arXiv subjects

Olaf Hartwig

Publications and source records attributed to Olaf Hartwig.

At least 19 recordsLinked to original sources

arXiv2026

Impact of Spacecraft Orbit Uncertainties and Velocity Mismodeling on the LISA Gravitational-Wave Response

The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave observatory that consists of three spacecraft in a near-equilateral triangular formation. The spacecraft orbits are typically assumed to be perfectly known in LISA data analysis studies, but in reality, the orbit determination process introduces uncertainties in the spacecraft positions and velocities. In this work, we investigate how these uncertainties propagate into the LISA detector output and the impact of neglecting the spacecraft velocities. We quantify these errors in the knowledge of the LISA response using mismatches and discuss the implications for gravitational wave data analysis. We find that spacecraft orbit uncertainties impact the LISA response knowledge at high frequencies with worst mismatch below $10^{-7}$. The effect of neglecting the spacecraft velocities is largest at frequencies around $10^{-4}$ Hz with mismatches of order $10^{-4}$. For a galactic binary with frequency $10^{-4}$ Hz and SNR=200 observed for one year, we find that neglecting the spacecraft velocities in the response leads to less than 1-$\sigma$ biases in the parameter estimates. This work provides the first characterization of how errors in the LISA gravitational wave response propagate from gravitational wave strain through detector output to estimated parameters.

gr-qc↗

arXiv2026

LISA science ground segment conventions

This document sets out the conventions used for data simulations, waveforms, and analysis pipelines within the Distributed Data Processing Centre (DDPC) of the Laser Interferometer Space Antenna (LISA). It can also be considered a best practice guide for all publications related to the LISA mission. Topics covered include time-to-frequency transformations, gravitational-wave source parametrization, the instrumental response to gravitational waves, time-delay interferometry, and reference frame definitions.

astro-ph.IM↗

arXiv2025

Searching systematically for coupling of laser and phase-modulation noise in heterodyne interferometry

Heterodyne interferometry for precision science often comes with an optical phase modulation, for example, for intersatellite clock noise transfer for gravitational wave (GW) detectors in space, exemplified by the Laser Interferometer Space Antenna (LISA). The phase modulation potentially causes various noise couplings to the final phase extraction of heterodyne beatnotes by a phasemeter. In this paper, in the format of space-based GW detectors, we establish an analytical framework to systematically search for the coupling of various noises from the heterodyne and modulation frequency bands, which are relatively unexplored so far. In addition to the noise caused by the phase modulation, the high-frequency laser phase noise is also discussed in the same framework. The analytical result is also compared with a numerical experiment to confirm that our framework successfully captures the major noise couplings. We also demonstrate a use case of this study by taking the LISA-like parameters as an example, which enables us to derive requirements on the level of the laser and phase modulation noises in the high frequency regimes.

astro-ph.IM↗

arXiv2025

A flexible, GPU-accelerated approach for the joint characterization of LISA instrumental noise and Stochastic Gravitational Wave Backgrounds

LISA data analysis represents one of the most challenging tasks ahead for the future of gravitational-wave (GW) astronomy. Characterizing the instrument's noise properties while fitting for all the other detectable sources is a key requirement of any robust inference pipeline. Noise estimation will also play a crucial role in searches and parameter estimation of cosmological and astrophysical stochastic signals. Previous studies have tackled this topic by assuming perfect knowledge of the spectral shape of the instrumental noise and of different possible types of GW Stochastic Backgrounds (SGWBs), usually resorting to parametrized templates. Recently, various works that employ template-agnostic methods have been presented. In this work, we take an additional step further, introducing flexible spectral shapes in both the instrumental noise and the stochastic signals. We account for the lack of knowledge of the exact shape of the individual contributions to the overall power spectral density by using splines to represent arbitrary perturbations of the noise and signal spectral densities. We implement a data-driven Reversible Jump MCMC algorithm to fit different components simultaneously and to infer the level of flexibility required under different scenarios. We test this approach on simulated LISA data produced under different assumptions. We investigate the impact of this increased flexibility on the reconstruction of both the injected signal and the noise level, and we discuss the prospects for claiming a successful SGWB detection.

