Escalas de tiempo y sistemas de referencia E.F. Arias Director, BIPM Time Department Metrología de tiempo y frecuencia Taller AGGO La Plata, 25 de septembre 2017

Contenido Conceptos básicos asociados a la medida Escalas de tiempo Escalas de tiempo de referencia TAI / UTC / TT Servicios del BIPM Calibración de sistemas de recepción GNSS UTC rápido Servidor ftp Bade de Datos del Departamento de Tiempo

Resultado de una medición El resultado de una medición es válido si está acompañado de la incertidumbre; La incertidumbre es un número que indica la calidad de la medida; Indica el nivel de confianza que merece el resultado; Es imprescindible para comparar medidas; La Guía para la Expresión de la Incertidumbre de Medida (GUM, 1995) fija las reglas para la evaluación y expresión de la incertidumbre unificar los criterios para caracterizar la incertidumbre en forma universal, proporcionar las bases para la comparación de los resultados de medida, GUM fue elaborada por: BIPM, IEC, ISO, OIML (1995)

Guide to the Expression of Uncertainty in Measurement La GUM recomienda reglas para la evaluación y la expresion de la incertidumbre Estas reglas encuentran aplicación en metrología científica, normalización, calibración, acreditación Arreglo de Mutuo Reconocimiento del CIPM (CIPM MRA), comparaciones “clave” (key comparisons), capacidades de calibración y medición (CMCs) declaradas por los laboratorios. Se complementa con: El VIM (Vocabulario de términos básicos y generales de metrología), definiendo una cantidad de términos metrológicos relacionados con ella, Las normas ISO donde se adoptan definiciones de términos básicos en estadística.

Algunas definiciones básicas cantidad a medirse, es una descripción de una cantidad y no tiene un valor asociado una definición incompleta agrega una incertidumbre al resultado mensurando magnitud realizada aproximación al mensurando magnitud realizada, corregida mejor estimación del valor real valor « real » error Valor medido – valor de referencia estimación de la probabilidad de estar próximo al mejor valor incertidumbre

Algunas definiciones básicas infinito número de valores dispersos alrededor del resultado incertidumbre evaluada utilizando métodos estadísticos incertidumbre de tipo A evaluada utilizando otros métodos incertidumbre de tipo B u = (uA2 + uB2)½ incertidumbre combinada incertidumbre expandida factor de cobertura U = k u

Algunas definiciones básicas acuerdo entre los resultados de una serie de medidas del mismo mesurando, en idénticas condiciones repetibilidad dispersión de los resultados acuerdo entre los resultados de una serie de medidas del mismo mesurando, en distintas condiciones reproducibilidad

Precisión, exactitud y estabilidad (1) Precisión magnitud que indica el acuerdo entre valores medidos en forma repetida en condiciones especificadas Ella puede expresarse mediante la desviación típica, la varianza o la variación relativa Exactitud Magnitud que indica el acuerdo entre el resultado de una medición y el valor real del mesurando Problema de conocer el valor real (?) Conjunto de valores compatibles con la definición de una magnitud, Las constantes fundamentales de la física tienen un único valor real, Valor convencional (estimación del valor real)

Precisión, exactitud y estabilidad (2) Ejemplos Exactitud de un reloj/patrón de frecuencia Desviación del segundo realizado por el artefacto con respecto al segundo del SI Exactitud del tiempo atómico internacional Desviación del intervalo unitario de la escala atómica libre con respecto al segundo del SI ftp://ftp2.bipm.org/pub/tai//Circular-T/cirthtm/cirt.356.html

Precisión, exactitud y estabilidad (3) Caracterización de las series temporales de mediciones, Indica la capacidad de un instrumento o de un sistema de medición de mantener sus propiedades metrológicas constantes en el tiempo Métodos estadísticos que determinan el cambio de una propiedad sobre un intervalo de tiempo Varianza de Allan (varianza de pares) Ejemplos: Estabilidad de la escala de tiempo atómico internacional Estabilidad de un reloj/patrón de frecuencia

Precisión, exactitud y estabilidad (4) Frequency stability Capacity to maintain a fixed ratio between its unitary scale interval and its theoretical counterpart The Allan’s variance is used to quantify the stability of a timescale (time/frequency) (or of a clock) over a time interval; Frequency accuracy Aptitude of its scale unit interval for reproducing its theoretical counterpart The frequency accuracy of a timescale is determined by comparing the frequency of the scale with that of a primary standard.

