The cost of inertial navigation systems (INS) has decreased significantly during recent years using micro-electro-mechanical system technology in production of inertial measurement units (IMUs). However, these IMUs do not provide the accuracy and stability of their classical mechanical counterparts which limit their applications. Hence, the error control of such systems is of the great importance which is achievable using external information via an appropriate fusion algorithm. Traditionally, this external information can be derived from global positioning system (GPS). But it is well known that GPS data availability and accuracy are vulnerable to signal-degrading circumstances and satellite visibility. We introduce a standalone attitude and heading reference system (AHRS) algorithm which employs the IMU and magnetometers data in an averaging manner. The averaging method is different from a simple smoothing procedure, since it takes the rotations of the platform (during the averaging interval) into account. The proposed AHRS solution is further used to provide additional attitude updates with adaptive noise variances for the integrated INS/GPS system during GPS outages via a refined loosely coupled filtering procedure, making the error growth well restrained. Functionality of the algorithm has been assessed via a field test. The results indicate that the proposed procedure outperforms the traditional integration scheme in different situations, while the latter almost loses track of the movements of the vehicle after 60-second GPS outages.