On the application of kalman filtering to correct errors due to vertical deflections in inertial navigation

There is a large literature on the application of Kalman Filtering to Inertial Navigation Systems. (See e.g., [2], [7], [8], [12]). In this paper in order to present a concrete problem, we shall deal only with Shipboard Inertial Navigation Systems (SINS), and in particular, we shall discuss only the application of Kalman filtering for correcting errors due to vertical deflection (VD) of gravity. After briefly reviewing the basic physical theory, we shall formulate the main problems and indicate some current engineering solution, emphasizing the potential unsolved problems and research areas. Of particular mathematical interest here is the way in which random fields enter a "time-domain" filtering problem.