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Cited by 4Direction-of-Arrival Estimation TechniquesSpeech and Audio ProcessingUnderwater Vehicles and Communication Systems

Research on the Improvement of the Signal Time Delay Estimation Method of Acoustic Positioning for Anti-Low Altitude UAVs

Open access
Liu, Miao, Yu, Jiyan, Yang, Zhengpeng·2025·Sensors
DOI 10.3390/s25092735PMC PMC12074323
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Abstract

With the popularity of low-altitude small unmanned aerial vehicles (UAVs), UAVs are often used to take candid photos or even carry out malicious attacks. Acoustic detection can be used to locate UAVs in order to prevent malicious attacks by UAVs. Aiming at the problem of a large error in the time delay estimation algorithm under a low SNR, a time delay estimation algorithm based on an improved weighted function combined with a generalized cubic cross-correlation is introduced. By analyzing and comparing the performance of generalized cross-correlation time delay estimation of different traditional weighting functions, an improved weighting function that combines improved smooth coherent transform (SCOT) and phase transform (PHAT) is proposed. Compared with the traditional generalized cross-correlation weighted function, the improved weighted function has a sharper and higher peak value, and the time delay estimation error is smaller at a low SNR. Secondly, by combining the improved weight function with the generalized cubic cross-correlation, the main peak value is further increased and sharpened, and the time delay estimation performance is better than that when combined with the generalized cubic cross-correlation and the generalized quadratic correlation. Experimental results show that in complex outdoor scenes, the positioning error of the unimproved GCC PHAT method is 45.22 cm, and the positioning error of the improved weighted function generalized cubic cross-correlation algorithm is no more than 22.1 cm. Compared with the unimproved GCC PHAT method, the performance is improved by 35.55%. It is proven that this method is helpful for improving the positioning ability of low-flying UAVs and can provide help for anti-terrorism security against malicious attacks by UAVs.

AI snapshot

Written from the paper’s full text.

TL;DR

This paper proposes an improved generalized cross-correlation time-delay estimation method for acoustic UAV positioning under low SNR, combining an improved SCOT/PHAT weighting function with generalized cubic cross-correlation. In outdoor tests, the proposed GTCC SCOTg/PHAT algorithm reduced positioning error at 19.18 m in a noisy environment to 22.10 cm, versus 45.22 cm for conventional GCC PHAT.

Key findings

  • The improved weighting function uses an exponential factor α and constant β; for the recorded UAV signal at 48 kHz, correct time delay was obtained when α ≤ 0.7, with the most prominent main peak at α = 0.7, while α > 0.7 caused spurious peaks to exceed the correct peak.
  • In simulations, at 10 dB all four weighting functions obtained correct delay; at 0 dB ROTH failed while SCOT, PHAT, and the improved weighting function still worked; at −5 dB ROTH, SCOT, and PHAT failed, but the improved weighting function still produced a relatively accurate delay. Combining the improved weighting function with generalized cubic cross-correlation gave the largest peak and best low-SNR performance among GCC, GSCC, and GTCC.
  • The UAV acoustic signal had a main frequency band of 130–5000 Hz and a main frequency of 424.3 Hz; measured sound pressure level at 10 m was 62.35 dB.
  • In noisy outdoor experiments at 19.18 m, RMSE and positioning error were: GCC PHAT 0.00133 s / 45.22 cm; GCC SCOTg/PHAT 0.00110 s / 37.40 cm; GSCC SCOTg/PHAT 0.00088 s / 29.92 cm; GTCC SCOTg/PHAT 0.00065 s / 22.10 cm. The proposed algorithm was reported as 35.55% more accurate than traditional PHAT and 22.78% more accurate than the improved weighting function combined with first-order cross-correlation. In quiet environments, RMSE was less than 0.1 ms and positioning error less than 0.03 m.

