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Cited by 67Speech and Audio ProcessingDirection-of-Arrival Estimation TechniquesMusic and Audio Processing

Performance of GCC- and AMDF-Based Time-Delay Estimation in Practical Reverberant Environments

Open access
Chen, Jingdong, Benesty, Jacob, Huang, Yiteng (Arden)·2005·EURASIP Journal on Advances in Signal Processing
DOI 10.1155/asp.2005.25
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Abstract

Recently, there has been an increased interest in the use of the time-delay estimation (TDE) technique to locate and track acoustic sources in a reverberant environment. Typically, the delay estimate is obtained through identifying the extremum of the generalized cross-correlation (GCC) function or the average magnitude difference function (AMDF). These estimators are well studied and their statistical performance is well understood for single-path propagation situations. However, fewer efforts have been reported to show their performance behavior in real reverberation conditions. This paper reexamines the GCC- and AMDF-based TDE techniques in real room reverberant and noisy environments. Our contribution is threefold. First, we propose a weighted cross-correlation (WCC) estimator in which the GCC function is weighted by the reciprocal of AMDF. This new method can sharpen the peak of the GCC function, which corresponds to the true time delay and thus leads to a better estimation performance as compared to the conventional GCC estimator. Second, we propose a modified version of the AMDF (MAMDF) estimator in which the delay is determined by jointly considering the AMDF and the average magnitude sum function (AMSF). Third, we compare the performance of the GCC, AMDF, WCC, and MAMDF estimators in real reverberant and noisy environments. It is shown that the AMDF estimator can yield better performance in favorable noise conditions and is slightly more resilient to reverberation than the GCC method. The GCC approach, however, is found to outperform the AMDF method in strong noisy environments. Weighting the correlation function by the reciprocal of AMDF can improve the performance of the GCC estimator in reverberation conditions, yet its improvement in noisy environments is limited. The MAMDF algorithm can enhance the AMDF estimator in both reverberant and noisy environments.

AI snapshot

Written from the paper’s full text.

TL;DR

This paper reexamines GCC- and AMDF-based time-delay estimation in real reverberant and noisy room environments and proposes two improved estimators: weighted cross-correlation (WCC) and modified AMDF (MAMDF). It finds that AMDF-based methods can outperform GCC in favorable noise and are slightly more resilient to reverberation, while GCC is more robust in strong noise.

Key findings

  • In high-SNR experiments (SNR = 25 dB) versus reverberation time, the percentage of anomalous estimates increased for all estimators as T60 increased; AMDF exhibited fewer anomalies than GCC, and WCC reduced anomalies relative to GCC. If the acceptable anomaly level is 10%, all studied methods could not be used reliably when T60 > 0.5 second.
  • In noise experiments at T60 = 0.31 second, high-SNR conditions gave almost identical bias across the four estimators; at lower SNR, AMDF had higher bias, while GCC showed smaller deviation, indicating GCC robustness to noise. MAMDF enhanced AMDF in both reverberant and noisy environments, whereas WCC in noisy conditions was basically a tradeoff between AMDF and GCC.
  • Additional experiments varying source location and microphone pairs showed that the percentage of anomalies did not vary much with source position, but bias and standard deviation fluctuated a lot. At T60 = 0.31 second and SNR = 30 dB, biases of the four estimators were almost identical, while GCC had slightly higher anomaly percentage and standard deviation than AMDF-based methods.

Methods

  • The paper formulates TDE from two microphone signals and evaluates GCC, AMDF, WCC, and MAMDF. WCC weights the GCC function by the reciprocal of AMDF; MAMDF combines AMDF and the average magnitude sum function (AMSF). PHAT weighting is adopted for GCC, signals are prewhitened, frames are 128 ms at 16 kHz, and 3-point Lagrange interpolation refines delay estimates.
  • Experiments used the Varechoic Chamber at Bell Laboratories (6.7 × 6.1 × 2.9 m, 369 active panels, T60 from 0.2 to almost 1 second), a 22-microphone linear array with 10 cm spacing, and 46 source positions. A 4-minute female speech signal was convolved with measured impulse responses and then added white Gaussian or NYSE noise; the paper reports approximately 1.8 million estimates per condition and about 90 million delay estimates in total across 5 reverberation times and 10 SNRs.
  • Performance was assessed by the percentage of anomalous estimates, bias, and standard deviation of nonanomalous estimates. An estimate was anomalous if its absolute error exceeded Tc/2, where Tc was computed as 4.3 samples in the experiment.

