MeLISA: End-to-End LISA Data Pipeline

• MeLISA is an end-to-end LISA data processing system that converts raw L0 telemetry into synchronized, science-ready L1 observables for gravitational-wave analysis.
• It employs realistic instrument simulation including relativistic timing, onboard clock noise mitigation, laser frequency locking, and Doppler compensation.
• The pipeline bridges measurement simulation and astrophysical inference by validating noise reduction, TDI reconstruction, and Bayesian parameter estimation methods.

Searching arXiv for the specified LISA/MeLISA papers to ground the article in current records. MeLISA denotes an end-to-end LISA measurement, pre-processing, and analysis pipeline whose purpose is to demonstrate that the raw telemetry downlinked by the future space-based millihertz gravitational-wave detector LISA can be transformed into science-ready observables through a realistic chain of simulation and ground processing. In this usage, MeLISA is not merely a detector-response simulator: it spans the instrument measurement chain, the timing and laser-control architecture, the generation of L0-like telemetry, the reduction of dominant instrumental noises, the reconstruction of synchronized L1 observables, and subsequent parameter estimation on gravitational-wave sources (Bayle et al., 2023). Within the LISA ecosystem, it functions as a bridge between instrument realism and astrophysical inference, extending earlier LISA Data Challenge-style workflows by incorporating relativistic timing, realistic orbit handling, clock synchronization observables, laser frequency planning and locking, Doppler shifts, and improved onboard processing (Bayle et al., 2022).

1. Definition and position in the LISA data system

MeLISA is situated between raw instrument outputs and the inference layer used for gravitational-wave astronomy. The central premise is that LISA telemetry at L0 cannot be used directly for science; it must first be converted on the ground into calibrated, synchronized, and noise-reduced L1 observables. MeLISA is the end-to-end demonstration of that conversion, from optical beams and onboard clocks to TDI observables and Bayesian parameter estimation (Bayle et al., 2023).

The pipeline is explicitly framed as a demonstration chain comprising simulation of L0 data, first versions of noise-reduction and calibration algorithms, re-synchronization to a global time frame, and parameter estimation on the resulting L1 data. This establishes MeLISA as a full data-processing ecosystem for LISA rather than a narrowly scoped instrument model. A plausible implication is that its primary value lies in validating interfaces between traditionally separate subsystems: measurement simulation, telemetry formation, timing reconstruction, TDI, and source analysis.

A closely related foundation is the unified LISA measurement and instrument simulation model introduced in "Unified model for the LISA measurements and instrument simulations" (Bayle et al., 2022). That work provides the physically grounded measurement-chain formalism and two implementations—LISANode and LISA Instrument—that underpin MeLISA-style end-to-end modeling. It covers laser generation, propagation, interferometric readout, clock and timing effects, onboard processing, pseudoranging, and TDI-ready telemetry products, thereby supplying the simulation substrate on which a pipeline such as MeLISA can operate.

2. Measurement-chain simulation and architectural scope

The first layer of MeLISA is a simulation of the full measurement chain. The authors use LISA Instrument to model propagation of optical beams, onboard measurement devices, phasemeter readout, clocks, onboard computers, and the resulting telemetered quantities (Bayle et al., 2023). This includes carrier and sideband beams, interferometric beatnotes, phasemeter sampling and filtering, onboard processing, and the final ground-track and telemetry products.

The broader unified framework in (Bayle et al., 2022) specifies the standard LISA architecture of 3 spacecraft, 2 optical benches per spacecraft, and 3 interferometer types: ISI for the interspacecraft interferometer, TMI for the test-mass interferometer, and RFI for the reference interferometer. It also describes the explicitly telemetered beatnote outputs, including $\text{isi}_{12,c}$, $\text{isi}_{12,sb}$, $\text{rfi}_{12,c}$, $\text{rfi}_{12,sb}$, $\text{tmi}_{12,c}$, and $\text{mprs}$, thereby showing how physically continuous optical and timing processes are mapped into discrete telemetry streams.

