EP0593243B1 - Improved time scale computation system - Google Patents
Improved time scale computation system Download PDFInfo
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- EP0593243B1 EP0593243B1 EP19930308081 EP93308081A EP0593243B1 EP 0593243 B1 EP0593243 B1 EP 0593243B1 EP 19930308081 EP19930308081 EP 19930308081 EP 93308081 A EP93308081 A EP 93308081A EP 0593243 B1 EP0593243 B1 EP 0593243B1
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- G04—HOROLOGY
- G04G—ELECTRONIC TIME-PIECES
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- an ensemble of atomic clocks be used to keep time for a number of reasons. Typically, no two identical clocks will keep precisely the identical time. This is due to a number of factors, including differing frequencies, noise, frequency aging, etc. Further, such clocks are not 100% reliable; that is, they are subject to failure. Accordingly, by using an ensemble of clocks in combination, a more precise estimate of the time can be maintained.
- an ensemble time system includes a plurality or ensemble of clocks, a mechanism for measuring differences in time related parameters between pairs of clocks, and a device for providing an ensemble time that uses the differences and an ensemble time definition with a constrained number of solutions for the ensemble time.
- An ensemble time system is also provided that provides a substantially unbiased estimate of the state of each clock in the system thereby permiting the system to be adaptive.
- the estimates of the state of each clock is weighted in a fashion that is proportional to the rms noise of the state of the clock.
- the ensemble time (in contrast to the estimates of the states) is also weighted but with a different set of weights than the state estimates, to achieve robustness and other desirable characteristics in the system.
- Figure 1 is a circuit diagram of an implementation of the present invention.
- the novel clock model utilized in the present invention takes into account the time, the frequency, and the frequency aging.
- the general form of the clock model consists of a series of integrations.
- the frequency aging is the integral of white noise, and therefore exhibits a random walk.
- the frequency is the integral of the frequency aging and an added white noise term, allowing for the existence of random walk frequency noise.
- the time is the integral of the frequency and an added white noise term which produces random walk phase noise, usually called white frequency noise.
- An unintegrated additive white noise on the phase state produces additive white phase noise.
- the relative states are the differences between the state vectors of the individual clocks.
- the state vector of a clock i will be referred to as x i . Only the differences between clocks can be measured.
- the differences between a clock j and a clock k at time t is denoted by x jk ( t ) ⁇ x j ( t )- x k ( t )
- the same approach will be used below to denote the time of a clock with respect to an ensemble.
- the ensemble is designated by the subscript e. Since ensemble time is a computed quantity, the ensemble is only realizable in terms of its difference from a physical clock.
- the 4 x 4 dimensional state transition matrix ⁇ ( ⁇ ) embodies the system model described above.
- the state transition matrix is assumed to depend on the length of the interval, but not on the origin, such that
- t) contains the noise input to the system during the interval from t to t+ ⁇ , where and where ⁇ ' jk (t+ ⁇ ) is the white time noise input between clocks j and k at time (t+ ⁇ ), ⁇ ' jk (t+ ⁇
- t) is normally distributed with zero mean and is uncorrelated in time.
- the four-dimensional vector p (t) contains the control input made at time t.
- Equation 2 generates a random walk in the elements of the state vector.
- a single observation z(t) can be described by a measurement equation.
- An observation made at time t is linear-related to the four elements of the state vector (Equation 1) by the 1 x 4 dimensional measurement matrix H(t) and the scalar white noise v(t).
- R (t) E [ v jk ( t ) v jk ( t ) T ]
- E[] is an expectation operator
- v jk (t) T is the transpose of the noise vector.
- ⁇ 2 vxjk is the variance of the phase measurement process.
- t) is the covariance matrix of the system (or plant) noise generated during an interval from t to t+ ⁇ , and is defined by Q jk ( t + ⁇
- t ) E [ s jk ( t + ⁇
- the system covariance matrix can be expressed in terms of the spectral densities of the noises such that where f h is an infinitely sharp high-frequency cutoff. Without this bandwidth limitation, the variance of the white phase additive noise would be infinite.
- Equations 13 - 22 It is this form of the plant covariance (i.e., Equations 13 - 22) which will be used to calculate the plant covariance of the reference clock versus the ensemble.
