Research On Improvement And Application Of Unscented Kalman Filter Algorithm

The Kalman filter is a method of time-domain filter which based on the minimum variance.It describes the system state by the state space equations and recursively estimates the output of system state.It has the advantages of small storage of history data and easily implemented.However,the Kalman filter is only suitable for linear systems and most actual systems have varying degrees of nonlinearity,which limits the development and application of Kalman filter,The Unscented Kalman Filter(UKF)is a method for nonlinear systems.The main research in this paper is about the UKF.This paper mainly researched on the improvement of UKF algorithm and its application in continuous-discrete nonlinear navigation systems.UKF is based on the Unscented Transform(UT)to sample the system state vector and calculate the corresponded weight and the obtained sampling point is called the Sigma point set.The Gaussian density of the system approximated by system's nonlinear function and solved the problem of nonlinear transfer of the mean and covariance.The main work of the thesis is as follows:First of all,this paper introduces and analyzes the sampling strategy and the scale factor adaptation of UKF algorithm.The three main UT sampling strategies: Scaled unscented transform,Simplex min skew sampling,and Simplex sphere sampling are analyzed based on the sampling accuracy and real-time performance.The advantages and disadvantages and the scope of application are introduced in detail.Based on that,an adaptive UKF filter algorithm based on sampling strategy is proposed and the influence of the scale factor on the sampling accuracy is introduced.The experimental simulations verified the effectiveness of the improved algorithm,and analyzed the existing problems and applicable scope of the algorithm.Then,this paper focused on the application of UKF in a continuous-discrete nonlinear system and researched on the ACD-UKF(Accurate Continuous-Discrete Unscented Nonlinear Kalman Filter,ACD-UKF)algorithm for continuous-discretenonlinear systems.The Stochastic Differential Equation(SDE)which is used to describe the system state space in the ACD-UKF is analyzed and two major solutions are proposed: Euler–Maruyama(E-M)and Milstein high-order method.The numerical solution convergence and stability are analyzed and the ACD-UKF algorithm with variable step size error precision is improved with the method:ACD-UKFn,which improves the accuracy of global error cost function.The improved algorithm is simulated on MATLAB and the performance of the improved algorithm is compared to the original algorithm,experiments show that the improved algorithm has better performance on the estimation accuracy and stability,and effectively reduces the estimation of divergence.At last,this paper researched on Adaptive Unscented Kalman Filter(AUKF).The accuracy of the UKF algorithm is greatly affected by the noise of the system model,and the unknown statistical characteristics of the noise may cause the filter accuracy decreased and even the estimation of divergence.In practical applications,statistical characteristics of the sample are difficult to obtain.Therefore,relevant adaptive algorithms need to be researched on.Based on this,the adaptive UKF based on Sage-Husa algorithm is researched on.The basic principle and algorithm of Sage-Husa algorithm and adaptive UKF combined with Sage-Husa algorithm are introduced.Analyzed the system that noise statistical characteristics are unknown and used the measured information to estimate and correct the mean and covariance of the noise in real time,So that the algorithm has the adaptive characteristics of dealing with time-varying noise.On this basis,a new adaptive UKF algorithm is proposed.The attenuation factor is updated online and the effectiveness and feasibility of the algorithm are verified by experimental simulations.