{"id":"ae936037-1eef-444d-9580-fa5038e47061","arxiv_id":"2412.01058","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"An adaptive recursive least squares filter, referenced to mains-power monitor channels, suppresses the 60 Hz line in LIGO data so that a hidden Markov model can recover an injected, frequency-wandering continuous wave signal.","lead":"The authors show that an adaptive noise cancellation filter, using LIGO's mains-power monitor as a reference, suppresses the 60 Hz power-line interference and lets a hidden Markov model track an injected gravitational-wave signal whose frequency wanders across the line. Tests on synthetic noise and real LIGO Livingston data report 20 to 40 dB line suppression and frequency-tracking errors near 0.05 to 0.06 Hz.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Reported 20 dB real-data suppression at 60 Hz exceeds the stationary linear bound from Eq. (8) with C=0.85 by about 12 dB; the paper never resolves this, and its real-data demonstration depends on that suppression.","rationale":"The reader's weakest assumption flagged the scaled-replica model in Section II B and the gap between Eq. (8) and the reported 20 dB suppression. I partly agree. The sharpest formulation is not whether the coupling is exactly linear, but whether the paper's reported real-data suppression is compatible with its own coherence bound. The real-data test is the only evidence that breaks circularity, because the synthetic clutter is generated from the same FIR-replica assumption used by the ANC filter. If the 20 dB figure were inflated, or if it depends on an unstated multiple-coherence effect, the headline claim that the HMM recovers an injected signal after ANC on real noise could still hold but would rest on a non-quantified empirical claim. The proposed test is decisive: compute the multiple coherence for the nine PEMs used in Section VI A; if it explains 20 dB, the discrepancy disappears. Other issues identified by the reader, such as a single realization, no error bars, and the constant-frequency real-data injection, are real but secondary, and they do not threaten the logic as directly as an unexplained factor-of-16 inconsistency in the suppression measurement. I therefore keep the reader's CONDITIONAL verdict unchanged.","tokens_in":20180,"tokens_out":8546,"duration_ms":80880,"concrete_test":"Re-run the Fig. 10 cancellation on the same O3a segment with exactly one PEM reference and with all nine references. For each case, compute the achieved 60 Hz suppression in ASD and compare it with the bound 10 log10[1/(1-C)] using (a) the pairwise coherence C between the strain and that one PEM and (b) the multiple coherence between the strain and the nine-PEM vector, both over the same 10-min window. If one-PEM suppression exceeds the pairwise bound by more than ~3 dB, the reported suppression or the linear model is wrong; if the nine-PEM multiple coherence predicts ~20 dB, the discrepancy is resolved and the central claim is supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central real-data claim (Section VI B) is that ANC removes the 60 Hz line enough for the HMM to recover the injection. For that claim to be trustworthy, the reported ~20 dB suppression must be consistent with the assumed linear, scaled-replica coupling of Section II B. The paper's own bound, Eq. (8) with the measured Cxr(60 Hz) ≈ 0.85, gives R = 1/(1 - 0.85) ≈ 6.7, i.e. at most ~8 dB of power cancellation under a stationary linear model. Section VI B reports ~20 dB suppression in the Fourier spectrum, without computing the coherence of the actual filter output. Because Section VI A states that nine PEM references are used, one possible reconciliation is that the relevant quantity is the multiple coherence across all nine channels, which can exceed the pairwise 0.85; but the paper neither computes this multiple coherence nor connects it to Eq. (8). If the 20 dB figure is correct only because multiple references are used, the claim should be stated that way; if it is claimed for a single reference, it appears to exceed the bound by a factor of ~16 in power, suggesting either an error in the suppression measurement or a failure of the scaled-replica model. This is load-bearing because the real-data demonstration is the main non-circular evidence that the method generalizes beyond synthetic clutter generated with the same FIR-replica assumption.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":20316,"tokens_out":5790,"duration_ms":56276,"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":[{"comment":"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.","section":"II C / VI B, Eq. (8), Fig. 10"},{"comment":"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.","section":"V, Figs. 8-9"},{"comment":"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.","section":"IV A, Eqs. (22)-(23)"}],"minor_comments":[{"comment":"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.","section":"VI B, Fig. 11"},{"comment":"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.","section":"IV B"},{"comment":"The abstract contains a typo: 'on a injected continuous wave signals' should read 'on an injected continuous wave signal'.","section":"Abstract"},{"comment":"Several occurrences of 'ppd' in the text (e.g. 'ppd(0.05)') should be 'pd'.","section":"V B"},{"comment":"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.","section":"VI"},{"comment":"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.","section":"VI B"}],"recommendation":"major_revision","confidential_remarks":"The main technical risk is the 20 dB versus Eq. (8) discrepancy in the real-data demonstration; if the authors can resolve it by computing the multiple-reference coherence or by correcting the suppression measurement, the paper would be suitable for publication. The missing error bars on the ROC curves should also be addressed. The topic fits the journal's scope and the real-data injection experiment is a genuine step beyond purely synthetic validation."