惯导初对准中的平方根无轨迹卡尔曼滤波

Square-Root Unscented Kalman Filter for Inertial Navigation System Alignment

针对无轨迹卡尔曼滤波(UKF)在递推过程中,有些情况下出现状态协方差逐渐失去正定性,导致计算发散现象,对状态协方差进行矩阵分解,在滤波中用其平方根进行计算,保证其正定性.采用平方根无轨迹卡尔曼滤波(SRUKF)对大失准角情况下惯性导航系统初始对准非线性ψ角模型进行估计.蒙特卡罗仿真结果表明,SRUKF与UKF在滤波精度和收敛速度上基本一致,SRUKF的数值稳定性优于UKF.

Covariance matrix of state gradually loses its positive definition, thus bringing about computational divergence in some recursive processes in unscented Kalman filters （UKF）. The covariance matrix of state is here decomposed and guaranteed nonnegative while its square-root used in the computation of the filter. The paper presents the square-root unscented Kalman filter （SRUKF） to estimate the psi-angle in the inertial navigation system having large misalignment on stationary and moved-base. Monte Carlo simulation results showed that SRUKF and UKF are basically uniform in their precision of filtering and rate of convergence yet SRUKF has the better performance in numerical stability than UKF.