Inter-satellite laser interferometric ranging frequency deviation calibration method and device

Abstract

This application belongs to the field of satellite precision measurement technology and discloses a method and apparatus for calibrating the frequency deviation of inter-satellite laser interferometric ranging (LRI). The method includes: acquiring the position vectors of two satellites and calculating the inter-satellite baseline vector; calculating the inter-satellite distance variation based on the inter-satellite baseline vector; acquiring the interferometric phase and the initial absolute laser frequency and calculating the instantaneous LRI distance variation; calculating the LRI instantaneous variation scale factor based on the inter-satellite distance variation and the LRI instantaneous distance variation; obtaining the day-scale factor value based on the LRI instantaneous variation scale factor; constructing a linear trend model based on the day-scale factor value and obtaining the scale factor observation value; iteratively calculating the scale factor observation value to obtain the iteratively calculated scale factor observation value; determining whether the convergence condition is met; if so, outputting the iteratively calculated scale factor observation value. This application can improve the calculation accuracy and efficiency of the absolute laser frequency in inter-satellite laser ranging using satellite orbit data.

Description

Technical Field

[0001] This application relates to the field of satellite precision measurement technology, and in particular to a method and apparatus for calibrating frequency deviation in inter-satellite laser interferometric ranging. Background Technology

[0002] LRI calculates distance changes using interferometric phase analysis, but the calculated distance changes for on-orbit satellites are... M Significant deviations exist; firstly, there is the initial frequency deviation during the ground calibration phase; secondly, the onboard optical cavity resonant frequency is affected by temperature changes and material aging, leading to a shift in the optical cavity resonant frequency. These frequency deviations introduce systematic errors into inter-satellite distance measurements, thereby affecting the accuracy of subsequent gravity field inversion and scientific applications.

[0003] Currently, LRI frequency deviation calibration methods mainly fall into four categories, all of which have significant limitations. First, there is the cross-calibration method relying on the KBR system, which suffers from significant non-sustainability; next-generation missions (such as Tianqin-2 and GRACE-C) will eliminate the KBR system, losing their calibration benchmark. Second, there is the iodine molecular spectroscopy method, which requires a complex system and additional onboard hardware, significantly increasing technical difficulty and power consumption. Third, there is the telemetry data modeling method, whose model accuracy is insufficient, failing to meet the requirements of gravity field inversion and carrying the risk of model failure due to material aging. Fourth, there is the method of directly estimating using orbital data, which has a large accuracy error. Summary of the Invention

[0004] This application provides a method and apparatus for calibrating frequency deviation in inter-satellite laser interferometric ranging. It can use existing orbital data of gravity satellites as a reference for calculation, replacing the traditional KBR cross-calibration algorithm. Furthermore, it suppresses orbital random errors and gross errors by jointly using an iterative weight function adjustment strategy and a linear trend model, obtaining scale factor observations after multiple iterations. Based on the scale factor observations after multiple iterations, frequency deviation calibration is achieved without additional hardware, improving the accuracy and efficiency of calculating the absolute laser frequency in inter-satellite laser ranging using satellite orbital data.

[0005] In a first aspect, embodiments of this application provide a method for calibrating the frequency deviation of inter-satellite laser interferometric ranging, the method comprising:

[0006] Based on GNSS precise orbit determination, the position vectors of the two satellites are obtained, and the inter-satellite baseline vector is calculated.

[0007] The inter-satellite distance variability is calculated based on the inter-satellite baseline vector;

[0008] The interference phase and initial absolute laser frequency are obtained, and the instantaneous distance variation rate of LRI is calculated.

[0009] The LRI instantaneous distance variation scale factor is calculated based on the inter-satellite distance variation and the LRI instantaneous distance variation.

[0010] The day-scale factor value is obtained based on the LRI instantaneous distance variability scaling factor;

[0011] A linear trend model is constructed based on the daily scale factor values, and the scale factor observation values ​​are obtained based on the linear trend model.

[0012] The iterative process involves using the least squares method and an iterative weight function adjustment strategy to iteratively calculate the scale factor observations and obtain the iterative scale factor observations.

[0013] Determine whether the scale factor observations after iteration meet the convergence condition; if yes, output the scale factor observations after iteration; otherwise, return to the iteration step.

[0014] Furthermore, based on the precise orbit determination of GNSS to obtain the position vectors of the two satellites, the inter-satellite baseline vector is calculated, including:

[0015] The position vectors of the two satellites are obtained based on precise orbit determination using GNSS, and the inter-satellite baseline vector is calculated according to the formula for calculating the inter-satellite baseline vector. The position vectors of the two satellites include the positions of the first satellite and the second satellite.

