Research Of Nonlinear Kalman Filtering Algorithm

Nonlinear filtering has a crucial role in information and communication systems,control systems,and many other areas,such as in radio and television communication systems,satellite navigation and positioning systems and tracking systems.It can be said that nonlinear filtering techniques influence our lives.For the nonlinear filtering problem,many methods have been intensively studied and proposed.The linearization-based extended Kalman filter(EKF)is widely applied to industrial nonlinear systems.As extended Kalman filter is limited to its accuracy and reliability,it is unsuitable for high dimensional system with large nonlinearities.Particle filter(PF)can obtain ideal accuracy based on importance sampling with huge random samples and positive weights.But it will face the dimension curse and degeneracy problem.The unscented Kalman filter(UKF)and cubature Kalmam filter(CKF)are presented which may get adequate accuracy more efficiently by selecting specific and deterministic set of samples and weights determined by the covariance.While these two may encounter negative weights and numerical instability in some cases.Inspired by cubature Kalman filter,unscented Kalman filter and particle filter,this paper develops a new deterministically sampling scheme based upon Gaussian distribution.The new method can be seen as a mixture of deterministically sampling of cubature Kalman filter and importance sampling of particle filter,which is called umbrella sampling(US).So the new nonlinear Gaussian filter is called umbrella sampling filter(USF).The umbrella sampling filter propagates like cubature Kalman filter.Its samples' distribution is a generalization of cubature Kalman filter.And the samples' weights are positive and possess a property similar to importance sampling of particle filter.Thus the umbrella sampling filter not only has the accuracy and computational complexity of cubature Kalman fiter and unscented Kalman filter and the stability of Particle filter,but also can avoid the non-positive weights of cubature Kalman or unscented Kalman filter in some cases.Totally,the umbrella sampling filter is a scalable method to high dimensional nonlinear problem.