CN113075873B - Rubidium atom small optical clock based on Kalman filtering temperature and frequency control and implementation method - Google Patents
Rubidium atom small optical clock based on Kalman filtering temperature and frequency control and implementation method Download PDFInfo
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Abstract
The invention discloses a rubidium atom small optical clock based on Kalman filtering temperature and frequency control and an implementation method, wherein the implementation method comprises the following steps: the system comprises a one-dimensional Kalman filtering module, a two-dimensional Kalman filtering module, a temperature servo controller, a frequency servo controller, a temperature control module with a Kalman filtering functional interface and a frequency control module with a Kalman filtering functional interface; the temperature servo controller and the Kalman filter are utilized to realize closed-loop temperature control on the laser and the atomic gas chamber, and the self-adjustment of temperature control parameters is realized; the influence of process noise and measurement noise on the control parameters is attenuated in an order of magnitude; meanwhile, the state of the frequency measurement system is dynamically estimated in a signal containing noise by using Kalman filtering, the noise of the rubidium atomic clock is corrected to a lower noise reference in a short time, and the frequency stability of the laser is further improved.
Description
Technical Field
The invention belongs to the technical field of atomic clocks and frequency standards, relates to a temperature and frequency control atomic clock technology, and particularly relates to a rubidium atomic small optical clock based on Kalman filtering temperature and frequency control and an implementation method thereof.
Background
The stable improvement of the time frequency measurement precision promotes the application of high-precision time measurement aspects such as ultra-precise spectrum, astronomical observation, deep space exploration, physical basic constant measurement and the like. Meanwhile, the method has wide influence on the fields of high-speed communication, navigation positioning, geodetic surveying, national defense and military and the like. At present, atomic clocks are the most accurate time frequency devices at present, with the best optical clock frequency stability having reached 10-19In order of magnitude, most of internationally applied atomic clocks are cesium, hydrogen and rubidium atomic clocks, wherein the rubidium atomic clocks are most widely applied.
The rubidium atom small optical clock system is roughly divided into a physical system, an optical system and a control system, wherein the physical system is a core component of the rubidium atom small optical clock and mainly comprises a semiconductor narrow line width laser, a rubidium atom air chamber and a photoelectric detector; the semiconductor narrow linewidth laser is a device for converting electrons into photons in a system, and because loss exists in a cavity for forming the narrow linewidth laser, the temperature of the semiconductor narrow linewidth laser is increased when the semiconductor narrow linewidth laser works, so that the laser frequency is changed to some extent, and the stability of laser wavelength is influenced; meanwhile, the long-term operation of the semiconductor narrow linewidth laser at high temperature affects the service life. The atomic gas chamber provides quantum reference for the rubidium atom small optical clock, the precise temperature control can ensure that enough atoms interact with the laser, and if the temperature phase difference between the atomic gas chamber and the cold finger is too large, the atoms are condensed on the cold finger port too much to influence the number of atoms resonating with photons; in addition, the accurate temperature control at the position close to the light through hole of the atom air chamber can further accurately monitor the utilization condition of the atom number, and the atoms are prevented from being condensed in the light through hole to reduce the number of photons acting with the atoms.
The existing PID temperature control technology is mainly characterized in that a controller is formed by linear combination of proportion, integral and differential of deviation values of a set value and a measured value, and a temperature control object is controlled; in the temperature monitoring process, noise is generated by the thermistor, a cable between monitoring systems and the response bandwidth of devices, so that the measured temperature data has noise; meanwhile, the temperature control precision is higher and higher in the high-precision measurement of the atomic frequency standard, particularly in a system with an interference environment, due to the limitation of a PID temperature control technology, the parameters of the controller cannot realize automatic adjustment of control parameters to meet the requirement of the environment, the high-precision temperature control effect cannot be realized, and the medium-term and long-term frequency stability indexes of the rubidium atomic small optical clock are further limited.
In the current atomic clock research, for example, a signal of a servo loop controller introduced in the frequency control principle of the fourth section of the quantum frequency standard principle is directly fed back to a controlled crystal oscillator, that is, is directly output to a laser current, PZT or an AOM for modulating laser frequency, the fed back signal includes radio frequency amplification noise and analog line noise of phase detection, the noise prediction and processing capability is not realized, and meanwhile, the frequency stability and accuracy of the rubidium atomic small optical clock are further limited by the influence of external physical environment noise.
For the part of Kalman filtering, the state equation and measurement equation expressions of Kalman are:
X(k+1)＝ΦX(k)+W(k)
Y(k)＝H X(k)+V(k)
wherein, x (k) is a state signal of the system, y (k) is a measurement signal of the system, Φ is a state transition matrix, H is an observation matrix, w (k) is system noise, a corresponding variance matrix is Q, and v (k) is a variance matrix corresponding to the observation noise is R.
The kalman filtering process can be expressed by formula derivation, where formula (1) is to predict the state of the system at time k +1 from the optimal frequency X ^ (k | k) at time k, formula (2) is to predict the prediction covariance derived from the last error covariance P (k | k) and the process noise Q, formula (3) is the kalman gain at time k +1, formula (4) is to update the optimal estimation value at time k +1 with the measured value, and formula (5) is to update the error covariance at time k + 1.
