2023年 05期

考虑有色测量噪声的Kalman平滑算法在pH计校准电压预估中的应用

Colored Measurement Noise Kalman Smoothing Algorithm for Estimation of pH Meter Calibration Voltage


摘要(Abstract):

为了提高pH计校准电压预估精度,提出考虑有色测量噪声的Kalman平滑算法;该算法以电压和电压采集周期作为状态向量,以设定的采样周期和无线pH计所采集的电压值作为观测向量,构建数据融合模型;以考虑有色测量噪声的 Kalman 滤波作为前向滤波,通过马氏距离计算当前时刻最优的有色测量噪声因子,利用Rauch-Tung-Striebel平滑算法对前向滤波的输出值进行平滑,最终得到当前时刻电压的预估值,并将所提出的算法应用于pH计校准电压预估。结果表明,与传统 Kalman 滤波算法相比,所提出的算法的电压预估的精度提高约10%。

关键词(KeyWords): 数据融合; 电压预估;Kalman 平滑算法;有色测量噪声

基金项目(Foundation): 国家自然科学基金项目(61803175)

作者(Author):邢文芳,拓锐,刘俊聪,刘爱云,徐元

DOI: 10.13349/j.cnki.jdxbn.20230720.002

参考文献(References):

[1] 梅青,吴丹.在线pH计的校准与日常维护[J].计量与测试技术,2015,42(4):39.

[2] 何持平.水厂在线pH计的安装、校准及维护[J]. 城镇供水,2010(4):46.

[3] 丁海铭.自动校准型pH计电计输入阻抗引起的示值误差检定方法的探讨[J].化学分析计量,2010,19(3):88.

[4] 孙墨杰,陈长安,靳世久,等.在线恒温pH计的研究[J].东北电力学院学报,2001,21(2):24.

[5] 梁嘉贤.探究pH计是否可替代滴定法对盐酸浓度进行测定[J].中国检验检测,2021,29(4):49.

[6] ZHAO S Y, HUANG B. Trial⁃and⁃error or avoiding a guess? Ini⁃ tialization of the Kalman filter[J]. Automatica,2020,121:109184.

[7] WANG J, ZHANG T, JIN B N, et al. Student’s t⁃based robust Kalman filter for a SINS/USBL integration navigation strategy[J].IEEE Sensors Journal , 2020,20(10):5540.

[8] ZHAO S Y, SHMALIY Y S, AHN C K, et al. Adaptive⁃horizon iterative UFIR filtering algorithm with applications[J].IEEE Transactions on Industrial Electronics, 2018,65(8):6393.

[9] XU Y, CAO J, SHMALIY Y S, et al. Distributed Kalman filter forUWB/INS integrated pedestrian localization under colored meas⁃ urement noise[J]. Satellite Navigation, 2021,2:22.

[10] 贾嵘,杨可,原丽,等.基于卡尔曼滤波和加窗插值谐波分析法的介损测量方法[J]. 电网技术,2007,31(19):52.

[11] 薛尚青,蔡金锭.基于Sage-Husa卡尔曼滤波的三相电压暂降检测[J]. 电力系统自动化,2012,36(1):71.

[12] HUANG Y L, BAI M M, LI Y F, et al. An improved variational adaptive Kalman filter for cooperative localization[J]. IEEE Sensors Journal, 2021 ,21(9):10775.

[13] ZHANG Z Q, DONG P, TUO H Y, et al. Robust variational Bayesian adaptive cubature Kalman filtering algorithm for simultaneous localization and mapping with heavy⁃tailed noise [J].Journal of Shanghai Jiaotong University (Science), 2020,25:76.

[14] SHMALIY Y S, ZHAO S Y. Ultimate iterative UFIR filtering algorithm[J]. Measurement, 2016,92:236.

[15] XU Y, SHMALIY Y S, CHEN X Y, et al. Robust inertial navi-gation system/ultra wide band integrated indoor quadrotor locali-zation employing adaptive interacting multiple model⁃unbiased finite impulse response/Kalman filter estimator[J]. Aerospace Science and Technology, 2020,98:105683.

[16] BU L L, ZHANG Y, XU Y. Indoor pedestrian tracking by combining recent IMU and UWB measurements[C]//2017 International Conference on Advanced Mechatronic Systems(ICAMechS 2017), December 06-09, 2017, Xiamen, China. New York :IEEE , 2017:17649576.

[17] XU Y, KARIMI H R, LI Y Y, et al. Real-time accurate pede……strian tracking using extended finite impulse response filter bank for tightly coupling recent inertial navigation system and ultra⁃wideband measurements[J]. Proceedings of the Institution of Mechanical Engineers: Part I : Journal of Systems and Control Engineering, 2018,232(4):464.