The robustness of navigation systems based on a Global Satellite Navigation System (GNSS) is crucial and can be achieved in many ways, e.g. by using smart antennas or switched beam antennas) or complementing the GNSS with a jamming resistent sensor system. In order to investigate this latter method, a comparison has been performed between a relatively new type of state estimator, called the Particle method based on a linear Kalman Estimator (KE) when both are applied to the problem of combining information from a GNSS with an Inertial Navigation System (INS). This report is a detailed description of this comparison. The comparison of the two estimators regards essentially their robustness towards different types of unmodeled errors in the three acceleration measurements. These errors consist of different combinations of white noise components and constant components (biases). KE uses a continuous linear error model. The task for the KE is to estimate the errors of the INS solution by using the difference between external measurements of velocity and position (from e.g. GPS) and the velocity and position as calculated by the INS. As the PE does not require linear system equations, it uses a nonlinear full state discrete model. The same external measurements are used as for the KE.english.