# Remote Synchronization Simulation of Onboard Crystal Oscillator for QZSS Using L1/L2/L5 Signals

Authors: Toshiaki Iwata; Michito Imae; Tomonari Suzuyama; Yuji Hashibe; Satoshi Fukushima; Akira Iwasaki; Kenji Kokubu; Fabrizio Tappero; Andrew G. Dempster
Journal: International Journal of Navigation and Observation
 (2008)

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## Abstract

A new error adjustment method for remote synchronization of the onboard crystal oscillator for the quasi-zenith satellite system (QZSS) using three different frequency positioning signals (L1/L2/L5) is proposed. The error adjustment method that uses L1/L2 positioning signals was demonstrated in the past.  In both methods, the frequency-dependent part and the frequency-independent part were considered separately, and the total time information delay was estimated.  By adopting L1/L2/L5, synchronization was improved by approximately 15% compared with that using L1/L2 and approximately 10% compared with that using L1/L5 and a synchronization error of less than 0.77 nanosecond was realized.


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## Body

## 1. Introduction

The Japanese Quasi-Zenith  Satellite (QZS) System (QZSS) is a three-satellite
navigation/positioning system conceived to improve the positioning performance
(satellite availability and  position accuracy) of the presently available global
positioning system (GPS)  in urban areas where high-rise buildings reduce the number
of visible GPS  satellites [1]. A new timekeeping
method of the QZSS, named the remote synchronization system for an onboard crystal
oscillator (RESSOX), has been planned by the National Institute of Advanced
Industrial Science and Technology (AIST, Tasukuba, Japan)
[2]. RESSOX is a remote-control method that
permits synchronization between a ground station standard and QZS clocks.
In its original concept, various delay models are used for the estimation of the
delay of the RESSOX control signal that includes time information of QZSS time
and is advanced with respect to QZSS-time to compensate the delay during
transmission. This is considered to be the feed-forward control. Furthermore, pseudoranges
of positioning signals obtained at the ground station, named the time management
station (TMS), are used for error adjustment, where QZSS-Time is a standard time of
QZSS, like GPS time for GPS, and refers to UTC (NICT). This is considered to be
the feedback control. RESSOX is realized by combining feed-forward and feedback
control. The RESSOX control signal is transmitted with the Ku-band from the TMS.The proposed Japanese QZSS has the following properties regarding its timekeeping
system (TKS): (1) it is possible to control the system over a 24-hour period as
long as good visibility of QZS is obtained; (2) a high-stability crystal oscillator
is superior to an atomic standard in terms of short-term frequency stability
[3]; and (3) the QZSS employs a maximum of three
satellites, which are not too many to monitor from the ground.RESSOX reduces overall costs, satellite power consumption, and onboard weight and
volume; and it has a longer lifetime than a system with onboard atomic clocks.RESSOX ground experiments and computer simulations have been conducted since 2003.
QZS broadcasts four positioning signals as  availability enhancement signals: L1C/A,
L1C, L2C, and L5 [4]. The tentative target of our
research is synchronization to within 10 nanoseconds between the ground standard
time and the QZS site at any time and frequency stability better than
1 × 10−13 for 100,000 seconds. Initial experimental results
using only L1/L2 positioning signals and experimental apparatus have been
introduced previously [5–10].
We have developed a new feedback method that uses L1/L2/L5 positioning
signals of the QZSS and proved that we could improve synchronization by 15%
compared with the former L1/L2 method. Since experimental apparatuses for L5 are not
available at the moment, only simulation results are presented in this paper.Evaluations of the effects of the range error magnitude and the least-squares
filter used at the ground site are also discussed.


