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摘要:
针对弹性高速飞行器非线性、不确定性和刚体/弹性耦合的特点，提出了一种基于QR分解和滚动时域估计的状态/参数联合估计方法。首先，通过引入滚动时域策略，将状态/参数估计问题转化为固定变量数目的优化问题，能够较好地处理时变参数的估计问题。然后，利用前向动态规划原理，将到达代价的计算转化为最小二乘问题，并利用QR分解进行求解，从而给出了基于QR分解的到达代价更新方法。这样使得整个滚动时域估计方法都建立在优化的基础上，且引入了反馈机制，提高了估计精度和速度。仿真结果表明：滚动时域估计的精度明显优于扩展卡尔曼滤波，且基于QR分解的到达代价更新方法在速度上优于传统的基于估计误差协方差的到达代价更新方法。
Abstract:Considering the nonlinearity, uncertainty and rigid/elastic coupling of elastic hypersonic vehicles, a state/parameter joint estimation method based on QR decomposition and moving horizon estimation is proposed. First, this method transforms the state/parameter estimation problem into an optimization problem with fixed-number variables by introducing moving horizon strategy, and it can deal with the time-varying parameter estimation better than Kalman filter. Second, by utilizing the forward dynamic programming principle, the computation of arrival-cost is converted into a least-square problem that is solved by QR decomposition, and the arrival-cost update algorithm based on QR decomposition is given. In this way, the moving horizon estimation is based on optimization, and the feedback mechanism is introduced to improve the estimation accuracy and speed. The simulation results demonstrate that the accuracy of moving horizon estimation is obviously higher than that of extended Kalman filter, and the arrival-cost update strategy based on QR decomposition is better than the traditional arrival-cost update method based on the estimated error covariance in speed.
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图 2 EKF、MHE-EKF和MHE-QR方法估计结果的均方根误差
Figure 2. RMSE of estimation results of EKF, MHE-EKF and MHE-QR methods
图 3 不同方案时MHE-QR方法估计结果的均方根误差
Figure 3. RMSE of estimation results of different schemes using MHE-QR method
表 1 不同方法估计结果的均方根误差均值
Table 1. Average RMSE mean values of estimation results of different methods
方法 RMSE 
ωz/(10-3(°)· s-1) η1 
ω1/ (rad·s-1) MHE-QR1 0.536 3.4 0.037 7 0.15 0.87 MHE-QR2 0.472 3.3 0.029 6 0.097 0.62 MHE-EKF 0.548 3.4 0.039 0 0.17 0.90 EKF 1.2 5.2 0.088 3 0.47 2.86 MHE-S 3.2 5.7 0.39 1.41 EKF-S 3.5 7.0 0.37 2.47 
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表 2 不同方法的计算耗时
Table 2. Run time of different methods
方法 平均时间/(10-2 s) 最大时间/(10-2 s) MHE-QR1 2.44 4.74 MHE-QR2 2.35 4.78 MHE-EKF 2.48 7.56 EKF 0.66 1.27
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