman filter. However, these existing problems play a key role in spacecraft formation flying missions, even cause failure to the mission. It is important to develop some robust/adaptive filtering methods to address the aforementioned problems.This dissertation improves the performance of the Kalman filter and the second-order divided difference filters using the robust and adaptive approaches, and then applies to some particular areas of spacecraft. The main contents including:First, for the non-robustness of the attitude estimation problem due to the non-Gaussian measurement errors and the measurement uncertainties in the attitude measurement sensors, a robust Kalman filter is proposed based on the Huber’s generalized maximum likelihood estimation, in which the measurement update is recast to the linear regression problem between the predicted estimations and the observations, and the state and measurement residuals are not weighted equally. The effectiveness of the proposed filter algorithm is validated by the numerical simulations.Second, in order to let the attitude estimation procedure is robust to the modeling and approximation errors due to the use of the error quaternion to represent the attitude error dynamics; an adaptive Kalman filter method is developed based on estimating the upper bound of the predicted covariance of the states in real time. Simulation results indicate that the proposed filter algorithm outperform the previous method in estimation accuracy and robustness to the modeling and approximation errors and the large initial estimation errors.Third, the two mentioned algorithms are combined and applied to attitude estimation problem, which not only address the non-Gaussian measurements problem but also can provide the robustness to the modeling and approximation errors and the large initial estimation errors.Fourth, in order to address the lower estimation accuracy of the relative navigation for spacecraft formation flying due to the use of the traditional extended Kalman filter, a reduced second-order divided difference filter is derived by taking into account that the measurement model is nonlinear based on GPS sensing equipment. Simulation results indicate that this simplified DDF is valid for the design of the relative navigation estimator for spacecraft formation flying.Fifth, for the non-Gaussian measurement noises existed in the measurements based on GPS equipment, a Huber-based simplified divided difference filter is proposed to address the mentioned problems based on Huber’s generalized maximum likelihood estimation, the effectiveness of this H-SDDF is demonstrated by a formation flying example.Sixth, for the shortcomings of the nonlinear estimation problems by using the traditional iterated versions of DDF, in other words, the state estimation is no longer statistically orthogonal with measurement noise, which will degrade the filter performance. A state augmentation based iterated DDF is developed to address the above problem, in which the measurement noise is augmented in states and lead to the new measurement noise relative to the new states is zero. So the problem can be addressed by computing the predicted measurement covariance accurately. Also, the effectiveness of the proposed filter is validated by simulations.Seventh, an improved robust Huber-based divided difference filter is derived by improving the Huber-based divided difference filter proposed by Karlgaard, in which the nonlinear measurement equation is directly used in nonlinear regression problem. This robust filter algorithm can also be considered as a special iterated DDF, which uses 1l and 2l norm method to deal with full nonlinear non-Gaussian measurement noises. Simulation results for target tracking demonstrate that the IHDDF performs better than HDDF, DDF and EKF in terms of estimation accuracy and robustness when the filter’s output is stable.In summary, this dissertation mainly focuses on the robust adaptive filter algorithms and their applications, covering the spacecraft attitude estimation, the design of the relative navigation estimator for formation flying and the nonlinear state estimation problems. The main problems including improvement of estimation accuracy and robustness of the filtering procedure are solved. The performance improvement of the filter algorithms in this dissertation are validated through the theoretical analysis and numerical simulations.