Time Accuracy in Modern Systems

• Time accuracy is the degree to which clocks or timestamping systems reproduce a reference time scale, ensuring reliable event recording across diverse applications.
• It involves sophisticated calibration and correction techniques—such as polynomial drift adjustments and Kalman filtering—to mitigate hardware and environmental errors.
• Advances in timing architectures and synchronization methods, from GPS-based systems to digital two-way transfer, have pushed precision to sub-nanosecond levels.

Searching arXiv for recent and relevant papers on time accuracy across space missions, laboratory timing infrastructure, clock theory, and precision timestamping. Time accuracy is the degree to which a clock, timestamping facility, or time-assignment procedure reproduces a reference time scale or the true occurrence time of an event. In contemporary research it is treated at several levels: as absolute timing accuracy for space observatories, as the uncertainty of event timestamps in laboratory and underground facilities, as the long-term stability and correctness of continuously realized time scales, and as an operational figure of merit for autonomous clocks. Reported regimes span from $\sim 0.12 \pm 0.06\,\mathrm{s}$ absolute clock accuracy for JWST to $15\,\mathrm{ns}$ $(1\sigma)$ for a GPS-based underground timestamp facility, sub-nanosecond performance in hybrid microwave-optical time scales, and $\sim 60$–$70\,\mathrm{ps}$ time precision in two-way wireless synchronization experiments (Shaw et al., 2024, Deo et al., 2019, Yao et al., 2019, Merlo et al., 8 Jun 2025).

1. Error models and figures of merit

In operational timing systems, the central quantity is usually an absolute error relative to a reference scale. For XRISM in GPS unsynchronized mode, the residual is defined as $\Delta t_k \equiv TIME(TI_k)-TAI_k$, where $TIME(TI_k)$ is the reconstructed absolute time and $TAI_k$ is the true packet-derived time (Shidatsu et al., 3 Jun 2025). In the Gran Sasso timestamp facility, the event time is written as

$$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$

so that coarse time, fine time, GPS Clock Bias, leap-second handling, and calibrated fiber delay all contribute explicitly to the assigned timestamp (Deo et al., 2019).

Clock theory uses more abstract figures of merit. In the thermodynamic formulation of clock performance, the resolution is $\nu := 1/\mu$ and the accuracy is $15\,\mathrm{ns}$0, where $15\,\mathrm{ns}$1 and $15\,\mathrm{ns}$2 are the mean and variance of the waiting-time random variable between successive ticks. In that terminology, $15\,\mathrm{ns}$3 is “the average number of ticks until the clock is off by one tick” (Meier et al., 2023). Yang et al. define an $15\,\mathrm{ns}$4-inaccuracy $15\,\mathrm{ns}$5 for the $15\,\mathrm{ns}$6th tick time $15\,\mathrm{ns}$7 as the smallest relative width of a confidence interval that contains $15\,\mathrm{ns}$8 with probability at least $15\,\mathrm{ns}$9, together with the variance-based quantity

$(1\sigma)$0

which bounds $(1\sigma)$1 through Chebyshev’s inequality (Yang et al., 2019).

Astronomical timing introduces an additional layer: the distinction between the local clock standard and the coordinate time in which an astrophysical event is reported. Eastman, Siverd, and Gaudi recommend quoting times as $(1\sigma)$2, with the conversion

$(1\sigma)$3

where the terms are the Roemer delay, clock correction, Shapiro delay, and Einstein delay (Eastman et al., 2010). This formulation makes time accuracy inseparable from the chosen time standard.

2. Timing-system architectures

Space missions illustrate layered timing architectures. Hitomi distributed GPS-derived time from a GPS Receiver through the Satellite Management Unit and a large SpaceWire network, with each payload instrument maintaining a free-running LOCAL_TIME counter that was periodically tied to the master Time Indicator (Terada et al., 2017). XRISM retains the same basic logic but emphasizes the fallback case in which the Satellite Management Unit loses GPS lock and reverts to a free-run quartz oscillator; in that mode, each Time Indicator is stamped by counting oscillator pulses, and all times must be corrected on the ground against true GPS time (Shidatsu et al., 3 Jun 2025).