- clock j one of the clocks in the ensemble is used as a reference and is designated as clock j.
- the choice of clock j as the reference clock is arbitrary and may be changed computationally.
- the role of the reference clock j is to provide initial estimates and to be the physical clock whose differences from the ensemble are calculated.
- each of the other N-1 clocks is used as an aiding source. That is, each of the remaining clocks provides an independent representation of the states of clock j with respect to the ensemble. As indicated, these states are time, frequency, and frequency aging.
- the present invention defines the states of each clock with respect to the ensemble to be the weighted average of these representations, and the present invention provides a user with full control over the weighting scheme.
- time, frequency, and frequency aging of a multiple weight ensemble can be defined as follows: Each new time of a clock j with respect to the ensemble depends only on the prior states of all the clocks with respect to the ensemble and the current clock difference states.
- the ensemble definition uses the forecasts of the true states from time t to t+ ⁇ , that is, x ( t + ⁇
- t ) ⁇ ( t + ⁇
- Equation 23 Prior approaches have frequently used relations superficially similar to that found in Equation 23 to define ensemble time. However, as the present inventor has found, Equation 23 alone does not provide a complete definition of the ensemble time. Since the prior art does not provide a complete definition of the ensemble time, the filters employed in the prior art do not yield the best estimate of ensemble time. The present invention provides a more complete definition of ensemble time based not only on the time equation (Equation 23), but also on the frequency and frequency aging relations (Equations 24 and 25).
- the time-scale is used to correct the time of its individual members.
- t) û e (t
- Equations 23, 24, and 25 are still not a unique definition because the individual clock states are not observable and only clock differences can be measured. Thus, an infinite number of solutions satisfy Equations 23, 24, and 25. For example, if u 1 , u 2 ,..., u n , u e is a solution, then u 1 +p, u 2 +p,..., u n +p, u e +p is also a solution. What the clocks actually did is unknown and difference measurements cannot detect what truly happened. The correction term discussed above is not affected by the ambiguity of the individual clock and time-scale estimates since it involves their differences. However, the ambiguity produces practical problems.
- the covariance matrix elements grow on each cycle of the Kalman recursion since these states are not observable.
- the increasing size of the covariance matrix elements will eventually cause computational problems due to the finite accuracy of double precision math in a computer.
- the mixture of the two components of the covariance matrix elements may also cause problems with algorithms that use the covariance matrix elements to estimate the uncertainty of the state estimates.
- the covariance matrix elements are used in parameter estimation and also to detect outlier observations before they are used in the state estimation process.
- the coefficients a' i , b' i, and c' i are selected so that the noises on the estimated states of each clock are nearly equal to the true noises of that clock for all possible combinations of clocks with different levels of noise.
- the coefficients are proportional to the rms noise on the clock states: When these coefficients are used to scale the noise inputs to the clocks, the scaled noises all have unit variance. The constraint equations say that the sum of the unit variance noise inputs from all the ensemble members is zero. Heuristically, this seems very reasonable.
- the constraining equations result in solutions for the clock states that are centered about zero and is a particular case of the time-scale definition. Using the constraint equations has a beneficial effect on the Kalman filter solution to the estimation problem. They relieve the nonobservability of the problem, and the covariance matrix approaches a finite asymptotic value.
- constraining equations are applicable to ensembles of other types of clocks than high quality atomic clocks. Further, comparable constraining equations can be applied to the ensemble time definition taught in the article by Richard H. Jones and Peter V. Tryon entitled “Estimating Time From Atomic Clocks", Journal of Research of the National Bureau of Standards, Vol. 88, No. 1, pp.17-24, January-February 1983, incorporated herein by reference.
- a i (t), b i (t), and c i (t) represent weights to be chosen for each of the three relations described in Equations 23 through 25 for each of the N clocks in the ensemble.
- the weights may be chosen in any way subject to the restrictions that all of the weights are positive or 0 and the sum of the weights is 1. That is, The weights may be chosen to optimize the performance (e.g., by heavily weighting a higher quality clock relative to the others) and/or to minimize the risk of disturbance due to any single clock failure.
- the present invention provides a time scale algorithm that utilizes more than one weighting factor for each clock. Accordingly, the present invention is actually able to enhance performance at both short and long times even when the ensemble members have wildly different characteristics, such as cesium standards, active hydrogen masers and mercury ion frequency standards.
