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浙江大学学报(工学版)  2025, Vol. 59 Issue (12): 2459-2471    DOI: 10.3785/j.issn.1008-973X.2025.12.001
电子与通信工程     
利用改进卡尔曼滤波提高回波信号ToF精度
陈宇豪(),吴瑾*(),李懿峰,陆小霞,王奕媛
南京航空航天大学 民航学院,江苏 南京 211106
Improving ToF accuracy of echo signals using improved Kalman filtering
Yuhao CHEN(),Jin WU*(),Yifeng LI,Xiaoxia LU,Yiyuan WANG
College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China
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摘要:

道面覆盖物(水/冰/雪)的超声波回波信号信噪比(SNR)较低,导致起振点难以准确提取,影响渡越时间(ToF)的估计精度. 为此,提出基于总变差和贝叶斯估计的自适应卡尔曼滤波方法(TV-BAKF). 该方法利用总变差法分析滑动窗口内的噪声分布,获取反映信号噪声水平和特征的差分因子,并结合贝叶斯估计动态调整过程噪声协方差和测量噪声协方差. 进行仿真测试,并与其他滤波方法(改进小波变换、改进Savitzky-Golay(S-G)滤波、自适应无迹卡尔曼滤波(AUKF)、变分贝叶斯自适应卡尔曼滤波 (VBAKF))的效果进行对比. 结果表明,TV-BAKF在兼顾滤波后信号平滑度的同时,相位和幅值保真度分别达0.915 rad和0.917,且噪声滤除效果较好,均方误差低于0.342. 对5类覆盖物(水、冰、雪浆、湿雪和干雪)的测试表明,TV-BAKF对冰、水和雪浆的深度检测的平均误差小于0.55 mm,对湿雪和干雪的平均误差不超过0.96 mm,验证了其在低信噪比条件下ToF估计的高精度特性.

关键词: 水/冰/雪深度超声波回波信号自适应卡尔曼滤波总变差法贝叶斯估计    
Abstract:

The ultrasonic echo signals from pavement coverings (water/ice/snow) typically exhibited low signal-to-noise ratio (SNR), making it challenging to accurately extract the onset point and thus affecting the time-of-flight (ToF) estimation precision. To address this issue, a total variation and Bayesian-based adaptive Kalman filtering (TV-BAKF) method was proposed. The method employed total variation analysis to assess noise distribution within a sliding window, deriving a differential factor that reflected both noise levels and signal characteristics. Combined with Bayesian estimation, it dynamically adjusted the process noise covariance and measurement noise covariance. Simulation tests were conducted and comparative analysis was performed with other filtering methods (improved wavelet transform, improved Savitzky-Golay (S-G) filter, Adaptive Unscented Kalman Filter (AUKF), and Variational Bayesian Adaptive Kalman Filter (VBAKF)), and the results showed that the TV-BAKF method maintained signal smoothness while achieving 0.915 rad phase fidelity and 0.917 amplitude fidelity, respectively, with favorable noise removal performance and a mean square error below 0.342. Testing on five types of coverings (water, ice, slush, wet snow, and dry snow) showed average depth detection errors below 0.55 mm for ice, water, and slush and no more than 0.96 mm for wet snow and dry snow, confirming its high-precision ToF estimation capability for low-SNR conditions .

Key words: water/ice/snow depth    ultrasonic echo signal    adaptive Kalman filtering    total variation method    Bayesian estimation
收稿日期: 2025-05-21 出版日期: 2025-11-25
CLC:  TB 551  
基金资助: 机场跑道表面冰/雪/水自动化检测评估技术(SA152);2025年江苏省研究生科研与实践创新计划资助项目(KYCX25_0616).
通讯作者: 吴瑾     E-mail: 992535572@qq.com;wujin@nuaa.edu.cn
作者简介: 陈宇豪(1997—),男,博士生,从事机场跑道智能检测研究. orcid.org/0000-0002-9340-0913. E-mail:992535572@qq.com
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引用本文:

陈宇豪,吴瑾,李懿峰,陆小霞,王奕媛. 利用改进卡尔曼滤波提高回波信号ToF精度[J]. 浙江大学学报(工学版), 2025, 59(12): 2459-2471.

Yuhao CHEN,Jin WU,Yifeng LI,Xiaoxia LU,Yiyuan WANG. Improving ToF accuracy of echo signals using improved Kalman filtering. Journal of ZheJiang University (Engineering Science), 2025, 59(12): 2459-2471.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2025.12.001        https://www.zjujournals.com/eng/CN/Y2025/V59/I12/2459

图 1  不同Q、R组合的滤波结果影响(幅值、信噪比和相位滞后)
图 2  TV-BAKF算法框架
图 3  不同信噪比下的超声波窄带回波信号模拟
图 4  低温环境舱、各类覆盖物样本及试验装置图片
图 5  探头型号比选流程
图 6  3种信噪比下卡尔曼滤波器关键参数的变化
图 7  3种信噪比下遗忘因子α和β
图 8  4种Q、R初参数组合下P和K变化及滤波效果
图 9  不同卡尔曼滤波方法(及Q-R组合)的Lissajous图
SNR/dBMSE$ {J_{{\text{smooth}}}} $$ {J_{{\text{phase}}}} $/rad$ {J_{{\text{amp}}}} $
改进小波变换250.0134.340.0650.975
200.0788.420.0840.943
140.51318.270.1080.922
改进S-G滤波250.0256.240.0620.946
200.16813.160.1040.914
140.82122.030.1710.881
UAKF250.0223.190.0820.928
200.1028.130.1510.877
140.69817.240.2450.823
VBAKF250.0152.140.0520.938
200.0925.320.2340.897
140.44615.880.2080.843
TV-BAKF250.0152.770.0420.984
200.0636.530.0940.947
140.34217.320.1450.917
表 1  5种滤波方法下的滤波效果评价
图 10  不同覆盖物(包括水/冰/雪浆/湿雪/干雪和混合覆盖物)的信噪比和波形特征研究流程
图 11  3种滤波方法的起振点估计结果
图 12  5种滤波方法对于5种覆盖物的深度计算误差与SNR分布的散点图
图 13  5种滤波方法下5种覆盖物深度计算误差小提琴图
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