## 2. Simulation Model

To investigate this new RESSOX method, a specific software simulator has been
developed. The actual onboard crystal oscillator is MINI-OCXO manufactured by
C-MAC MicroTechnology (Buckinghamshire, UK), and is modeled as follows:(1)f=1.023×107(1.0+3.2500048×10−8(V-5.352333)),
where f is the output frequency
and V is the applied voltage (when V = 5.352333 V,
f = 10.23 MHz).To control MINI-OCXO using the difference between uplinked time information with
RESSOX control signal and MINI-OCXO time, modified PI control of the control voltage
was employed. The following formula  that describes modified PI control was used:(2)vk=offset−k1l+1∑i=k−lk(tOCXO−tRESSOX)i−k2∑i=0k−1∫ii+p(tOCXO−tRESSOX)dt.
Here, vk is the kth output voltage, offset = 5.352333 (V),
k1 is a proportional gain set at 7.0 × 106,
k2 is an integral gain set at 3.0 × 104,
l is the number of past data used for
proportional control and is set at 1, k is the data number from
the beginning of the simulation, p is the integral interval, which
means an overlapping integral number, set at 2, and
tRESSOX is time information of the received RESSOX
control signal.Control repetition at the TMS is once every second, and that on the QZS is once
every 1.5 seconds.The simulation conditions are shown
in Table1. Typical Keplerian orbit elements of
the QZS, shown in Table 1, were assumed. To
calculate the orbit precisely, the EGM96 geopotential model with the spherical
harmonic coefficient of degree and order 360, the gravity effects of the sun,
the moon, and other planets taken from the Jet Propulsion Laboratory
(JPL, NASA, Pasadena, Calif, USA) ephemeris DE405, the radiation pressure, and the solid tide
effects were considered. To calculate ionospheric delay, data (COD10426.ION)
from the Center for Orbit Determination in Europe (CODE, University of Bern, Bern,
Switzerland) was used. The simulation period was all day, January 1, 2000.
This means that positions of the sun, the moon, and other planets and ionospheric
data for that day were used. The meteorological conditions for tropospheric delay
calculation were assumed to be constant at
15°C, 1013.25 hPa, and 70% relative humidity,
and the Saastamoinen model was used. The position of the TMS was assumed to be in
Okinawa (26.5 N, 127.9 E, elevation = 0.0 m). The calculations using these
parameters correspond to the authentic range in Figure
1, and the “Orbit/Delay calculation
(without error)” in Figure 2.
These conditions can be  expressed as x = −22,881,059.583 m,
y = −32,625,645.367 m,
z = 19,898,922.824 m,
vx = 2,207.153 m/s,
vy = −839.448 m/s, and vz = 1,693.581 m/s as the initial conditions in the
International Celestial Reference Frame (ICRF).Table 1
Simulation conditions.
ItemsValuesItemsValuesSimulation period2000.1.1Satellite cross section,m230.000:00:00UTC-2000.1.2CODE data of ionosphereCOD10426.ION00:00:00UTCSemimajor axis, m42164170.0Meteorological condition15°C, 1013.25 hPa, 70% (relative humidity)Eccentricity, m0.099Inclination, deg45.0Radiation pressure coefficient (Cr)4.56 × 10−6 N/m2 (McCarthy 1996), Cr = 1.2Right ascension of the ascending node, deg205.0Argument of perigee, deg270.0Position of ground station26.5 N, 127.9 E, Height = 0.0 m (Okinawa)Mean motion, deg120.0Solid Earth tideMoon and Sun are considered, k2 = 0.3 (IAG 1999)Geopotential modelEGM96, n, m = 360Other celestial bodiesMoon, Sun, Mercury, Venus, Mars, Jupiter, Saturn,
Uranus, Neptune, Pluto(JPL-DE405)Satellite mass, kg3000.0Figure 1
Differences in initial conditions between authentic delay and estimated
one.Figure 2
Simulation block diagram. Number in parenthesis indicates the step explained in the text.  Our goal is synchronization between a
ground atomic clock at TMS and an onboard crystal oscillator on QZS.For the orbit information used at the TMS, an initial
error of −5 m for each axis of ICRF, that is, the initial conditions ofx = −22,881,064.583 m,
y = −32,625,640.367 m, and
z = 19,898,917.824 m of the equation of
motion (vx, vy, and
vz are the same as the authentic values) are assumed in
order to create the time adjustment file for the transmitting time
adjuster (TTA) and the database of L1/L2/L5 in Figure
2. The ionospheric and tropospheric delays were not
considered. The differences in initial conditions between authentic delay and
estimated delay are shown in Figure 1.


