[Paper Review] State space modelling and data analysis exercises in LISA Pathfinder

M. Nofrarías, F. Antonucci+84 more|arXiv (Cornell University)|Jun 19, 2013

Computational Physics and Python Applications1 references3 citations

TL;DR

This paper presents a state space modeling framework and data analysis toolbox (LTPDA) for the LISA Pathfinder mission, enabling real-time, low-latency analysis of gravitational wave technology validation data. The approach improves noise characterization and system modeling, achieving a differential acceleration noise floor of $3\times10^{-14}\,\text{m/s}^2/\sqrt{\text{Hz}}$ at 3 mHz, critical for future space-based gravitational wave detection.

ABSTRACT

LISA Pathfinder is a mission planned by the European Space Agency to test the key technologies that will allow the detection of gravitational waves in space. The instrument on-board, the LISA Technology package, will undergo an exhaustive campaign of calibrations and noise characterisation campaigns in order to fully describe the noise model. Data analysis plays an important role in the mission and for that reason the data analysis team has been developing a toolbox which contains all the functionalities required during operations. In this contribution we give an overview of recent activities, focusing on the improvements in the modelling of the instrument and in the data analysis campaigns performed both with real and simulated data.

Motivation & Objective

• To develop a low-latency, real-time data analysis framework for LISA Pathfinder mission operations.
• To improve noise modeling and system identification through state space representations of the LTP experiment.
• To enable operational data analysis using both simulated and real on-ground test data.
• To support the calibration and noise characterization campaigns essential for achieving the mission's sensitivity goals.
• To ensure close integration between data analysis and hardware development during mission operations.

Proposed method

• Development of the LTPDA toolbox, an object-oriented MATLAB framework for end-to-end data analysis during LISA Pathfinder operations.
• Adoption of state space models to represent the dynamics of the LISA Technology Package (LTP), including the Optical Metrology Subsystem and Gravitational Reference Sensor.
• Implementation of state space equations using system matrices (A, B, C, D) to model sensor dynamics and signal propagation.
• Use of block-structured matrices in the D matrix to represent interferometer inputs: test mass displacements, read-out noise, position noise, and injected signals.
• Application of the framework to both simulated data (for algorithm validation) and real on-ground test data (for operational readiness).
• Integration of state space models into closed-loop control systems, particularly for drag-free and attitude control (DFACS).

Experimental results

Research questions

• RQ1 How can state space modeling improve the accuracy and efficiency of noise characterization in the LISA Pathfinder experiment?
• RQ2 What are the key advantages of using a state space framework over traditional transfer function modeling in complex space-based metrology systems?
• RQ3 How can a real-time data analysis toolbox be designed to support tight operational timelines during a 200-day mission?
• RQ4 To what extent can simulated data be used to validate data analysis algorithms before flight operations?
• RQ5 How do state space models support the integration of noise sources and control loops in the LTP experiment?

Key findings

• The LTPDA toolbox successfully enabled low-latency data analysis, supporting real-time decision-making during LISA Pathfinder operations.
• State space modeling provided a more structured and maintainable framework for representing complex, multi-input, multi-output systems in the LTP experiment.
• The implementation of state space models allowed for accurate representation of interferometer dynamics, including differential mode measurement through block-structured D matrices.
• The framework was validated using simulated data, demonstrating robustness and scalability for flight operations.
• On-ground testing with real data confirmed the effectiveness of the state space models and data analysis tools in characterizing noise sources.
• The system achieved a differential acceleration noise level of $3\times10^{-14}\,\text{m/s}^2/\sqrt{\text{Hz}}$ at 3 mHz, meeting the mission’s primary sensitivity goal.