Ground infrastructures often adopt a master–slave distribution model. The Gran Sasso National Laboratory facility uses a surface Master unit locked to a GPS receiver and Rubidium oscillator, plus underground Slave units that latch CoarseTime and Clock Bias on each PPSX packet, reset ten $(1\sigma)$4 timing counters, record FineTime at $(1\sigma)$5 resolution, and stream timestamp records over USB (Deo et al., 2019). The design is explicitly intended to provide both accurate timestamps and reference frequencies to experiments.

Time scales are constructed differently. In the hybrid microwave-optical time scale of Yao et al., the flywheel oscillator is AT1, NIST’s ensemble of hydrogen masers and commercial cesium clocks, while an ytterbium optical lattice clock runs only $(1\sigma)$6 per day and intermittently calibrates the ensemble (Yao et al., 2019). In TA(Sr), the flywheel is a continuously running hydrogen maser, the calibrator is an intermittently operated $(1\sigma)$7 optical lattice clock, and a phase-micro-stepper applies the steering correction in real time (Hachisu et al., 2018).

Other architectures pursue precision without a global timing infrastructure. A fully digital two-way time transfer system for coherent distributed antenna arrays exchanges pulsed two-tone waveforms between nodes and estimates internode clock offset from the half-difference of reciprocal time-of-arrival measurements, thereby cancelling the common time-of-flight component so long as the channel is reciprocal over the synchronization epoch (Merlo et al., 8 Jun 2025). iHorology addresses Internet-scale synchronization by treating path asymmetry as the dominant obstacle and deriving offset bounds from one-way-delay lower bounds obtained from speed-of-light, landmark, or hop-by-hop information (Mani et al., 2020).

3. Calibration, correction, and reconstruction

High time accuracy is typically achieved not by a single accurate oscillator, but by repeated calibration and explicit correction models. XRISM’s GPS-unsynchronized mode is a direct example. In thermal-vacuum testing, the free-running clock frequency was measured as a function of Satellite Management Unit board temperature and fitted by a third-order polynomial,

$(1\sigma)$8

The polynomial is stored in CALDB, housekeeping provides $(1\sigma)$9 every $\sim 60$0, and the tool chain xamktim + xatime constructs a TI$\sim 60$1TIME look-up table by using $\sim 60$2 for short-term drift correction and packet-derived $\sim 60$3 pairs for long-term linear correction (Shidatsu et al., 3 Jun 2025).

Hitomi used the same general principle for GPS-OFF fallback. Its free-running quartz was cycled from $\sim 60$4 to $\sim 60$5 in vacuum, its $\sim 60$6 output was measured to $\sim 60$7 every $\sim 60$8, and the resulting lookup table of frequency versus temperature was placed in CALDB so that ahmktim/ahtrendtemp could correct Time Indicator drift from on-board housekeeping reports (Terada et al., 2017).

Laboratory facilities similarly reduce timing uncertainty through explicit calibration of transport delays. At Gran Sasso, the one-way fiber delay was measured with a high-precision time interval counter and a “sum and difference” two-path method; for the first underground Slave, the result was

$\sim 60$9

The total $70\,\mathrm{ps}$0 uncertainty was then assembled from independent contributions, $70\,\mathrm{ps}$1, $70\,\mathrm{ps}$2, and $70\,\mathrm{ps}$3, giving $70\,\mathrm{ps}$4 (Deo et al., 2019).

Time-scale realization adds control-theoretic steering. Yao et al. represent the state of AT1 relative to the optical reference by $70\,\mathrm{ps}$5 and update it with a Kalman filter whenever the optical clock is running (Yao et al., 2019). Hachisu et al. instead fit recent optical calibrations $70\,\mathrm{ps}$6 with a linear model, predict

$70\,\mathrm{ps}$7

and command the phase-micro-stepper to impose $70\,\mathrm{ps}$8 (Hachisu et al., 2018). In both cases, the time scale is accurate because the flywheel is regularly re-anchored to a higher-accuracy reference.

