Filtering And Information Fusion Algorithms Under Non-ideal Conditions For Nonlinear Systems

With the development of Bayesian theorem,Gaussian filter has become one of the most important techniques in modern filtering field.It has been widely used in aerospace,communication,transportation and chemical engineering fields,especially in navigation field,and it has become the current research hotspot.Because there are modeling errors and observation errors in the system,it is necessary to design a high precision and performance filtering algorithm to process the original noise-containing signal and output the desired signal.Several hypothetical conditions should be satisfied for the normal operation of Gaussian filtering algorithm.In the actual engineering,due to the existence of non-ideal conditions,Gaussian filter can not work properly.In addition,to make up for the defects of single sensor and ensure the engineering system to work steadily and normally,the cooperative work of multiple sensors has become a common method.High efficiency,high precision and high stability information fusion algorithm is the core of multi-sensor cooperative work.To ensure the normal operation of the engineering system,it is necessary to design filtering algorithms with high accuracy,strong stability and strong anti-interference ability,as well as efficient,high-stability and high-precision information fusion algorithms.Due to the particularity and complexity of the engineering environment,there are always some problems in engineering systems,such as random delayed observation,system model with multiplicative noise,non-Gaussian noise and so on.To solve these problems,several corresponding improved filtering algorithms are proposed to obtain effective state estimation results in this paper.In addition,to improve the stability and accuracy of the multi-sensor system,several information fusion algorithms are designed for further fusion of the state estimation in this paper.The main contents of this paper are as follows:Firstly,to solve the problem of multiplicative noise in the system,an improved GF algorithm is designed by combining the statistical characteristics of multiplicative noise with the GF framework.Considering the assumption that multiplicative noise satisfies the Gauss distribution,the conditional mean variance of multiplicative noise is substituted in the prediction and updating process,and the GF framework is improved according to Bayesian estimation theory.In addition,to solve the problems of random delayed measurement,noise correlation and the center offset of cubature points,combine the improved Gaussian filtering algorithm with state expansion method and improved cubature points.Then the improved Gaussian filtering algorithm can achieve high estimation accuracy in the presence of multiple non-ideal states.Then,to solve the problem of nonlinear systems with heavy-tailed noise,a robust GF algorithm is designed by combining the GF framework with the robust cost function.Maximum entropy criterion and M estimation criterion are used to design the cost function,which is substituted in GF framework.Otherwise,PF and Student's t filter are used to replace GF,so as to make the improved GF algorithm robust to heavy-tailed noise.At the same time,the robust filtering based on M-estimation is used to approximate the important density function to reduce the particle poverishment.The time dependence of noise is removed by observational difference method,and the problem that conditional mean of the noise is not zero is solved by state expansion method.The scope of application of the designed robust filtering algorithm is increased.Next,for real-time monitoring the consistency of GF estimation results,a novel monitoring algorithm is designed.Considering the inconsistency of the estimated values of GF algorithm due to the dissatisfied Gauss approximation assumption or the modeling error,a new consistency monitoring algorithm is proposed based on the statistical hypothesis detection method,in which the difference between the prior and the prior estimates is measured.This algorithm not only avoids the dependence on the true state value,and meets the real-time monitoring requirements,but also monitors the posterior estimation directly.Moreover,the monitoring is carried out automatically,which avoids the interaction of user during operation,simplifies the structure and improves the calculation efficiency.The monitoring algorithm is embedded in the cubature quaternion filter to test the performance of the algorithm in practical application,so as to ensure the effectiveness of the designed algorithm.Finally,to solve the problem of information fusion of integrated navigation system in the non-ideal situation,the improved information fusion algorithm is designed by combining the previous research results with the information fusion algorithm.Firstly,considering multiplicative noise and the correlation between observation noises,a centralized fusion algorithm for multiplicative noise is designed based on the improved Gauss filtering framework and the observation matrix expansion method.Secondly,considering the problem that noises are Student's t distribution,a distributed fusion algorithm based on Student t is presented,which is based on the improved student filtering framework and the Lagrange multiplier method.Finally,considering the different sampling rates of multi-sensor and the correlation between system noise and observation noise,an improved covariance intersection fusion algorithm is proposed based on the multi-scale system theory and the first-order Stirling interpolation method.And the consistency of the estimated results is monitored by the proposed consistency monitoring algorithm.