Stabilized temperature Precisión, exactitud y estabilidad (5) Mod. y() 1 hour 1 day 1 year Loran- C GPS CV 1CH GPS + GLONASS CV MCH Stabilized temperature GLONASS P-code 1 CH TWSTFT Carrier phase GPS HM CS

Resources in use PRIMARY FREQ. STANDARDS Stability 1x10-14 @1 day Accuracy 5 x10-13 CLOCKS IN TAI Contribute regularly to TAI uncertainty few 10-16 Stability 7x10-16 @1 day CLOCK COMPARISONS Frequency (optical clocks), some time comparisons SECONDARY REP. OF THE SECOND 87Rb Contributes regularly to TAI ns uncertainty Uncertainty (intrinsic) low 10-18 (limited to 10-16 by Cs) hundred-ps uncertainty In use for UTC(k) comparisons

To represent physical phenomena we weed: x3 Space-time coordinates O x1 t x2 (t, x1, x2, x3) The choice of the coodinate system depends of the needs

Spatial reference systems (coordinate systems) Barycentric system (non rotating)- (ICRS, ICRF) Origin: centre of mass of the Solar System Axes: fixed with respect to a set of compact, stable extragalactic radio sources– non-rotating constraint is applied. Geocentric system (non rotating) Origin: centre of mass of the Earth Axes: idem barycentric Geocentric system (rotating)- (ITRF) Axes: rotating of the Earth, defined through the positions and velocities of a set of sites on the surface

Time based on the reproducibility of local phenomena proper time (local) measured by a clock used for local experiments / observations Time based on the Newtonian dynamics coordinate time in a system of space-time coordinates arbitrarily chosen applications depending on the system (astronomy, geodesy, etc.) Time metrology Representations of the unit of proper time to be used in local experiments Representations of various coordinate times with different applications, beyond the limits of a laboratory.

Coordinate times TT = TAI + 32.184 s on 1977 Jan 1, 0 h TAI IAU Resolutions 2000 (B1.3, 1.4, 1.5, 1.9) readings of proper time of an observer expressed in SI seconds can be recomputed into Barycentric Coordinate Time (TCB) Geocentric Coordinate Time (TCG) d(TT)/d(TCG) = 1 – LG (LG defining constant) Terrestrial Time (TT) TCB, TCG coincide with TT in origin by TT = TAI + 32.184 s on 1977 Jan 1, 0 h TAI Realizations of TT are: TT(BIPMXY) TAI by TT(TAI) = TAI + 32.184 s

In a relativistic frame Any clock realises a proper local time The unit of time (second), is established by a standard located in the laboratory Proper second A timescale to be used as a worldwide reference must be defined as a coordinate. It is a coordinate time. TAI is a coordinate time obtained as the average of many different proper times

Why conventional timescales? Need of international coordination in time Reference in time suitable to all applications Science Space / satellite navigation Precise positionning on Earth and in space Network synchronisation Communications Commerce and business Civil applications ….

To measure time we need a unit; a timescale considered as a world standard for dating events; a periodic phenomenon is at the basis natural reproducible in time and space constant duration (ideally) ability to specify the causes of deviation ability to eliminate any cause of perturbation its frequency serves to derive the definition of the unit

periodic phenomena used to define timescales: Earth’s rotation (universal time) Earth’s orbital motion (dynamical time) atomic transition (atomic time) a process able of reproducing the unit (approx.); concept of unit interval; an origin, arbitrarily defined at this step, we have a timescale measuring time = determining a time interval

Metrological qualities of a conventional reference timescale Reliability (redundancy) Relies on the participating clocks Continuity Not suffer from discontinuities (« unexpected », UTC?) Changes Nature of the scale Unit (definition, realization) Accessibility Aptitude for providing a way of datation of events to all users Post-processed to reach ultimate precision Minimization of measurement noise Data sampling intervals

Integrated time scale (based on reproducibility) Achieved seconds differ from the ideal Discrepancies can be minimised by time averaging averaging over realisations of the second in different laboratories As seconds cumulate, their errors also cumulate discrepancy [ideal – realised] time scale increases in time If we average, we need algorithms Best algorithm???? Well adapted to the constraints we impose to the time scale (stability, accuracy) Errors leave their prints on the time scale

