Methods of estimating frequency skew in networks using timestamped packets

1. A method of estimating and adjusting frequency skew of clocks in a packet processing network, comprising:

transmitting packets containing timestamps between master and slave devices in the packet processing network, which are synchronized with respective clocks and separated from each other by a packet network over which: (i) a first plurality of the packets are transmitted in-sync with a master clock generated within the master device, and (ii) a second plurality of packets are transmitted in-sync with a slave clock generated within the slave device;

generating an initial estimate of frequency skew of the slave clock relative to the master clock, from the timestamps within the first and second pluralities of the packets;

determining a representation of a packet delay variation (PDV) sequence from the initial estimate of the frequency skew and the timestamps;

determining a statistical characterization of the representation of the PDV sequence;

extracting a statistical mode from the statistical characterization and determining first indices of a first plurality of points in the representation of the PDV sequence that are above the statistical mode and second indices of a second plurality of points in the representation of the PDV sequence that are below the statistical mode, said extracting comprising extracting the statistical mode from an empirical probability density function (PDF) of the representation of the PDV sequence, where the statistical mode corresponds to a value at which the PDF has its maximum value;

generating an updated estimate of the frequency skew by determining a slope between the timestamps at the determined indices, said slope specifying a change in master and slave time-of-day (TOD) offsets associated with the timestamps relative to a change in index of the timestamps; and

adjusting, based on the updated estimate of the frequency skew, at least one of the master and slave clocks in the master and slave devices, respectively, to thereby improve synchronization therebetween.

2. The method of claim 1 , wherein said generating an initial estimate of frequency skew comprises normalizing the timestamps.

3. The method of claim 2 , wherein said determining a representation of a packet delay variation (PDV) sequence comprises determining a representation of a packet delay variation (PDV) sequence from the initial estimate of the frequency skew and the normalized timestamps; and wherein said generating an updated estimate of the frequency skew comprises generating an updated estimate of the frequency skew by determining a slope between the normalized timestamps at the determined first and second indices.

4. The method of claim 1 , wherein the packet network is electrically coupled to the master and slave devices.

5. The method of claim 3 , wherein said extracting a statistical mode and said generating an updated estimate of the frequency skew are performed iteratively to thereby narrow a region around the extracted statistical mode.

6. The method of claim 1 , wherein said adjusting comprises adjusting a frequency of the slave clock in the packet processing network to thereby improve a frequency skew of the slave clock relative to the master clock.

7. The method of claim 6 , wherein packet processing network operates in a non-stationary network environment.

8. The method of claim 1 , wherein said transmitting, generating, determining, extracting and adjusting steps are performed by the packet processing network.

9. A method of estimating and adjusting frequency skew of clocks in a packet processing network, comprising:

determining a representation of a packet delay variation (PDV) sequence from an initial estimate of frequency skew between master and slave devices in the packet processing network and packets containing timestamps transmitted therebetween, said packets comprising; (i) a first plurality of packets transmitted across a packet network in-sync with a master clock within the master device, and (ii) a second plurality of packets transmitted across the packet network in-sync with a slave clock within the slave device;

determining a statistical characterization of the representation of the PDV sequence from the initial estimate of the frequency skew and the timestamps;

extracting a statistical mode from the statistical characterization by extracting the statistical mode from an empirical probability distribution function (PDF) of the representation of the PDV sequence, where the statistical mode corresponds to a value at which the PDF has its maximum value;

generating an updated estimate of the frequency skew by determining a slope between timestamps at indices associated with a plurality of points in the representation of the PDV sequence that are within a range of the statistical mode, said slope specifying a change in master and slave time-of-day (TOD) offsets associated with the timestamps relative to a change in index of the timestamps; and

adjusting, based on the updated estimate of the frequency skew, at least one of the master and slave clocks in the master and slave devices, respectively, to thereby improve synchronization therebetween.

10. The method of claim 9 , wherein the packet network is electrically coupled to the master and slave devices.

11. The method of claim 9 , wherein said adjusting comprises adjusting a frequency the slave clock in the packet processing network to thereby improve a frequency skew of the slave clock relative to the master clock.

12. The method of claim 11 , wherein packet processing network operates in a non-stationary network environment.

13. The method of claim 9 , wherein said determining, extracting, generating and adjusting steps are performed by the packet processing network.

14. A method of estimating and adjusting frequency skew of clocks in a packet processing network, comprising:

generating an initial estimate of frequency skew from timestamps transmitted in packets between master and slave devices in the packet processing network, which are separated from each other by a packet network, said packets comprising; (i) a first plurality of packets transmitted across the packet network in-sync with a master clock within the master device, and (ii) a second plurality of packets transmitted across the packet network in-sync with a slave clock within the slave device;

determining a representation of a packet delay variation (PDV) sequence from the initial estimate of the frequency skew and the timestamps;

determining a statistical characterization of the representation of the PDV sequence from the initial estimate of the frequency skew and the timestamps;

extracting a statistical mode from the statistical characterization, said extracting comprising extracting the statistical mode from an empirical probability distribution function (PDF) of the representation of the PDV sequence;

generating an updated estimate of the frequency skew from a set of modal points extracted from the probability density function (PDF) of the representation of the PDV sequence, said modal points aligned to a line having a slope that specifies a change in master and slave time-of-day (TOD) offsets associated with the timestamps relative to a change in index of the timestamps; and

adjusting, based on the updated estimate of the frequency skew, at least one of the master and slave clocks in the master and slave devices, respectively, to thereby improve synchronization therebetween.

15. The method of claim 14 , wherein said generating an initial estimate of frequency skew comprises normalizing the timestamps.

16. The method of claim 14 , wherein the packet network is electrically coupled to the master and slave devices.

17. The method of claim 14 , wherein said adjusting comprises adjusting a frequency of the slave clock in the packet processing network to thereby improve a frequency skew of the slave clock relative to the master clock.

18. The method of claim 17 , wherein packet processing network operates in a non-stationary network environment.

19. The method of claim 14 , wherein said generating, determining and adjusting steps are performed by the packet processing network.