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CN119814210A - A time synchronization method for space laser communication - Google Patents

A time synchronization method for space laser communication Download PDF

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Publication number
CN119814210A
CN119814210A CN202411921189.8A CN202411921189A CN119814210A CN 119814210 A CN119814210 A CN 119814210A CN 202411921189 A CN202411921189 A CN 202411921189A CN 119814210 A CN119814210 A CN 119814210A
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time
frequency
communication
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丁劲锋
刘念
莫玲莹
覃发超
华鸣峰
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Jiangsu Intelligent Workshop Technology Research Institute Co ltd
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    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention provides a time synchronization method of space laser communication, which relates to the technical field of laser communication and comprises the steps of encoding a time signal, modulating a frequency signal, compositing the time signal and the frequency signal into an original communication signal, transmitting the original communication signal from a ground end to a space end, transmitting the original communication signal in space, receiving the signal by the space end, demodulating the received communication signal by the space end, synchronizing the obtained received time signal by a time synchronization algorithm, demodulating the received communication signal by the space end, compensating the phase error of the obtained frequency signal, compositing the synchronized time signal and the frequency signal after compensating the phase error by a multiplexing module, and completing the frequency time synchronization of the communication signal.

Description

Time synchronization method for space laser communication
Technical Field
The invention relates to the technical field of laser communication, in particular to a time synchronization method for space laser communication.
Background
With the continuous progress of the spatial technology, the spatial laser communication technology is mature and is continuously fused with other technologies such as quantum communication and the like. The space laser communication has the advantages of high bandwidth, strong confidentiality and the like, is widely applied to the fields of data transmission, quantum communication, time-frequency transmission, ranging and the like, and particularly in the space quantum communication, the laser communication can provide time synchronization and other services for the quantum communication, and the combination of the space laser communication and the time synchronization has a huge application prospect.
In many fields, such as basic research, aerospace, national security, etc., high-precision time metering and time synchronization techniques are of paramount importance. With the development of the related technology, the requirements on time synchronization precision are also higher and higher, for example, when the quantum communication rate is improved, the requirements on time synchronization precision and the time precision of the detector are better than the order of magnitude of 50ps, so as to meet the requirements on high-speed data transmission, accurate control and the like.
The traditional time synchronization method based on electronics has certain limitations when facing high-speed space laser communication. The synchronization precision of the low-frequency synchronization signal extracted from laser communication is about 100ps, so that the synchronization requirement of higher precision is difficult to meet, and researchers are prompted to explore a new time synchronization method to improve the synchronization precision.
Disclosure of Invention
In order to solve the technical problems, the invention provides a time synchronization method for space laser communication, which comprises the following steps:
S1, after time signal coding and frequency signal modulation, compounding the time signal coding and frequency signal modulation into an original communication signal, transmitting the original communication signal from a ground end to a space end, and receiving the signal by the space end after the signal is transmitted in space;
S2, demodulating the received communication signal by the space end, and carrying out synchronous processing on the obtained received time signal by a time synchronous algorithm;
And S3, demodulating the received communication signal by the space end, compensating the phase error of the obtained frequency signal, and compositing the synchronized time signal and the frequency signal subjected to phase error compensation by the multiplexing module to complete the frequency-time synchronization of the communication signal.
Further, in step S2, the linear correction clock expression is:
wherein L i (t) is the logic time of the second time signal node i at time t, For the drift correction parameter of the second time signal node i,For the offset correction parameter of the second time signal node i, τ i (t) is the hardware time and V is the set of time nodes.
3. The method of time synchronization for spatial laser communication of claim 2, wherein the drift correction parameterAnd drift correction parametersThe updated iterative expression of (a) is:
Where η is the learning rate and E is the time error function.
