Application of conditional averaging to time delay estimation of random signals

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The article presents the possibilities of using the function of conditional average value of a delayed signal (CAV) and the function of conditional average value of a delayed signal absolute value (CAAV) to determine the time delay estimation (TDE) of random signals. For discrete CAV and CAAV estimators, the standard uncertainties of the estimation of function values at extreme points and the standard uncertainties of the TDE were given and compared with the corresponding uncertainties for the direct discrete cross-correlation function (CCF) estimator. It was found that the standard uncertainty of TDE for CAV is lower than for CCF independent of signal-to-noise ratio (SNR) for parameter values of α ≥ 2 and M/N ≥ 0.25 (where: α - relative threshold value, M/N - quotient of number of averaging and number of samples). The standard uncertainty of TDE for CAAV will be lower than for CCF for SNR values greater than 0.35 (for N/M = 1).

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  • [1] Bendat J.S. Piersol A.G. (2010). Random Data: Analysis and Measurement Procedures (Fourth Edition). Wiley.

  • [2] Assous S. Linnett L. (2012). High resolution time delay estimation using sliding discrete Fourier transform. Digital Signal Processing 22 820-827.

  • [3] Waschburger R. Kawakami R. Galvao H. (2013). Time delay estimation in discrete-time state-space models. Signal Processing 93 904-912.

  • [4] Jacovitti G. Scarano G. (1993). Discrete time technique for time delay estimation. IEEE Transactions on Signal Processing 41 (2) 525-533.

  • [5] Chen J. Benesty J. Huang Y. (2006). Time delay estimation in room acoustic environments: An overview. EURASIP Journal on Advances in Signal Processing 2006 026503.

  • [6] Hanus R. Zych M. Petryka L. Świsulski D. (2014). Time delay estimation in two-phase flow investigation using the γ-ray attenuation technique. Mathematical Problems in Engineering 2014 475735.

  • [7] Chen J. Huang Y. Benesty J. (2004). Time delay estimation. In Audio Signal Processing for Next- Generation Multimedia Communication Systems. Springer 197-227.

  • [8] Blok E. (2002). Classification and evaluation of discrete subsample time delay estimation algorithms. In 14th International Conference on Microwaves Radar and Wireless Communications (MIKON-2002) May 20-22 2002. IEEE 764-767.

  • [9] So H.C. (2001). On time delay estimation using an FIR filter. Signal Processing 81 1777-1782.

  • [10] Zych M. Hanus R. Vlasak P. Jaszczur M. Petryka L. (2017). Radiometric methods in the measurement of particle-laden flows. Powder Technology 318 491-500.

  • [11] Mosorov V. (2008). Flow pattern tracing for mass flow rate measurement in pneumatic conveying using twin plane electrical capacitance tomography. Particle & Particle Systems Characterization 25 (3) 259-265.

  • [12] Zhang L. Wu X. (2006). On the application of cross correlation function to subsample discrete time delay estimation. Digital Signal Processing 16 682-694.

  • [13] Beck M.S. Pląskowski A. (1987). Cross-Correlation Flowmeters. CRC Press.

  • [14] Mosorov V. (2006). Phase spectrum method for time delay estimation using twin-plane electrical capacitance tomography. Electronics Letters 42 (11) 630-632.

  • [15] Hanus R. Zych M. Petryka L. Mosorov V. Hanus P. (2015). Application of the phase method in radioisotope measurements of the liquid - solid particles flow in the vertical pipeline. EPJ Web of Conferences 92 02020.

  • [16] Hanus R. (2015). Application of the Hilbert Transform to measurements of liquid-gas flow using gamma ray densitometry. International Journal of Multiphase Flow 72 210-217.

  • [17] Shors S.M. Sahakian A.V. Sih H.J. Swiryn S. (1996). A method for determining high-resolution activation time delays in unipolar cardiac mapping. IEEE Transactions on Biomedical Engineering 43 (12) 1192-1196.

  • [18] Hanus R. (2001). Accuracy comparison of some statistic methods of time delay measurements. Systems Analysis Modelling Simulation 40 (2) 239-244.

  • [19] Kowalczyk A. Szlachta A. (2010). The application of conditional averaging of signals to obtain the transportation delay. Przegląd Elektrotechniczny 86(1) 225-228. (in Polish)

  • [20] Kowalczyk A. Hanus R. Szlachta A. (2011). Time delay estimation of stochastic signals using conditional averaging. In 8th International Conference on Measurement (Measurement 2011) April 27-30 2011. Bratislava Slovakia: Institute of Measurement Science SAS 32-37.

  • [21] Kowalczyk A. Szlachta A. Hanus R. Chorzępa R. (2017). Estimation of conditional expected value for exponentially autocorrelated data. Metrology and Measurement Systems 24 (1) 69-78.

  • [22] Hanus R. (2010). Standard uncertainty comparison of time delay estimation using cross-correlation function and the function of conditional average value of the absolute value of delayed signal. Przegląd Elektrotechniczny 86 (6) 232-235. (in Polish)

  • [23] Kowalczyk A. Hanus R. Szlachta A. (2011). Investigation of the statistical method of time delay estimation based on conditional averaging of delayed signal. Metrology and Measurement Systems 18 (2) 335-342.

  • [24] Szlachta A. Hanus R. Kowalczyk A. (2011). Virtual instrument for the estimation of the time delay using conditional averaging of random signals. In International Workshop on ADC Modelling Testing and Data Converter Analysis and Design and IEEE 2011 ADC Forum June 30 - July 1 2011. IMEKO 81-86.

  • [25] Kowalczyk A. Hanus R. Szlachta A. (2016). Time delay measurement method using conditional averaging of the delayed signal module. Przegląd Elektrotechniczny 92 (9) 279-282.

  • [26] Hanus R. Szlachta A. Kowalczyk A. Petryka L. Zych M. (2012). Radioisotope measurement of twophase flow in pipeline using conditional averaging of signal. In 16th IEEE Mediterranean Electrotechnical Conference (MELECON 2012) March 25-28 2012. IEEE 144-147.

  • [27] Hanus R. Zych M. Kowalczyk A. Petryka L. (2015). Velocity measurements of the liquid-gas flow using gamma absorption and modified conditional averaging. EPJ Web of Conferences 92 02021.

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