Bayesian Estimation Of The State Of Systems In The Presence Of Unknown Noise Statistics

State estimation of systems is based on a set of available noise-containing measurements to estimate states that are implicit in it or cannot be directly measured.State estimation plays an important role in ensuring the operational safety and benefits of engineering systems,and the knowledge of noise statistics is particularly important for accurate estimation of the state of systems.The incorrect use of noise statistics can lead to inaccurate state estimation and even filter divergence.This paper discusses and studies state estimation problems in situations with unknown noise statistics,and proposes state estimation methods suitable for several complex systems,which provide a certain theoretical basis and application value for actual engineering systems.The main work of this paper is summarized as follows:(1)For general nonlinear systems,a method is proposed to estimate the unknown measurement noise covariance and the state of systems at the same time.Through variational Bayesian(VB)inference,the joint posterior probability density function(PDF)of the state and measurement noise covariance is approximated to two independent PDFs.At the same time,a set of weighted particles is generated to describe the PDF of the state,and the inverse gamma(IG)distribution with conjugate characteristics is used to describe the PDF of measurement noise covariance.(2)For the jump Markov nonlinear system,a joint state estimation method is given when the statistical information of measurement noise is unknown.The interacting multiple model(IMM)algorithm is combined with the VB inference to deal with the state estimation under the multi-mode of jump systems.A set of weighted particles are used to describe the PDF of the state under each mode.At the same time,the PDF of measurement noise covariance is described by the IG distribution.The combination of IMM algorithm and particle filter(PF)ensures that the number of particles in each mode is fixed,thereby avoiding the problem of computational complexity and the amount of calculation increasing over time.(3)For linear high-dimensional systems,considering the huge computational cost required for state estimation,the entire high-dimensional system state vector is divided into multiple low-dimensional state blocks.By minimizing Kullback-Leibler(KL)divergence to minimize the approximated error.According to the dynamic characteristics of systems,two different scenarios depending on the state dynamics are considered.One is that the state transition matrix is block-diagonal,and the other is not.Considering the relationship between state variables and the requirement of state estimation accuracy,the size of state blocks can be chosen flexibly.This algorithm provides a theoretical basis for the state estimation of high-dimensional systems with unknown noise statistics.