Further, in step S3, the actual crystal oscillator frequency f i (t) is expressed as:
fi(t)=αi(t)f0,i∈V
Wherein alpha i (t) is clock drift of a communication signal node i at the moment t, f 0 is nominal frequency of a crystal oscillator, and V is a set of time nodes;
At time t, the phase expression of the oscillation source of the signal transmitted by the ground transmitting terminal i is as follows:
fi=f0+Δfi
Wherein i is a transmitting end, j is a receiving end, f i is the frequency of the ground transmitting end at time t 0, f 0 is a nominal frequency, Δf i is a frequency offset relative to the nominal frequency, N i (t) is phase noise for the initial phase;
At time t+t ij, the phase expression of the oscillation source of the synchronous signal received by the space receiving end j is:
Wherein, For the spatial receiver to receive the initial phase of the signal, n j(t+tij) is the spatial receiver phase noise.
Further, after the signals are received at the space and the ground, the signals are demodulated, and a phase synchronization error compensation expression is obtained as follows:
Wherein, Is a space endAfter modulation, the initial phase of the signal is received by the space receiving endIs used for the phase difference of (a),Is a ground endAfter modulation, the initial phase of the signal is received by the ground receiving endIs a phase difference of (a) and (b).
In step S1, the time signal is divided into a plurality of time nodes, corresponding pulse positions are set for different time nodes, the time signal is encoded by the pulse positions, and the obtained encoded signal carries the original time signal information in the distribution of pulses at different time nodes.
Compared with the prior art, the invention has the following beneficial technical effects:
The accurate time synchronization effect is that the time reference of the space end and the ground end can be effectively calibrated by encoding the time signal at the ground end and then processing the time signal at the space end by adopting a time synchronization algorithm. For example, in some satellite communication systems, this approach may enable accurate synchronization of device time on the satellite with time at the ground control center, providing a uniform time standard for subsequent data transmission and command interaction. Accurate time synchronization is helpful to improve the overall efficiency of the communication system, for example, in the timing data transmission task, the data can be ensured to be transmitted and received at an accurate time point, and the data transmission error caused by time deviation is reduced.
The high-precision compensation effect of the frequency signal is that the phase error compensation of the frequency signal can correct the frequency deviation caused by various interferences (such as atmospheric refraction, equipment noise and the like) of the signal in the space transmission process. This ensures sound quality by recovering the true frequency of the sound by compensating for phase errors, as compared to a high-precision audio transmission system. In space laser communication, high-precision compensation of frequency signals can improve communication quality and reduce error rate. For example, in a high-speed data transmission scenario, an accurate frequency signal may ensure correct demodulation of the digital signal, avoiding bit errors in the data transmission.
The efficient communication signal multiplexing effect is that the time signal subjected to time synchronization and the frequency signal subjected to phase error compensation are compounded through the multiplexing module, so that the communication signal subjected to frequency time synchronization is realized. The multiplexing mode can more effectively utilize communication channel resources and improve the transmission capacity of a communication system. Just like in a multi-tasking communication system, signals with different functions (such as voice signals and data signals) are transmitted in the same channel by multiplexing technology, which increases the practicability and flexibility of the system. In space laser communication, the multiplexed signal can simultaneously transmit various types of data, such as scientific detection data, control instructions and the like, on the premise of ensuring time and frequency precision, thereby enhancing the comprehensive performance of a communication system.
The enhanced communication reliability has the effect that the anti-interference capability of communication signals is improved through the accurate control of time and frequency in the whole process from the transmission and the transmission of the signals to the processing after the receiving. In a complex spatial environment, signals are susceptible to distortion or error from various interfering factors. This time synchronization and frequency compensation technique corrects these problems so that the communication system operates more stably in the face of interference. For example, during peak solar activity, electromagnetic interference in a space environment is enhanced, and a communication system adopting the technology can better maintain the reliability of communication and ensure accurate transmission of information.
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 to a person skilled in the art.
