State estimation for time synchronization
In one embodiment, a local clock is synchronized to a master clock using a Kalman filter to determine state variables using a state transition matrix that includes at least one coefficient that is associated with a digital-to-analog converter (DAC), where the state variables include a unit step variable indicative of a unit step for the system. The local clock is controlled based on the state variables determined using the Kalman filter. The unit step is indicative of an amount by which the frequency of the local clock signal changes in response to a change in the digital input of the DAC.
1. A system comprising:
a local clock configured to output a local clock signal as a function of an analog control input, the local clock signal having a frequency; and
a digital-to-analog converter (DAC) configured to output an analog output signal as a function of a digital input, wherein the analog control input used by the local clock is a function of the analog output signal output by the DAC;
wherein the system has a unit step that is indicative of an amount by which the frequency of the local clock signal changes in response to a change in the digital input of the DAC;
wherein the system is configured to synchronize the local clock to a master clock using a Kalman filter to determine state variables using a state transition matrix that includes at least one coefficient that is associated with the DAC, wherein the state variables include a unit step variable indicative of the unit step; and
wherein the system is used to control the local clock based on the state variables determined using the Kalman filter.
2. The system of claim 1 , wherein the local clock signal has a phase; and
wherein the system is configured so that the state variables further include higher-order derivatives of a phase of the local clock signal.
3. The system of claim 1 , wherein the local clock signal has a phase; and
wherein the system is configured so that the state variables include a frequency variable indicative of the frequency of the local clock, a phase variable indicative of the phase of the local clock, and the unit step variable indicative of the unit step.
4. The system of claim 3 , wherein the master clock has a frequency and a phase;
wherein the system is configured so that the frequency variable is a frequency error variable indicative of an error between the frequency of the local clock and the frequency of the master clock; and
wherein the system is configured so that the estimated phase variable is a phase error variable indicative of an error between the phase of the local clock and the phase of the master clock.
5. The system of claim 1 , wherein the system is configured to use at least one of the Network Timing Protocol (NTP), the IEEE 1588 Precision Time Protocol (PTP), and the global positioning system (GPS) in order to make measurements for use with the Kalman filter.
6. The system of claim 1 , wherein the at least one coefficient that is associated with the DAC included in the state transition matrix comprises a coefficient that is indicative of a change between the digital input of the DAC between successive samples.
7. The system of claim 1 , wherein the system is configured to synchronize the local lock to the master clock using the Kalman filter by: estimating the state variables using a Kalman model that uses the following:
x n =F n x n-1 +w n ;
wherein x n comprises the state variables for sample n and is represented by:
x
n
=
[
θ
e
,
n
f
e
,
n
k
v
,
n
]
;
wherein θ e,n comprises a phase error for the sample n;
wherein f e,n comprises a frequency error for the sample n;
wherein k v,n comprises the unit step for the sample n;
wherein F n comprises the state transition matrix for the sample n and is represented by:
F
n
=
[
1
T
0
0
1
(
d
n
-
d
n
1
)
0
0
1
]
;
wherein T comprises the time between each sample;
wherein d n comprises the digital input for the DAC for the sample n;
wherein d n-1 comprises the digital input for the DAC for the sample n−1;
wherein x n-1 comprises the state variables for the sample n−1; and
wherein w n comprises the process noise for the sample n.
8. The system of claim 1 , wherein the local clock comprises an oscillator.
9. The system of claim 8 , wherein the oscillator comprises a voltage controlled crystal oscillator (VCXO).
10. The system of claim 1 , wherein the system comprises a node of a radio access network.
11. The system of claim 10 , wherein the node comprises at least one of a baseband unit (BBU) and a remote radio head (RRH).
12. The system of claim 10 , wherein the node comprises at least one of an Open Radio Access Network (O-RAN) central unit (CU), O-RAN distributed unit (DU), and an O-RAN remote unit (RU).
13. The system of claim 1 , further comprising at least one programmable device that is programmed to synchronize the local lock to the master clock using the Kalman filter.
14. The system of claim 1 , further comprising circuitry configured to synchronize the local lock to the master clock using the Kalman filter.
15. A method of synchronizing a local lock to a master clock, the method comprising:
outputting, by the local clock, a local clock signal as a function of an analog control input, the local clock signal having a frequency;
outputting, by a digital-to-analog converter (DAC), an analog output signal as a function of a digital input, wherein the analog control input used by the local clock is a function of the analog output signal output by the DAC, wherein a unit step is indicative of an amount by which the frequency of the local clock signal changes in response to a change in the digital input of the DAC; and
using a Kalman filter to determine state variables using a state transition matrix that includes at least one coefficient that is associated with the DAC, wherein the state variables include a unit step variable indicative of the unit step; and
controlling the local clock based on the state variables determined using the Kalman filter.
16. The method of claim 15 , wherein the local clock has a phase; and
wherein the state variables further include higher-order derivatives of the phase of the local clock signal.
17. The method of claim 15 , wherein the local clock has a phase; and
wherein the state variables include a frequency variable indicative of the frequency of the local clock, a phase variable indicative of the phase of the local clock, and the unit step variable indicative of the unit step.
18. The method of claim 17 , wherein the master clock has a frequency and a phase;
wherein the frequency variable is a frequency error variable indicative of an error between the frequency of the local clock and the frequency of the master clock; and
wherein the system is configured so that the estimated phase variable is a phase error variable indicative of an error between the phase of the local clock and the phase of the master clock.
19. The method of claim 15 , wherein using the Kalman filter to the determine state variables comprises:
using at least one of the Network Timing Protocol (NTP), the IEEE 1588 Precision Time Protocol (PTP), and the global positioning system (GPS) in order to make measurements for use with the Kalman filter.
20. The method of claim 15 , wherein the at least one coefficient that is associated with the DAC included in the state transition matrix comprises a coefficient that is indicative of a change between the digital input of the DAC between successive samples.
21. The method of claim 15 , wherein using the Kalman filter to the determine state variables comprises:
estimating the state variables using a Kalman model that uses the following:
x n =F n x n-1 +w n ;
wherein x n comprises the state variables for sample n and is represented by:
x
n
=
[
θ
e
,
n
f
e
,
n
k
v
,
n
]
;
wherein θ e,n comprises a phase error for the sample n;
wherein f e,n comprises a frequency error for the sample n;
wherein k v,n comprises the unit step for the sample n;
wherein F n comprises the state transition matrix for the sample n and is represented by:
F
n
=
[
1
T
0
0
1
(
d
n
-
d
n
1
)
0
0
1
]
;
wherein T comprises the time between each sample;
wherein d n comprises the digital input for the DAC for the sample n;
wherein d n-1 comprises the digital input for the DAC for the sample n−1;
wherein x n-1 comprises the state variables for the sample n−1; and
wherein w n comprises the process noise for the sample n.
22. The method of claim 15 , wherein the local clock comprises an oscillator.
23. The method of claim 22 , wherein the oscillator comprises a voltage controlled crystal oscillator (VCXO).