Open Access
 Issue JNWPU Volume 37, Number 6, December 2019 1231 - 1237 https://doi.org/10.1051/jnwpu/20193761231 11 February 2020

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

## 1 卡尔曼滤波及其改进算法

### 1.2 卡尔曼滤波平滑

1) 固定点平滑:令yk=[y1, y2, …, yk]为k时刻内所有观测值组成的向量, 通过yk估计0到k-1时刻中某个时刻j(k=j+1, j+2, …)的状态xj的平滑称作固定点平滑。其平滑公式如下

2) 固定滞后平滑:利用yk来估计k-N时刻的状态xk-N, N为某个确定的固定滞后值, 该平滑称作固定滞后平滑。其平滑公式为

3) 固定区间平滑:利用固定时间区间(0, M]中得到的所有测量值yM=[y1, y2, …, yM]来估计区间中每个时刻的状态xk(k=1, 2, …, M), 该平滑称作固定区间平滑。平滑公式表示为

1) E步骤

2) M步骤

## 2 颤振时域判据

Z变换应用于(11)式并假设机翼系统有2个主要模态, 即M=4, 可得系统TVAR部分的特征多项式及展开形式

## 3 仿真与实测分析

### 3.1 仿真分析

 图1仿真信号时间历程
 图2仿真信号频率估计对比
 图3仿真信号FBP结果对比

### 3.2 实测分析

 图4实测信号时间历程与速度变化
 图5实测信号频率估计与FBP

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## All Figures

 图1仿真信号时间历程 In the text
 图2仿真信号频率估计对比 In the text
 图3仿真信号FBP结果对比 In the text
 图4实测信号时间历程与速度变化 In the text
 图5实测信号频率估计与FBP In the text

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