The digital implementation is simplified to two sampling rates in the MeLISA pipeline: 16 Hz for continuous analog and high-frequency digital signals, and 4 Hz for final telemetry data, with a single downsampling/filtering step used to avoid aliasing (Bayle et al., 2023). This is a deliberately simplified but still realistic treatment of onboard processing. The significance of this design choice is methodological: it preserves the structure of the onboard-to-ground transition while keeping simulation and algorithm development tractable.

Within the ecosystem described in (Bayle et al., 2022), LISA Instrument and LISANode implement the same unified model but target different workflows. LISA Instrument is Python-based, vectorized with NumPy/SciPy, easier to use interactively, and faster for short to moderate simulations, while LISANode is a modular node-based framework better suited to long simulations because its memory usage stays roughly constant. This dual-implementation strategy is important because MeLISA requires both development agility and scalability for realistic studies.

3. Relativistic timing, reference frames, and orbit handling

A defining realism upgrade in MeLISA is the explicit treatment of reference frames and time scales. Physics on each spacecraft is simulated in the proper time of that spacecraft, denoted $\tau_i$, and then related to the global barycentric coordinate time $t$ in TCB (Bayle et al., 2023). The pipeline computes deviations between the spacecraft time-proper scale and TCB because quantities exchanged between spacecraft must be referred correctly between these frames.

The unified measurement model makes this structure more explicit by distinguishing three time coordinates: global barycentric coordinate time $t$, spacecraft proper time $\tau_i$, and onboard clock time $\text{isi}_{12,sb}$0 (Bayle et al., 2022). Scalar phase invariance under coordinate transformation is written as

$\text{isi}_{12,sb}$1

with clock deviations introduced through

$\text{isi}_{12,sb}$2

This separation preserves the distinction between relativistically defined ideal times and imperfect onboard timekeeping.

The orbit model currently used in the MeLISA pipeline is a first-order Keplerian approximation for equal-armlength orbits optimized to keep the constellation stable (Bayle et al., 2023). These orbits provide the spacecraft positions and light-travel times required for the time-varying gravitational-wave response. The architecture is, however, intended to accept any realistic orbit set, including those provided by ESA; thus the current orbit model is presented as a first realistic step rather than a hard limitation.

The propagation model in (Bayle et al., 2022) further decomposes proper pseudo-range as

$\text{isi}_{12,sb}$3

where $\text{isi}_{12,sb}$4 is the gravitational-wave contribution, and writes the received phase as

$\text{isi}_{12,sb}$5

The associated frequency-domain forms include Doppler-delay terms and first-order expansion in small fluctuations. This matters because the combined effects of light-travel delay, constellation motion, and relativistic time transfer are not secondary bookkeeping details; they are intrinsic to how LISA measurements are defined and processed.

4. Clock architecture, synchronization observables, and telemetry formation

Each spacecraft hosts its own clock, and the onboard clocks define separate time frames $\text{isi}_{12,sb}$6 used for measurements. These differ from the proper times $\text{isi}_{12,sb}$7 because of clock imperfections (Bayle et al., 2023). Clock modeling is therefore central to MeLISA, not ancillary.

The clock-noise architecture follows the LISA approach in which laser beams are phase-modulated to imprint clock jitter: $\text{isi}_{12,sb}$8 Here $\text{isi}_{12,sb}$9 is the carrier phase, $\text{rfi}_{12,c}$0 is the modulation index, and $\text{rfi}_{12,c}$1 is the clock-derived modulation (Bayle et al., 2023). The resulting sidebands are approximately 2.4 GHz away from the carrier. These sidebands generate additional beatnotes that are tracked by the phasemeter and later used on the ground for clock-noise correction.

The unified model in (Bayle et al., 2022) expresses the same concept in a carrier-plus-sideband decomposition: $\text{rfi}_{12,c}$2 with the upper and lower sideband phases

$\text{rfi}_{12,c}$3

The model simulates the carrier and upper sideband explicitly, and these sidebands are used to support timing correction and clock-noise removal.