- time scale A has a sampling interval of ⁇ that is in the region where all the clocks are dominated by short-term noise such as white frequency noise. Further suppose that the clocks have widely varying levels of long-term noise such as random walk frequency. The apportionment of noise and the estimation of frequencies for time scale A is done based on time predictions over the short interval ⁇ where the effects of the long-term noises are visible with a signal-to-noise ratio that is significantly less than 1.
- time scale B has a sampling interval of k ⁇ , where k is large compared to 1, that is in the region where all of the clocks are dominated by the long-term random walk frequency noise.
- the apportionment of noise and the estimation of frequencies for time scale B is done based on the time predictions over the long interval k ⁇ where the effects of the long-term noises are visible with a signal-to-noise ratio that is significantly greater than 1.
- This time scale will have more accurate apportionment of the long-term noises between the clocks because there will be no errors made in the apportionment of the short-term noise (an incorrect fraction of 0 is still 0).
- Time scale A may be phase locked to time scale B to produce a single time scale with more nearly optimal performance over a wider range of sample times than the individual time scales.
- This method may be used to combine as many time scales as necessary.
- Each time scale is phase locked to the time scale with the next largest sampling interval.
- the time scale with the longest sampling interval is allowed to free run.
- a second order phase lock loop should be used to combine two time scales. This type of loop results in zero average closed loop time error between two time scales no matter how large the open loop frequency differences between the two scales.
- Equation 29 represents the additive white phase noise
- Equation 30 represents the random walk phase
- Equation 31 represents the random walk frequency
- Equation 32 represents the random walk frequency aging.
- This version of the ensemble definition is in the form required for the application Kalman filter techniques.
- the advantage of the Kalman approach is the inclusion of the system dynamics, which makes it possible to include a high degree of robustness and automation in the algorithm.
- Kalman Method 1 In order to apply Kalman filters to the problem of estimating the states of a clock obeying the state equations provided above, it is necessary to describe the observations in the form of Equation 6. This is accomplished by a transformation of coordinates on the raw clock time difference measurements or clock frequency difference measurements. Since z may denote either a time or a frequency observation, a pseudomeasurement may be defined such that This operation translates the actual measurements by a calculable amount that depends on the past ensemble state estimates and the control inputs.
- the error in the estimate of the state vector after the measurement at time t 1 is x (t 1
- K opt The desired or Kalman gain, K opt , is determined by minimizing the square of the length of the error vector, that is, the sum of the diagonal elements (i.e., the trace) of the error covariance matrix, such that Finally, the updated error covariance matrix is given by where I is the identity matrix.
- Equations 40 - 43 define the Kalman filter.
- the Kalman filter is an optimal estimator in the minimum squared error sense.
- Each application of the Kalman recursion yields an estimate of the state of the system, which is a function of the elapsed time since the last filter update. Updates may occur at any time. In the absence of observations, the updates are called forecasts.
- Equations 40 - 43 As will be appreciated by those skilled in the art, implementation of the relationships defined in Equations 40 - 43 as a Kalman filter is a matter of carrying out known techniques.
- the first step is the selection of a reference clock for this purpose.
- the reference clock referred to herein is distinguished from a hardware reference clock, which is normally used as the initial calculation reference. However, this "software" reference clock normally changes each time the ensemble is calculated for accuracy.
- the plant covariance matrix may be calculated. There are ten independent elements, seven of which are nonzero. These ten elements, which correspond with Equations 13 - 22, are as follows:
- the initial state estimate at time t 2 is a forecast via the reference clock r.
- the initial covariance matrix is the covariance before measurement.
- the data from all the remaining clocks are used to provide N-1 updates.
- the pseudomeasurements are processed in order of increasing difference from the current estimate of the time of the reference clock r with respect to the ensemble. Pseudomeasurement I(k) is the "k"th pseudomeasurement processed and I(1) is the reference clock forecast.
- Outliers i.e., data outside an anticipated data range
- ⁇ k / re (t 2 ) the innovation or difference between the pseudomeasurment and the forecast, such that This equation can be rearranged in the form After squaring and taking the expectation value, the result is
- the estimates of the clocks relative to reference clock r are obtained from N-1 independent Kalman filters of the type described above.