gr-qc↗

arXiv2025

Applying TDI to Hardware-Simulated Data

Many years of development have gone into producing instruments that meet the required noise performance of the LISA interferometric detection system. Concurrently, software simulations have been used to extensively develop the data analysis libraries to be used in the LISA pipeline, not least among which are the Time Delay Interferometry (TDI) algorithms. To bridge the gap between these two, we are developing a hardware-in-the-loop testbed to apply realistic, time-varying delays to signals traveling between phasemeters. We have shown that the testbed adds a sufficiently low amount of noise across the entire relevant LISA spectrum. We have also injected a realistic gravitational wave signal, generated via the LISA Data Challenge codebase, and successfully extracted it using TDI to remove the obscuring frequency noise of the carrier signal. Future efforts will expand the testbed to create a representative simulation of the entire LISA constellation, with an eye towards its use as a tool to aid in the development of the LISA data analysis pipelines.

gr-qc↗

arXiv2025

A pipeline for searching and fitting instrumental glitches in LISA data

Instrumental artefacts, such as glitches, can significantly compromise the scientific output of LISA. Our methodology employs advanced Bayesian techniques, including Reversible Jump Markov Chain Monte Carlo and parallel tempering to find and characterize glitches and astrophysical signals. The robustness of the pipeline is demonstrated through its ability to simultaneously handle diverse glitch morphologies and it is validated with a 'Spritz'-type data set from the LISA Data Challenge. Our approach enables accurate inference on Massive Black Hole Binaries, while simultaneously characterizing both instrumental artefacts and noise. These results present a significant development in strategies for differentiating between instrumental noise and astrophysical signals, which will ultimately improve the accuracy and reliability of source population analyses with LISA.

gr-qc↗

arXiv2025

Observable-based reformulation of time-delay interferometry

Spaceborne gravitational-wave observatories utilize a postprocessing technique known as time-delay interferometry (TDI) to reduce the otherwise overwhelming laser frequency noise by around 8 orders of magnitude. While, in its traditional form, TDI considers the spacecraft as point masses, recent studies have enhanced this simplified scenario by incorporating more realistic metrology chain models, which include onboard optical, electronic, and digital delays. These studies have updated the TDI algorithm to include onboard delays obtained from prelaunch and in-flight calibrations. Conversely, the processing scheme presented in this article treats onboard delays as an integral part of the TDI combinations: instead of having separate calibration stages, it directly expresses all delays appearing in the algorithm in terms of onboard measurements, especially pseudo-random-noise ranging (PRNR) measurements. The only onboard delays that need to be corrected in our processing scheme are PRNR delays in the digital domain, which are determined by commandable digital-signal-processing parameters; hence, they can be easily managed in postprocessing. Furthermore, our processing scheme does not require a prior interspacecraft clock synchronization, and it automatically corrects for potential relative drifts between the clocks driving local phase measurement systems. The proposed observable-based formulation closely relates TDI to the actual metrology system, and it clearly outlines how to manage onboard measurements in postprocessing. Hence, it is expected to lead to fundamental advancements in TDI, providing both conceptual completeness and unique practical benefits.

astro-ph.IM↗

arXiv2024

Optimal design of interpolation methods for time-delay interferometry

Time-delay interferometry (TDI) suppresses laser frequency noise by forming linear combinations of time-shifted interferometric measurements. The time-shift operation is implemented by interpolating discretely sampled data. To enable in-band laser noise reduction by eight to nine orders of magnitude, interpolation has to be performed with high accuracy. Optimizing the design of those interpolation methods is the focus of this work. Previous research that studied constant time-shifts suggested Lagrange interpolation as the interpolation method for TDI. Its transfer function performs well at low frequency but requires a high number of coefficients. Furthermore, when applied in TDI we observed prominent time-domain features when a time-varying shift scanned over a pure integer sample shift. To limit this effect we identify an additional requirement for the interpolation kernel: when considering time-varying shifts the interpolation kernel must be sufficiently smooth to avoid unwanted time-domain transitions that produce glitch-like features in power spectral density estimates. The Lagrange interpolation kernel exhibits a discontinuous first derivative by construction, which is insufficient for the application to LISA or other space-based GW observatories. As a solution we propose a novel design method for interpolation kernels that respect a predefined requirement on in-band interpolation residuals and that possess continuous derivatives up to a prescribed order. Using this method we show that an interpolation kernel with 22 coefficients is sufficient to respect LISA's picometre-requirement and to allow for a continuous first derivative which suppresses the magnitude of the time-domain transition adequately. The reduction from 42 (Lagrange interpolation) to 22 coefficients enables us to save computational cost and increases robustness against artefacts in the data.