Methods

  • The paper studies TDOA acoustic positioning using generalized cross-correlation with weighting functions, then proposes an improved weighting function combining SCOT and PHAT: φ(ω)=|Gx1x2(ω)|/([Gx1x1(ω)Gx2x2(ω)]^α + β), simplified when β is ignored for non-low-energy signals. This weighting is applied to generalized cubic cross-correlation.
  • Simulations used a recorded UAV sound signal, 48 kHz sampling, a set delay of 0.002 s, stationary Gaussian white noise, and SNR varied from 10 dB to −10 dB in 2 dB steps; 50 tests were run per fixed SNR and RMSE was used as the evaluation index. The α value was determined by varying 0 < α < 1.
  • Experimental verification used a five-element microphone array with 48 kHz sampling per microphone and 63.64 cm array spacing; data were collected in two environments (quiet noon playground and noisy after-school road/basketball court) at UAV-to-array-center distances of 13.95 m, 14.64 m, and 19.18 m. Four algorithms were compared: GCC PHAT, GCC SCOTg/PHAT, GSCC SCOTg/PHAT, and GTCC SCOTg/PHAT, with processing in MATLAB R2021b.

Limitations

  • The paper states that the optimal α must be determined by multiple experiments and may need slight adjustment when the sampling rate changes; β can be ignored for non-low-energy signals. It also notes that the improved weighting function still shows sub-peak fluctuation.
  • The paper does not include a dedicated limitations section. Evident from the text: validation is limited to one UAV acoustic dataset, three distances, two outdoor environments, and a five-element microphone array, so broader generalization across UAV types, array geometries, and environments is not established.

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

Integrity signals

Registry

Crossref · 10.3390/s25092735

Cites

7 of 7 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

3 of 12 cited sources checked · 1 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Traditional weighting functions and the generalized cross-correlation algorithm have limited time delay estimation effect at a low SNR.

    “Due to the limited time delay estimation effect of the traditional weighting function and generalized cross-correlation algorithm at a low SNR, many scholars have studied various improved weighting functions [7,8,9,10].”
    Quote in the paperSubstantial claim2 of 4 sources checked
    • cites [7] Yu, 2023, A generalized quadratic correlation delay estimation algorithm based on joint weighting, Comput. Simul.

      Not checked in the free run.

    • cites [8] Liu, W., Li, M., Wang, T., Jin, M., and Fang, Q. (2023). Research on Time Delay Estimation Method of Partial Discharges Signal with Improved Weighted Function. Electronics, 12. source
    • cites [9] Jiang, A., and Liu, W. (2023, January 27). An improved SCOT double weighted quadratic correlation time delay estimation algorithm based on infrasound signal. Proceedings of the Third International Conference on Electronics, Electrical and Information Engineering (ICEEIE 2023), Xiamen, China. source
    • cites [10] Liu, 2023, A sound source localization method based on improved second correlation time delay estimation, Meas. Sci. Technol. source

      The Introduction states that the SQC and HQC methods use generalized weighting functions but still fail to estimate time delay accurately at low SNR. It does not make the same finding about traditional weighting functions or the generalized cross-correlation algorithm as a whole; Section 2.2 instead uses a weighted generalized cross-correlation function in the proposed method. No page numbers are available in our copy. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • Premisecitation

    The positioning accuracy of TDOA is closely related to the time delay difference, array error, and array deployment mode.

    “The positioning accuracy of TDOA is closely related to the time delay difference, array error, and array deployment mode [3], so the time delay estimation error has received extensive attention.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [3] Xing, X., Zhong, Z., Li, X., and Yue, Y. (2025). Node Selection and Path Optimization for Passive Target Localization via UAVs. Sensors, 25. source

      Section 2.1 models errors in measured time differences, and Section 2.2 links those measurement errors to a bound on localization accuracy. Section 5.3 reports that changing UAV positions improves measurement geometry and localization accuracy. Our copy does not address array-position error as a separate factor, so that part of the claim is unsupported. (LLM, conf=0.84)

      Experimental — accuracy not yet measured
  • Findingown data

    In complex outdoor scenes, the positioning error of the unimproved GCC PHAT method is 45.22 cm.

