Doppler Differential Positioning Method, Device, Equipment and Medium for Low-Earth Orbit Satellites

Abstract

The present application relates to a Doppler differential positioning method, device, equipment and medium for low-earth orbit satellites. The method includes: calculating the correction value of the ionospheric delay rate and calculating the correction value of the tropospheric delay rate; establishing an observation equation including the ephemeris error term for the reference station and the rover station; constructing a differential correction quantity by taking the difference between the observed value and the theoretical observed value of the reference station; constructing a differential correction quantity for the residual atmospheric error; calculating the corrected observed value of the rover station by using the observed value of the rover station, the differential correction quantity and the differential correction quantity of the residual atmospheric error; constructing an observation equation based on the corrected observed values of multiple satellites and constructing a state equation by using the constant acceleration model, defining the state vector as the joint estimator of the three-dimensional motion state of the rover station and the receiver clock drift, and using the unscented Kalman filter algorithm to real-time solve the precise position of the rover station on the basis of the observation equation and the state equation. Using this method can improve the differential positioning performance.

Description

Technical Field

[0001] This application relates to the field of satellite navigation technology, and particularly to a Doppler differential positioning method, device, equipment, and medium for low-Earth orbit satellites. Background Art

[0002] In recent years, the construction of low-Earth orbit satellites is in a stage of rapid deployment. Since the Doppler frequency shift of low-satellite signals is usually used as a velocity measurement observable. And due to the high-speed motion characteristics of low-Earth orbit satellites, the Doppler frequency shift of their ground signals can also be used as an effective positioning observable. Therefore, the positioning technology based on low-Earth orbit satellite Doppler frequency shift information has become one of the research hotspots of backup navigation technology. In 2022, Neinavaie et al. obtained the Doppler differential positioning accuracy of 10 m horizontally for the first time using the observations of a complete arc of 6 Starlink satellites. Scholars such as Wang and Schüler respectively modeled the tropospheric and ionospheric errors, improving the simulation accuracy.

[0003] Differential Doppler positioning refers to the synchronous observation of a reference station (with known precise coordinates) and a rover station (user terminal), and uses the Doppler frequency shift difference generated when both receive the same satellite signal to correct the positioning error of the rover station in real time. However, different from the differential correction of GNSS, due to the low-orbit characteristics of satellites, the differential correction amount cannot completely cancel the atmospheric Doppler error of the rover station, and there is currently a lack of research on the baseline length and the degree of atmospheric error correction. In the real-time Doppler positioning experiment of low-Earth orbit satellite downlink signals in the actual measurement environment, the single-point positioning accuracy is still low, and there are limitations in dealing with random errors such as the ionosphere and troposphere in the existing methods. Due to the low-orbit characteristics, the residual atmospheric error will significantly affect the differential positioning performance. Summary of the Invention

[0004] Based on this, in view of the above technical problems, it is necessary to provide a Doppler differential positioning method, device, equipment, and medium for low-Earth orbit satellites that can improve the differential positioning performance.

[0005] A Doppler differential positioning method for low-Earth orbit satellites, the method includes:

[0006] Construct an ionospheric error model considering the low-Earth orbit Doppler characteristics according to the Nequick-G model, and calculate the STEC change rate at the reference epoch according to the error model; use the STEC change rate to calculate the ionospheric delay rate correction value in real time; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model;

[0007] Establish the observation equations of the reference station and the rover station that include the ephemeris error term; construct the differential correction quantity by taking the difference between the observed value and the theoretical observed value of the reference station; construct the differential correction quantity of the residual atmospheric error by taking the difference between the atmospheric error model correction values of the reference station and the rover station; calculate the corrected observed value of the rover station by using the observed value of the rover station, the differential correction quantity, and the differential correction quantity of the residual atmospheric error;

[0008] Construct the observation equation based on the corrected observed values of the rover station for multiple satellites and construct the state equation by using the constant acceleration model. Define the state vector as the joint estimator of the three-dimensional motion state of the rover station and the receiver clock drift, and use the unscented Kalman filter algorithm to real-time solve the precise position of the rover station based on the observation equation and the state equation.

