一种U—D分解自适应推广卡尔曼滤波及应用

为了改善自适应卡尔曼滤波的数值稳定性和计算效率,防止滤波发散,本文在自适应推广卡尔曼滤波的基础上,利用U-D分解滤波,提出一种U-D分解自适应推广卡尔曼滤波新算法,并把该算法应用于飞行状态估计问題,仿真及实际飞行数据计算结果证明了本文方法的有效性.

A U-D Factorization-Based Adaptive Extended Kalman Filter and its Application to Flight State Estimation

In general, flight state estimation can be formulated as a non-linear time-variant state reconstruction problem that can be solved by extended Kalman filter (EKF). However, EKF, in fact, is not quite suitable for estimating flight state and parameters simultaneously; the situation gets even worse in the case where a prior value of parameter is not available and noise statistics are unknown. In view of this, a new U-D factorization-based robust adaptive EKF is proposed and applied to the flight state and parameter estimation of longitudinal motion of two types of Chinese aircrafts. The main features of the algorithm proposed here are: (1) By using Bierman's U-D factorization filter5], which has excellent numerical characteristics, the numerical stability of adaptive EKF can be greatly improved. (2) In order to insure that the estimation for noise covariance matrices Q and R are semi-positive and positive respectively, the computation formulations (eqs.21 and 22) for continuous on-line revision are introduced. These make the new algorithm robust and efficient. The results of both simulated and actual flight test data computations show that the new algorithm will give more accurate estimation results (see Table 1) than EKF for different initial values and noise statistics, especially for solving flight state estimation problem corrupted by time-variant noises. Moreover, the new algorithm has less requirements than EKF for aircraft maneuvering shapes, sample period, data length, initial values and noise statistic information, and has much better numerical stability and convergence than those of EKF or conventional adaptive EKF. The new algorithm can effectively prevent the divergence of adaptive Kalman filter. Even when conventional adaptive EKF diverges, the new algorithm can still give good estimation results. The new algorithm is also suitable for the real-time estimation of flight state.