    “Experimental results show that in complex outdoor scenes, the positioning error of the unimproved GCC PHAT method is 45.22 cm, and the positioning error of the improved weighted function generalized cubic”
    Quote in the paperSubstantial claim
  • Findingown data

    At SNR −5 dB, the spurious spectral peaks of generalized cross-correlation and generalized quadratic correlation exceed the correlation peaks, resulting in time delay estimation errors.

    “When the SNR is reduced to −5 dB, the spurious spectral peaks of generalized cross-correlation and generalized quadratic correlation exceed the correlation peaks, resulting in time delay estimation errors, but the correlation peaks are still obvious in the generalized cubic cross-correlation algorithm with improved weighted function, and it is easy to obtain the correct delay estimation.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.
  • Findingown data

    When the SNR is lower than 4 dB, the ROTH weighted time delay estimation error increases sharply.

    “When the SNR is lower than 4 dB, the time delay estimation error increases sharply, and when the SNR is lower than 0 dB, the algorithm fails completely.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
  • May combine two claims. 33
  • The quote only partly states this claim. 2
  • Classified as probably not a substantial claim. 8

  • May combine two claims.

    Findingown data

    The time delay estimation errors of SCOT and PHAT weighted algorithms are similar, and an accurate time delay can be obtained above 0 dB.

    “The time delay estimation errors of SCOT and PHAT weighted algorithms are similar, and an accurate time delay can be obtained above 0 dB.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    When α is greater than 0.7, the spurious peak exceeds the correct peak, and the time delay cannot be estimated correctly.

    “When α is greater than 0.7, the spurious peak exceeds the correct peak, and the time delay cannot be estimated correctly.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    At SNR 0 dB, the ROTH weighted generalized cross-correlation algorithm completely fails, and a large number of false peaks appear.

    “When the SNR drops to 0 dB, the ROTH weighted generalized cross-correlation algorithm has completely failed, and a large number of false peaks appear.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    At SNR −5 dB, the correlation peaks are still obvious in the generalized cubic cross-correlation algorithm with improved weighted function, and it is easy to obtain the correct delay estimation.

    “but the correlation peaks are still obvious in the generalized cubic cross-correlation algorithm with improved weighted function, and it is easy to obtain the correct delay estimation.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

  • May combine two claims.

    Findingown data

    At SNR −5 dB, the generalized cross-correlation algorithms weighted by ROTH, SCOT, and PHAT all fail, and a large number of spurious peaks exceed the main peak.

    “When the SNR drops to −5 dB, the generalized cross-correlation algorithms weighted by ROTH, SCOT, and PHAT all fail, and a large number of spurious peaks exceed the main peak.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • The quote only partly states this claim.

    Findingown data

    In complex outdoor scenes, the positioning error of the improved weighted function generalized cubic cross-correlation algorithm is no more than 22.1 cm.

    “the positioning error of the unimproved GCC PHAT method is 45.22 cm, and the positioning error of the improved weighted function generalized cubic cross-correlation algorithm is no more than 22.1 cm.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    At SNR 10 dB and 0 dB, the joint generalized cubic cross-correlation algorithm has the largest peak value and is much higher than the sidelobes.

    “It can be seen from the simulation diagram that the three algorithms can obtain the correct time delay when the SNR is 10 dB and 0 dB, but the joint generalized cubic cross-correlation algorithm has the largest peak value and is much higher than the sidelobes.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

  • May combine two claims.

    Findingown data

    At SNR 0 dB, although the main peak value of SCOT, PHAT, and the improved weighting function is reduced, the correct time delay can still be obtained.

    “Although the main peak value of SCOT, PHAT, and the improved weighting function is reduced, the correct time delay can still be obtained.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    At SNR −5 dB, the generalized cross-correlation algorithm with improved weighting function produces a little error but has certain anti-noise performance compared with other traditional weighting functions.