Limitations

  • The paper states that, for brevity, only representative results are presented from the full set of conditions. It also notes that the WCC method is heuristic and “may not necessarily be the optimum way” to combine GCC and AMDF.
  • The paper reports that all studied methods cannot be used reliably when T60 > 0.5 second if a 10% anomaly level is acceptable, and that bias and standard deviation fluctuate substantially with source location because echo structure varies.
  • Evident from the text: the evaluation is confined to one room facility, one female speech source, and simulated noise added after convolution with measured impulse responses; representative experiments use specific microphone pairs (e.g., Microphones 1 and 3, or 1 and 2), and advanced TDE techniques mentioned in the introduction are not evaluated.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1155/asp.2005.25

Cites

33 of 33 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

0 of 18 cited sources checked · 0 supported · 0 flagged

  • Findingreasoning

    The percentage of anomalous time-delay estimates of all estimators increases with reverberation time.

    “Obviously, the percentage of the anomalous estimates of all estimators increases with the reverberation time.”
    Quote in the paperSubstantial claim
  • Findingown data

    If the acceptable level of anomalous estimates is set to 10%, all studied methods cannot be used reliably when T60 > 0.5 second.

    “However, if the acceptable level of anomalous estimates is set to 10%, according to Figure 5, all the studied methods cannot be used reliably when T 60 > 0.5 second.”
    Quote in the paperSubstantial claim
  • Findingnone given

    The improvement of the WCC estimator in noisy environments is limited.

    “Weighting the correlation function by the reciprocal of AMDF can improve the performance of the GCC estimator in reverberation conditions, yet its improvement in noisy environments is limited.”
    Quote in the paperSubstantial claim
  • Findingcitation

    The AMDF estimator yields better performance than the GCC method in favorable noise conditions.

    “First, the performance of the AMDF estimator in favorable noise conditions is better than that of the GCC method as reported in [17].”
    • Also stated in: § 2.2.3. The weighted cross-correlation estimator · hedged
      “In comparison, AMDF generally produces more accurate estimates.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Findingown data

    The four estimators exhibit similar bias and standard deviation in light reverberation conditions.

    “The four estimators exhibit a similar bias and standard deviation in light reverberation conditions.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. 6
  • The quote only partly states this claim. 4
  • May combine two claims. 10

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingown data

    For the measured impulse response from Microphone 22 when 30% of the panels are closed and the loudspeaker is placed at position S21, the reverberation time T60 is approximately 0.37 second.

    “We show in Figure 3 an impulse response measured from Microphone 22 when 30% of the panels are closed and the loudspeaker is placed at the position S21 (shown in Figure 2).Also shown in Figure 3 is the backward integrated decay curve of the measured impulse response.One can see from this decay curve that the reverberation time T 60 is approximately 0.37 second.”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Findingown data

    The MAMDF estimator, which determines the delay by jointly considering AMDF and AMSF, enhances the AMDF estimator in both reverberant and noisy environments.

    “The MAMDF algorithm can enhance the AMDF estimator in both reverberant and noisy environments.”
    • Also stated in: § 1. INTRODUCTION · plain
      “We show that the combination of AMDF and AMSF can enhance the performance of the AMDF estimator.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In a moderately reverberant but noise-free condition, the estimated GCC function between two microphone signals has two large peaks: one at 0.625 milliseconds corresponding to the true time delay, and another at 1.125 milliseconds; the maximum peak at 1.125 milliseconds leads to an estimation failure.

    “Figure 1 shows one estimated GCC function between two microphone signals in a moderately reverberant but noise-free condition.As can be seen, the GCC function has two large peaks.One appears at 0.625 milliseconds which corresponds to the true time delay, and another one appears at 1.125 milliseconds.Unfortunately, the maximum peak appears at 1.125 milliseconds which leads to an estimation failure.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Biases of the four investigated estimators are almost identical, whereas the percentage of anomalies and standard deviation of nonanomalous estimates of the GCC method is slightly higher than the AMDF-based methods.

    “It is interesting to note that biases of the four investigated estimators are almost identical, whereas the percentage of anomalies and standard deviation of nonanomalous estimates of the GCC method is slightly higher than the AMDFbased methods.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Findingreasoning

    The correlation coefficient ρ(n) is approximately zero.

    “It is trivial then to show that ρ(n) ≈ 0.”
    Quote in the paperNot a substantial claim
    • The authors state this as an assumption: Both the signal and the noise can be modeled as zero-mean Gaussian processes.
    • The authors state this as an assumption: The signal is a Gaussian process with zero mean and variance σ_s^2.
    • The authors state this as an assumption: The noise observed from different microphones has the same variance σ_w^2.
    • The authors state this as an assumption: The relative propagation attenuation between two microphones is negligible, that is, α = 1.

  • Classified as probably not a substantial claim.

    Premisecitation

    An early study showed that the performance of the GCC approach to TDE severely deteriorated as the reverberation time increased.

