Research On The Smooth Variable Structure Filter Algorithms And Their Applications To Initial Alignment Of The Inertial Navigation System

In the Strapdown Inertial Navigation System(SINS),the Kalman type filtering is the core part of the fine alignment process,and its fast convergence characteristic is the convenient condition for the application in various fields.The Kalman type filtering methods require the system model to be accurate and statistical characteristics to be known,thus the system performance is affected by the measurement interference and unknown noise interference.In order to enhance the stability and accuracy of the state estimation in the presence of the measurement interference and noise interference,the Smooth Variable Structure Filter(SVSF)is studied,and realized its application in the process of SINS initial alignment.Firstly,aiming at the problem of the linear SVSF algorithm application in the nonlinear invariant systems,the SVSF-VBL estimation strategy in the presence of linear is adopted,the several common nonlinear filtering methods is combined with the SVSF method to construct a nonlinear SVSF estimation method.A new nonlinear SVSF estimation method is proposed based on the combined strategy,which uses the fifth degree cubature rules to compute the cubature points of the nonlinear system state variable.In the new method,one step prediction of the state variables and the state covariance matrix are completed,and the diagonal elements of the optimal gain matrix are used to form a new smooth bounded layer and gain calculation,thereby removing the restriction on existing subspace.The effectiveness and feasibility of the new nonlinear SVSF method are verified by the simulation of target tracking.Secondly,as the effects of chattering interference surviving in the gain switching process of the SVSF algorithm,the two order sliding mode control theory is applied to the SVSF algorithm,and the second order SVSF algorithm is derived based on the first order and second order sliding conditions.The stability of the second order SVSF estimation process is proved by Lyapunov stability theory,and the gain expression of the second order SVSF is derived.The priori and posteriori error covariance matrix are calculated on account of the five degree cubature rules for the second order SVSF algorithm,and then the gain and cut-off frequency is optimized by error covariance matrix for the construction of optimal second order SVSF.According to the Luenberger reduced order observer method,the second order SVSF algorithm is extended in the condition that the dimension of the measurement variables is less than the dimension of the system state variables.The feasibility and effectiveness of the optimal gain and second order SVSF method applied in the universal system.Then,due to the unobservable problem of the alignment model under the conditions of linear initial alignment model,a reduced order Kalman Filter(KF)combined alignment method based on the strapdown gyrocompass alignment.The method adopts misalignment angle calculated by the gyrocompass alignment feedback to measurement equation of the reduced order KF initial alignment,and then an augmented measurement model is constructed.Through the switching between measurement models,the observability of the conventional KF initial alignment model is improved.The observability and effectiveness of the combined alignment model are analyzed by observability degree and mathematical derivation.The simulation results show the feasibility of the proposed method,and also provide the convenient conditions for the application of the SVSF algorithm.Finally,aiming at the slow convergence of strapdown gyrocompass alignment results under the nonlinear condition and the poor robustness under the noise interference,a nonlinear combined alignment method based on the variable parameter strapdown gyrocompass alignment is proposed.The method uses the misalignment angle calculated by the variable parameter strapdown gyrocompass alignment feedback to measurement equation of the reduced order nonlinear KF initial alignment,and then the augmented measurement model is constructed.The state estimation process after the measurement model switching is completed by the nonlinear SVSF method,thus the convergence rate and the stability of the initial alignment results is improved.Simulation results show that the method has the fast convergence and insensitivity to noise,and its alignment results are more stable and robust.In this paper,the gain of the first order SVSF algorithm is improved,and the gain of the second order SVSF algorithm is optimized.The SVSF nonlinear estimation method based on the fifth degree cubature Kalman filter is proposed.These all enriches the SVSF theory.And the SVSF theory is applied to solve the estimation divergence and noise sensitive issues in the initial alignment of SINS,the simulation results show the effectiveness and feasibility initial alignment method of SINS based on the SVSF algorithm.This has a certain reference significance for solving the problem of the state estimation in SINS and related fields.