CN110554597A - hydrogen cesium time scale fusion method based on Vondark-Cepek filtering - Google Patents
hydrogen cesium time scale fusion method based on Vondark-Cepek filtering Download PDFInfo
- Publication number
- CN110554597A CN110554597A CN201910787030.4A CN201910787030A CN110554597A CN 110554597 A CN110554597 A CN 110554597A CN 201910787030 A CN201910787030 A CN 201910787030A CN 110554597 A CN110554597 A CN 110554597A
- Authority
- CN
- China
- Prior art keywords
- clock
- time scale
- cesium
- hydrogen
- time
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Granted
Links
- 229910052792 caesium Inorganic materials 0.000 title claims abstract description 73
- TVFDJXOCXUVLDH-UHFFFAOYSA-N caesium atom Chemical compound [Cs] TVFDJXOCXUVLDH-UHFFFAOYSA-N 0.000 title claims abstract description 72
- 229910052739 hydrogen Inorganic materials 0.000 title claims abstract description 71
- 239000001257 hydrogen Substances 0.000 title claims abstract description 71
- 238000001914 filtration Methods 0.000 title claims abstract description 26
- 238000007500 overflow downdraw method Methods 0.000 title claims abstract description 12
- 125000004435 hydrogen atom Chemical class [H]* 0.000 title 1
- UFHFLCQGNIYNRP-UHFFFAOYSA-N Hydrogen Chemical compound [H][H] UFHFLCQGNIYNRP-UHFFFAOYSA-N 0.000 claims abstract description 50
- 230000004927 fusion Effects 0.000 claims abstract description 25
- 238000000034 method Methods 0.000 claims abstract description 23
- 150000002431 hydrogen Chemical class 0.000 claims abstract description 20
- 230000007774 longterm Effects 0.000 claims abstract description 9
- 238000009499 grossing Methods 0.000 claims description 19
- 238000004364 calculation method Methods 0.000 claims description 13
- 238000005259 measurement Methods 0.000 claims description 6
- 230000002159 abnormal effect Effects 0.000 claims description 4
- 238000007781 pre-processing Methods 0.000 claims description 4
- 238000010183 spectrum analysis Methods 0.000 claims description 4
- 238000012937 correction Methods 0.000 claims description 3
- -1 cesium hydride Chemical compound 0.000 claims 1
- 230000002401 inhibitory effect Effects 0.000 abstract description 2
- 238000004422 calculation algorithm Methods 0.000 description 4
- 239000011159 matrix material Substances 0.000 description 3
- 238000011160 research Methods 0.000 description 3
- 238000010586 diagram Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012935 Averaging Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- MRMBZHPJVKCOMA-YJFSRANCSA-N biapenem Chemical compound C1N2C=NC=[N+]2CC1SC([C@@H]1C)=C(C([O-])=O)N2[C@H]1[C@@H]([C@H](O)C)C2=O MRMBZHPJVKCOMA-YJFSRANCSA-N 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000000354 decomposition reaction Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000007123 defense Effects 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000012886 linear function Methods 0.000 description 1
- 238000012067 mathematical method Methods 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000012887 quadratic function Methods 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G04—HOROLOGY
- G04F—TIME-INTERVAL MEASURING
- G04F5/00—Apparatus for producing preselected time intervals for use as timing standards
- G04F5/14—Apparatus for producing preselected time intervals for use as timing standards using atomic clocks
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
- Stabilization Of Oscillater, Synchronisation, Frequency Synthesizers (AREA)
Abstract
the invention provides a hydrogen cesium time scale fusion method based on Vondark-Cepek filtering, which comprises the steps of firstly, respectively generating a clock group time scale for a hydrogen clock group and a cesium clock group by using an exponential filtering method, then selecting key parameters of Vondark-Cepek combined filtering according to the principle of least square, and further performing performance enhancement on the cesium clock group time scale through differential information of a hydrogen clock group time scale time sequence so as to obtain the hydrogen cesium fusion time scale. The invention can give consideration to the characteristics of two types of hydrogen and cesium atomic clocks while effectively inhibiting noise, and can be fused on the scale of a clock group to generate a time scale with good long-term and short-term stability.
Description
Technical Field
The invention belongs to the field of time frequency and signal processing, and relates to a time scale fusion method.
background
At present, high-precision time becomes a vital parameter in national science and technology, economy, military and social life, is widely applied to the fields of navigation, electric power, communication, aviation, national defense and the like, and has a fundamental effect on improving the national scientific research level as the most basic physical quantity. For this reason, each time frequency laboratory in the world has its own set of atomic clocks, each of which can produce a time scale. But timekeeping cannot rely on only a single atomic clock because each physical device may have an exception. The time scale algorithm is to calculate a standard time according to the time of each clock of the time keeping clock group, and aims to find a mode to minimize the uncertainty and maximize the stability of the algorithm.
