卡尔曼滤波方法在腔衰荡光谱技术探测气体中的应用

doi:10.3964/j.issn.1000-0593(2024)10-2727-06

摘要
参考文献
相关文章 (15)

全文: PDF (6864 KB)
输出: BibTeX | EndNote (RIS)

摘要：腔衰荡光谱技术(CRDS)是一种高灵敏度的痕量气体浓度测量技术，其中衰荡时间的处理尤为重要。为减小由采集和实时测量过程中的噪声影响而引入的衰荡信号测量误差，采用了卡尔曼(Kalman)滤波处理腔衰荡光谱。该方法通过传统滤波方法预处理获取卡尔曼滤波参数观测噪声协方差σ²_v(R)，并调整过程激励噪声协方差σ²_w(Q)，评估滤波效果来优化测量结果。采用含有白噪声的模拟衰荡信号，利用线性回归总和法(LRS)拟合出本底衰荡时间和衰荡时间并进行卡尔曼滤波处理。从均值、标准偏差、残差标准偏差(RMSE)和不同噪声水平四个方面来比较分析，获取合适的Q值范围，分别是小于1×10^-7和0.001。实验条件下，应用基于中心波长405 nm的二极管激光器和反射率达99.99%以上的高反镜搭建的CRDS气体检测系统，进行大气环境下的NO₂浓度测量。采用卡尔曼滤波对本底衰荡时间和衰荡时间进行处理分析。实验结果表明：(1)选取Q值小于1×10^-7的卡尔曼滤波处理本底衰荡时间，滤波后的最低检测限提高了9.12倍，并达到4.9×10^-11；(2)取Q值为0.001处理衰荡时间，保留了时间响应信息，达到明显的降噪作用；(3)系统时间分辨率为1 s，相比于以往降低时间分辨率以提高检测限的方法，卡尔曼滤波方法提升了系统灵敏度。实验结果与模拟结果的吻合度，验证了卡尔曼滤波在稳定性和降噪方面的效果。卡尔曼滤波方法在CRDS光谱探测气体的应用，具有很好的实用性，为其他气体的测量优化提供了方法和参考依据。

关键词：腔衰荡光谱；卡尔曼滤波；气体检测；降噪；检测限

Abstract：Cavity Ring-Down Spectroscopy (CRDS) is a highly sensitive trace gas concentration measurement technique in which the processing of ring-down time is crucial. This paper adopts the Kalman filter to process the cavity ring-down spectroscopy to reduce the measurement error introduced by noise during the collection and real-time measurement process. This method preprocesses with the traditional filtering method to obtain the observation noise covariance σ²_v(R) of the Kalman filter parameters, adjusts the process excitation noise covariance σ²_w(Q), and evaluates the filtering effect to optimize the measurement results. Using simulated ring-down signals with white noise, the linear regression summation method (LRS) fits the background rendering-downtimesto perform Kalman filtering. From four aspects of mean, standard deviation, residual standard deviation (RMSE), and different noise levels, the appropriate Q value range is obtained, which is less than 1×10^-7 and 0.001, respectively. An experimental gas detection system based on CRDS technology is constructed, using a 405 nm center wavelength diode laser and a high-reflectivity mirror with a reflectivity of over 99.99%, with NO₂ as the target gas, and the background ring-down time and ring-down time are processed and analyzed using Kalman filtering. The experimental results show that: (1) Selecting a Q value less than 1×10^-7 for Kalman filtering of the background ring-down time increases the lowest detection limit by 9.12 times and reaches 4.9×10^-11 after filtering; (2) Taking Q value of 0.001 for processing the ring-down time retains the time response information and achieves significant noise reduction; (3) The system's time resolution is 1 s, and compared to the method of reducing time resolution to improve detection limit in the past, the Kalman filtering method improves the system's sensitivity. The agreement between experimental and simulated results verifies the effectiveness of Kalman filtering in stability and noise reduction. Applying the Kalman filtering method in the CRDS spectroscopic detection of gases is practical and provides methods and references for optimizing other gas measurement results.

