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The laser interferometer space antenna (LISA) senses gravitational waves by measuring distance fluctuations between three spacecraft (SC). These measurements rely on precise tracking of a beat note phase that is formed on a quadrant-photo-diode (QPD) at each SC by interference of a local laser with a laser sent from a distant SC. The crucial prerequisite of the phase tracking is a successful acquisition of the beat note frequency. This article aims to optimize the carrier-to-noise density ratio (CNR) during this process, and to evaluate the resulting probability of detection (PD). CNR is generally lowest during the beat note acquisition process since pointing accuracy relies on coarse acquisition techniques. Based on analytical models, we examine which combinations of QPD segments for the signal read-out yield the highest CNR, i.e., they are least susceptible to pointing errors. We find from simulations that the highest CNR is ensured by taking the maximum of a combination of two segments in vertical and horizontal direction. For pointing errors (3$\sigma$) of 3.9 $\mu$rad and 4.3 $\mu$rad this yields an improvement of around 3.7 dB and 5.6 dB in CNR, respectively, in comparison to a combination of all four segments. In addition, the PD for various configurations of the baselined Fourier peak detection is analyzed. Here we find that the PD is most sensitive to the CNR compared to the design parameters of the acquisition scheme, in particular the FFT length. Moreover, it is shown that aforementioned improvements in CNR can lead to a significant enhancement of the PD., Comment: 19 pages, 8 figures

In the context of the Laser Interferometer Space Antenna (LISA), the laser subsystems exhibit frequency fluctuations that introduce significant levels of noise into the measurements, surpassing the gravitational wave signal by several orders of magnitude. Mitigation is achieved via time-shifting individual measurements in a data processing step known as time-delay interferometry (TDI). The suppression performance of TDI relies on accurate knowledge and consideration of the delays experienced by the interfering lasers. While considerable efforts have been dedicated to the accurate determination of inter-spacecraft ranging delays, the sources for onboard delays have been either neglected or assumed to be known. Contrary to these assumptions, analog delays of the phasemeter front end and the laser modulator are not only large but also prone to change with temperature and heterodyne frequency. This motivates our proposal for a novel method enabling a calibration of these delays on-ground and in-space, based on minimal functional additions to the receiver architecture. Specifically, we establish a set of calibration measurements and elucidate how these measurements are utilized in data processing, leading to the mitigation of the delays in the TDI Michelson variables. Following a performance analysis of the calibration measurements, proposed calibration scheme is assessed through numerical simulations. We find that in the absence of the calibration scheme, the assumed drifts of the analog delays increase residual laser noise at high frequencies of the LISA measurement band. A single, on-ground calibration of the analog delays leads to an improvement by roughly one order of magnitude, while re-calibration in space may improve performance by yet another order of magnitude. Towards lower frequencies, ranging error is always found to be the limiting factor for which countermeasures are discussed., Comment: 14 pages, 6 figures

Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded hardware. To solve this problem, this paper proposes to compute a sequence of one-step optimizations aided by pre-computed inner approximations of reachable sets rather than solving the full-horizon optimal control problem at once. This feature can be used to virtually predict the future system behavior with a low computational footprint. Proofs for recursive feasibility and for the sufficient conditions for asymptotic stability under mild assumptions are given. The presented approach is demonstrated in simulation for functional verification., Comment: Submitted to 62nd IEEE Conference on Decision and Control 2023

Future space observatories achieve detection of gravitational waves by interferometric measurements of a carrier phase, allowing to determine relative distance changes, in combination with an absolute distance measurement based on the transmission of pseudo-random noise chip sequences. In addition, usage of direct-sequence spread spectrum modulation enables data transmission. Hereafter, we report on the findings of a novel performance evaluation of planned receiver architectures, performing phase and distance readout sequentially, addressing the interplay between both measurements. An analytical model is presented identifying the power spectral density of the chip modulation at frequencies within the measurement bandwidth as the main driver for phase noise. This model, verified by numerical simulations, excludes binary phase-shift keying modulations for missions requiring pico-meter noise levels at the phase readout, while binary offset carrier modulation, where most of the power has been shifted outside the measurement bandwidth, exhibits superior phase measurement performance. Ranging analyses of the delay-locked loop reveal strong distortion of the pulse shape due to the preceding phase tracking introducing ranging bias variations. Numerical simulations show that these variations, however, which originate from data transitions, are compensated by the delay tracking loop, enabling sub-meter ranging accuracy, irrespective of the modulation type., Comment: 10 pages, 6 figures

The Laser Interferometer Space Antenna (LISA) mission features a three-spacecraft long-arm constellation intended to detect gravitational wave sources in the low-frequency band up to 1 Hz via laser interferometry. The paper presents an open-loop control strategy for point-ahead angle (PAA) correction required to maintain the optical links of the moving constellation. The control strategy maximizes periods between adjustments at the constellation level and is shown to be optimal from the perspective of estimating and correcting tilt-to-length (TTL) coupling. TTL is a noise source that couples angular spacecraft jitter and jitter of optical subassemblies with longitudinal interferometer measurements. Without precise TTL noise estimation and correction, TTL coupling fundamentally limits the detector's sensitivity., Comment: Preprint 22-556 2022 AAS/AIAA Astrodynamics Specialist Conference, Charlotte, North Carolina, August 7-11 2022

Reinforcement learning-based path planning for multi-agent systems of varying size constitutes a research topic with increasing significance as progress in domains such as urban air mobility and autonomous aerial vehicles continues. Reinforcement learning with continuous state and action spaces is used to train a policy network that accommodates desirable path planning behaviors and can be used for time-critical applications. A Long Short-Term Memory module is proposed to encode an unspecified number of states for a varying, indefinite number of agents. The described training strategies and policy architecture lead to a guidance that scales to an infinite number of agents and unlimited physical dimensions, although training takes place at a smaller scale. The guidance is implemented on a low-cost, off-the-shelf onboard computer. The feasibility of the proposed approach is validated by presenting flight test results of up to four drones, autonomously navigating collision-free in a real-world environment., Comment: For associated source code, see https://github.com/MarcSchlichting/LSTMSpatialEncoding , For associated video of flight test, see https://schlichting.page.link/lstm_flight_test , 17 pages, 11 figures

This article presents a detailed overview and assessment of contact-free UV light discharge systems (UVDS) needed to control the variable electric charge level of free-flying test masses which are part of high precision inertial sensors in space. A comprehensive numerical analysis approach on the basis of experimental data is detailed. This includes UV light ray tracing, the computation of time variant electric fields inside the complex inertial sensor geometry, and the simulation of individual photo-electron trajectories. Subsequent data analysis allows to determine key parameters to set up an analytical discharge model. Such a model is an essential system engineering tool needed for requirement breakdown and subsystem specification, performance budgeting, on-board charge control software development, and instrument modeling within spacecraft end-to-end performance simulators. Different types of UVDS design concepts are presented and assessed regarding their robustness and performance. Critical hardware aspects like electron emission from air-contaminated surfaces, interfaces with other subsystems, and spacecraft operations are considered. The focus is on the modeling and performance evaluation of the existing UVDS on board LISA Pathfinder, an ESA technology demonstrator spacecraft to be launched in 2014. The results have motivated the design of a more robust discharge system concept for cubical test mass inertial sensors for future space missions. The developed analysis tools have been used for design optimization and performance assessment of the proposed design. A significant improvement of relevant robustness and performance figures has been achieved., Comment: 16 pages, two columns, 15 figures, 2 tables