In recent years, to reduce positioning cost for civil and robotic applications, low-cost inertial sensors especially Micro Electro Mechanical System (MEMS) types have been produced. Positioning Error of an inertial navigation system comprising low-cost inertial sensors increases due to significant uncertainty of noises, bias and drift of MEMS sensors in short times. Therefore, combination with an auxiliary system such as the Global Positioning System (GPS) is proposed in order to reduce the errors trough integration estimator algorithms. This paper aims developing a new estimation algorithm for integrated attitude and heading reference system (AHRS) with GPS. Kalman Filter is commonly used for linear systems and its extended version has been used for nonlinear system. Generally, the Kalman type estimators fall in trouble when the system exhibits nonlinear behavior and to overcome these issues, the predictive estimator is considered in the paper. Design process of Model Predictive Observer (MPO) is proposed based on the duality between the problems of control and estimation in linear systems. To assess the performance of the proposed method compared with the extended Kalnman filter, practical tests of AHRS/GPS have been done on car and flight vehicles. The test results of the designed MPO during all tests show the significant superiority in comparison to the extended Kalman filter.