A note on the application of the Hilbert transform to time delay estimation

Cabot, Richard C.

doi:10.1109/tassp.1981.1163564

Cited by 82 publications

(22 citation statements)

References 3 publications

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“…Using the computer simulation it is possible to examination of influence of experimental parameters for CAAV and CCF characteristics. Reciprocally delayed stochastic signals were generated, which corresponded to the model (1), followed by the determination of discrete CCF (12) and CAAV (14) estimators for the given SNR values, taking into account the non-correlated sample pairs.…”

Section: Results Of Simulationsmentioning

confidence: 99%

“…Among the traditional methods used for stationary signals, the most common one is direct cross-correlation (CCF) in the time domain and the phase of cross-spectral power density in the frequency domain [3,[9][10][11][12]. Other approaches can be used in specific conditions: differential methods [4,6], the correlation method with the Hilbert transform [1,[13][14][15] or relatively unpopular methods based on conditional averaging of signals [16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

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Investigation of the Statistical Method of Time Delay Estimation Based on Conditional Averaging of Delayed Signal

Kowalczyk¹,

Hanus²,

Szlachta³

2011

Metrology and Measurement Systems

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This paper presents the results of the theoretical and practical analysis of selected features of the function of conditional average value of the absolute value of delayed signal (CAAV). The results obtained with the CAAV method have been compared with the results obtained by method of cross correlation (CCF), which is often used at the measurements of random signal time delay. The paper is divided into five sections. The first is devoted to a short introduction to the subject of the paper. The model of measured stochastic signals is described in Section 2. The fundamentals of time delay estimation using CCF and CAAV are presented in Section 3. The standard deviations of both functions in their extreme points are evaluated and compared. The results of experimental investigations are discussed in Section 4. Computer simulations were used to evaluate the performance of the CAAV and CCF methods. The signal and the noise were Gaussian random variables, produced by a pseudorandom noise generator. The experimental standard deviations of both functions for the chosen signal to noise ratio (SNR) were obtained and compared. All simulation results were averaged for 1000 independent runs. It should be noted that the experimental results were close to the theoretical values. The conclusions and final remarks were included in Section 5. The authors conclude that the CAAV method described in this paper has less standard deviation in the extreme point than CCF and can be applied to time delay measurement of random signals.

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Section: Results Of Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Investigation of the Statistical Method of Time Delay Estimation Based on Conditional Averaging of Delayed Signal

Kowalczyk¹,

Hanus²,

Szlachta³

2011

Metrology and Measurement Systems

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“…The Hilbert transform of the cross-correlation function is calculated and its zero crossing is searched as opposed to the peak of the R r 1 r 2 ðsÞ (Cabot 1981). This is illustrated in Fig.…”

Section: Average Magnitude Difference Function (Amdf)mentioning

confidence: 99%

Passive interference localization within the GNSS environmental monitoring system (GEMS): TDOA aspects

2014

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Due to their low power levels, global positioning system (GPS) signals are very susceptible to interference from intentional and unintentional sources. With ever increasing reliance on global navigation satellite systems (GNSS) for everyday operation of safety-critical infrastructure, the detection, localization and elimination of interference to GNSS is of paramount importance. The GNSS environmental monitoring system (GEMS) II provides the capability to detect and localize interferers in real time in a given area. It consists of a number of spatially distributed sensor nodes connected to a central processing unit. Interference is localized using hybrid direction-ofarrival (DOA) and time-difference-of-arrival (TDOA) techniques. We describe the GEMS II environment and provide an in-depth analysis and evaluation of the TDOA aspects of the system. During evaluation, signals generated from Spirent GPS signal generators as well as data from actual field-test trials are used to provide extensive performance analysis and comparison, with a view to final system integration.

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“…The cross-correlation function (CCF) is the most known methods of time delay estimation applied for stationary random signals [12 -16]. Other methods in time domain includes differential methods [17], or one based on the conditional averaging of signals [18 -20], as well as combination of the above and CCF [21,22] or cross-correlation analysis with the Hilbert Transform [14,23,24]. In the frequency domain the phase of cross-spectral density function (CSDF) or the spectral density of differential signal can be used [14, 25 -28].…”

Section: Introductionmentioning

confidence: 99%

Application of the phase method in radioisotope measurements of the liquid - solid particles flow in the vertical pipeline

Hanus

Zych

Petryka

et al. 2015

EPJ Web of Conferences

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Abstract. The paper presents idea and an application of the gamma-absorption method to a two-phase flow investigation in a vertical pipeline, where the flow of solid particles transported by water was examined by a set of two 241 Am radioactive sources and probes with NaI(Tl) scintillation crystals. In the described experiments as solid phase the ceramic models representing natural polymetallic ocean nodules were used. For advanced analysis of electrical signals obtained from detectors the phase of cross-spectral density function has been applied. Results of the average solid-phase velocity measurements were compared with one obtained by application of the classical cross-correlation. It was found that the combined uncertainties of the velocity of solid particles evaluation in the presented experiment did not exceed 0.6% in phase method and 3.2% in crosscorrelation method.

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A note on the application of the Hilbert transform to time delay estimation

Cited by 82 publications

References 3 publications

Investigation of the Statistical Method of Time Delay Estimation Based on Conditional Averaging of Delayed Signal

Investigation of the Statistical Method of Time Delay Estimation Based on Conditional Averaging of Delayed Signal

Passive interference localization within the GNSS environmental monitoring system (GEMS): TDOA aspects

Application of the phase method in radioisotope measurements of the liquid - solid particles flow in the vertical pipeline

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