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A Prediction of How TAI and TT Will Be Computed in 2020
International Astronomical Union Joint Discussion # 6 Rio de Janeiro August 7, 2009 Demetrios Matsakis


My 1999 Prediction for 21st Century


The ideas presented here borrow heavily from the works of:
· · · · · · · · · · Felicitas Arias (BIPM) John Davis (NPL) Chuck Greenhall (JPL) Niko Kalouptsides (U. Athens) Paul Koppang (USNO) Gianna Panfilo (BIPM) Gerard Petit (BIPM) Ken Senior (NRL) Jim Skinner (USNO) Patricia Travella (INRIM)


Current System
· EAL = Free-running average of secondary standards
­ Weighted by monthly frequency stability
· Very democratic · Maximum weight ensures robustness
­ See Petit, Metrologia, 2003, 40 No3 252-256

­ Simple, robust clock model
· Optimal for driftless clocks, white phase noise · Being modified for high-drift clocks (masers)

­ Algorithm has steady record of incremental improvements

· TAI = EAL frequency-steered to primaries · Terrestrial Time (TT) = Post-processed TAI


Relative Precision of USNO Masers and Cesiums (y)
· @80days (vs. EAL or USNO Maser Mean)
­ Maser slightly better than cesium

· @40 days (vs. EAL or USNO Maser Mean)
­ Maser ~3 times better than cesium

· Daily at USNO
­ Maser ~20 times better than cesium

· Hourly at USNO
­ Maser ~40 times better than cesium ­ Limited by operational measurement system


Masers and Cesiums as Phase-Linear EAL Predictors
(Displaying maser frequency drift, 2006-2008)
5 0

30 20 Na no s e c on ds
0 5 10 15 20 25 30

Nanoseconds

-5 -10 -15 -20 -25

10 0 -10 -20 -30 0

5

10

Day s

15 Days

20

25

30

Maser deviations after fit period

Cesium deviations after fit period

Viewgraph and Analysis from Panfilo and Arias, EFTF-09


Time Transfer Noise's Bleak Future
· Less and less uncertainty
­ GPS carrier-phase time-transfer precision
· 20 ps @ 5 minutes; 100-ps level issues at 24 hours · Software in use at BIPM · Calibration issues addressable

­ GPS =>GNSS
· Improved robustness and precision · Enhanced multipath reduction in some planned signals · Paper by Uhrich and Tuckey, this session

­ Steadily falling component price => redundant systems

· Real-time Carrier-Phase GPS Networks Operational
­ Latency measured in seconds

· Possibility to optimize around short-term stability of masers
­ Rubidium Fountains too


The Full Kalman Approach
· Kalman Filter
1. Cesium-only scale
· · · · Can be daily points Incorporates primary standards as frequency measurement Where the noise is whitest Two-state characterization (frequency and frequency drift)

2. Maser frequencies referenced to cesium scale's frequency 3. Maser phases corrected for frequency and drift 4. Corrected maser phases steered to cesium scale 5. Global maser average gives TAI/UTC

·

Terrestrial Time (TT)
­ TT is average of forward and backwards filters


Pros and Cons of Kalman Basis
· Parameter tuning and selection requires care
­ But non-WFM noise can also be modeled
· Davis et al, Metrologia 42, 1-10

· Measurement error correlations
­ Off-diagonal terms ­ Time-transfer noise correlations between links ­ Redundant time-transfer systems

· Process Noise
­ Can model clocks sharing common environment ­ Raising a Q helps alleviate modeling errors
· Although a high Q is itself a modelling error

­ Minimum Q

Maximum Weight

· Helps protect against Narcissus Effect


Will it really work?
· Download BIPM's 5-day data via anonymous ftp
­ None of it is by carrier phase

· Use Kalman Filter to generate EAL-maser
­ Use EAL as reference, for now ­ Outlier removal via standard Kalman techniques

· Create "Global Maser Average"
­ Global average of all masers reporting to BIPM
· Remove frequencies and frequency drift · Integrate back to phase, steer phase @ 60 day time constant

­ Weighting by performance in any of several ways

· Compare with independent references
­ USNO Cesium and Maser Means, and TA(NIST)
· Do not include reference's masers in the Global Maser Average

­ For short , Global Maser Average agrees as better with the references than EAL does ­ For large , Global Maser Average of course agrees with EAL


USNO and NIST Internal Means referenced to EAL and Global Maser Ave (which does not include reference's clocks)

EAL-TA(NIST) EAL-USNO Cesium Average EAL-USNO Maser Average

References versus Global Maser Ave (ref-removed)


Conclusion: My Predictions for 2020
· There will be >2 fully interoperable GNSS systems operating
­ They will want an improved short-term UTC

· Time Transfer noise >1 ns on any scale will be considered an embarrassment · TAI algorithms will utilize full precision of masers and fountains over << 1 month


Backups


USNO Algorithms
· Cesium-only average
­ Characterization in frequency-space

· Masers characterized/steered to cesium average
­ Rubidium fountains under evaluation

· All averages have copies steered to UTC
­ Equations allow for coupling of the averages

· UTC(USNO) steered to steered maser average · Human oversight required · Not yet fully operational


A Similar Approach For UTC
· Benefit from large number of cesiums on monthly scales · Utilize full power of masers on short periods
­ Example: IGS Time Scale ­ Continuously-contributing fountains

· Optimally incorporate scattered primary frequency standard data


Issues That Can Be Addressed In Several Ways
· All masers are not equivalent · Clock noise is not white FM and TT noise is not white PM
­ Particularly over long scales

· Noise is correlated
­ Even on subdaily scales


Kalman Parameters
· Rate and drift for all clock types · Process Noise (Q)
­ Provides for stochastic change in frequency/drift over time ­ Published formulas relate noise to math ­ Gauss-Markov approximation possible for red noise

· Maximum weight limit

Minimum Q

­ ~ Petit, Metrologia, 2003, 40 No3 252-256
­ Raising a Q helps alleviate modeling errors in Kalman Filters