FIG. 1 is a flow chart of a method for synchronizing time of space laser communication according to the present invention;
fig. 2 is a schematic diagram of a spatial laser communication system according to the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
In the drawings of the specific embodiments of the present invention, in order to better and more clearly describe the working principle of each element in the system, the connection relationship of each part in the device is represented, but only the relative positional relationship between each element is clearly distinguished, and the limitations on the signal transmission direction, connection sequence and the structure size, dimension and shape of each part in the element or structure cannot be constructed.
Fig. 1 is a schematic flow chart of a time synchronization method for space laser communication according to the present invention, which includes the following steps:
S1, after time signal coding and frequency signal modulation, the time signal coding and frequency signal modulation are combined into an original communication signal, the original communication signal is transmitted from a ground end to a space end, and the signal is received by the space end after being transmitted in space.
As shown in fig. 2, in space laser communication, the transmission and the reception of the communication signal of each ground station need to pass through the lidar, the lidar of the transmitting end and the lidar of the receiving end are not on the same carrier platform, and the transmitting end and the receiving end use independent frequency local vibration sources, so that the signal has the influence of synchronization errors in the communication process. At this time, the laser radars at the receiving end and the transmitting end generate time synchronization errors due to the influence of various factors in the space due to the non-uniform trigger pulse time sequence. On the other hand, signals of the ground station and the space satellite are derived from different oscillation sources, and the fixed frequency deviation and the random frequency deviation between the receiving frequency vibration sources and the receiving frequency vibration sources can cause phase errors in communication signals, so that the accuracy of the frequency signals is further affected.
In the embodiment, the time signal is divided into a plurality of time nodes, and corresponding pulse positions are set for different time nodes, so that the time signal is encoded by the pulse positions, and the subsequent time synchronization operation is more convenient.
And (3) time node division, namely determining the total duration of the time signal, and reasonably dividing the whole time signal into a plurality of time nodes with equal intervals or unequal intervals according to the factors such as the requirement of the follow-up synchronous operation precision, signal characteristics and the like. For example, if the total duration of the time signal is T, the plan is divided into n time nodes, and the time nodes may be divided at equal intervals Δt=t/n, to obtain a time node sequenceWhere t 0=0,t1=Δt,t2 = 2 Δt, and so on.
Pulse position setting, namely, for each divided time node, determining whether a pulse and specific characteristics (such as pulse amplitude and the like if related requirements exist) of the pulse are set on the time node according to a preset coding rule. For example, a simple rule may be set that odd numbered time nodes set pulses and even numbered time nodes not set pulses. Or to pulse 0 and 1 at the corresponding time nodes or not according to more complex coding logic, such as binary coding according to some data correspondence.
And the coding is realized by processing the whole time signal one by one time node according to the pulse position setting rule, and finally realizing the coding of the time signal by using the pulse position. The obtained coded signals carry the related information of the original time signals according to the distribution condition of pulses at different time nodes, thereby being convenient for subsequent operations such as time synchronization and the like.
The frequency signal is phase modulated, and the change in frequency is reflected by changing the phase of the carrier wave.
The carrier signal is determined by first selecting an appropriate carrier signal, typically in the form of carrier amplitude, carrier angular frequency, and carrier initial phase. The parameters of the carrier signal are determined according to practical application situations, such as transmission channel characteristics, receiving end requirements, and the like.
Analyzing the change of the frequency signal, namely acquiring the frequency signal to be subjected to phase modulation, and setting the expression as the expression. It is necessary to define the time-dependent law of the frequency signal, for example it may be a frequency signal which varies according to a certain functional law (such as a sinusoidal function, a sawtooth function, etc.), or a complex signal comprising a plurality of frequency components.
And determining a phase modulation rule, namely establishing the phase modulation rule according to the relation between the frequency signal change and the change expected to be reflected by the phase modulation. A common simple rule is linear phase modulation, i.e. to let the phase of the carrier change in a linear relation with the change of the frequency signal, e.g. a proportionality constant, the value of which can be determined according to specific modulation requirements, in order to make the frequency change accurately reflected by the change of the carrier phase.
