This thesis presents an estimation algorithm to combine Global Positioning System (GPS) and Inertial Navigation System (INS) measurements to estimate the sideslip, yaw rate, heading and yaw rate gyroscope bias using a model based estimator. Detailed nonlinear models are developed and are linearized in order to simplify the model of the lateral dynamics for the estimator model. Additionally, a non-linear roll model is developed and used to help demonstrate the effects of weight transfer on the lateral dynamics of the vehicle. A Kalman filter is used to combine the GPS and INS measurements in the model based estimator. A method to determine the estimation errors due to the model error is also developed. The estimation algorithm is tested in simulation with a correct and incorrect estimator model using a single GPS antenna and a dual GPS attitude system. Residuals are used to provide insight into the accuracy of the estimator model. Additionally, the algorithm is tested on experimental data using a 2000 Blazer with known model parameters. Finally, a method for estimating the tire cornering stiffness to improve the state estimation is shown for both experimental and simulated data.