The hydrogen cesium atomic clock is two atomic frequency standards with different types, and the hydrogen cesium atomic clock has good short-term stability and long-term stability respectively, and is two punctual atomic clocks which are most common in laboratories at various times around the world currently. The fusion method of hydrogen cesium time scale mainly researches effective combination of two different atomic clocks to generate more stable and accurate time scale. A time laboratory emphasizes the stability of the time scale.
At present, many time-keeping laboratories adopt a mode of hydrogen and cesium for mutual reference to perform fusion of time scales of two different types of atomic clocks: respectively taking the time of a hydrogen clock, a cesium clock or a cesium clock group as a reference, performing clock error measurement on another atomic clock to form a time sequence, correcting the short-term fluctuation of the cesium clock in the cesium clock group or subtracting the speed and frequency drift of the hydrogen clock, and then obtaining a final time scale by weighted averaging. In the above research method, a single clock of another atomic clock is evaluated and corrected mainly based on hydrogen or cesium, and then all clocks in the time keeping clock group are weighted and averaged together to calculate the final time scale. The method has the following disadvantages: when the hydrogen atomic clock is used as a reference to measure the cesium atomic clock, the main noise is phase white noise, and after the phase white noise is filtered by a mathematical method, the short-term stability of the time scale of the phase white noise is still influenced by the noise of the cesium atomic clock. And the hydrogen clock is corrected by the time scale of the cesium clock group, and when the hydrogen clock fails, the reliability of the generated time scale cannot be guaranteed.
Disclosure of Invention
in order to overcome the defects of the prior art, the invention provides a hydrogen cesium time scale fusion method based on Vondark-Cepek filtering, which can give consideration to the characteristics of two types of atomic clocks of hydrogen cesium while effectively inhibiting noise, and can be used for fusion in a clock group scale level to generate a time scale with good long-term and short-term stability.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1, grouping cesium atomic clocks and hydrogen atomic clocks, and generating time scale TA of an exponential filtering cesium clock group through clock error prediction, frequency estimation and weight estimation steps respectivelyCsand hydrogen time scale TAH；
Step 2: carrying out primary difference on the hydrogen clock group time scale sequence to obtain corresponding frequency data;
Step 3, Fourier transform is carried out on the time scale sequence of the cesium clock set to convert the time scale sequence into a frequency domain, and a signal f or a period P to be suppressed is determined through spectrum analysis; calculating a time scale smoothing factor of the cesium clock group according to the least square theoryAnd hydrogen clock group time scale smoothing factorWherein T and T' are each TACsAnd TAHA corresponding frequency response;
and 4, taking the cesium clock group time scale and the hydrogen clock group frequency sequence as input, using the smoothing factor in a Vondark-Cepek combined filtering method, generating a time scale fusion result, and realizing the fusion of the cesium clock group time scale and the hydrogen clock group time scale.
The method comprises the following steps that 1, atomic clock difference data measured in a laboratory are preprocessed, atomic clocks with the best long-term and short-term stability in a cesium atomic clock group and a hydrogen atomic clock group are respectively selected as reference clocks, and clock difference data of other atomic clocks in the same clock group and the reference clocks are measured by using a time interval counter.
Removing abnormal points from the clock error data obtained by preprocessing by adopting a 3 sigma rule, detecting the continuity of the clock error data, and repairing a clock error sequence with continuous missing data less than 5 measurement periods by adopting an interpolation method; and if the clock error data are continuously missing for more than 5 measurement periods, the clock is removed from the clock group.
In the step 1, if the weight of each atomic clock is greater than the set maximum weight upper limit, the weight of the atomic clock is set as the maximum weight; h 'is'i(t) is the atomic clock H at time tiTime correction quantity is weight, atomic clock data, h'i(t) by the formulaCalculation of where xij(t) is an atomic clock HjAnd atomic clock HiThe clock difference at time t, N being the number of atomic clocks involved, xi(t) is the difference between the mean time scales of the laboratory atomic clock and the laboratory atomic clock set, wiis the weight of each atomic clock.
In the step 1, the maximum weight is set to be 2.5/N.
