Research On Variational Nonlinear Filter And The Application In Underwater Vehicle Integrated Navigation System

With the advantages of facile implement,high precision,effective convergent and so on,the filter based on Bayesian estimation principle has been one of the current research focuses.This author develops the variational nonlinear filter method systematically around the application requirement of state estimation from underwater vehicle integrated navigation system,and the major research could be concluded as follows:Aiming at the characteristic of underwater vehicle integrated navigation system,the state estimation model is established and the weak solution equation of model is provided by Kolmogorov's forward equations.Hence the thought of filter design is produced by adopting variational method.For the low dimension state space system,this paper utilizes cubic spline interpolation and biquadratic interpolation to approach the probability solutions of one-dimensional system and two-dimensional system.It is also elaborating the theoretical derivation and algorithm process,and analyzing algorithm complexity and convergence rate.By taking the nonlinear non-gaussian system model as the instance and performing the comparison analysis with the particle filter,interpolation method can improve the filter accuracy,the feasibility of solving stochastic differential model by using the interpolation method is confirmed through simulation experiment.For the high dimension state space system,this paper proposed a nonlinear linear method based on Finite Element Method(FEMF),which takes advantage of the thought of space division and piecewise interpolation and theoretically deduces the process of approaching navigational state probability solution in function space.It also provides the analysis of the convergence property,convergence rate and algorithm complexity.The simulation results indicate that the algorithm proposed has better performance than particle filter.By carrying out the contrastive analysis with Extended Kalman Filtering,Unscented Kalman Filter and Particle Filter,Finite Element Method can improve the filter accuracy.The feasibility of solving of stochastic differential model by using FEMF is confirmed through simulating experiment results.In order to solve the problem of low real-time performance,this thesis puts forward a hybrid filter algorithm consisting of Yau-Yau method and FEMF.This algorithm utilizes Yau-Yau method to determine the point-estimate in shape function tectonic model,and estimates the system state probability solution,which enhances the algorithm operating efficiency effectively.By taking the nonlinear non-gaussian system model as the instance and carrying out the contrastive analysis with Particle Filter,the feasibility of solving of stochastic differential model by using YY-FEMF is confirmed through simulating experiment results.In order to solve the problem of FEMF method smoothness restrictions on the interpolation function,it presents a projection filter algorithm on the basis of Hermit primary function.This algorithm could construct a interpolation function that has the property of higher order differentiation derivative in the whole continuous space without any matrix or integral manipulation,which reduces the calculated amount greatly and improves the real-time performance of filter algorithm.By taking the nonlinear model as the instance and carrying out the contrastive analysis with Extended Kalman Filtering,Unscented Kalman Filter and Particle Filter,Projection Filter can improve the filter accuracy and reduce calculation.At last,the performance tests are carried out by adopting two applications of inertial/terrain,inertial/magnetic to assess the filter algorithm performance in underwater vehicle novel integrated navigation mode.The simulation results demonstrate that the algorithm proposed has good performance of output accuracy and engineered timeliness.