CN117518229A - Beam position measurement method and system based on pilot frequency - Google Patents
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Abstract
The invention discloses a beam position measuring method and a system based on pilot frequency, which are one-to-one schemes, wherein the schemes comprise: generating two asymmetric pilot signals based on the beam signal; combining the two pilot signals and then coupling the combined pilot signals with beam signals; conditioning and digitally converting the coupled information; the amplitude of the two pilot signals and the amplitude of the beam signal are measured from the digitized signals, the amplitude of the beam signal is compensated by using the amplitudes of the two pilot signals, and then the beam position is calculated by using the compensated beam signal amplitude. According to the scheme, the asymmetric pilot signals are adopted, so that the influence of the third-order intermodulation components of the pilot signals and the beam signals on the position measurement is reduced, the position resolution of the full-digital beam position measurement system is remarkably improved, the influence of Wen Piaochang drift on the position measurement can be effectively restrained, and the stability of the full-digital beam position measurement system is improved.
Description
Technical Field
The present invention relates to the field of digital signal processing, and in particular, to a method and system for measuring a beam position based on pilot frequency.
Background
The high-precision beam position measurement plays a vital role in the stability of the beam track of the accelerator, in order to provide the real-time transverse position of the beam cluster in the beam track, the high-precision amplitude extraction of four channels is required to be realized, along with the development of electronics technology, the performances of an ADC (analog-to-digital conversion) chip in terms of sampling rate, analog bandwidth, resolution and the like are obviously improved, meanwhile, the FPGA (field programmable gate array) technology for digital signal processing is mature, and currently, the mainstream BPM (beam position measurement system) system is a full-digital architecture BPM system for performing down-conversion in a digital domain, and an analog circuit is generally only responsible for few functions such as filtering, gain control and the like.
Because gains of analog devices and analog-to-digital conversion devices in the circuit are different, gain inconsistency is necessarily existed among channels, and the gains of the analog devices and the analog-to-digital conversion devices drift with different degrees along with temperature and time, so that the position accuracy of the finally measured beam current is reduced and drift occurs. A method for compensating the gain inconsistency between channels in real time features that pilot signal is added to original signal to make the gain received by pilot signal approximately same as that of original signal, digital signal processing is carried out to extract the amplitude of beam signal and pilot signal, and the amplitude of pilot signal is used to compensate.
However, with the continuous development of synchrotron radiation light sources, the brightness is higher and the emittance is smaller, and the requirement on the stability of beam current orbit is higher and higher, especially for the fourth generation synchrotron radiation light source based on diffraction limit storage ring, the resolution and stability of the beam current position measuring system are highly required. At present, some beam position measuring methods for compensating gain inconsistency among channels exist, but the requirements of a fourth generation synchronous radiation light source based on a diffraction limit storage ring are difficult to meet, and the problems of insufficient resolution, insufficient temperature stability and the like exist.
In view of this, the present invention has been made.
Disclosure of Invention
The invention aims to provide a beam position measurement method and system based on pilot frequency, which adopts an asymmetric pilot frequency signal to reduce the influence of the pilot frequency signal and a third-order intermodulation component of the beam signal on position measurement, obviously improves the position resolution of a full-digital beam position measurement system, can effectively inhibit the influence of Wen Piaochang drift on position measurement, and improves the stability of the full-digital beam position measurement system.