Key words：Cavity ring-down spectroscopy; Kalman filter; Gas measurement; Noise reduction; Detection limit

收稿日期: 2023-07-21 修订日期: 2023-10-20

中图分类号:

O433

基金资助: 国家自然科学基金项目(41905130，42275150)，江苏省高等学校自然科学研究面上项目(22KJB460035)资助

通讯作者: 王丹 E-mail: wangdan5@ahut.edu.cn

作者简介: 李德浩，1998生，安徽工业大学微电子与数据科学学院硕士研究生 e-mail: iopenli@163.com

引用本文:

李德浩，王丹，李治艳，陈浩. 卡尔曼滤波方法在腔衰荡光谱技术探测气体中的应用[J]. 光谱学与光谱分析, 2024, 44(10): 2727-2732.
LI De-hao, WANG Dan, LI Zhi-yan, CHEN Hao. Application of Kalman Filter in Gas Detection by Cavity Ring-Down Spectroscopy. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(10): 2727-2732.

链接本文:

https://www.gpxygpfx.com/CN/10.3964/j.issn.1000-0593(2024)10-2727-06 或 https://www.gpxygpfx.com/CN/Y2024/V44/I10/2727

[1] Maity A, Maithani S, Pradhan M. Analytical Chemistry, 2020, 93(1): 388.
[2] Berden G, Peeters R, Meijer G. International Reviews in Physical Chemistry, 2000, 19(4): 565.
[3] LIU Wen-qing, WANG Xing-ping, MA Guo-sheng, et al（刘文清, 王兴平, 马国盛, 等）. Acta Optica Sinica（光学学报）, 2021, 41(1): 434.
[4] ZHANG Zhi-rong, XIA Hua, SUN Peng-shuai, et al(张志荣，夏滑，孙鹏帅，等). Acta Photonica Sinica(光子学报), 2023, 52(3): 0352108.
[5] Wang D, Xie P, Hu R, et al. Atmosphere, 2022, 13(8): 1268.
[6] ( Cˇ )ermák P, Chomet B, Ferrieres L, et al. Review of Scientific Instruments, 2016, 87(8): 083109.
[7] Long D A, Fleisher A J, Wojtewicz S, et al. Applied Physics B, 2014, 115: 149.
[8] Li J, Yu B, Zhao W, et al. Applied Spectroscopy Reviews, 2014, 49(8): 666.
[9] Welch G F. Kalman Filter. In: Computer Vision. Springer, 2021.
[10] Montgomery D D, Kalman D A. Applied Industrial Hygiene, 1989, 4(1): 17.
[11] SHEN Xiao-yan, BI Zhi-hui, LIU Hua-feng（沈小燕, 毕智慧, 刘华锋）. Opto-Electronic Engineering（光电工程）, 2008, 35(12): 54.
[12] De Ridder K, Kumar U, Lauwaet D, et al. Atmospheric Environment, 2012, 50: 381.
[13] LI Jin-yi, YANG Xue, ZHANG Chen-ge，et al（李金义, 杨雪, 张宸阁，等）. Acta Optica Sinica（光学学报）, 2022, 42(18): 207.
[14] HU Ren-zhi, WANG Dan, XIE Pin-hua, et al（胡仁志，王丹，谢品华，等）. Acta Physica Sinica（物理学报）, 2014, 63(11): 110707.
[15] Wang D, Hu R Z, Xie P H, et al. Journal of Quantitative Spectroscopy & Radiative Transfer, 2015, 166: 23.
[16] Brown S S, Stark H, Ravishankara A R. Applied Physics B, 2002, 75(2-3): 173.
[17] Leleux D P, Claps R, Chen W, et al. Applied Physics B, 2002, 74: 85.
[18] ZHAO Gang, MA Wei-guang, LI Zhi-xin, et al（赵刚, 马维光, 李志新, 等）. Chinese Patent(中国专利)：CN103884679B, 2016.
[19] Welch G, Bishop G. Proc of SIGGRAPH, Course, 2001, 8(27599-23175): 41.
[20] Daley R, Ménard R. Monthly Weather Review, 1993, 121(5): 1554.
[21] Mehra R K. IEEE Transactions on Automatic Control, 1970, 15(2): 175.
[22] Almagbile A, Wang J, Ding W. Journal of Global Positioning Systems, 2010, 9(1): 33.
[23] WANG Dan, HU Ren-zhi, XIE Pin-hua, et al（王丹, 胡仁志, 谢品华, 等）. Spectroscopy and Spectral Analysis（光谱学与光谱分析）, 2014, 34(10): 2845.