Research On Nonlinear Information Filter Algorithms

Many problems in real life can be described by nonlinear stochastic system models, for example rocket guidance and control, radar detection, satellite orbit and attitude estimation and so forth. Nonlinear filter technology is the optimal state estimation of the nonlinear stochastic system. For nonlinear stochastic system, information filter has the advantage that the state estimation equation is simple and directly propagates the inverse matrix of the covariance matrix. How to improve the estimation accuracy of information filter algorithm is one of the hotspots of information filter. In this paper, several nonlinear information filter algorithms are proposed to improve the estimation performance of the original algorithm. The main research works are as follows:1. Square root filter can improve the estimation accuracy and numerical stability of the algorithm, combining with the spherical simplex radial cubature Kalman filter, the square root spherical simplex radial Kalman filter is proposed. The new algorithm utilizes spherical simplex radial rule for the selection of integral points and the computation of corresponding weights. In the time update step and measurement update step, the square root factor of the covariance matrix is used to propagate and improve the stability and estimation accuracy of the algorithm.Combine with the algorithm and information filter algorithm, we propose a square root spherical simplex radial information filter algorithm. The simulation experiment of 3 dimensions Lorenz system and the multi-sensor fusion experiment of a two permanent magnet synchronous motor show that the new algorithm has higher estimation accuracy and better stability, and improves the accuracy and the numerical stability of the fusion results. Aiming at the specific nonlinear-linear combination system, to improve the square root spherical simplex radial information filter, we propose a nonlinear-linear square root spherical simplex radial information filter algorithm. The new algorithm utilized spherical simplex radial rule for the selection of integral points only in the time update step, the measurement update does not require the calculation of the integral points, and the calculation amount is reduced.The simulation results show that the new algorithm can reduce the running time when the estimated performance is the same as that of the general square root spherical simplex radial information filter.Due to strong tracking filter is robust to the model which is not accurate or has bad measurement,the square root spherical simplex radial Kalman filter based on strong tracking and the square root spherical simplex radial information filter based on strong tracking are proposed respectively.The error covariance matrix and its square root factors are updated in real time by introducing the time-varying fading factor,then the updated value is used to measurement update step and filter update step.The simulation results show that the new algorithm based on strong tracking has improved the estimation precision of system state significantly.2.According to the condition that the noise contained in the nonlinear system is non-Gaussian noise or the noise state is uncertain,the?H filter has better effect,combined with?H filter and square root spherical simplex radial information filter,a square root spherical simplex radial?H information filter is proposed.The simulation results of low-Gaussian noise,high-Gaussian noise,low non-Gaussian noise,high non-Gaussian noise and multi-sensor fusion system verify the effectiveness of the new algorithm.3.In order to further study the noise obey the non-Gaussian distribution system,based on rank statistics principle,a rank information filter algorithm is proposed.The new algorithm utilized rank sampling to select a series of integral points,which improves the estimation accuracy of the information state.The simulation results show that the rank information filter has higher estimation precision than the extended information filter and rank filter,and can better track state change of the system.Fused with rank information filter and?H filter,a rank?H information filter is proposed.The simulation results show that the rank?H information filter improves the estimation precision of the algorithm compared with the extended information filter and rank information filter.