The invention aims at realizing the following technical scheme:
a pilot-based beam position measurement method, comprising:
step 1, generating two asymmetric pilot signals based on beam signals;
step 2, coupling the two pilot signals with the beam signal after synthesizing the two pilot signals;
step 3, conditioning and digitally converting the coupled information;
and 4, measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
A pilot-based beam position measurement system, comprising:
a pilot signal generation circuit for generating two asymmetric pilot signals based on the beam signal;
the pilot frequency coupling module is used for coupling the two pilot frequency signals after being synthesized with the beam current signals;
the analog conditioning and digital conversion module is used for conditioning and digital converting the coupled information;
the digital signal processing module is used for measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
The technical scheme provided by the invention can be used for measuring the beam position in the synchronous accelerator and compensating gain inconsistency among channels caused by Wen Piaochang drift and other factors so as to obviously improve the measurement accuracy of a DBPM system (Digital Beam Position Monitor, full-digital beam position measuring system), and the basic idea is to add two asymmetric pilot signals into a beam signal, so that the gain received by the pilot signals is approximately the same as that of the beam signal, and the gain inconsistency among channels is compensated and corrected by extracting the pilot signal amplitude through digital down-conversion.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings that are needed in the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a beam position measurement method based on pilot frequency according to an embodiment of the present invention;
FIG. 2 is a time domain waveform diagram of a coupled signal according to an embodiment of the present invention;
FIG. 3 is a graph of a coupled signal provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of a DBPM system according to an embodiment of the present invention;
FIG. 5 is a graph of the results of a horizontal resolution test during an experiment provided by an embodiment of the present invention;
FIG. 6 is a graph of the results of a vertical resolution test during an experiment provided by an embodiment of the present invention;
FIG. 7 is a graph showing the comparison of the position measurements before and after horizontal position compensation under temperature change according to an embodiment of the present invention;
FIG. 8 is a graph showing the comparison of vertical position compensation before and after position measurement under temperature change according to an embodiment of the present invention;
fig. 9 is a schematic diagram of a beam position measurement system based on pilot frequency according to an embodiment of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are only some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to fall within the scope of the invention.
The terms that may be used herein will first be described as follows:
the terms "comprises," "comprising," "includes," "including," "has," "having" or other similar referents are to be construed to cover a non-exclusive inclusion. For example: including a particular feature (e.g., a starting material, component, ingredient, carrier, formulation, material, dimension, part, means, mechanism, apparatus, step, procedure, method, reaction condition, processing condition, parameter, algorithm, signal, data, product or article of manufacture, etc.), should be construed as including not only a particular feature but also other features known in the art that are not explicitly recited.
The term "consisting of … …" is meant to exclude any technical feature element not explicitly listed. If such term is used in a claim, the term will cause the claim to be closed, such that it does not include technical features other than those specifically listed, except for conventional impurities associated therewith. If the term is intended to appear in only a clause of a claim, it is intended to limit only the elements explicitly recited in that clause, and the elements recited in other clauses are not excluded from the overall claim.
The method and system for measuring the beam position based on the pilot frequency provided by the invention are described in detail below. What is not described in detail in the embodiments of the present invention belongs to the prior art known to those skilled in the art. The specific conditions are not noted in the examples of the present invention and are carried out according to the conditions conventional in the art or suggested by the manufacturer. The apparatus used in the examples of the present invention did not identify the manufacturer and was a conventional product commercially available.
Example 1
The embodiment of the invention provides a beam position measuring method based on pilot frequency, which is used for measuring the beam transverse position of an accelerator and correcting gain inconsistency of each channel caused by temperature drift and long drift in a DBPM system (Digital Beam Position Monitor, full-digital beam position measuring system). The invention is suitable for a full-digital beam position measuring system for calculating the position by extracting multi-channel amplitude, and the gain of a pilot signal is kept the same as the gain moment of the beam signal by coupling two pilot signals which are asymmetric with respect to the frequency of the beam signal into the beam signal, and the gain of the pilot signal is obtained by digital signal processing after the digitization, so that the gain of the beam signal is compensated. The invention adopts the asymmetric pilot signal to reduce the influence of the third-order intermodulation component of the pilot signal and the beam signal on the position measurement, obviously improves the position resolution of the system, can effectively inhibit the influence of Wen Piaochang drift on the position measurement, and improves the stability of the full-digital beam position measurement system.
As shown in fig. 1, the method mainly comprises the following steps:
step 1, generating two asymmetric pilot signals based on the beam signals.
In the embodiment of the invention, with the accelerator machine clock as a reference, two pilot signals which are homologous to the beam signal and have asymmetric frequencies with respect to the frequency of the beam signal are generated through a Phase Lock Loop (PLL).