In the step 4, a time scale TA of the cesium clock group is definedCsData is m (t)i) Is a time tiI-1, 2,3, … at tiThe derivative of time m' (t) ═ m (t)i+1)-m(ti)]/(ti+1-ti) (ii) a Definition of M (t)j) Is the hydrogen clock time scale (TA)H) The derivative M' (t) thereof is [ M (t) ]j+1)-M(tj)]/(tj+1-tj) Wherein j is 1,2,3, …; when t isi＝tjWhen M ' (t) is M ' (t), M (MJD2) is M (MJD1) + M ' (t)j)ΔtjMJD denotes reduced julian days; suppose input observation sequence 1 is represented as y'jCorresponding time scale is xjWeight p ofj(ii) a First derivative of observation sequence 2 is expressed asCorresponding time scale isThe weight isThe output sequence is then the smooth curve y to be obtainediCorresponding time scale is xiDefining the smoothness of the curveIn the formula,Is unknown, based on the smoothed data, on its third derivativeCarrying out estimation; at two points [ x ]i+1,yi+1]and [ x ]i+2,yi+2]the smooth curve between is defined as a lagrange polynomial of third order derived from four adjacent points i, i +1, i +2, i +3third derivative thereofDefining the fidelity of a smooth curve to an observed valueDefining the fidelity of the smooth curve to the first derivative of the observed value
The invention has the beneficial effects that: fusion of hydrogen and cesium time scale layers is realized, and optimal weighting under three conditions of absolute smoothness and absolute fidelity of the time scale of the cesium clock group and absolute fitting of the first-order derivative of the time scale of the hydrogen clock group is discussed. On the basis of an exponential filtering algorithm, filtering on a clock group time scale is further realized, and the influence of short-term fluctuation of the cesium clock on a fusion result is effectively improved. Meanwhile, the reliability of the weighted average time scale only once is further improved by fusing the two time scales. The method can effectively inhibit noise, and fully utilize the characteristics of the hydrogen cesium atomic clock, so that the long-term and short-term stability of the fusion time scale is good.
Drawings
Fig. 1 is a schematic flow chart of the present invention for generating a fusion time scale (taking three cesium clocks and three hydrogen clocks as an example).
Fig. 2 is a schematic time scale diagram, in which (a) is a time scale of a cesium clock set and (b) is a time scale of a hydrogen clock set.
FIG. 3 is a diagram illustrating the fusion results of the time scale of the present invention, wherein (a) is the fusion result and (b) is the Allan bias.
Detailed Description
The present invention will be further described with reference to the following drawings and examples, which include, but are not limited to, the following examples.
The invention provides a hydrogen cesium time scale fusion method based on Vondark-Cepek filtering, which comprises the steps of firstly, respectively generating a clock group time scale for a hydrogen clock group and a cesium clock group by using an exponential filtering method, then selecting key parameters of Vondark-Cepek combined filtering according to the principle of least square, and further performing performance enhancement on the cesium clock group time scale through difference information of a hydrogen clock group time scale time sequence so as to obtain the hydrogen cesium fusion time scale.
The invention specifically comprises the following steps:
Step 1: and preprocessing the atomic clock error data measured by the laboratory. Firstly, selecting an atomic clock with the best long-term and short-term stability in a clock group as a reference clock, and measuring clock difference data of other atomic clocks and the reference clock by using a time interval counter. The clock error is measured once per hour. And removing abnormal points by adopting a 3 sigma rule, and simultaneously detecting the continuity of the clock error data. Repairing a clock error sequence with continuous missing data for less than 5 hours by adopting an interpolation method; and if the clock error data are continuously missing for more than 5 hours, removing the clock from the time keeping clock group.
Step 2: grouping cesium atomic clocks and hydrogen atomic clocks, and generating exponential filtering cesium clock time scale TA through clock error prediction, frequency estimation and weight estimation steps (once per hour)CsAnd hydrogen time scale TAH. (calculation of a time scale of 3 months is exemplified below)
And if the weight of each atomic clock is greater than the set maximum weight upper limit, setting the weight of the atomic clock as the maximum weight. According to a preferred embodiment of the method, the maximum weighting is set to 2.5/N. Wherein N is the number of atomic clocks involved in the calculation. H 'is'i(t) is the atomic clock H at time titime correction quantity is weight, atomic clock data, h'i(t) is calculated by the following formula:
Wherein x isij(t) is an atomic clock HjAnd atomic clock HiThe clock difference at time t; x is the number ofi(t) is the difference between the mean time scales of the laboratory atomic clock and the laboratory atomic clock set, wiis the weight of each atomic clock.
And step 3: and (3) carrying out primary difference on the hydrogen clock group time scale sequence obtained by calculation in the step (2) to obtain corresponding frequency data.
