Abstract: In this paper, a Nonlinear Adaptive Square-Root Unsented Kalman Filtering（NASRUKF） approach is described for 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 Unscented Kalman Filtering（SRUKF） for nonlinear filtering. The process noise covariance matrix Q or the measurement noise covariance matrix R is estimated straightforwardly in proposed NASRUKF. Thus, the positive semidefiniteness and symmetrical properties of the filter are improved. Simulation results show that NASRUKF performs better than SRUKF in the aspects of the accuracy, stability and self-adaptability.

Key words: Nonlinear Adaptive Square-Root Unsented Kalman Filtering（NASRUKF）, Kalman filtering, Square Root Unscented Kalman Filtering（SRUKF）, Sage-Husa filtering, nonlinear filtering, estimating

摘要： 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。

关键词: 非线性自适应平方根无迹卡尔曼滤波方法（NASRUKF）, 卡尔曼滤波, 平方根无迹卡尔曼滤波（SRUKF）, Sage-Husa滤波, 非线性滤波, 预估