Low earth orbit satellite doppler single point positioning method, apparatus, and medium

Abstract

Embodiments of the present application provide a low-orbit satellite Doppler single point positioning method, device and medium. The method comprises: acquiring Doppler observations of low-orbit satellites received by a receiver in two consecutive ephemeris and ephemeris data of each low-orbit satellite, establishing a plurality of grid points in a preset area range, and obtaining a theoretical Doppler frequency shift rate according to the ephemeris data; calculating the measured Doppler frequency shift rate of each low-orbit satellite according to the Doppler observations in two consecutive ephemeris; calculating the rate difference; summing the absolute values of the rate difference corresponding to each grid point, selecting a target grid point, taking its coordinates as the initial coordinates of the receiver, and using it for low-orbit satellite Doppler single point positioning filter initialization to obtain the position of the receiver. The problem that it is difficult to obtain the initial position of the receiver without other observation assistance and prior position information in the GNSS signal weakening or denial environment, leading to the difficulty of correct convergence of low-orbit satellite Doppler single point positioning, is solved.

Description

Technical Field

[0001] This application relates to the field of satellite navigation and positioning technology, specifically to a low-orbit satellite Doppler point positioning method, device, and medium. Background Technology

[0002] Global Navigation Satellite System (GNSS) provides users with positioning, navigation, and timing services. In environments with good observation conditions, such as open areas or minimal obstruction, GNSS satellite signals combined with positioning technologies such as Real-time Kinematics (RTK) and Precise Point Positioning (PPP) can obtain highly accurate receiver position information. Therefore, it is widely used in fields such as autonomous driving, precision agriculture, and robot path planning.

[0003] However, in environments such as urban canyons and densely wooded areas, GNSS satellite signals are easily blocked by buildings, trees, etc., leading to signal weakening or even complete failure to receive them. In such cases, users may struggle to obtain effective GNSS observation data, and Positioning, Navigation, and Timing (PNT) services may be interrupted. Furthermore, even after GNSS signals are restored, if available position assistance information is lacking, it may take a considerable amount of time to regain effective positioning results, affecting the continuity and real-time performance of navigation and positioning services. Low Earth Orbit (LEO) satellites, characterized by higher signal power upon landing, faster Earth-to-ground motion, and larger Doppler frequency shifts, still offer the possibility of positioning using LEO satellite signals even when GNSS signals are severely blocked or denied. Point positioning based on LEO satellite Doppler observations can serve as a positioning method in scenarios where GNSS positioning is limited. However, LEO satellite Doppler point positioning is somewhat dependent on the receiver's initial position. When the receiver's initial position error is large, Doppler point positioning may fail to converge to the correct receiver position.

[0004] Existing technologies typically require prior receiver position information or other types of observation information to pre-determine the receiver's initial position. Therefore, in the absence of other observational aids and prior receiver position information, obtaining an initial receiver position that satisfies the convergence requirements of subsequent Doppler point localization becomes a problem that needs to be solved. Summary of the Invention

[0005] The purpose of this application is to provide a low-orbit satellite Doppler single-point positioning method, device, and medium.

[0006] To achieve the above objectives, the first aspect of this application provides a low-Earth orbit satellite Doppler point positioning method, comprising: Acquire Doppler observations from at least one low-Earth orbit satellite received by the receiver in two consecutive epochs, as well as ephemeris data from each low-Earth orbit satellite; Multiple grid points are established within a preset area, and the theoretical Doppler shift of each grid point for each low-Earth orbit satellite in two consecutive epochs is calculated based on ephemeris data. The theoretical Doppler shift rate of change for each grid point for each low-Earth orbit satellite is calculated based on the theoretical Doppler shift corresponding to two consecutive epochs. Based on the Doppler observations of each low-Earth orbit satellite corresponding to two consecutive epochs, the measured Doppler frequency shift rate of each low-Earth orbit satellite is calculated. Calculate the difference between the theoretical Doppler frequency shift rate of change for each grid point and the corresponding measured Doppler frequency shift rate of change for each low-Earth orbit satellite; The absolute values ​​of the rate of change differences of each low-orbit satellite corresponding to each grid point are summed, and the grid point with the smallest sum of the absolute values ​​of the rate of change differences is determined as the target grid point. The coordinates corresponding to the target grid points are determined as the initial coordinates of the receiver, and the initial coordinates of the receiver are used as the initialization parameters for low-Earth orbit satellite Doppler single-point positioning filtering. Low-Earth orbit satellite Doppler single-point positioning filtering is performed to obtain the position of the receiver.