The clocks are also used for PRN code modulation. By correlating pseudorandom codes on different beams, the pipeline estimates absolute pseudoranges between spacecraft, with the pseudoranges containing both light-travel times and differential clock noise (Bayle et al., 2023). Combining sideband measurements, PRN correlations, and ground-tracking observations allows reconstruction of a precise and accurate pseudorange estimate. In the present implementation, Earth-based observations are used to infer spacecraft positions, velocities, and the relation between onboard clock times and TCB, although these quantities are assumed to be recovered perfectly.

The measurement model in (Bayle et al., 2022) also gives the mapping from proper-time signals to sampled onboard-clock telemetry. Clock time is written as

$\text{rfi}_{12,c}$4

and frequency sampling acquires a Doppler-like rescaling: $\text{rfi}_{12,c}$5 This is the formal bridge from the instrument’s physical time evolution to the telemetered observables that ground processing receives. In practical terms, MeLISA’s importance lies precisely in operationalizing that bridge.

5. Laser frequency modeling, locking, Doppler management, and noise structure

Laser frequency modeling in MeLISA uses the decomposition

$\text{rfi}_{12,c}$6

where $\text{rfi}_{12,c}$7 is the central laser frequency, $\text{rfi}_{12,c}$8 models MHz Doppler shifts and programmed offsets, and $\text{rfi}_{12,c}$9 contains instrumental noise up to about 100 Hz together with tiny gravitational-wave signals at around 100 nHz (Bayle et al., 2023). The closely related unified model gives $\text{rfi}_{12,sb}$0 THz and motivates simulating frequency rather than phase in order to avoid numerical overflow from the optical carrier (Bayle et al., 2022).

This decomposition is critical because LISA beatnotes must remain within a phasemeter bandwidth of roughly 5–25 MHz (Bayle et al., 2023). The pipeline therefore includes laser locking, frequency planning, and Doppler compensation. One primary laser is locked to its cavity, and the other lasers are locked to each other according to a precomputed frequency plan solved using computational-geometry-based methods. Under the assumption of perfect locking, some beatnotes contain only the slow MHz offsets, while non-locking beatnotes include the full noise and gravitational-wave content.

The unified model further resolves how Doppler-delayed carrier components transform under propagation: $\text{rfi}_{12,sb}$1 and

$\text{rfi}_{12,sb}$2

These expressions show why Doppler management is inseparable from realistic laser simulation.

The noise model in (Bayle et al., 2022) includes explicit PSDs for laser noise, clock noise, modulation noise, test-mass acceleration noise, backlink noise, readout noise, and ranging noise. For example, laser noise is written as

$\text{rfi}_{12,sb}$3

while clock noise is modeled through

$\text{rfi}_{12,sb}$4

These component-level models establish the noise landscape that MeLISA’s downstream reduction algorithms must confront. Their inclusion also explains why the pipeline is framed as an end-to-end demonstration rather than a simple source-injection exercise.

6. Ground processing, TDI reconstruction, and parameter estimation

The central scientific requirement for MeLISA is that realistic L0 telemetry be convertible into synchronized, noise-reduced observables suitable for inference. The processing sequence reported in (Bayle et al., 2023) is: combine sideband and PRN measurements to estimate ranging delays and derivatives; estimate inter-spacecraft light travel times using ground tracking; compute second-generation TDI $\text{rfi}_{12,sb}$5 combinations; re-synchronize $\text{rfi}_{12,sb}$6 to the global TCB time frame; and form quasi-orthogonal $\text{rfi}_{12,sb}$7 combinations for inference.

Several observables structure this chain. Interferometers produce beatnotes at the difference between two laser frequencies,

$\text{rfi}_{12,sb}$8

within which gravitational-wave signals appear as tiny fluctuations at the hundred-nHz level (Bayle et al., 2023). The ground-side TDI stage forms second-generation Michelson combinations $\text{rfi}_{12,sb}$9, then quasi-orthogonal $\text{tmi}_{12,c}$0 combinations for parameter estimation. The unified model independently demonstrates TDI reconstruction with second-generation observables $\text{tmi}_{12,c}$1 using PyTDI, showing that the simulated telemetry is analysis-compatible (Bayle et al., 2022).