P(k+1|k)＝ΦP(k|k)ΦT+ΓQΓTFormula (2)
K(k+1)＝P(k+1|k)HT[HP(k+1|k)HT+R]TFormula (3)
P (K +1) ═ 1-K (K +1) H ] P (K +1| K) formula (5)
In the existing patents and documents, the difference between a rubidium atomic clock and a standard reference source is mostly adopted for evaluating the performance of the rubidium atomic clock, for example, a rubidium atomic clock parameter estimation algorithm based on improved kalman filtering disclosed in chinese patent 201811561770.8 mainly evaluates the clock difference prediction capability of the rubidium atomic clock through the difference between the rubidium atomic clock and the standard reference source, the reference clock is usually a cesium clock or a hydrogen clock, and the application range of the rubidium atomic small optical clock is limited by the higher experimental environment requirement and the expensive price. The existing literature "study on the control of a crystal oscillator based on a Kalman filter [ J ]. how much a fan is contained, etc.. time and frequency study, 2019 (03)" also evaluates the performance of a rubidium atomic clock by estimating the parameters of the rubidium atomic clock through the difference between the rubidium atomic clock and a standard reference source.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, including the technical problem that the long-term frequency stability of a rubidium atomic small optical clock is influenced by temperature fluctuation caused by PID temperature control in the prior art and the limitation of low-precision control on noise parameters caused by direct feedback of a servo signal in the prior atomic clock to a local oscillator, so that the performance of the long-term stability in the rubidium atomic clock is greatly limited, and the invention firstly provides the rubidium atomic small optical clock based on Kalman filtering temperature and frequency control, wherein a temperature power supply of the rubidium atomic small optical clock is combined with a servo control technology and a Kalman filtering algorithm to realize dynamic regulation of the servo parameters and reduce the influence of process noise and measurement noise on the control parameters in a magnitude order; meanwhile, the state of the frequency measurement system is dynamically estimated in a signal containing noise by using Kalman filtering, the noise of the rubidium atomic clock is corrected to a lower noise reference in a short time, and the frequency stability of the laser is further improved.
The invention applies the Kalman filtering module to the rubidium atom small optical clock for the first time internationally, and the novelty and the creativity of the invention are realized as follows: firstly, the invention overcomes the limitation that the control parameters of the PID controller can not realize automatic adjustment brought by environmental parameters, integrates the temperature control parameters and the measured values of the laser and the atomic gas chamber by combining the temperature servo controller and the Kalman filter, realizes the closed-loop temperature control of the laser and the atomic gas chamber, and can achieve the purpose of self-adjustment of the temperature control parameters. Secondly, the invention utilizes the filtering function of the Kalman filter to feed back the filtered signals to the temperature servo controller and the frequency servo controller, thereby greatly reducing the noise generated by the response bandwidth of devices, cables and devices in the process of monitoring the temperature and achieving the purpose of improving the influence of the noise in the system on the temperature and frequency control data. Finally, the frequency value of the next moment can be estimated by using the frequency value of the previous moment through Kalman filtering, the frequency state in the measurement process can be efficiently predicted by using a filtering equation, the estimated mean square error is minimized, and meanwhile, frequency data are corrected; and the ideal effect of the Kalman filtering applied to the rubidium atom small optical clock is verified by analyzing the frequency stability result which is not subjected to the Kalman filtering.
The technical scheme of the invention is as follows:
the invention provides a method for realizing a rubidium atom small optical clock based on Kalman filtering temperature and frequency control, wherein the rubidium atom small optical clock comprises a temperature control device with a one-dimensional Kalman filtering functional interface, a frequency control device with a one-dimensional Kalman filtering functional interface, a temperature servo controller and a frequency servo controller;
the temperature control device with the one-dimensional Kalman filtering functional interface comprises: the temperature control system comprises a temperature power supply, a TEC (Thermo Electric Cooler), a first thermistor, a heating plate, a second thermistor and a one-dimensional Kalman filtering temperature control module;
the frequency control device with the one-dimensional Kalman filtering functional interface comprises: the device comprises a laser power supply, a laser, a rubidium atom gas chamber and a one-dimensional Kalman filtering frequency control module;
the method comprises the following concrete steps:
step 1), arranging a TEC (Thermo Electric Cooler) at the bottom of a narrow-linewidth laser, and winding a heating plate on the outer side of a rubidium atom gas chamber;
step 2) arranging a first thermistor at the narrow-linewidth laser, and arranging a second thermistor at the atomic gas chamber;
step 3) measuring a set of voltages V1outAnd V2out(V1outSet voltage value for temperature power supply, V2outA temperature voltage value measured by the first thermistor), namely: v1out1-V2out1、V1out2-V2out2、...V1outi-V2outi...V1outn-V2outn(V1out1、V1out2...V1outi...V1outnV2 for the set voltage value of the temperature power supply at the time 1, 2.. i.. n of the sampling pointout1、V2out2...V2outi...V2outnThe temperature voltage value measured by the first thermistor at the sampling point at the moment i (1,2, …, i., n), i represents the sampling moment, i represents any one of the sampling moments from 1 to n, the sampling rate can be set to millisecond or minute, and the sampling time is set to millisecond or minuteTens of minutes or hours (in practice, every 1 second is taken as a sampling point, and the sampling time is 5 minutes);
