有色噪声下的平方根UKF在天文自主导航中的应用

Square-Root Unscented Kalman Filter for Satellite Autonomous Celestial Navi-gation System with Colored Measurement Noise

针对由星敏感器和光学导航相机组成的卫星天文自主导航系统,传统的平方根UKF不能很好地解决测量噪声为有色噪声情况下的非线性滤波问题,导致导航系统的精度下降.为此,提出了一种有色噪声情况下的平方根UKF方法.同时,为了避免在数值计算的过程中,由于舍入误差而破坏误差协方差矩阵的正定性和对称性,在整个递推计算过程中,借鉴平方根Kalman滤波理论,采用协方差矩阵平方根进行递推计算,改善滤波算法的稳定性,协方差矩阵的平方根更新用cholesky分解和qr分解来计算.将该方法应用于卫星天文自主导航系统中,实验仿真结果表明,相对于传统的平方根UKF算法,所设计的平方根UKF算法能够很好地解决测量噪声为有色噪声情况下估计精度低问题.

To address the satellite autonomous celestial navigation system based-on star sensor/optical camera, traditional square-root unscented Kalman filter can not well solve the nonlinear filtering problem with colored noise, which leads to the navigation system accuracy decreased. So a square-rootunscented Kalman filter （CSRUKF） applied to measurement system with colored noise is proposed in this paper. In addition, in order to avoid destructing the positive and symmetry of covariance matrix caused by the errors of numerical calculation during the filtering procedure, the square-root of covariance matrix is adopted throughout recursive calculation, which improves the stability of filter. The square-root of covariance matrix update is calculated by cholesky decomposition and qr decomposition. The method was applied to satellite autonomous navigation systems. The simulation results show that, compared to traditional SRUKF, this proposed SRUKF can well solve the problem of poor estimation accuracy in measurement system with colored noise.