    “An early study [18] examined the effects of the simulated room reverberation on the performance of the GCC approach to TDE.It was shown that the performance of this algorithm severely deteriorated as the reverberation time increased.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [18]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    Combination of open and closed panels can produce 2^369 different acoustic environments where the 60 dB reverberation time T60 can change from 0.2 to almost 1 second.

    “Combination of open and closed panels can produce 2 369 different acoustic environments where the 60 dB reverberation time T 60 can change from 0.2 to almost 1 second (refer to [33,34] for more details).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [33]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [34]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationown data

    The present finding that AMDF has higher bias in lower SNR is inconsistent with the result reported in [17], where AMDF is shown to have much lower bias than GCC in high SNR and almost the same bias as GCC in strong noise.

    “This is inconsistent with the result reported in [17], in which the AMDF is shown to have much lower bias than the GCC method in high SNR conditions and has almost the same bias as GCC in strong noise environments.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning

    Weighting the GCC function by the reciprocal of AMDF sharpens the peak corresponding to the true time delay and improves time-delay estimation performance compared with the conventional GCC estimator.

    “First, we propose a weighted crosscorrelation (WCC) estimator in which the GCC function is weighted by the reciprocal of AMDF.This new method can sharpen the peak of the GCC function, which corresponds to the true time delay and thus leads to a better estimation performance as compared to the conventional GCC estimator.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationnone given

    If both signal and noise are uncorrelated Gaussian processes, when two microphone signals are synchronized, the AMDF reaches its minimum while the AMSF approaches its maximum.

    “If both signal and noise are assumed to be uncorrelated Gaussian processes, when two microphone signals are synchronized, the AMDF will reach its minimum while the AMSF will approach its maximum.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Both signal and noise are uncorrelated Gaussian processes.

  • May combine two claims.

    Interpretationreasoning

    As reverberation time increases, more reflected signals with different delay reach the microphone, increasing erroneous peaks or valleys of the cost function, leading to more mistakes in extremum searching and more anomalous time-delay estimates.

    “As the reverberation time increases, more reflected signals with different delay will reach the microphone sensor and as a result, the erroneous peaks (for GCC and WCC) or valleys (for AMDF and MAMDF) of the cost function increase, which leads to more mistakes in extremum searching, and eventually leads to more anomalous time-delay estimates.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    In single-path propagation situations, the GCC and AMDF algorithms have been extensively investigated and their statistical performance is well understood.

    “In single-path propagation situations, the GCC and AMDF algorithms have been extensively investigated and their statistical performance is well understood [8,17].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [8]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • May combine two claims.

    Interpretationreasoning

    Weighting the GCC function by the reciprocal of AMDF can sharpen the desired peak and suppress other peaks in the GCC function, leading to more accurate time-delay estimates.

    “This weighting process can sharpen the desired peak and suppress the other peaks in the GCC function, hence leading to more accurate time-delay estimates.”
    Quote in the paperSubstantial claim

  • The quote only partly states this claim.

    Interpretationcitation

    The difference between the present results and [17] is attributable to [17] not distinguishing between estimates as anomalies and nonanomalies.

    “Finally, the results reported in [17] did not distinguish between estimates as anomalies and nonanomalies.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Interpretationreasoning

    The result that GCC has slightly higher anomalies and standard deviation than AMDF-based methods is consistent with previous experiments because this experiment is at very high SNR and moderate reverberation.

    “This is consistent with the observation from the previous experiments since this experiment is carried out at very high SNR and moderate reverberation environments.”
    Quote in the paperNot a substantial claim

  • The quote only partly states this claim.

    Interpretationcitation

    The difference between the present results and [17] is attributable to the GCC estimator tested in [17] being based on the direct cross-correlation function rather than the GCC function.

    “Secondly, the GCC estimator tested in [17] is based on the direct cross-correlation function rather than the GCC function.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • The quote only partly states this claim.

    Interpretationcitation

    The difference between the present results and [17] is attributable to [17] being performed only in high noise conditions where reverberation is absent.

    “Firstly, the experiment in [17] was performed only in high noise conditions where reverberation is absent.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [17]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

17 of 17

  • The paper relies on this without support.

    The GCC and AMDF methods are formulated based on an ideal propagation model with no multipath effect.

    “Both the GCC and AMDF methods are formulated based on the ideal propagation model where no multipath effect is taken into account.”

  • The authors state this as an assumption.

    The source signal s(t) can be modeled as a zero-mean Gaussian process.

    “Assuming that the signal s(t) can be modeled as a zeromean Gaussian process, from the invariance technique [29,30], we can derive the expectation of the AMDF as follows (see the appendix):”

  • The authors state this as an assumption.

    The additive noise w_m(n) is a real zero-mean stationary random process uncorrelated with both s(n) and the noise signal from the other microphone.