TAI: integrated time scale which unit is the SI second SI second is defined as… …the duration of 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium 133 atom SI second is realized by… …Primary Frequency Standards developed and maintained in metrology institutes, with an uncertainty of a few parts in 1016. “International Atomic Time (TAI) is a realization of Terrestrial Time (TT) as defined by the IAU Resolution B1.9 (2000) with TT-TAI = 32.184 s exactly at 1977 January 1, 0h TAI; TAI is a continuous time-scale maintained by the BIPM based on the best realizations of the SI second;”

What’s in a reference time scale? + A clock ensemble Algorithms Characterize the clocks’ frequencies Preserve stability as needed [depends on applications] Calculate the unit interval Calibrate the unit interval (frequency steering) Preserve accuracy as needed Other time scale unit interval Primary(ies) standard(s)

Choices Data Real time Post- processing Algorithm Frequency stability Input Data sample interval Length of the data interval Algorithm Clock comparison Structure Methods Clock frequency prediction Clock weighting Frequency steering Reference frequency Method Real time Post- processing Frequency stability @ interval Frequency accuracy Match to a reference

Which is the world reference time scale? 13th CGPM, 1967 defines the atomic second CCDS, 1970 defines TAI (uniform) CGPM, 1971 asks to realize TAI considering user’s requirements UT represented the time scales based on the rotation of the Earth UT1 contains the irregularities of the Earth rotation Some users required < 1 s synchronization to UT1 UTC was defined as derived from TAI but with 1 s insertions (positive or negative) to keep ǀUT1-UTCǀ < 0.9 s from UT1 (ITU-R) (1970-1972) UTC is the international reference for metrology, science and the basis of civil time

Time scales from metrology Interval unit is the SI second Continuous, optimized frequency accuracy and 30-day frequency stability Monthly No clock representation/ no dissemination International Atomic Time (TAI) Equal in rate to TAI, with 1 s discontinuity at the insertion of a leap second Monthly Represented by clocks [UTC(k)], largely disseminated Weekly prediction UTCr since 2013 Coordinated Universal Time (UTC) Rapid (weekly) solution UTCr Continuous, optimized long term accuracy and frequency stability Annual, TAI provides a good monthly extrapolation No clock representation/ no dissemination Terrestrial Time (TT(BIPMxx))

Frequency steering algorithm Calculation of UTC Echelle atomique libre Atomic clocks 500 Contributors  80 Prediction algorithm Weighting algorithm EAL Freq. Stability 4 x 10-16 @30-40 days Frequency standards: Primaries: 15 Secondaries: 1 Frequency steering algorithm International Atomic Time TAI Leap second Earth Rotation Measure (IERS) Freq. accuracy few 10-16 Coordinated Universal Time UTC(k) Circular T UTC

The prediction algorithm UTC is computed over one calendar-month data Clock data are provided at 5-day intervals at 0 h UTC Clock data are differences UTC(k)-clock and clock steps and clock frequency corrections Two successive monthly calculations are independent, but… the clock frequency behavior is checked by comparing the clock frequency in a month to its prediction a quadratic model has been adopted to predict the frequency drift

The weighting algorithm Case 1: good clock  stable clock The weight attributed to clock Hi is the reciprocal of the individual classical variance σi2 (classical variance, Allan variance,...) Case 2: good clock  predictable clock The difference between the predicted 𝑦 (𝐸𝐴𝐿− ℎ 𝑖 ) and real frequencies 𝑦 𝐸𝐴𝐿− ℎ 𝑖 of the atomic clocks are evaluated The statistics are made over 12 months of data (when available) Two particular situations are checked: Clock Hi shows abnormal behaviour The weight is bigger then the upper limit fixed to avoid that a clock has a predominant role. ALGOS A = empirical constant Current BIPM algorithm

Metrological quality of EAL

Process of (monthly) calculation of UTC Step 1- Computation of EAL hi, wi are the reading and weight of clock Hi, h’i is its predicted frequency, N is the number of participating clocks in the month Step 2- the frequency of EAL is computed by comparison to all available primary (and secondary frequency standards), and a frequency shift (frequency steering correction) is applied to EAL to ensure that the frequency of TAI conforms to its definition. f(TAI) = f(EAL) + corr

