Controlling oscillators
This disclosure relates to controlling an oscillator based on a measurement of a frequency reference. A controller determines a control value to control the oscillator based on multiple error values. Each error value is indicative of a measurement of a frequency difference between the oscillator and a frequency reference over a period of time. The determination of the error value is further based on an application time value indicative of a time of application of the control value to the oscillator. Since the control value is based on the application time the controller can compensate for inaccuracies arising from both evolution of the oscillator between measurements and applying the correction at a later time after the measurement. Further, since the multiple error values represent a frequency difference over different periods of time, the controller can compensate for wide range of statistical effects.
1. A computer implemented method for controlling an oscillator, the method comprising:
determining a first statistical correlation between multiple error values, each error value being indicative of a measurement of a frequency difference between the oscillator and a frequency reference over a period of time, and
determining a control value to control the oscillator by maximising a second statistical correlation between a frequency difference at a time of application of the control value to the oscillator and a correction caused by the application of the control value, the frequency difference being a statistical variable estimated based on the first statistical correlation and an application time value indicative of the time of application of the control value to the oscillator.
2. The method of claim 1 , wherein
each of the multiple error values is associated with a measurement time value indicative of a time of the measurement of the frequency difference, and
determining the control value comprises determining the control value based on the measurement time value associated with each of the multiple error values.
3. The method of claim 1 , wherein determining the control value comprises determining the control value based on noise data indicative of statistical noise characteristics of the oscillator.
4. The method of claim 3 , wherein the noise data is indicative of a noise power spectrum.
5. The method of claim 1 , wherein determining the control value comprises:
determining multiple weighting coefficients for the multiple error values based on the multiple error values; and
determining the control value to control the oscillator based on the multiple error values modified according to the multiple weighting coefficients.
6. The method of claim 5 , wherein determining the control value comprises determining a linear combination of the multiple error values weighted by the multiple weighting coefficients.
7. The method of claim 1 , wherein
each of the multiple error values is associated with a measurement duration value indicative of a duration of the measurement of the frequency difference, and
determining the control value comprises determining the control value based on the measurement duration value associated with each of the multiple error values.
8. The method of claim 6 , wherein
the multiple error values comprise a first error value associated with a first measurement duration value indicative of a first duration of a first measurement of the frequency difference and a second error value associated with a second measurement duration value indicative of a second duration of a second measurement of the frequency difference,
the first duration of the first measurement is relatively long to sample low frequency noise of the oscillator, and
the second duration of the second measurement is relatively short to sample high frequency noise of the oscillator.
9. The method of claim 7 , wherein the duration of the measurement is defined between two exposure periods of the frequency reference to the frequency of the oscillator such that each of the multiple error values is indicative of an accumulated phase difference between the oscillator and the frequency reference.
10. The method of claim 7 , further comprising performing an optimisation to determine the multiple duration values for obtaining the multiple error values.
11. The method of claim 1 , wherein determining the control value comprises determining the control value based on a transfer function indicative of an influence of fluctuations of the oscillator on the multiple error values.
12. The method of claim 11 , further comprising determining a covariance matrix based on the transfer function wherein determining the control value comprises determining the control value based on the covariance matrix.
13. A non-transitory computer readable medium with an executable program stored thereon that when executed causes the computer to perform the method of claim 1 .
14. A computer system for controlling an oscillator, the computer system comprising:
an input port to receive multiple error values, each error value being indicative of a measurement of a frequency difference between the oscillator and a frequency reference over a period of time; and
a processor
to determine a first statistical correlation between the multiple error values; and
to determine a control value to control the oscillator by maximising a second statistical correlation between a frequency difference at the time of application of the control value to the oscillator and a correction caused by the application of the control value, the frequency difference being a statistical variable estimated based on the first statistical correlation and an application time value indicative of the time of application of the control value to the oscillator.
15. A method for generating a clock signal, the method comprising:
generating the clock signal based on oscillations of an oscillator;
performing multiple measurements of a frequency difference between the oscillator and a frequency reference over a period of time;
determining multiple error values such that each error value is indicative of one of the multiple measurements;
determining a first statistical correlation between the multiple error values;
determining a control value to control the oscillator by maximising a second statistical correlation between a frequency difference at a time of application of the control value to the oscillator and a correction caused by the application of the control value, the frequency difference being a statistical variable estimated based on the first statistical correlation and an application time value indicative of the time of application of the control value to the oscillator; and
applying the control value to the oscillator at the time of application.
16. The method of claim 15 , wherein measuring the frequency difference comprises measuring an accumulated phase difference.
17. A clock comprising:
an oscillator and a detector to generate a clock signal based on oscillations of the oscillator;
a frequency reference;
a measurement system
to perform multiple measurements of a frequency difference between the oscillator and the frequency reference over a period of time; and
a processor
to determine multiple error values such that each error value is indicative of one of the multiple measurements;
to determine a first statistical correlation between the multiple error values;
to determine a control value to control the oscillator by maximising a second statistical correlation between a frequency difference at a time of application of the control value to the oscillator and a correction caused by the application of the control value, the frequency difference being a statistical variable estimated based on the first statistical correlation and an application time value indicative of the time of application of the control value to the oscillator; and
to apply the control value to the oscillator at the time of application.
18. The clock of claim 17 , wherein the frequency reference is an atomic frequency reference.