[0007] In this embodiment of the application, the theoretical Doppler shift of each grid point for each low-Earth orbit satellite over two consecutive epochs is calculated based on ephemeris data, including: Determine the position and velocity of each low-Earth orbit satellite in two consecutive epochs based on ephemeris data; Using the coordinates of each grid point as the receiver position and setting the receiver velocity to zero, the theoretical Doppler shift for each grid point for each low-Earth orbit satellite in two consecutive epochs is calculated based on the satellite position, satellite velocity, and receiver position.

[0008] In this embodiment of the application, the theoretical Doppler frequency shift rate is:

[0009] The measured Doppler frequency shift rate is:

[0010] in, The theoretical Doppler frequency shift rate, To measure the Doppler frequency shift rate, and These represent the theoretical Doppler frequency shifts of the same grid point for the same low-Earth orbit satellite at two consecutive epochs. and These are the Doppler observations from a low-Earth orbit satellite at two consecutive epochs. and These represent the times corresponding to two consecutive epochs.

[0011] In this embodiment of the application, the preset area ranges from 3° to 54° north latitude and from 73° to 136° east longitude. Within the preset area, multiple grid points are established along the longitude and latitude directions with a step size of 0.5°.

[0012] In this embodiment of the application, the receiver's initial coordinates are used as the initialization parameters for low-Earth orbit satellite Doppler point positioning filtering, including: The initial coordinates of the receiver are used as the initial values ​​of the receiver's three-dimensional position, and the initial values ​​of the receiver's three-dimensional velocity and clock speed are zero.

[0013] In this embodiment, the low-Earth orbit satellite Doppler single-point positioning filter adopts the extended Kalman filter. The extended Kalman filter calculates the state variables, including the receiver's three-dimensional position, receiver's three-dimensional velocity, and receiver's clock speed, based on the Doppler observations of each low-Earth orbit satellite.

[0014] In this embodiment of the application, the theoretical Doppler shift of each grid point for each low-Earth orbit satellite is:

[0015] in, For theoretical Doppler frequency shift, The transmission signal frequency for low-Earth orbit satellites. At the speed of light, For low-Earth orbit satellites, This refers to the satellite position of the low-Earth orbit satellite. The receiver positions corresponding to the grid points. This represents the distance between the receiver position corresponding to the grid point and the satellite position of the low-Earth orbit satellite.

[0016] In this embodiment of the application, during the extended Kalman filtering process, the iteration is stopped when the norm of the iterative correction of the state variable is less than a first preset threshold, or when the number of iterations reaches a second preset threshold.

[0017] A second aspect of this application provides a low-Earth orbit satellite Doppler point positioning device based on frequency shift rate of change grid search, comprising: The memory is configured to store instructions; The processor is configured to retrieve instructions from memory and, when executing instructions, to implement a low-Earth orbit satellite Doppler point positioning method.

[0018] A third aspect of this application provides a machine-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform a low-Earth orbit satellite Doppler point positioning method.

[0019] This application proposes a low-Earth orbit (LEO) satellite Doppler point positioning method. Based on LEO satellite Doppler observations and ephemeris data from two consecutive epochs, the theoretical Doppler frequency shift rate of change for each grid point is calculated and matched with the measured Doppler frequency shift rate of change to determine the initial coordinates of the receiver. This enables the acquisition of the initial receiver position for LEO satellite Doppler point positioning filtering and positioning without other observation aids or prior position information. This solves the problem that it is difficult to obtain the initial receiver position in environments with weakened or denied GNSS signals, where there are no other observation aids or prior position information, leading to the difficulty in correctly converging LEO satellite Doppler point positioning.

