SINS的SRC-KF姿态估计算法

The SINS'SRC-KF Attitude Estimation Modeling Algorithm

基于飞行器载体SINS姿态计算精度要求,提出了一种SINS(strap-down inertial navigation system)的球面径向容积卡尔曼(spherical-radial cubature Kalman filtering,SRC-KF)姿态确定算法。该算法把笛卡尔坐标系中状态向量变换到球坐标系中,通过Gauss-Hermite求积计算获得2n个球面径向容积点及其权值系数来逼近计算系统状态估计及其方差矩阵,其计算精度可达到三阶;采用四元数姿态建模方法构建新型SINS状态变量与噪声向量相关的姿态方程模型,利用伪观测向量构建观测噪声与四元数相关的观测方程模型,设计系统噪声方差分离计算算法进行系统噪声方差计算,引入拉格朗日乘子算法计算四元数估计均值,最后利用SINS/CCD姿态估计仿真系统开展的SINS的SRC-KF姿态模型算法进行仿真验证。通过与中心差滤波(CDKF)和无迹卡尔曼滤波(UKF)算法计算结果进行对比,可以看出SRC-KF算法具有计算精度高以及数值计算稳定等特点。

We propose the spherical-radial cubature integral Kalman filtering （SRC-KF） algorithm based on the high-precision requirements for oSINS＇ attitude determination on aircraft according to Bayesian optimal estimation theory. We obtain the 2n spherical-radial cubature sampling points and their designed sampling points＇ weights to achieve optimal estimation of the system state vector, thier parameters and their variance matrix through the Gauss-Hermite Quadrature numerical approximation method and the state vectors coordinates transformation from Cartesian coordinate system to spherical coordinate frame, the calculation precision of which can be up to the third order. Using the attitude quaternion method we constructed a new SINS attitude determination nonlinear error model, whose system noise vector depends on system state vector. Meanwhile we constructed a measurement equa- tion whose measurement noise vector depends on quaternion measurement vector by the pseudo obser- vation vector method, and calculated the weighted average of estimated quaternion with Lagrangian operator, and carried out the system noise variance calculation with the system noise variance separa- tion algorithm we designed. Finally we conducted the SINS attitude estimation SRC-KF algorithm simulation on the SINS/CCD attitude estimation experiment platform. It can be seen that the SRC-KF algorithm calculation accuracy was higher than others and has better numerical stability through com- parison of the CDKF and UKF algorithms; verifying the feasibility and calculation accuracy of SRC- KF algorithm.