RESULTS

1
Poster G11B-0632 AGU Fall Meeting 2009
Results from the New IGS Time Scale Algorithm
K. Senior, J.
Ray
U.S. Naval
Research Laboratory
U.S. National Geodetic Survey

peaks at N x (2.0029 0.0005) cpd
CLOCK MEASUREMENTS Measurements of
each clocks phase relative to a fixed reference
clock (GPS Time) were obtained from the REPRO1
combination over the period 1 January 2006 to 15
March 2006. Tabulated at five-minute intervals
these geodetic estimates are a weighted
combination of estimates submitted from up to 9
IGS analysis centers (ACs) for the satellite
clocks and up to 6 ACs for the ground clocks
Kouba and Springer, 2001. They are used as
input measurements in the following time scale
algorithm. TIME SCALE ALGORITHM The geodetic
estimation technique necessarily produces
observations of each clock that are rank
deficient in the sense that each clock must be
referenced to some other reference clock, or time
scale. The goal of a timescale algorithm is to
generate a stable reference, or equivalently to
produce better estimates of each individual
clock. These are equivalent since for example
estimating perfectly an individual clock is
equivalent to generating a perfect reference.
The rank deficiency represents an observability
problem in estimating the individual clocks and
is addressed by introducing ensemble average
assumptions about the set of clocks in order to
constrain the individual clock estimation. Since
each type of random walk inputrandom walk phase
(RWPH), random walk frequency (RWFR), and random
walk drift (RWDR)represents a separate ensemble
of noises, three separate recursive weighted
conditions are imposed to constrain the solution
Stein, 1993 These constraints
stipulate that the weighted sum of the
differences between the clocks true states and
their predicted states be zero on (ensemble)
average. Since each clocks state differs from
its prediction by its random noise inputs, the
clock weights ai, bi, and ci are chosen inversely
to the RMS of the noises contributing to that
state, that is inverse to the level of each
random walk noise input. This both normalizes
each clocks contribution to the noise of the
ensemble and has the effect of improving the
observability of the individual clocks.

• Other algorithm features and enhancements
  include
• Kalman filter implementation (also true for the
  earlier version)
• a bank of filters running nominally at different
  intervals, allowing for increased sensitivity to
  clock break detection adaptive estimation
  of clock parameters
• graceful outlier downweighting to reduce the
  impact of clock events or bad data on the time
  scale
• clocks may enter/leave the ensemble with minimal
  impact on the time scale
• alignment of the time scale to Coordinated
  Universal Time (UTC) realized by slowly adjusting
  the drift of the timescale to align it to
  an average of UTC realizations at timing
  laboratories (included in the IGS network)
  using an LQG algorithm Senior et al., 2003

INTRODUCTION Since 2004 the IGS Rapid and Final
clock products have been aligned to a highly
stable time scale derived from a weighted
ensemble of clocks in the IGS network Senior et
al., 2003. The time scale is driven mostly by
Hydrogen Maser ground clocks though the GPS
satellite clocks also carry non-negligible
weight, resulting in a time scale having a
one-day frequency stability of about .
However, because of the relatively simple
weighting scheme used in the legacy time scale
algorithm and because the scale is aligned to UTC
by steering it to GPS Time the resulting
stability over shorter intervals and beyond
several days suffers. A new time scale algorithm
(version 2.0) has been implemented to address
these limitations. The algorithm has been
evaluated to a subset of data in the IGS REPRO1
reprocessing campaign, presented here. It is
expected that the new algorithm will be applied
in the final release of the REPRO1 results in
early 2010. New CLOCK MODEL Basic Model
for all Clocks The basic clock model used in the
new (version 2.0) IGS timescale for each clock
(both ground GPS satellite clocks) includes the
clocks time (or phase), its first derivative
(frequency), and its second derivative (drift),
each modeled stochastically with a random walk as
shown in Fig. 1 below. An additional phase state
is included to model a pure white phase noise as
well as harmonic terms.
Additional Pure Harmonic States Because the GPS
satellite clocks are subject to harmonics of up
to 2 nanoseconds nominally at 12-h, 6-h, 4-h and
3-h periods (see Fig. 2), four additional states
are included for each GPS satellite clock in
order to compensate the largest two harmonics
(12-h and 6-h) Senior et al., 2008 .
Fig. 2. Amplitude spectrum for the GPS clocks.
Spectra were calculated individually for each
satellite and averaged over the entire
constellation of clocks.
RESULTS Time Scale Stability The instability
of the new time scale compared to the old was
calculated using the Hadamard deviation and is
shown in Figure 3 below. The new time scale
(blue) is improved at almost all averaging
intervals, especially for times much shorter than
1d and for multi-day periods.

phase constraints
Each clock has 3 weights, dynamically set
inversely to the level of random walk driving
each state
frequency constraints
drift constraints
Fig. 3 The frequency instability of the old
(black) and new (blue) time scales over the
period 3 March (MJD 53800) to 3 August 2006
(53950) calculated using the Hadamard deviation.
improved performance in the short run
improved performance in the medium run
2
Sample Filter Outputs
Fig. 4 Filter output (above) for the clock
ONSA at Onsala over the period 10 January to 6
March 2006. The filter phase (gray and black),
frequency (red), and drift (blue) states are
shown in the top panel, all referenced to the
steered IGS timescale. The middle panel shows
corresponding state sigmas, while the bottom
panel shows the clock weights used in the
timescale. A separate polynomial has been
removed from each time series in the top panel,
its value shown in the legend. The legend also
shows any phase or frequency breaks
detected/removed during filtering. Note that for
this very stable clock, the phase state with
white noise and harmonics (black) is
indistinguishable from the simple phase estimate
(gray).
Fig. 5 Filter output for the GPS satellite clock
for PRN11 over the period 1 to 21 May 2006. The
filter phase (gray and black), frequency (red),
and drift (blue) states are shown in the top
panel, all referenced to the steered IGS
timescale. The middle panel shows corresponding
state sigmas, while the bottom panel shows the
clock weights used in the timescale. A separate
polynomial has been removed from each time series
in the top panel, its value shown in the legend.
The legend also shows any phase or frequency
breaks detected/removed during filtering. Note
that for this satellite clock possessing strong
periodic variations near 12h and 24h, that the
phase state with white noise and harmonics
(black) differs noticeably from the simple phase
estimate (gray).
REFERENCES Senior K., Ray J., Beard R.,
Characterization of periodic variations in the
GPS satellite clocks, GPS Solutions, DOI
10.1007/s10291-008-0089-9, 2008. Kouba J.,
Springer T., New IGS station and satellite clock
combination. GPS Solutions 43136, 2001. Senior
K., Koppang P., Ray J., Developing an IGS time
scale. IEEE Trans Ultrason Ferroelectr Freq
Control 50585593, 2003. Stein, S. R. ,
Advances in time-scale algorithms, Proc. of the
24th Annual Precise Time Time Interval (PTTI)
Applications and Planning Meeting, Greenbelt,
Maryland, 289303, 1993.
Alignment to UTC
Fig. 6 Estimates (right) over 150 d of the new
time scale versus UTC using an average of several
calibrated timing lab sites.