Method for adjusting clocks of multiple data processors to a common time base

• US 4,882,739 A
• Filed: 01/26/1988
• Issued: 11/21/1989
• Est. Priority Date: 01/26/1988
• Status: Expired due to Term

• Current Assignee: Computer Sports Medicine, Inc.
• Original Assignee: Computer Sports Medicine, Inc.
• Inventors: Potash, Richard J., Burns, Steven K.
• Primary Examiner(s): Griffin, Robert L.
• Assistant Examiner(s): Huseman, Marianne
• Application Number:
  US07/148,493
• Time in Patent Office: 665 Days
• Field of Search: 375/107, 375/109, 455/69, 342/88, 364/569
• US Class Current: 375/358
• CPC Class Codes: H04J 3/0682 by delay compensation, e.g. by compensation of propagation delay or variations thereof, by ranging

Abstract

A master clock is situated at a central data gathering station, and slave clocks are situated at one or more (functionally or spatially) remote stations. Time signals are exchanged between the master clock at the central station and each slave clock at the corresponding remote station. From these signals (i) the transmission time between the central station and the corresponding remote station is determined, and (ii) the ratio between the frequencies of the central station master clock and the corresponding remote station slave clock is determined. The transmission time and clock ratio so determined are averaged between successive determinations to provide improved accuracy. The transmission time value is used to set the slave clock to a reference value accurately corresponding to the time kept by the master clock; and thereafter the clock ratio value is used to insure that the slave clock is incremented at a rate corresponding to the frequency of the oscillator in the master clock. If desired, the master clock can be synchronized to a reference time which is the average of the reference times of the various clocks, and/or to a frequency which is the average of the frequencies of the oscillators in the various clocks.

Claims

1. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a second time signal having the value MT₀ ;

(4) subsequently transmitting from said master clock to said slave clock a third time signal having a value MT₁ corresponding to the value of said master clock time signal when said third time signal is transmitted;

(5) determining a value ST₁ of said slave clock time signal when said third time signal is received by said slave clock;

(6) upon receipt of said second and third time signals at said slave clock, determining a virtual clock reference time t_ref given by

space="preserve" listing-type="equation">t.sub.ref =[(MT.sub.0 +MT.sub.1)-(ST.sub.0 +ST.sub.1)* k.sub.clkratio ]/2

where k_clkratio =(MT₁ -MT₀)/(ST₁ -ST₀); and

(7) at said slave clock, generating a virtual clock time signal having a value T_vc synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc * k.sub.clkratio

where n_pc is the number of slave clock time signal increments.

2. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a second time signal having the value MT₀ ;

(4) subsequently transmitting from said master clock to said slave clock a third time signal having a value MT₁ corresponding to the value of said master clock time signal when said third time signal is transmitted;

(5) determining a value ST₁ of said slave clock time signal when said third time signal is received by said slave clock;

(6) upon receipt of said second and third time signals at said slave clock, determining a virtual clock reference time t_ref given by

space="preserve" listing-type="equation">t.sub.ref =[(MT.sub.0 +MT.sub.1)-(ST.sub.0 +ST.sub.1)]/2; and

(7) at said slave clock, generating a virtual clock time signal having a value T_vc synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc

where n_pc is the number of slave clock time signal increments.

3. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) subsequently transmitting from said master clock to said slave clock (i) a second time signal having a value corresponding to the value of said master clock time signal when said first time signal was received by said master clock, and (ii) a third time signal having a value corresponding to the value of said master clock time signal when said third time signal is transmitted;

(3) upon receipt of said second and third time signals at said slave clock, determining (i) the reference time value required to reference the slave clock to the master clock and (ii) the clock ratio k_clkratio of the frequency of the master clock to the frequency of the slave clock; and

(4) at said slave clock, generating a virtual clock time signal having a value T_vc synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc * k.sub.clkratio

where n_pc is the number of slave clock time signal increments.

