Inertial Navigation Systems (I) typically employ an Inertial Measurement Unit (IMU) to detect the angular velocity and the linear acceleration accurately using three orthogonal rate-gyroscopes and three orthogonal accelerometers, respectively. Error propagation analysis is one of the most important issues in INS which is addressed in many valuable research works. Even small errors in INS sensors are integrated and propagated over the processing time. These errors determine the performance and the accuracy of navigation using INS. Error analysis is based on error models. Error models also serve for real-time failure detection and also for the data fusion filter implementation in the INS algorithms. In this dissertation, individual analytical models are proposed for each INS error source. The proposed models accurately describe the position error of INS based on each measured error. The separate error models for gyroscopes, accelerometers and other error sources improve the accuracy of estimated velocity and position in INS, but the calculation cost increases compared with conventional error models. Then, all calculated errors along with the systematic errors due to variations of INS parameters such as acceleration and velocity variations of the earth are employed to propose a new method for INS error modeling in the Phi-angle frame work. This approach leads to design a new algorithm in the true frame which particularly considers all errors in INS such as earth rate variations and initial misalignments. In addition, the algorithm not only works for small angular between true frame and platform frame, but also it covers the whole range of the angular between these frames.