[0009] A Doppler differential positioning device for low Earth orbit satellites, the device includes:

[0010] An atmospheric error model correction value calculation module, which is used to construct an ionospheric error model considering the low Earth orbit Doppler characteristics according to the Nequick-G model, calculate the STEC change rate at the reference epoch according to the error model; calculate the ionospheric delay rate correction value in real time by using the STEC change rate; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the atmospheric error model correction values;

[0011] A differential correction quantity module, which is used to establish the observation equations of the reference station and the rover station that include the ephemeris error term; construct the differential correction quantity by taking the difference between the observed value and the theoretical observed value of the reference station; construct the differential correction quantity of the residual atmospheric error by taking the difference between the atmospheric error model correction values of the reference station and the rover station; calculate the corrected observed value of the rover station by using the observed value of the rover station, the differential correction quantity, and the differential correction quantity of the residual atmospheric error;

[0012] A positioning module, which is used to construct the observation equation based on the corrected observed values of the rover station for multiple satellites and construct the state equation by using the constant acceleration model. Define the state vector as the joint estimator of the three-dimensional motion state of the rover station and the receiver clock drift, and use the unscented Kalman filter algorithm to real-time solve the precise position of the rover station based on the observation equation and the state equation.

[0013] A computer device, including a memory and a processor, the memory stores a computer program, and when the processor executes the computer program, the following steps are implemented:

[0014] Construct an ionospheric error model considering the low-orbit Doppler characteristics according to the Nequick-G model, and calculate the STEC change rate at the reference epoch according to the error model; use the STEC change rate to calculate the ionospheric delay rate correction value in real time; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model.

[0015] Establish the observation equations of the reference station and the roving station including the ephemeris error term; construct the differential correction quantity by taking the difference between the observed value of the reference station and the theoretical observed value; construct the differential correction quantity of the residual atmospheric error by taking the difference between the correction values of the atmospheric error models of the reference station and the roving station; calculate the corrected observed value of the roving station by using the observed value of the roving station, the differential correction quantity and the differential correction quantity of the residual atmospheric error.

[0016] Construct the observation equations according to the corrected observed values of the roving station for multiple satellites and construct the state equations by using the constant acceleration model. Define the state vector as the joint estimator of the three-dimensional motion state of the roving station and the receiver clock drift, and use the unscented Kalman filter algorithm to real-time solve the precise position of the roving station based on the observation equations and the state equations.

[0017] A computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the following steps are implemented:

[0018] Construct an ionospheric error model considering the low-orbit Doppler characteristics according to the Nequick-G model, and calculate the STEC change rate at the reference epoch according to the error model; use the STEC change rate to calculate the ionospheric delay rate correction value in real time; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model.

[0019] Establish the observation equations of the reference station and the roving station including the ephemeris error term; construct the differential correction quantity by taking the difference between the observed value of the reference station and the theoretical observed value; construct the differential correction quantity of the residual atmospheric error by taking the difference between the correction values of the atmospheric error models of the reference station and the roving station; calculate the corrected observed value of the roving station by using the observed value of the roving station, the differential correction quantity and the differential correction quantity of the residual atmospheric error.

[0020] Construct the observation equations according to the corrected observed values of the roving station for multiple satellites and construct the state equations by using the constant acceleration model. Define the state vector as the joint estimator of the three-dimensional motion state of the roving station and the receiver clock drift, and use the unscented Kalman filter algorithm to real-time solve the precise position of the roving station based on the observation equations and the state equations.