astro-ph.IM↗

arXiv2024

Clock synchronization and light-travel-time estimation for space-based gravitational-wave detectors

Space-based gravitational-wave detectors, such as LISA, record interferometric measurements on widely separated satellites. Their clocks are not synced actively. Instead, clock synchronization is performed in on-ground data processing. It relies on measurements of the so-called pseudoranges, which entangle the interspacecraft light travel times with the clock desynchronizations between emitting and receiving spacecraft. For interspacecraft clock synchronization, we need to isolate the differential clock desynchronizations, i.e., disentangle the pseudoranges. This further yields estimates for the interspacecraft light travel times, which are required as delays for the laser frequency noise suppression via time-delay interferometry. Previous studies on pseudorange disentanglement apply various simplifications in the pseudorange modeling and the data simulation. In contrast, this article derives an accurate pseudorange model in the barycentric celestial reference system, complemented by realistic state-of-the-art LISA data simulations. Concerning pseudorange disentanglement, this leads to an a priori under-determined system. We demonstrate how on-ground orbit determinations, as well as onboard transmission and on-ground reception time tags of the telemetry data, can be used to resolve this degeneracy. We introduce an algorithm for pseudorange disentanglement based on a nonstandard Kalman filter specially designed for clock synchronization in systems where pseudorange measurements are conducted in different time frames. This algorithm achieves interspacecraft clock synchronization and light travel time estimation with submeter accuracy, thus fulfilling the requirements of time-delay interferometry.

gr-qc↗

arXiv2024

Experimental end-to-end demonstration of intersatellite absolute ranging for LISA

The Laser Interferometer Space Antenna (LISA) is a gravitational wave detector in space. It relies on a post-processing technique named time-delay interferometry (TDI) to suppress the overwhelming laser frequency noise by several orders of magnitude. This algorithm requires intersatellite-ranging monitors to provide information on spacecraft separations. To fulfill this requirement, we will use on-ground observatories, optical sideband-sideband beatnotes, pseudo-random noise ranging (PRNR), and time-delay interferometric ranging (TDIR). This article reports on the experimental end-to-end demonstration of a hexagonal optical testbed used to extract absolute ranges via the optical sidebands, PRNR, and TDIR. These were applied for clock synchronization of optical beatnote signals sampled at independent phasemeters. We set up two possible PRNR processing schemes: Scheme 1 extracts pseudoranges from PRNR via a calibration relying on TDIR; Scheme 2 synchronizes all beatnote signals without TDIR calibration. The schemes rely on newly implemented monitors of local PRNR biases. After the necessary PRNR treatments (unwrapping, ambiguity resolution, bias correction, in-band jitter reduction, and/or calibration), Scheme 1 and 2 achieved ranging accuracies of 2.0 cm to 8.1 cm and 5.8 cm to 41.1 cm, respectively, below the classical 1 m mark with margins.

astro-ph.IM↗

arXiv2024

Time-delay interferometry with onboard optical delays

Time-delay interferometry (TDI) is a data processing technique for space-based gravitational-wave detectors to create laser-noise-free equal-optical-path-length interferometers virtually on the ground. It relies on the interspacecraft signal propagation delays, which are delivered by intersatellite ranging monitors. Also delays due to onboard signal propagation and processing have a nonnegligible impact on the TDI combinations. However, these onboard delays were only partially considered in previous TDI-related research; onboard optical path lengths have been neglected so far. In this paper, we study onboard optical path lengths in TDI. We derive analytical models for their coupling to the second-generation TDI Michelson combinations and verify these models numerically. Furthermore, we derive a compensation scheme for onboard optical path lengths in TDI and validate its performance via numerical simulations.

