基于Gauss-Hermite求积分卡尔曼滤波的SINS非线性初始对准方法

SINS nonlinear initial alignment using Gauss-Hermite quadrature Kalman filter

为了改善大方位角初始对准精度和缩短收敛时间,在SINS动基座初始对准中引入了简化的Gauss-Hermite求积分卡尔曼滤波(QKF)方法.首先分析了Gauss-Hermite求积分中的单变量Gauss点及其系数配置方法,然后采用直接张量积法将单变量配置扩展后得到多变量Gauss点及其系数配置方法,给出了简化的QKF滤波算法.最后通过数学仿真分析比较了单变量积分点数为3的QKF(3点QKF)与比例对称采样UKF的对准性能,以及单变量积分点数取不同值(3,5和7)对QKF滤波性能的影响.结果表明:在动基座SINS大方位角初始对准中,3点QKF的对准精度远高于UKF的精度,方位角估计收敛速度也快于UKF,并且随着单变量Gauss积分点数的增加,QKF对准精度会进一步提高.

In order to improve the precision and shorten the convergence time of SINS（strapdown in-ertial navigation system）initial alignment with a large azimuth misalignment angle,a simplified Gauss-Hermite quadrature Kalman filter （QKF）is introduced into the SINS initial alignment on a moving base.First,the configuration method for one-dimensional Gauss points and their correspond-ing coefficients in Gauss-Hermite quadrature is derived,which is then extended to form the multidi-mensional Gauss points and their coefficients using the direct tensor method.A simplified QKF is presented.Finally,by means of mathematical simulation,the filter performance of UKF（unscented Kalman filter）based on scaled symmetric sampling and QKF using 3 points in one dimension in SINS initial alignment with a large azimuth misalignment angle is compared,and the influence of different point numbers（3 ,5 and 7 ）of one dimension on the QKF filter performance is also ana-lyzed.The simulation results show that under the condition of a large azimuth misalignment angle on a moving base,the alignment accuracy of a 3-point QKF is much higher than that of the UKF,and the azimuth angle estimation error convergence rate of the three-point QKF is also much faster than that of the UKF.With the increase in the number of one-dimensional Gauss-Hermite quadrature points,the alignment accuracy of the QKF can be further improved.