- the four dimensional state vectors are for the clock states relative to the reference clock r Every clock pair has the same state transition matrix and ⁇ matrix, which are provided for above in Equations 3 and 5.
- the system covariance matrices are Q ir (t+ ⁇
- Equation 41 is one of the equations which define the Kalman filter. No attempt is made to independently detect outliers. Instead, the deweighting factors determined in the reference clock versus ensemble calculation are applied to the Kalman gains in the clock difference filters.
- the state estimates for the clocks with respect to the ensemble are calculated from the previously estimated states of the reference clock r with respect to the ensemble and the clock difference states, such that x je ( t 2
- t 2 ) x re ( t 2
- Kalman Filter Method 2 The ensemble definition can be implemented using the Kalman filter method by combining the states of all the clocks into a single state vector which also explicitly contains the states of the time-scale.
- the state transition matrix, ⁇ depends on the length of the interval, but not on the origin.
- Equation 3 N + 1 identical 4 + 4 submatrices, ⁇ , arranged on the diagonal of a 4(N + 1) dimensional matrix that has zeros in all other positions.
- ⁇ is state transition matrix for an individual clock (or clock pair) given in Equation 3.
- t) contains the noise inputs to the system during the interval from t to t + ⁇ .
- t) is normally distributed with zero mean and is uncorrelated in time.
- the 4(N + 1) dimensional vector p (t) contains the control inputs made at time t. Equation 64-2 generates a random walk in the elements of the state vector.
- phase measurements of clocks 2 and 3 relative to clock 1 in a three clock ensemble are described by: If the measurements are made simultaneously by a dual mixer measurement system the measurement covariance matrix is: where ⁇ 2 v x is the variance of the phase measurement process. Similarly, the frequency measurements are described by:
- the system (or plant) covariance matrix is defined as follows Q ( t + ⁇
- t ) E [ s ( t + ⁇
- Kalman recursion described here is the discrete Kalman filter documented in "Applied Optimal Estimation", A. Gelb, ed., MIT Press, Cambridge, 1974. His derivation assumes that the perturbing noises are white and are normally distributed with mean zero. He further assumes that the measurement noise and the process noise are uncorrelated.
- the error in the estimate of the state vector after the measurement at time t 1 is x (t 1
- the diagonal elements of this n x n matrix are the variances of the error in the estimates of the components of x (t 1 ) after the measurement at time t 1 .
- the error covariance matrix just prior to the measurement at time t 2 is defined as The error covariance matrix evolves according to the system model.
- the ensemble definition is used to generate those plant covariance matrix elements that involve ensemble states. It should also be used to connect the individual clock states to the ensemble states. This may be accomplished in an approximate manner by implementing three pseudomeasurements. We rearrange the ensemble definition and replace the forecasts based on the true states by the forecasts based on the prior estimates to obtain The measurements on the left side of these equations are described in the H by adding three additional rows.
- the constraint equations may also be implemented using pseudomeasurements. This is particularly simple when the coefficients of the constraint equations are the weights.
- Outliers are detected using the method developed by Jones et al., "Estimating Time From Atomic Clocks", NBS Journal of Research, Vol. 80, pp. 17-24, January-February 1983, and are deweighted following the recommendation of Percival, "Use of Robust Statistical Techniques in Time Scale Formation", 2nd Symposium on Atomic Time Scale Algorithms, June, 1982.
- Outliers are not detected by dividing each element of the innovation vector by the corresponding element of the covariance matrix since clock differences are being measured and the elements of the innovation vector are correlated.
- a constant bias will occur in all of the measurements.
- there is an error in any other clock the error will occur in only those measurements involving that clock (usually one).
- clock j changes time by an amount f j
- the error vector, g has covariance matrix C .
- the column vector, g j has all ones when clock j is the reference clock.
- g j has zeros for measurements that don't involve that clock and minus one for any measurement that does.
- Deweighting of erroneous measurements, rather than rejection, of the outlier data is used to enhance the robustness of the state estimation process. Deweighting preserves the continuity of the state estimates. On the other hand, rejecting outliers results in discontinuous state estimates that can destabilize the time-scale computation by causing the rejection of all members of the time-scale.