Astronomical event timing requires correction of the observer’s clock to a relativistically appropriate coordinate time. Eastman et al. emphasize that UTC is discontinuous because of leap seconds, TT removes the discontinuities but retains periodic relativistic rate errors, and TDB corrects those periodic terms; they therefore recommend $70\,\mathrm{ps}$9 for extra-terrestrial transients when better than $\Delta t_k \equiv TIME(TI_k)-TAI_k$0 precision is desired (Eastman et al., 2010). For camera systems, NEXTA provides a practical calibration route: one images a GNSS-synchronized LED strip, decodes the LED state in each frame, computes the exposure time from the optical pattern, and defines the camera bias as $\Delta t_k \equiv TIME(TI_k)-TAI_k$1 (Kamiński et al., 2023).

4. Reported performance regimes

The published literature reports widely different numerical accuracies because the underlying tasks differ: some systems assign absolute spacecraft times, some maintain continuous civil-scale realizations, and some calibrate local sensor biases. The following figures are therefore comparable only within their stated contexts.

System	Reported figure	Context
XRISM timing system	within a $\Delta t_k \equiv TIME(TI_k)-TAI_k$2 error in the absolute time	GPS unsynchronized mode requirement satisfied in thermal-vacuum conditions (Shidatsu et al., 3 Jun 2025)
Hitomi timing system	better than $\Delta t_k \equiv TIME(TI_k)-TAI_k$3	GPS-ON mission requirement satisfied under nominal conditions (Terada et al., 2017)
Gran Sasso facility	$\Delta t_k \equiv TIME(TI_k)-TAI_k$4 $\Delta t_k \equiv TIME(TI_k)-TAI_k$5	GPS-based underground timestamp facility (Deo et al., 2019)
JWST clock calibration	$\Delta t_k \equiv TIME(TI_k)-TAI_k$6	weighted average absolute clock offset from two eclipsing-binary epochs (Shaw et al., 2024)
Hybrid microwave-optical time scale	rms time deviation of $\Delta t_k \equiv TIME(TI_k)-TAI_k$7	five-month campaign relative to UTC (Yao et al., 2019)
TA(Sr)	$\Delta t_k \equiv TIME(TI_k)-TAI_k$8 after five months	drift of TA(Sr)$\Delta t_k \equiv TIME(TI_k)-TAI_k$9TT(BIPM16) (Hachisu et al., 2018)
NEXTA	$TIME(TI_k)$0 resolution	GNSS-based exposure timing analyzer (Kamiński et al., 2023)
Digital wireless TWTT	$TIME(TI_k)$1–$TIME(TI_k)$2 time precision	coherent distributed antenna arrays at $TIME(TI_k)$3 SNR (Merlo et al., 8 Jun 2025)
Moon–Earth synchronization proposal	$TIME(TI_k)$4 one-way synchronization error	predicted performance with optical frequency comb and RF spiral scanning deflector (Gurzadyan et al., 2020)

Several studies also report internal relative precision that is much better than the absolute offset. For JWST, the relative spacing between integrations is stable to $TIME(TI_k)$5 even though the absolute offset is $TIME(TI_k)$6 (Shaw et al., 2024). XRISM’s thermal-vacuum verification found a maximum observed $TIME(TI_k)$7 of $TIME(TI_k)$8, and on-orbit simulations with long-term correction every $TIME(TI_k)$9 kept $TAI_k$0 for $TAI_k$1 (Shidatsu et al., 3 Jun 2025). The hybrid microwave-optical time scale reached $TAI_k$2 and $TAI_k$3, while TA(Sr) showed $TAI_k$4 against TT(BIPM16) (Yao et al., 2019, Hachisu et al., 2018).

5. Fundamental limits and enhancement mechanisms

Time accuracy is limited both by hardware imperfections and by formal bounds. For clocks whose elementary thermalization events are memoryless and whose instantaneous tick rate is bounded by $TAI_k$5, Erker et al. prove the universal accuracy–resolution bound

$TAI_k$6

or equivalently $TAI_k$7 (Meier et al., 2023). In that framework, no autonomous modulation of the no-tick dynamics can beat the fundamental scale set by $TAI_k$8.