[0021] The above-mentioned Doppler differential positioning method, device, equipment and medium for low-earth orbit satellites. In this application, an ionospheric error model is constructed based on the Nequick-G model, and the low-earth orbit Doppler characteristics are fully considered to accurately calculate the STEC change rate at the reference epoch, and then the ionospheric delay rate correction value is obtained in real time to accurately compensate for the ionospheric delay error. At the same time, combining the zenith tropospheric delay and the satellite elevation angle, the tropospheric delay rate correction value is calculated to effectively reduce the tropospheric delay error. Secondly, the observation equations including the ephemeris error terms for the reference station and the roving station are constructed to comprehensively cover the error factors. By taking the difference between the observed values of the reference station and the theoretical observed values, the differential correction amount is constructed to reduce the common errors between the reference station and the roving station. Then, by taking the difference between the corrected values of the atmospheric error models of the reference station and the roving station, the differential correction amount of the residual atmospheric error is obtained to further correct the deviation of the roving station caused by the residual atmospheric error. Finally, according to the corrected observed values of multiple satellites for the roving station, the observation equation is constructed, and the state equation is constructed using the constant acceleration model. The state vector is set as the joint estimator of the three-dimensional motion state of the roving station and the receiver clock drift. According to the unscented Kalman filter algorithm, integrating the observation information of multiple satellites and considering the motion and clock drift of the roving station, high-precision real-time positioning is achieved, effectively overcoming the adverse effects of the residual atmospheric error under the low-orbit characteristics on the differential positioning performance, and significantly improving the accuracy and reliability of positioning. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a schematic flowchart of a Doppler differential positioning method for a low-earth orbit satellite in an embodiment;

[0023] Figure 2 It is a schematic diagram of an inter-station differential model in an embodiment;

[0024] Figure 3 It is a structural block diagram of a Doppler differential positioning device for a low-earth orbit satellite in an embodiment;

[0025] Figure 4 It is an internal structure diagram of a computer device in an embodiment. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0026] In order to make the objectives, technical solutions and advantages of this application clearer, the following further elaborates on this application in combination with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0027] In one embodiment, as Figure 1 shown, a Doppler differential positioning method for a low-earth orbit satellite is provided. Under the inter-station differential model shown in Figure 2 , the method includes the following steps:

[0028] Step 102: Construct an ionospheric error model considering the characteristics of low-orbit Doppler according to the Nequick-G model, and calculate the STEC change rate at the reference epoch according to the error model; Use the STEC change rate to calculate the ionospheric delay rate correction value in real time; Calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; The ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model.

[0029] First, a real-time correction method based on the Nequick-G (Galileo single-frequency ionospheric correction algorithm) model is designed. The Nequick-G model calculates the effective ionization factor through the ionospheric coefficients in the corresponding broadcast ephemeris (solar activity parameters ), and the calculation formula is as follows:

[0030] ;

[0031] ;

[0032] where is the transmitted ionospheric coefficient, is the modified magnetic declination (MODIP) at the receiver location.

[0033] The conversion formula between F10.7 (the average value of the solar radiation flux at a wavelength of 10.7 cm) and R12 (the 12-month moving average sunspot number) is as follows:

[0034] ;

[0035] ;

[0036] The calculation process of

[0037] ;

[0038] ;

[0039] ;

[0040] ;

[0041] ;

[0042] ;

[0043] ;

[0044] In the formula, the [] symbol represents rounding; is the geographical latitude, is the longitude; is the MODIP grid attribute value ; is the third-order interpolation function; is the interpolation function at x.

[0045] Specifically, using the known satellite velocity at the reference epoch, recursively calculate the satellite position after, and regard it as a virtual epoch. Then, substitute the satellite position of this virtual epoch into the Nequick-G model to obtain the correction value at the virtual epoch. Next, take the difference with the correction value at the reference epoch to obtain the STEC change rate at the reference epoch. The specific mathematical expression is as follows:

[0046] ;

[0047] Among them, is the satellite coordinate, is the Nequick-G model, and the expression adds and two adaptation parameters on the basis of the Nequick-G model, so it is called the Adaptive Nequick-G (A-Nequick) model. can effectively reduce the jump of the correction value caused by the epoch difference; while can adjust the systematic deviation caused by the movement of low-orbit satellites in the ionosphere.

[0048] By calculating the STEC (slant total electron content) change rate at the reference epoch, the dynamic change of the ionospheric electron content can be grasped in real time, and then the ionospheric delay rate correction value can be calculated by using it to effectively compensate for the ionospheric delay error. The process of obtaining the ionospheric delay rate correction value in real time according to the STEC change rate at the reference epoch is an existing technology and will not be elaborated too much in this application.

