A Real-Valued Kalman Estimation Method for Harmonic Signal Analysis in Biomedical Applications
DOI:
https://doi.org/10.17488/RMIB.45.3.1Keywords:
biomedical signal analysis, harmonics estimates in ECG, derivative estimation in biomedical signalsAbstract
This work presents a methodology for obtaining the harmonic estimation of biomedical signals such as electrocardiogram, cardiorespiratory and blood pressure signals. The proposed methodology is achieved using polynomial approximation and the Kalman filter. As advantage, the technique includes instant estimations of signal harmonics and its derivatives using a real-valued model. Furthermore, a comparison of the results is conducted with the Savitzky-Gola, nonlinear tracking differentiator methods, extended state observer and digital differentiator base on Taylor series. The results suggest that the proposed method has the potential to enhance the quality of signal measurements, especially in the presence of noise.
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W. Bouaziz, E. Schmitt, G. Kaltenbach, B. Geny and T. Vogel, “Health benefits of cycle ergometer training for older adults over 70: a review,” Eur. Rev. Aging. Phys. Act., vol. 12, Nov. 2015, Art. no. 8, doi: https://doi.org/10.1186/s11556-015-0152-9
R. M. Rangayyan, Biomedical Signal Analysis, 2nd ed. Wiley-IEEE Press, 2015.
K. Najarian and R. Splinter, Biomedical Signal and Image Processing, 2nd ed. Boca Raton, FL, United State: CRC Press, 2012, doi: https://doi.org/10.1201/b11978
R. M Rangayyan, Biomedical Signal Analysis: A Case-Study Approach, Wiley-IEEE Press, 2002.
T. U. Zaman, D. Hossain, T. Arefin, A. Rahman, S. N. Islam, F. Haque, “Comparative analysis of de-noising on ECG signal,” Int. J. Emerging Technol. Adv. Eng., vol. 2, no. 11, pp. 479-486, 2012.
N. Pombo, B. M. C. Silva, A. M. Pinho, and N. Garcia, “Classifier Precision Analysis for Sleep Apnea Detection Using ECG Signals,” IEEE Access, vol. 8, pp. 200477-200485, 2020, doi: https://doi.org/10.1109/ACCESS.2020.3036024
L. R. Castro and S. M. Castro, “Wavelets y sus aplicaciones,” in I Congreso Argentino de Ciencias de la Computación, Argentgina, Oct. 1995. [Online]. Available: http://sedici.unlp.edu.ar/handle/10915/24289
G. Saripalli, P. H. Prajapati, and A. D. Darji, “CSD Optimized DWT Filter for ECG Denoising,” in 2020 24th International Symposium on VLSI Design and Test (VDAT), Bhubaneswar, India, 2020, pp. 1-6, doi: https://doi.org/10.1109/VDAT50263.2020.9190624
J. Feng, G. Li, W. Wang, and X. Liang, “The Application of Improved Tracking-differentiator Filter in ECG Data,” DEStech, Apr. 2018, doi: https://doi.org/10.12783/dtcse/mso2018/20519
Y. Tang, Y. Wu, M. Wu, X. Hu, and L. Shen, “Nonlinear Tracking-Differentiator for Velocity Determination Using Carrier Phase Measurements,” IEEE J. Sel. Top. Signal Process., vol. 3, no. 4, pp. 716–725, Aug. 2009, doi: https://doi.org/10.1109/ JSTSP.2009.2024591
J. Rodríguez-Maldonado, C. Posadas-Castillo, and E. Zambrano-Serrano, “Alternative Method to Estimate the Fourier Expansions and Its Rate of Change,” Mathematics, vol. 10, no. 20, Jan. 2022, Art. no. 20, doi: https://doi.org/10.3390/math10203832
J. Rodriguez Maldonado, “Total Harmonic Distortion Estimation, Minimization Inter Harmonic Amplitude and Expanding Bands Rejection in TKF filters,” IEEE Lat. Am. Trans., vol. 14, no. 2, pp. 652–656, Feb. 2016, doi: https://doi.org/10.1109/TLA.2016.7437206
