Error resolving and compensating method for four-satellite ground laser one-way time service based on atmospheric turbulence influence

Abstract

The invention provides an error resolving and compensating method for four-satellite ground laser one-way time service based on atmospheric turbulence influence, and relates to the technical field of satellite time service. Comprising the following steps: constructing an atmospheric turbulence model and a phase screen model; obtaining coordinate values of observation points and coordinate values of a plurality of satellites observed within a preset time length, and selecting four satellites with coincident zenith angles from the observation points; the zenith angles corresponding to the four satellites are imported into the atmospheric turbulence model and the phase screen model, optical pulse signals disturbed by turbulence are reconstructed, and jitter at the arrival time of the optical pulse signals is calculated; on the basis of the coordinate values of the four satellites and the jittering at the arrival time of the optical pulse signal corresponding to each satellite, calculating the earth laser one-way time service error of the satellites and the coordinate calculation value of the observation point; and processing the satellite to-ground laser one-way time service error by using moving average filtering to obtain the compensated and optimized satellite to-ground laser one-way time service error. By using the method, the stability of the one-way time service error is obviously improved.

Description

Technical Field

[0001] The invention relates to the technical field of satellite timing, and in particular to an error solving and compensation method for one-way laser timing of four satellites to the ground under the influence of atmospheric turbulence. Background Art

[0002] In recent years, with the increasing exploration of outer space, satellite navigation systems and precision measurement technologies have been widely used and developed, and the demand for high-precision time synchronization has increased. In fields such as financial transactions, power system synchronization, geophysical measurements, etc., accurate time synchronization is crucial to the performance and stability of the system. The existing space-ground time and frequency synchronization systems that provide timing services to end users mainly include radio wave navigation systems, global satellite navigation systems (GPS / Beidou / GLONASS / Galileo), satellite two-way time comparison systems, etc. However, the radio wave navigation system is limited by factors such as low operating frequency bands, electromagnetic environment, and susceptibility to interference and cannot achieve timing accuracy within microseconds. Although the GPS / Beidou navigation system can achieve a timing accuracy of 10ns, it requires long-term measurement averaging to achieve it. As countries have successively elevated time security to national laws, the importance of higher timing accuracy has become increasingly reflected. How to achieve a more accurate, flexible and stable timing system has become a hot issue at present.

[0003] In this context, laser time transfer technology has emerged. At present, all schemes are based on the classic round-trip time measurement and two-way time comparison method, which benefits from the high symmetric reciprocity of the point-to-point two-way transmission laser atmospheric link. However, in most cases of practical applications, the position of the ground observation station is not fixed, and the two-way time comparison method is difficult to apply. Therefore, we propose a potential high-precision time synchronization method-based on satellite-to-ground laser one-way timing technology. Compared with traditional transmission methods, one-way laser timing technology gives full play to the advantages of short laser wavelength, good directionality, large channel capacity, small influence by the ionosphere, small device volume, power consumption and weight. It overcomes the problem of asymmetric two-way transmission delay and reduces the attenuation of optical signals by the atmosphere. This technology uses multiple (≥4) satellites to transmit laser signals, and ground receivers receive and analyze the signals, so as to achieve high concealment of "receiving but not sending". Dynamically construct "fine time and space" at the required time and area, and realize ultra-high precision navigation and positioning services within the range of multiple laser beam intersections.

[0004] However, the real-time dynamic changes of the non-uniform atmosphere in the near-ground area cause the atmospheric refractive index to fluctuate randomly, forming atmospheric turbulence. This turbulence effect will cause random changes in the light field of the light beam, which is manifested in the degradation of the spatial coherence of the light field, the fluctuation of the beam drift, the fluctuation of the arrival angle and the flicker of the light intensity, resulting in the deterioration of the beam quality of the signal light at the receiving end. Therefore, how to realize the error solution and compensation method of the four-satellite one-way laser timing under the influence of atmospheric turbulence is a problem that technicians in this field need to solve urgently. Summary of the invention

[0005] Purpose of the invention: To propose an error solution and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence, so as to solve the above-mentioned problems existing in the prior art.