[0049] At the same time, a simplified tropospheric Doppler model considering the wet component, receiver height, and seasonal temperature is proposed:

[0050] ;

[0051] ;

[0052] Among them, is the tropospheric delay rate correction value in m / s. ZTD(m) is the zenith tropospheric delay empirical value, which is a function of the month value and is obtained from Table 2. and Is the random angular measurement of the dry and wet components. Is the zenith tropospheric delay at altitude 0; Is the altitude in km. Is the satellite elevation angle in radians. E is the base of the natural logarithm (approximately equal to 2.71828).

[0053] Table 1

[0054]

[0055] It can be seen from Table 1 that in a wide range from high latitudes (Ulan Bator, 47.865°) to low latitudes (Bangkok, 13.736°), it can reflect the tropospheric delay characteristics under different climate conditions. In high-latitude regions, the temperature is usually lower and the water vapor is less, resulting in smaller tropospheric delays; in mid-latitude regions (such as Beijing and Wuhan), the four seasons change, and the water vapor and temperature fluctuate greatly; while in low-latitude regions (such as Hong Kong and Bangkok), it is high temperature and high humidity, which may lead to larger tropospheric delays.

[0056] Table 2 shows the mean values of ZTD measurement data of five stations in different months (January - February, March - April, May - June, July - August, September - October, and November - December), reflecting the climate characteristics of each region in different seasons. The measured values in Ulan Bator are relatively stable, while Beijing reaches the highest value in spring and summer, showing obvious seasonal variations. The values in Wuhan are relatively balanced, and Hong Kong and Bangkok show higher measured values in summer, reflecting the characteristics of tropical climate. Considering the influence of seasonal temperature, the model takes the mean values in Table 2 as the values of ZTD(m).

[0057] Table 2

[0058]

[0059] Step 104, establish the observation equations including the ephemeris error term for the reference station and the rover station; construct the differential correction quantity by taking the difference between the observed value and the theoretical observed value of the reference station; construct the differential correction quantity of the residual atmospheric error by taking the difference between the corrected values of the atmospheric error models of the reference station and the rover station; calculate the corrected observed value of the rover station by using the observed value of the rover station, the differential correction quantity, and the differential correction quantity of the residual atmospheric error.

[0060] In view of the influence of the ephemeris error of low-earth-orbit communication satellites, establish the observation equations including the ephemeris error term. The complete observation equation can be expressed as:

[0061] ;

[0062] In the formula, the subscript Is a wildcard (replaced by When it is the reference station, and replaced by ), represents the geometric distance from the satellite to the receiver, is the observation noise. The formula contains four physical terms: the theoretical Doppler observation term characterizes the Doppler observation of the receiver and the true satellite state, and for the rover, it includes the position and velocity parameters to be estimated; the ephemeris error term reflects the influence of satellite position and velocity errors; the clock drift term includes the satellite clock drift and the rover clock drift ; the propagation delay term mainly considers the ionosphere and the troposphere time-varying effects. The relativistic effect is not listed separately because its magnitude is small and it is easily coupled to the clock error term.

[0063] Since the coordinates of the reference station are known, the theoretical observation value of the reference station can be defined as:

[0064] ;

[0065] Thus, the differential correction amount is constructed. In addition, according to the error model, the differential correction amount of the residual atmospheric error is constructed:

[0066] ;

[0067] where is the residual atmospheric error correction amount. and[[ID=3�]] are the correction values of the atmospheric error models of the reference station and the rover respectively. The receiver coordinates required to calculate the rover correction value can be approximately replaced by the initial positioning result. Compensating the correction amount to the rover observation value, we can get:

[0068] ;

[0069] is the rover observation value corrected by the differential correction information. Based on the "parallel" assumption in the previous text, contains errors such as ephemeris, atmosphere, and satellite clock drift that are approximately equal to the various errors of the rover. And contains a part of the residual atmospheric error caused by spatio-temporal correlation. Therefore, this inter-station differential operation can effectively suppress the common error terms including ephemeris error in the rover, and significantly improve the positioning accuracy. The corrected rover observation value only contains the difference between the receiver clock drift and the uncorrected observation noise, and the specific expression is

[0070] ;

[0071] where They are the observation noise values of the rover station and the reference station respectively. While eliminating the systematic errors, this model retains the Doppler observables directly related to the motion state of the rover station, providing an observation basis for subsequent UKF filtering.