    “We assume that w m (n) is a (real) zero-mean stationary random process which is uncorrelated with both s(n) and the noise signal from the other microphone.”

  • The authors state this as an assumption.

    The source signal s(n) is reasonably broadband.

    “It is also assumed that s(n) is reasonably broadband.”

  • The authors state this as an assumption.

    Both signal and noise are uncorrelated Gaussian processes.

    “If both signal and noise are assumed to be uncorrelated Gaussian processes, when two microphone signals are synchronized, the AMDF will reach its minimum while the AMSF will approach its maximum.”

  • The paper relies on this without support.

    Multipath propagation and reverberation effects are more common in practice.

    “However, multipath propagation and reverberation effects are more common in practice.”

  • The paper relies on this without support.

    Fewer efforts have been reported to show the performance behavior of these algorithms in practical reverberant environments.

    “Unfortunately, fewer efforts have been reported to show the performance behavior of these algorithms in practical reverberant environments.”

  • The authors state this as an assumption.

    Both the signal and the noise can be modeled as zero-mean Gaussian processes.

    “Assuming that both signal and noise can be modeled as zeromean Gaussian processes, we know from [29] that”

  • The authors state this as an assumption.

    The signal is a Gaussian process with zero mean and variance σ_s^2.

    “we further assume that the signal is also a Gaussian process with zero-mean and variance σ 2 s”

  • The authors state this as an assumption.

    The noise observed from different microphones has the same variance σ_w^2.

    “the noise observed from different microphones has the same variance denoted by σ 2 w”

  • The authors state this as an assumption.

    The relative propagation attenuation between two microphones is negligible, that is, α = 1.

    “the relative propagation attenuation between two microphones is negligible, that is, α = 1.”

  • The paper relies on this without support.

    The echo structure varies appreciably as the source position moves, while the change of reverberation time T60 is generally negligible.

    “According to our experience, though in general the change of the reverberation time T 60 is negligible, the echo structure varies appreciably as the source position moves.”

  • The paper relies on this without support.

    In a practical situation, TDE has to deal with both reverberation and noise.

    “In a practical situation, however, the TDE has to deal with both reverberation and noise.”

  • The paper relies on this without support.

    In the context of TDE, N is often taken between a few hundreds and a few thousands.

    “In the context of TDE, N is often taken between a few hundreds and a few thousands.”
14 of 14

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The AMDF approach should exhibit a similar performance to the CC method from a statistical point of view.

    “As a result, the AMDFapproach should exhibit a similar performance to the CC method from a statistical point of view [43].”

    From Time Delay Estimation in Room Acoustic Environments: An Overview (2006) · cites this paper as [43]

    Section 3.2.3 (page unavailable) reports almost identical biases for GCC and AMDF-based estimators, supporting similarity in one statistical measure. But Section 3.2.2 reports different deviations as noise increases, and Section 2.2.2 says AMDF is less robust to noise. The paper therefore does not support a general expectation of similar statistical performance. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

Cites

Flagged first, then by citations

3 of the 36 references couldn’t be matched to a known paper.

Research works printed but not linked: 1

  1. W. C. Ward, G. W. Elko, R. A. Kubli, and W. C. McDougald, "The new varechoic chamber at AT&T Bell Labs," in Proc. Wallace Clement Sabine Centennial Symposium, pp. 343-346, Woodbury, NY, USA, June 1994.

Cited by

Sorted by citations

Related

Authors
Chen, J., Benesty, J., & Huang, Y. (.
Affiliations
Institut National de la Recherche Scientifique (CA)
Corresponding author
Chen, Jingdong
ORCID
Venue
EURASIP Journal on Advances in Signal Processing
Publisher
Springer Science and Business Media LLC
Published
2005-01-21
Volume
2005
Issue
1
ISSN
  • 1110-8657 (ISSN-L)
  • 1687-6180
DOI
10.1155/asp.2005.25
OpenAlex
W2107461080
Cited by
67
References
36
Citations by year
2024: 2 · 2022: 3 · 2021: 2 · 2020: 4 · 2019: 4 · 2018: 3 · 2017: 2 · 2016: 4 · 2015: 3 · 2014: 11 · 2013: 7 · 2012: 3
FWCI
2.43
Type
journal article
Language
en
Open access
Licence
cc-by
Locations
  • EURASIP Journal on Advances in Signal Processing (publishedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Topics
  • Physical Sciences › Computer Science › Signal Processing › Speech and Audio Processing
  • Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
  • Physical Sciences › Computer Science › Signal Processing › Music and Audio Processing
Keywords
time delay estimation, generalized cross-correlation, average magnitude difference function, reverberation, noise robustness, acoustic source localization, room acoustics

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