    “The time delay estimated by the generalized cross-correlation algorithm with improved weighting function also produces a little error, but it has certain anti-noise performance compared with other traditional weighting functions.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    The main peak of the correlation function of the improved weighted function algorithm is less affected by the sub-peak, and the anti-noise interference ability is improved, showing good stability.

    “From the above simulation results, it can be seen that the main peak of the correlation function of the improved weighted function algorithm is less affected by the sub-peak, and the anti-noise interference ability is improved, showing good stability; however, there is also the phenomenon of sub-peak fluctuation.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    The main frequency band of the drone's sound is concentrated between 130 and 5000 Hz, with the main frequency at 424.3 Hz.

    “As can be seen from Figure 2, the main frequency band of the drone’s sound is concentrated between 130 and 5000 Hz, with the main frequency at 424.3 Hz.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    Compared with the traditional generalized cross-correlation weighted function, the improved weighted function has a sharper and higher peak value and a smaller time delay estimation error at a low SNR.

    “Compared with the traditional generalized cross-correlation weighted function, the improved weighted function has a sharper and higher peak value, and the time delay estimation error is smaller at a low SNR.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    At SNR 10 dB, the modified weighted function has the highest peak and the smallest number of false peaks.

    “However, the ROTH weighted generalized cross-correlation function has the largest number of false peaks, the SCOT and PHAT weighted functions have the same effect, and the modified weighted function has the highest peak and the smallest number of false peaks.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    In the time delay estimation of the UAV acoustic signal detection in the real scene, the accuracy of the proposed algorithm is 35.55% higher than that of the traditional PHAT weighted algorithm and 22.78% higher than that of the improved weighted function combined first cross-correlation algorithm.

    “In the time delay estimation of the UAV acoustic signal detection in the real scene, the RMSE of different SNR algorithms is compared. The accuracy of the proposed algorithm is 35.55% higher than that of the traditional PHAT weighted algorithm and 22.78% higher than that of the improved weighted function combined first cross-correlation algorithm.”
    Quote in the paperSubstantial claim

  • May combine two claims. The quote only partly states this claim.

    Findingown data

    At a distance of 19.18 m, the positioning errors of the GCC PHAT algorithm, the GCC SCOTg/PHAT algorithm, and the GSCC SCOTg/PHAT algorithm are 45.22 cm, 37.40 cm, and 29.92 cm, respectively.

    “The positioning errors are 45.22 cm, 37.40 cm, and 29.92 cm, respectively.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The generalized cubic cross-correlation algorithm with the improved combination of weighted functions has the smallest time delay estimation error among the three algorithms, further improving the accuracy of the algorithm's time delay estimation at a low SNR.

    “The generalized cubic cross-correlation algorithm with the improved combination of weighted functions has the smallest time delay estimation error among the three algorithms, which further improves the accuracy of the algorithm’s time delay estimation at a low SNR.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

  • May combine two claims.

    Findingown data

    In a noisy environment, the false peaks produced by the cross-correlation function of the other three algorithms have exceeded the main peaks, which seriously affects the accuracy of time delay estimation.

    “The false peaks produced by the cross-correlation function of the other three algorithms have exceeded the main peaks, which seriously affects the accuracy of time delay estimation.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    In a quiet environment, the GTCC SCOTg/PHAT algorithm has more sub-peaks compared with the other three algorithms, but due to the large difference between the main peak and the sub-peak, the correct main peak is not affected.

    “Although there are more sub-peaks in the GTCC SCOTg/PHAT algorithm compared with the other three algorithms in a quiet environment, due to the large difference between the main peak and the sub-peak, the correct main peak is not affected.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    At low SNR, the improved weighted function combined generalized cubic cross-correlation algorithm has the highest correlation peak-to-peak value, which further improves the anti-noise performance of the algorithm.

    “At low signal-to-noise ratio (SNR), the improved weighted function combined generalized cubic cross-correlation algorithm has the highest correlation peak-to-peak value, which further improves the anti-noise performance of the algorithm.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

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

    Findingown data

    At a distance of 19.18 m, the position coordinate of the UAV is (0, −12.2 m, 14.8 m).