[0006] The present invention proposes a method for error calculation and compensation of one-way laser timing of four satellites to the ground under the influence of atmospheric turbulence, comprising the following steps:

[0007] Construct atmospheric turbulence model and phase screen model;

[0008] Obtain the coordinate value of the observation point and the coordinate values ​​of several satellites observed within a predetermined time, and select four satellites whose zenith angles meet the preset conditions;

[0009] The zenith angles corresponding to the selected four satellites are introduced into the atmospheric turbulence model and the phase screen model to reconstruct the optical pulse signal disturbed by turbulence and calculate the arrival time jitter of the optical pulse signal;

[0010] Based on the coordinate values ​​of the four satellites and the jitter of the arrival time of the optical pulse signal corresponding to each satellite, the satellite-to-ground laser one-way timing error and the coordinate calculation value of the observation point are calculated;

[0011] The satellite-to-ground laser one-way timing error is processed by using a sliding average filter to obtain a compensated and optimized satellite-to-ground laser one-way timing error.

[0012] In a further embodiment, all coordinate values ​​are based on an Earth-centered, Earth-fixed coordinate system.

[0013] In a further embodiment, the atmospheric turbulence model is constructed as follows:

[0014] The Hufnagel-Valley model is selected to calculate the change of refractive index structure constant with height, and the expression is as follows:

[0015]

[0016] Where v is the average wind speed at an altitude of 5 to 20 km; is the surface turbulence refractive index structure constant;

[0017] When v = 21m / s, When , the Hufnagel-Valley model is an atmospheric turbulence model.

[0018] In a further embodiment, the phase screen model is constructed as follows: the atmospheric channel with a transmission distance of L is divided into multiple small parts, and the effect of atmospheric turbulence on the light beam at each ΔL distance is approximately equivalent to an infinitely thin phase screen. The power spectrum inversion method is used to perform numerical simulation of the atmospheric phase screen. , and the Kolmogorov spectrum is used. Due to the uneven intensity of the refractive index fluctuation on the satellite-to-ground path, if equally spaced phase screens are set, the strong fluctuation area cannot be fully sampled, and the weak fluctuation area will be oversampled, resulting in calculation errors. Use equal Rytov index interval phase screens, and set the Rytov index intervals between phase screens to be constant c R , and then the position of the phase screen is obtained by calculation. And due to the problem of Fourier transform sampling frequency, the phase screen does not contain the low-frequency part, and the subharmonic compensation method is used to compensate the low frequency of the phase screen. In this way, the entire phase screen model is constructed.

[0019] In a further embodiment, the process of selecting four satellites whose zenith angles meet preset conditions specifically includes: first, through a star selection algorithm, the precise ephemeris of the whole day is screened to find satellite coordinates whose zenith angle range meets the atmospheric turbulence and phase screen model, that is, whose zenith angle is less than 70° from the observation point; then, by traversing the GDOP values ​​of the satellite coordinates with zenith angles less than 90° observed at the same time in the four-star positioning system, a combination of four satellites with smaller GDOP values ​​is selected; here, the four satellite coordinate values ​​with the smallest GDOP value in one day are selected together with their corresponding zenith angles for subsequent timing error calculation and compensation, and their GDOP value is 2.6425.

[0020] In a further embodiment, the process of reconstructing the optical pulse signal disturbed by turbulence and calculating the arrival time jitter of the optical pulse signal specifically includes:

[0021] The zenith angle corresponding to each satellite is brought into the constructed atmospheric turbulence and phase screen model. Due to the light intensity flicker caused by the influence of atmospheric turbulence, the arrival time jitter of the pulse light signal after turbulent disturbance can be obtained. The pulse light signal always has a certain spectral width. For the optical band, the coherent bandwidth of the atmospheric turbulent medium is very wide. When the bandwidth of the pulse light signal is much smaller than the carrier frequency, the pulse time waveform change caused by atmospheric turbulence is very subtle. Therefore, this light intensity value is set to the peak point of the Gaussian pulse after turbulent disturbance, and the Gaussian pulse half-peak full width T is given. P and the mean pulse arrival time Where L is the transmission distance, thus reconstructing the Gaussian pulse disturbed by turbulence.