5. The method according to claim 3 or 4, comprising the steps of:

transmitting from said master clock to said slave clock a time interval commencement signal having a value corresponding to the value of said master clock time signal when said time interval commencement signal is transmitted;

subsequently transmitting from said master clock to said slave clock a time interval termination signal having a value corresponding to the value of said master clock time signal when said time interval termination signal is transmitted;

after receipt of said time interval termination signal at said slave clock, determining the value of the clock ratio of the frequency of the master clock to the frequency of the slave clock as the ratio of (i) the difference between the values of said time interval termination and time interval commencement signals to (ii) the elapsed time between reception of said time interval commencement and time interval termination signals as determined by said slave clock; and

generating said virtual clock time signal utilizing the clock ratio so determined to compensate for any difference in frequency between the master clock and the slave clock.

4. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting a number of first reference time signals from the slave clock to the master clock;

(2) accumulating at the master clock time values corresponding to the times of reception of said first reference time signals as measured by the master clock;

(3) subsequently transmitting a number of second reference time signals from said master clock to said slave clock;

(4) accumulating at the master clock time values corresponding to the times of transmission of said second reference time signals as measured by the master clock;

(5) accumulating at the slave clock time values corresponding to (i) the times of transmission of said first reference time signals as measured by the slave clock, and (ii) the times of reception of said second reference time signals as measured by the slave clock;

(6) transmitting from the master clock to the slave clock a signal having a value corresponding to a weighted sum of the master clock time values accumulated at Steps (2) and (4);

(7) computing a reference time t_ref of the sleeve clock relative to the master clock from said weighted sum and a weighted sum of the slave clock time values accumulated at Step (5); and

(8) at said slave clock, generating a virtual clock time signal having a value T_vc synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc

where n_pc is the number of slave clock time signal increments.

6. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said master clock to said slave clock a time interval commencement signal having a value corresponding to the value of said master clock time signal when said time interval commencement signal is transmitted;

(2) subsequently transmitting from said master clock to said slave clock a time interval termination signal having a value corresponding to the value of said master clock time signal when said time interval termination signal is transmitted; and

(3) after receipt of said time interval termination signal at said slave clock, generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the clock ratio of (i) the difference between the values of said time interval termination and time interval commencement signals to (ii) the elapsed time between reception of said time interval commencement and time interval termination signals as determined by said slave clock.

7. The method according to claim 6, comprising the additional steps of repeating the transmission of said time interval termination signal a number of times, determining each new corresponding value of said clock ratio utilizing said time interval commencement signal and the most recent time interval termination signal, and generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the most recently determined new value of said clock ratio.

8. A method for referencing a plurality of slave clocks to a master clock, said master clock providing a master clock time signal, each slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from each slave clock to said master clock a first time signal having a value corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) subsequently transmitting from said master clock to said slave clock a time interval termination signal having a value corresponding to the value of said master clock time signal when said time interval termination signal is transmitted; and

(3) after receipt of said time interval termination signal at said slave clock, generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the clock ratio of (i) the difference between the values of said time interval termination and time interval commencement signals to (ii) the elapsed time between reception of said time interval commencement and time interval termination signals as determined by said slave clock.

9. The method according to claim 8, comprising the additional step of determining a virtual clock reference time value equal to the average of the reference time values.

10. A method for referencing a plurality of slave clocks to a master clock, said master clock providing a master clock time signal, each slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said master clock to each slave clock a time interval commencement signal having a value corresponding to the value of said master clock time signal when said time interval commencement signal is transmitted;

(2) subsequently transmitting from said master clock to each slave clock a time interval termination signal having a value corresponding to the value of said master clock time signal when said time interval termination signal is transmitted; and

(3) after receipt of said time interval termination signal at each slave clock, generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the clock ratio of (i) the difference between the values of said time interval termination and time interval commencement signals to (ii) the elapsed time between reception of said time interval commencement and time interval termination signals as determined by the corresponding slave clock.

11. The method according to claim 10, comprising the additional step of generating at one or more of said clocks an adjusted time signal having a value which increases with time at a rate corresponding to the average frequency of said clocks.

