Method and devices for time transfer using end-to-end transparent clocks
This invention relates to methods and devices for time transfer. The invention has particular application in the alignment of slave clocks to a master clock and dealing with packet delay variations. In embodiments of the invention, the slave clock uses the residence times measured by end-to-end transparent clocks to compensate for clock synchronization errors that arise due to variability in message transfer delays. Embodiments provide a simple linear approximation technique and a Kalman filter-based technique for estimating offset and skew of the slave clock.
1. A method for estimating the skew and offset of a slave clock in a slave device in relation to a master clock in a master device, the slave device and the master device being connected by a network, the method including the steps of:
exchanging timing messages between the master device and the slave device over the network, each timing message passing through at least one end-to-end transparent clock;
recording timestamps which are the times of the sending and receiving said messages according to the respective clocks;
recording the residence times, r ftotal,n and r rtotal,n , which are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock;
estimating the skew and offset of the slave clock using the said timestamps and said residence times; and
synchronizing the output of the slave clock to the master clock using said estimated offset and skew; and
wherein the step of estimating the skew and offset estimates the skew α as the average of the skew α 1 calculated in the forward direction from master to slave and the skew α 2 calculated in the reverse direction from the slave to the master:
α
1
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
r
ftotal
,
n
-
r
ftotal
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
&
α
2
=
(
T
4
,
n
-
T
4
,
n
-
1
)
+
(
r
rtotal
,
n
-
r
rtotal
,
n
-
1
)
(
T
3
,
n
-
T
3
,
n
-
1
)
-
1
,
wherein
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 4,n is the time of receipt of the nth Delay_Req message as recorded by the master clock; and
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
estimates the offset θ as
θ
=
(
T
1
,
n
+
T
4
,
n
)
-
(
1
+
α
)
(
T
2
,
n
+
T
3
,
n
)
2
+
(
d
f
-
d
r
)
2
+
(
r
rtotal
,
n
-
r
rtotal
,
n
)
2
,
wherein:
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
and updates the offset and skew according to the update equations:
{circumflex over (α)} n =μα n +(1−μ){circumflex over (α)} n−1 , 0<μ<1 and
{circumflex over (θ)} n =μθ n +(1−μ){circumflex over (θ)} n−1 , 0<μ<1.
2. A method according to claim 1 wherein the step of estimating the skew and offset uses an exponentially weighted moving average filter applied to said timestamps and said residence times.
3. A method according to claim 1 wherein the step of estimating the skew and offset uses a Kalman filter.
4. A method according to claim 3 wherein, to estimate the skew α n and the offset θ n at time n, the Kalman filter is applied to:
the state equation
X
n
=
[
θ
n
α
n
]
=
[
1
(
T
1
,
n
-
T
1
,
n
-
1
)
0
1
]
[
θ
n
-
1
α
n
-
1
]
+
[
w
θ
,
n
w
α
,
n
]
and
to the measurement equation
y n =D n X n +v n
wherein:
y n =(T 1,n −T 2,n )+(T 4,n −T 3,n )+(d f −d r )+(r ftotal,n −r ntotal,n ) is a scalar,
D n =[2 (T 2,n +T 3,n )] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
v n =(γ n −ε n ) is the measurement noise, and wherein:
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 4,n is the time of receipt of the nth Delay_Req message as recorded by the master clock;
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
ε is the stochastic delay in the transmission of messages between the master and the slave device; and
γ is the stochastic delay in the transmission of messages between the slave and the master device.
5. A slave device connected to a master device having a master clock by a network containing at least one end-to-end transparent clock, the slave device having a slave clock and a processor, the slave device being arranged to:
exchange timing messages with the master device over said network and record timestamps which are the times of sending and receiving said messages according to the respective clocks; and
extract from said messages the residence times, r ftotal,n and r rtotal,n , which are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock, wherein:
the processor is arranged to:
estimate the skew and offset of the slave clock compared to the master clock using said timestamps and said residence times; and
wherein the processor is further arranged to synchronize the output of the slave clock to the master clock using said estimated offset and skew; and
wherein the processor estimates the skew α as the average of the skew α 1 calculated in the forward direction from master to slave and the skew α 2 calculated in the reverse direction from the slave to the master:
α
1
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
r
ftotal
,
n
-
r
ftotal
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
&
α
2
=
(
T
4
,
n
-
T
4
,
n
-
1
)
+
(
r
rtotal
,
n
-
r
rtotal
,
n
-
1
)
(
T
3
,
n
-
T
3
,
n
-
1
)
-
1
,
wherein
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 4,n is the time of receipt of the nth Delay_Req message as recorded by the master clock; and
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
estimates the offset θ as
θ
=
(
T
1
,
n
+
T
4
,
n
)
-
(
1
+
α
)
(
T
2
,
n
+
T
3
,
n
)
2
+
(
d
f
-
d
r
)
2
+
(
r
ftotal
,
n
-
r
rtotal
,
n
)
2
,
wherein:
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
and updates the offset and skew according to the update equations:
{circumflex over (α)} n =μα n +(1−μ){circumflex over (α)} n−1 , 0<μ<1 and
{circumflex over (θ)} n=μθ n +(1−μ){circumflex over (θ)} n−1 , 0<μ<1.
