Method and devices for time transfer using peer-to-peer transparent clocks
This invention relates to methods and devices for time synchronization. The invention has particular application in the alignment of slave clocks to a master clock and in dealing with packet delay variation and dynamic asymmetries in the network links between them. In embodiments of the invention, the slave clock uses the peer link delay and residence times measured by peer-to-peer 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:
sending timing messages from the master device to the slave device over the network, each timing message passing through at least one peer-to-peer transparent clock;
recording timestamps which are the times of the sending and receiving said messages according to the respective clocks;
in each transparent clock, estimating the residence time of each message passing through the transparent clock and the propagation delay between the sending of the message by the previous transparent clock, or the master device if there is no previous transparent clock, and the receipt of the message by the transparent clock;
estimating the total transit delay experienced by each timing message, using the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks;
communicating said total transit delay to the slave device;
estimating the skew and offset of the slave clock using the said timestamps and said total transit delay; 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
α
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
d
total
,
n
-
d
total
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
wherein:
T 1,n is the time of departure of the nth timing 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 timing message;
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks,
estimates the offset θ as θ=(T 1,n +d total,n )−(1+α)T 2,n ,
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 total transit delay.
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 +ν n
wherein:
y n =(T 1,n −T 2,n )+d total,n is a scalar,
D n =[1 T 2,n ] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
ν n is the measurement noise, and wherein:
T 1,n is the time of departure of the nth timing 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 timing message; and
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks.
5. A slave device connected to a master device having a master clock by a network, the slave device having a slave clock and a processor, the slave device being arranged to:
receive timing messages from the master device over the network, each timing message passing through at least one peer-to-peer transparent clock;
record timestamps which are the times of the sending and receiving said messages according to the respective clocks;
extract from each message a total transit delay which is the cumulative estimate by the transparent clocks of the residence time of the message passing through each transparent clock and the propagation delay between the sending of the message by the previous transparent clock, or the master device if there is no previous transparent clock, and the receipt of the message by the 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 total transit delay; 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
α
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
d
total
,
n
-
d
total
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
wherein:
T 1,n is the time of departure of the nth timing 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 timing message;
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks,
estimates the offset θ as θ=(T 1,n +d total,n )−(1+α)T 2,n ,
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 total transit delay.
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 +ν n
wherein:
y n =(T 1,n −T 2,n )+d total,n is a scalar,
D n =[1 T 2,n ] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
ν n is the measurement noise, and wherein:
T 1,n is the time of departure of the nth timing 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 timing message; and
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks.
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 peer-to-peer transparent clock, wherein
the slave device is arranged to:
receive timing messages from the master device over the network, each timing message passing through at least one peer-to-peer transparent clock;
record timestamps which are the times of the sending and receiving said messages according to the respective clocks;
the transparent clock is arranged to:
estimate the residence time of each message passing through the transparent clock and the propagation delay between the sending of the message by the previous transparent clock, or the master device if there is no previous transparent clock, and the receipt of the message by the transparent clock; and
communicate said residence time and said propagation delay to the slave device, and
the processor is arranged to:
estimate the total transit delay experienced by each timing message, using the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks; and
estimate the skew and offset of the slave clock compared to the master clock using said timestamps and said total transit delay; 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
α
=
(
T
1
,
n
-
T
1
,
n
-
1
)
+
(
d
total
,
n
-
d
total
,
n
-
1
)
(
T
2
,
n
-
T
2
,
n
-
1
)
-
1
wherein:
T 1,n is the time of departure of the nth timing 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 timing message;
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks,
estimates the offset θ as θ=(T 1,n +d total,n )−(1+α)T 2,n ,
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 total transit delay.
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 +ν n
wherein:
y n =(T 1,n −T 2,n )+d total,n is a scalar,
D n =[1 T 2,n ] is a 1×2 matrix,
X n T =[θ n α n ] is a vector and
ν n is the measurement noise, and wherein:
T 1,n is the time of departure of the nth timing 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 timing message; and
d total,n is the total transit delay experienced by the nth timing message, being the total of all the residence times experienced in the transparent clocks and all of the measured propagation delays determined by the transparent clocks.