    “When obtaining the data at a distance of 19.18 m as an example, the position coordinate of the UAV is (0, −12.2 m, 14.8 m), and the theoretical time delay between the UAV’s acoustic signal and the reference microphone 1 and microphone 2 is 0.0012 s.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    In a quiet environment, the RMSE of the four algorithms is less than 0.1 ms, the time delay estimation accuracy is higher, and the positioning error is less than 0.03 m.

    “In a quiet environment, the RMSE of the four algorithms is less than 0.1 ms, the time delay estimation accuracy is higher, and the positioning error is less than 0.03 m.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    The ROTH weighting function has the worst time delay estimation effect, and the performance of the SCOT and PHAT weighting functions is similar when the SNR drops to 0 dB.

    “The ROTH weighting function has the worst time delay estimation effect, and the performance of the SCOT and PHAT weighting functions is similar when the SNR drops to 0 dB.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

  • May combine two claims.

    Findingown data

    In a quiet environment, the estimated time delay value of GTCC SCOTg/PHAT is 0.0011875 s, which is the smallest error among the four algorithms.

    “among which the estimated time delay value of GTCC SCOTg/PHAT is 0.0011875 s, which is the smallest error among the four algorithms.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Findingown data

    By applying the improved weighting function to the cubic cross-correlation algorithm, the main peak value with the larger peak value can be obtained, and a more accurate time delay estimate can be calculated at a low SNR.

    “By applying the improved weighting function to the cubic cross-correlation algorithm, the main peak value with the larger peak value can be obtained, and a more accurate time delay estimate can be calculated at a low SNR.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).
    • The authors state this as an assumption: In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

  • May combine two claims.

    Findingown data

    At a distance of 19.18 m, the positioning error of the GTCC SCOTg/PHAT algorithm is 22.10 cm, which is smaller than the error of the first two algorithms.

    “The RMSE of the GTCC SCOTg/PHAT algorithm is 0.00065 s, and the positioning error is 22.10 cm, which is smaller than the error of the first two algorithms.”
    Quote in the paperSubstantial claim

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

    Findingown data

    At a distance of 19.18 m, the theoretical time delay between the UAV's acoustic signal and the reference microphone 1 and microphone 2 is 0.0012 s.

    “When obtaining the data at a distance of 19.18 m as an example, the position coordinate of the UAV is (0, −12.2 m, 14.8 m), and the theoretical time delay between the UAV’s acoustic signal and the reference microphone 1 and microphone 2 is 0.0012 s.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Findingown data

    For the UAV sound signal, when the exponential factor α is not more than 0.7, the correct time delay can be obtained; when α is 0.7, the main peak is the most prominent and the noise suppression effect is the best; if α exceeds 0.7, the correct latency value cannot be obtained.

    “When the exponential factor α is not more than 0.7, the correct time delay can be obtained, and when α is 0.7, the main peak is the most prominent, and the noise suppression effect is the best. If the latency exceeds 0.7, the correct latency value cannot be obtained.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).
    • The authors state this as an assumption: The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

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

    Premisecitation

    Li Dahua et al. proposed that the generalized cubic cross-correlation algorithm of the Eckart weighted method has better anti-noise performance than other algorithms under strong noise.

    “Li Dahua et al. proposed that the generalized cubic cross-correlation algorithm of the Eckart weighted method has better anti-noise performance than other algorithms under strong noise.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [12] Li, 2022, Generalized mutual correlation time delay estimation method based on cubic correlation improvement in localized discharge ultrasonic localization, Acoust. Technol.

      Not checked in the free run.

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    Li Dahua et al.'s time delay estimation accuracy largely depends on understanding of the signal propagation medium and accurate identification of the transmission function of the propagation medium, and the algorithm requires a large amount of computation.