[0020] Other features and advantages of the embodiments of this application will be described in detail in the following detailed description section. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the embodiments of this application and form part of the specification. They are used together with the following detailed description to explain the embodiments of this application, but do not constitute a limitation on the embodiments of this application. In the drawings: Figure 1 The schematic diagram illustrates a flow chart of a low-Earth orbit satellite Doppler point positioning method according to an embodiment of this application; Figure 2 The schematic diagram illustrates the process of Doppler frequency shift rate grid search in the low-Earth orbit satellite Doppler single-point positioning method according to an embodiment of this application; Figure 3 The schematic diagram illustrates the low-Earth orbit satellite Doppler point positioning filtering process of the low-Earth orbit satellite Doppler point positioning method according to an embodiment of this application; Figure 4 The diagram illustrates the internal structure of a computer device according to an embodiment of this application. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are only for illustration and explanation of the embodiments of this application and are not intended to limit the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0023] Figure 1 A schematic flowchart illustrating a low-Earth orbit satellite Doppler point positioning method according to an embodiment of this application is shown. Figure 1 As shown, in one embodiment of this application, a low-Earth orbit satellite Doppler point positioning method is provided, including the following steps: Step 102: Obtain the Doppler observations of at least one low-Earth orbit satellite received by the receiver in two consecutive epochs, as well as the ephemeris data of each low-Earth orbit satellite; Step 104: Establish multiple grid points within a preset area, and calculate the theoretical Doppler shift of each grid point for each low-orbit satellite in two consecutive epochs based on ephemeris data; Step 106: Calculate the theoretical Doppler frequency shift change rate for each grid point for each low-Earth orbit satellite based on the theoretical Doppler frequency shift corresponding to two consecutive epochs; Step 108: Calculate the measured Doppler frequency shift rate of each low-Earth orbit satellite based on the Doppler observations of each low-Earth orbit satellite corresponding to two consecutive epochs. Step 110: Calculate the difference between the theoretical Doppler frequency shift rate of change for each grid point and the corresponding measured Doppler frequency shift rate of change for each low-Earth orbit satellite; Step 112: Sum the absolute values ​​of the rate of change differences of each low-orbit satellite corresponding to each grid point, and determine the grid point with the smallest sum of the absolute values ​​of the rate of change differences as the target grid point; Step 114: Determine the coordinates corresponding to the target grid points as the initial coordinates of the receiver, and use the initial coordinates of the receiver as the initialization parameters for low-Earth orbit satellite Doppler single-point positioning filtering. Perform low-Earth orbit satellite Doppler single-point positioning filtering to obtain the position of the receiver.

[0024] like Figure 2 As shown, in one specific implementation, when performing a Doppler frequency shift rate grid search, the receiver remains stationary for two consecutive observation epochs. The receiver's coarse position is searched using the low-orbit satellite Doppler observations and corresponding ephemeris data from the two consecutive epochs, without the need for other types of positioning observations or prior position information of the receiver.

[0025] A preset area is determined based on the potential location of the receiver, and multiple grid points with different coordinates are set within this area. Each grid point represents a candidate location for the receiver. For each grid point, the theoretical Doppler shift for each low-Earth orbit (LEO) satellite over two consecutive epochs is calculated based on ephemeris data. For the same grid point and the same LEO satellite, the corresponding theoretical Doppler shift rate of change is calculated based on the theoretical Doppler shift over two consecutive epochs and the time interval between those two epochs. Following the same method, the theoretical Doppler shift rate of change for each grid point for each LEO satellite can be obtained. Simultaneously, the measured Doppler shift rate of change for each LEO satellite is calculated based on the Doppler observations actually obtained by the receiver over two consecutive epochs. The theoretical Doppler shift rate of change characterizes the theoretical Doppler shift when the receiver is located at the corresponding grid point, while the measured Doppler shift rate of change characterizes the Doppler shift when the receiver actually receives LEO satellite signals.

[0026] For each grid point, the difference between the theoretical Doppler frequency shift rate of change for each low-Earth orbit (LEO) satellite and the measured Doppler frequency shift rate of change for the corresponding LEO satellite is calculated. This difference can be used to characterize the discrepancy between the theoretical and actual observed Doppler frequency shift changes for the current grid point.

[0027] Furthermore, the absolute values ​​of the rate of change differences corresponding to the same grid point are taken separately, and the absolute values ​​of the rate of change differences are summed to obtain the matching evaluation result corresponding to that grid point. After obtaining the matching evaluation results corresponding to each grid point in the above manner, the grid point with the smallest sum of the absolute values ​​of the rate of change differences is determined as the target grid point. Thus, the target grid point is a candidate location within the preset area where the theoretical Doppler frequency shift change and the actual Doppler frequency shift change have a high degree of matching. After determining the target grid point, the coordinates corresponding to the target grid point are determined as the initial coordinates of the receiver, and the low-Earth orbit satellite Doppler single-point positioning filter is initialized using these initial coordinates. After initialization, positioning filtering is performed based on the Doppler observations of the low-Earth orbit satellite, and the receiver position is obtained based on the result of the positioning filtering.

[0028] In this embodiment, the measured Doppler frequency shift rate is obtained through two consecutive epochs of low-Earth orbit (LEO) satellite Doppler observations, and the theoretical Doppler frequency shift rate corresponding to each grid point is obtained within a preset area. Target grid points are searched based on the difference between the theoretical and measured Doppler frequency shift rates, and the coordinates of these target grid points are used to initialize LEO satellite Doppler point positioning filtering. Therefore, in the absence of an accurate prior receiver position, initial position values ​​for positioning filtering can be obtained first, reducing the impact of excessive initial receiver position errors on LEO satellite Doppler point positioning convergence. When the GNSS signal is severely obstructed or cannot provide effective positioning observations, LEO satellite Doppler observations can continue to obtain receiver position information and provide position auxiliary information for the corresponding positioning calculation after the GNSS signal is recovered.

