**Part 1**

**Literature Review and Theoretical Developments** 

**0**

**1**

*USA*

*University of Florida*

**Fundamentals of GNSS-Aided Inertial Navigation**

GNSS-aided inertial navigation is a core technology in aerospace applications from military to civilian. It is the product of a confluence of disciplines, from those in engineering to the geodetic sciences and it requires a familiarity with numerous concepts within each field in order for its application to be understood and used effectively. Aided inertial navigation systems require the use of kinematic, dynamic and stochastic modeling, combined with optimal estimation techniques to ascertain a vehicle's navigation state (position, velocity and attitude). Moreover, these models are employed within different frames of reference, depending on the application. The goal of this chapter is to familiarize the reader with the

The goal of a navigation system is to determine the state of the vehicle's trajectory in space relevant to guidance and control. These are namely its position, velocity and attitude at any time. In inertial navigation, a vehicle's path is modeled kinematically rather than dynamically, as the full relationship of forces acting on the body to its motion is quite complex. The kinematic model incorporates accelerations and turn rates from an inertial measurement unit (IMU) and accounts for effects on the measurements of the reference frame in which the model is formalized. The kinematic model relies solely on measurements and known physical properties of the reference frame, without regard to vehicle dynamic characteristics. On the other hand, in incorporating aiding systems like GNSS, a dynamic model is used to predict error states in the navigation parameters which are rendered observable through the external measurements of position and velocity. The dynamics model is therefore one in which the errors are related to the current navigation state. As will be shown, some errors are bounded while others are not. At this point, we make the distinction between the aided INS and free-navigating INS. Navigation using the latter method represents a form of "dead reckoning", that is the navigation parameters are derived through the integration of measurements from some defined initial state. For instance, given a measured linear acceleration, integration of the measurement leads to velocity and double integration results in the vehicle's position. Inertial sensors exhibit biases and noise that, when integrated, leads to computed positional drift over time. The goal of the aiding system is therefore to help

**1. Introduction**

**2. Background**

**2.1 Modeling motion**

relevant fundamental concepts.

estimate the errors and correct them.

Ahmed Mohamed and Apostolos Mamatas
