Cubature Kalman Filter And Application Research On Navigation

Cubature Kalman filter (CKF) is a superior nonlinear filter that has a simple algorithm, high precision and good convergence, etc. And it is becoming a hot and efficient method to study the nonlinear estimation problems for the current and future. The thesis focuses on CKF to spread related research. The main works are as follows.The nonlinear function mean captured in the nonlinear filter process is executed the Taylor expansion to derive the different estimation precision between CKF and UKF (Unscented Kalman Filter) under the nonlinear systems of different dimensions. And the main reasons for above difference are pointed out:the approaching degree between Taylor expansion high-order item of function mean captured by two filters and the true is not the same, besides,their numerical stabilities are different under different dimensions. The selection principle of the two filters under different dimension nonlinear systems is proposed after analysis and research.The mean, variance and odd order moment of the function’s statistical information captured in filter process is analyzed and researched to obtain the difference between augmented CKF and non-augmented CKF based on cubature transformation and point out that the filter precision is different and the reasons under the different dimension nonlinear systems:for one dimension system, the augmented CKF gains higher precision through capturing and propagating the mean,variance which are closer to true and also extra odd-order moment. But for the two dimension system and above, the function statistical information done by the augmented CKF largely deviates from true to make augmented CKF inferior to non-augmented CKF. Thus how to choose a better method from the two filters is put forward under different dimension systems.The CKF-KF hybrid filter is proposed for conditionally linear Gaussian state model involving nonlinear state and linear state. The CKF and KF are introduced into the two different stages of the filter process; the hybrid algorithm firstly uses the CKF to estimate the nonlinear state and then uses KF to do the linear state. The CKF and KF are matched together through successively conducting cubature-sample to nonlinear and linear state, and cubature-sample to linear state is the key to their combination. On account of CKF using less sample points, the calculation amount of CKF-KF which loses slight precision is far less than the RBPF algorithm. The CKF-KF which performs a feedback correction to the linear state through the nonlinear state estimation error has higher precision than directly using CKF. Importance density function lacking of the latest observation information and the re-sampling damaging the particle diversity are the important reasons for particle degradation and filter precision reduction. So the CKF, Gaussian mixture model and EM algorithm are introduced into particle frame to improve the algorithm, and the CPF (Cubature Particle Filter) and GMCPF (Gaussian Mixture Cubature Particle Filter) algorithm are proposed respectively. The two algorithms both use the latest observation information through CKF designing of the importance density function, and GMCPF use Gaussian mixture model to truly approach the posterior probability density. At the same time, importance sampling is not performed after re-sampling instead of using EM algorithm to regain Gaussian model from the importance sampling particle set, and thus the particle degradation and filter precision are improved.At last, this thesis uses CKF to estimate the misalignment angle error under large azimuth misalignment angle initial alignment, CPF and GMCPF are carried out to solve the estimation problem when the observation equation can not be obtained precisely in the gravity anomaly assisted inertial navigation system. Simulation results show the effectiveness of the above nonlinear filters.