And (3) performing phase modulation, namely applying the determined phase modulation rule to the carrier signal to obtain a modulated signal. Taking linear phase modulation as an example, the modulated signal expression becomes. In this way, it is achieved that the change of the frequency signal is reflected by changing the phase of the carrier wave, so that the modulated signal characteristics can be used later in the links of signal transmission, processing, etc.
The coded time signal and the modulated frequency signal are compounded to a laser carrier wave through a wavelength division multiplexing module to obtain an original communication signal, and after the original communication signal is transmitted through space communication, the signal is interfered by various media and noise in the space, so that the original communication signal received in the space is called a received communication signal.
S2, demodulating the received communication signal by the space end, and carrying out synchronous processing on the obtained received time signal by a time synchronous algorithm;
When the space end processes the received communication signal, the time synchronization of the communication is calculated by using a time synchronization algorithm, and the time synchronization algorithm has the characteristics of strong stability and high reliability. The consistency time synchronization algorithm is to integrate time data of all or most time nodes to obtain a time reference, and the time synchronization of the whole network is not greatly influenced by faults or clock disorder of individual time nodes. Meanwhile, each time node of the consistency time synchronization algorithm has no hierarchy, so that the energy consumption of each node in the time synchronization process is balanced, and the network life of the space communication is effectively prolonged.
The time nodes are synchronized to a consistent time, which is referred to as the global time. The global time is selected by integrating all or most of the node time, and the linear correction clock expression is:
wherein L i (t) is the logic time of node i at time t in the received communication signal, To receive the drift correction parameters for node i in the communication signal,For receiving an offset correction parameter for node i in a communication signal, τ i (t) is the hardware time and V is the set of time nodes.
The drift correction parameters and the updated iterative expression of the drift correction parameters are as follows:
Where η is the learning rate and E is the time error function.
Iterative updating of its own drift correction parameters according to the expression of the algorithmOffset correction parameter
And (3) carrying out multiple iterations through a time synchronization algorithm, and updating drift correction parameters and cheap correction parameters in the model. The logical time of all time nodes tends to be global. Global time refers to a consistent time reference that all time nodes commonly follow in the time synchronization process. For the consistent time synchronization algorithm, the global time is derived based on a combination of all or most of the node time. After the time synchronization starts, the node periodically broadcasts a time data packet. The time data packet at least contains the hardware time of the time node when the data packet is transmitted. After receiving the time data packet, the arbitrary time node i records the hardware time tau i (t) of the received data packet, according to the current parameter value and the received time information, the logic time of the node can be calculated, the logic time is compared with the time of other nodes or the global time, the time error is calculated, and the time difference with a certain reference node or the deviation of the global time obtained by the time integration of a plurality of nodes can be calculated.
The space terminal demodulates the received communication signal to obtain a received time signal, and through the steps, the logic time obtained by iteration of the received time signal is used as global time, namely the time synchronization time which is needed to be obtained, and the synchronized time signal is used as a recovery time signal.
And S3, demodulating the received communication signal by the space end, compensating the phase error of the obtained frequency signal, and compositing the synchronized time signal and the frequency signal subjected to phase error compensation by the multiplexing module to complete the frequency-time synchronization of the communication signal.
In the communication transmission process, the time of the time node is usually composed of a crystal oscillator and peripheral circuits thereof, the crystal oscillator is a key component for generating a clock signal, the actual oscillation frequency of the crystal oscillator cannot be identical to the nominal frequency thereof, and the problems cause that the crystal oscillator cannot provide absolute accurate time.
The actual crystal oscillator frequency expression is:
fi(t)=αi(t)f0,i∈V
Where α i (t) is the clock drift of the communication signal node i at time t, f 0 is the nominal frequency of the crystal oscillator, and V is the set of time nodes.
After the actual crystal oscillator frequency is obtained, the frequency error caused by the difference of the nominal frequency and other factors can be eliminated.
