| In practical applications,a large number of dynamic systems and observations are described by nonlinear equations,and the estimation of complex nonlinear systems has become a hot topic.The filter algorithm represented by Kalman filter（KF）has the advantages of strong real-time performance and low algorithm complexity in state estimation.The nonlinear filtering algorithms derived from KF,such as extended Kalman filter（EKF）and iterated extended Kalman filter（IEKF）,are widely used in intelligent robot,unmanned driving,intelligent transportation and other fields.However,the above nonlinear filtering algorithms are usually based on Taylor series expansion and linearized to first-order terms,and their accuracy depends on two factors,namely the degree of uncertainty of the system and the local nonlinear quantity.How to improve the accuracy and robustness of nonlinear system state estimation is one of the hot research topics in the control field.This thesis focuses on this problem as follows:Firstly,this study deals with the second-order EKF based process and measurement white noises estimation problem for nonlinear continuous-discrete systems.The design of the white noise filter and smoother are firstly converted into a linear estimation problem by the second-order Taylor series expansion approximation and the function that makes the second-order term approximately equivalent to the estimation error variance.Secondly,based on the projection formula and the expected lemma of quadratic and quartic product traces of random vectors,the second-order EKF is derived,and the expected lemma of matrix traces is proved in detail.Then the recursive solutions of the white noise filter and the smooth filter are obtained by using the innovation analysis method.we derive a recursive solution using an innovation method.Finally,a numerical example is given to verify that the second-order EKF algorithm has better estimation effect than EKF.Secondly,multi-sensor fusion filtering for bilinear systems with delayed state is studied.The classical KF is considered as the optimal estimator for linear systems.This thesis proves that it is feasible to use this method to solve the problem of state estimation for bilinear systems with delayed state.By defining a new estimation error covariance matrix,an optimal state estimator is designed by using projection formula and innovation sequence.In addition,the problem of multi-sensor fusion filtering is also discussed.The research shows that the multi-sensor fusion filtering algorithm can improve the state estimation effect of the system to a certain extent.Finally,a numerical example is given to discuss the performance of the algorithm.Thirdly,a new filtering algorithm,Extended Risk-sensitive Fusion Filter（ERSFF）,was proposed for simultaneous localization and mapping（SLAM）of unmanned helicopter autonomous landing.The risk-sensitive filter has good robustness and generalization ability.The filtering algorithm can have bothH2 performance andH∞performance according to the choice of risk sensitive parameters.In the case that the mathematical characteristics of noise signal are difficult to determine,the filter can be degraded toH∞filter,which enhances the robustness of the model.Based on EKF-SLAM algorithm and Krein space linear estimation theory,a risk-sensitive estimator for nonlinear systems is proposed in this thesis.Then,the scalar weighted fusion filtering algorithm with low algorithm complexity is selected for multi-sensor data fusion.Finally,the algorithm is applied to the autonomous landing problem of unmanned helicopter,and the effectiveness of the algorithm is proved. |
