Design method for PNKF-VB

Abstract

The invention provides a design method for PNKF-VB and relates to the field of a filter. According to the method, variational distribution approximate to a posterior probability density function is constructed under a Gaussian assumption condition; iteration approximation of state estimation is realized by taking KL (Kullback-Leibler) divergence as a penalty function; and the PNKF-VB is derived bytaking confidence lower bound maximization as a target function according to a variational Bayesian frame. According to the method, a relatively tight approximation form of the nonlinear state posterior probability density function can be obtained, so the state estimation precision is improved. The difficult solution problem of the integral of the posterior probability density function in a system state estimation process can be transformed into the problem of optimizing ELBO lower bound. The adaptive weighted KL divergence is taken as the penalty function, so the optimization flexibility isimproved and the state estimation precision is improved. The method has very high significance to nonlinear state estimation theory and practical engineering application.

Description

technical field [0001] The invention relates to the filter field, in particular to a design method of a Kalman filter. Background technique [0002] Traditional nonlinear filters generally use sampling methods to approximate the posterior probability density function of the state or linearize the nonlinear function, and then calculate the expected value of the state and error covariance according to the approximate result to simplify the posterior probability density function (PDF) points problem. [0003] The Extended Kalman Filter (EKF) and Iterative Extended Kalman Filter (IEKF) are representative of the linearization method, and the nonlinear state function and measurement function are linearized through the Taylor expansion, so that the Kalman filter (KF ) framework, but because it only retains first-order items and ignores higher-order items, it is easy to cause filtering divergence when the system has strong nonlinear characteristics. Particle filter (PF) is a Monte...

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Problems solved by technology

However, the random sampling nonlinear filter requires a large amount of calculation, and a

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