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GPS and Inertial Navigation Systems (INS) are increasingly used for positioning and attitude determination in a wide range of applications. Until recently, the very high cost of the INS components limited their use to high accuracy navigation and geo-referencing applications. Over the last few years, a number of low cost inertial sensors have come on the market. Although they exhibit large errors, GPS measurements can be used to correct the INS and sensor errors to provide high accuracy real-time navigation. The integration of GPS and INS is usually achieved using a Kalman filter which is a sophisticated mathematical algorithm used to optimise the balance between the measurements from each sensor. The measurement and process noise matrices used in the Kalman filter represent the stochastic properties of each system. Traditionally they are defined a priori and remain constant throughout a processing run. In reality, they depend on factors such as vehicle dynamics and environmental conditions. In this research, three different algorithms are investigated which are able to adapt the stochastic information on-line. These are termed adaptive Kalman filtering algorithms due to their ability to automatically adapt the filter in real time to correspond to the temporal variation of the errors involved. The algorithms used in this research have been tested with the IESSG's GPS and inertial data simulation software. Field trials using a Crossbow AHRS-DMU-HDX sensor have also been completed in a marine environment and in land based vehicle trials. The use of adaptive Kalman filtering shows a clear improvement in the on-line estimation of the …