gr-qc↗

arXiv2024

LISA Definition Study Report

The Laser Interferometer Space Antenna (LISA) is the first scientific endeavour to detect and study gravitational waves from space. LISA will survey the sky for Gravitational Waves in the 0.1 mHz to 1 Hz frequency band which will enable the study of a vast number of objects ranging from Galactic binaries and stellar mass black holes in the Milky Way, to distant massive black-hole mergers and the expansion of the Universe. This definition study report, or Red Book, presents a summary of the very large body of work that has been undertaken on the LISA mission over the LISA definition phase.

astro-ph.CO↗

arXiv2023

Ranging Sensor Fusion in LISA Data Processing: Treatment of Ambiguities, Noise, and On-Board Delays in LISA Ranging Observables

Interspacecraft ranging is crucial for the suppression of laser frequency noise via time-delay interferometry (TDI). So far, the effects of on-board delays and ambiguities on the LISA ranging observables were neglected in LISA modelling and data processing investigations. In reality, on-board delays cause offsets and timestamping delays in the LISA measurements, and pseudo-random noise (PRN) ranging is ambiguous, as it only determines the range up to an integer multiple of the PRN code length. In this article, we identify the four LISA ranging observables: PRN ranging, the sideband beatnotes at the interspacecraft interferometer, TDI ranging, and ground-based observations. We derive their observation equations in the presence of on-board delays, noise, and ambiguities. We then propose a three-stage ranging sensor fusion to combine these observables in order to gain accurate and precise ranging estimates. We propose to calibrate the on-board delays on ground and to compensate the associated offsets and timestamping delays in an initial data treatment (stage 1). We identify the ranging-related routines, which need to run continuously during operation (stage 2), and implement them numerically. Essentially, this involves the reduction of ranging noise, for which we develop a Kalman filter combining the PRN ranging and the sideband beatnotes. We further implement crosschecks for the PRN ranging ambiguities and offsets (stage 3). We show that both ground-based observations and TDI ranging can be used to resolve the PRN ranging ambiguities. Moreover, we apply TDI ranging to estimate the PRN ranging offsets.

gr-qc↗

arXiv2023

Laser noise residuals in LISA from onboard processing and time-delay interferometry

Time-delay interferometry (TDI) is a crucial step in the on-ground data processing pipeline of the Laser Interferometer Space Antenna (LISA), as it reduces otherwise overwhelming laser noise and allows for the detection of gravitational waves. This being said, several laser noise couplings have been identified that limit the performance of TDI. First, on-board processing, which is used to decimate the sampling rate from tens of MHz down to a few Hz, requires careful design of the anti-aliasing filters to mitigate folding of laser noise power into the observation band. Furthermore, the flatness of those filters is important to limit the effect of the flexing-filtering coupling. Secondly, the post-processing delays applied in TDI are subject to ranging and interpolation errors. All of these effects are partially described in the literature. In this paper, we present them in a unified framework and give a more complete description of aliased laser noise and the coupling of interpolation errors. Furthermore, for the first time, we discuss the impact of laser locking on laser noise residuals in the final TDI output. To verify the validity of the analytic PSD models we derive, we run numerical simulations using LISA Instrument and calculate second-generation TDI variables with PyTDI. We consider a setup with six independent lasers and with locked lasers (locking configuration N1-12). We find that laser locking indeed affects the laser noise residual in the TDI combination as it introduces correlations among the six lasers inducing slight modulations of the PSD compared to the case of six independent lasers. This implies further studies on laser noise residuals should consider the various locking configurations to produce accurate results.