And 4, step 4: and transforming the time scale sequence of the cesium clock set into a frequency domain through Fourier transform, and determining a signal f or a period P to be suppressed through spectrum analysis. Determining TA based on the frequency f or period P, experience and actual algorithmCsAnd TAHCorresponding frequency responses T and T' are calculated according to the least square theory to obtain the time scale smoothing factor epsilon of the cesium clock group and the time scale smoothing factor epsilon of the hydrogen clock group
And 5: and (3) taking the time scale of the cesium clock set generated by calculation in the step (2) and the frequency sequence of the hydrogen clock set generated in the step (3) as input, using the smoothing factor obtained in the step (4) in a Vondark-Cepek combined filtering method, generating a time scale fusion result, and realizing the fusion of the time scales of the cesium clock set and the hydrogen clock set.
Establishing a hydrogen cesium time scale fusion model, namely defining a cesium clock group time scale (TA)Cs) Data is m (t)i) Is a time tiI-1, 2,3, … at tiThe derivative of the time instant is defined as m' (t) ═ m (t)i+1)-m(ti)]/(ti+1-ti)。M(tj) Is the hydrogen clock time scale (TA)H) The derivative of which is defined as M' (t) ═ M (t)j+1)-M(tj)]/(tj+1-tj). Wherein j is 1,2,3, …. The physical meanings of M '(t) and M' (t) are consistent and are both the rates of the time scale sequence. Therefore, when t isi＝tjWhen M '(t) is M' (t).
m(MJD2)＝m(MJD1)+M′(tj)Δtj (3)
Wherein MJD is a simplified julian day.
Since the time intervals of the time scales of the selected cesium clock set and the hydrogen clock set are the same, the clock difference estimation at the next moment of the cesium clock set can be expressed by the sum of the clock difference of the cesium clock set at the moment and the product of the time scale rate and the time interval of the hydrogen clock set according to the formula (3).
Suppose input observation sequence 1 is represented as y'jCorresponding time scale is xjWeight p ofj(ii) a First derivative of observation sequence 2 is expressed asCorresponding time scale isThe weight isthe output sequence is then the smooth curve to be obtained, denoted yiCorresponding time scale is xi. Three quantities are defined:
1) Smoothness of the curve:
in the formula,Is unknown, based on the smoothed data, on its third derivativeAnd (6) estimating. At two points [ x ]i+1,yi+1]And [ x ]i+2,yi+2]The smooth curve between is defined as a lagrange polynomial L of third order derived from four adjacent points i, i +1, i +2, i +3i(x)：
The third derivative is:
The third derivative between each pair of data points is set to a constant, and equation (1) can be expressed as:
Wherein
This smooth definition means that the ideal smoothing function is a quadratic function of time (the first derivative of which is a linear function).
2) Fidelity of the smoothed curve to the observed values:
3) Fidelity of the smooth curve to the first derivative of the observed value:
first derivative ofCan be based on the smoothing function value yiAnd (4) showing.
using lagrange polynomials L to define Si(x) Is denoted as L'i(x)：
L′i(x)＝Ai(x)yi+Bi(x)yi+1+Ci(x)yi+2+Di(x)yi+3 (10)
Wherein,
To use the smoothing function value yismoothed values representing first derivativesFor each time instant xiThere is a certain freedom in the choice of the surrounding four points. The constraint of the following formula ensuresThe value of (b) is on a smooth curve.
1) To calculateUsing the time x1，x2，x3，x4That is, the formula (11) can be obtained
Wherein,
2) For the first half of the input dataN/2, using time xi-1，xi，xi+1，xi+2I.e. by
Wherein,
3) For the second half of the input dataI ═ N/2+1, N/2+2, … N-1, using the time xi-2，xi-1，xi，xi+1i.e. by
Wherein,
4) For theUsing the time xN-3，xN-2，xN-1，xNI.e. by
wherein,
ThenCan be expressed as:
The V-C combined filtering method aims at determining a smoothing value yiEqualization under three different conditions, each different setting will lead to different results:
(a) The curve needs to be smoothed (minimize S)
(b) Smooth values require observations that are close to a function (minimize F)
(c) The first derivative of the smooth curve requires an observed value (minimum) close to the first derivativeTransforming)
The least square method is adopted to minimize the above constraint conditions to adjust each parameter, and the method is expressed as follows:
Wherein epsilon is more than or equal to 0,The degree of equalization for the three conditions can be determined by selecting the values of these two parameters: smoothing coefficients ε and ∈The larger the smoothing coefficient value, the larger the weight of the fidelity with respect to the observation function value or its first derivative, and the closer the smoothing value is to the observation value.
The embodiment of the invention provides a method for realizing hydrogen cesium time scale fusion by using Vondark-Cepek combined filtering. The fusion of the hydrogen cesium clock group time scale layer is put forward for the first time, and the problem that white noise generated by hydrogen cesium mutual reference influences a time scale result is avoided. The hydrogen clock group time scale and the cesium clock group time scale respectively have good short-term stability and long-term stability, so that the hydrogen clock group time scale and the cesium clock group time scale can be subjected to performance enhancement by utilizing the excellent short-term stability of the hydrogen clock group time scale under the condition of not influencing the long-term stability of the cesium clock group time scale, and a fusion time scale with good long stability and good short stability can be generated.