    “The accuracy of its time delay estimation largely depends on the understanding of the signal propagation medium and accurate identification of the transmission function of the propagation medium, and as such, the algorithm requires a large amount of computation [12].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [12] Li, 2022, Generalized mutual correlation time delay estimation method based on cubic correlation improvement in localized discharge ultrasonic localization, Acoust. Technol.

      Not checked in the free run.

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

    Premisecitation

    Dou Huijing et al. proposed a generalized quadratic cross-correlation based on generalized cross-correlation and quadratic correlation to improve the accuracy of time difference estimation.

    “Dou Huijing et al. proposed a generalized quadratic cross-correlation based on generalized cross-correlation and quadratic correlation to improve the accuracy of time difference estimation [11].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [11] Dou, 2016, Quadratic correlation-based generalized mutual correlation time difference estimation algorithm, J. Beijing Inst. Technol.

      Not checked in the free run.

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

    Interpretationown data

    The audio in the main frequency band is mainly generated by the propeller stirring the air, while the audio above 5000 Hz is produced by friction of the internal components of the motor.

    “The audio in this frequency band is mainly generated by the propeller stirring the air, while the audio above 5000 Hz is produced by the friction of the internal components of the motor.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The improved method is helpful for improving the positioning ability of low-flying UAVs and can provide help for anti-terrorism security against malicious attacks by UAVs.

    “It is proven that this method is helpful for improving the positioning ability of low-flying UAVs and can provide help for anti-terrorism security against malicious attacks by UAVs.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    When the signal-to-noise ratio is low, using the improved algorithm for time delay estimation can help obtain more accurate time delay estimation and has strong anti-noise performance.

    “In summary, when the signal-to-noise ratio is low, using the improved algorithm for time delay estimation can help obtain more accurate time delay estimation and has strong anti-noise performance.”
    Quote in the paperSubstantial claim

  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation

    The cross-correlation algorithm is simple to implement and can provide quite accurate time delay estimation for signals with sufficient SNR, and is widely used in acoustic localization.

    “At present, in the study of delay estimation, the cross-correlation algorithm is simple to implement and can provide quite accurate time delay estimation for signals with sufficient SNR, which is widely used in the field of acoustic localization [4,5].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [4] Yiwere, 2015, Fast Time Difference of Arrival Estimation for Sound Source Localization using Partial Cross Correlation, J. Inf. Technol. Appl. Manag.
    • cites [5] Glentis, G.O., and Angelopoulos, K. (2022, January 16–19). Using Generalized Cross-Correlation estimators for leak signal velocity estimation and spectral region of operation selection. Proceedings of the 2022 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), Ottawa, ON, Canada. source

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

    Premisecitation

    Acoustic positioning is a common and rapidly developing method for UAV positioning.

    “Among the UAV positioning technologies in recent years, acoustic positioning is a relatively common and rapidly developing method [1].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [1] Dong, Q. (2021). Research on UAV Acoustic Detection and Localization Method and System, Northeastern University.

      Not checked in the free run.

  • May combine two claims.

    Premisecitation

    Li Dahua et al.'s algorithm requires additional frequency domain analysis of the signal, which increases the complexity of the algorithm.

    “However, the algorithm requires additional frequency domain analysis of the signal, which increases the complexity of the algorithm.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [12] Li, 2022, Generalized mutual correlation time delay estimation method based on cubic correlation improvement in localized discharge ultrasonic localization, Acoust. Technol.

      Not checked in the free run.

  • May combine two claims.

    Interpretationown data

    The improved algorithm is helpful in improving the positioning ability of low-altitude UAVs and can provide a reference for signal processing of anti-low-altitude UAV combat systems and low-altitude UAV early warning systems.

    “In summary, the improved algorithm is helpful in improve the positioning ability of low-altitude UAVs and can provide a reference for signal processing of anti-low-altitude UAV combat systems and low-altitude UAV early warning systems.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    The GTCC SCOTg/PHAT algorithm has better noise resistance and effectiveness.