In order to improve the precision and the safety of the space laser communication, the time synchronization of the communication signals is corrected by compensating the phase synchronization error, so that at the time t, the phase expression of the oscillation source of the signals transmitted by the ground transmitting end i is as follows:
Wherein i is a transmitting end, j is a receiving end, f i is the frequency of the ground transmitting end at time t 0, f 0 is a nominal frequency, Δf i is a frequency offset relative to the nominal frequency, For the ground receiving end to receive the initial phase of the signal, n i (t) is phase noise.
At time t+t ij, the phase expression of the oscillation source of the synchronous signal received by the space receiving end j is:
Wherein, For the spatial receiver to receive the initial phase of the signal, n j(t+tij) is the spatial receiver phase noise.
After signals are received in space and ground, the signals are modulated, and a phase synchronization error compensation expression is obtained as follows:
Wherein, Is a space endAfter modulation, the initial phase of the signal is received by the space receiving endIs used for the phase difference of (a),Is a ground endAfter modulation, the initial phase of the signal is received by the ground receiving endIs a phase difference of (a) and (b).
Since the frequency signal is previously phase modulated, the phase change of the signal demodulated in the communication signal reflects the change of the signal frequency, using phase synchronization error compensationAnd compensating the phase of the frequency signal demodulated by the transmitted communication signal, eliminating phase errors generated by the frequency signal in the transmission of the communication signal, and further reducing the influence of the frequency on the accuracy of the frequency signal.
The synchronous time signals and the phase error compensated frequency signals in the S2 and the S3 are combined to the laser carrier wave through a wavelength division multiplexing module, the multiplexing module plays a crucial role, and the two key signals subjected to different processing can be effectively integrated together to complete frequency and time synchronization of communication signals.
The synchronized time signal has high accuracy and stability, in the communication system, the time synchronization is the basis for ensuring accurate coordination and interaction among the nodes, and the time signal can provide an accurate time reference for the communication process after the synchronization processing, so that the communication among different devices can be performed on the correct time node, and communication confusion and errors caused by inconsistent time are avoided.
The frequency signal after phase error compensation also has higher quality and reliability, the existence of the phase error can possibly produce adverse effects on the transmission and processing of the signal, and through effective compensation measures, the effects can be greatly reduced, the frequency signal after compensation is obviously improved in the aspects of frequency stability and the like, and powerful guarantee is provided for high-quality transmission of communication signals.
By using the phase synchronization error compensation, the unconventional phase caused by factors such as non-ideal antenna characteristics, change of transmission path length and the like can be reduced, the receiving and transmitting phase noise can be extracted more conveniently, the phase noise is better removed from the signal, and the influence on signal communication transmission is reduced.
By extracting and removing the frequency and phase errors, the reliability and safety of the signals in the space laser communication are better improved, and the influence received in the time synchronization process is greatly reduced, so that the communication signals have lower time delay.
In a preferred embodiment, according to the above-mentioned time synchronization method of space laser communication, space laser communication is not susceptible to electromagnetic interference and radio frequency interference, and compared with conventional radio communication, laser communication has stronger anti-interference capability, and can realize reliable time synchronization in a complex electromagnetic environment.
In the above embodiments, it may be implemented in whole or in part by software, hardware, firmware, or any combination thereof. When implemented in software, may be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When loaded and executed on a computer, produces a flow or function in accordance with embodiments of the present application, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a computer network, or other programmable apparatus. The computer instructions may be stored in or transmitted across a computer-readable storage medium. The computer readable storage medium may be any available medium that can be accessed by a computer or a data storage device such as a server, data center, etc. that contains an integration of one or more available media. The usable medium may be a magnetic medium (e.g., floppy disk, hard disk, tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid State Disk (SSD)), etc.
While the application has been described with reference to certain preferred embodiments, it will be understood by those skilled in the art that various changes and substitutions of equivalents may be made and equivalents will be apparent to those skilled in the art without departing from the scope of the application. Therefore, the protection scope of the application is subject to the protection scope of the claims.