12. A method for determining the frequency relationship between at least one slave clock and a master clock, wherein the master clock provides a master clock time signal and the slave clock provides a slave clock time signal, said method comprising the steps of:

transmitting a time interval commencement signal from the master clock to the slave clock, the time interval commencement signal having a value corresponding to the value of the master clock time signal when the time interval commencement signal is transmitted;

subsequently transmitting a time interval termination signal from the master clock to the slave clock, the time interval termination signal having a value corresponding to the value of the master clock time signal when the time interval termination signal is transmitted;

after receipt of the time interval termination signal at the slave clock, generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the clock ratio of the two clock frequencies as the ratio of (i) the difference between the values of the time interval commencement and time interval termination signals to (ii) the elapsed time between reception of the time interval commencement and time interval termination signals as determined by the slave clock.

13. The method according to claim 12, comprising the additional steps of repeating the transmission of said time interval termination signal a number of times, determining at each corresponding termination signal a new value of said clock ratio, and generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and the ratio of (i) the difference between the values of the time interval commencement signal and the most recent time interval termination signal to (ii) the elapsed time between reception of the time interval commencement signal and said most recent time interval termination signal.

14. A method for establishing a reference time of at least one slave clock to correspond with the reference time of a master clock, wherein the master clock provides a master clock time signal and the slave clock provides a slave clock time signal, said method comprising the steps of:

transmitting a first reference time signal from the slave clock to the master clock, said first reference signal having a value corresponding to the value of the slave clock time signal when the first reference time signal is transmitted;

subsequently transmitting a second reference time signal from the master clock to the slave clock, said second reference time signal having a value corresponding to the value of the master clock time signal when the first reference time signal was received by the master clock;

transmitting a third reference time signal from the master clock to the slave clock, said third reference time signal having a value corresponding to the value of the master clock time signal when the third reference time signal is transmitted;

after receipt of the third reference time signal at the slave clock, determining the reference time value by;

adding the value of said slave clock time signal at the time of transmission of said first reference signal, to the value of said slave clock time signal at the time of reception of said third reference signal at said slave clock, to obtain a first subtotal value;

subtracting said first subtotal value from the sum of the values of said second and third reference time signals, to obtain a second subtotal value;

dividing said second subtotal value by two to obtain a reference time value t_ref ; and

at said slave clock, generating a virtual clock time signal T_vc having a value synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc

where n_pc is the number of slave clock time signal increments.

15. The method according to claim 14, comprising the additional steps of:

prior to said subtracting step, modifying said first subtotal value by multiplying said first subtotal value by the ratio of the frequency of said master clock to the frequency of said slave clock, to obtain an adjusted first subtotal value; and

utilizing said adjusted first subtotal value instead of said first subtotal value in said subtracting step, so that the value of said virtual clock time signal is given by the relation

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc * k.sub.clkratio.

16. The method according to claim 14 or 15, comprising the additional steps of:

(1) transmitting a number of said first reference time signals from the slave clock to the master clock;

(2) accumulating at the master clock time values corresponding to the times of reception of said first reference time signals as measured by the master clock;

(3) subsequently transmitting a number of said third reference time signals from said master clock to said slave clock;

(4) accumulating at the master clock time values corresponding to the times of transmission of said third reference time signals as measured by the master clock;

(5) accumulating at the slave clock time values corresponding to (i) the times of transmission of said first reference time signals as measured by the slave clock, and (ii) the times of reception of said third reference time signals as measured by the slave clock;

(6) transmitting from the master clock to the slave clock a signal having a value corresponding to a weighted sum of the master clock time values accumulated at Steps (2) and (4);

(7) computing the reference time t_ref of the slave clock relative to the master clock from said weighted sum and a weighted sum of the slave clock time values accumulated at Step (5); and

(8) at said slave clock, generating a virtual clock time signal having a value synchronized to said master clock time signal, the value T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc * k.sub.clkratio

where n_pc is the number of slave clock time signal increments and k_clkratio is the ratio of the frequency of the master clock to the frequency of the slave clock.