step 4) taking the measured voltage output value difference data as an initial value of a Kalman filtering module, and further continuously observing to obtain temperature data; setting a covariance initial value, a noise variance initial value and an observation noise initial value of covariance; setting a sampling point when Kalman filtering is started to be represented as j (j is Kalman filtering temperature control sampling time), (the sampling point of Kalman filtering is recorded as 1, 2.. j.. m, and j represents any sampling time from 1 to m), and assigning an initial value (j ═ 1) for the Kalman filtering process by using a measured voltage difference value; the initial value (j is 1) of Kalman filtering, namely T, can be obtained according to the relation between the voltage value and the temperaturej＝A(V1outj-V2outj)+T0(j＝1)，Tj(j is 1) is an initial value of Kalman filtering, A is a variation coefficient between a voltage difference value and a temperature relation formula, and T is0A constant that is a voltage difference and temperature relationship; the initial value of the temperature covariance p (j) is set to the square of the measured voltage difference, i.e.: p (j) ═ V1outj-V2outj)2(j ═ 1); setting an initial value Q (j) of the noise variance influencing the frequency drift as the square of the difference value between the temperature value at the moment and all the current measured temperature values, namely:
setting the observation noise initial value R (j) as the square of the difference between the voltage difference value at the next moment and the voltage difference value at the moment: r (j) [ (V1 out)j-V2outn)-(V1outj-V1outn)]2(j＝1)。
And step 5) the temperature is a one-dimensional space matrix which changes along with time, and in Kalman filtering calculation, a state transition matrix phi, a noise driving matrix gamma and an observation matrix H are assigned to be 1, namely phi is 1, gamma is 1 and H is 1. Then the predicted covariance at the next time is P (j + i | j) ═ P (j) + Q (j), and the gain at the next time is K (j +1) ═ P (j +1| j)/[ P (j +1| j) + R (j)]. Updating the covariance of the Kalman filter at the next time to be P (j +1) ═ 1-K (j +1)]P (j +1| j), and updating the temperature estimation value after kalman filtering at the next time to be T (j +1) ═ T (j) + K (j +1) × a [ (V1 out)j+1-V2outj+1)-(V1outj-V2outj)]。
Step 6) obtaining a noise variance, an observation noise value, a prediction covariance and a gain which influence the temperature drift at the next moment, and further obtaining an updated temperature estimation value after the next moment Kalman filtering;
and j +1 is made to obtain a noise variance Q (j +1) affecting the temperature drift at the moment j +1 and an observation noise value R (j +1) at the moment j +1, a prediction covariance P (j +2| j +1) at the next moment and a gain K (j +2) at the next moment are obtained from the obtained P (j +1), Q (j +1) and R (j +1), an updated temperature estimation value T (j +2) after Kalman filtering at the next moment is further obtained, and the like, so that a Kalman filtering temperature estimation value at the next moment is obtained.
Step 7) measuring to obtain a group of error signal values; and calculating according to the relation between the error signal and the laser frequency to obtain an initial value of Kalman filtering.
Through accurate accuse temperature control, narrow linewidth laser power drive narrow linewidth laser output laser, during laser incided atomic air chamber, obtained a set of error signal, measure the value of a set of error signal: err1、Err2...Errk...ErrSK denotes a sampling time, k denotes any one of sampling times 1 to S, each millisecond is taken as a sampling point, and the sampling time is 5 minutes (the sampling rate may be set to milliseconds or minutes, and the sampling time is set to tens of minutes or hours). Let z be the sampling point when kalman filtering is started (z is the sampling time of frequency control of kalman filtering) (the sampling point of kalman filtering is denoted by 1, 2.. z.. R, z is any sampling time from 1 to R). The relationship between the error signal and the laser frequency can be deduced according to the error signal, and an initial value f (z) of Kalman filtering, namely f (z) B Err can be obtainedz+f0(z ═ 1), the initial covariance value of the covariance p (z) is set to the square of the measurement error signal, i.e. the square of the measurement error signal
The initial value of the noise variance q (z) affecting the frequency drift is set as the square of the difference between the frequency value at the moment and all the current measured frequency values, i.e.:
the initial value of the observed noise r (z) is set to the square of the difference between the error signal of the next moment and the current error signal, i.e.: r (z) ═ Errz-ErrS]2(z＝1)。
Step 8) performing Kalman filtering calculation to obtain the prediction covariance, the gain, the covariance after Kalman filtering and the temperature estimation value after Kalman filtering at the next moment;
the frequency is a one-dimensional space matrix which changes with time, and in the kalman filter calculation, a state transition matrix Φ, a noise driving matrix Γ, and an observation matrix H are assigned to 1, that is, Φ is 1, Γ is 1, and H is 1. Then the predicted covariance at the next time is P (z +1| z ═ P (z + q (z)), and the gain at the next time is K (z +1) ═ P (z +1| n + i)/[ P (z +1| z) + r (z))]. Updating the covariance of the Kalman filter at the next time to P (z +1) ═ 1-K (z +1)]P (z +1| z), and f (z +1) ═ f (z) + K (z +1) × B (Err) as the temperature estimation value after updating the kalman filter at the next timez+1-Errz)。
Step 9) further obtaining the prediction covariance, the gain, the covariance after Kalman filtering and the temperature estimation value after Kalman filtering at the next moment after the step 8);
and obtaining a noise variance Q (z +1) influencing temperature drift at the moment z +1 and an observation noise value R (z +1) at the moment z +1 by making z equal to z +1, obtaining a prediction covariance P (z +2| z +1) at the next moment and a gain K (z +2) at the next moment from the obtained P (z +1), Q (z +1) and R (z +1), further obtaining an updated frequency estimation value f (z +2) after Kalman filtering at the next moment, and obtaining a Kalman filtering frequency estimation value at the next moment by analogy. The one-dimensional Kalman filtering module outputs a Kalman filtering frequency estimation value to the frequency servo controller, the frequency servo controller feeds back the filtered temperature control parameters to the laser power supply, prediction of frequency of the rubidium atom small optical clock is achieved, influence of noise in a loop on frequency data is reduced, automatic adjustment of the frequency control parameters is achieved, the laser frequency is locked on a transition spectral line of rubidium atoms, and the high-frequency stability rubidium atom small optical clock based on Kalman filtering temperature and frequency control is obtained.
In step 4), the filtering algorithms in the one-dimensional kalman filtering temperature control module and the one-dimensional kalman filtering frequency control module of the rubidium atomic small optical clock based on the kalman filtering temperature control and frequency control may be filtering methods such as bayes estimation, regression algorithm or exponential smoothing.
The narrow linewidth laser in the rubidium atom small optical clock based on Kalman filtering temperature and frequency control can be an external cavity semiconductor narrow linewidth laser, a DFB narrow linewidth laser or a DBR narrow linewidth laser.