[0016] The formula for calculating the inter-satellite baseline vector is:

[0017] b = r M -r T ;

[0018] Where b is the inter-satellite baseline vector, r M The first satellite position; r T This is the location of the second satellite.

[0019] Furthermore, the inter-satellite distance variability is calculated based on the inter-satellite baseline vector, including:

[0020] The inter-satellite distance variation is calculated based on the inter-satellite baseline vector and the inter-satellite distance variation calculation formula.

[0021] The formula for calculating the interstellar distance variability is:

[0022]

[0023] in, denoted as , and b as the inter-satellite distance variation.

[0024] Furthermore, by obtaining the interference phase and the initial absolute frequency of the laser, the instantaneous distance variation of the LRI is calculated, including:

[0025] The interference phase and initial absolute laser frequency are obtained, and the instantaneous distance variation of LRI is calculated according to the formula for calculating the instantaneous distance variation of LRI.

[0026] The formula for calculating the instantaneous distance variation rate of LRI is:

[0027]

[0028] in, Let φ be the instantaneous distance variation of the LRI, φ be the interference phase, c0 be the speed of light in vacuum, and v be the velocity of light. M The initial absolute frequency of the laser for the first satellite.

[0029] Furthermore, the LRI instantaneous distance variation scaling factor is calculated based on the inter-satellite distance variation and the LRI instantaneous distance variation, including:

[0030] The LRI instantaneous distance variation scale factor is calculated based on the inter-satellite distance variation, LRI instantaneous distance variation, and LRI instantaneous calculation formula.

[0031] The instantaneous calculation formula for LRI is:

[0032]

[0033] Where s is the instantaneous distance variability scaling factor of LRI. For LRI instantaneous distance variability, For the interstellar distance variability, Δt LRI-orb This represents the time offset between LRI data and GNSS data.

[0034] Furthermore, based on the LRI instantaneous distance variability scaling factor, the diurnal scaling factor value is obtained, including:

[0035] Calculate the standard deviation of the LRI instantaneous distance variability scaling factor based on the LRI instantaneous distance variability scaling factor;

[0036] Based on the outlier range formula and the standard deviation of the LRI instantaneous distance variability scaling factor, the daily scaling factor value is obtained by screening the LRI instantaneous distance variability scaling factor.

[0037] Furthermore, a linear trend model is constructed based on the daily scale factor values, and the scale factor observations are obtained from the linear trend model, including:

[0038] A linear trend model is constructed based on the daily scale factor value, scale factor drift rate, initial bias and residual. The linear trend model is then converted into matrix form to obtain the scale factor observation value.

[0039] The linear trend model is as follows:

[0040] s orb =a(k) ·t+b (k) +v (k) ;

[0041] The linear trend model can be represented in matrix form as follows:

[0042] s orb =Bx (k) +v (k) ;

[0043] The observed values ​​for the scaling factor are:

[0044] s est (k) =Bx (k) ;

[0045] Where, x (k) =[a (k) ,b (k) ], a (k) b is the scale factor drift rate. (k) For the initial deviation, s orb v represents the diurnal scale factor value of an n*1 observation vector, where n is the number of scale factor observations. (k) denoted as the residual of the scale factor observations, k is the number of iterations; B is an n*2 design matrix, where the first column represents the average event t and the second column represents the average event 1.

[0046] Further, in the iterative step, the least squares method and an iterative weight function adjustment strategy are used to iteratively calculate the scale factor observations, obtaining the iteratively calculated scale factor observations, including:

[0047] The least squares method is used to solve for the scale factor observations output by the linear trend model to obtain the least squares solution;

[0048] The residuals in the least squares solution are input into the iterative weight function to adjust the strategy, resulting in the iterative weight matrix;

[0049] The iterative weight function adjustment strategy is as follows:

[0050]

[0051] in, Let be the diagonal element in the iteration weight matrix of the k-th iteration, i be the i-th scale factor observation, σ be the standard deviation of the daily scale factor value, and ω be a small constant to prevent denominator overflow. The residual of the observation value of the i-th scale factor at the (k-1)-th iteration;

[0052] The least squares solution is updated based on the iterative weight matrix. The updated least squares solution is then substituted into the linear trend model to obtain the iterative scale factor observations.

