Lightweight Real-Time Positioning Method and Device for Low-Earth Orbit Opportunity Signals Coupled with Elevation Constraints

Abstract

This invention discloses a lightweight real-time positioning method and device for LEO (Low Earth Orbit) opportunistic signals coupled with elevation constraints, belonging to the field of LEO satellite opportunistic signal navigation and positioning technology. Addressing the technical bottlenecks of traditional non-cooperative LEO satellite opportunistic signal positioning methods, such as high computational complexity, poor real-time performance, and insufficient positioning accuracy in the elevation direction, this invention proposes a recursive least squares (RLS) positioning solution framework coupled with elevation information. This method uses Doppler frequency shift observation as its core, employing a lightweight update framework of the RLS algorithm to couple elevation constraints epoch-by-epoch, achieving real-time dynamic correction of the receiver position. The single-epoch solution time can be controlled within milliseconds, effectively reducing the system's computational complexity. Simultaneously, it achieves a comprehensive improvement in key indicators such as computational real-time performance and positioning accuracy, providing crucial technical support for navigation, positioning, and timing (PNT) systems in GNSS-denied environments, and possessing significant engineering application value and promising prospects for widespread adoption.

Description

Technical Field

[0001] This invention belongs to the field of low-Earth orbit satellite opportunistic signal navigation and positioning technology, specifically relating to a lightweight real-time positioning method, device, electronic device and storage medium for low-Earth orbit opportunistic signals coupled with elevation constraints. Background Technology

[0002] Low Earth Orbit (LEO) satellite non-cooperative signal positioning technology serves as an important supplement and backup to the Global Navigation Satellite System (GNSS), playing a crucial role in the construction of national positioning, navigation, and timing (PNT) systems. LEO constellations (such as Iridium, Starlink, and Globalstar) possess advantages such as large constellation size, strong signal delivery power, and rapid changes in satellite geometry. They effectively compensate for the vulnerability of traditional GNSS signals in complex environments (such as electromagnetic interference and physical obstruction), providing reliable positioning solutions for scenarios without GNSS coverage or subject to interference.

[0003] However, existing LEO non-cooperative signal localization methods still face significant technical bottlenecks. Due to the limitations of the LEO constellation and signal sparsity, traditional methods typically rely on long-term (5-30 minutes) accumulation of Doppler observations and employ batch least squares algorithms for batch processing of redundant epochs. While this approach can achieve single-point localization, it suffers from poor real-time performance, high computational complexity, and large memory consumption, making it difficult to meet the real-time and efficiency requirements of engineering applications. Furthermore, most LEO satellites are polar-orbiting constellations, and their Doppler observations lack sensitivity to the vertical direction, resulting in low elevation positioning accuracy, further limiting their application effectiveness in real-world scenarios.

[0004] To address the aforementioned issues, academia and industry have proposed various improvement methods, including multi-constellation fusion, positioning algorithm optimization, and system error correction. While these methods have improved positioning accuracy to some extent, they still cannot effectively resolve the trade-off between accuracy and efficiency, and real-time performance and robustness are difficult to balance. Therefore, a lightweight, high-precision real-time solution method is urgently needed to overcome the shortcomings of existing technologies and promote the engineering application of LEO non-cooperative signal positioning technology. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a lightweight real-time positioning method, device, electronic equipment, and storage medium for LEO (Low Orbit) opportunistic signals coupled with elevation constraints. By fusing the Recursive Least Squares (RLS) algorithm with elevation-aided information, a real-time solution framework is constructed. The elevation constraint is modeled as a virtual observation equation embedded in the recursive estimation process, significantly improving positioning accuracy in the elevation direction. Simultaneously, utilizing the incremental update mechanism of the RLS algorithm, lightweight solution with low computational complexity and low memory consumption is achieved, with single-epoch solution time reaching millisecond levels. This provides a feasible technical solution for the real-time and engineering application of LEO non-cooperative signal positioning terminals.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] In a first aspect, the present invention provides a lightweight real-time positioning method for low-orbit opportunity signals coupled with elevation constraints, the method comprising:

[0008] Step 1: Receive and process non-cooperative low-Earth orbit satellite signals, construct and linearize the Doppler observation equations, and calculate the initial position of the receiver based on the linearized Doppler linear observation equations.