- the first step in the outlier deweighting process is to find a good reference clock. Once this is accomplished, all the measurements are processed and deweighting factors are computed for the remaining clocks as necessary.
- the outlier detection algorithm of the ensemble calculation identifies the measurements which are unlikely to have originated from one of the processes included in the model. These measurements are candidate time steps.
- the immediate response to a detected outlier in the primary ensemble Kalman filter is to reduce the Kalman gain toward zero so that the measurement does not unduly influence the state estimates.
- the occurrence of M 1 successive outliers is interpreted to be a time step.
- the time state of the clock that experienced the time step is reset to agree with the last measurement and all other processing continues unmodified. If time steps continue until M 2 successive outliers have occurred, as might happen after an extremely large frequency step, then the clock should be reinitialized. The procedure for frequency steps should be used to reinitialize the clock.
- the clock weights are positive, semidefinite, and sum to one, without any other restriction. It is possible to calculate a set of weights which minimizes the total noise variance of the ensemble.
- the variance of the noise in the ensemble states is calculated. This is represented by the following equations:
- the situation can be improved by changing the weights associated with the time state and keeping the frequency and frequency aging weights.
- the weights are used with the optimum b and c weights.
- This weighting scheme produces optimum long-term performance and slightly suboptimum short-term performance in some circumstances, but is much superior to the time-scale noise minimizing weights when the clocks have very dissimilar performances.
- the weights of Equation 71-1 are strictly optimum when the clocks have equal performance.
- the clock weights are chosen in advance of the calculation. However, if there is one or more outliers, the selected weights are modified by the outlier rejection process.
- the actual weights used can be calculated from where K' I(1) is defined as 1 and the indexing scheme is as previously described. To preserve the reliability of the ensemble, one usually limits the weights of each of the clocks to some maximum value a max . Thus, it may be necessary to readjust the initial weight assignments to achieve the limitation or other requirements. If too few clocks are available, it may not be possible to satisfy operational requirements. Under these conditions, it may be possible to choose not to compute the ensemble time until the requirements can be met. However, if the time must be used, it is always better to compute the ensemble than to use a single member clock.
- Another problem to be considered in the Kalman approach is the estimation of the parameters required by a Kalman filter.
- the techniques that are normally applied are Allan variance analysis and maximum likelihood analysis.
- the Allan variance is defined for equally spaced data. In an operational scenario, where there are occasional missing data, the gaps may be bridged. But when data are irregularly spaced, a more powerful approach is required.
- the maximum likelihood approach determines the parameter set most likely to have resulted in the observations. Equally spaced data are not required, but the data are batch processed. Furthermore, each step of the search for the maximum requires a complete recomputation of the Kalman filter, which results in an extremely time consuming procedure. Both the memory needs and computation time are incompatible with real time or embedded applications.
- a variance analysis technique compatible with irregular observations has been developed.
- the variance of the innovation sequence of the Kalman filter is analyzed to provide estimates of the parameters of the filter.
- the innovation analysis requires only a limited memory of past data.
- the forecast produced by the Kalman filter allows the computation to be performed at arbitrary intervals once the algebraic form of the innovation variance has been calculated.
- the innovation sequence has been used to provide real time parameter estimates for Kalman filters with equal sampling intervals.
- the conditions for estimating all the parameters of the filter include (1) the system must be observable, (2) the system must be invariant, (3) number of unknown parameters in Q (the system covariance) must be less than the product of the dimension of the state vector and the dimension of the measurement vector, and (4) the filter must be in steady state.
- This approach was developed for discrete Kalman filters with equal sampling intervals, and without modification, cannot be used for mixed mode filters because of the irregular sampling which prevents the system from ever reaching steady state.
- the first method uses clock time difference estimates, while the second method uses the estimates of the clocks with respect to the ensemble.
- Adaptive modeling begins with an approximate Kalman filter gain K.
- K the variance of the innovations on the left side of Equation 74 is also computed.
- the right side of this equation is written in terms of the actual filter element values (covariance matrix elements) and the theoretical parameters. Finally, the equations are inverted to produce improved estimates for the parameters.