    “Therefore, the GTCC SCOTg/PHAT algorithm has better noise resistance and effectiveness.”
    Quote in the paperSubstantial claim
38 of 38

  • The authors state this as an assumption.

    The received signal model is x1(t)=A1s(t)+n1(t) and x2(t)=A2s(t−d)+n2(t).

    “Assume that the received signal model is:{x1(t)=A1s(t)+n1(t); x2(t)=A2s(t−d)+n2(t)”

  • The authors state this as an assumption.

    The noises n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t).

    “Assuming that n1(t) and n2(t) are stationary and uncorrelated Gaussian white noise independent of s(t), the cross-correlation function of the two noises n1(t) and n2(t) and the signal s(t) is:”

  • The authors state this as an assumption.

    In the cubic cross-correlation, noise is uncorrelated, so Rnnn(τ)=0.

    “assuming noise is uncorrelated, then Rnnn(τ)=0.”
3 of 3

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Correlation peak has the opposite delay sign under the stated definitions

    Minor

    The stated signal model and correlation definition pair s(t) with s(t−d−τ), so their correlation peaks at τ=−d, not τ=d. The displayed Rss(τ−d) and claimed peak at τ=d use the opposite lag sign.

1 of 1

Cites

Flagged first, then by citations

Research works printed but not linked: 10

  1. Liang, 2024, An improved generalized mutual correlation delay estimation algorithm for sound source localization, Opt. Commun. Technol., 48, 28
  2. Zhu, 2018, Research on delay estimation algorithm based on generalized mutual correlation, Commun. Technol., 51, 1030
  3. Yu, 2023, A generalized quadratic correlation delay estimation algorithm based on joint weighting, Comput. Simul., 40, 400
  4. Dou, 2016, Quadratic correlation-based generalized mutual correlation time difference estimation algorithm, J. Beijing Inst. Technol., 42, 197
  5. Li, 2022, Generalized mutual correlation time delay estimation method based on cubic correlation improvement in localized discharge ultrasonic localization, Acoust. Technol., 41, 774
  6. Tang, 2019, Analysis of GCC delay estimation algorithm based on microphone array, Comput. Syst. Appl., 28, 140
  7. Li, 2022, Exponential form of quadratic correlation GCC-PHAT-β delay estimation algorithm, Sci. Technol. Eng., 22, 14779
  8. Peng, 2023, A fast localization algorithm for flat plate structure impacts with low signal-to-noise ratio, Vib. Shock, 42, 180
  9. Wei, 2021, Research on a GCC delay estimation method with improved weighting function, Comput. Simul., 38, 16
  10. Wang, 2024, Generalized cubic mutual correlation pipeline leakage localization detection based on VMD, Press. Vessel, 41, 72

Cited by

Still being checked.

Related

Authors
Liu, M., Yu, J., & Yang, Z.
Affiliations
Nanjing University of Science and Technology (CN)
Corresponding author
Yu, Jiyan
ORCID
Venue
Sensors
Publisher
MDPI AG
Published
2025-04-25
Volume
25
Issue
9
Pages
2735
ISSN
1424-8220 (ISSN-L)
DOI
10.3390/s25092735
PMC
PMC12074323
OpenAlex
W4409799453
Semantic Scholar
c96cd0d2a66d145d1ba2dc8f5ff33cca1cc2a961
Cited by
4
References
7
Citations by year
2026: 3 · 2025: 1
FWCI
1.87
Type
journal article
Language
en
Open access
Licence
Locations
  • Sensors (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
Funders
Nanjing University of Science and Technology
Topics
  • Physical Sciences › Computer Science › Signal Processing › Direction-of-Arrival Estimation Techniques
  • Physical Sciences › Computer Science › Signal Processing › Speech and Audio Processing
  • Physical Sciences › Engineering › Ocean Engineering › Underwater Vehicles and Communication Systems
Keywords
time delay estimation, acoustic positioning, generalized cross-correlation, PHAT, weight functions, low signal-to-noise ratio, UAV positioning

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-28.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-28.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

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