## 3. Control Method

To realize RESSOX, L1, L2, and L5 pseudoranges were considered separately, and the
delay of the frequency-dependent part (i.e., ionospheric delay) and that of the
frequency-independent part (i.e., clock error, range error, and tropospheric delay)
were estimated. The following is the simulation sequence of this new method, as
shown in Figure2. In the simulation, some
experimental apparatuses, such as the onboard crystal oscillator (MINI-OCXO), TTA,
the time comparator, and the QZS signal receiver are modeled based on the ground
experiments.Initialization (Steps1 to 3)
Step 1.
Four estimated delays (L1-, L2-, L5-, andKu-bands) are prepared. These estimated delays include model errors such as those
due to the orbit, ionosphere, or troposphere, and we assume that they are used at
the TMS as the measurement results. The estimated delays of the L1-,
L2-, and L5-bands make up the  database of L1, L2, and L5 delays in the RESSOX
controller to be used for comparison with the L1-, L2-, and L5-band
pseudoranges in Step 7. In contrast, the estimated delay of the
Ku-band is described in the time adjustment file for TTA, and is used as
feed-forward control.Step 2.
Four authentic delays (L1-, L2-, L5-, andKu-bands) are prepared. These delays do
not contain any errors. Three of these delays are contained in the L1, L2, and L5 authentic delay file, and the fourth
one is contained in the Ku authentic delay file.Step 3.
The time adjustment file for TTA is fed into
the TTA as feed-forward control. The timing for transmitting
time information using the RESSOX control signal is adjusted to give the time
comparator the correct time when the signal arrives at the QZS.Process Routine (Steps4–10)
Step 4.
The Delay of the RESSOX Control Signal during
Transmission is Realized by theKu Authentic Delay File.Step 5.
The onboard crystal oscillator is controlled using the time difference
between the RESSOX control signal and the time of the crystal oscillator
itself. Some noise generated by the crystal oscillator and the time comparator is
assumed in this step and is generated by STable 32, a clock-simulation software
[10].  We assume that the onboard crystal oscillator
has a stability of 1.0 × 10−12 from 1 to 100 seconds and 5.0 × 10−11 for one day (86400 s), giving
random walk frequency noise = 5.0 × 10−14,
flicker frequency noise = 6.5 × 10−13, and frequency drift per
second = 6 × 10−16, and the time comparator has
a stability of 2.5 × 10−10 for 1 second and has only
phase-white noise. The Allan deviation is shown in Figure
3.Step 6.
The pseudoranges of L1, L2, and L5 are calculated using the L1, L2, and L5
authentic delay file and the onboard crystal oscillator error. Noise that has
1 nanosecond standard deviation is added during transmission.Step 7.
The pseudoranges of L1, L2, and L5, obtained
by the QZS signal receiver, are compared with the database of L1, L2, and L5
delay, and the differences between the pseudoranges and the database are
designated asE1 for L1
(frequency fL1= 1.57542 × 109 Hz), E2
for L2 (fL2= 1.2276 × 109 Hz), and
E3 for L5
(fL5= 1.17645 × 109 Hz).Step 8.
Simultaneous equations (3), which
include E1, E2, and
E3, delays due to the nonfrequency-dependent term
e, and the coefficient of delay k due to the
frequency-dependent term (i.e., ionospheric delay) as unknowns, are solved:
(3)e+kfL12=E1,fL1=1.57542×109[Hz],e+kfL22=E2,fL2=1.2276×109[Hz],e+kfL52=E3,fL5=1.17645×109[Hz].
These equations are expressed using a matrix as follows:
(4)[11/fL1211/fL2211/fL52][ek]=Ax=[E1E2E3]=E.
Since A is not a square matrix,
to solve the equations, pseudoinverse x=(ATA)−1ATE is used.Step 9.
Using the solutions of the simultaneous equations, we obtain the time to
be adjusted with formula (5), of the RESSOX control signal using the Ku-band
(fKu=1.43453×1010 Hz)
for the TTA(5)e+k/fKu2,fKu=1.43453×1010[Hz].Step 10.
As a result of combining the delay estimation file in
Step3 and the time to be adjusted for the TTA, the TTA is controlled. This process
is considered to be the feedback control. We consider some filters in this
step, as described later. Then we go back to Step 4. The calculation of the time to
be adjusted is conducted every second. The default filter is constructed using
100 data values of the time to be adjusted (result of formula (5) using the difference
between measured pseudoranges of L1/L2/L5 and estimated pseudoranges of
L1/L2/L5 prepared as the database of L1/L2/L5 delay) from 6 to 105 seconds
before every second. In our first consideration, the change of the time to be
adjusted would depend on mainly the tropospheric delay in Figure
4. Since tropospheric delay depends on the
elevation angle, the change of tropospheric delay can be
approximated in the first order for such a short period as 100 seconds. Therefore,
100 data values of time to be adjusted are used for the first-order
least-squares filtering, and the time to be adjusted is extrapolated to the
current time, as shown in Figure 4.  To calculate
and send the filtering  result to the TTA as the time adjustment command, six seconds
are assumed to be required.
Control is conducted every second on the ground and every 1.5 seconds on the QZS.
These control frequencies will be actually adopted in the QZSS project.
In Figure2, the three pink blocks indicate the
key processes of this method.Figure 3
Assumed allan deviation
of onboard system.Figure 4
Default control method at TMS.


