In this thesis, a simple model that statistically represents an Inertial Measurement Unit (IMU) output has been studied. This model is then expanded to produce a model that incorporates terms that account for errors associated with high dynamics. Several techniques are used to determine the error statistics of the IMU model and categorize the performance of the IMU. These techniques include Allan variance charts, Monte Carlo simulations and autocorrelation functions. Equations for the position, velocity and heading error in a two and six degree of freedom system are developed. These analytical equations for the error growth are then verified using Monte Carlo simulations. Monte Carlo simulations are also used to compare the error bounds using both the simple model and high dynamic model. A novel Kalman filter is developed to couple GPS with an inertial measurement unit in order to bound the error growth. The Kalman filter estimates both a constant and drifting bias. The error bounds on the position, velocity and heading state estimations are compared to the error bounds in the simple modelís uncoupled case. The framework formulated from these models is intended as an aid for understanding the effects that the different error sources have on position, velocity, and heading calculations. With this information it is possible to determine the correct inertial measurement unit with identified error characteristics for a specific application.