6. A slave device according to claim 5 wherein the processor estimates the skew and offset using an exponentially weighted moving average filter applied to said timestamps and said residence times.
7. A slave device according to claim 5 wherein the processor estimates the skew and offset using a Kalman filter.
8. A slave device according to claim 7 wherein, to estimate the skew α n and the offset θ n at time n, the Kalman filter is applied to:
the state equation
X
n
=
[
θ
n
α
n
]
=
[
1
(
T
1
,
n
-
T
1
,
n
-
1
)
0
1
]
[
θ
n
-
1
α
n
-
1
]
+
[
w
θ
,
n
w
α
,
n
]
and
to the measurement equation
y n =D n X n +v n
wherein:
y n =(T 1,n −T 2,n )+(T 4,n −T 3,n )+(d f −d r )+(r ftotal,n −r rtotal,n is a scalar,
D n =[2 (T 2,n +T 3,n )] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
v n =(γ n −ε n ) is the measurement noise, and wherein:
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 4,n is the time of receipt of the nth Delay_Req message as recorded by the master clock;
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
ε is the stochastic delay in the transmission of messages between the master and the slave device; and
γ is the stochastic delay in the transmission of messages between the slave and the master device.
9. A system including:
a master device having a master clock;
a slave device having a slave clock and a processor; and
a network connecting said master device and said slave device and having at least one end-to-end transparent clock, wherein
the slave device is arranged to:
exchange timing messages with the master device over said network and record timestamps which are the times of sending and receiving said messages according to the respective clocks;
the or each transparent clock is arranged to:
record the residence times, r ftotal,n and r rtotal,n , which are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the transparent clock, and further wherein:
the processor is arranged to:
estimate the skew and offset of the slave clock compared to the master clock using said timestamps and said residence times; and
wherein the processor is further arranged to synchronize the output of the slave clock to the master clock using said estimated offset and skew; and
wherein the processor estimates the skew α as the average of the skew α 1 calculated in the forward direction from master to slave and the skew α 2 calculated in the reverse direction from the slave to the master:
α
1
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
r
ftotal
,
n
-
r
ftotal
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
&
α
2
=
(
T
4
,
n
-
T
4
,
n
-
1
)
+
(
r
rtotal
,
n
-
r
rtotal
,
n
-
1
)
(
T
3
,
n
-
T
3
,
n
-
1
)
-
1
,
wherein
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 4,n is the time of receipt of the nth Delay_Req message as recorded by the master clock; and
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
estimates the offset θ as
θ
=
(
T
1
,
n
+
T
4
,
n
)
-
(
1
+
α
)
(
T
2
,
n
+
T
3
,
n
)
2
+
(
d
f
-
d
r
)
2
+
(
r
ftotal
,
n
-
r
rtotal
,
n
)
2
,
wherein:
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
and updates the offset and skew according to the update equations:
{circumflex over (α)} n =μα n +(1−μ){circumflex over (α)} n−1 , 0<μ<1 and
{circumflex over (θ)} n =μθ n +(1−μ){circumflex over (θ)} n−1 , 0<μ<1.
10. A system according to claim 9 wherein the processor estimates the skew and offset using an exponentially weighted moving average filter applied to said timestamps and said residence times.
11. A slave device according to claim 9 wherein the processor estimates the skew and offset using a Kalman filter.
12. A slave device according to claim 11 wherein, to estimate the skew α n and the offset θ n at time n, the Kalman filter is applied to:
the state equation
X
n
=
[
θ
n
α
n
]
=
[
1
(
T
1
,
n
-
T
1
,
n
-
1
)
0
1
]
[
θ
n
-
1
α
n
-
1
]
+
[
w
θ
,
n
w
α
,
n
]
and
to the measurement equation
y n =D n X n +v n
wherein:
y n −(T 1,n −T 2,n )+(T 4,n −T 3,n )+(d f −d r )+r ftotal,n −r rtotal,n ) is scalar,
D n =[2 (T 2,n +T 3,n )] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
v n =(γ n −ε n ) is the measurement noise, and wherein:
T 1,n is the time of departure of the nth Sync message as measured by the master clock;
T 2,n is the time of receipt as recorded by the slave clock on receipt of the nth Sync message;
T 3,n is the time of transmission of the nth Delay_Req message as recorded by the slave clock;
T 45n is the time of receipt of the nth Delay_Req message as recorded by the master clock;
r ftotal,n and r rtotal,n are the residence times of the nth packet in the forward and reverse directions respectively, of each message passing through the or each transparent clock,
d f is the fixed physical link delay in the forward direction; and
d r is the fixed physical link delay in the reverse direction,
ε is the stochastic delay in the transmission of messages between the master and the slave device; and
γ is the stochastic delay in the transmission of messages between the slave and the master device.