[0072] Step 106: Construct an observation equation based on the corrected rover station observations of multiple satellites and a state equation using a constant acceleration model. Define the state vector as the joint estimator of the three-dimensional motion state of the rover station and the receiver clock drift, and use the unscented Kalman filter algorithm to solve the precise position of the rover station in real time based on the observation equation and the state equation.

[0073] Define the state vector at the kth epoch as the three-dimensional motion state of the rover station and the receiver clock drift of the joint estimator:

[0074] ;

[0075] The observation equation is composed of the differential corrected Doppler frequency shifts of N satellites output by the satellite selection algorithm:

[0076] ;

[0077] The state transition model uses a constant acceleration model, and its discrete state equation is:

[0078] ;

[0079] where is the epoch interval, and the process noise covariance matrix needs to be adjusted according to the dynamic characteristics of the carrier.

[0080] UKF accurately propagates the state distribution through unscented transformation, and its core steps are as follows: First, generate a Sigma point set to capture the statistical characteristics of the state mean and covariance; propagate the Sigma points through the nonlinear observation model, calculate the predicted observables and their covariance; update the state estimate by combining the actual observations. To improve the calculation efficiency, a symmetric sampling strategy is adopted to reduce the number of Sigma points, and a dynamic adjustment mechanism is introduced to optimize the scaling parameter , balancing the high-order moment approximation accuracy and numerical stability. Regarding the design problem of the observation noise covariance matrix, since the atmospheric error is strongly correlated with the elevation angle, the elevation angle weighted model commonly used in GNSS is adopted. The specific formula for the weight value is as follows:

[0081] ;

[0082] where is the elevation angle of the th satellite.

[0083] The process of using the unscented Kalman filter algorithm to calculate the precise position of the rover in real time is shown in Table 3.

[0084] Table 3

[0085]

[0086] For the above Doppler differential positioning method of low Earth orbit satellites, the present application constructs an ionospheric error model according to the Nequick - G model, fully considers the characteristics of low Earth orbit Doppler, accurately calculates the STEC change rate at the reference epoch, and then obtains the ionospheric delay rate correction value in real time to accurately compensate for the ionospheric delay error. At the same time, combining the zenith tropospheric delay and the satellite elevation angle, the tropospheric delay rate correction value is calculated to effectively reduce the tropospheric delay error. Secondly, the observation equations of the reference station and the rover including the ephemeris error term are constructed to comprehensively cover the error factors. By taking the difference between the observed value of the reference station and the theoretical observed value, the differential correction amount is constructed to reduce the common errors between the reference station and the rover. Then, by taking the difference between the correction values of the atmospheric error models of the reference station and the rover, the differential correction amount of the residual atmospheric error is obtained to further correct the deviation of the rover caused by the residual atmospheric error. Finally, according to the observed values of the rover corrected by multiple satellites, the observation equation is constructed, and the state equation is constructed using the constant acceleration model. The state vector is set as the joint estimator of the three - dimensional motion state of the rover and the receiver clock drift. According to the unscented Kalman filter algorithm, integrating the observation information of multiple satellites and considering the motion and clock drift of the rover, high - precision real - time positioning is achieved, effectively overcoming the adverse effects of the residual atmospheric error under the low - orbit characteristics on the differential positioning performance, and significantly improving the accuracy and reliability of positioning.

[0087] In one embodiment, calculating the STEC change rate at the reference epoch according to the ionospheric error model includes:

[0088] Using the known satellite velocity at the reference epoch, recursively calculate the satellite position after, and regard it as a virtual epoch. Substitute the satellite position of this virtual epoch into the Nequick - G model, and take the difference between the correction value at the virtual epoch and the correction value at the reference epoch to obtain the STEC change rate at the reference epoch. The specific formula is as follows:

[0089] ;

[0090] where, is the satellite coordinate, is the Nequick - G model, represents a value that can reduce the jump of the correction value caused by the difference between epochs; represents the time interval.