[0022] Set the decision threshold Ith , the pulse arrival time ξ is obtained, and the entire solution process can be expressed mathematically as:

[0023]

[0024] In a further embodiment, the calculation process of the satellite-to-earth laser one-way timing error t′ and the coordinate calculation value (x0, y0, z0) of the observation point is as follows:

[0025] A set of four satellite coordinate values ​​and the arrival time jitter corresponding to each satellite are brought into the four-satellite positioning calculation formula. Since the formula does not consider error factors other than light intensity flicker, the clock error t' here is the one-way timing error introduced by light intensity flicker in the four-satellite one-way timing mechanism and receiving station solution mode. Therefore, the calculation can obtain the satellite-to-ground laser one-way timing error t' and the coordinate calculation value of the observation point (x0, y0, z0).

[0026]

[0027] In the formula, represents the time jitter from the i-th satellite to the receiving station, t u represents the ground receiver time, t s represents the satellite time, ζ represents the delay caused by the light intensity flicker; (x i ,y i ,z i ) represents the position coordinates of the i-th satellite at the current moment.

[0028] In a further embodiment, the sliding average filtering method is to smooth the random noise or fluctuation in the data by taking the average value of a certain number of continuous data points (i.e., the window size). This method can effectively reduce the local fluctuation of the data while retaining the overall trend of the data. The satellite-to-earth laser one-way timing error is processed using the sliding average filtering to obtain the compensated and optimized satellite-to-earth laser one-way timing error.

[0029] The present invention also discloses an electronic device, which includes a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the error solution and compensation method of four-satellite one-way laser timing synchronization to the ground under the influence of atmospheric turbulence as described in the first aspect.

[0030] The present invention also discloses a computer-readable storage medium, which stores at least one executable instruction. When the executable instruction is executed on an electronic device, the electronic device executes the error solution and compensation method for four-satellite one-way laser timing synchronization to the ground under the influence of atmospheric turbulence as described in the first aspect.

[0031] Beneficial effect: The present invention proposes a method for solving and compensating the error of one-way laser timing from four satellites to the ground under the influence of atmospheric turbulence. A group of four satellites with a GDOP value of 2.6425 whose zenith angles meet the model requirements are obtained through a star selection algorithm. By bringing their respective zenith angles into the atmospheric turbulence and phase screen model to calculate the light intensity flicker caused by the influence of atmospheric turbulence, the arrival time jitter of the pulse light signal after turbulent disturbance can be obtained. A group of four satellite coordinate values ​​and the arrival time jitter corresponding to each satellite are brought into the four-star positioning calculation formula to obtain the satellite-to-ground laser one-way timing error and the coordinate calculation value of the observation point. Analysis shows that the RMS residual of the satellite-to-ground laser one-way timing error is 0.32195ns, and the RMS residual is 0.14092ns after the sliding average filter compensation optimization, and the stability has been significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of the error solution and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence.

[0033] Figure 2 Schematic diagram of a four-star positioning system in an embodiment of the present invention.

[0034] Figure 3 This is a schematic diagram of the results of the error compensation optimization method for four-satellite one-way laser timing under the influence of atmospheric turbulence. DETAILED DESCRIPTION

[0035] In the following description, a large number of specific details are provided to provide a more thorough understanding of the present invention. However, it is apparent to those skilled in the art that the present invention can be implemented without one or more of these details. In other examples, in order to avoid confusion with the present invention, some technical features known in the art are not described.

[0036] Figure 1 The flowchart of the error calculation and compensation method of the present invention based on the one-way laser timing of four satellites to the ground under the influence of atmospheric turbulence. Figure 1 As shown, the method includes the following stages:

[0037] Determine the observation point and satellite selection algorithm: obtain the observation point coordinates and the satellite coordinates observed within a day and perform the next step of satellite screening on this basis. All coordinates are based on the Earth-centered Earth-fixed coordinate system (ECEF).

