# Backup Hydrogen Maser Steering System for Galileo Precise Timing Facility

Authors: Qinghua Wang; Pascal Rochat; Xavier Stehlin
Journal: International Journal of Navigation and Observation
 (2008)

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## Abstract

Two hydrogen masers (HMs) are used in the Precise Timing Facility to provide the physical realization of Galileo System Time, insuring the extremely high short-term stability required for the navigation functions.  In order to allow a smooth switch over between backup and primary HMs, the “backup HM steering algorithm” is developed.  This acquires the phase difference measured between two HMs, computes a steering correction, and generates the steering correction to the backup HM via a PicoStepper with a 0.1-picosecond resolution. The algorithm design is based on outlier removal and a proportional-integral filtering controller. To verify the steering operability and the loop performance, the overall backup HM steering system is simulated using real HM-HM measurements, and  with simulated anomalies (phase/frequency spikes, jumps, and drift).


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## Body

## 1. Introduction

The  Precise Timing Facility (PTF)
is one of the key
facilities of the Galileo ground segment. Its scope is to provide an accurate,
stable,  and precise Galileo System Time Master Clock (GST(MC)) to the
Orbitography and Synchronization Processing Facility and to the other Galileo
Control Center facilities.Two PTFs are currently under development by two separate
teams in Germany and Italy. The discussion provided in this paper refers to the
Italian development [1], coordinated by the Consorzio Torino Time (CTT) in
Torino, Italy, with the partnership and support of SpectraTime (former Temex
Time) and T4Science in Neuchâtel, Switzerland, and Astrogeodynamic Observatory,
Poland.Two active hydrogen masers (a primary HM1 and a backup
HM2) externally steered via a precision PicoStepper, provide the physical
realization of GST(MC), insuring the extremely high short-term stability
required for the navigation functions, in particular, to perform a reliable
satellite clock modeling.The “backup HM steering algorithm” is implemented in
order to allow a smooth switch over between backup and primary HM in case of
failure of the latter, without producing
any significant effect in the GST continuity, uniformity, or short-term
frequency stability. The algorithm acquires the phase difference between two
HMs measured by a multichannel phase comparator (MCPC), and generates a
steering correction to be applied to the backup HM via a PicoStepper with a 0.1-picosecond
resolution.


## 2. Architecture

Figure1 shows the architecture of the backup HM steering system, consisting of an MCPC, PicoSteppers (one per HM), and the algorithm.Figure 1
Architecture of the backup HM steering system.In the nominal situation, PicoStepper1
applies the steering correction from PTF GST algorithm to steer the primary HM1
with “GST running” (GSTR) obtaining the GST(MC1). The phases of the two
PicoSteppers’ outputs are compared by MCPC, whose output is used by the “backup
HM steering algorithm” to obtain the steering command to PicoStepper2 whose
input is the backup HM2. Thus, the steered output of HM2 is kept in phase with
HM1.In case of the HM1 failure, the hot backup HM2 becomes the
primary one by the PTF switching matrix. The previous phase offset “HM2(steered)-HM1”
provides the seamless switch-over signal via PicoStepper2 which is now applied
by the GSTR correction for GST(MC).


## 3. Picostepper

A high-resolution PTF PicoStepper (i.e., microphase
stepper), based on the existing PicoStepper by
SpectraTime [2], is
being developed to provide frequency correction of HMs signals (Figure 2).PTF PicoStepper.
(a)(b)The unit is being designed to meet the following two PTF requirements:(i)
increase of the resolution by a factor of 100 to obtain a minimum phase step of±0.1 picosecond;(ii)
reduction of output jitter to get negligible degradation of the HM signal phase noise and short term stability.The design is based on a double heterodyne architecture where a first structure is used for
positive phase/frequency adjustment and the second structure for negative
adjustment.As shown in the high-level block diagram (Figure3), each
positive/negative loop contains a voltage-controlled xtal oscillator (VCXO), a phase detector, a frequency
mixer, a frequency multiplier, a pulse removing circuit, a frequency divider
and a loop filter. A microcontroller
is in charge to manage the stepping commands sent by RS232. It has also the
capability to execute a self-test of the unit.Figure 3
Block diagram of PTF PicoStepper (i.e., microphase stepper).The 0.1-picosecond
resolution of the system is obtained by using the appropriate VCXO frequency
multiplication factor and divider ratio.
TakingN=10 and M=105,
the frequency resolution is Δf/fIN=10−6/10M=±10−13,
which corresponds in terms of phase of 0.1 picosecond.The
frequency beats (F1, F2, F3, and F4) in both loops while not stepping is equal
to 1 KHz which is the comparison frequencies of the phase detectors. Thus, the
nominal frequency of the local oscillator is equal to 10 MHz–1 KHz/N=9.999900 MHz.In order
not to degrade the HM performances, a phase noise figure (Figure4) analysis has
been performed. The comparison between the HM specification and the best
performances VCXO available on the market in terms of phase noise close to the
carrier gives the required cutoff frequency to be implemented. It shows that
the optimum cutoff frequency should be around 4 Hz. Since the frequency beats used as comparison
signal are 1 kHz, it is easy to implement the desired 4 Hz cutoff frequency.Figure 4
Phase noise figure.