[0091] In one embodiment, calculating a tropospheric delay rate correction value based on the zenith tropospheric delay and the satellite elevation angle includes:

[0092] Calculating the tropospheric delay rate correction value based on the zenith tropospheric delay and the satellite elevation angle as

[0093] ;

[0094] ;

[0095] wherein, is the tropospheric delay rate correction value in m / s, ZTD(m) is the empirical value of the zenith tropospheric delay, and are the random angular quantities of the dry and wet components, is the zenith tropospheric delay at an altitude of 0; is the altitude in km, is the satellite elevation angle in radians.

[0096] In one embodiment, establishing the observation equations including the ephemeris error terms for the reference station and the rover includes:

[0097] ;

[0098] wherein, the subscript is a wildcard, which is replaced by when it is the reference station, and replaced by when it is the rover, represents the geometric distance from the satellite to the receiver, is the observation noise, and the theoretical Doppler observation value term characterizes the Doppler observation of the receiver and the true satellite state, represents the velocity vector of the satellite, represents the velocity vector of the reference station or the rover, represents the unit direction vector from the satellite to the reference station or the rover, represents the satellite position, represents the speed of light, and for the rover, it includes the position and velocity parameters to be estimated; the ephemeris error term reflects the influence of the satellite position and velocity errors; the clock drift term includes the satellite clock drift and the receiver clock drift ; represents the propagation delay term of the ionosphere, represents the propagation delay term of the troposphere.

[0099] In one embodiment, calculating the corrected rover observation value by using the rover observation value, the differential correction amount, and the differential correction amount of the residual atmospheric error includes:

[0100] The corrected rover observations are calculated using the rover observations, differential corrections, and differential corrections for residual atmospheric errors as

[0101] ;

[0102] where, represents the rover observations, represents the differential corrections, represents the theoretical observations, represents the velocity vector of the reference station, represents the unit direction vector of the reference station, represents the carrier frequency, represents the velocity vector of the rover, represents the unit direction vector of the rover, represents the receiver clock drift term, represents the observations of the reference station, represents the differential corrections for residual atmospheric errors, and are the correction values of the atmospheric error models for the reference station and the rover respectively, are the observation noise values of the rover and the reference station respectively.

[0103] In one embodiment, the state vector is defined as the joint estimator of the three-dimensional motion state of the rover and the receiver clock drift, including:

[0104] Define the k epoch state vector as the joint estimator of the three-dimensional motion state of the rover and the receiver clock drift as

[0105] ;

[0106] where T represents the transpose operation.

[0107] In one embodiment, an observation equation is constructed based on the corrected rover observations of multiple satellites and a state equation is constructed using a constant acceleration model, including:

[0108] The observation equation constructed based on the corrected rover observations of multiple satellites is:

[0109] ;

[0110] The state equation constructed using a constant acceleration model is:

[0111] ;

[0112] where, Nrepresents the serial number of the satellite, represents the corrected rover observation value, is the epoch interval, represents the process noise covariance matrix.

[0113] It should be understood that although Figure 1 each step in the flowchart of Figure 1 is shown in sequence according to the indication of the arrow, these steps are not necessarily executed in the order indicated by the arrow. Unless otherwise clearly stated in this article, there is no strict order restriction for the execution of these steps, and these steps can be executed in other orders. Moreover,

[0114] In one embodiment, as Figure 3 shown, a Doppler differential positioning device for low-earth orbit satellites is provided, including: an atmospheric error model correction value calculation module 302, a differential correction amount module 304, and a positioning module 306, where:

[0115] The atmospheric error model correction value calculation module 302 is used to construct an ionospheric error model considering the Doppler characteristics of low-earth orbit according to the Nequick-G model, calculate the STEC change rate at the reference epoch according to the error model; calculate the ionospheric delay rate correction value in real time using the STEC change rate; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the atmospheric error model correction values;