By adopting the method, the rubidium atomic small optical clock based on the Kalman filtering temperature and frequency control comprises a one-dimensional Kalman filtering module, a two-dimensional Kalman filtering module, a temperature servo controller, a frequency servo controller, a temperature control module with a Kalman filtering functional interface and a frequency control module with a Kalman filtering functional interface; the temperature control module with the Kalman filtering functional interface comprises: the temperature control system comprises a temperature power supply, a TEC, a first thermistor, a heating plate, a second thermistor and a one-dimensional Kalman filtering temperature control module; the frequency control module with the Kalman filtering functional interface comprises: the device comprises a laser power supply, a narrow linewidth laser, a rubidium atom air chamber and a one-dimensional Kalman filtering frequency control module.
The temperature power supply in the temperature control module with the Kalman filtering function interface is connected with a TEC and a heating plate, the TEC is tightly attached to a narrow-line-width laser in a frequency control module with the Kalman filtering function interface, the heating plate is wound outside a rubidium atom air chamber in the frequency control module with the Kalman filtering function interface, a first thermistor is arranged at the narrow-line-width laser, a second thermistor is arranged at the rubidium atom air chamber, the temperature power supply in the temperature control module with the Kalman filtering function interface outputs V1out and V1 'out and inputs the output to a one-dimensional Kalman filtering temperature control module, the first thermistor and the second thermistor respectively output V2out and V2' out and input to the one-dimensional Kalman filtering module, wherein V1outSet voltage value for temperature power supply to narrow linewidth laser temperature, V2outThe measured narrow linewidth laser temperature voltage value of the first thermistor, V1' out is the set voltage value of the temperature power supply for the temperature of the rubidium atom gas chamber, V2outIs a second heat-sensitive electrodeAnd the temperature and voltage value of the rubidium atom gas chamber is measured by resistance, the one-dimensional Kalman filtering module is connected with a temperature servo controller, and the temperature servo controller is connected with a temperature power supply, so that the temperature of the narrow-line-width laser and the rubidium atom gas chamber is controlled by Kalman filtering.
The laser power supply is connected with the narrow linewidth laser, the narrow linewidth laser outputs light to enter an error signal Err obtained by the rubidium atom air chamber and then is input into the one-dimensional Kalman filtering module, the one-dimensional Kalman filtering module is connected with the frequency servo controller, and the one-dimensional Kalman filtering module is connected with the laser power supply, so that the frequency of the rubidium atom small optical clock is controlled through Kalman filtering.
The Kalman filtering temperature control module is controlled by a frequency servo controller, and filtering parameters are fed back to a laser power supply, so that the frequency of the rubidium atom small optical clock is predicted, the influence of noise in a loop on frequency data is reduced, the frequency control parameters are automatically adjusted, the laser frequency is locked on a transition spectral line of rubidium atoms, and the high-frequency stability rubidium atom small optical clock based on Kalman filtering temperature control and frequency control is obtained.
Preferably, the narrow linewidth laser in the rubidium atom small optical clock based on Kalman filtering temperature control can be an external cavity semiconductor narrow linewidth laser, a DFB narrow linewidth laser or a DBR narrow linewidth laser.
Preferably, the Kalman filter in the rubidium atom small optical clock based on Kalman filtering temperature control can be a prediction method such as Bell estimation, regression algorithm or exponential smoothing.
Compared with the prior art, the invention applies the Kalman filtering module to the rubidium atom small optical clock, and the novelty and innovation of the invention are as follows:
the invention overcomes the limitation that the control parameters of the PID controller can not be automatically adjusted, integrates the temperature control parameters and the measured values of the laser and the atomic gas chamber by combining the temperature servo controller and the Kalman filter, realizes the closed-loop temperature control of the laser and the atomic gas chamber, and can achieve the purpose of self-adjustment of the temperature control parameters.
The invention utilizes the filtering function of the Kalman filter to feed back the filtered signal to the servo controller, thereby greatly reducing the noise generated by the response bandwidth of devices, cables and devices in the process of monitoring the temperature and improving the influence of the noise in the system on the temperature control data.
According to the method, the frequency value of the next moment can be estimated by using the frequency value of the previous moment through Kalman filtering, the frequency state in the measurement process can be efficiently predicted by using a filtering equation, the estimated mean square error is minimized, and meanwhile, frequency data are corrected; and the ideal effect of the Kalman filtering applied to the rubidium atom small optical clock is verified by analyzing the frequency stability result which is not subjected to the Kalman filtering.
The invention can realize the advantages of reducing the noise in the system and realizing the self adjustment of the temperature and frequency control parameters by combining the servo controller and the Kalman filter, provides an important basis for realizing the temperature control effect with high stability by low-noise and high-precision servo control, and can improve the medium-term and long-term frequency stability of the rubidium atomic small optical clock by orders of magnitude, break through the bottleneck that the rubidium atomic small optical clock in the prior art is limited by the long-term stable temperature control precision and the related noise in the system, and realize the rubidium atomic small optical clock with ultrahigh performance index and capable of continuously operating for a long time.
Drawings
FIG. 1 is a block diagram of a one-dimensional Kalman filtering temperature control device according to an embodiment of the present invention;
the device comprises a 1-temperature power supply, a 2-TEC, a 3-laser, a 4-first thermistor, a 5-heating plate, a 6-rubidium atom air chamber, a 7-second thermistor, an 8-temperature servo controller and a 10-one-dimensional Kalman filtering module.
FIG. 2 is a flow chart of a one-dimensional Kalman filtering temperature control method according to an embodiment of the present invention;
FIG. 3 is a block diagram of a one-dimensional Kalman filtering frequency control device according to an embodiment of the present invention;
wherein: the device comprises a 3-laser, a 6-rubidium atom air chamber, a 9-frequency servo controller, a 10-one-dimensional Kalman filtering module and an 11-laser power supply.
