Metrology: from physics fundamentals to quality of life July 2016 International School of Physics Patrizia Tavella Istituto Nazionale Ricerca Metrologica Torino Italy In 1612 Galileo wrote a letter to the King of Spain, proposing the use of the Juppiter satellites for navigation “….these stars display conjunctions, separations, eclipses, and other precise configurations…more than 100 a year…and they are so unique, identifiable, and so exact that nobody, of medium intelligence, is not able to use them to estimate the longitude and the position of the ship based on the ephemerids I have computed for the next years to come.” Sept 7th, 1612 2 Navigation by “moon” observation 3 In spherical navigation position is estimated by measuring distance from 3 known fixed points the distance measurement are measurement of the flight time of an electromagnetic signal 4 Where are we? Electromagnetic signals cover 1 meter in 3 nanoseconds 5 We therefore need: good clocks (on Ground and in Space) good clock synchronisation system good reference time scale good algorithms for clock evaluation 6 GNSS: Where are the clocks and why? Clocks on board: nav message, pseudorange Time dissemination Ground stations, pseudorange Universal Time Coordinated by the Bureau International des Poids et Mesures Control station, reference time User clocks estimated as additional unknown 7 Space Rubidium Atomic Frequency Standard (RAFS) Frequency Stability RAFS1-R2 EQM5 December 2002 Averaging Time (Tau), sec. 100 1000 10000 100000 1.0E-12 RAFS Galileo Specification 1.0E-13 Allan Dev., Sigma y (Tau) 1.0E-14 measured data 8 FIRST Space H-Maser Atomic Clocks 9 Ground Clocks inside the Control Centres 4 Cesium beam clocks 2 Active H maser 10 Cryogenic cesium Fountain INRIM ITCsF2 Relative accuracy 2x10‐16 Laser cooling 1 µK; Cryogenic structure 89 K; Italian realization of the definition of the second 11 Next generation Miniaturized atomic clocks Ground clocks New conception of miniaturized clocks is leading towards atomic clocks of a few mm dimension http://www.nist.gov/pml/div688/grp90/index.cfm They could be implemented in GNSS receivers to improve the positioning (altitude estimate), reduce the noise of the phase measures, allowing holdover navigation … Close-up on the physics package of the Swiss Miniature Atomic Clock , 24x24 mm2 Having a good space clock is not enough… http://www.gpsworld.com/first-galileo-foc-satellite-heads-to-testing/ Relativity effects Travelling clock are slowing down Clock at high altitude are going faster The relative effect is 10-13 / km 3 microsec / year for one km in altitude On board GPS/Galileo at 20000 km The effect is about 4 10-10 which means 40 microseconds in a day corresponding to about 10 km error in positioning in one day The clock signal is emitted from space and then measured on ground Courtesy of P.Defraigne, ORB 15 range equations Information from satellite Unknowns sat Prec,1 c(trec tsat1) | xsat1 xrec | sat Prec,2 c(trec tsat 2 ) | xsat 2 xrec | sat Prec,3 c(trec tsat3 ) | xsat3 xrec | ec at From space clock to ground receiver Satellite clock Courtesy of P.Defraigne, ORB Satellite orbit Atmosphere (Ionosphere + troposphere) multipath Receiver clock Ground 17 displacements Observation equations Range : sat Prec,1 c(trec tsat1) | xsat1 xrec | Unknowns to be estimated Pseudorange : sat Clock error versus tref Prec,1 c(trec tsat ) | xsat xrec | c(trec tref ) (tsat tref ) Irec,1 Tr rec,1 rec,1, tropo Hardware delay iono Information from satellite ec tref = reference time at The ionosphere is due to the to solar radiation, which ionizes the atoms and molecules in the upper atmosphere, producing a sea of ions and free electrons 19 Solar flares shape ionosphere NASA https://archive.org/details/CIL-10104 20 https://www.ras.org.uk/news-and-press/news-archive/157-news2010/1776- space-storms-could-threaten-the-uk-power-grid 21 Solar flare effect on quartz clocks J. Vig, PTTI 2004, Tutorial, http://www.umbc.edu/photonics/Menyuk/Phase- Noise/Vig-tutorial_8.5.2.2.pdf 22 Kclock: Flow Chart START Generation of the time axis t:t0,t1,…,tk,…,tN-1 where tk=kT (T is the sampling time, an internal constant) Generation of the ideal clock xid N x = TA(t) - h (t) w h '(t) x (t) i i j j ij Generation of the physical j1 clocks x using the function euclockn 1 1 w i N 2 1 i ( ) 2 Generation of the initial k1 k ( ) conditions x0 N Generation of the H xi ( t )= w j ˆxi(t) xij(t) matrix j1 xij = x j(t) - xi (t) Is the variance sigma given? NO YES 12 Generation of the Q Set default values for matrix sigma 10 8 Generation of the block-diagonal Q1 6 matrix 4 Generation of the block-diagonal PHI1 2 matrix 0 0 100 200 