Research On Nonlinear Filter Algorithm Based On Variational Learning

Space situational awareness technology is a vital prerequisite for maintaining national land security and protecting significant spacecrafts and space stations.Target tracking capability is the foundation for the realization of the space situational awareness.Due to the inherent characteristic of strong nonlinearity,in the existing nonlinear estimation algorithms,the estimation accuracy is poor and the numerical stability can not be guaranteed well.Hence,In order to overcome the drawback,variational Gaussian regression filter(VGRF)is proposed,which based on the variation inference(VI)framework and contain compensation parameters.The main contributions are as follows:1.It is demonstrated that traditional Gaussian filter is the nature result of the maximization of the lower bound in the variational inference framework.By demonstrating the equivalence of Kalman filtering and Gaussian filtering under certain conditions,the essential meaning of Gaussian hypothesis is analyzed,which provides a theoretical basis for the modeling of full data likelihood probability in this paper.From the point of view of variational inference,the standard Kalman filter and the Gaussian filter are re-derived,The consistency of the nature of these three framework is demonstrated,the objective functions of which both are the maximization of the lower bound,so as to minimize the corresponding relative entropy.Hence,different types of nonlinear filtering algorithm are grouped into a unified framework,and a unified index of performance evaluation between different nonlinear filtering algorithms is proposed,which includes two types of state information,i.e.mean value and their reliability(covariance).Based on a unified index,the comparison of approximate degree between the approximate posterior probability density and the true posterior probability density can be operated directly.But in most existing evaluation index,such as the mean square error,only the error of mean is considered as the criterion of the performance evaluation,and the covariance is not included.2.A variational Gaussian regression filter algorithm based on single measurement and multi-measurement is proposed.The core is that based on the discussion of the nature of Gaussian hypothesis,the full data likelihood probability,that is,the relationship between state and measurement is modeled as a linear Gaussian regression process(LGRP)with compensation parameters.Based on the modeling of the full-data likelihood probability,the maximization of the lower bound can be realized analytically in the variational inference framework,and then the joint state estimation and compensation parameter identification can be performed analytically as well.Two kinds of LGRPs based on single-measurement and multi-measurements are proposed,and correspondingly,two kinds of nonlinear VGRFs are developed.In the VI framework,the selection of initial variational hyperparameters is inevitable,which VGRF is quite sensitive to.Hence,an optimization algorithm for variational hyperparameters is proposed,in which the variational lower bound is taken as the objective function.When the filtering algorithm is working,the variational hyperparameters can be optimized synchronously so that the robustness of VGRF for the initial variational hyperparameter selection is enhanced greatly.The simulation results demonstrate that the joint CPs identification and state estimation contribute to the improvement of accuracy.3.A variational Gaussian regression filter based on prior information inference is proposed.In order to improve the credibility of the estimate mean of state,the priori information about the system state is reconstructed and new prior variational parameters are introduced.Utilizing the reconstruction of prior state information and the modeling of the relationship between the state and the measurement,a prior information inference-based VGRF is proposed.In the filtering process at each time,based on the VI framework,state estimation and prior variational parameter identification can be achieved iteratively.Therefore,under the premise of ensuring the estimation accuracy,the credibility of the estimation result can be strengthened as well.The simulation analysis can demonstrate the improvement of the credibility of the filtering results.