As shown in fig. 1, the method of generating a fusion timescale comprises the steps of:
Step 1, preprocessing atomic clock difference data measured in a laboratory, and removing abnormal points by adopting a 3 sigma rule.
The gross error elimination is realized by using a 3 sigma criterion, and the detected atomic clock frequency difference data is { x1,x2,x3,…,xN-1,xNMean of samples isStandard deviation ofThe 3 sigma criterion is the measured valuethe value is singular and should be eliminated.
Step 2, grouping the cesium atomic clocks and the hydrogen atomic clocks, and calculating time scales of the respective clock groups by using the clock difference data processed in the step 1 and adopting an exponential filtering method to obtain TACsAnd TAHAs shown in fig. 2.
Clock error estimation: clock error data X of each watch clock and reference clockij(t), the measurement interval is τ. The clock difference estimate at time (t + τ) is calculated from equation (1) based on the clock difference and clock speed at time t. The optimal estimate of the reference clock relative to the time scale clock difference is calculated from equation (2) based on a weighted average principle.
Wherein, Xi(t),Yi(t) estimates of the time difference and frequency difference, respectively, for the clock i at time t with respect to a reference time scale;Is the clock error forecast for clock i at time t.
frequency estimation: the average frequency difference estimation of the clock i at the time of (t + tau) is obtained by adopting the first difference of clock difference data and then calculating through an exponential filter, such as the formulas (3) and (4).
WhereinIs the frequency difference forecast of the clock i over the time interval from time t to t + τ; m isiIs an exponential frequency-averaged time constant, is the error introduced in the minimized time difference estimation equation (1), and is estimated according to equation (5).
Wherein tau isminiTaking the Allen variance curve as the most stable time interval of the clock iThe value of τ at the minimum.
And (3) weight estimation: the weight is determined by the difference between the clock difference of each clock relative to the page clock and the calculated value of the current time.
As in equation (6):
Wherein KiThe deviation for error estimation is calculated according to equation (10). The mean square time error per clock is determined by the exponential filter of equation (7).
Wherein epsiloni(τ) is the accumulated error of the moveout estimate of clock i over the time interval τ;<ε2 x(τ)>Is the mean square error of time t on the paper surface with time interval tau, and the initial value is generally takenNτIs the time constant of an exponential filter used to estimate the current averageVariance, NτGenerally, it is taken for 20 days.
and n is the number of atomic clocks. The weights are applied in equation (2), which is calculated as shown in equation (9).
First reading the clock error file, for Xi(t)、Yi(t) taking an initial value. For the initial value selection, the clock difference of the atomic clock relative to the UTC at the start time is chosen for simplicity. The BIPM's T publication discloses the clock difference between UTC and UTC (ntsc), and it is known that the clock difference between three hydrogen clocks and UTC (ntsc) clock difference at that time are subtracted from each other to obtain the clock difference between three hydrogen clocks and UTC. Clock speed YiAnd (t) and the initial value of the drift parameter d are selected according to the clock error data of the previous ten days by secondary fitting. Secondly, the next time forecast clock error is calculated according to the formula (1)Then calculateIs generally taken as the initial value ofThen the allen variances for three clocks should be calculated first. Because the measured clock difference between each species and the main clock needs to be solved by using a triangular cap method to obtain the respective Allen variance of each clock, the known clock difference data needs to be subtracted from each other, the main clock is removed, and the clock difference between the three hydrogen atomic clocks is obtained. Then calculating the Allan variance between each two atomic clocks, solving the Allan variance of each clock according to the triangular cap calculation formula (11), and solving the Allan variance of each clock according to the formulaComputingAnd (5) initial value. And calculating the initial weight value according to the formula (8-9). Then, according to the formula (2) and the data of each atomic clock, calculating the clock error of the main clock relative to the paper clock at the next moment, and carrying out weighted average to obtain the final clock error estimation Xj(t + τ) is the difference between the calculated average time at time (t + τ) and the reference clock, TACsOr TAH. Then, based on the estimated clock difference, the clock speed at the next time (t + τ) is predicted. According to Xi＝Xj+XijAnd calculating the clock difference between each clock and the paper clock, and substituting the clock difference into the formula (3) to calculate the frequency difference estimation. Then calculating the exponential frequency constant according to the formula (5), substituting the exponential frequency constant into the formula (4) to calculate Yi(t + τ) for the calculation of the clock error prediction at the next time instant (t +2 τ). Finally, the clock difference, weight, and frequency estimation at the next time (t +2 τ) are performed. In this case, the time difference estimation is the same as the previous calculation method, the weight calculation is calculated according to equations (6) - (10), and the parameter K is determined according to equation (10)iThen, the current weighting is calculated according to the formulas (6) to (9). And circulating in sequence, and performing prediction calculation at the next moment.