FIG. 4 is a flow chart of a one-dimensional Kalman filtering frequency control method according to an embodiment of the present invention;
FIG. 5 is a block diagram of a two-dimensional Kalman filtering module for controlling temperature and frequency according to an embodiment of the present invention;
wherein: the device comprises a 1-temperature power supply, a 2-TEC, a 3-laser, a 4-first thermistor, a 5-heating plate, a 6-rubidium atom air chamber, a 7-second thermistor, an 8-temperature servo controller, a 9-frequency servo controller, an 11-laser power supply and a 12-two-dimensional Kalman filtering module.
Detailed Description
In order to make the aforementioned and other features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in detail below.
The invention provides a rubidium atom small optical clock based on Kalman filtering temperature control, which comprises: the device comprises a temperature power supply 1, a TEC2, a narrow linewidth laser 3, a first thermistor 4, a heating plate 5, a rubidium atom air chamber 6, a second thermistor 7, a temperature servo controller 8, a frequency servo controller 9, a one-dimensional Kalman filtering module 10, a laser power supply 11 and a two-dimensional Kalman filtering module 12.
Fig. 1 shows a structure of a one-dimensional kalman filter temperature control apparatus according to an embodiment of the present invention. The one-dimensional Kalman filtering temperature control device comprises a temperature power supply 1, a TEC2, a laser 3, a first thermistor 4, a heating plate 5, a rubidium atom air chamber 6, a second thermistor 7, a temperature servo controller 8 and a one-dimensional Kalman filtering module 10. Fig. 2 is a flow chart of a one-dimensional kalman filter temperature control method according to an embodiment of the present invention, and a measurement flow is shown in the figure. Arranging TEC2 at the bottom of the laser 3, and winding a heating plate 5 outside a rubidium atom gas chamber 6; the first thermistor 4 is arranged at the laser 3, and the second thermistor 7 is arranged at the rubidium atom air chamber 6; measure a set of V1outAnd V2outThe difference in the output values of the voltages, namely: v1out1-V2out1、V1out2-V2out2、...V1outn-V2outn，(V1out1、V1out2...V1outnV2 for the set voltage value of the temperature power supply at the time 1, 2.. i.. n of the sampling pointout1、V2out2...V2outnThe temperature voltage value measured by the first thermistor 4 at the sampling point of 1, 2.. i.. n), i represents the sampling time, i represents any one of the sampling times from 1 to n, and the sampling rate can be setSetting the sampling time to be tens of minutes or hours (in the specific implementation, every 1 second is taken as a sampling point, and the sampling time is 5 minutes); taking the measured voltage output value difference data as an initial value of the one-dimensional Kalman filtering module 10, and further continuously observing to obtain temperature data; setting a covariance initial value, a noise variance initial value and an observation noise initial value of covariance; setting a sampling point (a first sampling point) when Kalman filtering is started as j-1, (the sampling point of the Kalman filtering is marked as 1, 2.. j.. m, and j represents any sampling time from 1 to m), and assigning an initial value (j ═ 1) for the Kalman filtering process by using a measured voltage difference value; the initial value (j is 1) of Kalman filtering, namely T, can be obtained according to the relation between the voltage value and the temperaturej＝A(V1outj-V2outj)+T0(j＝1)，Tj(j is 1) is an initial value of Kalman filtering, A is a variation coefficient between a voltage difference value and a temperature relation formula, and T is0A constant that is a voltage difference and temperature relationship; the initial value of the temperature covariance p (j) (j ═ 1) is set as the square of the measured voltage difference, i.e.: p (j) ═ V1outj-V2outj)2(ii) a Setting an initial value Q (j) of the noise variance influencing the frequency drift as the square of the difference value between the temperature value at the moment and all the current measured temperature values, namely:
setting the observation noise initial value R (j) as the square of the difference between the voltage difference value at the next moment and the voltage difference value at the moment: r (j) [ (V1 out)j-V2outj)-(V1outn-V2outn)]2(j＝1)。
The temperature is a one-dimensional space matrix which changes with time, and in the kalman filter calculation, a state transition matrix Φ, a noise driving matrix Γ, and an observation matrix H are assigned to 1, that is, Φ is 1, Γ is 1, and H is 1. Then the predicted covariance at the next time is P (j + i | j) ═ P (j) + Q (j), and the gain at the next time is K (j +1) ═ P (j +1| j)/[ P (j +1| j) + R (j)]. Updating the covariance of the Kalman filter at the next time to be P (j +1) ═ 1-K (j +1)]P (j +1| j), and updating the temperature estimation value after kalman filtering at the next time to be T (j +1) ═ T (j) + K (j +1) × a [ (V1 out)j+1-V2outj+1)-(V1outj-V2outj)]。
And j +1 is made to obtain a noise variance Q (j +1) affecting the temperature drift at the moment j +1 and an observation noise value R (j +1) at the moment j +1, a prediction covariance P (j +2| j +1) at the next moment and a gain K (j +2) at the next moment are obtained from the obtained P (j +1), Q (j +1) and R (j +1), an updated temperature estimation value T (j +2) after Kalman filtering at the next moment is further obtained, and the like, so that a Kalman filtering temperature estimation value at the next moment is obtained.
Through precise temperature control and control, the laser power supply 11 drives the narrow-linewidth laser 3 to output laser, the laser enters the rubidium atom air chamber 6 to obtain a group of error signals, and the values of the group of error signals are measured: err1、Err2...Errk...ErrSK denotes a sampling time, k denotes any one of sampling times 1 to S, each millisecond is taken as a sampling point, and the sampling time is 5 minutes (the sampling rate may be set to milliseconds or minutes, and the sampling time is set to tens of minutes or hours). Let z be 1 (the first sample point) when kalman filtering is started, (the sample point of kalman filtering is denoted by 1, 2.. z.. R, z is any sampling time from 1 to R),
the relationship between the error signal and the laser frequency can be derived from the error signal, and an initial value (z ═ 1) of kalman filtering, that is, f (z) ═ B · Err can be obtainedz+f0The initial value of the covariance is set to the square of the measurement error signal, i.e.