- the method of solving the parameters for discrete Kalman filters with equal sampling intervals is inappropriate here because the autocovariance function is highly correlated from one lag to the next and the efficiency of data utilization is therefore small. Instead, only the autocovariance of the innovations for zero lags, i.e., the covariance of the innovations, is used.
- E [ ⁇ ij ( t + ⁇ ) ⁇ ij ( t + ⁇ ) T ] P ij 00 ( t
- t )+ S ij ⁇ ( t ) ⁇ + S ij ⁇ ( t ) ⁇ 3 3 + S ij ⁇ ( t ) ⁇ 5 20 + ⁇ 2 vij ( t )+ S ij ⁇ h for the case of a time measurement, and E [ ⁇ ij ( t + ⁇ ) ⁇ ij ( t + ⁇ ) T ] P ij 22 ( t
- Equation 75 It is assumed the oscillator model contains no hidden noise processes. This means that each noise in the model is dominant over some region of the Fourier frequency space. The principal of parsimony encourages this approach to modeling. Inspection of Equation 75 leads to the conclusion that each of the parameters dominates the variance of the innovations in a unique region of prediction time interval, ⁇ , making it possible to obtain high quality estimates for each of the parameters through a bootstrapping process. It should be noted that the white phase measurement noise can be separated from the clock noise only by making an independent assessment of the measurement system noise floor.
- a Kalman filter For each parameter to be estimated, a Kalman filter is computed using a subset of the data chosen to maximize the number of predictions in the interval for which that parameter makes the dominant contribution to the innovations.
- the filters are designated 0 through 4, starting with zero for the main state estimation filter, which runs as often as possible.
- Each innovation is used to compute a single-point estimate of the variance of the innovations for the corresponding ⁇ .
- Equation 75 is solved for the dominant parameter, and the estimate of that parameter is updated in an exponential filter of the appropriate length, for example, ⁇ 2 vij ( t + ⁇ )+ S ij ⁇ ( t + ⁇ ) h ⁇ ⁇ ij ( t + ⁇ ) ⁇ ij ( t + ⁇ ) T - P ij 00 ( t
- a Kalman filter can be used to obtain an optimum estimate for all F i , given all possible measurements F ij .
- the F i for a given noise type are formed into an N dimensional vector
- the state transition matrix is just the N dimensional identity matrix.
- the noise vector is chosen to be nonzero in order to allow the estimates to change slowly with time. This does not mean that the clock noises actually experience random walk behavior, only that this is the simplest model that does not permanently lock in fixed values for the noises.
- the variances of the noises perturbing the clock parameters can be chosen based on the desired time constant of the Kalman filter.
- the Kalman gain is approximately ⁇ F / ⁇ meas .
- the parameter value will refresh every M measurements when its variance is set to 1/M 2 of the variance of the single measurement estimate of the parameter.
- a reasonable value for the variance of a single measurement is ⁇ 2 meas being approximately equal to 2F i .
- N element state vectors There are five N element state vectors, one for each of the possible noise types (white phase noise, white frequency noise, white frequency measurement noise, random walk frequency noise, and random walk frequency noise aging). There are also five N x N covariance matrixes. A total of 5N(N-1)/2 cycles of the Kalman recursion are currently believed necessary for the parameter update.
- Parameter Estimation Method 2 A variance analysis technique compatible with irregular observations has been developed. The variance of the innovation sequence of the time-scale calculation is analyzed to provide estimates of the parameters of the filter. Like the Allan variance analysis, which is performed on unprocessed measurements, the innovation analysis requires only limited memory of past data. However, the forecasts allow the computation to be performed at arbitrary intervals once the algebraic form of the innovation variance has been calculated.
- Each cycle of the filter is used to compute a primitive estimate of the variance of the innovations, where the innovation is a scalar equal to û j (t + ⁇
- Equation 64-37 the white phase measurement noise can be separated from the clock noise only by making an independent assessment of the measurement system noise floor.
- a Kalman filter is computed using a subset of the data chosen to maximize the number of predictions in the interval for which that parameter makes the dominant contribution to the innovations.
- Five filters should be sufficient to estimate parameters in a time-scale of standard and high performance cesium clocks, active hydrogen masers, and mercury ion frequency standards. The filter are designated 1 through 5, starting with 1 for the main state estimation filter.