[0053] Furthermore, the convergence conditions include:

[0054]

[0055] in, The scale factor observation value after the k-th iteration. The scale factor observation value after the (k-1)th iteration.

[0056] Secondly, embodiments of this application provide an inter-satellite laser interferometric ranging frequency deviation calibration device, the device comprising:

[0057] The vector module is used to obtain the position vectors of the two satellites based on GNSS precise orbit determination and to calculate the inter-satellite baseline vector.

[0058] The inter-satellite variability module is used to calculate the inter-satellite distance variability based on the inter-satellite baseline vector.

[0059] The instantaneous rate module is used to obtain the interference phase and the initial absolute laser frequency, and to calculate the instantaneous distance rate of the LRI.

[0060] The calculation module is used to calculate the LRI instantaneous distance variation scale factor based on the inter-satellite distance variation and the LRI instantaneous distance variation.

[0061] The filtering module is used to obtain the day-scale factor value based on the LRI instantaneous distance variability scale factor;

[0062] The model building module is used to construct a linear trend model based on the daily scale factor values, and to obtain the scale factor observation values ​​based on the linear trend model.

[0063] The iterative module is used to iteratively calculate the scale factor observations using the least squares method and an iterative weight function adjustment strategy, and obtain the iterative scale factor observations.

[0064] The judgment module is used to determine whether the scale factor observations after iteration meet the convergence condition; if yes, the scale factor observations after iteration are output; if no, the iteration module is returned.

[0065] Furthermore, the vector module is also used to obtain the position vector of the two satellites based on GNSS precise orbit determination, and to calculate the inter-satellite baseline vector according to the inter-satellite baseline vector calculation formula; the position vector of the two satellites includes the position of the first satellite and the position of the second satellite;

[0066] The formula for calculating the inter-satellite baseline vector is:

[0067] b = r M -r T ;

[0068] Where b is the inter-satellite baseline vector, r MThe first satellite position; r T This is the location of the second satellite.

[0069] Furthermore, the inter-satellite variability module is also used to calculate the inter-satellite distance variability based on the inter-satellite baseline vector and the inter-satellite distance variability calculation formula;

[0070] The formula for calculating the interstellar distance variability is:

[0071]

[0072] in, denoted as , and b as the inter-satellite distance variation.

[0073] Furthermore, the instantaneous rate module is also used to obtain the interference phase and the initial absolute frequency of the laser, and to calculate the instantaneous distance rate of the LRI according to the LRI instantaneous distance rate calculation formula;

[0074] The formula for calculating the instantaneous distance variation rate of LRI is:

[0075]

[0076] in, Let φ be the instantaneous distance variation of the LRI, φ be the interference phase, c0 be the speed of light in vacuum, and v be the velocity of light. M The initial absolute frequency of the laser for the first satellite.

[0077] Thirdly, embodiments of this application provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the steps of an inter-satellite laser interferometric ranging frequency deviation calibration method as described in any of the above embodiments.

[0078] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of an inter-satellite laser interferometric ranging frequency deviation calibration method as described in any of the above embodiments.

[0079] In summary, compared with the prior art, the beneficial effects of the technical solution provided in this application include at least the following:

[0080] This application provides a method for calibrating the frequency deviation in inter-satellite laser interferometric ranging. This method can use existing orbital data of gravity satellites as a reference for calculation, replacing the traditional KBR cross-calibration algorithm. Furthermore, it uses an iterative weight function adjustment strategy and a linear trend model to jointly suppress orbital random errors and gross errors, obtaining scale factor observations after multiple iterations. Based on the scale factor observations after multiple iterations, frequency deviation calibration without additional hardware is achieved, improving the accuracy and efficiency of calculating the absolute laser frequency in inter-satellite laser ranging using satellite orbital data. Attached Figure Description

[0081] Figure 1 This is a flowchart of a frequency deviation calibration method for inter-satellite laser interferometry provided as an exemplary embodiment of this application.

[0082] Figure 2 This is a structural diagram of an inter-satellite laser interferometry frequency deviation calibration device provided as an exemplary embodiment of this application. Detailed Implementation

[0083] The technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments.

[0084] Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0085] Please see Figure 1 This application provides a method for calibrating the frequency deviation of inter-satellite laser interferometric ranging, which specifically includes the following steps:

[0086] Step S1: Obtain the position vectors of the two satellites based on GNSS precise orbit determination, and calculate the inter-satellite baseline vector.

