Research On Nonlinear Filtering And The Application In Transfer Alignment Of Inertial Navigation System

Non-linear filtering technique is increasingly applied to various fields. This dissertation directs mainly at the researches on the two representative non-linear filtering algorithm: unscented Kalman filter and particle filter, and applies them to transfer alignment of inertial navigation system in large misalignment angle. The contents of the dissertation includes the following parts.Firstly, it briefly introduces several different non-linear filtering algorithms, and the application of non-linear filtering in initial alignment of inertial navigation system.Secondly, it presents in detail the principle of unscented transformation, the frame of unscented Kalman filter, and the sampling strategies of several unscented transformations widly used nowadays. In addition, this disseration analyses the limitations and functions of different sampling strategies, and studies main parameters influencing the precision of unscented transformation in the symmetrically distributed and simplex sampling through typical example simulations. UKF is one of Gaussian filter,and it is simple and easy to implement, but it must be confined to the condition that the nonlinear system model can be assumed as Gaussian distribution. Thus, UKF has no reliable convergence guarantee for nonlinear and non-Gaussian system.Thirdly, it introduces and analyzes the basic structure of particle filters, as well as the three problems restricting its functions: excessive calculation, particle degeneracy, and sample impoverishment. Aimming the three problems, the filter function of the algorithm is improved through the two steps - the creation of importance function and resampling.Fourthly, as an important improved algorithm of PF, UPF includes the up-to-date observation in the importance density function, and lowers the degree of particle degeneracy. Aimming to the disadvantage of poor real-time character of filter caused by excessive calculation, the standard UPF is optimized. This dissertation advances a new UPF algorithm, and confirms its rationality and validity. The specific steps are as follows: 1. Adopt combination of proposal distribution in the step of importance sampling. Namely, a part of particles are created through UKF, with the others through prior distribution to decrease the calculation. 2. Adopt SSUT based on the hyperspherical sampling; the number of sigma points in the symmetrically distributed sampling is 2n+1, and the number of SSUT is n+2. For the high-dimensional system like this, the calculaiton of the new SSUPF algorithm is slightly over half of the standard UPF.Fifthly, the intelligent computational algorithm has its unique advantage in terms of the complicated problems which can hardly be sovled by traditional optimizing techniques. The example simulations confirm the fact that the algorithm function is improved obviously with the intelligent computational algorithm in PF. This disseration mainly studies the PF algorithm based on particle swarm optimization, advances the new SSUPF algorithm based on the particle swarm optimization and the PSO-SSUPF algorithm based on combination of proposal distribution, and studies the influence of ratio parameter c on filter precision and rapidity in this algorithm.Sixthly, transfer alignment is an important approach in inertial navigation system. Since the conventional linear error model performs ineffectively the perfect filter result, this dissertation advocates the rapid tranfer alignment error model based on attitude angle, and conducts the filter estimation on the misalignment angle with UKF, SSUPF, and PSO-SSUPF based on combination of proposal distribution. The simulations confirm the feasibility and rationality of the non-linear algorithm in transfer alignment, and show the distinctions in terms of precision and rapidity in simulations of the three filters.