## 4. Steering Approach

The backup HM steering algorithm together with the MCPC
and PicoStepper form a basic phase-locked loop (PLL), which locks the phase of
the backup HM to the primary one. Figure5 shows the block diagram of the backup
HM steering model.Figure 5
Block diagram of the backup HM steering model.The algorithm design is based on a digital proportional integral
(PI) filtering controller, which contains the PI filter and periodical
generation of the steering commands accepted by the PicoStepper.To eliminate the impact of anomalies of the primary HM
output signal (e.g., phase spikes) on the steered backup HM, the algorithm
first removes the phase outliers of the dynamic least-square linear fit (LSLF). Because the outlier routine is sensitive only to the difference between the two HMs, the steering computation is equally
efficient at rejecting phase outliers from both the primary and the backup HMs. These outliers in the backup HM, however, remain in the steered output.


### 4.1. Phase-Locked Loop and PI Filter

Figure6 illustrates the PLL control system block diagram in
the continuous (Laplace) domain.Figure 6
Block diagram of the phase-locked loop.Thes-transfer function of second-order closed loop is
(1)C(s)=2ξτs+1τ2s2+2ξτs+1,
where τ is the loop time constant (in seconds), 1000
seconds, which is selected as the tradeoff of the time offset and the frequency
stability [2]; ξ is the damping factor, 1; Kc is MCPC gain, 1013 step/s; and Km is the PicoStepper gain, 10−13/step.In discrete
domain, basic digital filtering functions can be used. Therefore, thez-transfer function of the discrete PI filter is
(2)D(z)=Kp+Kizz−1,
where Ki and Kp are coefficients of the discrete integrator and proportional regulator.


### 4.2. Dynamic Least-Square Linear Fitting and  Outlier Removing

Figure7 illustrates the block diagram of the Outlier
Remover. The input data from MCPC, e0 is checked by LSLF over the previous 100-second
data in sliding windows. If the absolute value of the deviation from the
fitting line exceeds the outlier criterion C (30 picoseconds), the data are removed
and replaced by the previous value.
Therefore, the phase outliers of the primary HM are filtered before the
steering.Figure 7
Block diagram of the outlier remover.


## 4.1. Phase-Locked Loop and PI Filter

Figure6 illustrates the PLL control system block diagram in
the continuous (Laplace) domain.Figure 6
Block diagram of the phase-locked loop.Thes-transfer function of second-order closed loop is
(1)C(s)=2ξτs+1τ2s2+2ξτs+1,
where τ is the loop time constant (in seconds), 1000
seconds, which is selected as the tradeoff of the time offset and the frequency
stability [2]; ξ is the damping factor, 1; Kc is MCPC gain, 1013 step/s; and Km is the PicoStepper gain, 10−13/step.In discrete
domain, basic digital filtering functions can be used. Therefore, thez-transfer function of the discrete PI filter is
(2)D(z)=Kp+Kizz−1,
where Ki and Kp are coefficients of the discrete integrator and proportional regulator.


## 4.2. Dynamic Least-Square Linear Fitting and  Outlier Removing

Figure7 illustrates the block diagram of the Outlier
Remover. The input data from MCPC, e0 is checked by LSLF over the previous 100-second
data in sliding windows. If the absolute value of the deviation from the
fitting line exceeds the outlier criterion C (30 picoseconds), the data are removed
and replaced by the previous value.
Therefore, the phase outliers of the primary HM are filtered before the
steering.Figure 7
Block diagram of the outlier remover.


