Inertial Navigation Systems are one of the most important systems used to determine position, velocity and attitude ofmoving vehicles such as ships, airplanes, missiles, and so on. The base of this science is Newton’s laws. In these systems, three accelerometers and three gyroscopes are used to measure linear accelerations and angular velocities of vehicles, respectively. By using of output of these sensors and special inertial algorithms in different frames, parameters of vehicle such as position, velocity and attitude are calculated. In this paper, firstly, different frames such as body, inertial, ECEF and NED coordinate system are introduced. Then algorithms of inertial navigation in these frames are proposed and diagrams of navigation in any coordinate system will be presented in suitable method. In the following, simulations of INS in inertial, ECEF and NED frame are carried out by Simulink software. For this purpose, three different motion scenarios in two and three-dimensional coordinates are investigated and their simulation results will be brought. The results of simulation show that the algorithms of inertial navigation in different frames have good performance and suitable accuracy in navigation. Also for simulation of any other motion scenarios, navigation of vehicle is done by outputs of accelerometers and gyroscopes and presented simulator profile. At the end of this paper, performance evaluation of inertial navigation systems, general model of inertial sensors and integration between INS and GPS using Kalman filter will be noted.