In the embodiment of the invention, two phase-locked loops with different frequency dividing ratios can be utilized to respectively generate a pilot signal, and the interval between the frequency of the two pilot signals and the frequency of the beam signal is more than 0.5 f TBT ，f TBT For the convolution frequency, i.e. the spacing is greater than 0.5 times the convolution frequency, two pilot signals are on either side of and about the frequency of the beam signalAnd the asymmetry is realized, so that the aliasing of the third-order intermodulation component of one pilot signal and the beam signal with the other pilot signal is avoided. The difference between the frequency of the two pilot signals and the frequency interval of the beam signal is more than 0.5 and 0.5 f TBT The DBPM system is guaranteed to filter out third-order intermodulation components through filtering extraction even in a TBT mode (the position update rate is equal to the convolution frequency), and the influence of intermodulation harmonics on the position resolution is effectively avoided.
Exemplary: the frequency of the beam signal can be 499.8 MHz, the cyclotron frequency of the accelerator is 624.75 kHz, the two pilot signal frequencies generated by the pilot signal generating circuit are 498.238125 MHz and 500.737125 MHz respectively, and the interval between the two pilot signal frequencies and the frequency of the beam signal is 2.5 times of the cyclotron frequency and 1.5 times of the cyclotron frequency respectively.
And step 2, coupling the two pilot signals with the beam current signals after synthesizing the two pilot signals.
In the embodiment of the invention, two pilot signals are synthesized through a power synthesizer, the synthesized signals are equally divided into four parts through a power distributor and are sent to four channels of a full-digital beam position measuring system, and one part of input pilot signals and beam signals are coupled in each channel to obtain coupling signals of the four channels.
The signal after coupling of each channel has three frequency components, corresponding to two pilot signals and beam signals, respectively.
Taking the example provided in the step 1 as an example, the coupled signal includes three frequency components of 499.8 MHz,498.238125 MHz and 500.737125 MHz, and the time domain waveform diagram and the spectrogram are shown in fig. 2 to 3.
And step 3, conditioning and digitally converting the coupled information.
In the embodiment of the invention, the coupled signals of each channel are amplified and filtered respectively, and then the digitized signals of the four channels are obtained through digital conversion.
And 4, measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
In the embodiment of the invention, the gain inconsistency is compensated for the beam signal amplitude based on the pilot signal amplitude information and the position information is calculated, and because the amplitude-frequency response can be regarded as approximate linearity in a shorter frequency interval, the gain inconsistency is compensated by using the two pilot signal amplitudes to carry out linear interpolation, and the same multiplication and division of the channel amplitudes in the calculation process of the position information has no influence on the result.
Specifically: measuring the amplitude of each channel in two pilot signals and beam signals, and marking four channels as A, B, C, D in turn, and marking the amplitudes of the four channels of the first pilot signal as A, B, C, D in turn、/>、/>、/>The amplitudes of the four channels of the second pilot signal are marked as +.>、/>、/>、/>The amplitudes of the four channels of the beam signal are marked as +.>、/>、/>、/>The frequency interval between the first pilot signal and the beam signal is a, and the frequency interval between the second pilot signal and the beam signal is b.
Taking a horizontal position as an example, the calculation process is as follows:
wherein,、/>、/>、/>original amplitude of the channel for beam signal A, B, C, D, < >>、/>、/>、/>Corresponding to the gain of A, B, C, D channel, V P The pilot signal original amplitude representing each channel is divided into four parts by the power divider, so that the four channels are the same; />、/>、/>、/>Is the measured amplitude of the two pilot signals for each channel.
In the embodiment of the invention, the dual pilot frequency is used, so the concrete calculation mode can be expressed as follows:，/>，/>，the calculation method for obtaining the horizontal position of the beam current signal by taking the above formula into consideration is expressed as follows:
；
in a similar manner, the vertical position of the beam signal can be calculated as:
；
wherein X is the horizontal position of the beam signal, Y is the vertical position of the beam signal,is the sensitivity coefficient in the horizontal direction, < >>Is the vertical sensitivity coefficient.