The basic data: clock differences Clocks compared using time interval counters (< 500 ps @ 1 s) Clocks compared using time transfer techniques satellite based (GNSS, TWSTFT) (few to tens ns) optic fibres (some ps)

Clock comparisons have the form of UTC(k)-UTC(pivot) The present scheme has a unique pivot (PTB)

Time transfer techniques involved in UTC GPS all satellites-in-view single-frequency dual-frequency link combinaton GPS-GLONASS GPS-TWSTFT GLONASS satellite common-views 4% 22% 16% 18% TWSTFT 40%

Impact of time transfer in the access to UTC (1) BIPM Circular T

Impact of time transfer in the access to UTC (2) The uncertainty of [UTC-UTC(k)] depends on The clock uncertainty (small) The uncertainty of the link between clocks in a laboratory (negligible) The uncertainty of the link between UTC(k) and UTC(l) The uncertainty of [UTC(k)-UTC(l)] can be expressed by two components: The statistical uncertainty (statistical noise) The calibration uncertainty [UTC(k)-UTC(l)] provides the largest contribution to the uncertainty of the access to UTC

Time link uncertainty uStb accounts for measurement noise and random effects @ 1 to 30 days Link stability Calibration Calib. aging Alignement

GNSS equipment calibrations improving the accuracy of UTC-UTC(k) by implementing continuous calibration campaigns for reducing time link uncertainty from 5 ns to 1.5 - 2.5 ns BIPM calibrates equipment in selected labs per region (G1) + G2* RMOs calibrate equipment in other labs (G2) G1 BIPM validates RMO calibrations and computes final results http://www.bipm.org/jsp/en/TimeCalibrations.jsp * G2 where there is not yet capacity for calibrations

uB GPS BIPM/RMO calibration G2 RMO calib. G1 BIPM calib. Exactitude de UTC-UTC(k) 1~2 ns

UTC rapid solution (UTCr) - weekly Features Based on daily data reported (daily) by contributing laboratories, independently of the report for the monthly UTC computation Weekly access to daily values of [UTCr-UTC(k)] Automatically generated weekly solution over four weeks of data (sliding solution) Weighting scheme similar to ALGOS Linear frequency prediction (to start with) Steered to UTC Properties Stability of UTCr comparable to UTC since: Interval of calculation covers one month approximately and the algorithm is similar to that for UTC (however weighting should be updated) Participating laboratories represent ~ 50% of the clocks in UTC and 70% of the total clock weight in UTC Accuracy ensured by steering to UTC over common interval

Distribution of data and results through interactive Circular T and Time Department Data Base http://webtai.bipm.org/database/html/ www.bipm.org/en/bipm/tai/

Some realizations of UTC [Max Some realizations of UTC [Max. 100 ns offset from UTC recommended] Source: BIPM Circular T (data since 1998)

GRACIAS!

EXTRA SLIDES

Latest developments in GNSS t&f transfer Integer-PPP technique for solving the phase ambiguities present in the GPS PPP solution uA (GPS PPP) ~ 1x10-15 @ 1 d 1x10-16 @ 30 d uA (GPS I-PPP) ~ 1x10-16 @ 1 d Petit et al., Metrologia 52, 2015

Latest developments in GNSS t&f transfer (cont.) Assessment of GPS-link calibration using self-calibrated optical fibre GPS cal Optic fibre Jiang et al., Metrologia 52, 2015 200 ps accurate self-calibrated optical link in Poland allowed the validation of the BIPM calibration device and demonstrated that GPS-link calibration is possible at better than 2 ns acuracy.

Latest developments in GNSS t&f transfer (cont.) Common GNSS Generic Time Transfer Standard VO1  GPS satellites only (Allan, Thomas, Metrologia 31, 1994) V02  GPS + GLONASS satellites (Azoubib, Lewandowski, 7th CGGTTS meeting, 1998) V2E  GPS+GLONASS+Galileo+BeiDou+QZSS (Defraigne, Petit, Metrologia 52, 2015)

Latest developments in GNSS t&f transfer (cont.) Remote optical and fountain clock comparison Statistical uncertainty Broadband TWSTFT, GPS PPP, low 10-16 GPS IPPP < 1 x 10-16 Reidel et al.,. Proceedings EFTF 2016 Target: t&f transfer for optical clock comparison (10-17 – 10-18)