[0009] Step 2: Obtain elevation information and use the elevation information to correct the initial position;

[0010] Step 3: Model the corrected initial position as a virtual observation, update the initial position of the receiver in conjunction with the initial solution results, and initialize the state covariance matrix;

[0011] Step 4: Continuously receive and process non-cooperative LEO satellite signals. For each epoch of satellite signals, construct an augmented observation equation set based on the newly added observations of the current epoch and linearize it. Combine the state covariance matrix of the previous epoch to calculate the Doppler Kalman gain of the current epoch. Each epoch corresponds to one receiver positioning operation.

[0012] Step 5: Determine the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch based on the Doppler Kalman gain of the current epoch; and determine the real-time position of the current epoch based on the updated Doppler parameters to be estimated for the current epoch.

[0013] Step 6: Correct the real-time position of the current epoch using the elevation information, construct a virtual observation equation based on the corrected real-time position of the current epoch, and calculate the elevation Kalman gain and the elevation residual vector of the current epoch using the virtual observation equation.

[0014] Step 7: Based on the real-time position of the current epoch, the elevation Kalman gain of the current epoch, and the elevation residual vector of the current epoch, jointly calculate the updated real-time position of the current epoch, and update the state covariance matrix of the current epoch.

[0015] In a second aspect, the present invention provides a lightweight real-time positioning device for low-orbit opportunity signals coupled with elevation constraints, the device comprising:

[0016] The receiving module is configured to receive and process non-cooperative LEO satellite signals, construct and linearize the Doppler observation equations, and solve the initial position of the receiver based on the linearized Doppler linear observation equations.

[0017] An elevation correction module is configured to acquire elevation information and use the elevation information to correct the initial position;

[0018] The initial positioning module is configured to model the corrected initial position as a virtual observation, update the initial position of the receiver in conjunction with the initial solution results, and initialize the state covariance matrix.

[0019] The real-time positioning module is configured to continuously receive and process non-cooperative LEO satellite signals. For each epoch of satellite signals, it constructs and linearizes an augmented observation equation set based on the newly added observations of the current epoch, and calculates the Doppler Kalman gain of the current epoch by combining the state covariance matrix of the previous epoch. Each epoch corresponds to one receiver positioning operation.

[0020] The real-time positioning module is further configured to determine the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch based on the Doppler Kalman gain of the current epoch, and to determine the real-time position of the current epoch based on the updated Doppler parameters to be estimated for the current epoch.

[0021] The elevation correction module is also configured to use the elevation information to correct the real-time position of the current epoch, construct a virtual observation equation based on the corrected real-time position of the current epoch, and use the virtual observation equation to calculate the elevation Kalman gain and the elevation residual vector of the current epoch.

[0022] The real-time positioning module is further configured to jointly calculate the updated real-time position of the current epoch based on the real-time position of the current epoch, the elevation Kalman gain of the current epoch, and the elevation residual vector of the current epoch, and update the state covariance matrix of the current epoch.

[0023] Thirdly, the present invention provides a computer device, including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor, when executing the computer program, implements the above-mentioned lightweight real-time positioning method for low-orbit opportunity signals with coupled elevation constraints.

[0024] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the computer is executed by a processor, it implements the above-mentioned lightweight real-time positioning method for low-orbit opportunity signals with coupled elevation constraints.

[0025] The beneficial effects of this invention are as follows:

[0026] Lightweight real-time computation with significantly reduced resource consumption: This invention constructs a lightweight computation framework based on the Recursive Least Squares (RLS) algorithm. Through an incremental parameter update mechanism, it only needs to process new observations on an epoch-by-epoch basis, eliminating the need to store historical data, thus significantly reducing computational complexity and memory consumption. The single-epoch computation time is stable at the millisecond level, significantly improving the system's real-time response capability, making it suitable for resource-constrained terminal devices.