The scheme provided by the embodiment of the invention mainly has the following advantages:
(1) The invention adopts an asymmetric double pilot frequency structure, improves the compensation effectiveness, simultaneously avoids the aliasing of the third-order intermodulation components of the pilot frequency signal and the beam current signal to the other pilot frequency signal, and ensures that the frequency difference between the intermodulation harmonic wave and the effective signal is at least more than half of the convolution frequency, so that the DBPM system can filter the third-order intermodulation components through filtering extraction even in a TBT mode, and effectively avoids the influence of the intermodulation harmonic wave on the position resolution.
(2) The digital signal processing process is realized in the FPGA, the position calculation can be realized by shifting addition except division, the resource and the power consumption are saved, and the calculated delay is far smaller than the group delay of digital filtering.
For ease of understanding, an example is provided below to illustrate the above method.
In this example, a high-precision low-latency DBPM system based on nuclear detection and nuclear power national emphasis laboratory autonomous design completes a complete exemplary implementation. Fig. 4 is a schematic diagram of the DBPM system in this example, mainly including: the system comprises a pilot signal generating circuit, a sampling circuit, an FPGA (which is used as a digital signal processing module), a pilot coupling module and an analog conditioning module; the sampling circuit, the FPGA and the pilot signal generating circuit are commonly called an analog-to-digital conversion and digital processing module. The pilot signal generation circuit generates two pilot signals (pilot signal 1, pilot signal 2) which are homologous to the beam signal and whose frequencies are asymmetric with respect to the frequency of the beam signal. In the pilot frequency coupling module, two pilot frequency signals are synthesized through a power synthesizer (not shown in the figure), the synthesized signals are equally divided into four parts through a power distributor (called a power distributor for short), the four parts are sent to four channels (called A, B, C, D) of a full-digital beam position measuring system, and one part of the input pilot frequency signals and the beam signals are coupled in each channel to obtain coupling signals of the four channels. The analog conditioning module amplifies and filters the coupling signals of the four channels respectively. The sampling circuit internally comprises four high-speed ADC (analog-to-digital conversion) circuits, and one-to-one undersamples the coupling signals to obtain intermediate frequency digital signals. The intermediate frequency digital signals are sent to an FPGA (field programmable gate array), the amplitude of each channel pilot signal and the amplitude of the beam current signal are obtained through digital signal processing in the FPGA, and the position information of the X direction (horizontal direction) and the Y direction (vertical direction) is obtained through calculation after the compensation is completed by utilizing the pilot signal amplitude. Finally, the FPGA transmits the position information to the upper computer through the high-speed data interface while carrying out digital processing, and provides information required by feedback control.
In order to illustrate the effect of the present invention, the following experiments were performed. In the experiment, a sine wave generator is used for generating 499.8 MHz sine waves, the sine waves are equally divided into four parts by a power distributor to be used as the input (namely beam current signals) of a DBPM system, each part is input into one channel, the pilot frequency signal frequency is 498.238125 MHz and 500.737125 MHz respectively, the interval between the pilot frequency signal frequency and the beam current signal frequency is 2.5 times of the convolution frequency and 1.5 times of the convolution frequency respectively, namely, a is 2.5, and b is 1.5. Finally, 20000 sample data in the FA (Fast Acquisition) mode are selected to calculate standard deviation to obtain the position resolution of the system, the test result is that the resolution in the horizontal direction is 79 nm, the resolution in the vertical direction is 84nm, and compared with the use of symmetrical double pilot frequencies, the resolution is obviously improved, as shown in fig. 5-6. Fig. 7 to 8 show the comparison between the horizontal and vertical positions before and after compensation under the temperature change, and it can be seen that the position drift due to the temperature change is significantly suppressed after the pilot compensation is used.
Fig. 2, 3, 5, 6, 7 and 8 are illustrations of dense line formation in practical situations.
