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Improved generalized cross correlation phase transform based time delay estimation using frequency domain low pass filter and circular moving average filter

저역 필터 및 원형 이동 평균 필터를 결합한 위상 변환 일반 상호 상관 시간 지연 추정기 성능 개선

Jun-Seok Lim1*
임 준석1*
1세종대학교 AI융합전자공학과
*Corresponding Author
30 September 2026. pp. 528-535
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Abstract

Among methods that estimate the time delay between signals arriving at two sensors using cross correlation, the Generalized Cross Correlation–Phase Transform (GCC-PHAT) method, which employs cross correlation between the two signals together with whitening preprocessing, achieves excellent performance and is thus widely used. The Generalized Cross Correlation with Low Pass Filter–Phase Transform (GCC-LP-PHAT), which applies a low pass filter in the frequency domain of this GCC-PHAT to further improve estimation performance, has also been studied. Noting that the whitened output of GCC-PHAT is a complex signal lying on the unit circle, this paper proposes the Generalized Cross Correlation with Low Pass Filter and Circular Moving Average–Phase Transform (GCC-LP-CMA-PHAT), which additionally applies a Circular Moving Average (CMA) filter to statistically suppress the residual phase noise remaining within the effective band. Through simulations with a white Gaussian source, we confirm that, over a Signal to Noise Ratio (SNR) range of –6 dB to 10 dB, the mean squared estimation error is improved by up to approximately 21.9 dB compared to conventional GCC-PHAT, and we show that the proposed GCC-LP-CMA-PHAT method yields additional performance improvement over the GCC-LP-PHAT method alone.

Keywords
Time Delay Estimation (TDE)
Generalized Cross Correlation(GCC)
Low pass filter
Circular Moving Average (CMA)

상호 상관관계를 이용하여 두 개 센서에 도래하는 신호 간의 시간 지연을 추정 방법 중에서 두 신호 간의 상호 상관과 그에 대한 백색화 전처리를 사용하는 Generalized Cross Correlation–Phase Transform(GCC-PHAT) 방법은 우수한 성능을 내어 널리 사용되는 방법이다. 이 GCC-PHAT의 주파수 영역에 저역 필터 사용하여 추정 성능을 향상시킨 Generalized Cross Correlation with Low Pass Filter–Phase Transform(GCC-LP-PHAT)가 연구되었다. 본 논문은 GCC-PHAT의 백색화 출력이 단위 원 위의 복소 신호임에 착안하여 원형 이동 평균(Circular Moving Average, CMA) 필터를 추가로 적용함으로써 유효 대역 내에 잔존하는 위상 잡음을 통계적으로 억제하는 Generalized Cross Correlation with Low Pass Filter and Circular Moving Average–Phase Transform(GCC-LP-CMA-PHAT)를 제안한다. 모의실험을 통하여 백색 가우시안 신호원인 경우 신호대잡음비(Signal to Noise Ratio, SNR) –6 dB부터 10 dB 사이에서 기존 GCC-PHAT 대비 평균 자승 추정 오차가 최대 약 21.9 dB 향상됨을 확인하고, 제안된 GCC-LP- CMA-PHAT 방법이 GCC-LP-PHAT 단독 방법보다 추가적인 성능 향상을 가져옴을 보인다.

키워드
시간 지연 추정(Time Delay Estimation, TDE)
일반 상호 상관(Generalized Cross Correlation, GCC)
저역 필터
원형 이동 평균(Circular Moving Average, CMA)
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Information
  • Publisher :The Acoustical Society of Korea
  • Publisher(Ko) :한국음향학회
  • Journal Title :The Journal of the Acoustical Society of Korea
  • Journal Title(Ko) :한국음향학회지
  • Volume : 45
  • No :5
  • Pages :528-535
  • Received Date : 2026-07-08
  • Accepted Date : 2026-08-05
  • DOI :https://doi.org/10.7776/ASK.2026.45.5.528
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