The initial value of the noise variance affecting the frequency drift is set as the square of the difference between the frequency value at the moment and all the current measured frequency values, i.e.:
the initial value of the observation noise is set as the square of the difference between the error signal of the next moment and the current error signal, namely: r (z) ═ Errz-ErrS]2。
The frequency is a one-dimensional space matrix which changes along with the time, and the state is transferred in Kalman filtering calculationThe matrix Φ, the noise driving matrix Γ, and the observation matrix H are assigned to 1, that is Φ equals 1, Γ equals 1, and H equals 1. Then the predicted covariance at the next time is P (z +1| z ═ P (z + q (z)), and the gain at the next time is K (z +1) ═ P (z +1| n + i)/[ P (z +1| z) + r (z))]. Updating the covariance of the Kalman filter at the next time to P (z +1) ═ 1-K (z +1)]P (z +1| z), and f (z +1) ═ f (z) + K (z +1) × B (Err) as the temperature estimation value after updating the kalman filter at the next timez+1-Errz)。
And obtaining a noise variance Q (z +1) influencing temperature drift at the moment z +1 and an observation noise value R (z +1) at the moment z +1 by making z equal to z +1, obtaining a prediction covariance P (z +2| z +1) at the next moment and a gain K (z +2) at the next moment from the obtained P (z +1), Q (z +1) and R (z +1), further obtaining an updated frequency estimation value f (z +2) after Kalman filtering at the next moment, and obtaining a Kalman filtering frequency estimation value at the next moment by analogy. The one-dimensional Kalman filtering module 10 outputs a Kalman filtering frequency estimation value to the frequency servo controller 9, the frequency servo controller 9 feeds back the filtered temperature control parameters to the laser power supply 11, prediction of frequency of the rubidium atom small optical clock is achieved, influence of noise in a loop on frequency data is reduced, automatic adjustment of the frequency control parameters is achieved, the laser frequency is locked on a transition spectral line of rubidium atoms, and the high-frequency stability rubidium atom small optical clock based on Kalman filtering temperature control and frequency control is obtained.
The invention provides a two-dimensional Kalman filtering temperature and frequency control rubidium atom small optical clock, as shown in FIG. 5, a two-dimensional related state matrix is established according to the influence of different temperatures and frequencies on the frequency stability and frequency accuracy of the rubidium atom small optical clock, and specific parameters in a state transition matrix phi, a noise driving matrix gamma and an observation matrix H are determined according to the influence relationship, so that the medium-term and long-term frequency stability and frequency accuracy of the rubidium atom small optical clock can be further improved.
Finally, it should be noted that the above-mentioned embodiments are only preferred embodiments of the present invention, and do not limit the scope of the present invention. Specifically, in the process of controlling the temperature of the narrow linewidth laser and the atomic gas chamber, the precision temperature control of the narrow linewidth laser and the atomic gas chamber can be influenced by the process noise which is fed back to the servo control port by the acquisition noise and the signal in the temperature acquisition process; meanwhile, the Kalman filtering can be used for fully utilizing the frequency of the previous moment to predict the frequency of the next moment, the filtering equation can be used for efficiently predicting the frequency state in the measurement process, the estimated mean square error is minimized, and meanwhile, the frequency data is corrected to ensure a high-precision frequency measurement value; meanwhile, the multidimensional Kalman filtering technology with more parameter influences is also suitable for implementation. These techniques are well known to those skilled in the art and will not be described in detail. It will be understood by those skilled in the art that various modifications and equivalent substitutions may be made to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Therefore, the protection scope of the present invention is subject to the limitation of the claims.
Claims (5)
1. A rubidium atom small optical clock realizing method based on Kalman filtering temperature and frequency control integrates temperature control parameters with measurement values of a laser and an atom gas chamber by using a temperature servo controller and a Kalman filter, realizes closed-loop temperature control of the laser and the atom gas chamber, and achieves self-adjustment of the temperature control parameters; filtering is carried out by utilizing a Kalman filter, and the filtered signal is fed back to the temperature servo controller, so that the noise generated by the devices, cables and the response bandwidth of the devices in the temperature monitoring process is reduced; estimating the frequency value of the next moment by using the frequency value of the previous moment through Kalman filtering, efficiently predicting the frequency state in the measurement process by using a filtering equation, minimizing the estimated mean square error, and correcting frequency data; the method comprises the following steps:
step 1) arranging a semiconductor cooler TEC at the bottom of a narrow-linewidth laser, and winding a heating plate on the outer side of an atomic gas chamber;
step 2) arranging a first thermistor at the narrow-linewidth laser, and arranging a second thermistor at the atomic gas chamber;
step 3) measuring a set of voltages V1outAnd V2outThe difference of the output values of (a); v1outSet voltage value for temperature power supply, V2outThe temperature voltage value measured by the first thermistor;
measure a set of voltages V1outAnd V2outThe difference in output values of (a), i.e.: v1out1-V2out1、V1out2-V2out2、...V1outn-V2outn，V1out1、V1out2...V1outnSet voltage value of temperature power supply at sampling point at time 1, 2.. n, V2out1、V2out2...V2outnThe temperature voltage value measured by the first thermistor at the sampling point at the time 1, 2.. n, wherein n represents the sampling time;
step 4), taking the measured voltage output value difference data as an initial value of a Kalman filtering module, and observing to obtain temperature data; setting a covariance initial value, a noise variance initial value and an observation noise initial value of covariance;