19. The method according to claim 16 or 17, comprising the additional steps of:

(1) transmitting a number of said first reference time signals from the slave clock to the master clock;

(2) accumulating at the master clock time values corresponding to the times of reception of said first reference time signals as measured by the master clock;

(3) subsequently transmitting a number of said third reference time signals from said master clock to said slave clock;

(4) accumulating at the master clock time values corresponding to the times of transmission of said third reference time signals as measured by the master clock;

(5) accumulating at the slave clock time values corresponding to (i) the times of transmission of said first reference time signals as measured by the slave clock, and (ii) the times of reception of said third reference time signals as measured by the slave clock;

(6) transmitting from the master clock to the slave clock a signal having a value corresponding to a weighted difference of the master clock time values accumulated at Steps (2) and (4); and

(7) computing the transmission time of the slave clock relative to the master clock from said weighted difference and a weighted difference of the slave clock time values accumulated at Step (5).

17. A method for determining the transmission time between a slave clock and a master clock and generating a virtual clock time signal which is synchronized to the master clock, wherein the master clock provides a master clock time signal and the slave clock provides a slave clock time signal, said method comprising the steps of:

transmitting a first reference time signal from the slave clock to the master clock, said first reference time signal having a value corresponding to the value of the slave clock time signal when the first reference time signal is transmitted;

subsequently transmitting a second reference time signal from the master clock to the slave clock, said second reference time signal having a value corresponding to the value of the master time clock signal when the first reference time signal was received by the master clock;

transmitting a third reference time signal from the master clock to the slave clock, said third reference time signal having a value corresponding to the value of the master clock time signal when the third reference time signal is transmitted;

after receipt of the third reference time signal at the slave clock, determining the value of the time required for transmission of a signal between the master and slave clocks by;

subtracting the value of said third reference time signal from the value of said second reference time signal, to obtain a first subtotal value;

subtracting the value of said slave clock time signal at the time of transmission of said first reference time signal from the value of said slave clock time signal at the time of reception of said third reference time signal at said slave clock, to obtain a second subtotal value;

adding said first subtotal value to said second subtotal value to obtain a summation value, and dividing the summation value by two to obtain the transmission time value; and

generating a virtual clock time signal by adjusting the value of said slave clock time signal by an amount equal to the sum of (i) a master clock time signal value received by the slave clock after transmission thereto by the master clock and (ii) said transmission time less (iii) the value of said slave clock time signal.

18. The method according to claim 17, comprising the additional steps of:

prior to said adding step, modifying said second subtotal value by multiplying said second subtotal value by the ratio of the frequency of said master clock to the frequency of said slave clock, to obtain an adjusted second subtotal value; and

utilizing said adjusted second subtotal value instead of said second subtotal value in said adding step.

20. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a time interval commencement signal having a value ST₀ corresponding to the value of said slave clock time signal when said time interval commencement signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said time interval commencement signal is received by said master clock;

(3) transmitting from said slave clock to said master clock a time interval termination signal having a value ST₁ corresponding to a value of said slave clock time signal when said time interval termination signal is transmitted;

(4) determining a value MT₁ of said master clock time signal when said time interval termination signal is received at said master clock;

(5) subsequently transmitting from said master clock to said slave clock a time signal containing information sufficient to define the value MT₁ -MT₀ ;

(6) upon receipt of said time interval termination signal at said slave clock, determining a ratio k_clkratio of the frequency of the master clock to the frequency of the slave clock by means of the equation

space="preserve" listing-type="equation">k.sub.clkratio =(MT.sub.1 -MT.sub.0)/(ST.sub.1 -ST.sub.0); and

generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and k_clkratio.

21. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said master clock to said slave clock a time interval commencement signal having a value MT₀ corresponding to the value of said master clock time signal when said time interval commencement signal is transmitted;

(2) determining a value ST₀ of said slave clock time signal when said time interval commencement signal is received by said slave clock;

(3) transmitting from said master clock to said slave clock a time interval termination signal having a value MT₁ corresponding to the value of said master clock time signal when said time interval termination signal is transmitted;

(4) determining a value ST₁ of said slave clock time signal when said time interval termination signal is received by said slave clock; and

(5) upon receipt of said time interval termination signal at said slave clock, determining a ratio k_clkratio of the frequency of the master clock to the frequency of the slave clock by means of the equation

space="preserve" listing-type="equation">k.sub.clkratio =(MT.sub.1 -MT.sub.0)/(ST.sub.1 -ST.sub.0); and

generating a virtual clock time signal having a value which increases with time by an amount proportional to the product of the number of slave clock time signal increments and k_cklratio.

22. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a second time signal having the value MT₀ ;

(4) subsequently transmitting from said master clock to said slave clock a third time signal having a value MT₁ corresponding to the value of said master clock time signal when said third time signal is transmitted;

(5) determining a value of ST₁ of said slave clock time signal when said third time signal is received by said slave clock;

(6) upon receipt of said third time signal at said slave clock, determining a virtual clock reference time t_ref given by

space="preserve" listing-type="equation">t.sub.ref =[(MT.sub.0 +MT.sub.1)-(ST.sub.0 +ST.sub.1)]/2; and

(7) at said slave clock, generating a virtual clock time signal having a value T_vc synchronized to said master clock time signal, the value of T_vc of said virtual clock time signal being given by

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc

where npc is the number of periodic slave clock time increment signals generated.

23. The method according to claim 22, wherein the virtual clock reference time is adjusted for any difference between the frequencies of the master and slave clocks, comprising the steps of:

at said Step (6), determining the virtual clock reference time t_ref according to the equation

space="preserve" listing-type="equation">t.sub.ref =[(MT.sub.0 +MT.sub.1)-(ST.sub.0 +ST.sub.1) * k.sub.clkratio ]/2;

where k_clkratio is the ratio of the frequency of said master clock to the frequency of said slave clock; and

at said Step (7), generating a virtual clock time signal with a value T_vc according to the equation

space="preserve" listing-type="equation">T.sub.vc =t.sub.ref +n.sub.pc * k.sub.clkratio.

24. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a second time signal having the value MT₀ ;

(4) subsequently transmitting from said master clock to said slave clock a third time signal having a value MT₁ corresponding to the value of said master clock time signal when said third time signal is transmitted;

(5) determining a value of ST₁ of said slave clock time signal when said third time signal is received by said slave clock;

(6) upon receipt of said second and third time signals at said slave clock;

determining a ratio k_clkratio of the frequency of the master clock to the frequency of the slave clock according to the relation

space="preserve" listing-type="equation">k.sub.clkratio =(MT.sub.1 -MT.sub.0)/(ST.sub.1 -ST.sub.0); and

(7) at said slave clock, multiplying the number of increments of said slave clock time signal by k_clkratio to generate a virtual clock time signal having a value which increases with time at the same rate as said master clock time signal.

25. A method for referencing at least one slave clock to a master clock, said master clock providing a periodically incremented master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

sequentially transmitting a first set of signals from said slave clock to said master clock and a second set of signals from said master clock to said slave clock, at least one of said sets of signals containing the reference information respecting said time signals, the other of said sets of signals being indentifiable as having been transmitted from a corresponding one of said clocks;

at one of said clocks, determining a clock ratio of the frequency of said master clock to the frequency of said slave clock, by calculating the ratio of (i) the time interval between the times of transmission of two signals successively transmitted by one of said clocks as a transmitting clock to the other of said clocks as a receiving clock, as measured by the transmitting clock, to (ii) the time interval between the times of reception of said signals as measured by the receiving clock;

utilizing said clock ratio, said time reference information and information respecting the other of said sets of signals to determine a reference time value corresponding to the difference between the values of said master and slave clock time signals at a particular time corresponding to a predetermined value of said slave clock time signal; and

at said slave clock, generating a virtual clock time signal by adjusting said slave clock time signal by an incremental amount corresponding to the product of the number of increments of said slave clock time signal between a current value of said slave clock time signal and said particular time and said clock ratio, and adding said reference time value to the adjusted slave clock time signal value.

26. A method for referencing at least one slave clock to a master clock, said master clock having a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a second time signal having the value MT₀ ;

(4) subsequently transmitting from said master clock to said slave clock a third time signal having a value MT₁ corresponding to the value of said master clock time signal when said third time signal is transmitted;

(5) determining a value ST₁ of said slave clook time signal when said third time signal is received by said slave clock;

(6) upon receipt of said third time signal at said slave clock, determining a transmission time given by

space="preserve" listing-type="equation">T.sub.TR =[(MT.sub.0 -MT.sub.1)+(ST.sub.1 -ST.sub.0)]/2; and

generating a virtual clock time signal by adjusting the value of said slave clock time signal by an amount equal to the sum of (i) a master clock time signal value received by the slave clock after transmission thereto by the master clock and (ii) said transmission time less (iii) the value of said slave clock time signal.