[0038] Select the atmospheric turbulence model: Select the Hufnagel-Valley model to calculate the variation of the refractive index structure constant with altitude.

[0039] Construct a phase screen model: divide the atmospheric channel with a transmission distance of L into multiple small parts. The influence of atmospheric turbulence on the light beam at each ΔL distance is approximately equivalent to an infinitely thin phase screen. The power spectrum inversion method is used to perform numerical simulation of the atmospheric phase screen.

[0040] Obtain four satellite coordinates with appropriate zenith angles: First, use the star selection algorithm to screen satellite coordinates whose zenith angle range conforms to the atmospheric turbulence and phase screen model, and then traverse the GDOP values ​​of the satellite coordinates observed at the same time in the four-star positioning system to select a combination of four satellites with the smallest GDOP value.

[0041] Calculate the arrival time jitter of the laser pulse signal: bring the zenith angle corresponding to each satellite into the constructed atmospheric turbulence and phase screen model. The light intensity flicker caused by the influence of atmospheric turbulence can be used to obtain the arrival time jitter of the pulse light signal after turbulent disturbance.

[0042] Calculate the one-way timing error of four satellites to the ground: Substitute a set of four satellite coordinate values ​​and the arrival time jitter corresponding to each satellite into the four-satellite positioning calculation formula to obtain the one-way laser timing error of the satellite to the ground and the calculated coordinate value of the observation point.

[0043] The timing error is compensated and optimized by the sliding average filtering method: the calculated satellite-to-earth laser one-way timing error is processed by the sliding average filtering to obtain the compensated and optimized satellite-to-earth laser one-way timing error.

[0044] In the embodiment, a group of four satellites with a GDOP value of 2.6425 whose zenith angles meet the model requirements are obtained by the star selection algorithm. By bringing their respective zenith angles into the atmospheric turbulence and phase screen model to calculate the light intensity flicker caused by the influence of atmospheric turbulence, the arrival time jitter of the pulse light signal after turbulent disturbance can be obtained. A group of four satellite coordinate values ​​and the arrival time jitter corresponding to each satellite are brought into the four-star positioning calculation formula to obtain the satellite-to-earth laser one-way timing error and the coordinate calculation value of the observation point. Analysis shows that the RMS residual of the satellite-to-earth laser one-way timing error is 0.32195ns, and the RMS residual is 0.14092ns after the sliding average filter compensation optimization, and the stability has been significantly improved.

[0045] The specific implementation principle of the present invention is as follows: the atmospheric turbulence model is selected to select the Hufnagel-Valley model to calculate the change of the refractive index structure constant with altitude, that is:

[0046]

[0047] Where v is the average wind speed at an altitude of 5 to 20 km, is the ground turbulence refractive index structure constant when v = 21m / s, When 5 / 7 Model.

[0048] The basic idea of ​​the multi-phase screen method is to divide the atmospheric channel with a transmission distance of z into multiple small parts. The effect of atmospheric turbulence on the light beam at each distance Δz is approximately equivalent to an infinitely thin phase screen. When the light field passes through the phase screen, the phase disturbance caused by the atmospheric turbulence at the distance Δz will be superimposed on the wavefront of the light wave, and then transmitted to the position of the next phase screen through a vacuum. The process is repeated until it reaches the receiving end on Earth, generating a distorted light field affected by atmospheric turbulence. Therefore, during the atmospheric transmission process, the optical signal is transmitted from position z to the next phase screen. i Propagate to z i+1 =z i The solution of the position of +Δz (i = 1, 2, 3, ...) (i is the phase screen number) can be achieved through two processes: vacuum propagation and random phase superposition of the phase screen. The specific process can be expressed by mathematical expression:

[0049]

[0050] In formula (1), FT and FT -1 are Fourier transform and inverse Fourier transform respectively; U(r,z i ) and U(r,z i+1 ) are respectively the distance from the transmitter to z i and z i+1 The complex amplitude of the light wave at K x and K y are the spatial wave numbers in the x and y directions respectively; k is the wave number, λ is the wavelength; is the random phase corresponding to the i-th phase screen during the propagation process.