[0087] Among them, the inter-satellite baseline vector is calculated based on the position vector of the two satellites obtained by precise GNSS orbit determination, including:

[0088] Obtain the position vectors of the two satellites, and calculate the inter-satellite baseline vector according to the formula for calculating the inter-satellite baseline vector; the position vectors of the two satellites include the positions of the first satellite and the second satellite.

[0089] The formula for calculating the inter-satellite baseline vector is:

[0090] b = r M -r T ;

[0091] Where b is the inter-satellite baseline vector, r M The first satellite position; rT This is the location of the second satellite.

[0092] Specifically, by obtaining the accurate position vectors of the two satellites (i.e., the positions of the first and second satellites), and then calculating the inter-satellite baseline vector based on these accurate position vectors, the accuracy of satellite orbit data can be guaranteed. Vector calculation can further lay a solid data foundation for the precise processing of satellite orbit data.

[0093] Step S2: Calculate the inter-satellite distance variation based on the inter-satellite baseline vector.

[0094] The inter-satellite distance variation calculated from the inter-satellite baseline vector includes:

[0095] The inter-satellite distance variation is calculated based on the inter-satellite baseline vector and the inter-satellite distance variation calculation formula.

[0096] The formula for calculating the interstellar distance variability is:

[0097]

[0098] in, denoted as , and b as the inter-satellite distance variation.

[0099] Specifically, based on the inter-satellite baseline vector obtained in step S1, the first derivative of the inter-satellite baseline vector and the magnitude of the inter-satellite baseline vector are calculated. These values ​​are then substituted into the aforementioned formula for calculation, thereby obtaining the inter-satellite distance variation. Using the inter-satellite distance variation avoids systematic errors when estimating ambiguity deviations.

[0100] In some embodiments, it also includes obtaining acceleration. The formula for calculating acceleration is:

[0101]

[0102] in, Let be the acceleration and b be the inter-satellite baseline vector. Further calculations of the inter-satellite baseline vector yield the inter-satellite acceleration, providing a data foundation for potential subsequent data use.

[0103] Step S3: Obtain the interference phase and the initial absolute frequency of the laser, and calculate the instantaneous distance variation rate of the LRI.

[0104] The process of obtaining the interference phase and the initial absolute laser frequency, and calculating the instantaneous distance variation rate of the LRI, includes:

[0105] The interference phase and initial absolute laser frequency are obtained, and the instantaneous distance variation of LRI is calculated according to the formula for calculating the instantaneous distance variation of LRI.

[0106] The formula for calculating the instantaneous distance variation rate of LRI is:

[0107]

[0108] in, Let φ be the instantaneous distance variation of the LRI, φ be the interference phase, c0 be the speed of light in vacuum, and v be the velocity of light. M This is the initial absolute laser frequency of the first satellite (i.e., the nominal value in orbit).

[0109] Step S4: Calculate the LRI instantaneous distance variation scaling factor based on the inter-satellite distance variation and the LRI instantaneous distance variation.

[0110] The orbital LRI instantaneous distance variation trajectory scale factor, calculated based on inter-satellite distance variation and LRI instantaneous distance variation, includes:

[0111] The LRI instantaneous distance variation scale factor is calculated based on the inter-satellite distance variation, LRI instantaneous distance variation, and LRI instantaneous calculation formula.

[0112] The instantaneous calculation formula for LRI is:

[0113]

[0114] Where s is the instantaneous distance variability scaling factor of LRI. For LRI instantaneous distance variability, For the interstellar distance variability, Δt LRI-orb This represents the time offset between LRI data and GNSS data.

[0115] Specifically, similar to the calculation method of the KBR system, the calculation method of the orbital scale factor is optimized. This application uses satellite orbital data for further calculations, replacing the traditional scheme that relies on the calculation data of the KBR system, which makes the data more accurate and the calculation in the frequency deviation calibration of satellite data faster.

[0116] Specifically, the formula for the cross-calibration method relying on the KBR system is as follows:

[0117]

[0118] in:

[0119]

[0120] in, For LRI instantaneous distance variability, For KBR instantaneous distance variability, For LRI, there is a biased distance variability. For KBR to have biased distance variability, For LRI light time-corrected distance variability, For KBR optical time correction distance variability, Let s be the range variation rate corrected for the phase center of the KBR antenna, s be the instantaneous range variation rate scaling factor for the LRI, and Δt be the range variation rate. LRI-KBR This refers to the time deviation between the LRI and KBR ranging systems.