Growing / Future resources FREQUENCY STANDARDS CLOCKS New Cs and H-masers New Cs fountains? Portable fountains, in space Industrial optical clocks? Optical standards continuously operating (10-18 / 10-19) and contributing to TAI Miniature clocks CLOCK COMPARISONS Improved TWSTFT (phase, dedicated satellite, etc) Optical clock comparisons by VLBI Optical fibre links Multi-GNSS (GPS, GLONASS, Galileo, BeiDou, etc.) ACES MWL

Institutes contributing to UTC Time dissemination Time signals Rec. ITU-R 460-6 Pulses and Frequency modulation Services operate at various freqs Institutes contributing to UTC Time Dissemination Services Telephone services (local) Broadcast predictions of UTC(k) (global) NTP servers ~50 ms timing accuracy (global) Optical fibres (local) few hundred ps – μs accuracy Time Stamping [trusted time] (global)

Evolution  of the relative accuracy of caesium frequency standards

GPS time transfer Calibrated receivers Common-views Corrections for the orbital motion of the satellite Signal propagation delays Ionosphere Troposphere Quasi continuous observations single frequency receivers Single-channel Multi-channel Dual frequency receivers, multi-channel Iono-free observations

TWSTFT Calibrated receiving/emitting stations Telecommunications satellite No clock on board used Geostationnary Two-way comparison Iono delays almost eliminated Well organised observing schedules Non-continuous observations But many points per day are possile at present

How Timing Labs Steer to UTC Some don’t steer at all Others wait until UTC-UTC(k) is “too large” - Step rate and/or phase of UTC(k) Better method: Use UTCr as an approximation to UTC Estimate current and future UTCr-UTC(k) Steer so as to reduce UTCr-UTC(k) Adjust Master Clock’s voltage parameters Or adjust microstepper/AOG/equivalent Or software steer

Improvement Due to Steering (plot range: 33 ns)

The first step: Predict/Estimate

Simple Way to Predict Start with time series UTC-UTC(k) Remove steers, create time series Y(n) Linear Extrapolation rate =[Y(n)-Y(n-m)]/m Y(n+k)=Y(n)+rate*k 4. Re-install steers => prediction of UTC-UTC(k) and its frequency (we will later call these x and y)

Three Ways to Set Gains LQG Theory Pole Placement Gentle Steering A compromise between goals Pole Placement Set response times Gentle Steering Minimum amount of steering to achieve desired phase and frequency shift See Koppang, 2016, “State space control of frequency standards”, Metrologia 53, R 60-64

Steer =gX * Phase + gY * Freq + gZ * Drift LQG Steer =gX * Phase + gY * Freq + gZ * Drift ALL steering involves a trade-off between: frequency offset time offset control effort Control perturbs local clock Linear Quadratic Gaussian (LQG) theory can compute the optimal gains for your goals. See Koppang and Leland, 1999, IEEEE Trans. Ultrason. Ferroelect., Freq. Control 46, pp 517-522. See also Appendix IV.

another way: Critically Damped Gains if data updated daily Dt=Time Interval between data (= 1 day) Tc= time constant = (14 days) From the formula: gx=.00475 gy=.133

A Simple Way, for Weekly Updates Start with published weekly values of UTCr-UTC(k) Predict what UTCr-UTC(k) will be 7 days in the future x=predicted future time offset y=predicted future frequency offset Linear prediction model will do Steer so as to remove half the frequency and half the phase offset over the week (x/2 and y/2) “Gently” adjust clock frequency once a day: ∆𝑓= 𝑔 𝑥 𝑥/2+ 𝑔 𝑦 𝑦/2

“Gentle Steering” Change clock’s time by Dx and frequency by Dy Use N steers of magnitude Un spaced in time by t Minimum Amount of Control Effort (U) http://www.pttimeeting.org: Koppang and Matsakis, PTTI-00, pp. 277-284 Day g_x g_y S(g_y) S(g_x) S(S(g_x)) 1 0.10714 0.46429 0.1071 2 0.07143 0.35714 0.82143 0.17857 0.2857 3 0.03571 0.25 1.07143 0.21428 0.5000 4 0.14286 1.21429 0.7143 5 -0.03571 1.25 0.8928 6 -0.07143 1.17857 1.0000 7 -0.10714 -0.17857

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With bad data ignored

Be careful what you ask for ... With control theory, you might get it. Warning ! Be careful what you ask for ... With control theory, you might get it. Therefore, simulate control performance