[0051] The power spectrum inversion method is used to perform numerical simulation of the atmospheric phase screen. The power spectrum function that conforms to the atmospheric turbulence phase disturbance is used. For the Hermitian complex Gaussian random matrix function h(K x ,K y ) is filtered, and then the random phase screen function is obtained by inverse Fourier transform. Using Kolmogorov spectrum, the whole process can be expressed as:

[0052]

[0053] In formula (2), ΔK x and ΔK y are the spatial wave number intervals in the x-direction and y-direction respectively; K is the three-dimensional spatial wave number; r0 is the atmospheric coherence length, which is used to reflect the atmospheric turbulence intensity, and its mathematical expression is: Where α is the launch zenith angle of the laser link.

[0054] In the phase screen model, due to the uneven refractive index fluctuation intensity on the satellite-to-ground path, if the phase screens are set with equal spacing, the strong fluctuation area cannot be fully sampled, and the weak fluctuation area will be oversampled, resulting in calculation errors. Use equal Rytov index interval phase screens, and set the Rytov index interval between phase screens to be a constant c R , and the Δz thus calculated is i As the i-th and i+1-th phase screen spacing. i When the phase screen are approximately equal, and assuming plane beam propagation, we have Then we get the position z of the phase screen i =z i-1 +Δz i .

[0055] In the spatial domain, x = mΔx, y = mΔy (Δx and Δy are sampling intervals). For the convenience of calculation, let Δx = Δy, m and n be integers; in the wave number domain, K x =m′ΔK x , K y =n′ΔK y , m′ and n′ are integers, M and N are the number of sampling points in the x and y directions respectively. For the convenience of calculation, let M = N, then we can get:

[0056]

[0057] In constructing the phase screen model, the subharmonic compensation method can be used to compensate the low frequency of the phase screen. Due to the problem of Fourier transform sampling frequency, the minimum and maximum spatial frequencies of the phase screen are Where Δf is the spatial frequency interval, L p is the size of the phase screen, so the phase screen does not include Low frequency part. When p (p ≥ 1) level subharmonics are superimposed, the corresponding subharmonic sampling interval is When the subharmonic order is N p When , the entire subharmonic phase expression is:

[0058]

[0059] Obtain the four satellite coordinates with suitable zenith angles through the star selection algorithm. First, the precise ephemeris of the whole day is screened to find the satellite coordinates with a zenith angle range that meets the atmospheric turbulence and phase screen model, that is, the satellite coordinates with a zenith angle less than 70° from the observation point. Then, the satellite coordinates with a zenith angle less than 90° observed at the same time are selected in the four-star positioning system ( Figure 2The GDOP value in the figure is shown in the figure. A combination of four satellites with smaller GDOP values ​​is selected. Here, the coordinate values ​​of the four satellites with the smallest GDOP value in one day and their corresponding zenith angles are selected for subsequent timing error calculation and compensation. The GDOP value is 2.6425.

[0060] Calculate the arrival time jitter of the laser pulse signal. The zenith angle corresponding to each satellite is brought into the constructed atmospheric turbulence and phase screen model. The light intensity flicker caused by the influence of atmospheric turbulence can be used to obtain the arrival time jitter of the pulse light signal after turbulent disturbance. Pulse light signals always have a certain spectral width. For the optical band, the coherent bandwidth of the atmospheric turbulent medium is very wide. When the bandwidth of the pulse light signal is much smaller than the carrier frequency, the change in the pulse time waveform caused by atmospheric turbulence is very subtle. Therefore, this light intensity value is set to the peak point of the Gaussian pulse after turbulent disturbance, and the Gaussian pulse half-peak full width T is given. P and the mean pulse arrival time Where L is the transmission distance, thus reconstructing the Gaussian pulse disturbed by turbulence. Set the decision threshold I th , and the pulse arrival time ξ is obtained. The entire solution process can be expressed mathematically as:

[0061] Assume that the actual distance between the satellite and the ground is l, and the ground receiver time is t u , the clock difference between the ground station receiver and GPS time is t′, and the satellite time is t s , the clock difference between the satellite and GPS time is δ t , c is the speed of light, considering the delay caused by various factors and noise in the atmosphere during the signal propagation process is ξ, then:

