Nonlinear Gaussian Filtering Algorithm And Its Application On Navigation System

The nature of the world is nonlinear.For nearly half a century,nonlinear filtering technology has always been a research hotspot in the field of engineering application.And it is widely used in many engineering fields,such as aircraft attitude estimation,navigation,target tracking,signal processing,image processing,fault diagnosis,and even agricultural cultivation.Among the numerous Gaussian approximation filter algorithms,Gauss-Hermite quadrature filter(GHQF)has been proved to be the one and only one numerical stability analytic nonlinear Gauss approximation filter,which has the highest estimation accuracy.But for high dimensional systems,the traditional GHQF algorithm extends one-dimensional Gauss-Hermite quadrature rules for the multidimensional system using the tensor product directly.This also leads to the exponential growth of the number of integral points along with the growth of state variable dimension.And the filter efficiency declines greatly,even result in the "curse of dimension",so the traditional GHQF algorithm is difficult to apply in high dimensional system.Therefore,since this algorithm is proposed,it has not been paid attention and well developed.This paper focuses on improving the efficiency of the GHQF algorithm,and tries to solve the "curse of dimension" problem of the GHQF algorithm.Then,the accuracy advantage of GHQF algorithms can be used in engineering applications.The main research works of this paper are as follows:1.Several typical nonlinear filtering algorithms are studied in this paper,and it is analyzed the accuracy of these algorithms using the accuracy of the Taylor expansion where CKF,UKF and GHQF are able to capture.And it is pointed out that GHQF has an unparalleled advantage among these sampling filtering algorithms.The efficiency of these algorithms is compared quantitatively by computing floating point operations of these algorithms.It is found that GHQF has high precision,but its amount of calculation has exponential growth as the system dimension increases.So it is difficult to be applied in high dimensional systems,this also provides a theoretical basis for the later research.2.Consider that in practical nonlinear system model,only partial state variables are nonlinear.Thus,we refine a nonlinear system with special structure,and compare it with the previous nonlinear models.The results show that the proposed nonlinear model is more general.For this kind of model,a dimension reduction GHQF filter is proposed,which can reduce the unnecessary calculation of these nonlinear systems.So GHQF with high precision can be applied in this kind system.And the floating point operations of dimension reduction GHQF are computed and result show that the calculation of dimension reduction GHQF runs much lower than that of GHQF.And compared with RBPF,the dimension reduction GHQF has higher accuracy and lower amount of calculation.3.In order to reduce the calculation of GHQF further,a dimension reduction SGHQF algorithm based on sparse grid quadrature rules is proposed.Then,through the comparision and analysis,it is found that UKF is a special case of SGHQF.And the order of accuracy is GHQF>SGHQF>UKF.The simulation results show that the accuracy of SGHQF is slightly lower than that of GHQF,and higher than that of UKF and CKF.The efficiency of the algorithm is further improved as well.4.In engineering application,the initial alignment of SINS is reserched.The initial alignment model of large misalignment angle in strapdown inertial navigation system is derived and the error model of dimension reduction GHQF is presented.The dimension reduction GHQF is applied to initial alignment of SINS.This paper proposes an improved alignment algorithm in inertial frame,which based on the idea that the projection of gravity in the horizontal frame is zero and horizontal alignment is rapid.First,we establish an accurate horizontal coordinate system with the dimension reduction GHQF algorithm,so that the swing disturbance is separated.Then,the initial alignment is carried out with the principle of inertial system.Simulations and experiments show the effectiveness of the proposed algorithm,and the accuracy of the inertial system is improved.