[0029] In one embodiment, calculating the theoretical Doppler shift of each grid point for each low-Earth orbit satellite over two consecutive epochs based on ephemeris data includes: determining the satellite position and satellite velocity of each low-Earth orbit satellite over two consecutive epochs based on ephemeris data; using the coordinates of each grid point as the receiver position and setting the receiver velocity to zero; and calculating the theoretical Doppler shift of each grid point for each low-Earth orbit satellite over two consecutive epochs based on the satellite position, satellite velocity, and receiver position.

[0030] Specifically, based on the ephemeris data of the low-Earth orbit (LEO) satellites, the satellite position and velocity of each LEO satellite are determined for two consecutive observation epochs. For each grid point within a preset area, the coordinates of that grid point are used as the assumed receiver position. During the grid search phase, the receiver velocity is set to zero. Based on the LEO satellite's position, velocity, and the receiver position corresponding to the current grid point, the motion of the LEO satellite relative to that grid point in the line-of-sight direction can be determined, and the corresponding theoretical Doppler shift can be calculated accordingly. When there is relative motion between the LEO satellite and the receiver, a Doppler shift occurs between the actual received signal frequency and the transmitted signal frequency of the LEO satellite. The Doppler shift is related to the relative velocity of the LEO satellite and the receiver in the line-of-sight direction and can be equivalently expressed as the relationship between the pseudorange change rate and the transmitted signal frequency of the LEO satellite, i.e.:

[0031] in, For Doppler frequency shift, The transmission signal frequency for low-Earth orbit satellites. At the speed of light, This represents the pseudorange variation rate between the satellite and the receiver. Therefore, the corresponding pseudorange variation rate can also be determined based on Doppler observations.

[0032] For the same grid point and the same low-Earth orbit satellite, the theoretical Doppler frequency shift for that grid point relative to the low-Earth orbit satellite over two consecutive epochs can be obtained by calculating the satellite position and velocity at those two epochs. In this way, theoretical Doppler information corresponding to actual Doppler observations can be constructed for each grid point within a preset area, providing a basis for subsequent calculations of the theoretical Doppler frequency shift rate of change. The specific calculation relationship of the theoretical Doppler frequency shift will be further explained in subsequent embodiments.

[0033] In one embodiment, the theoretical Doppler frequency shift rate is:

[0034] The measured Doppler frequency shift rate is:

[0035] in, The theoretical Doppler frequency shift rate, To measure the Doppler frequency shift rate, and These represent the theoretical Doppler frequency shifts of the same grid point for the same low-Earth orbit satellite at two consecutive epochs. and These are the Doppler observations from a low-Earth orbit satellite at two consecutive epochs. and These represent the times corresponding to two consecutive epochs.

[0036] Specifically, for any grid point and any low-Earth orbit (LEO) satellite, the theoretical Doppler frequency shift rate is determined using the difference between the theoretical Doppler frequency shift at the grid point and the theoretical Doppler frequency shift at the previous epoch, along with the time interval between two consecutive epochs. Correspondingly, for the same LEO satellite actually received by the receiver, the measured Doppler frequency shift rate is determined using the difference between the Doppler observations at the previous epoch and the same epoch time interval. Since both the theoretical and measured Doppler frequency shift rates are calculated using the same two consecutive epochs and the same time interval, they can be directly compared to obtain the corresponding rate difference. For example, the difference between the theoretical and measured Doppler frequency shift rates at the same grid point for the same LEO satellite can be obtained. After performing the above calculations for each low-orbit satellite observed at the same grid point, the absolute values ​​of the differences in the rates of change are summed, and this summation is used to evaluate the degree of matching between the current grid point and the actual position of the receiver.

[0037] By using the Doppler frequency shift changes between adjacent epochs as the basis for grid point matching, the characteristics of low-Earth orbit satellites, such as high orbital speed and significant changes in Doppler frequency shift over time, can be utilized to distinguish different candidate grid locations.

[0038] In one embodiment, the preset area ranges from 3° to 54° north latitude and 73° to 136° east longitude. Within the preset area, multiple grid points are established along the longitude and latitude directions with a step size of 0.5°.

