Analysis Of Nonlinear Alignment Methods And Analytical Performance Of Aided Navigation Systems

Strapdown inertial navigation system (SINS) has been more and more widely used in both civil and military fields. SINS is established based on Newton’s kinematics law, and therefore the integration is needed, which determines the initial alignment must be com-pleted first before SINS entering work. It is impossible for long endurance of navigation simply rely on SINS due to the drifts of inertial measurement units (EVIU), various inte-grated navigation systems are brought into being for further improving the performance of SINS. The analytical performance of aided SINS is studied under different auxiliary means, which may helpful for the design of integrated navigation system.Firstly, the mechanization of SINS is studied and the error equations are deduced in detail based on the arrangement. From the deduction process, it can be seen that the error equations of SINS is essentially nonlinear. In order to simplify the analysis and design, the error equations can be simplified through small angle approximation. The initial alignment and performance analysis of aided SINS are based on these error models.Secondly, the linear Kalman filtering algorithm is no longer applicable for solving the problem of initial alignment in the case of large azimuth misalignment. In order to solve the problem, EKF, UKF and CKF which are typical algorithms under Gaussian fil-tering framework are studied in detail. EKF algorithm is carried out by first order Taylor approximation, which introduces the linearization error, and need to solve the Jacobian matrix of the nonlinear function, all these make it complex to achieve; UKF is simply based on the idea that " it is easier to approximate a Gaussian distribution than it is to approximate arbitrary nonlinear functions", which makes it lack of rigorous mathematical proof; The realization step of CKF can be considered as the special case of UKF, but it is based on " Spherical-Radial" integral rule which makes the algorithm more theoretical than UKF. In order to reveal the difference of UKF and EKF, typical nonlinear functions are studied. It shows that UKF estimates the mean more accurate than EKF, but estimate variance less accurate in some case.Then the three filters are used to solve the alignment problem, simulation results show that the UKF algorithm is the proper one.For real SINS, the system noise and measurement noise are unknown or no-Gaussian, the Sage-Husa estimator based on maximum a posteriori estimation which is used to es-timate the variance of the noise in real time, together with UKF is used to carry out ini- tial alignment of large azimuth misalignment. It is derived through simulation that the adaptive UKF method can improve the accuracy of alignment but reduce the speed of alignment.Thirdly, EKF, UKF, CKF and other filtering algorithms in initial alignment belong to open-loop control strategy, the accuracy is generally inferior to closed-loop control strat-egy. In order to improve the accuracy of alignment, the star sensor is introduced to provide high precision attitude information as a reference input to form a closed-loop system, in this case, the initial alignment problem can be converted into attitude determination prob-lem. The attitude determination problem can be solved by SO(3) attitude observer and its simplified form, and the calibration of the gyroscope constant is completed at the same time by an observer. The attitude observer is proved stable in the sense of Lyapunov. The feasibility of the observer for initial alignment and gyroscope constant calibration is verified by simulations.Finally, in order to improve the performance of SINS, more and more navigation systems are introduced as auxiliary part to constitute integrated navigation systems, which not only improve the accuracy but also enhance fault tolerance of system. Yet, the SINS error-state-model dependency on time and trajectory implies no closed-form solution for the performance. Based on the stability of Kalman filter, the relationship of aided SINS performance, inertial measurement units quality, measurement quality and sort of auxil-iary is established through algebraic Riccati equations. From this point of view, it bring insight into the design of an integrated navigation system.