Robust Estimation Theory For Stochastic Dynamic Systems And Its Applications In Aerospace Engineering

Dynamic state estimation can be found in various areas such as auto-driving cars,target tracking,audio signal processing,and information fusion.The Gaussian approximation estimator（GAE）,which is based on Bayesian theory,has attracted public attentions in the recent half century due to its proper computational burden,easy implementation and recursive framework.The GAE has been widely utilized to deal with engineering problems such as aircraft navigation,aerodynamic model identification,fault detetion and airplane target tracking.In most applications,however,sensors may provide outliers due to sensor faults or environment interferences.These outliers have negative effects on the GAE,leading to the degradation of the GAE’s performance or even resulting in the divergence of the GAE.Improving the robustness of the GAE has a significant meaning,i.e.,making the GAE more flexible and practicable.How to improve the robustness of the GAE is still a leading-edge research topic.After analyzing the performance of the GAE for dynamic systems involving outliers,this thesis has proposed several strategies for designing robust estimators.Main contents and contributions of this thesis are as follows:（1）The unified framework for dynamic state estimation based on Bayesian theory is introduced,followed by the general framework of the GAE（including Gaussian Kalman filter/smoother,GKF/GKS）under the Gaussian assumptions（i.e.,both the process and measurement noises are Gaussian）.A cubature rule is integrated into the GAE,leading to the cubature Kalman filter and smoother（CKF/CKS）.The superiority of the CKF/CKS has been illustrated by an aerodynamic parameter identification problem.A comparison study has been presented to demonstrate the fact that the performance of the Kalman filter and smoother degrades in the presence of outliers.The main reason for such a degradation is provided from the perspective of maximum a posterior estimation（MAP）.（2）A robust Huber-Kalman smoother（RHKS）is proposed,and the general design framework for a robust smoother based on M-estimation is studied.The optimization problem for the Huber robust smoothing is formulated by replacing the quadratic loss in the GKS by a Huber cost.With the surrogate function of Huber’s loss,the majorization-minimization（MM）method is utilized to solve the aforementioned optimization problem,resulting in the RHKS.Furthermore,the design method of the RHKS is extended to other robust penalties from M-estimation,leading to a general framework for the M-estimation based robust smoothing algorithm.Numerical simulations on both the reentry-target tracking and aerodynamic parameter identification have demonstrated the efficiency of these robust smoothers.（3）The Laplace distribution and Student’s t distribution are employed to model the measurement noise,and under such a circumstance the methodology for designing robust filters and smoothers is explored.From the MAP perspective,the optimization objectives are formulated,i.e.,mixed（?）₁/（?）₂for the Laplace filtering/smoothing and mixed log/（?）₂for the Student’s t filtering/smoothing.With the surrogate functions for both the（?）₁and log functions,the MM method is employed to derive several robust estimators.The performance of this kind of robust filters/smoothers is verified not only by estimating a non-stationary system but also the Mars entry and landing navigation problem.（4）The methodology for designing a robust estimator by utilizing correntropy and mixture correntropy is explored.A general framework for robust filtering and smoothing based on the maximum correntropy criterion（MCC）is proposed.In addition,the convergence properties of the proposed solutions are provided.Simulation results show that the MCC based methods with some carefully selected kernel parameters can achieve a substantial performance improvement.However,the MCC based solutions are sensitive to the kernel size.To deal with this issue,two kernel-size-insensitive robust filters based on mixture correntropy are proposed,and their performance is illustrated by numerical simulations.（5）The outlier detect-and-reject（ODR）idea is employed to design a novel Kalman filter via the variational Bayesian inference,and then this idea is extended to deal with the information fusion problem of networked systems,resulting in both the centralized and decentralized solutions.An outlier-indicator with a beta-Bernoulli prior is introduced to each measurement,leading to a new hierarchical measurement model with the ability of detecting outliers.The variational Bayesian method is utilized to estimate the state as well as the indicator,resulting in a robust filter based on the ODR idea.Numerical simulation results show the superior performance of the proposed method over the most existing robust filters.Furthermore,the ODR idea is utilized to deal with the information fusion problem over networked systems with measurement outliers.Both the centralized and decentralized solutions are presented,and their performance is verified by not only the multiple UAVs cooperatively tracking a surface maneuver target problem but also the airplane air data sensor information fusion problem.