二阶段H_∞滤波在捷联惯导/里程计组合导航系统中的应用  

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

作　　者：赵洪松[1,2] 缪玲娟[1] 邵海俊 

机构地区：[1]北京理工大学自动化学院 [2]中国人民解放军94032部队

出　　处：《中国惯性技术学报》2015年第5期615-623,共9页Journal of Chinese Inertial Technology

基　　金：国家自然科学基金(61153002);总装备部预先研究项目(51309030104)

摘　　要：针对一类包含未知常值偏置的线性系统的状态估计问题,比如捷联惯导/里程计组合导航系统,由于扩展未知常值偏置为系统状态,导致系统状态维数比较高。当应用H∞滤波进行估计时,就会引起滤波算法的计算量大大增加,进而会影响其估计性能。为了解决这个问题,将H$滤波问题转化为Krein空间下的求解某种二次型的最小值问题,而求解该最小值可以使用Kalman滤波来解决。因此,通过采用二阶段Kalman滤波理论,在Krein空间下建立了二阶段H∞滤波算法,将H$滤波中的高维矩阵计算解耦成并行的低维矩阵计算,有效地解决了高维矩阵计算所带来的数值计算问题,降低了计算量,并且该算法有利于硬件并行运算设计,为进一步提高算法执行速度提供了可能。通过在捷联惯导/里程计组合导航系统中的仿真实验,验证了算法的有效性。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.

关 键 词：H∞滤波 二阶段Kalman滤波 状态估计 KREIN空间 RICCATI方程 

分 类 号：V249.3[航空宇航科学与技术—飞行器设计]