Integration of inertial navigation system and Global Positioning System

In order to reduce the errors of an inertial navigation system (INS) and, at the same time, remain cost effective, an integration of the INS with the Global Positioning System (GPS) is considered. This integration proves to be quite beneficial and the errors of the INS are reduced greatly. In effect, a not very costly INS (one having considerable errors) can be integrated with a GPS system and the output can have the same, or even more, accuracy then a more costly INS. A strapped down inertial navigation system is considered and a single channel GPS receiver is integrated by using a Kalman filter. The mathematical treatment of the problem is presented.