[0121] Step S5: Obtain the day-scale factor value based on the LRI instantaneous distance variability scaling factor.

[0122] Among them, the diurnal scale factor value is obtained based on the LRI instantaneous distance variability scaling factor, including:

[0123] Calculate the standard deviation of the LRI instantaneous distance variability scaling factor based on the LRI instantaneous distance variability scaling factor;

[0124] Based on the outlier range formula and the standard deviation of the LRI instantaneous distance variability scaling factor, the daily scaling factor value is obtained by screening the LRI instantaneous distance variability scaling factor.

[0125] Specifically, the formula for the outlier range is:

[0126] s orb <mean(s) orb )-3std(s orb ), or s orb >mean(s orb )+3std(s orb );

[0127] Where std(s orb ) represents the standard deviation of the LRI instantaneous distance variability scaling factor, s orb This represents the day-scale factor value.

[0128] In some embodiments, the scale factor calculated using orbit data is often subject to significant random errors and gross errors; therefore, this application requires the removal of outliers. An absolute value of the residual between orbit data and laser ranging data exceeding three times their standard deviation is considered a gross error. For example, the standard deviation of the residual between the distance variability measured from orbit data and the distance variability measured from laser ranging is typically 1 × 10⁻⁶. -5 m / s, then the absolute value of the residual exceeds 3×10 -5 Data in m / s are considered gross errors.

[0129] Specifically, the range of outliers is set to the daily scale factor value s. orb Three times the standard deviation. The removal step is: calculate the scale factor estimate s. orb standard deviation (std(s) orb If s orb The value is less than mean(s)orb )-3std(s orb ) or greater than mean(s) orb )+3std(s orb Values ​​exceeding a certain threshold are considered outliers. Removing outliers makes the remaining data more accurate, further improving the accuracy of laser interferometric ranging. Setting a range for outliers prevents erroneous removal of values ​​within that range, ensuring data integrity; it also removes values ​​outside the range, ensuring data accuracy.

[0130] Step S6: Construct a linear trend model based on the daily scale factor values, and obtain the scale factor observation values ​​based on the linear trend model.

[0131] Specifically, a linear trend model is constructed based on the daily scale factor values, and the observed scale factor values ​​are obtained from the linear trend model, including:

[0132] A linear trend model is constructed based on the daily scale factor value, scale factor drift rate, initial bias and residual. The linear trend model is then converted into matrix form to obtain the scale factor observation value.

[0133] The linear trend model is as follows:

[0134] s orb =a (k) ·t+b (k) +v (k) ;

[0135] The linear trend model can be represented in matrix form as follows:

[0136] s orb =Bx (k) +v (k) ;

[0137] The observed values ​​for the scaling factor are:

[0138] s est (k) =Bx (k) ;

[0139] Where, x (k) =[a (k) ,b (k) ], a (k) b is the scale factor drift rate. (k) For the initial deviation, s orb v represents the diurnal scale factor value of an n*1 observation vector, where n is the number of scale factor observations. (k) denoted as the residual of the scale factor observations, k is the number of iterations; B is an n*2 design matrix, where the first column represents the average event t and the second column represents the average event 1.

[0140] Step S7, the iterative step, uses the least squares method and the iterative weight function adjustment strategy to iteratively calculate the scale factor observations and obtain the iterative scale factor observations.

[0141] The scale factor observations are calculated iteratively using the least squares method and an iterative weight function adjustment strategy to obtain the iterative scale factor observations, including:

[0142] The least squares method is used to solve for the scale factor observations output by the linear trend model to obtain the least squares solution.

[0143] The residuals in the least squares solution are input into the iterative weight function to adjust the strategy, thus obtaining the iterative weight matrix.

[0144] The iterative weight function adjustment strategy is as follows:

[0145]

[0146] in, Let be the diagonal element in the iteration weight matrix of the k-th iteration, i be the i-th scale factor observation, σ be the standard deviation of the daily scale factor value, and ω be a small constant to prevent denominator overflow. It represents the residual of the i-th scale factor observation value during the (k-1)-th iteration.

[0147] Preferably, ω can be set to 1×10 in this application. -10 .

[0148] The least squares solution is updated based on the iterative weight matrix. The updated least squares solution is then substituted into the linear trend model to obtain the iterative scale factor observations.

[0149] The least squares calculation process in the first iteration is as follows:

[0150] x (1) = (B T P (1) B) -1 B T P (1) s orb ;

[0151] v (1) =s orb -Bx (1) ;

[0152]

[0153] Among them, P (1) This is the iteration weight matrix for the first iteration.

