﻿ 弹性高速飞行器的状态/参数滚动时域估计<sup>*</sup>
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State/parameter moving horizon estimation for elastic hypersonic vehicles
CHEN Erkang, JING Wuxing, GAO Changsheng
School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
Received: 2018-05-15; Accepted: 2018-07-28; Published online: 2018-08-22 18:07
Foundation item: National Natural Science Foundation of China (11572097)
Corresponding author. JING Wuxing, E-mail: jingwuxing@hit.edu.cn
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.
Keywords: hypersonic vehicle     elasticity     moving horizon estimation     state estimation     parameter estimation     QR decomposition

1 弹性高速飞行器数学模型

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2 基于QR分解的滚动时域估计 2.1 问题描述

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2.2 基于QR分解的到达代价计算方法

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2.3 滚动时域估计问题的求解

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3 仿真分析

 图 1 输入信号 Fig. 1 Input signal

 图 2 EKF、MHE-EKF和MHE-QR方法估计结果的均方根误差 Fig. 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 Fig. 3 RMSE of estimation results of different schemes using MHE-QR method

 方法 RMSE / (10-3(°)) ωz/(10-3(°)· s-1) η1 1 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

 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

4 结论

1) 状态/参数联合估计方法的精度远高于只估计状态的方法。由于弹性高速飞行器弹性模态的固有频率并非常数，会随飞行器状态变化而变化，因此对其进行在线估计是非常必要的，能够有效提高状态估计的精度。

2) 滚动时域估计的精度明显高于EKF。相较于传统的EKF更新方法，QR分解更新到达代价在精度类似的同时，具有更快的计算速度(最大计算耗时优于EKF)。这得益于QR分解更新到达代价的策略利用了滚动时域估计的结果，形成了反馈机制，并通过直接求解优化问题更新到达代价。

3) 传感器采用布置方案2时的滚动时域估计结果好于布置方案1。这是由于方案2通过引入有效信息预估而进一步提升了估计效果。

4) QR分解更新到达代价的滚动时域估计方法的最长计算耗时低于采样速率，具有实际应用的潜力，后续应继续研究更快的优化算法，提高计算速度。

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#### 文章信息

CHEN Erkang, JING Wuxing, GAO Changsheng

State/parameter moving horizon estimation for elastic hypersonic vehicles

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(2): 291-298
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0273