## 4. Simulation Results

The simulation was conducted according to the block diagram shown in Figure2.The atomic standard at the TMS and the onboard crystal oscillator can be
synchronized to within 1 nanosecond throughout 24 hours, even
though the noise of the pseudorange has a 1 nanosecond standard deviation, as
shown in Figure5. The change of range error during
simulation is shown in Figure 6. For the orbit
information used at the TMS, which corresponds to “Orbit/Delay calculation
(with error)” in Figure 2, an initial error
of −5 m for each axis of ICRF is assumed as measurement error. The
difference in range between authentic and measured errors corresponds to the
range error. Even though the range error (i.e., orbit estimation) is
considerably large (0–12 m), the proposed method functions
correctly.Figure 5
Synchronization result. The
synchronization is within 1 ns.Figure 6
Change of range error during simulation.Using the solutions ofe and k of simultaneous
equations (3), the time to be adjusted was calculated.
The two terms of the time to be adjusted, that is, e and
k/fKu2, correspond to delays other than ionospheric delay and to the
ionospheric delay of the RESSOX control signal using the Ku-band.
As shown in Figure 7, although
e and
k/fKu2 of the time to be adjusted vary by about ±30 nanoseconds and
0.5 nanosecond, respectively, because of the noise of the pseudorange, the results of
these solutions show good agreement with the actual delays of these origins, that is,
the range error plus tropospheric delay and the ionospheric delay shown in Figure
8.Elements of time to be adjusted.e and
K/fKu2 correspond to the range error plus
tropospheric delay and the ionospheric delay shown in Figure 8, respectively.
(a)(b)Authentic delay of range error plus tropospheric delay and ionospheric
delay.
(a)(b)The actual time adjustment command calculated using a combination of 100
elements of the time to be adjusted and the first-order least-squares filter
shown in Figure4 is shown in Figure
9. Since the element of the time
to be adjusted, k/fKu2, is approximately two orders smaller than that of the time to
be adjusted, e, the graph shape is similar to that for
e in Figure 7.
The filter has the effect of reducing the noise.Figure 9
Actual time adjustment command calculated using a combination of 100
elements of time to be adjusted and first-order least-squares filter shown in
Figure4.


