插值改进EKF算法在组合导航中的应用

Application of interpolation-based improved EKF algorithm in integrated navigation

为了提高GPS/DR组合导航定位的精度和稳定性,提出一种基于插值公式的EKF(扩展卡尔曼滤波)改进算法。插值滤波算法继承了EKF实时递推结构,利用基于Stirling插值公式的差分方法代替EKF中非线性函数导数的计算。将插值公式展开的一阶项和二阶项作为函数近似分别得到DD1、DD2(一阶、二阶差分)滤波算法。插值滤波不必计算函数稚可比矩阵,大大降低了计算的复杂度,并改善了EKF算法中泰勒展开线性化造成的较大误差。根据GPS/DR组合系统的状态和观测方程,采用EKF、DD1和DD2滤波算法分别估计目标的状态信息。对比分析表明,插值滤波的精度和稳定性好于EKF算法,应用范围更为广泛。

In order to enhance position accuracy and stability of GPS/DR integrated navigation, an interpolationbased improved EKF （extended Kalman filtering） is still adopted, and difference arithmetic based on algorithm is presented. The recursion structure of EKF algorithm Stirling ＇s interpolation formula is used to substitute for derivative calculation of nonlinear functions. DD1 and DD2 （ first- and second-order differences） filtering algorithms are derived from the first- and second-order term function approximations in interpolation formula expansion. Due to avoiding computing Jacobian matrix, the calculation complexity of interpolation filtering is greatly reduced, and large model error caused by Taylor expansion linearization in traditional EKF is also improved. According to the state and observation equations of GPS/DR integrated system, EKF, DD1 and DD2 filtering algorithms are employed to estimate the states information of a given target respectively. Simulation results indicate that interpolation-based filtering could obtain higher stability and accuracy than EKF, and has better performance and larger application scope.