Analytic Evaluation of Fine Alignment for Velocity Aided INS

Coarse attitude initialization procedure is used to determine the initial attitude of the inertial navigation system. To improve the accuracy of the attitude to a desired value, fine alignment (FA) process is employed. In stationary conditions, zero velocity updates are usually used to achieve such goal. In this paper, an analytic evaluation of the steady-state properties of the FA process is presented. The contribution of this paper is twofold: 1) closed-form analytic solutions to the error-state covariance of the FA process are derived and 2) semianalytic solutions to the convergence time of the error-state covariance are shown. With such closed-form solutions at hand, insight can be gained into the parameters involved in the FA process in preliminary design process. Simulation and field experiments are given to support the analytical expressions.