the sampling point when the Kalman filtering is started is represented as j, and j is a certain sampling moment of Kalman filtering temperature control;
obtaining an initial value of Kalman filtering, namely T according to the relation of the voltage value, the resistance value and the resistance and the temperaturej＝A(V1outj-V2outj)+T0(j＝1)，Tj(j is 1) is an initial value of Kalman filtering, A is a variation coefficient between a voltage difference value and a temperature relation formula, and T is0A constant that is a voltage difference and temperature relationship;
the initial value of the temperature covariance p (j) is set to the square of the measured voltage difference, i.e.: p (j) ═ V1outj-V2outj)2(j ═ 1); setting an initial value Q (j) of the noise variance influencing the frequency drift as the square of the difference value between the temperature value at the moment and all the current measured temperature values, namely:
setting the observation noise initial value R (j) as the square of the difference between the voltage difference value at the next moment and the voltage difference value at the moment: r (j) [ (V1 out)j-V2outj)-(V1outn-V1outn)]2(j＝1)；
Step 5), performing Kalman filtering calculation;
in the kalman filter calculation, a state transition matrix Φ, a noise drive matrix Γ, and an observation matrix H are assigned to 1, that is, Φ ═ 1, Γ ═ 1, and H ═ 1, the prediction covariance at the next time is P (j + i | j) ═ P (j) + q (j), and the gain at the next time is K (j +1) ═ P (j +1| j)/[ P (j +1| j) + r (j)]Updating the covariance after Kalman filtering at the next moment to be P (j +1) ═ 1-K (j +1)]P (j +1| j), and updating the temperature estimation value after kalman filtering at the next time to be T (j +1) ═ T (j) + K (j +1) × a [ (V1 out)j+1-V2outj+1)-(V1outj-V2outj)]；
Step 6) obtaining a noise variance, an observation noise value, a prediction covariance and a gain which influence the temperature drift at the next moment, and further obtaining an updated temperature estimation value after the next moment Kalman filtering;
obtaining a noise variance Q (j +1) influencing temperature drift at the moment j +1 and an observation noise value R (j +1) at the moment j +1 by using j as j +1, obtaining a prediction covariance P (j +2| j +1) at the next moment and a gain K (j +2) at the next moment from the obtained P (j +1), Q (j +1) and R (j +1), further obtaining an updated temperature estimation value T (j +2) after Kalman filtering at the next moment, and so on to obtain a Kalman filtering temperature estimation value at the next moment;
step 7) measuring to obtain a group of error signal values; calculating according to the relation between the error signal and the laser frequency to obtain an initial value of Kalman filtering; setting a covariance initial value of covariance, a noise variance initial value influencing frequency drift and an observation noise initial value;
through accurate accuse temperature control, narrow linewidth laser power drive narrow linewidth laser output laser, during laser incided atomic air chamber, obtained a set of error signal, measure the value of a set of error signal: err1、Err2...Errk...ErrSK represents a sampling time, and k represents any one of sampling time from 1 to S;
let z be taken as a sampling point when Kalman filtering is started, wherein z is the frequency control sampling time of Kalman filtering, and the sampling point of Kalman filtering is recorded as 1, 2.. z.. R, and z is taken as any one of 1 to RSampling time; the relationship between the error signal and the laser frequency can be deduced according to the error signal, and an initial value f (z) of Kalman filtering, namely f (z) B Err can be obtainedz+f0(z ═ 1), the initial covariance value of the covariance p (z) is set to the square of the measurement error signal, i.e. the square of the measurement error signal
The initial value of the noise variance q (z) affecting the frequency drift is set as the square of the difference between the frequency value at the moment and all the current measured frequency values, i.e.:
the initial value of the observed noise r (z) is set to the square of the difference between the error signal of the next moment and the current error signal, i.e.: r (z) ═ Errz-ErrS]2(z＝1)；
Step 8) performing Kalman filtering calculation to obtain the prediction covariance, the gain, the covariance after Kalman filtering and the temperature estimation value after Kalman filtering at the next moment;
the frequency is a one-dimensional space matrix which changes along with time, and in Kalman filtering calculation, a state transition matrix phi, a noise driving matrix gamma and an observation matrix H are assigned to be 1, namely phi is 1, gamma is 1 and H is 1; the prediction covariance at the next time is P (z +1| z ═ P (z + q (z)), and the gain at the next time is K (z +1) ═ P (z +1| n + i)/[ P (z +1| z) + r (z))](ii) a Updating the covariance of the Kalman filter at the next time to P (z +1) ═ 1-K (z +1)]P (z +1| z), and f (z +1) ═ f (z) + K (z +1) × B (Err) as the temperature estimation value after updating the kalman filter at the next timez+1-Errz)；
Step 9) further obtaining the prediction covariance, the gain, the covariance after Kalman filtering and the temperature estimation value after Kalman filtering at the next moment after the step 8);
obtaining a noise variance Q (z +1) affecting temperature drift at the moment z +1 and an observation noise value R (z +1) at the moment z +1 by making z equal to z +1, obtaining a prediction covariance P (z +2| z +1) at the next moment and a gain K (z +2) at the next moment from P (z +1), Q (z +1) and R (z +1), and further obtaining an updated frequency estimation value f (z +2) after next Kalman filtering, thereby obtaining a Kalman filtering frequency estimation value at the next moment;
the one-dimensional Kalman filtering module outputs a Kalman filtering frequency estimation value to the frequency servo controller, the frequency servo controller feeds back the filtered temperature control parameters to the laser power supply, prediction of frequency of the rubidium atom small optical clock is achieved, influence of noise in a loop on frequency data is reduced, automatic adjustment of the frequency control parameters is achieved, the laser frequency is locked on a transition spectral line of rubidium atoms, and the high-frequency stability rubidium atom small optical clock based on Kalman filtering temperature and frequency control is obtained.