### 5. Effect of Adopting Three Frequencies

To compare the effects of using three frequencies, synchronization error was
evaluated. Three different combinations were investigated: L1 and L2, L1 and L5, and
L1, L2, and L5. The combination of L1 and L2 means the current usable
combination, and that of L1 and L5 means the most separate frequencies for which a
small error is expected.  First, we considered the optimum number of data values with
the first-order least-squares filter. The number of data values was increased
to 1,000. The tendency of the number of data values being greater with smaller
synchronization error was confirmed, and the best results were obtained in the case
of using three frequencies, as shown in
Figure10. In any case, when the number of data
values was smaller than 50, the maximum synchronization error was larger than 10
nanoseconds, and the smallest synchronization error was obtained when the number of
data values was 1,000. Synchronization using L1/L2/L5 was improved by
approximately 15% compared with that using L1/L2 and by approximately 10% compared
with that using L1/L5.Figure 10
Relationship between number of data values and maximum
synchronization error. Three different combinations were investigated.Next, we compared the effect of the order of the filter, using three
frequencies; the results are shown in Figure11. In
the case of the zeroth-order filter, when the number of data values
was small, the maximum synchronization error was  smaller than 3 nanoseconds;
however, it increased when the number of data values was larger than 200. In the
case of a first- or higher-order filter, when the number of data values was small,
the maximum synchronization error became unacceptably large.
The smallest maximum synchronization error was obtained when the first-order filter
and 1,000 samples were used.Figure 11
Relationship between number of data values and maximum synchronization error.
The effect of the order of the filter is compared.


### 6. Conclusions

This study is summarized as follows.(1)
A new error-adjustment
method for remote synchronization of the onboard crystal oscillator (RESSOX) for the QZSS using L1/L2/L5 positioning signals was demonstrated
by simulation.(2)
Synchronization to within 1 nanosecond between the onboard crystal oscillator and the ground
standard time was achieved in a 24-hour simulation.(3)
The ionospheric delay and the
combination of tropospheric delay and range error of the RESSOX control signal
were estimated in the calculation and efficiently compensated.(4)
On the ground, the number
of data values and the order of the least-squares filter can be changed.  The
first-order least-squares filter using 1000 data values and three frequencies is the best, yielding a synchronization
error of less than 0.77 nanosecond.(5)
Synchronization using L1/L2/L5 was
improved by approximately 15% compared with that using L1/L2 and by
approximately 10% compared with that using L1/L5.


## 5. Effect of Adopting Three Frequencies

To compare the effects of using three frequencies, synchronization error was
evaluated. Three different combinations were investigated: L1 and L2, L1 and L5, and
L1, L2, and L5. The combination of L1 and L2 means the current usable
combination, and that of L1 and L5 means the most separate frequencies for which a
small error is expected.  First, we considered the optimum number of data values with
the first-order least-squares filter. The number of data values was increased
to 1,000. The tendency of the number of data values being greater with smaller
synchronization error was confirmed, and the best results were obtained in the case
of using three frequencies, as shown in
Figure10. In any case, when the number of data
values was smaller than 50, the maximum synchronization error was larger than 10
nanoseconds, and the smallest synchronization error was obtained when the number of
data values was 1,000. Synchronization using L1/L2/L5 was improved by
approximately 15% compared with that using L1/L2 and by approximately 10% compared
with that using L1/L5.Figure 10
Relationship between number of data values and maximum
synchronization error. Three different combinations were investigated.Next, we compared the effect of the order of the filter, using three
frequencies; the results are shown in Figure11. In
the case of the zeroth-order filter, when the number of data values
was small, the maximum synchronization error was  smaller than 3 nanoseconds;
however, it increased when the number of data values was larger than 200. In the
case of a first- or higher-order filter, when the number of data values was small,
the maximum synchronization error became unacceptably large.
The smallest maximum synchronization error was obtained when the first-order filter
and 1,000 samples were used.Figure 11
Relationship between number of data values and maximum synchronization error.
The effect of the order of the filter is compared.


## 6. Conclusions

This study is summarized as follows.(1)
A new error-adjustment
method for remote synchronization of the onboard crystal oscillator (RESSOX) for the QZSS using L1/L2/L5 positioning signals was demonstrated
by simulation.(2)
Synchronization to within 1 nanosecond between the onboard crystal oscillator and the ground
standard time was achieved in a 24-hour simulation.(3)
The ionospheric delay and the
combination of tropospheric delay and range error of the RESSOX control signal
were estimated in the calculation and efficiently compensated.(4)
On the ground, the number
of data values and the order of the least-squares filter can be changed.  The
first-order least-squares filter using 1000 data values and three frequencies is the best, yielding a synchronization
error of less than 0.77 nanosecond.(5)
Synchronization using L1/L2/L5 was
improved by approximately 15% compared with that using L1/L2 and by
approximately 10% compared with that using L1/L5.



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*Source: 462062-2008-01-03.xml*