GPS非线性估计中无导数卡尔曼滤波研究

Study of Derivative-Free Kalman Filting on nonlinear estimation for GPS

在GPS领域应用的非线性估计方法中,扩展Kalman滤波(EKF)存在稳定性差、计算量大等缺陷。基于非线性变换思想的UKF(Unscented Kalman Filtering)中状态方差阵易失去半正定性。本文引入了一种无导数卡尔曼滤波-基于重复确定性采样的平方根UKF(Square Root-Unscented Kalman Filter,SR-UKF)估计方法,并对其状态方差阵及随机噪声方差阵Cholesky分解更新公式做了改进,避免了导数的运算,有效地确保方差阵及其平方根的正定性从而抑止了发散。将这种无导数卡尔曼滤波应用于GPS/DR组合导航系统的状态估计上,仿真结果表明本文所改进的方法在滤波的精度和鲁棒性上均优于EKF和UKF。

The Extended Kalman Filter （EKF） as estimation algorithm for nonlinear systems on Global Positioning System（GPS）, providing an insufficiently stable representation in many cases , and it is difficult to operate .The Unscented Kalman Filtering（UKF） as a method based on nonlinear transformation is introduced. But the state covariance matrix of UKF can easily loses its positive semi- definiteness. A kind of derivative-fred Kalman tilting-Square Root-Unscented Kalman filter based on repeatedly definite sampling is proposed in this paper. Especially, formulas of state and random noise covariance matrix＇s Cholesky decomposition update are improved. The improvement avoids derivative calculation, guarantees positive definiteness Of covariance matrix and its square root so as to inhibit divergence. The improved SR-UKF method is applied to state estimation for GPS/DR integrated navigation system. Simulation results show that the improved SR-UKF method can obtain higher accuracy and better robustness than EKF, UKF.