300 400 500 600 700 800 900 1000 t Initialization of the covariance matrix23 P sat Satellite clock error =offset versus the Ref time Prec,1 c(trec tsat ) | xsat xrec | c(trec tref ) (tsat tref ) Irec,1 Tr rec,1 rec,1, 1. tref is the System Reference Time to be defined from the ensemble of space/ground clocks (as any national ref time scale) GPS time is a paper time scale estimated with a Kalman filter and steered versus UTC(USNO), Galileo System Time is a weighted average of the ground clocks steered versus UTC 2. The offset tsat - tref is estimated by a complex algorithm using the same pseudorange measures and estimating orbits and clocks (Kalman filter in case of GPS, Batch least square in case of Galileo, …) 3. The real time offset tsat - tref transmitted to the user is a prediction based on previous measures 24 sat Predicted clock error Prec,1 c(trec tsat ) | xsat xrec | c(trec tref ) (tsat tref ) Irec,1 Tr rec,1 rec,1, Predicted clock offsets (and predicted orbits) are estimated on ground and uploaded to the satellite They are transmitted to the user as part of the navigation message and should be valid for a certain period in the future (GPS needs one day validity, Galileo plans 100 minutes validity, …) The uploaded navigation message contains orbit prediction, clock prediction... 25 After synchronisation, any clock accumulate an error Galileo requirement for maximum offset = 1.5 ns 30 20 10 RA FS Rubidium 0 H maser Cesium -10 Cs clock nanoseconds USO -20 Ultra Stable 0 100000 200000 Oscillator 2 days (quartz) seconds 26 The clock signal affected by White and Random Walk frequency noises plus deterministic drifts can be handled exactly with Iterative solution useful for simulations, filter, … t0 0 t1 t2 ... t 2 tk1 Phase deviation X1tk 1 X1 tk X 2 tk a 1 W1,k 2 W2 s ds t 2 k Freq component X 2 tk 1 X 2 tk a 2W2,k correlated with initial conditionsX10 x0 processes X 2 0 y0 Stochastic processes helps the clock prediction Example: White Random walk of phase x(t) frequency noise At time t after synchronisation, the time error x(t) is described by a Gaussian probability density with Diffusion coefficient linked to Allan Deviation E[x(t)]=0 2 q1 t= AVAR(t) · t Variance[x(t)]=q t 0.015 1 0.01 0.005 /st 0 10 20 30 40 0 100 0 -100 real clocks: good clocks: 29 L. Galleani, P. Tavella IEEE FCS/ EFTF 2013 Prague 30 a) W hite freq noise b) Flicker freq. noise c) Random walk freq. noise 31 P sat c (t t ) The User clock error =offset versus the Ref rec,1 rec sat time is estimated by the receiver | xsat xrec | c(trec tref ) (tsat tref ) Irec,1 Tr rec,1 rec,1, GNSS receiver and its antenna Timing receiver Fixed (and known) location External frequency reference for receiver Atomic clocks (H-maser, Cesium…) Physical time scale the difference Local clock – GPS time = (trec –tref) is estimated Signals-in-space (SIS) transmitted by the GNSS satellites contains also a prediction of (UTCSIS –tref) as for example the predicted (UTC(USNO) – GPStime) SIS (trec –tref) (UTCSIS –tref) allows to estimate Local clock – UTCSIS The timing user can get UTCSIS from GNSS A navigation system is also a mean for 33 For centuries The time was given by the rotating Earth on which we set the clock From 1967 The time is given by atomic clock used to study Earth rotation Along centuries... • day and night are the “natural” time unit • it was observed that during the year the length of day changes but the “Mean Solar Day” was deemed constant and Universal •Universal Second = 1/86400 of rotational day (Mean Solar Time) •1884 Greenwich reference meridian •1925 International Astronomical Union fixes the beginning of the mean solar day at h. 00 and defines the Universal Time the rotation rate is constant? Polar motion Suspected around 1850 from astronomers That’s odd! The The Polar is higher! Polar seems lower! Polar motion can be measured but is not predictable Polar motion, 1995-1998 Solid line : mean pole displacement, About 10 m http://www.iers.org International Earth Rotation and Reference Systems Service Seasonal variation: in summer we spin faster • A. Scheibe, 1936 in Berlin • N. Stoyko, 1936 in Paris (BIH) with crystal clock the day was measured shorter of about 1.2 ms Variations in the duration of the day http://www.iers.org 40 Secular slowing down LENGTH OF DAY exceeding 86400 s -8,00 -6,00 Advance of one second per year -4,00 ms -2,00 0,00 Delay of one second per year 2,00 4,00 1630 1710 1782 1798 1814 1830 1846 1862 1878 1894 1910 1926 1942 1958 1974 Years The Universal Time was improved UT = Universal Time scale UT1 = Universal Time corrected by polar motion UT2 = Universal Time scale corrected by seasonal variations ….