Flapping-wing Micro Air Vehicles (FMAV) comprise a new type of remote-controlled, semi-autonomous or autonomous aircraft that is significantly smaller than conventional aircraft. The concept of flapping-wing flight is inspired by birds and insects, though birds and insects use strikingly different modes of flapping to achieve the same result. Flapping-wing flight has been a large domain of exploration in the last few years, aiming to understand and mimic the ingenious strategies developed by animals during the navigation in three dimensions. While ornithopters deriving all of their lift and thrust from sets of flapping wings, have been demonstrated, applying Micro Electro Mechanical Systems (MEMS) inertial sensors to their navigation systems is an extremely challenging area. This paper presents an approach to designing an INS/GPS based navigation system using a Discrete Time Extended Kalman Filter. Navigation is one of the applications of state estimation techniques, and the reliable determination of attitude, velocity and position of the aircraft is essential for good flight performance during fully autonomous flight. In the current navigation concept, an Inertial Measurement Unit (IMU), providing sensor measurements, is used for this purpose, and the sensors used for navigation system are comprised of a MEMS gyro, a MEMS accelerometer, a MEMS magnetometer and a Global Positioning System. The Kalman filter provides an efficient computational means to estimate the state of a process, as it supports estimations of past, present, and even future states. In this paper three different schemes for a Discrete Time Extended Kalman Filter are used for navigation system. These include a single-stage seven-state discrete time extended Kalman filter, a two-stage cascaded discrete time extended Kalman filter, and a three-stage cascaded discrete time extended Kalman filter. Comparison and analysis of the three schemes are carried out, and it is demonstrated that the proposed algorithm is useful technique for flapping-wing flight.