[0062] l=c[(t u -t′)-(t s -δ t )-ζ]

[0063] where δ t It can be given by GPS satellite. In the present invention, ζ only considers the delay caused by light intensity flicker, then ζ is the ξ in the pulse arrival time, t u -t s -ζ constitutes the time jitter t from the satellite to the receiving station laser Considering that the unknown coordinates of the receiving station are (x0, y0, z0) and the coordinates of the GPS satellite are (x, y, z), we get:

[0064]

[0065] This is the principle of satellite-to-ground laser one-way timing. For the multi-satellite-to-ground laser one-way timing method, considering the unknown coordinates of the receiving station and t′, a total of 4 unknowns, at least 4 satellites need to be selected according to the "multi-satellite coverage, monitoring and solution" mechanism in the satellite-to-ground laser one-way timing system. By receiving signals from 4 satellites, the position coordinates of the receiving station and the timing deviation are calculated to achieve precise positioning and timing. Figure 2 The four satellites are in their respective orbits and can be observed by the receiving station at the same time. α1, α2, α3, and α4 are the receiving zenith angles of the laser signals received by the receiving station from the corresponding satellites. When there are four GPS satellites, the equation group can be obtained:

[0066]

[0067] represents the time jitter from the i-th (i=1, 2, 3, 4) satellite to the receiving station, (x i ,y i ,z i ) represents the position coordinates of the i-th satellite at the current moment. The formula does not consider error factors other than light intensity flicker, so the clock error t′ here is the one-way timing error introduced by light intensity flicker in the four-satellite one-way timing mechanism and receiving station solution mode. Therefore, the calculation can obtain the satellite-to-ground laser one-way timing error t′ and the coordinate calculation value of the observation point (x0, y0, z0).

[0068] Furthermore, the sliding average filtering method is to smooth the random noise or fluctuation in the data by taking the average value of a certain number of continuous data points (i.e., the window size). This method can effectively reduce the local fluctuation of the data while retaining the overall trend of the data. The satellite-to-earth laser one-way timing error is processed using the sliding average filter to obtain the compensated and optimized satellite-to-earth laser one-way timing error.

[0069] like Figure 3 The present invention is a schematic diagram of the results of the error compensation optimization method of the four-satellite one-way laser timing service to the ground under the influence of atmospheric turbulence. A group of four satellites with a GDOP value of 2.6425 whose zenith angles meet the model requirements are obtained by the star selection algorithm. By bringing their respective zenith angles into the atmospheric turbulence and phase screen model to calculate the light intensity flicker caused by the atmospheric turbulence, 1000 result data of the arrival time jitter of the pulse light signal after turbulent disturbance can be obtained. A group of four satellite coordinate values ​​and 1000 arrival time jitters corresponding to each satellite are brought into the four-satellite positioning calculation formula to obtain 1000 satellite-to-ground laser one-way timing errors and the coordinate calculation values ​​of the observation point.

[0070] The sliding average filtering method is to smooth the random noise or fluctuations in the data by taking the average of a certain number of continuous data points (i.e., the window size). This method can effectively reduce the local fluctuations of the data while retaining the overall trend of the data. The satellite-to-ground laser one-way timing error is processed using a sliding average filter to obtain the compensated and optimized satellite-to-ground laser one-way timing error. Since the phase screen model is aimed at the case of a large laser emission period, the window size here is selected as 5, which can perform better real-time compensation processing on the data.

[0071] After 1000 one-way timing errors were analyzed and processed by sliding average filtering, 1000 compensation-optimized satellite-to-ground laser one-way timing errors were obtained. It can be clearly seen from the figure that the jitter of the satellite-to-ground laser one-way timing error after compensation optimization is significantly reduced compared to before, and the overall deviation from the center point is smaller. After analyzing the results, it can be obtained that the RMS residual of the satellite-to-ground laser one-way timing error is 0.32195ns, and the RMS residual after sliding average filtering compensation optimization is 0.14092ns, reflecting that the stability of the one-way timing error has been significantly improved.