[0116] The differential correction amount module 304 is used to establish an observation equation including the ephemeris error term for the reference station and the rover; construct a differential correction amount by taking the difference between the observed value of the reference station and the theoretical observed value; construct a differential correction amount for the residual atmospheric error by taking the difference between the atmospheric error model correction values of the reference station and the rover; calculate the corrected rover observation value using the observed value of the rover, the differential correction amount, and the differential correction amount of the residual atmospheric error;

[0117] The positioning module 306 is used to construct an observation equation according to the corrected rover observation values of multiple satellites and construct a state equation using the constant acceleration model, define the state vector as the joint estimator of the three-dimensional motion state of the rover and the receiver clock drift, and use the unscented Kalman filter algorithm to solve the exact position of the rover in real time based on the observation equation and the state equation.

[0118] For the specific limitations of the Doppler differential positioning device for low-earth orbit satellites, reference can be made to the limitations of the Doppler differential positioning method for low-earth orbit satellites in the above text, which will not be elaborated here. Each module in the above Doppler differential positioning device for low-earth orbit satellites can be implemented in whole or in part by software, hardware, and their combination. The above-mentioned modules can be embedded in the processor of the computer device in hardware form or be independent of it, or can be stored in the memory of the computer device in software form, so as to facilitate the processor to call and execute the operations corresponding to the above-mentioned modules.

[0119] In one embodiment, a computer device is provided. The computer device can be a terminal, and its internal structure diagram can be as Figure 4 shown. The computer device includes a processor, a memory, a network interface, a display screen, and an input device connected through a system bus. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it realizes a Doppler differential positioning method for low-earth orbit satellites. The display screen of the computer device can be a liquid crystal display screen or an electronic ink display screen. The input device of the computer device can be a touch layer covering the display screen, or a button, a trackball, or a touchpad provided on the housing of the computer device, or an external keyboard, touchpad, or mouse, etc.

[0120] Those skilled in the art can understand that Figure 4 the structure shown in

[0121] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, storage, database, or other medium used in the embodiments provided in the present application can include non-volatile and / or volatile memories. 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 many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDR SDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and Rambus dynamic RAM (RDRAM), etc.

[0122] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0123] The above-described embodiments merely represent several implementation manners of the present application. The description thereof is relatively specific and detailed, but it should not be construed as a limitation on the scope of the present application. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several modifications and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A Doppler differential positioning method for low-earth orbit satellites, characterized in that, The method includes: Constructing an ionospheric error model considering the low-orbit Doppler characteristics according to the Nequick-G model, and calculating the STEC change rate at the reference epoch according to the error model; calculating the ionospheric delay rate correction value in real time by using the STEC change rate; calculating the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model; Establishing the observation equations including the ephemeris error term for the reference station and the roving station; constructing the differential correction amount by taking the difference between the observed value of the reference station and the theoretical observed value; constructing the differential correction amount of the residual atmospheric error by taking the difference between the correction values of the atmospheric error models of the reference station and the roving station; calculating the corrected observed value of the roving station by using the observed value of the roving station, the differential correction amount and the differential correction amount of the residual atmospheric error; Constructing the observation equation according to the corrected observed values of multiple satellites for the roving station and constructing the state equation by using the constant acceleration model, defining the state vector as the joint estimator of the three-dimensional motion state of the roving station and the receiver clock drift, and solving the precise position of the roving station in real time by using the unscented Kalman filter algorithm based on the observation equation and the state equation.

2. The method according to claim 1, wherein Calculating the STEC change rate at the reference epoch according to the ionospheric error model, including: Using the known satellite velocity at the reference epoch, recursively calculate the satellite position after and regard it as a virtual epoch. Substitute the satellite position of this virtual epoch into the Nequick-G model, calculate the difference between the correction value at the virtual epoch and the correction value at the reference epoch to obtain the STEC change rate at the reference epoch. The specific formula is as follows: ； Among them, is the satellite coordinate, is the Nequick-G model, represents a value that can reduce the jump of the correction value caused by the difference between epochs; represents the time interval.

