U-D分解的固定点平滑新算法及其在飞行试验中的应用

 本文根据Rauch固定点平滑公式,提出了一种U-D分解的固定点平滑新算法。这一算法不仅具有良好的数值稳定性和可靠性,而且计算量较少;计算效率是Bryson-Ho Y C固定点平滑计算效率的1.5倍以上。将这种新算法用于飞机运动状态初值的确定,提高了飞机气动参数辨识精度。

A NEW U-D FACTORIZATION-BASED FIXED-POINT SMOOTHER AND APPLICATOIN TO FLIGHT TEST

A new computationally efficient U-D factorization-based fixed-point smoother is developed by using Kalman filter and Rauch fixed-point smoother. In the new algorithm, the estimated error covariance propagation is divided into two parts and the difference of positive(semi) definite matrices that is subject to numerical instability and Kalman filter estimate for the new smoother are simplitied, a computationally burdensome covariance matrix inversion and large amount matrix multiplications are not involved. In order to get high numerical stability and computational efficiency, U-D factorization is used for the propagations of estimated error covariance of both the Kalman filter and the new smoother. The results of operation count comparison show that the new smoother presented in this paper is more than 1.5 times as efficient as Rauch's, Bryson-Frazier's, and Bryson-Ho Y C's fixed-point smoothers. If the dimension of state ix much larger than the dimension of process noises, the new algorithm will 2-5 times as efficient as the ordinary ones. Moreover, a new scheme for flight state smoothing and aerodynamic coefficient identification is presented in this present paper, and the new algorithm has been applied to determine the initial values of flight state to get high accuracy of aerodynamic coefficient estimation.