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REVIEW 3 major objections 6 minor 1 cited by

Adaptive cancellation of mains power interference in continuous gravitational wave searches with a hidden Markov model

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read A recursive least-squares filter, using LIGO mains-voltage monitor references, suppresses the 60 Hz line so a hidden Markov model can detect an overlapping frequency-wandering continuous wave signal, in synthetic and real LIGO noise.

desk verdict A useful, honest engineering demonstration that RLS-based ANC plus an HMM can recover a CW signal overlapping LIGO's 60 Hz line, but the reported 20 dB real-data suppression exceeds the paper's own coherence-based bound and needs an explanation. read the letter →

arxiv 2412.01058 v1 pith:ZKMSHYXV submitted 2024-12-02 gr-qc astro-ph.IM

Tom Kimpson , Sofia Suvorova , Hannah Middleton , Changrong Liu , Andrew Melatos , Robin J. Evans , William Moran This is my paper · ORCID
classification gr-qcastro-ph.IM
keywords continuousgravitationalwavesadaptivenoisecancellationrecursiveleastsquareshiddenMarkovmodelmainspowerlineinstrumentallinesLIGOspectralsubtraction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper addresses a chronic loss in continuous gravitational-wave (CW) searches: candidates whose frequencies land on a known instrumental line, such as the 60 Hz mains-power artifact in LIGO data, are routinely vetoed rather than analysed. The authors try to lift that veto by subtracting the line before searching: a recursive least-squares adaptive filter, using LIGO's mains-voltage environmental-monitor (PEM) channels as references, estimates the 60 Hz clutter in the strain channel and removes it in the time domain, after which a hidden Markov model (HMM) tracker searches the cleaned data. On synthetic noise the line is suppressed by roughly 40 dB, and on real LIGO Livingston noise by about 20 dB; in both settings the HMM, which before filtering tracks the line and misses the signal, afterwards tracks an injected frequency-wandering CW signal at 59.5 Hz with a time-averaged RMS frequency error of about 0.05–0.06 Hz. If the method holds, the band around 60 Hz — including the frequency where the Crab pulsar's continuous emission is expected — becomes searchable rather than vetoed.

What carries the argument

The machinery is the adaptive recursive least squares (ARLS) filter: a finite-impulse-response (FIR) filter with $M$ taps that estimates the clutter at each time step as a weighted sum of delayed samples of the PEM reference signal, then subtracts that estimate from the strain channel; the residual drives both the filter's tap-weight update and the downstream HMM tracker. The weights are updated sample-by-sample through the RLS recursion — a gain vector built from the reference covariance matrix and a forgetting factor $\lambda$ that discounts old data — so the filter can track slow time-variations of the line (its wandering frequency and amplitude) without a stationary noise model. The argument's precondition is the measured coherence $C_{xr}(60\,\mathrm{Hz}) \approx 0.85$ between strain and PEM channels, which is used with the relation $R = 1/(1 - C_{xr})$ to argue that the reference is good enough for cancellation to bring the line below the HMM detection threshold.

What would settle it

Apply the ANC filter to a different, cleanly separated epoch of LIGO Livingston O3 data with the same injected 59.5 Hz signal and measure both the achieved suppression at 60 Hz and the HMM's detection probability; if the suppression falls well below the ~20 dB seen here (or if $p_d(0.05)$ at 5% false alarm drops toward the random-classifier limit), the linear scaled-replica assumption fails for that epoch. A cheaper test: measure $C_{xr}(60\,\mathrm{Hz})$ over many 10-minute blocks and check whether the achieved cancellation tracks the $R = 1/(1 - C_{xr})$ prediction.

Watch

Extended reading notes

Core claim

The central claim is that adaptive noise cancellation (ANC) based on a recursive least squares (RLS) algorithm, with LIGO mains-voltage PEM channels as reference inputs, suppresses the 60 Hz mains-power line in the GW strain channel sufficiently for a hidden Markov model to detect a quasi-monochromatic, frequency-wandering continuous wave signal that spectrally overlaps the line. The paper demonstrates this in two settings: with synthetic data whose interference follows a phenomenological model of mains power (frequency modulation, stochastic phase and amplitude noise, time delay relative to the reference), and with real O3a noise from LIGO Livingston. Before ANC, the HMM either fails to detect the injected signal or erroneously tracks the 60 Hz line; after ANC, the line is suppressed by about 40 dB (synthetic) or 20 dB (real data), and the HMM tracks the injected signal with time-averaged RMS frequency error of about 0.038 Hz (low spin-wandering, synthetic), 0.47 Hz (high spin-wandering, synthetic) and about 0.06 Hz (real data at constant 59.5 Hz). The paper also quantifies performance with ROC curves, finding detection probability at 5% false-alarm around 0.5, insensitive to the mains-power parameters (modulation amplitude, phase noise, modulation period) but improving with the number of PEM references, filter taps $M$, and the RLS forgetting factor $\lambda$.