J. Han, “A Class of Extended State Observers for Uncertain Systems,” Control Dec., vol. 10, no. 1, pp. 85–88, 1995.
B.-Z. Guo, Z.-L. Zhao, “Extended state observer for nonlinear systems with uncertainty,” IFAC Proc. Vol., vol. 44, no. 1, pp. 1855–1860, 2011, doi: https://doi.org/10.3182/20110828-6-IT-1002.00399
J. L. Vargas-Luna, W. Mayr, and J. A. Cortés-Ramírez, “Amplitude Modulation Approach for Real-Time Algorithms of ECG-Derived Respiration,” Rev. Mex. Ing. Biomed., vol. 35, no. 1, pp. 53–69, 2014.
J. R. Cárdenas-Valdez, F. Ramírez-Arzate, Á. H. Corral-Domínguez, C. Hurtado-Sánchez, A. Calvillo-Téllez, and E. E. García-Guerrero, “Development of an Adaptive Acquisition and Transmission System for Digital Processing of ECG Signals under Variable n-QAM Schemes,” Rev. Mex. Ing. Biomed., vol. 44, no. 4, pp. 117-127, 2023, doi: https://doi.org/10.17488/RMIB.44.4.8
M. E. Cano, R. A. Jaso, M. E. Tavares, J. C. Estrada, et al., “A simple alternative for modulating and recording the PQRST complex,” Rev. Mex. Ing. Biomed., vol. 32, no. 2, pp. 100–108, Dec. 2011.
D. Torres Guzmán and C. S. Carbajal Fernández, “Mejora de la Señal de Flujo Sanguíneo en Implantes Coronarios Mediante la Detección de Distorsiones Eventuales,” Rev. Mex. Ing. Biomed., vol. 36, no. 1, pp. 33–53, 2015.
X. Ning and I. W. Selesnick, “ECG Enhancement and QRS Detection Based on Sparse Derivatives,” Biomed. Signal Process. Control, vol. 8, no. 6, pp. 713–723, Nov. 2013, doi: https://doi.org/10.1016/j.bspc.2013.06.005
C. Lastre-Domínguez, O. Ibarra-Manzano, J. A. Andrade-Lucio, and Y. S. Shmaliy, “Denoising ECG Signals Using Unbiased FIR Smoother and Harmonic State-Space Model,” 2020 28th European Signal Processing Conference (EUSIPCO), Amsterdam, Netherlands, 2021, pp. 1279-1283, doi: https://doi.org/10.23919/Eusipco47968.2020.9287522
I.R. Khan, R. Ohba, “New design of full band differentiators based on taylor series,” IEE Proc. – Vis. Image Signal Process., vol. 146, no. 4, pp. 185–189, 1999, doi: https://doi.org/10.1049/ip-vis:19990380
P. H. Langner and D. B. Geselowitz, “First Derivative of the Electrocardiogram,” Circ. Res., vol. 10, pp. 220–226, Feb. 1962, doi: https://doi.org/10.1161/01.res.10.2.220
J. Rodriguez Maldonado and M. A. Platas Garza, “Comparative Load Reduction and Analysis of Taylor Kalman Fourier Filters in Synchrophasor Measurement,” IEEE Lat. Am. Trans., vol. 16, no. 8, pp. 2153–2160, Aug. 2018, doi: https://doi.org/10.1109/ TLA.2018.8528229
D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering and Array Processing. Boston, United State: Artech House Publishers, 2005.
D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches. Hoboken, JN, United State: John Wiley & Sons, 2006, doi: https://doi.org/10.1002/0470045345
C. Chabert, D. Mongin, E. Hermand, A. Collado, and O. Hue, “Cardiorespiratory measurement from graded cycloergometer exercise testing (version 1.0.0)”, PhysioNet, doi: https://doi.org/10.13026/2qs3-kh43
J. Kubicek, M. Penhaker, and R. Kahankova, “Design of a synthetic ECG signal based on the Fourier series,” 2014 International Conference on Advances in Computing, Communications and Informatics (ICACCI), Delhi, India, 2014, pp. 1881-1885, doi: https://doi.org/10.1109/ICACCI.2014.6968312
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