3. The method according to claim 1, wherein Calculating the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle, including: Calculating the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle as ； ； Among them, is the tropospheric delay rate correction value in m / s, and ZTD(m) is the zenith tropospheric delay empirical value. and are the random angular quantities of the dry and wet components. is the zenith tropospheric delay at an altitude of 0. is the altitude in km. is the satellite elevation angle in radians.

4. The method according to claim 1, characterized in that Establishing the observation equations including the ephemeris error term for the reference station and the roving station, including: ； Among them, the subscript is a wildcard, which is replaced by at the reference station and replaced by at the rover station. represents the geometric distance from the satellite to the receiver. is the observation noise. The theoretical Doppler observation term characterizes the Doppler observation of the receiver and the true satellite state. represents the velocity vector of the satellite. represents the velocity vector of the reference station or the rover station. represents the unit direction vector from the satellite to the reference station or the rover station. represents the satellite position. represents the speed of light, which includes the position and velocity parameters to be estimated for the rover station; the ephemeris error term reflects the influence of satellite position and velocity errors; the clock drift term includes the satellite clock drift and the receiver clock drift . represents the propagation delay term of the ionosphere. represents the propagation delay term of the troposphere.

5. The method according to claim 1, wherein Calculating the corrected observed value of the roving station by using the observed value of the roving station, the differential correction amount and the differential correction amount of the residual atmospheric error, including: Calculating the corrected observed value of the roving station by using the observed value of the roving station, the differential correction amount and the differential correction amount of the residual atmospheric error as ； Among them, represents the observed value of the rover station, represents the differential correction amount, represents the theoretical observed value, represents the velocity vector of the reference station, represents the unit direction vector of the reference station, represents the carrier frequency, represents the velocity vector of the rover station, represents the unit direction vector of the rover station, represents the receiver clock drift term, represents the observed value of the reference station, represents the differential correction amount of the residual atmospheric error, and are the correction values of the atmospheric error models of the reference station and the rover station respectively, are the observation noise values of the rover station and the reference station respectively.

6. The method according to claim 1, characterized in that Defining the state vector as the joint estimator of the three-dimensional motion state of the roving station and the receiver clock drift, including: Define the k epoch state vector as the combined estimator of the three-dimensional motion state of the rover station and the receiver clock drift is ； Where, T represents the transpose operation.

7. The method according to claim 1, characterized in that Constructing the observation equation according to the corrected observed values of multiple satellites for the roving station and constructing the state equation by using the constant acceleration model, including: Constructing the observation equation according to the corrected observed values of multiple satellites for the roving station as: ； Constructing the state equation by using the constant acceleration model as: ； Among them, N represents the serial number of the satellite, represents the observed value of the rover after correction, is the epoch interval, represents the process noise covariance matrix.

8. A Doppler differential positioning device for a low-earth orbit satellite, characterized in that, The device includes: An atmospheric error model correction value calculation module, configured to construct an ionospheric error model considering the low-orbit Doppler characteristics according to the Nequick-G model, calculate the STEC change rate at the reference epoch according to the error model; calculate the ionospheric delay rate correction value in real time by using the STEC change rate; calculate the tropospheric delay rate correction value according to the zenith tropospheric delay and the satellite elevation angle; the ionospheric delay rate correction value and the tropospheric delay rate correction value are the correction values of the atmospheric error model; The differential correction module is used to establish the observation equations including ephemeris error terms for the reference station and the rover station; construct differential corrections by taking the difference between the observed values and the theoretical observed values of the reference station; construct differential corrections for the residual atmospheric error by taking the difference between the corrected values of the atmospheric error models of the reference station and the rover station; and calculate the corrected observed values of the rover station by using the observed values of the rover station, the differential corrections, and the differential corrections for the residual atmospheric error. The positioning module is used to construct an observation equation based on the corrected observed values of the rover station for multiple satellites and construct a state equation by using a constant acceleration model, define the state vector as the joint estimator of the three-dimensional motion state of the rover station and the receiver clock drift, and use the unscented Kalman filter algorithm to solve the precise position of the rover station in real time based on the observation equation and the state equation.

9. A computer device, comprising a memory and a processor, the memory storing a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method according to any one of claims 1 to 7.

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