[0154] Step S8: Determine whether the scale factor observations after iteration meet the convergence condition; if yes, output the scale factor observations after iteration; if no, return to the iteration step.

[0155] The convergence conditions include:

[0156]

[0157] in, The scale factor observation value after the k-th iteration. The observed value of the iteration scale factor after the (k-1)th iteration.

[0158] In some embodiments, by KBR scaling factor estimation (s) kbr The root mean square value of the residuals (σ) s To evaluate the accuracy of the fit, i.e.: σ s The smaller the value, the higher the accuracy of the scale factor observations after iteration. Repeating the iteration process until the scale factor observations converge can improve the accuracy of the scale factor observations after iteration through multiple calculations, achieving frequency deviation calibration without additional hardware.

[0159] The above embodiments provide a frequency deviation calibration method for inter-satellite laser interferometric ranging. This method can use existing orbital data of gravity satellites as a benchmark for calculation, replacing the traditional KBR cross-calibration algorithm. Furthermore, it suppresses orbital random errors and gross errors by jointly using an iterative weight function adjustment strategy and a linear trend model, obtaining scale factor observations after multiple iterations. Based on the scale factor observations after multiple iterations, frequency deviation calibration without additional hardware is achieved, improving the accuracy and efficiency of calculating the absolute laser frequency in inter-satellite laser ranging using satellite orbital data.

[0160] Please see Figure 2 Another embodiment of this application provides an inter-satellite laser interferometric ranging frequency deviation calibration device, the device comprising:

[0161] Vector module 101 is used to obtain the position vectors of the two satellites based on GNSS precise orbit determination and to calculate the inter-satellite baseline vector.

[0162] Inter-satellite variation module 102 is used to calculate the inter-satellite distance variation based on the inter-satellite baseline vector;

[0163] The instantaneous rate module 103 is used to acquire the interference phase and the initial absolute frequency of the laser, and to calculate the instantaneous distance rate of the LRI.

[0164] Calculation module 104 is used to calculate the LRI instantaneous distance variation scale factor based on the inter-satellite distance variation and the LRI instantaneous distance variation.

[0165] Filtering module 105 is used to obtain the day-scale factor value based on the LRI instantaneous distance variability scale factor;

[0166] Model building module 106 is used to build a linear trend model based on the daily scale factor values ​​and obtain the scale factor observation values ​​based on the linear trend model.

[0167] Iteration module 107 is used to iteratively calculate the scale factor observations using the least squares method and an iterative weight function adjustment strategy to obtain the iterative scale factor observations.

[0168] The judgment module 108 is used to determine whether the scale factor observation value after iteration satisfies the convergence condition; if yes, it outputs the scale factor observation value after iteration; if no, it returns to the iteration module 107.

[0169] In some embodiments, the vector module is also used to obtain the position vector of the two satellites based on GNSS precise orbit determination, and to calculate the inter-satellite baseline vector according to the inter-satellite baseline vector calculation formula; the position vector of the two satellites includes the position of the first satellite and the position of the second satellite;

[0170] The formula for calculating the inter-satellite baseline vector is:

[0171] b = r M -r T ;

[0172] Where b is the inter-satellite baseline vector, r M The first satellite position; r T This is the location of the second satellite.

[0173] In some embodiments, the inter-satellite variability module is also used to calculate the inter-satellite distance variability based on the inter-satellite baseline vector and the inter-satellite distance variability calculation formula;

[0174] The formula for calculating the interstellar distance variability is:

[0175]

[0176] in, denoted as , and b as the inter-satellite distance variation.

[0177] In some embodiments, the instantaneous rate module is also used to obtain the interference phase and the initial absolute laser frequency, and to calculate the LRI instantaneous distance rate according to the LRI instantaneous distance rate calculation formula;

[0178] The formula for calculating the instantaneous distance variation rate of LRI is:

[0179]

[0180] in, Let φ be the instantaneous distance variation of the LRI, φ be the interference phase, c0 be the speed of light in vacuum, and v be the velocity of light. M This is the initial absolute laser frequency of the first satellite (i.e., the nominal value in orbit).

[0181] The specific limitations of the inter-satellite laser interferometric ranging frequency deviation calibration device provided in this embodiment can be found in the embodiment of the inter-satellite laser interferometric ranging frequency deviation calibration method described above, and will not be repeated here. Each module in the above-described inter-satellite laser interferometric ranging frequency deviation calibration device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0182] This application provides a computer device that may include a processor, memory, network interface, and database connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it causes the processor to perform the steps of an inter-satellite laser interferometry frequency deviation calibration method as described in any of the above embodiments.