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know up front. First, this is a genuine injection-recovery test: they inject a CW signal into real LIGO Livingston noise, filter with an RLS adaptive noise canceller referenced to nine PEM mains monitors, and show the HMM then tracks the signal instead of the 60 Hz line. That is non-circular evidence, and it is the heart of the paper. Second, the numbers don't quite line up. With measured pairwise coherence Cxr(60 Hz) ≈ 0.85, Eq. (8) caps cancellation at about 8 dB under a stationary linear model, yet Section VI B reports roughly 20 dB suppression on real data. The paper never resolves this. The likely reconciliation is that the relevant quantity is the multiple coherence across the nine PEM references, which can exceed the pairwise 0.85, but they neither compute it nor connect it to Eq. (8). Since the real-data demonstration leans on that suppression, this is the main thing a referee should push on.\n\nWhat is actually new: applying standard RLS ANC with PEM references to CW searches in the LIGO band around 60 Hz, and combining it with an HMM for wandering-frequency signals. The ROC characterization as a function of line parameters and filter parameters is a reasonable systematic study. The writing is clear, the method is sensible, and the real-data example is a legitimate step beyond a purely synthetic validation. They also honestly note the over-subtraction and the possibility of nonlinear coupling.\n\nThe soft spots are proportionate. The ROC curves have no error bars and no stated number of trials, and pd(0.05) ≈ 0.5 is modest relative to the zero-interference upper bound of 0.85. The real-data injection is constant-frequency, not the wandering-frequency case shown on synthetic data. There is no baseline comparison with existing PEM-based subtraction tools, so the practical advantage over established methods is unclear. The synthetic validation is partly circular—the clutter generator assumes the same scaled-replica linear coupling that the ANC filter models—but the real-data test mitigates that concern.\n\nWho is this for? Practitioners in CW searches and LIGO data analysis who want a concrete recipe for recovering signals near lines. The paper deserves a serious referee: the flaws are missing quantification, not a load-bearing conceptual error. I would send it to peer review with major revisions, and I would probably cite it if I were working on line subtraction.","headline":"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.","tokens_in":21015,"tokens_out":1761,"would_cite":true,"duration_ms":17960,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["continuous gravitational waves","adaptive noise cancellation","recursive least squares","hidden Markov model","mains power line","instrumental lines","LIGO","spectral line subtraction"],"falsifier":"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.","tokens_in":19806,"feed_emoji":"⚡","tokens_out":17975,"duration_ms":127210,"temperature":0.7,"pith_summary":"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.","feed_headline":"Filter lifts LIGO's 60 Hz line to reveal hidden signals","feed_subtitle":"Real LIGO data show a 59.5 Hz injected signal recovered after the 60 Hz line is subtracted.","key_machinery":"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.","core_discovery":"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 $\\lambda$.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the adaptive noise cancellation method: estimating and subtracting noise correlated with a reference input.","marker":"[54]"},{"why":"Provides the recursive least squares algorithm and its control parameters (M, λ, δ) used by the filter.","marker":"[55]"},{"why":"The hidden Markov model tracker that forms the detection and frequency-tracking stage of the pipeline.","marker":"[39]"},{"why":"Catalogues LIGO spectral lines, including the 60 Hz mains line's wandering frequency and width, informing the noise model.","marker":"[12]"},{"why":"The biaxial-rotor gravitational wave signal model used to generate the injected continuous wave signals.","marker":"[46]"},{"why":"Gives the relation between coherence and achievable noise cancellation used to justify that Cxr(60 Hz) ≈ 0.85 suffices.","marker":"[52]"},{"why":"Source of the O3a LIGO-Livingston strain and PEM data used in the real-data validation.","marker":"[44]"}],"fun_headline_variants":["Adaptive filter cancels LIGO mains hum to uncover CW signal","RLS noise canceller reveals hidden CW signals under LIGO's 60 Hz line","HMM plus adaptive cancellation digs out signals buried in power-line noise","Line subtraction revives hidden signals in LIGO data"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Adaptive filter cancels LIGO mains hum to uncover CW signal","RLS noise canceller reveals hidden CW signals under LIGO's 60 Hz line","HMM plus adaptive cancellation digs out signals buried in power-line noise","Line subtraction revives hidden signals in LIGO data"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000654,"raw_usage":{"total_tokens":3091,"prompt_tokens":1135,"completion_tokens":1956,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":751,"completion_tokens_details":{"reasoning_tokens":1877}},"tokens_in":751,"tokens_out":1956,"duration_ms":13308,"temperature":1.0,"reasoning_tokens":1877,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T04:43:37.313605+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"Schafer, M","cited_arxiv_id":null,"evidence_quote":"Supplies the adaptive noise cancellation method: estimating and subtracting noise correlated with a reference input."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the recursive least squares algorithm and its control parameters (M, λ, δ) used by the filter."},{"cited_title":"A new veto for continuous gravitational wave searches","cited_arxiv_id":"1707.05268","evidence_quote":"The hidden Markov model tracker that forms the detection and frequency-tracking stage of the pipeline."}],"review_version":1}