Direct Kalman Filtering of GPS/INS for Aerospace Applications

In integrated navigation systems Kalman filters are widely used to increase the accuracy and reliability of the navigation solution. Usually, an indirect Kalman filter formulation is applied to estimate the errors of an INS strapdown algorithm (SDA), which are used to correct the SDA. In contrast to that, in the direct Kalman filter formulation total quantities like position, velocity and attitude are among the state variables of the filter, which allows them to be estimated directly. This contribution investigates the influence of these two different approaches of Kalman filtering on the overall system performance of a loosely coupled GPS/INS system for aerospace applications. Both filter formulations were implemented and compared via Monte Carlo simulation runs with focus on the accuracy of the estimated inertial sensor biases and on GPS drop out situations. We found a comparable performance of both navigation algorithms concerning attitude and position errors as well as inertial sensor bias estimation as long as GPS aiding was available. However, the simulation results indicate a superior performance of the direct Kalman filter formulation in GPS drop out situations, which can by explained by the way the inertial measurements are processed.