[0183] The working process, working details and technical effects of the computer equipment provided in this embodiment can be found in the embodiment of an inter-satellite laser interferometric ranging frequency deviation calibration method described above, and will not be repeated here.

[0184] This application provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of an inter-satellite laser interferometric ranging frequency deviation calibration method as described in any of the above embodiments. The computer-readable storage medium refers to a data storage medium, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or Memory Sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.

[0185] The working process, working details, and technical effects of the computer-readable storage medium provided in this embodiment can be found in the embodiment of an inter-satellite laser interferometric ranging frequency deviation calibration method described above, and will not be repeated here.

[0186] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0187] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0188] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. An inter-satellite laser interferometric ranging frequency bias calibration method, characterized in that, The method comprises: Based on the GNSS precise orbit, the double star position vector is obtained, and the inter-satellite baseline vector is calculated; According to the inter-satellite baseline vector, the inter-satellite distance rate of change is calculated; The interference phase and the initial laser absolute frequency are obtained, and the LRI instantaneous distance rate of change is calculated; According to the inter-satellite distance rate of change and the LRI instantaneous distance rate of change, the LRI instantaneous distance rate of change scale factor is calculated; According to the LRI instantaneous distance rate of change scale factor, the daily scale factor value is obtained; According to the daily scale factor value, a linear trend model is constructed, and the scale factor observation value is obtained according to the linear trend model; Iterative step, using least square method and iterative weight function adjustment strategy to iteratively calculate the scale factor observation value, and obtaining the iterated scale factor observation value; Determine whether the iterated scale factor observation value meets the convergence condition; if yes, output the iterated scale factor observation value; if no, return to the iterative step.

2. The method of calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 1, characterized in that, The double star position vector is obtained based on the GNSS precise orbit, and the inter-satellite baseline vector is calculated, comprising: Based on the GNSS precise orbit, the double star position vector is obtained, and the inter-satellite baseline vector is calculated according to the inter-satellite baseline vector calculation formula; the double star position vector includes the first satellite position and the second satellite position; The inter-satellite baseline vector calculation formula is: b＝r M -r T ； where b is the inter-satellite baseline vector, r M is the first satellite position; r T is the second satellite position.

3. The method of claim 1, wherein, The inter-satellite baseline vector is calculated according to the inter-satellite baseline vector, comprising: According to the inter-satellite baseline vector and the inter-satellite distance rate of change calculation formula, the inter-satellite distance rate of change is calculated; The inter-satellite distance rate of change calculation formula is: wherein is the inter-satellite range rate, and b is the inter-satellite baseline vector.

4. The method of claim 1, wherein, The interference phase and the initial laser absolute frequency are obtained, and the LRI instantaneous distance rate of change is calculated, comprising: The interference phase and the initial laser absolute frequency are obtained, and the LRI instantaneous distance rate of change is calculated according to the LRI instantaneous distance rate of change calculation formula; The LRI instantaneous distance rate of change calculation formula is: wherein, is the LRI instantaneous range rate, φ is the interference phase, c0is the speed of light in vacuum, v M is the initial laser absolute frequency of the first satellite.

5. The method of calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 1, wherein, The LRI instantaneous distance rate of change scale factor is calculated according to the inter-satellite distance rate of change, the LRI instantaneous distance rate of change and the LRI instantaneous calculation formula; The LRI instantaneous calculation formula is: The daily scale factor value is obtained according to the LRI instantaneous distance rate of change scale factor, comprising: where s is the LRI instantaneous range rate scale factor, is the LRI instantaneous range rate, is the inter-satellite range rate, At LRI-orb is the time offset between LRI data and GNSS data.