Load-bearing premise

The load-bearing assumption is that the 60 Hz interference in the strain channel is an exact, amplitude-scaled replica of the PEM reference signal up to a fixed time delay, so that a fixed linear (FIR) filter trained on the reference can subtract the line; if the true coupling is nonlinear or time-varying, the observed cancellation may not generalize.

Editorial extensions

If this is right

  • Candidates overlapping a known instrumental line can be re-analysed rather than vetoed: run ANC first, then the usual continuous-wave search, provided a witness PEM channel for the line exists.
  • The approach works for signals whose frequency wanders, including paths that cross the 60 Hz line mid-observation, not just for constant-frequency signals at a safe offset.
  • With the nine O3 mains-voltage PEM channels, using two or more references already improves detection probability, with diminishing returns beyond two.
  • Performance is bounded below the zero-interference ideal: the best tuned filter (Nref = 9, M = 30, λ = 1) reaches pd(0.05) ≈ 0.55–0.58, so a minimum signal amplitude is still required for detection after ANC.
  • The RLS forgetting factor λ is the most sensitive control: λ = 1 (infinite memory) clearly outperforms λ = 0.9 on the quasi-stationary interference used here, so any practical implementation must choose λ to match the line's stationarity.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same ANC-HMM pipeline should transfer to other long-lived narrowband lines (50 Hz for Virgo, 60 Hz for KAGRA, plus mechanical lines with PEM witnesses), which would reopen most of the currently vetoed band below ~1 kHz; this is a direct extension the paper flags as future work.
  • The gap between the ~8 dB maximum cancellation predicted from Cxr ≈ 0.85 via Eq. (8) and the ~20–40 dB suppression observed on real data hints that the actual strain–PEM coupling is not an exact scaled replica; if so, the filter's real-data performance is epoch-dependent and should be re-measured per observing run before use in a production search.
  • Because the RLS update is recursive, the cleaned stream could in principle be produced online (latency permitting), enabling a live veto-free search over line-affected bands rather than an offline post-processing step.
  • The strong λ-dependence suggests an adaptive forgetting factor, tuned to the line's wandering statistics, could push detection probabilities closer to the zero-interference upper bound; the paper notes adaptive-λ algorithms exist but does not test them.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes an adaptive noise cancellation (ANC) scheme, implemented with a recursive least squares (RLS) filter, that uses LIGO PEM mains-voltage channels as references to subtract the 60 Hz power-line interference from the strain channel before a hidden Markov model (HMM) searches for a continuous-wave signal. The authors model the line and reference as an amplitude-scaled, delayed replica (Eqs. 2-4), validate the method on synthetic data generated from that same model with injections at 59.5 and 59.9 Hz, and report roughly 40 dB line suppression and successful HMM tracking. They also quantify performance with ROC curves as functions of mains line parameters (Δf_ac, σ_Θ, P) and filter parameters (N_ref, M, λ). The method is then applied to O3a LIGO Livingston data with a constant-frequency injection at 59.5 Hz, reporting about 20 dB suppression and HMM tracking with roughly 0.06 Hz RMS frequency error. The conclusion argues that the method can lift vetoes for candidates overlapping known instrumental lines.

Significance. If the reported performance is robust, the paper offers a practical way to recover continuous-wave candidates that would currently be vetoed because they overlap known spectral lines. The real-data injection-recovery test is a genuine, non-circular demonstration, and the before/after HMM comparison provides a clear yardstick for success. The paper also gives useful implementation details of the RLS algorithm and a ROC-based parameter study. Its significance is currently limited by an unresolved inconsistency between the coherence-based cancellation bound of Eq. (8) and the reported 20 dB real-data suppression, and by the absence of error bars or trial counts for the ROC curves. These issues must be addressed before the central claims can be fully accepted.

