Time delay interferometry and principal component analysis for noise cancellation of TianQin

doi:10.1088/1674-1056/ae12d4

中国物理B ›› 2026, Vol. 35 ›› Issue (5): 50401-050401.doi: 10.1088/1674-1056/ae12d4

Time delay interferometry and principal component analysis for noise cancellation of TianQin

Xinchun Hu(胡新春)^1,† and Yan Wang(王炎)²

1 School of Electrical and Information Engineering, Tongling University, Tongling 244000, China;
2 National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurements, Department of Astronomy and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2025-07-27 修回日期:2025-09-24 接受日期:2025-10-14 发布日期:2026-05-11
通讯作者: Xinchun Hu E-mail:030261@tlu.edu.cn
基金资助:
Project supported by “GrEAT network” in School of Physics and Astronomy, University of Glasgow. Wang Y gratefully acknowledges support from the National Key Research and Development Program of China (Grant Nos. 2023YFC2206702 and 2022YFC2205201), and the Major Science and Technology Program of Xinjiang Uygur Autonomous Region of China (Grant No. 2022A03013-4). Hu X C is supported by the Tongling University Talent Program (Grant No. 2021tlxyrc26) and Tongling University Natural Science Research Project (Grant No. 2024tlxykjZD10).

Time delay interferometry and principal component analysis for noise cancellation of TianQin

Xinchun Hu(胡新春)^1,† and Yan Wang(王炎)²

1 School of Electrical and Information Engineering, Tongling University, Tongling 244000, China;
2 National Gravitation Laboratory, MOE Key Laboratory of Fundamental Physical Quantities Measurements, Department of Astronomy and School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2025-07-27 Revised:2025-09-24 Accepted:2025-10-14 Published:2026-05-11
Contact: Xinchun Hu E-mail:030261@tlu.edu.cn
Supported by:
Project supported by “GrEAT network” in School of Physics and Astronomy, University of Glasgow. Wang Y gratefully acknowledges support from the National Key Research and Development Program of China (Grant Nos. 2023YFC2206702 and 2022YFC2205201), and the Major Science and Technology Program of Xinjiang Uygur Autonomous Region of China (Grant No. 2022A03013-4). Hu X C is supported by the Tongling University Talent Program (Grant No. 2021tlxyrc26) and Tongling University Natural Science Research Project (Grant No. 2024tlxykjZD10).

摘要/Abstract

摘要： TianQin is a proposed space-borne laser interferometer which aims to detect gravitational waves in the low frequency band ($10^{-4}$ Hz-$10^{0}$ Hz). However, for space-borne interferometry detectors the laser phase noise is expected to be 7-8 orders of magnitude higher than the gravitational wave signals, due to unequal and time-varying arm lengths. Time delay interferometry (TDI) is an effective method to cancel laser phase noise by synthesizing virtual equal arm interferometric measurements with time delayed Doppler data combinations. In previous work it has been shown that TDI variables can also be understood within the context of principal component analysis (PCA), as combinations of eigenvectors of the total noise covariance matrix. It is therefore possible to generate the same TDI variables using a PCA approach - by computing the eigenvectors of the noise covariance matrix at a specific time. In this paper we extend significantly the previous work on a PCA approach to generating TDI variables by presenting TDI sensitivity curves for TianQin approximated as both a static and moving constellation of satellites. We compare the covariance matrix for the static and moving case, from the point of view of performing statistical inference using PCA. We also demonstrate the equivalency between the `conventional' second generation TDI variables and those obtained using PCA.

关键词: gravitational waves, time delay interferometry, principal component analysis

Abstract: TianQin is a proposed space-borne laser interferometer which aims to detect gravitational waves in the low frequency band ($10^{-4}$ Hz-$10^{0}$ Hz). However, for space-borne interferometry detectors the laser phase noise is expected to be 7-8 orders of magnitude higher than the gravitational wave signals, due to unequal and time-varying arm lengths. Time delay interferometry (TDI) is an effective method to cancel laser phase noise by synthesizing virtual equal arm interferometric measurements with time delayed Doppler data combinations. In previous work it has been shown that TDI variables can also be understood within the context of principal component analysis (PCA), as combinations of eigenvectors of the total noise covariance matrix. It is therefore possible to generate the same TDI variables using a PCA approach - by computing the eigenvectors of the noise covariance matrix at a specific time. In this paper we extend significantly the previous work on a PCA approach to generating TDI variables by presenting TDI sensitivity curves for TianQin approximated as both a static and moving constellation of satellites. We compare the covariance matrix for the static and moving case, from the point of view of performing statistical inference using PCA. We also demonstrate the equivalency between the `conventional' second generation TDI variables and those obtained using PCA.

Key words: gravitational waves, time delay interferometry, principal component analysis

中图分类号: (Gravitational waves)

04.30.-w

04.80.Nn (Gravitational wave detectors and experiments) 04.20.Cv (Fundamental problems and general formalism)

Xinchun Hu(胡新春) and Yan Wang(王炎). Time delay interferometry and principal component analysis for noise cancellation of TianQin[J]. 中国物理B, 2026, 35(5): 50401-050401.

Xinchun Hu(胡新春) and Yan Wang(王炎). Time delay interferometry and principal component analysis for noise cancellation of TianQin[J]. Chin. Phys. B, 2026, 35(5): 50401-050401.

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Time delay interferometry and principal component analysis for noise cancellation of TianQin

Time delay interferometry and principal component analysis for noise cancellation of TianQin

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