- Each innovation is used to compute a single-point estimate of the variance of the innovations for the corresponding ⁇ .
- Substituting the estimated values of the remaining parameters, Eq. 24 is solved for the dominant parameter, and the estimate of that parameter is updated in an exponential filter of the appropriate length. If the minimum sampling interval is too long, it may not be possible to estimate one or more of the parameters.
- FILTER 2 Runs at a nominal sampling rate of 3 hours. This sampling rate is appropriate for estimating the white frequency noise of all the clocks including the mercury ion devices.
- To determine whether the white frequency noise may be estimated for a given clock verify that S and ⁇ 'h ⁇ S and ⁇ ⁇ and S and ⁇ ⁇ > S and ⁇ 3 /3. Frequency steps may be detected.
- FILTER 3 Runs at a nominal sampling rate of 1 day. This sampling rate is appropriate for estimating the random walk frequency noise for active hydrogen masers.
- Figure 1 illustrates a circuit for obtaining a computation of ensemble time from an ensemble of clocks 10.
- the ensemble 10 includes N clocks 12.
- the clocks 12 can be any combination of clocks suitable for use with precision time measurement systems. Such clocks may include, but are not limited to cesium clocks, rubidium clocks, hydrogen maser clocks and quartz crystal oscillators. Additionally, there is no limit on the number of clocks.
- Each of the N clocks 12 produces a respective signal ⁇ 1 , ⁇ 2 , ⁇ 3 ,..., ⁇ N which is representative of its respective frequency output.
- the respective frequency signals are passed through a passive power divider circuit 14 to make them available for use by a time measurement system 16, which obtains the time differences between designated ones of the clocks 12.
- the desired time differences are the differences between the one of the clocks 12 designated as a hardware reference clock and the remaining clocks 12.
- the clock 12 which acts as the reference clock can be advantageously changed as desired by an operator.
- clock 12 designated “clock 1" is chosen to be the reference clock
- the time measurement system 16 determines the differences between the reference clock and the remaining clocks, which are represented by z 12 , z 13 , z 14 ,... z 1N .
- These data are input to a computer 18 for processing in accordance with the features of the present invention as described above, namely, the complete ensemble definition as provided above.
- the ensemble definition as provided by Equations 23 - 25 is provided for in Kalman filters, and since the Kalman filters are software-implemented, the Kalman filters can be stored in memory 20.
- the computer 18 accesses the memory 20 for the necessary filters as required by the system programming in order to carry out the time scale computation.
- the weights and other required outside data are input by operator through a terminal 22.
- an estimate of the ensemble time is output from the computer 20 to be manipulated in accordance with the requirements of the user.
- Kalman filters have been previously used in connection with ensembles to obtain ensemble time estimates. These Kalman filters embodied the previous incomplete ensemble definitions in Kalman form for the appropriate processing. Accordingly, it will be appreciated by those skilled in the art that the actual implementation of the Kalman equations into a time measurement system as described above and the appropriate programming for the system are procedures known in the art. As also should be appreciated, by providing a complete definition of the ensemble, the present system generally provides a superior calculation of the ensemble time with respect to prior art.
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Description
If the test statistic,
FILTER 1 Runs at a nominal sampling rate of 300 seconds. Such fast data acquisition is important for real-time control. It is also fast enough to permit the estimation of the white phase noise for active hydrogen masers. The source of this noise is the measurement system. The same level of white phase noise should be assigned to all time measurement channels. No other parameters should be estimated using this filter. To determine whether the white phase noise may be measured for a given clock, verify that S andβ'h > S andξδ.
FILTER 2 Runs at a nominal sampling rate of 3 hours. This sampling rate is appropriate for estimating the white frequency noise of all the clocks including the mercury ion devices. To determine whether the white frequency noise may be estimated for a given clock, verify that S andβ'h < S andξδ and S andξδ > S andµδ3/3. Frequency steps may be detected.
FILTER 3 Runs at a nominal sampling rate of 1 day. This sampling rate is appropriate for estimating the random walk frequency noise for active hydrogen masers. To determine whether the random walk frequency noise may be estimated for a given clock, verify that S andξδ < S andµδ3/3 and S andµδ3/3 > S andζδ5/20. Frequency steps may be detected.