[0039] Specifically, the region from 3°N to 54°N and from 73°E to 136°E is defined as the search area for the receiver's initial position. Within this region, the area is divided along both the latitudinal and longitude directions with a step size of 0.5°, and each latitudinal and longitude position is combined to form multiple grid points. Each grid point corresponds to a candidate receiver position within the preset area, thus forming a set of candidate grid points for the receiver's initial position search. During the subsequent grid search, the corresponding Doppler frequency shift rate matching result can be calculated for each grid point in the candidate grid point set, and the target grid point can be determined from it. Using the aforementioned preset area range can cover the corresponding geographic area to be located; using a grid step size of 0.5° allows for the initial receiver position search over a large area while controlling the number of grid points involved in the search, thereby obtaining an initial position value that can be used for subsequent low-Earth orbit satellite Doppler single-point positioning filtering. Under this grid range, grid step size, and corresponding test conditions, the position error obtained by grid search using the Doppler frequency shift rate can be less than 300 km.

[0040] In one embodiment, using the receiver's initial coordinates as initialization parameters for low-Earth orbit satellite Doppler point positioning filtering includes: using the receiver's initial coordinates as the initial value of the receiver's three-dimensional position, the initial value of the receiver's three-dimensional velocity, and the initial value of the receiver's clock speed as zero.

[0041] Specifically, after determining the target grid point, the initial coordinates of the receiver corresponding to the target grid point are used as the initial values ​​for the receiver's three-dimensional position in the low-Earth orbit (LEO) satellite Doppler single-point positioning filter. The receiver's three-dimensional position characterizes its location in a three-dimensional coordinate system. If the coordinate system used for grid search differs from that used for LEO satellite Doppler single-point positioning filtering, the coordinates corresponding to the target grid point can be transformed to the coordinate system used for positioning filtering, and the transformed three-dimensional coordinates are used as the initial values ​​for the receiver's three-dimensional position. In addition to the receiver's three-dimensional position, the initial values ​​of all components of the receiver's three-dimensional velocity and the initial value of the receiver's clock velocity are set to zero, thus forming the initial state required for subsequent LEO satellite Doppler single-point positioning filtering.

[0042] In one specific implementation, the filter initialization state can be represented as:

[0043] in, , and This represents the initial value of the receiver's three-dimensional position determined by the target grid points. , and These are the initial velocity values ​​of the receiver in three directions. This represents the initial value of the receiver clock speed. Where:

[0044]

[0045] The above initialization method can be used to provide the initial position of the receiver for subsequent Doppler single-point positioning using the position results obtained from the grid search, without the need to obtain accurate prior information on the receiver's three-dimensional velocity and clock speed.

[0046] In one embodiment, the low-Earth orbit satellite Doppler single-point positioning filter adopts the extended Kalman filter, which calculates the state variables including the receiver's three-dimensional position, receiver's three-dimensional velocity, and receiver's clock speed based on the Doppler observations of each low-Earth orbit satellite.

[0047] Specifically, after initializing the low-orbit satellite Doppler single-point positioning filter, the receiver's three-dimensional position, receiver's three-dimensional velocity, and receiver's clock speed are used together as the state variables of the extended Kalman filter.

[0048] The state variable can be represented as:

[0049] in, , and These represent the three position components of the receiver's three-dimensional position. , and These represent the three velocity components of the receiver's three-dimensional velocity. This indicates the receiver clock speed.

[0050] In one specific implementation, an extended Kalman filter observation model can be established based on the pseudorange change rate corresponding to the Doppler observations. Considering the correlation errors during signal propagation, the pseudorange observations between the satellite and the receiver can be expressed as:

[0051] in, For pseudo-distance observation, The geometric distance between the receiver and the low-Earth orbit satellite. and These are receiver clock bias and satellite clock bias, respectively. This is the correction term corresponding to relativistic effects. For tropospheric error, For ionospheric error, This is the correction term for the Sagnac effect caused by Earth's rotation. This is pseudorange observation noise.

[0052] Taking the derivative of the above pseudorange observation equation with respect to time, we can obtain the pseudorange change rate observation model corresponding to the Doppler observations:

[0053] in, The rate of change of the geometric distance between the receiver and the low-Earth orbit satellite. and These are the receiver clock speed and the satellite clock speed, respectively. and These are the rates of change of tropospheric error and the rates of change of ionospheric error, respectively, which can be corrected using appropriate models. and These are the rates of change of the relativistic correction and the Sagnac correction, respectively. This is noise from the pseudorange change rate observation. The satellite clock speed can be obtained from the corresponding satellite ephemeris information.

