TABLE OF CONTENTS In this chapter, the following is presented for an integrated terrestrial navigation system:
strap-down navigation systems.
local level navigation frame mechanization equations.
perturbation form of navigation system error equations.
navigation system attitude error equations-psi formulation.
navigation system error equations using alternative velocity error.
baro-inertial vertical channel mechanization and error equations.
Inertial navigation systems for terrestrial navigation can be, and have been, mechanized in either a gimballed platform or as a strap-down unit. Most current navigation systems use strap-down sensors mechanized as a strap-down navigator. The mathematical forms for these two mechanizations differ slightly; therefore, only equations describing a strap-down mechanization are presented in detail.
Equations describing navigation states (position, velocity, and attitude) for strap-down navigation system implementation referenced to a local level navigation frame are developed. The resulting differential equations are nonlinear. In developing these equations, the objective is to form them in terms of sensed accelerations and rates, rather than as applied and reactionary forces and moments, as in the case of forming dynamic equations of motion. These sensed accelerations and rates are provided by inertial sensors described in Chapter 6.
An integrated navigation system combines data from navigation states generated by these dynamic equations with independently obtained redundant data in a Kalman filter algorithm. The form of the algorithm used requires a linearized error form of the navigation state equations; therefore, several error representations are presented. There are many different approaches (design alternatives) in forming these linearized equations, each with their advantages and disadvantages. Examples of different...