## 5. Backup HM Steering System Simulation and Performance Verification

The technical requirement on the backup HM steering system
imposed by PTF design is that the phase jump will not exceed 30 picoseconds in
the value of the GST(MC) to switch the primary and backup HMs.A simulation model [3] is created to analyze and verify
the steering operability and the loop performance under various test cases
including the nominal and degraded conditions with simulated anomalies or
feared events (phase/frequency spikes, jumps and drift) occurred in both HMs.Figures8, 9, 10, and 11 demonstrate the simulation results on various test cases. The backup HM2 is steered properly to the
primary HM1 under all test cases.
(i)
With phase spikes at the primary HM1, the algorithm properly
eliminates the anomalies. The peak value of the phase offset “HM2(steered)-HM1(outliers removed)” is 4 picoseconds, which depends on the initial phase difference,
and the standard deviation is 1.03 picoseconds after the loop is settled down.(ii)
In the presence of the phase step of 30 picoseconds (GST(MC) maximum phase jump) either at the primary
HM1 or the backup HM2, the maximum impacted phase offset “HM2(steered)-HM1” is
8 picoseconds.(iii)
When the HM signal is applied by GST(MC) maximum frequency
correction of1e-14, the impact on the phase offset “HM2(steered)-HM1” is 6.3 picoseconds.(iv)
Even if the HM frequency drift is seriously degraded, the phase
offset “HM2(steered)-HM1” returns to specifications with the loop settling
time, and the peak offset around the loop time constant is 27 picoseconds for
the frequency drift of1e-13/d (10 times worse of the specification of
T4science HM, whose typical value is few e-15/d). The maximum phase offset as 12.5 picoseconds observed near to 20 000 seconds is due to the accompanying frequency jump of 2.5e-14 in the HM
output signal.Simulation on phase/frequency spikes at primary HM1.
(a)(b)Simulation on phase jump of 30 picoseconds at HM1 (similar at HM2).
(a)(b)Simulation on frequency jump of1e-14 at HM1 (similar at HM2).
(a)(b)Simulation on frequency drift of1e-13 at HM1 (similar at HM2).
(a)(b)Table1 summarizes the overall performance budget, taking
into account the calibration errors of the cables between the input of the MCPC
and the input of the switching matrix, the MCPS resolution, and the PicoStepper
resolution. The total performance is within the PTF requirement on the switch over
phase jump of 30 picoseconds.Table 1
Overall performance budget.
Test
case12345Algorithm simulationTest eventNominalPhase/frequency spikesPhase jump of 30 ps(GST(MC) maximum
phase jump)Frequency jump of1e-14(GST(MC)
maximum frequency correction)Frequency
drift of1e-13/d(10
times worse of HM specification)Peak
phase offset4 ps4 ps8 ps6.3 ps27 psCalibration
accuracy5 psMCPC
resolution0.1 psPicoStepper
resolution0.1 psTotal
(phase offset)6.4 ps6.4 ps9.4 ps8 ps27.5 psBesides above phase offset analysis, the frequency offset
of “HM2(steered)-HM1” has been also calculated for all test cases, and it meets
the PTF requirement that the frequency jump shall not exceed4e-15 over the
averaging time of 100 minutes in the value of the GST(MC).In addition,
the worst cases are analysed.(i)
The PLL will be
beyond the  PicoStepper maximum control range (1e+4 steps) when the phase jump is bigger than 5 nanoseconds,
or the frequency jump is bigger than 8e-12.(ii)
For above latter case, the phase offset “HM2steered-HM1” is out of the specification of
30 picoseconds. To meet this specificaion, the frequency jump is allowed to be
less than5e-13.


## 6. Conclusion

We conclude that our steering system is capable of meeting the
Galileo specifications for keeping the backup HM close to the primary in phase
and frequency. Currently the algorithm is in the detailed design phase and is
passing a prototype phase subject to Galileo Software Standards. It will be
tested on PTF hardwares, and will be implemented into the PTF operational
software.



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*Source: 730284-2008-01-03.xml*