Application of two-stage H_∞ filter in SINS/Odometer integrated navigation system

For the state estimate of linear systems with unknown constant biases, such as SINS/Odometer integrated navigation system, the unknown biases are extended to be system states, which often make the state dimension significantly increased. When the H_∞ filter is used to estimate the system states, the computations required by the H_∞ filter may be significantly increased, hence the performance of the H_∞ filter would be degraded. In order to solve this problem, the H_∞ filtering problem is transformed into the problem of calculating the minimum value of certain quadratic forms in Krein space, and the Kalman filtering algorithm can be used to calculate the minimum value. Thus, by using the two-stage Kalman filtering theory, a two-stage H_∞ filtering algorithm is developed in Krein space. In this algorithm, the high dimensional matrix operations are decoupled into parallel low dimensional matrix operations, which effectively solve the problem of numerical calculations caused by high-dimensional matrix operations and reduce the computation amount. This algorithm is suitable for the parallel computing hardware design, which makes it possible to further improve the execution speed of this filtering algorithm. Simulation results of the SINS/Odometer integrated navigation system verify the effectiveness of this algorithm.