And 3, carrying out primary difference on the hydrogen clock group time scale sequence obtained by calculation in the step 2 to obtain corresponding frequency data.
Step 4, determining the frequency response T/T' according to the frequency f or the period P of the noise to be weakened, and calculating the smoothing factors epsilon and epsilon
Time scale sequence of cesium clock groupTACstransforming the frequency domain to a frequency domain through Fourier transform, determining a noise period P or a frequency f through spectral analysis, simultaneously determining a frequency response T/T', and finally calculating a smoothing factor according to a formula.
And 5, taking the time scale of the cesium clock set generated by calculation in the step 2 and the frequency sequence of the hydrogen clock set generated in the step 3 as input, and using the smoothing factor obtained in the step 4 in a Vondark-Cepek combined filtering method to generate a time scale fusion result.
First, system equationIn a matrix manner can be represented as
Wherein,
Wherein,
Since A is a positive definite matrix, the Cholesky decomposition can be used to solve system equation (14). Matrix a is decomposed by Cholesky to obtain:
A＝UTDU (15)
Let UTthe vector w can be found By taking w as By'. Then according to Uy ═ D-1w, y can be obtained. Namely:
y＝A-1By' (16)
Therefore, the time scale result of hydrogen-cesium fusion, i.e. the sequence y, can be obtained, and the result is shown in FIG. 3, wherein (a) is the time scale fusion result, and (b) is the Allan deviation.
the above embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the present invention. The scope of the invention is defined by the claims. Various modifications and equivalents may be made by those skilled in the art within the spirit and scope of the invention, and such modifications and equivalents should also be considered as falling within the scope of the invention.
Claims (6)
1. A hydrogen cesium time scale fusion method based on Vondark-Cepek filtering is characterized by comprising the following steps:
Step 1, grouping cesium atomic clocks and hydrogen atomic clocks, and generating time scale TA of an exponential filtering cesium clock group through clock error prediction, frequency estimation and weight estimation steps respectivelyCsAnd hydrogen time scale TAH；
Step 2: carrying out primary difference on the hydrogen clock group time scale sequence to obtain corresponding frequency data;
Step 3, Fourier transform is carried out on the time scale sequence of the cesium clock set to convert the time scale sequence into a frequency domain, and a signal f or a period P to be suppressed is determined through spectrum analysis; calculating a time scale smoothing factor of the cesium clock group according to the least square theoryAnd hydrogen clock group time scale smoothing factorWherein T and T' are each TACsAnd TAHA corresponding frequency response;
And 4, taking the cesium clock group time scale and the hydrogen clock group frequency sequence as input, using the smoothing factor in a Vondark-Cepek combined filtering method, generating a time scale fusion result, and realizing the fusion of the cesium clock group time scale and the hydrogen clock group time scale.
2. The Vondark-Cepek filtering-based hydrogen cesium time scale fusion method according to claim 1, characterized in that: the method comprises the following steps that 1, atomic clock difference data measured in a laboratory are preprocessed, atomic clocks with the best long-term and short-term stability in a cesium atomic clock group and a hydrogen atomic clock group are respectively selected as reference clocks, and clock difference data of other atomic clocks in the same clock group and the reference clocks are measured by using a time interval counter.
3. The Vondark-Cepek filtering-based hydrogen cesium time scale fusion method according to claim 2, characterized in that: removing abnormal points from the clock error data obtained by preprocessing by adopting a 3 sigma rule, detecting the continuity of the clock error data, and repairing a clock error sequence with continuous missing data less than 5 measurement periods by adopting an interpolation method; and if the clock error data are continuously missing for more than 5 measurement periods, the clock is removed from the clock group.
4. The Vondark-Cepek filtering-based hydrogen cesium time scale fusion method according to claim 1, characterized in that: in the step 1, if the weight of each atomic clock is greater than the set maximum weight upper limit, the weight of the atomic clock is set as the maximum weight; h 'is'i(t) is the atomic clock H at time tiTime correction quantity is weight, atomic clock data, h'i(t) by the formulaCalculation of where xij(t) is an atomic clock HjAnd atomic clock HiThe clock difference at time t, N being the number of atomic clocks involved, xi(t) is the difference between the mean time scales of the laboratory atomic clock and the laboratory atomic clock set, wiIs the weight of each atomic clock.