[0054] The rate of change of the geometric distance between the receiver and the low-Earth orbit satellite can be expressed as:

[0055] In the formula, and These represent the receiver speed and the low-Earth orbit satellite speed, respectively. and These represent the receiver position and the low-Earth orbit satellite position, respectively.

[0056] Furthermore, the aforementioned pseudorange rate of change observation model can be expanded using a first-order Taylor series at the current initial state, ignoring higher-order terms, thereby establishing a linearized relationship between the state correction and Doppler observation information. When the same solution time is obtained... When performing Doppler observations from multiple low-Earth orbit satellites, the linearized observation equations corresponding to each low-Earth orbit satellite can be combined as follows:

[0057] in, The observation vector is composed of the difference between the actual pseudorange rate of change and the theoretical pseudorange rate of change calculated from the current initial state. For the observation matrix, For state correction, Let the observed noise vector be the state correction vector.

[0058] Observation matrix Each element in the algorithm can be obtained by taking the partial derivatives of the pseudorange change rate with respect to the receiver's three-dimensional position, receiver's three-dimensional velocity, and receiver clock speed, respectively. Therefore, observational information for extended Kalman filter state updates can be generated based on the Doppler observations from each low-Earth orbit satellite.

[0059] In the extended Kalman filtering process, the current state variables are predicted based on the state model, and observation information is established based on the Doppler observations of each low-Earth orbit satellite. Since there is a correspondence between the Doppler observations and the receiver position, receiver velocity, and receiver clock speed, the predicted state variables can be corrected using the actually obtained Doppler observations.

[0060] Between two adjacent epochs, the filter state equation can be expressed as:

[0061] in, and They are respectively Time and The state quantity corresponding to time . Let be the state transition matrix.

[0062] The state transition matrix can then be expressed as:

[0063] Therefore, the state of the next epoch can be predicted based on the receiver's three-dimensional position, three-dimensional velocity, and clock speed of the previous epoch, and then the predicted state can be corrected based on the low-Earth orbit satellite Doppler observations obtained in the next epoch.

[0064] With continuous epochs of low-Earth orbit (LEO) satellite Doppler observations input into the extended Kalman filter, the receiver's three-dimensional position, three-dimensional velocity, and clock speed are updated and calculated. The calculated receiver three-dimensional position is then used as the corresponding positioning result. Therefore, based on the initial receiver position obtained through grid search, the receiver state can be further estimated using LEO satellite Doppler observations, thus refining the coarse position obtained from the grid search.

[0065] In one embodiment, the theoretical Doppler shift of each grid point for each low-Earth orbit satellite is:

[0066] in, For theoretical Doppler frequency shift, The transmission signal frequency for low-Earth orbit satellites. At the speed of light, For low-Earth orbit satellites, This refers to the satellite position of the low-Earth orbit satellite. The receiver positions corresponding to the grid points. This represents the distance between the receiver position corresponding to the grid point and the satellite position of the low-Earth orbit satellite.

[0067] Specifically, the distance between the receiver position corresponding to the grid point and the satellite position of the low-Earth orbit satellite can be expressed as:

[0068] The unit vector of the line of sight from a low-Earth orbit satellite to the receiver can be expressed as:

[0069] Therefore, the relative velocity between the low-Earth orbit satellite and the receiver in the line-of-sight direction can be determined based on their velocity difference and the aforementioned unit vector in the line-of-sight direction. After setting the receiver velocity to zero during the grid search phase, the theoretical Doppler shift can be simplified to the above calculation formula.

[0070] The velocity component of a low-Earth orbit (LEO) satellite along the line-of-sight between the LEO satellite and the current grid point can be determined based on the satellite's velocity, satellite position, and the receiver position corresponding to the grid point.

[0071] This represents the projection of the satellite velocity of a low-Earth orbit satellite onto the corresponding line-of-sight direction.

[0072] During the grid search phase, since the receiver velocity is set to zero, the theoretical Doppler shift of the current grid point relative to the corresponding low-Earth orbit satellite can be calculated based on the velocity component along the line of sight, the transmission signal frequency of the low-Earth orbit satellite, and the speed of light. For the same grid point and the same low-Earth orbit satellite, substituting the satellite position and velocity corresponding to two consecutive epochs into the above theoretical Doppler shift calculation formula yields the theoretical Doppler shift corresponding to two consecutive epochs, which is then used to calculate the theoretical Doppler shift rate of change of the grid point relative to the low-Earth orbit satellite.

[0073] In one embodiment, during the extended Kalman filtering process, when the norm of the iterative correction of the state variable is less than a first preset threshold, or when the number of iterations reaches a second preset threshold, the iteration is stopped to obtain the filtering result of the extended Kalman filter.

