Interval Kalman filtering algorithm and its application to carrier-phase integrated navigation system

The traditional Kalman filter cannot be used directly when some system parameters such as certain elements of the system matrix are not precisely known or gradually change with time. A system with some uncertain parameters can be described as an interval system; and a special robust filtering algorithm - interval Kalman filtering algorithm, is studied in this paper, which can be used to process a system with uncertain parameters according to the correlative interval algorithms. The detailed interval Kalman filtering equations are derived, its statistic performances and iterative form are similar to those of traditional Kalman filter, but its operators are interval matrixes. For a dual difference carrier-phase low-cost IMU/GPS (Inertial Measurement Unit/Global Positioning System) integrated navigation system, which is integrated with dual difference GPS measurement and IMU, the interval Kalman filtering algorithm is compared to the standard Kalman algorithm in the same simulation environment. Simulation results show that such filtering algorithm can provide the real-time accuracy error estimation to correlative navigation solution for improving the total performance of such integrated system. Its velocity accuracy can reach 0.01 m/s, the position error is less than 5 cm, and its attitude can be stabilized to 10-15 arc sec. Therefore, it can be applied to such kind of low-cost integrated navigation system.