5. The Vondark-Cepek filter-based hydrogen cesium time scale fusion method according to claim 4, characterized in that: in the step 1, the maximum weight is set to be 2.5/N.
6. The method for time-scale fusion of cesium hydride based on Vondark-Cepek filtering according to claim 1, characterized in thatIn the following steps: in the step 4, a time scale TA of the cesium clock group is definedCsData is m (t)i) Is a time ti1,2,3, which is at tithe derivative of time m' (t) ═ m (t)i+1)-m(ti)]/(ti+1-ti) (ii) a Definition of M (t)j) Is the hydrogen clock time scale (TA)H) The derivative M' (t) thereof is [ M (t) ]j+1)-M(tj)]/(tj+1-j) Wherein j is 1,2, 3.; when t isi＝tjwhen M ' (t) is M ' (t), M (MJD2) is M (MJD1) + M ' (t)j)ΔtjMJD denotes reduced julian days; suppose input observation sequence 1 is represented as y'jcorresponding time scale is xjWeight p ofj(ii) a First derivative of observation sequence 2 is expressed asCorresponding time scale isThe weight isThe output sequence is then the smooth curve y to be obtainediCorresponding time scale is xiDefining the smoothness of the curveIn the formula,Is unknown, based on the smoothed data, on its third derivativeCarrying out estimation; at two points [ x ]i+1，yi+1]And [ x ]i+2，yi+2]The smooth curve between is defined as a lagrange polynomial of third order derived from four adjacent points i, i +1, i +2, i +3Third derivative thereofDefining the fidelity of a smooth curve to an observed valuedefining the fidelity of the smooth curve to the first derivative of the observed value
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910787030.4A CN110554597B (en) | 2019-08-25 | 2019-08-25 | Hydrogen cesium time scale fusion method based on Vondark-Cepek filtering |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910787030.4A CN110554597B (en) | 2019-08-25 | 2019-08-25 | Hydrogen cesium time scale fusion method based on Vondark-Cepek filtering |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110554597A true CN110554597A (en) | 2019-12-10 |
| CN110554597B CN110554597B (en) | 2021-03-26 |
Family
ID=68737950
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910787030.4A Expired - Fee Related CN110554597B (en) | 2019-08-25 | 2019-08-25 | Hydrogen cesium time scale fusion method based on Vondark-Cepek filtering |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110554597B (en) |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110989326A (en) * | 2019-12-26 | 2020-04-10 | 中国计量科学研究院 | Local high-precision time frequency real-time comprehensive device |
| CN112269311A (en) * | 2020-09-22 | 2021-01-26 | 中国计量科学研究院 | Method and device for realizing real-time atomic time scale of remote distributed union |
| CN112329197A (en) * | 2020-09-23 | 2021-02-05 | 北京无线电计量测试研究所 | Comprehensive atomic time establishing method based on gray model |
| CN114047684A (en) * | 2021-10-21 | 2022-02-15 | 中国人民解放军61081部队 | Atomic clock combined time keeping method and device |
Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1014518B1 (en) * | 1998-12-17 | 2004-09-22 | Nippon Telegraph and Telephone Corporation | An atomic frequency standard laser pulse oscillator |
| CN2672698Y (en) * | 2003-12-19 | 2005-01-19 | 中国科学院国家授时中心 | Novel time interval measurer |
| CN104579340A (en) * | 2015-02-04 | 2015-04-29 | 上海航天测控通信研究所 | Passive hydrogen clock digital servo system based on FPGA |
| US9252795B2 (en) * | 2010-12-15 | 2016-02-02 | Raytheon Company | Distribution system for optical reference |
| CN105676627A (en) * | 2015-12-25 | 2016-06-15 | 中国科学院国家授时中心 | Time keeping system primary and standby main clock seamless switching system and method |
| CN105718642A (en) * | 2016-01-18 | 2016-06-29 | 中国科学院国家授时中心 | Reference time scale generation method based on threshold autoregressive model |
| CN105974777A (en) * | 2016-07-19 | 2016-09-28 | 北京工业大学 | Method for generating atomic time scale through Algos and Kalman combination |
| CN106506136A (en) * | 2016-11-24 | 2017-03-15 | 上海市计量测试技术研究院 | A kind of network time transmission method and device based on atomic clock group |
| CN106773610A (en) * | 2016-11-28 | 2017-05-31 | 北京工业大学 | A kind of cesium-beam atomic clock and hydrogen clock frequency difference predictor method |
-
2019
- 2019-08-25 CN CN201910787030.4A patent/CN110554597B/en not_active Expired - Fee Related
Patent Citations (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| EP1014518B1 (en) * | 1998-12-17 | 2004-09-22 | Nippon Telegraph and Telephone Corporation | An atomic frequency standard laser pulse oscillator |