[0074] Specifically, during the state calculation process of the extended Kalman filter, an iterative correction value for the state value is obtained based on the current state value and the Doppler observations of each low-Earth orbit satellite, and this iterative correction value is used to update the current state value. After each iteration, the norm of the iterative correction value of the state value is calculated and compared with a first preset threshold. When the norm of the iterative correction value of the state value is less than the first preset threshold, it indicates that the state value change generated by continued iteration is already small, and the current solution meets the preset convergence condition. Therefore, the iteration stops, and the current extended Kalman filter result is obtained. At the same time, the number of iterations in the extended Kalman filter process is accumulated. When the norm of the iterative correction value of the state value is not less than the first preset threshold, but the number of iterations has reached the second preset threshold, the current iteration calculation stops, and the corresponding filter result is output.

[0075] In one specific implementation, the norm corresponding to the difference between the current solution value and the current linearized initial value can be denoted as And the first preset threshold is denoted as ; Record the current iteration count as And the second preset threshold is denoted as The corresponding stopping condition is: ,or achieve .

[0076] The norm of the iterative correction of the state variable being less than the first preset threshold and the number of iterations reaching the second preset threshold constitute two parallel iteration stopping conditions. Iteration can be stopped if either condition is met.

[0077] like Figure 3 As shown, for the first low-Earth orbit satellite Doppler single-point positioning calculation, the initial coordinates of the receiver are first obtained using a grid search based on the Doppler frequency shift rate, and the filter is initialized before the aforementioned filtering and iterative judgment are performed. For subsequent epochs, state prediction and updates can be performed based on the filtering results of the previous epoch. By setting a first preset threshold, the iteration can be terminated in time when the state variables have stabilized. By setting a second preset threshold, the maximum number of iterations in a single positioning calculation can be limited, avoiding continuous iterative calculations before the preset convergence conditions are met, thus balancing the convergence judgment and computational load control of the positioning calculation.

[0078] This application also proposes a low-Earth orbit satellite Doppler point positioning device based on frequency shift rate of change grid search, comprising: The memory is configured to store instructions; The processor is configured to retrieve instructions from memory and, when executing instructions, to implement a low-Earth orbit satellite Doppler point positioning method.

[0079] This application also proposes a machine-readable storage medium storing instructions that, when executed by a processor, configure the processor to perform a low-Earth orbit satellite Doppler point positioning method.

[0080] Compared with existing technologies, this application proposes a low-Earth orbit (LEO) satellite Doppler point positioning method. Based on LEO satellite Doppler observations and ephemeris data from two consecutive epochs, the theoretical Doppler frequency shift rate of change for each grid point is calculated and matched with the measured Doppler frequency shift rate of change to determine the initial coordinates of the receiver. This enables the acquisition of the initial receiver position for LEO satellite Doppler point positioning filtering and positioning without other observation aids or prior position information. This solves the problem that it is difficult to obtain the initial receiver position in environments with weakened or rejected GNSS signals, without other observation aids or prior position information, which leads to the difficulty in correctly converging LEO satellite Doppler point positioning.

[0081] Figure 1 This is a flowchart illustrating a low-Earth orbit satellite Doppler point positioning method in one embodiment. It should be understood that, although... Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise explicitly stated herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0082] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 4As shown in the figure, the computer device includes a processor A01, a network interface A02, a display screen A04, an input device A05, and a memory (not shown) connected via a system bus. The processor A01 provides computing and control capabilities. The memory includes internal memory A03 and a non-volatile storage medium A06. The non-volatile storage medium A06 stores an operating system B01 and a computer program B02. The internal memory A03 provides an environment for the operation of the operating system B01 and the computer program B02 stored in the non-volatile storage medium A06. The network interface A02 is used for communication with external terminals via a network connection. When the computer program is executed by the processor A01, it implements a low-Earth orbit satellite Doppler single-point positioning method. The display screen A04 can be a liquid crystal display (LCD) or an e-ink display. The input device A05 can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0083] Those skilled in the art will understand that Figure 4 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0084] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0085] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0086] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0087] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0088] In a typical configuration, a computing device includes one or more processors (CPU), input / output interfaces, network interfaces, and memory.

[0089] Memory may include non-persistent memory in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0090] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0091] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element.

[0092] The above are merely embodiments of this application and are not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A low-Earth orbit satellite Doppler point positioning method, characterized in that, The method includes: Acquire Doppler observations of at least one low-Earth orbit satellite received by the receiver in two consecutive epochs, as well as ephemeris data of each of the said low-Earth orbit satellites; Multiple grid points are established within a preset area, and the theoretical Doppler shift of each grid point for each low-orbit satellite in two consecutive epochs is calculated based on the ephemeris data. The theoretical Doppler shift rate of change for each of the grid points for each of the low-Earth orbit satellites is calculated based on the theoretical Doppler shift corresponding to two consecutive epochs. Based on the Doppler observations of each of the low-Earth orbit satellites corresponding to the two consecutive epochs, calculate the measured Doppler frequency shift rate of each of the low-Earth orbit satellites; Calculate the difference between the theoretical Doppler frequency shift rate of change for each of the grid points and the corresponding measured Doppler frequency shift rate of change for each of the low-Earth orbit satellites; The absolute values ​​of the rate of change differences of each of the low-orbit satellites corresponding to each of the grid points are summed, and the grid point with the smallest sum of the absolute values ​​of the rate of change differences is determined as the target grid point; The coordinates corresponding to the target grid points are determined as the initial coordinates of the receiver, and the initial coordinates of the receiver are used as the initialization parameters for low-Earth orbit satellite Doppler single-point positioning filtering. Low-Earth orbit satellite Doppler single-point positioning filtering is performed to obtain the position of the receiver.

2. The low-orbit satellite Doppler point positioning method according to claim 1, characterized in that, The step of calculating the theoretical Doppler shift of each grid point for each low-Earth orbit satellite over two consecutive epochs based on the ephemeris data includes: The satellite position and velocity of each low-orbit satellite in the corresponding two consecutive epochs are determined based on the ephemeris data. Using the coordinates of each grid point as the receiver position and setting the receiver velocity to zero, the theoretical Doppler shift of each grid point for each low-Earth orbit satellite in two consecutive epochs is calculated based on the satellite position, the satellite velocity, and the receiver position.

3. The low-orbit satellite Doppler point positioning method according to claim 2, characterized in that, The theoretical Doppler frequency shift rate is: The measured Doppler frequency shift rate is: in, The theoretical Doppler frequency shift rate is... The measured Doppler frequency shift rate is... and These represent the theoretical Doppler frequency shifts of the same grid point for the same low-Earth orbit satellite at two consecutive epochs. and These are the Doppler observations of the low-orbit satellite at two consecutive epochs, respectively. and These are the times corresponding to the two consecutive epochs.

4. The low-orbit satellite Doppler point positioning method according to claim 1, characterized in that, The preset area is from 3° to 54° north latitude and from 73° to 136° east longitude. Within the preset area, multiple grid points are established along the longitude and latitude directions with a step size of 0.5°.

5. The low-orbit satellite Doppler point positioning method according to claim 1, characterized in that, The step of using the receiver's initial coordinates as initialization parameters for low-Earth orbit satellite Doppler point positioning filtering includes: The initial coordinates of the receiver are used as the initial values ​​of the receiver's three-dimensional position, and the initial values ​​of the receiver's three-dimensional velocity and clock speed are zero.

6. The low-orbit satellite Doppler point positioning method according to claim 5, characterized in that, The low-orbit satellite Doppler single-point positioning filter adopts an extended Kalman filter, which calculates state variables including receiver three-dimensional position, receiver three-dimensional velocity and receiver clock speed based on the Doppler observations of each low-orbit satellite.

7. The low-orbit satellite Doppler single-point positioning method according to claim 2, characterized in that, The theoretical Doppler shift for each of the aforementioned grid points relative to each of the aforementioned low-Earth orbit satellites is as follows: in, For the theoretical Doppler frequency shift, The transmission signal frequency of the low-orbit satellite is [frequency to be inserted]. At the speed of light, The satellite velocity of the low-orbit satellite is given. The satellite position of the low-orbit satellite. The location of the receiver corresponding to the grid point. The distance between the receiver position corresponding to the grid point and the satellite position of the low-orbit satellite.

8. The low-orbit satellite Doppler point positioning method according to claim 6, characterized in that, During the extended Kalman filtering process, the iteration stops when the norm of the iterative correction of the state variable is less than a first preset threshold, or when the number of iterations reaches a second preset threshold.

9. A low-Earth orbit satellite Doppler point positioning device based on frequency shift rate of change grid search, characterized in that, include: The memory is configured to store instructions; The processor is configured to retrieve the instructions from the memory and, when executing the instructions, to implement the low-Earth orbit satellite Doppler point positioning method according to any one of claims 1 to 8.

10. A machine-readable storage medium storing instructions thereon, characterized in that, When executed by a processor, this instruction causes the processor to be configured to perform the low-Earth orbit satellite Doppler point positioning method according to any one of claims 1 to 8.

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