Example two
The present invention also provides a system for measuring beam position based on pilot frequency, which is mainly used for implementing the method provided in the foregoing embodiment, as shown in fig. 9, and the system mainly includes:
a pilot signal generation circuit for generating two asymmetric pilot signals based on the beam signal;
the pilot frequency coupling module is used for coupling the two pilot frequency signals after being synthesized with the beam current signals;
the analog conditioning and digital conversion module is used for conditioning and digital converting the coupled information;
the digital signal processing module is used for measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
In an embodiment of the present invention, the pilot signal generating circuit includes: a phase locked loop; the phase-locked loop generates two pilot signals which are homologous to the beam signal and whose frequency is asymmetric with respect to the frequency of the beam signal with an accelerator machine clock.
In an embodiment of the present invention, the pilot coupling module includes: a power combiner, a power distribution and directional coupler;
the two pilot signals are synthesized by a power synthesizer, the synthesized signals are equally divided into four parts by a power distributor and are sent to four channels of a full-digital beam position measuring system, each channel utilizes a directional coupler to couple one input pilot signal with a beam signal, and the coupling signals of the four channels are obtained.
In an embodiment of the present invention, the analog conditioning and digital conversion module includes: the analog conditioning module and the sampling circuit;
the analog conditioning module is used for amplifying and filtering the coupling signals of each channel respectively;
and the sampling circuit is used for respectively undersampling the signals of each channel output by the analog conditioning module to obtain digitized signals of four channels.
In the embodiment of the invention, the amplitudes of the two pilot signals and the amplitude of the beam signal are measured from the digitized signals, the amplitudes of the beam signal are compensated by using the amplitudes of the two pilot signals, and the beam position is calculated by using the compensated beam signal amplitude, which comprises the following steps:
measuring the amplitude of each channel in two pilot signals and beam signals, and marking four channels as A, B, C, D in turn, and marking the amplitudes of the four channels of the first pilot signal as A, B, C, D in turn、/>、/>、/>The amplitudes of the four channels of the second pilot signal are marked as +.>、/>、/>、/>The amplitudes of the four channels of the beam current signal are sequentially recorded as、/>、/>、/>The frequency interval between the first pilot signal and the beam signal is a, and the frequency interval between the second pilot signal and the beam signal is b, so that the calculation modes of the horizontal and vertical positions of the beam signal are respectively expressed as follows:
；
；
wherein X is the horizontal position of the beam signal, Y is the vertical position of the beam signal,is the sensitivity coefficient in the horizontal direction, < >>Is the vertical sensitivity coefficient.
In view of the technical details related to each module or circuit of the system in the foregoing method embodiments, the details are described in detail, and thus will not be repeated.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional modules is illustrated, and in practical application, the above-described functional allocation may be performed by different functional modules according to needs, i.e. the internal structure of the system is divided into different functional modules to perform all or part of the functions described above.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (10)
1. A method for pilot-based beam position measurement, comprising:
step 1, generating two asymmetric pilot signals based on beam signals;
step 2, coupling the two pilot signals with the beam signal after synthesizing the two pilot signals;
step 3, conditioning and digitally converting the coupled information;
and 4, measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
2. The method of claim 1, wherein generating two asymmetric pilot signals based on the beam signal comprises:
two pilot signals which are homologous to the beam signal and whose frequency is asymmetric with respect to the frequency of the beam signal are generated by a phase-locked loop with reference to the accelerator machine clock.
3. The method for pilot-based beam position measurement according to claim 1, wherein coupling the two pilot signals after combining with the beam signal comprises:
and synthesizing the two pilot signals through a power synthesizer, equally dividing the synthesized signals into four parts through a power distributor, and transmitting the four parts to four channels of a full-digital beam position measuring system, and coupling one part of the input pilot signals with the beam signals in each channel to obtain coupling signals of the four channels.
4. A method of pilot-based beam position measurement according to claim 3, wherein said conditioning and digitizing the coupled information comprises:
the coupled signals of each channel are amplified and filtered respectively, and then the digitized signals of the four channels are obtained through digital conversion.
