H_∞滤波在无陀螺捷联惯导系统中的应用

Gyroscope-free strapdown inertial navigation system using H_∞ robust filtering

无陀螺捷联惯导系统角速度解算精度不高是其难以实现工程化瓶颈问题。为此,首先深入分析了无陀螺捷联惯导系统的角速度解算原理,并推导出了所用加速度计配置方案的角速度解算方程。然后创造性地构建了Kalman滤波器的状态方程和滤波方程,突破了以往采用Kalman滤波时必须引入额外观测信息(如GPS观测值)的模式。在此基础上构建了系统的H∞滤波器,并借助某型导弹的弹道数据,在外部噪声分别为白噪声和有色噪声的条件下对积分法、开方法、卡尔曼滤波器和H∞滤波器进行了仿真比较,验证了H∞滤波器具有较高的解算精度和对系统的不确定性具有良好的鲁棒性。

Gyroscope-Free Strap down Inertial Navigation System （GFS1NS） can play the role of inertial measurement and navigation by only using accelerometer. However, the low precision in calculating angular-velocity is always the bottleneck problem of application. The paper describes the principle of calculating angular-velocity in GFSINS and presents the calculating equations of the chosen nine accelerometers allocation scheme. Then the state and filter equations of Kalman filter are created, which breaks the conventional idea that additional measurement signal （such as GPS observations） is needed to build Kalman filter. A H∞ Robust Filter is designed to improve the calculation precision. In virtue of certain missile trajectory data, the simulation results of four calculating methods （integral, extraction, standard Kalman filter and H∞ robust filter） are given under the condition of white noise and colored noise respectively. After comparing all the simulation results, we can find that the H∞ Robust Filter has higher calculation precision and better robustness.