2. The method for implementing the rubidium atomic small optical clock based on the kalman filtering temperature and frequency control, as set forth in claim 1, wherein in step 4), the filtering in the one-dimensional kalman filtering temperature control module and the one-dimensional kalman filtering frequency control module of the rubidium atomic small optical clock based on the kalman filtering temperature and frequency control adopts a bayesian estimation, regression algorithm or exponential smoothing filtering method.
3. The method as claimed in claim 1, wherein step 5) is implemented by performing kalman filtering calculation, specifically assigning the state transition matrix Φ, the noise driving matrix Γ, and the observation matrix H to 1, that is, Φ ═ 1, Γ ═ 1, and H ═ 1, the predicted covariance at the next time is P (j +1| j) ═ P (j) + q (j), and the gain at the next time is K (j +1) ═ P (j +1| j)/[ P (j +1| j) + r j (j)) ];
updating the covariance of the Kalman filter at the next time to be P (j +1) ═ 1-K (j +1)]P (j +1| j), and updating the temperature estimation value after kalman filtering at the next time to be T (j +1) ═ T (j) + K (j +1) × a [ (V1 out)j+1-V2outj+1)-(V1outj-V2outj)]；
For the part of Kalman filtering, the state equation and measurement equation expressions of Kalman are:
X(k+1)＝ΦX(k)+W(k)
Y(k)＝HX(k)+V(k)
wherein, X (k) is a state signal of the system, Y (k) is a measurement signal of the system, phi is a state transition matrix, H is an observation matrix, W (k) is system noise, a corresponding variance matrix is Q, and V (k) is a variance matrix corresponding to the observation noise and is R;
the process of kalman filtering is represented by equations (1) - (5); the method comprises the following steps that (1) the state of a system at the moment k +1 is predicted by the optimal frequency X ^ (k | k) at the moment k, equation (2) a new error is predicted by the last error covariance P (k | k) and process noise Q, equation (3) a Kalman gain at the moment k +1, equation (4) an optimal value at the moment k +1 is updated by using a measured value, and equation (5) an updated error covariance at the moment k + 1;
P(k+1|k)＝ΦP(k|k)ΦT+ΓQΓTformula (2)
K(k+1)＝P(k+1|k)HT[HP(k+1|k)HT+R]TFormula (3)
P (K +1) ═ 1-K (K +1) H ] P (K +1| K) formula (5).
4. A rubidium atom miniatur clock based on Kalman filtering temperature and frequency control comprises: the system comprises a one-dimensional Kalman filtering module, a two-dimensional Kalman filtering module, a temperature servo controller, a frequency servo controller, a temperature control module with a Kalman filtering functional interface and a frequency control module with a Kalman filtering functional interface; the temperature control module with the Kalman filtering functional interface comprises: the temperature control system comprises a temperature power supply, a TEC, a first thermistor, a heating plate, a second thermistor and a one-dimensional Kalman filtering temperature control module; the frequency control module with the Kalman filtering functional interface comprises: the device comprises a laser power supply, a narrow linewidth laser, a rubidium atom air chamber and a one-dimensional Kalman filtering frequency control module;
the temperature power supply in the temperature control module with the Kalman filtering function interface is connected with the TEC and the heating plate, the TEC is tightly attached to the narrow linewidth laser in the frequency control module with the Kalman filtering function interface, the heating plate is wound outside a rubidium atom gas chamber in the frequency control module with the Kalman filtering function interface, the first thermistor is arranged at the narrow linewidth laser, and the second thermistor is arranged at the rubidium atom gas chamber;
the temperature power supply in the temperature control module with the Kalman filtering function interface outputs V1out and V1 'out and inputs the output to the one-dimensional Kalman filtering temperature control module, the first thermistor and the second thermistor respectively output V2out and V2' out and input to the one-dimensional Kalman filtering module, wherein V1outSet voltage value for temperature power supply to narrow linewidth laser temperature, V2outThe measured narrow linewidth laser temperature voltage value of the first thermistor, V1' out is the set voltage value of the temperature power supply for the temperature of the rubidium atom gas chamber, V2outFor the temperature and voltage value of the rubidium atom gas chamber measured by the second thermistor, the one-dimensional Kalman filtering module is connected with a temperature servo controller, and the temperature servo controller is connected with a temperature power supply, so that the temperature of the narrow-linewidth laser and the rubidium atom gas chamber is controlled by Kalman filtering;
the method comprises the following steps that a laser power supply is connected with a narrow line width laser, the narrow line width laser outputs light to enter a rubidium atom air chamber to obtain an error signal Err, the error signal Err is input into a one-dimensional Kalman filtering module, the one-dimensional Kalman filtering module is connected with a frequency servo controller, and the one-dimensional Kalman filtering module is connected with the laser power supply, so that the frequency of a rubidium atom small optical clock is controlled through Kalman filtering;
the Kalman filtering temperature control module is controlled by a frequency servo controller, and filtering parameters are fed back to a laser power supply, so that the frequency of the rubidium atom small optical clock is predicted, the influence of noise in a loop on frequency data is reduced, the frequency control parameters are automatically adjusted, the laser frequency is locked on a transition spectral line of rubidium atoms, and the high-frequency stability rubidium atom small optical clock based on Kalman filtering temperature control and frequency control is obtained.
5. The rubidium atomic small optical clock based on kalman filtering temperature and frequency control, according to claim 4, wherein the narrow linewidth laser in the rubidium atomic small optical clock based on kalman filtering temperature control is an external cavity semiconductor narrow linewidth laser, a DFB narrow linewidth laser or a DBR narrow linewidth laser.
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