[0072] As described above, although the present invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the present invention itself. Various changes may be made to it in form and detail without departing from the spirit and scope of the present invention as defined in the appended claims.

Claims

1. A method for error calculation and compensation of one-way laser timing from four satellites to the ground under the influence of atmospheric turbulence, characterized in that: The steps include: Construct atmospheric turbulence model and phase screen model; Obtain the coordinate value of the observation point and the coordinate values ​​of several satellites observed within a predetermined time, and select four satellites whose zenith angles meet the preset conditions; The zenith angles corresponding to the four selected satellites are introduced into the atmospheric turbulence model and the phase screen model to reconstruct the optical pulse signal disturbed by turbulence and calculate the arrival time jitter of the optical pulse signal; Based on the coordinate values ​​of the four satellites and the jitter of the arrival time of the optical pulse signal corresponding to each satellite, the satellite-to-ground laser one-way timing error and the coordinate calculation value of the observation point are calculated; The satellite-to-ground laser one-way timing error is processed by using a sliding average filter to obtain a compensated and optimized satellite-to-ground laser one-way timing error.

2. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 1 is characterized in that: All coordinate values ​​are based on the Earth-centered Earth-fixed coordinate system.

3. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 1 is characterized in that: The atmospheric turbulence model is constructed as follows: The Hufnagel-Valley model is selected to calculate the change of the refractive index structure constant with height. The mathematical expression of the Hufnagel-Valley model is as follows: Where v is the average wind speed at an altitude of 5 to 20 km; is the surface turbulence refractive index structure constant; When v = 21m / s, When , the Hufnagel-Valley model under this parameter is the atmospheric turbulence model.

4. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 1 is characterized in that: The phase screen model is constructed in the following manner: The atmospheric channel with a transmission distance of L is divided into multiple small parts, and the influence of atmospheric turbulence on the light beam at each distance ΔL is equivalent to a phase screen; Set multiple phase screens at equal intervals and calculate the positions of all current phase screens; The subharmonic compensation method is used to perform low-frequency compensation on all phase screens, and finally the entire phase screen model is obtained.

5. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 1 is characterized in that: The selecting of four satellites whose zenith angles meet the preset conditions specifically includes: First, the satellite coordinates whose zenith angle range conforms to the atmospheric turbulence model and the phase screen model are selected, and then the GDOP values ​​of the satellite coordinates observed at the same time in the four-star positioning system are traversed to select the combination of four satellites with the smallest GDOP value.

6. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 1 is characterized in that: The reconstructing the optical pulse signal disturbed by turbulence and calculating the arrival time jitter of the optical pulse signal specifically includes: This light intensity value is set as the peak point of the Gaussian pulse after turbulence disturbance, and the full width at half maximum of the Gaussian pulse is given as T P and the mean pulse arrival time Where L is the transmission distance, thus reconstructing the Gaussian pulse disturbed by turbulence; Set the decision threshold I th , and the pulse arrival time ξ is obtained:

7. The error calculation and compensation method for four-satellite one-way laser timing under the influence of atmospheric turbulence according to claim 6 is characterized in that: The satellite-to-ground laser one-way timing error t′ and the coordinate calculation value of the observation point (x0, y0, z0) are calculated according to the following equations: In the formula, represents the time jitter from the i-th satellite to the receiving station, t u represents the ground receiver time, t s represents the satellite time, ζ represents the delay caused by the light intensity flicker; (x i ,y i ,z i ) represents the position coordinates of the i-th satellite at the current moment.

8. An electronic device, characterized in that: The device includes: a processor and a memory storing computer program instructions; when the processor executes the computer program instructions, it implements the error solution and compensation method based on four-satellite one-way laser timing under the influence of atmospheric turbulence as described in any one of claims 1 to 7.

9. A computer-readable storage medium, characterized in that: The storage medium stores at least one executable instruction. When the executable instruction is executed on the electronic device, the electronic device executes the error solution and compensation method based on four-satellite one-way laser timing under the influence of atmospheric turbulence as described in any one of claims 1 to 7.

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