6. The method of calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 1, wherein, According to the LRI instantaneous distance rate of change scale factor, the standard deviation of the LRI instantaneous distance rate of change scale factor is calculated; According to the outlier range formula and the standard deviation of the LRI instantaneous distance rate of change scale factor, the LRI instantaneous distance rate of change scale factor is screened, and the daily scale factor value is obtained. According to the daily scale factor value, a linear trend model is constructed, and the scale factor observation value is obtained according to the linear trend model, comprising:

7. The method of calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 1, wherein, According to the daily scale factor value, the scale factor drift rate, the initial deviation and the residual, a linear trend model is constructed, the linear trend model is converted into a matrix form, and the scale factor observation value is obtained; The linear trend model is: The linear trend model is expressed in matrix form as: s orb = a (k) ·t + b (k) + v (k) ; The scale factor observation value is: s orb = Bx (k) + v (k) ; ​ s est (k) = Bx (k) ; where x (k) = [a (k) ,b (k) ], a (k) is the scale factor drift rate, b (k) is the initial bias, s orb is the daily scale factor value of the n*1 observation vector, n is the number of scale factor observations, v (k) is the residual of the scale factor observations, k is the iteration number; B is an n*2 design matrix, wherein the first column is t and the second column is 1.

8. The method of calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 7, characterized in that, The iterative step uses a least square method and an iterative weight function adjustment strategy to iteratively calculate the scale factor observation value to obtain an iterated scale factor observation value, including: The least square method is used to solve the scale factor observation value output by the linear trend model to obtain a least square solution; The residual in the least square solution is input into an iterative weight function adjustment strategy to obtain an iterative weight matrix; The iterative weight function adjustment strategy is: wherein, is the diagonal element in the iteration weight matrix for the kth iteration, i is the ith scale factor observation, σ is the standard deviation of the daily scale factor values, and ω is a small constant to prevent overflow of the denominator; is the residual of the ith scale factor observation at the k-1th iteration; The least square solution is updated according to the iterative weight matrix, and the updated least square solution is substituted into the linear trend model to obtain the iterated scale factor observation value.

9. The method of claim 8, wherein, The convergence condition includes: wherein is the scaled factor observation after iteration of the kth iteration, is the scaled factor observation after iteration of the k-1th iteration.

10. An apparatus for calibrating frequency bias of inter-satellite laser interferometric ranging, characterized in that, The device includes: A vector module configured to obtain a double-satellite position vector based on GNSS precise orbiting, and calculate an inter-satellite baseline vector; An inter-satellite variability module configured to calculate an inter-satellite distance variability based on the inter-satellite baseline vector; An instantaneous variability module configured to obtain an interference phase and an initial laser absolute frequency, and calculate an LRI instantaneous distance variability; A calculation module configured to calculate an LRI instantaneous distance variability scale factor based on the inter-satellite distance variability and the LRI instantaneous distance variability; A screening module configured to obtain a daily scale factor value based on the LRI instantaneous distance variability scale factor; A model construction module configured to construct a linear trend model based on the daily scale factor value, and obtain a scale factor observation value based on the linear trend model; An iteration module configured to use a least square method and an iterative weight function adjustment strategy to iteratively calculate the scale factor observation value to obtain an iterated scale factor observation value; A judgment module configured to judge whether the iterated scale factor observation value meets a convergence condition; if yes, output the iterated scale factor observation value; if no, return to the iteration module.

11. The device for calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 10, characterized in that, The vector module is further configured to obtain a double-satellite position vector based on GNSS precise orbiting, and calculate an inter-satellite baseline vector based on an inter-satellite baseline vector calculation formula; the double-satellite position vector includes a first satellite position and a second satellite position; The inter-satellite baseline vector calculation formula is: b＝r M -r T ； where b is the inter-satellite baseline vector, r M is the first satellite position; r T is the second satellite position.

12. The device for calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 10, wherein, The inter-satellite variability module is further configured to calculate an inter-satellite distance variability based on the inter-satellite baseline vector and an inter-satellite distance variability calculation formula; The inter-satellite distance variability calculation formula is: wherein is the inter-satellite range rate, and b is the inter-satellite baseline vector.

13. The device for calibrating frequency bias of inter-satellite laser interferometric ranging according to claim 10, wherein, The instantaneous variability module is further configured to obtain an interference phase and an initial laser absolute frequency, and calculate an LRI instantaneous distance variability based on an LRI instantaneous distance variability calculation formula; The LRI instantaneous distance variability calculation formula is: wherein, is the LRI instantaneous range rate, φ is the interference phase, c0is the speed of light in vacuum, v M is the initial laser absolute frequency of the first satellite.

14. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor implements the steps of the inter-satellite laser interferometric ranging frequency bias calibration method according to any one of claims 1 to 9 when executing the computer program.

15. A computer readable storage medium having stored thereon a computer program, characterized in that, The computer program implements the steps of the inter-satellite laser interferometric ranging frequency bias calibration method according to any one of claims 1 to 9 when executed by the processor.

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