major comments (3)
  1. [II C / VI B, Eq. (8), Fig. 10] The reported ~20 dB suppression on real data is not reconciled with Eq. (8). With Cxr(60 Hz) ≈ 0.85, Eq. (8) gives R ≈ 6.7, i.e. at most about 8 dB of cancellation under a stationary linear single-reference model. If the 20 dB figure is obtained with all nine PEM references, then the relevant quantity is the multiple coherence across those references, which must be computed and inserted into an appropriate multi-reference bound; if it is claimed for a single reference, it exceeds the bound by roughly a factor of 16 in power. Please also define how the suppression level is measured (e.g. peak ASD at 60 Hz before versus after, integrated power in a band, or a median over the observation). This discrepancy is load-bearing because the real-data demonstration is the main evidence that the method generalizes beyond the synthetic model.
  2. [V, Figs. 8-9] The ROC curves are plotted without error bars, and the number of independent noise realizations used to compute each (pd, pfa) point is not stated. As a result, differences such as pd(0.05) = 0.44 versus 0.50 across σΘ values, or 0.50 versus 0.57 across Δfac values, cannot be distinguished from Monte Carlo fluctuations. Please report the number of trials and add confidence intervals or standard errors; this is needed to support the claim that performance is insensitive to the mains power parameters.
  3. [IV A, Eqs. (22)-(23)] The synthetic data are generated from the same scaled-replica coupling model that the ANC filter assumes, so the synthetic ROC study validates the filter under ideal in-family conditions rather than testing robustness to coupling mismatch. This is a limitation of the parameter studies in Section V, not a fatal flaw, because the real-data test in Section VI provides an out-of-model check. I recommend adding at least one synthetic experiment with a different coupling structure (e.g. a nonlinear or slowly time-varying transfer function, or a measured coherence structure) and/or analyzing more than one real-data epoch, to establish how the method behaves when Eq. (4) is violated.
minor comments (6)
  1. [VI B, Fig. 11] The text refers to the injected signal as the green solid curve, while the Figure 11 caption says the GW signal is the orange curve; please make the color descriptions consistent.
  2. [IV B] The statement that the HMM frequency error without ANC is '≲ 1/(2∆t) = 0.03 Hz here' appears inconsistent with ∆t = 1/1024 s, for which 1/(2∆t) = 512 Hz; please check the intended frequency-resolution formula and correct the numerical value.
  3. [Abstract] The abstract contains a typo: 'on a injected continuous wave signals' should read 'on an injected continuous wave signal'.
  4. [V B] Several occurrences of 'ppd' in the text (e.g. 'ppd(0.05)') should be 'pd'.
  5. [VI] The duration of the real-data segment used in Figures 10 and 11 is not stated; please specify Tobs and the GPS start time for reproducibility.
  6. [VI B] The real-data injection has a constant frequency, so the 'randomly wandering frequency' claim in the abstract applies only to the synthetic test; please clarify this distinction or add a wandering-frequency injection into real noise.

Circularity Check

1 steps flagged · score 3.0 of 10

Real-data injection test is independent and non-circular, but the synthetic validation injects clutter generated by exactly the scaled-replica relation the ANC filter assumes, making that portion of the evidence self-fulfilling.

  1. self definitional [Section IV A, Eqs. (22)-(23); cf. Section II B Eq. (4) and Section III A Eq. (10)]
    "Under these assumptions, Equations (2) and (4) reduce to r(t)=ar cos[2π fac t + 2π Δfac cos(2π t/P) + nΘ(tn)] + nr(tn), (22) c(t)=ac cos[2π fac(tn − τdelay) + 2π Δfac cos(2π(tn − τdelay)/P) + nΘ(tn − τdelay)], (23)"

    The synthetic clutter in Eq. (23) is, by construction, an amplitude-scaled and time-delayed copy of the synthetic reference in Eq. (22), sharing the same phase-noise realization nΘ(tn − τdelay). This is exactly the 'exact, amplitude-scaled replica up to a delay' coupling assumed in Eq. (4) and the relationship an FIR filter (Eq. (10)) is designed to represent. Thus the synthetic validation confirms only that an adaptive FIR filter can cancel a scaled delayed copy of its own reference input; it does not independently test whether real LIGO clutter obeys that model. The real-data test in Section VI B, which injects a synthetic GW signal into genuine LIGO noise and uses nine real PEM references, is independent of this circularity and carries the central claim.

full rationale

The paper's central claim is an injection-recovery demonstration: after RLS-ANC filtering, the HMM tracks an injected 59.5 Hz CW signal in real LIGO-Livingston noise, whereas before filtering it tracks the 60 Hz line. That outcome is not determined by construction; it depends on the adaptive filter actually removing real clutter. The HMM is cited to the authors' earlier Suvorova et al. (2016) paper, but that is standard tooling with extensive independent LVK usage, and no argument in this paper reduces to it. The synthetic-data validation (Section IV) is the one partly circular element: Equations (22)-(23) generate c(t) from r(t) under the same scaled-replica linear model the ANC FIR filter assumes, so successful cancellation there is expected by construction and does not validate the coupling model. The real-data suppression of ~20 dB versus the ~8 dB bound implied by Eq. (8) with Cxr ≈ 0.85 is a consistency issue worth flagging, but it is a correctness/external-validity concern, not circularity. Overall, the central real-data demonstration has independent content, so the score is moderate rather than high.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central claim rests on the assumption that the line interference is linearly related to a reference channel, on the HMM frequency-wandering model, and on several free parameters of the ARLS filter. No new physical entities are introduced. The synthetic validation is partly self-fulfilling because the clutter generator shares the ANC's linear-replica assumption; the real-data test is the main independent check.