27. The method according to claim 26, wherein the calculation of transmission time is adjusted for any differences between the frequencies of the master and slave clocks, comprising the steps of:

at said Step (6), calculating the transmission time according to the equation

space="preserve" listing-type="equation">T.sub.TR =[(MT.sub.0 -MT.sub.1)+(ST.sub.1 -ST.sub.0) * k.sub.clkratio)]/2

where k_clkratio is the ratio of the frequency of said master clock to the frequency of said slave clock; and

generating said virtual clock time signal with a value T_vc according to the relation

space="preserve" listing-type="equation">T.sub.vc =MT.sub.1 +T.sub.TR -ST.sub.1 +n.sub.pc * k.sub.clkratio.

28. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) subsequently transmitting from said master clock to said slave clock (i) a second time signal having a value corresponding to the value of said master clock time signal when said first time signal was received by said master clock, and (ii) a third time signal having a value corresponding to the value of said master clock time signal when said third time signal is transmitted;

(3) upon receipt of said second and third time signals at said slave clock, determining a reference time value required to reference the slave clock to the master clock; and

(4) generating an adjusted slave clock time signal synchronized to said master clock time signal by adding said reference time value to the value of said slave clock time signal.

29. The method according to claim 28, comprising the steps of incrementing the value of said slave clock time signal at a rate corresponding to the product of the value of said slave clock time signal with the ratio of the frequency of said master clock to the frequency of said slave clock, and adding said reference time value to the incremented value of said slave clock time signal.

30. The method according to claim 29, wherein said ratio is determined by calculating the ratio of (i) the time interval between the times of transmission of two signals successively transmitted between the master and slave clocks as measured by one of said clocks to (ii) the time interval between the times of reception of said signals as measured by the other of said clocks.

31. A method for synchronizing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, said method comprising the steps of:

sequentially transmitting a first set of signals from said slave clock to said master clock and a second set of signals from said master clock to said slave clock, said second set of signals containing time reference information respecting said time signals;

at said slave clock, utilizing said time reference information and information respecting said first set of signals to adjust the slave clock time signal to be synchronous with the master clock time signal, so that the adjusted value of said slave clock time signal is equal to the value of said master clock time signals; and

incrementing the adjusted value of said slave clock time signal at a rate corresponding to the product of the number of slave clock time signal increments with the ratio of the frequency of said master clock to the frequency of said slave clock.

32. The method according to claim 31, comprising the additional step of determining said ratio as the ratio of (i) the time interval between the times of transmission of two signals successively transmitted between the master and slave clocks as measured by one of said clocks to (ii) the time interval between the times of reception of said signals as measured by the other of said clocks.

33. A method for referencing at least one slave clock to a master clock, said master clock providing a master clock time signal, said slave clock providing a periodically incremented slave clock time signal, and method comprising the steps of:

(1) transmitting from said slave clock to said master clock a first time signal having a value ST₀ corresponding to the value of said slave clock time signal when said first time signal is transmitted;

(2) determining a value MT₀ of said master clock time signal when said first time signal is received by said master clock;

(3) subsequently transmitting from said master clock to said slave clock a time information signal indicative of the difference MT₁ -MT₀ between (i) the value MT₁ of said master clock time signal when said time information signal is transmitted and (ii) the value MT₀ ;

(4) determining a value ST₁ of said slave clock time signal when said third time signal is received by said slave clock;

(5) upon receipt of said second and third time signals at said slave clock, determining a ratio k_clkratio of the frequency of the master clock to the frequency of the slave clock according to the relation

space="preserve" listing-type="equation">k.sub.clkratio =(MT.sub.1 -MT.sub.0)/(ST.sub.1 -ST.sub.0); and

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(7) at said slave clock, multiplying the number of increments of said slave clock time signal by k_clkratio to generate a virtual clock time signal having a value which increases with time at the same rate as said master clock time signal.