Quantum communication between clocks can improve operational accuracy. Yang et al. show that a $TAI_k$9-dimensional “Enhancing Clock” can reduce the output inaccuracy by essentially a factor $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$0. Without feedback this improvement is temporary, because the $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$1th output-tick inaccuracy grows as $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$2; with feedback the output ticks become i.i.d. and the bound

$$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$3

EDDP=W_{\rm diss}\cdot \tau_D,

$$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$4

EDDP \ge \frac{\mathcal W^2(\rho_0,\rho_1)}{\beta \gamma}, $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$5 the Bures–Wasserstein distance between the initial and final distributions (Rolandi et al., 7 Jan 2026). Although this result is not a clock theorem, it formalizes the same general point: high accuracy in finite time carries an irreducible resource cost.

6. Failure modes, standardization issues, and broader uses of the term

A recurrent misconception is that loss of GPS lock necessarily implies loss of useful absolute timing. XRISM’s on-ground and on-orbit verification shows otherwise: the temperature-versus-clock-frequency trend remained unchanged from the thermal-vacuum test, the observed time drift was consistent with the predicted drift, and the absolute timing requirement remained satisfied over the validated unsynchronized interval (Shidatsu et al., 3 Jun 2025). Hitomi had already been designed with the same fallback philosophy, allocating a separate $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$6 absolute-accuracy requirement to fail-safe GPS-OFF operation (Terada et al., 2017).

Another common source of error is not oscillator instability but the choice of time standard. Eastman et al. note that unspecified astronomical time standards can differ by as much as a minute, that HJD versus BJD can differ by up to $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$7, and that UTC leap seconds can introduce $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$8 discontinuities if not converted to TT and then TDB (Eastman et al., 2010). In this setting, time accuracy is partly a nomenclature and standardization problem.

Observed asymmetries are not always timing artifacts. In the JWST calibration study, the F322W2 eclipse ingress and egress were not mirror-symmetric, the mid-time shifted by $$T_{\rm unix} = CoarseTime\cdot10^{8} + FineTime_{DC} - CB + (T_{\rm offset}-\Delta_{gpsutc})\cdot10^{9} + T_{\rm fiber},$$9 relative to F070W, and the authors interpreted the effect as an intrinsic physical asymmetry rather than a clock problem; those data were excluded from the final timing calibration (Shaw et al., 2024). Camera testing leads to a similar conclusion: NEXTA revealed that practically all cameras had internal time bias of various level, but those biases were often stable and therefore calibratable, whereas rolling-shutter modes introduced row-dependent delays that required explicit per-row correction (Kamiński et al., 2023).

At network scale, iHorology argues that path asymmetry is the fundamental barrier to microsecond-level Internet timekeeping. By tightening one-way-delay bounds through SBBE, LBBE, or K-SBBE, clients can shrink systematic offset intervals from tens of milliseconds down into the $\nu := 1/\mu$0–$\nu := 1/\mu$1 range, but achieving the final $\nu := 1/\mu$2 requires dense server placement, deterministic route knowledge, or both (Mani et al., 2020). This suggests that beyond the laboratory, time accuracy is often constrained less by local clock quality than by transport asymmetry and incomplete path knowledge.

The phrase also appears in a broader methodological sense, where “time accuracy” denotes an explicit trade-off between elapsed time and decision quality. In early time classification, a calibrated stopping rule can guarantee finite-sample, distribution-free control of the accuracy gap between full and early-time classification while reducing up to $\nu := 1/\mu$3 of timesteps used for classification (Ringel et al., 2024). In sequential decision aggregation, the fastest rule drives decision time toward the earliest nonzero individual time, while the majority rule yields an exponential improvement in group accuracy when the individual correct-decision probability exceeds $\nu := 1/\mu$4 (Dandach et al., 2010). These uses are conceptually distinct from metrological time accuracy, but they share the same formal structure: a reference outcome is defined, an error relative to that reference is measured, and the system is optimized under explicit temporal constraints.