astro-ph.IM↗

arXiv2023

End-to-end simulation and analysis pipeline for LISA

The data produced by the future space-based millihertz gravitational-wave detector LISA will require nontrivial pre-processing, which might affect the science results. It is crucial to demonstrate the feasibility of such processing algorithms and assess their performance and impact on the science. We are building an end-to-end pipeline that includes state-of-the-art simulations and noise reduction algorithms. The simulations must include a detailed model of the full measurement chain, capturing the main features that affect the instrument performance and processing algorithms. In particular, we include in these simulations, for the first time, proper relativistic treatment of reference frames with realistic numerically-optimized orbits; a model for onboard clocks and clock synchronization measurements; proper modeling of total laser frequencies, including laser locking, frequency planning and Doppler shifts; and a better treatment of onboard processing. Using these simulated data, we show that our pipeline is able to reduce the most critical noises and form synchronized observables. By injecting signals from a verification binary, we demonstrate that good parameter estimation can be obtained on this more realistic setup, extending existing results from previous LISA Data Challenges.

astro-ph.IM↗

arXiv2023

Stochastic gravitational wave background reconstruction for a non-equilateral and unequal-noise LISA constellation

We explore the impact of choosing different sets of Time-Delay Interferometry (TDI) variables for detecting and reconstructing Stochastic Gravitational Wave Background (SGWB) signals and estimating the instrumental noise in LISA. Most works in the literature build their data analysis pipelines relying on a particular set of TDI channels, the so-called AET variables, which are orthogonal under idealized conditions. By relaxing the assumption of a perfectly equilateral LISA configuration, we investigate to which degree these channels remain orthogonal and compare them to other TDI channels. We show that different sets of TDI variables are more robust under perturbations of the perfect equilateral configuration, better preserving their orthogonality and, thus, leading to a more accurate estimate of the instrumental noise. Moreover, we investigate the impact of considering the noise levels associated with each instrumental noise source to be independent of one another, generalizing the analysis from two to twelve noise parameters. We find that, in this scenario, the assumption of orthogonality is broken for all the TDI variables, leading to a misestimation of measurement error for some of the noise parameters. Remarkably, we find that for a flat power-law signal, the reconstruction of the signal parameters is nearly unaffected in these various configurations.

gr-qc↗

arXiv2022

The influence of laser relative intensity noise in the Laser Interferometer Space Antenna

LISA is an upcoming ESA mission that will detect gravitational waves in space by interferometrically measuring the separation between free-falling test masses at picometer precision. To reach the desired performance, LISA will employ the noise reduction technique time-delay interferometry (TDI), in which multiple raw interferometric readouts are time shifted and combined into the final scientific observables. Evaluating the performance in terms of these TDI variables requires careful tracking of how different noise sources propagate through TDI, as noise correlations might affect the performance in unexpected ways. One example of such potentially correlated noise is the relative intensity noise (RIN) of the six lasers aboard the three LISA satellites, which will couple into the interferometric phase measurements. In this article, we calculate the expected RIN levels based on the current mission architecture and the envisaged mitigation strategies. We find that strict requirements on the technical design reduce the effect from approximately 8.7 pm/rtHz per inter-spacecraft interferometer to that of a much lower sub-1 pm/rtHz noise, with typical characteristics of an uncorrelated readout noise after TDI. Our investigations underline the importance of sufficient balanced detection of the interferometric measurements.

gr-qc↗

arXiv2022

Unified model for the LISA measurements and instrument simulations

LISA is a space-based mHz gravitational-wave observatory, with a planned launch in 2034. It is expected to be the first detector of its kind, and will present unique challenges in instrumentation and data analysis. An accurate preflight simulation of LISA data is a vital part of the development of both the instrument and the analysis methods. The simulation must include a detailed model of the full measurement and analysis chain, capturing the main features that affect the instrument performance and processing algorithms. Here, we propose a new model that includes, for the first time, proper relativistic treatment of reference frames with realistic orbits; a model for onboard clocks and clock synchronization measurements; proper modeling of total laser frequencies, including laser locking, frequency planning and Doppler shifts; better treatment of onboard processing and updated noise models. We then introduce two implementations of this model, LISANode and LISA Instrument. We demonstrate that TDI processing successfully recovers gravitational-wave signals from the significantly more realistic and complex simulated data. LISANode and LISA Instrument are already widely used by the LISA community and, for example, currently provide the mock data for the LISA Data Challenges.

gr-qc↗