The dominant noises reduced by this processing are laser frequency noise and clock noise. After preprocessing, the remaining dominant contributions are secondary noises, especially test-mass acceleration noise and shot/readout noise (Bayle et al., 2023). The paper reports that dominant laser and clock noise are suppressed by more than 8 orders of magnitude in the preprocessed data. In the unified model study, TDI suppresses laser and clock noise sufficiently that the injected verification binary becomes visible around $\text{tmi}_{12,c}$2 mHz (Bayle et al., 2022).

For source recovery, the pipeline injects a signal from the verification binary V407 Vul, described as a compact binary with a 569 s orbital period and an expected integrated 4-year SNR of 44 to 80 (Bayle et al., 2023). Because only 3 days of data are simulated, the signal amplitude is increased so that the short dataset has the same integrated SNR as the full 4-year case. Bayesian inference is then performed on the frequency-domain, re-synchronized TDI data using Nessai and Dynesty, with a Gaussian likelihood and the frequency-domain template generator FastGB.

The reported inference results are technically specific. All parameters are recovered correctly except the frequency derivative and sky-localization angles, which are not recoverable because the simulated span is too short. Posterior distributions agree excellently between the realistic MeLISA pipeline and simpler LDC-like data, and a p-p plot over 128 realizations indicates good statistical consistency (Bayle et al., 2023). A slight deviation in initial phase is attributed to filter delays introduced in the simulation but not yet modeled in the likelihood. The main implication is that added measurement-chain realism does not invalidate standard inference machinery for the tested verification-binary case.

7. Validation status, relation to prior challenge data, and limitations

A major conclusion of the MeLISA work is that increased realism need not degrade downstream science performance. Relative to previous LISA Data Challenge-style datasets, the pipeline adds relativistic time-frame handling, numerically optimized orbits, onboard clock noise and synchronization observables, laser frequency planning and locking, MHz Doppler management, and more detailed onboard processing, yet still yields posteriors consistent with those from simpler analyses (Bayle et al., 2023). This suggests that earlier LDC results were not merely artifacts of oversimplified simulation, at least for the verification-binary configuration studied.

The connection to the LISA Data Challenges is explicit in the unified-model paper: LISANode and LISA Instrument are already widely used by the LISA community and currently provide the mock data for the LISA Data Challenges (Bayle et al., 2022). In that sense, MeLISA extends a community-standard simulation base toward a fuller demonstration of the end-to-end path from realistic telemetry to synchronized observables and parameter estimation.

Validation in the MeLISA paper proceeds through several criteria: large suppression of laser and clock noise, visible injected gravitational-wave signals in the $\text{tmi}_{12,c}$3 channel, successful source-parameter recovery, and comparison with simpler LDC-like analyses (Bayle et al., 2023). These tests collectively support the claim that raw-like telemetry can be processed into scientifically usable L1 data products.

The stated limitations are equally important. Ground-tracking quantities are currently assumed to be recovered without error; the spacecraft and payload model is simplified; only a 3-day stretch is simulated; and a filtering delay remains unmodeled in the likelihood, producing a small phase discrepancy (Bayle et al., 2023). Planned next steps include correcting for filter delays, running month-long simulations to include sky-localization information, adding further noise-reduction steps such as tilt-to-length coupling corrections, and continuing to improve the ground-processing chain.

The term “MeLISA” can be a source of ambiguity because similarly named projects exist in unrelated domains. In the present context, however, it refers specifically to the LISA end-to-end measurement, pre-processing, and analysis pipeline described in (Bayle et al., 2023), together with the unified simulation framework developed in (Bayle et al., 2022). Its technical significance lies in showing that mission-realistic timing, laser-control, and telemetry effects can be incorporated without preventing TDI formation, synchronization, and conventional Bayesian gravitational-wave inference.