Claims (6)

1. A method for time synchronization of spatial laser communication, comprising the steps of:
S1, after time signal coding and frequency signal modulation, compounding the time signal coding and frequency signal modulation into an original communication signal, transmitting the original communication signal from a ground end to a space end, and receiving the signal by the space end after the signal is transmitted in space;
S2, demodulating the received communication signal by the space end, and carrying out synchronous processing on the obtained received time signal by a time synchronous algorithm;
And S3, demodulating the received communication signal by the space end, compensating the phase error of the obtained frequency signal, and compositing the synchronized time signal and the frequency signal subjected to phase error compensation by the multiplexing module to complete the frequency-time synchronization of the communication signal.
2. The method for time synchronization of spatial laser communication according to claim 1, wherein in step S2, the linear correction clock expression is:
wherein L i (t) is the logic time of the second time signal node i at time t, For the drift correction parameter of the second time signal node i,For the offset correction parameter of the second time signal node i, τ i (t) is the hardware time and V is the set of time nodes.
3. The method of time synchronization for spatial laser communication of claim 2, wherein the drift correction parameterAnd drift correction parametersThe updated iterative expression of (a) is:
Where η is the learning rate and E is the time error function.
4. The method of time synchronization for spatial laser communication according to claim 1, wherein in step S3, the actual crystal oscillator frequency f i (t) is expressed as:
fi(t)=αi(t)f0,i∈V
Wherein alpha i (t) is clock drift of a communication signal node i at the moment t, f 0 is nominal frequency of a crystal oscillator, and V is a set of time nodes;
At time t, the phase expression of the oscillation source of the signal transmitted by the ground transmitting terminal i is as follows:
fi=f0+Δfi
Wherein i is a transmitting end, j is a receiving end, f i is the frequency of the ground transmitting end at time t 0, f 0 is a nominal frequency, Δf i is a frequency offset relative to the nominal frequency, N i (t) is phase noise for the initial phase;
At time t+t ij, the phase expression of the oscillation source of the synchronous signal received by the space receiving end j is:
Wherein, For the spatial receiver to receive the initial phase of the signal, n j(t+tij) is the spatial receiver phase noise.
5. The method of time synchronization for spatial laser communication as set forth in claim 4, wherein the signal is demodulated after the signal is received at the space and the ground, and the phase synchronization error compensation expression is:
Wherein, Is a space endAfter modulation, the initial phase of the signal is received by the space receiving endIs used for the phase difference of (a),Is a ground endAfter modulation, the initial phase of the signal is received by the ground receiving endIs a phase difference of (a) and (b).
6. The method according to claim 1, wherein in step S1, the time signal is divided into a plurality of time nodes, corresponding pulse positions are set for different time nodes, the time signal is encoded by the pulse positions, and the obtained encoded signal carries the original time signal information in the distribution of pulses at different time nodes.
CN202411921189.8A 2024-12-25 2024-12-25 A time synchronization method for space laser communication Pending CN119814210A (en)

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Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070069739A1 (en) * 2005-09-27 2007-03-29 Ronald Quan Method and apparatus to measure differential phase and frequency modulation distortions for audio equipment
CN111708059A (en) * 2020-06-24 2020-09-25 中国科学院国家天文台长春人造卫星观测站 Laser time transfer processing method, system, storage medium, device and application
CN117169908A (en) * 2023-08-25 2023-12-05 中国电子科技集团公司第五十四研究所 A spatial laser ranging system based on microwave photon time-frequency transmission

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20070069739A1 (en) * 2005-09-27 2007-03-29 Ronald Quan Method and apparatus to measure differential phase and frequency modulation distortions for audio equipment
CN111708059A (en) * 2020-06-24 2020-09-25 中国科学院国家天文台长春人造卫星观测站 Laser time transfer processing method, system, storage medium, device and application
CN117169908A (en) * 2023-08-25 2023-12-05 中国电子科技集团公司第五十四研究所 A spatial laser ranging system based on microwave photon time-frequency transmission

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