| CN2672698Y (en) * | 2003-12-19 | 2005-01-19 | 中国科学院国家授时中心 | Novel time interval measurer |
| US9252795B2 (en) * | 2010-12-15 | 2016-02-02 | Raytheon Company | Distribution system for optical reference |
| CN104579340A (en) * | 2015-02-04 | 2015-04-29 | 上海航天测控通信研究所 | Passive hydrogen clock digital servo system based on FPGA |
| CN105676627A (en) * | 2015-12-25 | 2016-06-15 | 中国科学院国家授时中心 | Time keeping system primary and standby main clock seamless switching system and method |
| CN105718642A (en) * | 2016-01-18 | 2016-06-29 | 中国科学院国家授时中心 | Reference time scale generation method based on threshold autoregressive model |
| CN105974777A (en) * | 2016-07-19 | 2016-09-28 | 北京工业大学 | Method for generating atomic time scale through Algos and Kalman combination |
| CN106506136A (en) * | 2016-11-24 | 2017-03-15 | 上海市计量测试技术研究院 | A kind of network time transmission method and device based on atomic clock group |
| CN106773610A (en) * | 2016-11-28 | 2017-05-31 | 北京工业大学 | A kind of cesium-beam atomic clock and hydrogen clock frequency difference predictor method |
Non-Patent Citations (2)
| Title |
|---|
| 宋会杰等: "一种基于小波变换的氢铯联合守时算法研究", 《天文学报》 * |
| 管健安等: "基于Vondark模型平滑精密单点定位（PPP）授时钟差解", 《测绘工程》 * |
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110989326A (en) * | 2019-12-26 | 2020-04-10 | 中国计量科学研究院 | Local high-precision time frequency real-time comprehensive device |
| CN112269311A (en) * | 2020-09-22 | 2021-01-26 | 中国计量科学研究院 | Method and device for realizing real-time atomic time scale of remote distributed union |
| CN112329197A (en) * | 2020-09-23 | 2021-02-05 | 北京无线电计量测试研究所 | Comprehensive atomic time establishing method based on gray model |
| CN114047684A (en) * | 2021-10-21 | 2022-02-15 | 中国人民解放军61081部队 | Atomic clock combined time keeping method and device |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110554597B (en) | 2021-03-26 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110554597B (en) | Hydrogen cesium time scale fusion method based on Vondark-Cepek filtering | |
| CN111650617B (en) | Crystal oscillator frequency taming method, system and medium based on innovation weighted adaptive Kalman filtering | |
| CN106026919B (en) | The punctual compensation method of crystal oscillator | |
| Heo et al. | Improving prediction accuracy of GPS satellite clocks with periodic variation behaviour | |
| CN109581856B (en) | Time synchronization and time keeping method based on high-performance crystal oscillator frequency calibration | |
| CN105718642B (en) | A kind of reference time scale production method based on threshold autoregressive model | |
| KR100823832B1 (en) | Apparatus and method for estimating frequency of signal in power system | |
| CN112433235B (en) | Method, system and medium for determining time reference | |
| CN107086901A (en) | A kind of BDT method for building up and UTC (NTSC) method for building up | |
| Cheng et al. | Highly accurate real-time GPS carrier phase-disciplined oscillator | |
| CN112636857A (en) | High-precision time-frequency signal dynamic driving method based on residual error correction | |
| RU2463223C1 (en) | Method of determination and prediction of subjected to atmospheric braking aircraft motion on low orbits | |
| US11035902B2 (en) | Advanced fuel gauge | |
| CN115524725A (en) | Method for correcting Beidou and crystal oscillator second clock based on differential observation and regression equation model | |
| CN111610710B (en) | Local atomic time generation method based on cesium fountain clock and hydrogen atomic clock group | |
| CN112182864A (en) | Method for selecting clock error prediction based on drift condition of hydrogen atomic clock | |
| Howe | A new family of real-time redictor-corrector integration algorithms | |
| CN110865530A (en) | Atomic time calculation method | |
| CN110858309B (en) | Multi-reference time clock weighting synthesis method | |
| CN111711446A (en) | Method, system and medium for taming crystal oscillator frequency by using GPS signal | |
| Griffin et al. | Drift correction for active hydrogen MASERs | |
| Wang et al. | Enhanced stability for local atomic clock ensemble time scale using weighted moving average filter | |
| CN112329197A (en) | Comprehensive atomic time establishing method based on gray model | |
| Tseng et al. | Introduction of GNSS Up-Sampled All-in-View Time Transfers | |
| Xue et al. | An enhanced prediction model for BDS ultra-rapid clock offset that combines singular spectrum analysis, robust estimation and gray model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20210326 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |