Gaussian Filters For Nonlinear Systems Under A Class Of Non-Ideal Conditions And Their Applications

With the increase of demand of social production and deepening of the outside world exploration, it is clear that there are just a few systems to satisfy linear property in reality, and nonlinearity is the general nature of matters. Consequently, the problem of nonlinear system estimation is always a hot research topic in the field of control for its important theoretical significance and wide application prospect.Owing to many years of untiring effort by researchers, there are two major types of solutions for this issue in the framework of Bayesian approach, i.e., Gaussian filters and non-Gaussian filters. And the particle filter is very representative for the latter with its advantages of high precision and wide applicability. However, it is limited in the practical application for its huge calculation. And it leads the Gaussian filters to become the most active estimation methods in the application of modern engineering. For the reason of constrained knowledge and complicated environment, there always exists some non-ideal conditions in the course of application, such as unknown parameters, correlated noises and delayed measurements. To solve the abovementioned problems, researchers have proposed a series of methods. However, many works are just designed for only one filtering algorithm, and the universally adaptable result for Gaussian filters is few. Based on the in-depth study of the previous achievements, this thesis proposes corresponding approaches for status estimation of nonlinear systems under the non-ideal conditions of correlated noises, random delay and uncertain model in the form of Gaussian filter framework. And the problem of non-cooperative target rendezvous and docking is employed to verify the effectiveness of proposed algorithms. The main work of this dissertation is summarized as follows.(1) The problem of optimal estimation is studied for a non-linearly Gaussian system with correlated noises. Two algorithms of optimal estimation are designed for the synchronously and asynchronously correlated noises in the form of Gaussian filters framework, respectively. First, inspired by the fact that the probability of process noises conditioned on measurement noises can better represent its statistics in the situation of measurements data received, and the conditional Gaussian distributions is exploited to design the algorithm of optimal estimation with synchronously correlated noises. Second, the property of Stirling’s interpolation is utilized to approximate the Gaussian integrals with randomly multiplicative variables. Finally, the unscented transformation and the rule of third-degree spherical-radial cubature are employed to deduced the suboptimal estimation implementation of the proposed algorithms.(2) Based on the study of(1), the problem of optimal estimation is studied for a non-linearly Gaussian system with randomly delayed measurements and correlated noises. First, it takes independently random sequence of Bernoulli to describe the possible situation with respect to random delay in measurement data, and the model about this issue is established. Second, the measurement noises are regarded as augmented states to compute the prediction about measurements. Finally, two algorithms of optimal estimation with randomly delayed measurements and correlated noises are proposed by using the design approaches of(1). Likewise in(1), the Gaussian weighted integrals in the framework of filters are computed by the unscented transformation and the rule of third-degree spherical-radial cubature, and the suboptimal estimation is proposed.(3) The estimation problem is studied for a non-linearly Gaussian system with model uncertainty. Two aspects of this issue, the uncertainly delayed measurements and uncertain parameters, are taken into account, respectively. First, for the status estimation problem with uncertainly delayed measurements, the Bayesian approach is employed to connect the probability density functions between current states and delayed states. By virtue of the posterior estimation respect to the delayed states, the estimation about current states is obtained and then the Gaussian filter with the uncertainly delayed measurements is proposed. Second, it adopts the way of the cubature Kalman filter interlacing with a maximum a posteriori estimator to estimate the status under the condition of uncertain parameters. The status and parameter can be estimated simultaneously without increasing the dimension the system model. Furthermore, three novel methods about approximating the conditional probability density by exploiting special properties of Stirling’s interpolation, unscented transformation and spherical-radial rule are proposed.It should be noted that comparing with the general framework of Gaussian filter, the proposed frameworks of Gaussian filters involved in(1),(2) and(3) afford a much wider scope of application, and the former is the specific form of the latter under ideal condition.(4) The problem of relative navigation is studied for non-cooperative target. Based on stereo vision, two algorithms of motion estimation are proposed. First, the non-cooperative target is divided into two categories, incompletely and completely, according to whether the information of orbit elements and inertial tensor of target is known or not. Based on the division, two estimation algorithms for relative navigation are designed. Second, the model of relative spacecraft motion with unknown orbit elements is established on the eccentric orbit, and the kinematic coupling is considered to describe the effect of due to the location of vision sensor deviating from the chaser spacecraft’s center of mass. Furthermore, the problem of relative navigation with unknown inertial tensor is regarded as status estimation problem of uncertain parameters, and this issue is solved based on the study of(3), which estimates the status of relative navigation for the complete non-cooperative target.