FILTER 4 Runs at a nominal sampling rate of 4 days. To determine whether the random walk frequency noise may be estimated for a given clock, verify that S andξδ < S andµδ3/3 and S andµδ3/3 > S andζδ5/20. Frequency steps may be detected.
FILTER 5 Runs at a nominal sampling rate of 16 days. To determine whether the random walk frequency noise may be estimated for a given clock, verify that S andξδ < S andµδ3 and S andµδ3/3 > S andζδ5/20. Frequency steps may be detected.
Claims (8)
- A system for providing an ensemble time comprising:
a plurality of clocks, each of said plurality of clocks providing a clock signal;
first means for measuring differences between clock signal related parameters for pairs of clocks of said plurality of clocks; and
second means, which uses said differences, for providing a first ensemble time characterized in that, said second means includes means for implementing an ensemble time definition that has a plurality of solutions which are representative of an ensemble time and means for constraining said plurality of solutions to a number of solutions that is less than said first plurality of solutions. - A system, as claimed in Claim 1, wherein:
said second means includes means for providing an estimate of the state of each clock of said plurality of clocks and means for causing the variance of the estimate of the state of each clock of said plurality of clocks to be substantially equal to the true variance of the time states. - A system, as claimed in Claim 1, wherein:
said second means includes means for providing an estimate of the state of each clock of said plurality of clocks and means for weighting the estimate of the state of each clock of said plurality of clocks that is proportional to the rms noise of the state of each said clock. - A system, as claimed in Claim 1, wherein:
said second means includes means for providing an estimate of the state of each clock of said plurality of clocks, means for weighting the estimates of the state of each clock of said plurality of clocks to obtain better estimates of the true states of said plurality of clocks, said means for weighting includes a first set of weights, and said means for constraining includes a second set of weights that is different than said first set of weights to improve robustness of said first ensemble time. - A system, as claimed in Claim 1, wherein:
said second means includes means for providing a substantially unbiased estimate of the spectral density of each clock of said plurality of clocks. - A system, as claimed in Claim 1, wherein:
said first ensemble time has a first sampling interval and substantially optimal performance over a first range of sampling intervals;
said second means includes means for providing a second ensemble time has a second sampling interval that is different than said first sampling interval and substantially optimal performance over a second range of sampling intervals and means for combining said first ensemble time and said second ensemble time to provide a third ensemble time that has substantially optimal over a third range of sampling intervals that is greater than said first and second sampling intervals. - A system, as claimed in Claim 6, wherein:
said means for combining includes means for phase-locking said first ensemble time and said second ensemble time. - A system, as claimed in Claim 6, wherein:
said means for combining includes a second-order phase-locked loop for use in combining said first ensemble time and said second ensemble time.
Applications Claiming Priority (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US95941892A | 1992-10-13 | 1992-10-13 | |
US959418 | 1992-10-13 | ||
US08/080,970 US5315566A (en) | 1993-06-22 | 1993-06-22 | Time scale computation system |
US80970 | 2002-02-22 |
Publications (3)
Publication Number | Publication Date |
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EP0593243A2 EP0593243A2 (en) | 1994-04-20 |
EP0593243A3 EP0593243A3 (en) | 1996-01-31 |
EP0593243B1 true EP0593243B1 (en) | 1998-07-08 |
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EP19930308081 Expired - Lifetime EP0593243B1 (en) | 1992-10-13 | 1993-10-11 | Improved time scale computation system |
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EP (1) | EP0593243B1 (en) |
DE (1) | DE69319534D1 (en) |
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CN111641471B (en) * | 2020-05-28 | 2022-11-04 | 中国计量科学研究院 | Weight design method for prediction in atomic clock signal combination control |
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US5155695A (en) * | 1990-06-15 | 1992-10-13 | Timing Solutions Corporation | Time scale computation system including complete and weighted ensemble definition |
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- 1993-10-11 EP EP19930308081 patent/EP0593243B1/en not_active Expired - Lifetime
- 1993-10-11 DE DE69319534T patent/DE69319534D1/en not_active Expired - Lifetime
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Publication number | Publication date |
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EP0593243A3 (en) | 1996-01-31 |
EP0593243A2 (en) | 1994-04-20 |
DE69319534D1 (en) | 1998-08-13 |
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