5. The method of claim 3 or 4, wherein measuring the amplitudes of the two pilot signals from the digitized signal, and compensating the amplitudes of the beam signals with the amplitudes of the two pilot signals, and calculating the beam position with the compensated beam signal amplitudes comprises:
measuring the amplitude of each channel in two pilot signals and beam signals, and marking four channels as A, B, C, D in turn, and marking the amplitudes of the four channels of the first pilot signal as A, B, C, D in turn、/>、/>、/>The amplitudes of the four channels of the second pilot signal are marked as +.>、/>、/>、/>The amplitudes of the four channels of the beam signal are marked as +.>、/>、/>、The frequency interval between the first pilot signal and the beam signal is a, and the frequency interval between the second pilot signal and the beam signal is b, so that the calculation modes of the horizontal and vertical positions of the beam signal are respectively expressed as follows:
；
；
wherein X is the horizontal position of the beam signal, Y is the vertical position of the beam signal,is the sensitivity coefficient in the horizontal direction,is the vertical sensitivity coefficient.
6. A pilot-based beam position measurement system, comprising:
a pilot signal generation circuit for generating two asymmetric pilot signals based on the beam signal;
the pilot frequency coupling module is used for coupling the two pilot frequency signals after being synthesized with the beam current signals;
the analog conditioning and digital conversion module is used for conditioning and digital converting the coupled information;
the digital signal processing module is used for measuring the amplitude of the two pilot signals and the amplitude of the beam signal from the digital signal, compensating the amplitude of the beam signal by using the amplitude of the two pilot signals, and calculating the beam position by using the amplitude of the beam signal after compensation.
7. The pilot-based beam position measurement system of claim 6, wherein the pilot signal generation circuit comprises: a phase locked loop; the phase-locked loop generates two pilot signals which are homologous to the beam signal and whose frequency is asymmetric with respect to the frequency of the beam signal with an accelerator machine clock.
8. The pilot-based beam position measurement system of claim 6, wherein the pilot coupling module comprises: a power combiner, a power distribution and directional coupler;
the two pilot signals are synthesized by a power synthesizer, the synthesized signals are equally divided into four parts by a power distributor and are sent to four channels of a full-digital beam position measuring system, each channel utilizes a directional coupler to couple one input pilot signal with a beam signal, and the coupling signals of the four channels are obtained.
9. The pilot-based beam position measurement system of claim 8, wherein the analog conditioning and digitizing conversion module comprises: the analog conditioning module and the sampling circuit;
the analog conditioning module is used for amplifying and filtering the coupling signals of each channel respectively;
and the sampling circuit is used for respectively undersampling the signals of each channel output by the analog conditioning module to obtain digitized signals of four channels.
10. The pilot-based beam position measurement system of claim 8 or 9, wherein measuring the amplitudes of the two pilot signals from the digitized signal and the amplitudes of the beam signals, compensating the amplitudes of the beam signals with the amplitudes of the two pilot signals, and calculating the beam position with the compensated beam signal amplitudes comprises:
measuring the amplitude of each channel in two pilot signals and beam signals, and marking four channels as A, B, C, D in turn, and marking the amplitudes of the four channels of the first pilot signal as A, B, C, D in turn、/>、/>、/>The amplitudes of the four channels of the second pilot signal are marked as +.>、/>、/>、/>The amplitudes of the four channels of the beam signal are marked as +.>、/>、、/>The frequency interval between the first pilot signal and the beam signal is a, and the frequency interval between the second pilot signal and the beam signal is b, so that the calculation modes of the horizontal and vertical positions of the beam signal are respectively expressed as follows:
；
；
wherein X is the horizontal position of the beam signal, Y is the vertical position of the beam signal,is the sensitivity coefficient in the horizontal direction,is the vertical sensitivity coefficient.
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| US20160065286A1 (en) * | 2014-08-27 | 2016-03-03 | Intel IP Corporation | Apparatus, system and method of beam tracking |
| US20180042045A1 (en) * | 2015-03-09 | 2018-02-08 | Lg Electronics Inc. | Method for performing scanning in wireless access system supporting millimeter wave, and device supporting same |
| CN114706114A (en) * | 2022-06-06 | 2022-07-05 | 中国科学技术大学 | Electron storage ring beam current track measurement and control equipment and method |
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