Research On Nonlinear Filtering Methods Under Non-ideal Conditions And Algorithms For Multi-sensors Information Fusion

With the progress of space technology and the deepening of space exploration, the demand of spacecraft for navigation precision becomes higher and higher, especially for relative navigation of spatial non-cooperative targets, it has been a research hotspot in the aerospace field for a long time. Nonlinear filtering algorithm is the foundation of implementing the navigation precision, and it is able to achieve accurate estimation of navigation information. Therefore, in order to ensure that navigation system has properties of high precision, high stability and anti-interference, it is necessary to study the nonlinear filtering algorithm with stronger adaption.Since engineering environments are complicated, when the nonlinear filtering algorithms are being used in engineering, there usually exist problems of state delay, model uncertainty, non-Gaussian noise and etc. To solve these problems, this thesis proposes several improved state estimation algorithms to effectively estimate system state. Moreover, to obtain navigation information with high precision and high stability, this thesis also adopts a multi-sensor information fusion approach to further address corresponding estimation information. Major research content of this thesis is as follows:(1) The state estimation of system with state delay is studied, an improved Gaussian filtering algorithm framework is designed, and two realizations of the framework based on unscented transformation and third-degree spherical-radial cubature rule are given, respectively. At first, posterior probability density functions of current and delayed states are obtained through recursive operation of the algorithm, and time prediction process with state delay and measurement update process with state delay are presented, respectively. Afterwards, according to unscented transformation and third-degree spherical-radial cubature rule, a suboptimal realization of the improved Gaussian filtering algorithm framework is proposed. The classical filtering algorithm framework is a special case of the improved algorithm framework. As a universal nonlinear filtering algorithm framework, the improved framework is able to achieve different realizations according to different Gaussian weighted integral calculation approaches.(2) The state estimation of system with measurement model parameter uncertainty and non-Gaussian noise is studied, and an improved expectation-maximization nonlinear Gaussian filtering algorithm with joint estimation is designed to jointly estimate the system state and uncertain measurement model parameters. At expectation step, it is assumed that the system has obtained a group of model parameters. Based on measurement model with the obtained parameters, an improved particle filtering algorithm is employed to deal with non-Gaussian noise and to gain state estimation information with high precision. At maximization step, based on state information obtained at the expectation step, Gaussian mixture models are utilized to approximate nonlinear measurement equations, and maximum likelihood estimation is taken to estimate the unknown parameters in the Gaussian mixture models. Compared with the traditional Gaussian nonlinear filtering algorithms, the proposed algorithm is able to estimate the state information more accurately and suitable to be used in the state estimation with unknown model parameters.(3) The estimation of attitude information of spacecraft with multiple sensors is studied, under condition that characteristics of noise and cross covariance are unknown. First of all, in the estimation of each subsystem, in order to avoid redundancy phenomenon and singular problem caused by using quarternion and Rodrigues parameters to describe the attitude, respectively, through utilizing switch between error quaternion and error generalized modified Rodrigues parameters, under framework of cubature Kalman filter, by combing observation information of current moment, local estimation information of each subsystem at each moment is obtained. Afterwards, in order to gain high-precision state estimation information, a robust covariance cross fusion algorithm is proposed. The proposed algorithm takes minimizing nonlinear performance metric as rule to gain estimated information weights at first, then cross procedures of covariance is utilized to obtain locally estimated fusion information. Finally, in order to improve fusion efficiency of the attitude information of multiple sensors, through taking weighted linear minimum variance of matrices as optimal fusion rule, a fast continuous covariance cross fusion strategy is proposed. The proposed strategy transfers a multidimensional optimization problem into several optimization problems of unidimensional nonlinear cost functions, so that fusion time can be reduced, and optimal fusion estimation information can be achieved.(4) The estimation of relative navigation information of spatial non-cooperative spacecraft is studied. At first, systematic dynamic model of target and tracking spacecraft is built, strapdown inertial navigation system and celestial navigation system in tracking spacecraft are adopted to determine absolute motion parameters, and optical cameras are utilized to determine relative position and angular altitude between target and tracking spacecraft. Afterwards, for the case that parameters of optical measurement model are unknown, the proposed expectation maximization filtering algorithm is employed to jointly estimate relative navigation information and to recognize the unknown parameters of measurement model. At last, in order to improve estimation accuracy of the navigation information and the systematic robustness, an asynchronous multi-sensor distributed information fusion algorithm is designed. The designed algorithm utilizes cubature transformation to extend statistical linear errors to fusion process of nonlinear models, and then the high-precision navigation information can be obtained.