free parameters (4)
  • Filter order M = 10, 15, 30 (trialled); value used in worked examples not stated
    Number of FIR taps in the ARLS filter; detection probability increases with M and saturates (Section V B).
  • Forgetting factor lambda = 0.9, 0.9999, 1.0; default 0.9999
    Controls the memory of the RLS filter; pd(0.05) varies from 0.02 (lambda=0.9) to 0.83 (lambda=1.0) in Section V B.
  • Regularization parameter delta = 100
    Selected empirically for the ARLS covariance initialization (Section III B); affects convergence speed and variance.
  • HMM parameters (states, transition probabilities) = Not specified in this paper
    Inherited from Suvorova et al. 2016; not listed here, which is a reproducibility gap.
assumptions (5)
  • domain assumption The 60 Hz clutter in the strain channel is an exact, amplitude-scaled replica of the PEM reference up to a time delay (Eq. 4).
    Tested via coherence Cxr(60 Hz) ≈ 0.85, but Eq. (8) gives a cancellation ceiling of about 8 dB under the stationary linear model, in tension with the reported 20 dB suppression.
  • ad hoc to paper The reference and clutter follow the phenomenological model in Eqs. (2)-(4), with uniform and Gaussian random draws at each time step.
    No first-principles model of mains power statistics; used to generate synthetic data for validation (Section IV A).
  • domain assumption Detector noise n(t) is white Gaussian after preprocessing.
    The paper notes real noise is non-white but assumes whitening can make it approximately Gaussian (Section II B).
  • domain assumption GW frequency evolves as a Gaussian random walk (Eqs. 20-21).
    Standard HMM tracking assumption from Suvorova et al. 2016, used for injections and tracking.
  • domain assumption Doppler modulations can be neglected because the Doppler shift is small relative to the 60 Hz line width.
    Stated in Section IV A; this simplifies the synthetic tests but may affect how long a real signal overlaps the line.

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Cite this review

Pith. "Pith review of Adaptive cancellation of mains power interference in continuous gravitational wave searches with a hidden Markov model." pith.science (2026). https://pith.science/paper/ZKMSHYXV

@misc{pith2026241201058,
  author       = {Pith},
  title        = {Pith review of: Adaptive cancellation of mains power interference in continuous gravitational wave searches with a hidden Markov model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKMSHYXV}},
  note         = {Machine review of arXiv:2412.01058}
}
abstract

Continuous gravitational wave searches with terrestrial, long-baseline interferometers are hampered by long-lived, narrowband features in the power spectral density of the detector noise, known as lines. Candidate GW signals which overlap spectrally with known lines are typically vetoed. Here we demonstrate a line subtraction method based on adaptive noise cancellation, using a recursive least squares algorithm, a common approach in electrical engineering applications such as audio and biomedical signal processing. We validate the line subtraction method by combining it with a hidden Markov model (HMM), a standard continuous wave search tool, to detect an injected continuous wave signal with an unknown and randomly wandering frequency, which overlaps with the mains power line at $60 \, {\rm Hz}$ in the Laser Interferometer Gravitational Wave Observatory (LIGO). The performance of the line subtraction method is tested on an injected continuous wave signal obscured by (a) synthetic noise data with both Gaussian and non-Gaussian components, and (b) real noise data obtained from the LIGO Livingston detector. In both cases, before applying the line subtraction method the HMM does not detect the injected continuous wave signal. After applying the line subtraction method the mains power line is suppressed by 20--40 dB, and the HMM detects the underlying signal, with a time-averaged root-mean-square error in the frequency estimate of $\sim 0.05 $ Hz. The performance of the line subtraction method with respect to the characteristics of the 60 Hz line and the control parameters of the recursive least squares algorithm is quantified in terms of receiver operating characteristic curves.

Figures

Figures reproduced from arXiv: 2412.01058 by the authors.

Figure 1
Figure 1. FIG. 1. GW strain amplitude spectral density (abbreviated [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Coherence [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Coherence spectrogram between the strain channel [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figures from the paper (6 more)
Figure 5
Figure 5. Figure 5: FIG. 5. Block diagram of the ARLS method described in [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Spectrum (i.e. modulus of the Fourier transform) of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. HMM tracking of a CW signal with spin wandering in the presence of 60 Hz mains power interference before (left [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Spectrum (i.e. modulus of the Fourier transform) of [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Same as Figure [PITH_FULL_IMAGE:figures/full_fig_p014_11.png]

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Forward citations

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