Complex architectures for wireless communications, digital electronics and space-based navigation interlink several oscillator-based devices such as clocks, transponders and synthesizers. Estimators characterizing their stability are critical for addressing the impact of random fluctuations (noise) on the overall system performance. Manufacturers typically specify this as an Allan/Hadamard Variance (AVAR/HVAR) profile in the time domain. However, stochastic processes constituting the noise are more thoroughly described in the frequency domain by the power spectral density function (PSD). Both are second-moment measures of the time series, but it is only possible to translate unambiguously from the PSD to the AVAR/HVAR, not vice versa, except in the case of a single noise type, a rather unrealistic case. This note presents an analytical method to generate an approximated PSD expressed as a set of power-laws defined in specific intervals in the frequency domain, starting from an AVAR/HVAR expressed as a set of power-laws in the time domain. The proposed algorithm is straightforward to implement, applicable to all noise types (and combinations thereof) and can be self-validated by reconstructing the corresponding AVAR/HVAR by direct computation. Coupling with well-established algorithms relying on the PSD for power-law noise generation [18], the ensuing method encompasses the capability for generating multi-colored noise in end-to-end simulations, as demonstrated hereby for NASA’s Deep Space Atomic Clock. We also report on the limitations of the algorithm and analytical expressions of the continuous version of the algorithm.

Interplanetary missions have typically relied on Radio Science (RS) to recover gravity fields by detecting their signatures on the spacecraft trajectory. The weak gravitational fields of small bodies, coupled with the prominent influence of confounding accelerations, hinder the efficacy of this method. Meanwhile, quantum sensors based on Cold Atom Interferometry (CAI) have demonstrated absolute measurements with inherent stability and repeatability, reaching the utmost accuracy in microgravity. This work addresses the potential of CAI-based Gradiometry (CG) as a means to strengthen the RS gravity experiment for small-body missions. Phobos represents an ideal science case as astronomic observations and recent flybys have conferred enough information to define a robust orbiting strategy, whilst promoting studies linking its geodetic observables to its origin. A covariance analysis was adopted to evaluate the contribution of RS and CG in the gravity field solution, for a coupled Phobos-spacecraft state estimation incorporating one week of data. The favourable observational geometry and the small characteristic period of the gravity signal add to the competitiveness of Doppler observables. Provided that empirical accelerations can be modelled below the nm/s${}^2$ level, RS is able to infer the 6 × 6 spherical harmonic spectrum to an accuracy of 0.1–1% with respect to the homogeneous interior values. If this correlates to a density anomaly beneath the Stickney crater, RS would suffice to constrain Phobos’ origin. Yet, in event of a rubble pile or icy moon interior (or a combination thereof) CG remains imperative, enabling an accuracy below 0.1% for most of the 10 × 10 spectrum. Nevertheless, technological advancements will be needed to alleviate the current logistical challenges associated with CG operation. This work also reflects on the sensitivity of the candidate orbits with regard to dynamical model uncertainties, which are common in small-body environments. This brings confidence in the applicability of the identified geodetic estimation strategy for missions targeting other moons, particularly those of the giant planets, which are targets for robotic exploration in the coming decades.

Whitepaper #038 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: basic research. Additional topics: outer heliosphere; space-based missions/projects; emerging opportunities.

Whitepaper #324 in the Decadal Survey for Solar and Space Physics (Heliophysics) 2024-2033. Main topics: basic research. Additional topics: other basic research; ground-based missions/projects; space-based missions/projects.

Two-way satellite time and frequency transfer (TWSTFT) is among the most accurate techniques for comparing clocks over (inter)continental baselines, exchanging bidirectional signals through a geostationary satellite—but the cost and complexity of an active (Tx & Rx) terminal restrict it to a handful of Coordinated Universal Time (UTC)(k) laboratories. We show that a passive, receive-only user can reach those same laboratories by reducing a one-way pseudorange for the satellite-motion, atmospheric, and equipment delays. Using active-network observations over 130 d, the satellite ephemeris is reconstructed by orbit determination (OD). A portable terminal—a commercial TV dish and a software-defined-radio receiver—was calibrated in common-clock mode at INRiM and deployed to the Côte d”Azur Observatory (OCA). Over a 40 d campaign, time transfer to three UTC(k) laboratories agreed with independent GNSS and active-TWSTFT links at the nanosecond level; despite larger short-term noise from solar-radiation-pressure and wet-tropospheric mismodelling, the overlapping Allan deviation reaches ≈ 10 − 14 at one day, matching GNSS performance. The accuracy is bounded by an ≈ 7 ns ( 1 σ ) budget, and an INRiM–OCA–INRiM closure sequence confirmed robustness to relocation and traceability to UTC(k). Passive TWSTFT thus offers a scalable, interference-resilient, and low-cost route to UTC(k) dissemination, with future work targeting automated OD for quasi-real-time operation.