非线性自适应平方根无迹卡尔曼滤波方法研究

Research on adaptive square-root unsented Kalman filter for nonlinear system

针对带有附加噪声且噪声特性未知的系统,提出了一种非线性卡尔曼滤波方法——自适应平方根无迹卡尔曼滤波(NASRUKF)方法,该方法基于平方根滤波的思想,对传统的Sage-Husa自适应滤波算法进行了改进,并与平方根无迹卡尔曼滤波(SRUKF)算法相结合用来进行非线性滤波。该算法能直接对非线性系统的状态方差阵和噪声方差阵的平方根进行递推与估算,确保状态和噪声方差阵的对称性和非负定性。将所提方法通过计算机仿真技术与SRUKF算法进行对比,结果表明NASRUKF方法在滤波精度、稳定性和自适应能力方面均优于SRUKF方法。

In this paper, a Nonlinear Adaptive Square-Root Unsented Kalman Filtering(NASRUKF)approach is describedfor nonlinear systems with additive noise which have unknown statistical characteristics. Based on the square-root algorithm,the traditional Sage-Husa adaptive filter’s estimator is modified and combinated with the Square Root UnscentedKalman Filtering(SRUKF)for nonlinear filtering. The process noise covariance matrix Q or the measurement noise covariancematrix R is estimated straightforwardly in proposed NASRUKF. Thus, the positive semidefiniteness and symmetricalproperties of the filter are improved. Simulation results show that NASRUKF performs better than SRUKF in theaspects of the accuracy, stability and self-adaptability.