[0027] Enhanced elevation constraints improve positioning accuracy and robustness: Addressing the insufficient sensitivity of LEO polar orbit constellations in the elevation direction, this invention innovatively introduces elevation-aided information as a virtual observation, jointly constructing an augmented observation model with Doppler observations. Through coordinate consistency transformation and virtual pseudorange observation equations, elevation constraints are embedded in the recursive solution process, effectively improving positioning accuracy in the elevation direction. Simultaneously, this constraint continues to play a role in initialization and epoch recursion, enhancing the system's convergence speed and stability, and significantly improving the robustness of 3D positioning.

[0028] No additional hardware required, strong engineering applicability: This invention only needs to utilize existing LEO satellite downlink signals and elevation information (such as digital elevation models or barometer data) to achieve high-precision real-time positioning without increasing hardware costs. Its lightweight architecture and efficient computing capabilities make it highly practical in complex electromagnetic environments, obstructed scenarios, and emergency positioning applications, providing reliable support for the widespread deployment of LEO non-cooperative signal positioning technology. Attached Figure Description

[0029] Figure 1 This is a schematic diagram illustrating the application scenarios of the present invention.

[0030] Figure 2 This is a flowchart illustrating a lightweight real-time positioning method for low-orbit opportunity signals coupled with elevation constraints, provided by the present invention.

[0031] Figure 3 This is a flowchart illustrating the method for determining the initial position of a receiver provided in an embodiment of the present invention.

[0032] Figure 4 This is a flowchart illustrating the method for determining the updated initial position and initial state covariance matrix provided in an embodiment of the present invention.

[0033] Figure 5 This is a flowchart illustrating another lightweight real-time positioning method for low-orbit opportunity signals coupled with elevation constraints provided in an embodiment of the present invention.

[0034] Figure 6 This is a schematic diagram of the structure of the lightweight real-time positioning device for low-orbit opportunity signals with coupled elevation constraints provided in an embodiment of the present invention. Detailed Implementation

[0035] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0036] Figure 1 This is a schematic diagram illustrating an application scenario of the present invention. For example... Figure 1 As shown, LEO satellites operate in their respective orbits. For example, satellite LEO-1 can operate in satellite orbit 1, and satellite LEO-2 can operate in satellite orbit 2.

[0037] In related technologies, LEO satellite signals can be used for Doppler positioning of the receiver. When there is radial relative motion between the satellite and the ground receiver, the fixed-frequency signal transmitted by the satellite will experience frequency shift due to the Doppler effect. By continuously measuring the cumulative frequency shift over a period of time, an integral observation equation can be established to calculate the change in radial distance between the satellite and the receiver. Then, using multiple radial distance changes at different times, a hyperboloid equation of revolution with the satellite's orbital position as the focus can be constructed. The intersection point of multiple hyperboloids represents the receiver's three-dimensional coordinates.

[0038] Figure 2 This is a flowchart illustrating a lightweight real-time positioning method for low-Earth orbit opportunity signals coupled with elevation constraints, provided by the present invention. Figure 2 As shown, the method includes the following steps:

[0039] In step 1, non-cooperative low-Earth orbit satellite signals are received and processed, a set of Doppler observation equations is constructed and linearized, and the initial position of the receiver is calculated based on the linearized Doppler linear observation equations.

[0040] In step 2, elevation information is obtained, and the initial position is corrected using the elevation information.

[0041] In step 3, the corrected initial position is modeled as a virtual observation, the initial position of the receiver is updated in conjunction with the initial solution results, and the state covariance matrix is ​​initialized.

[0042] In step 4, non-cooperative low-Earth orbit satellite signals are continuously received and processed. For each epoch of satellite signals, an augmented observation equation set is constructed and linearized based on the newly added observations of the current epoch. The Doppler Kalman gain of the current epoch is calculated by combining the state covariance matrix of the previous epoch.

[0043] Each epoch corresponds to one receiver positioning operation.

[0044] In step 5, the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch are determined based on the Doppler Kalman gain of the current epoch, and the real-time position of the current epoch is determined based on the updated Doppler parameters to be estimated for the current epoch.

[0045] In step 6, the real-time position of the current epoch is corrected using elevation information. A virtual observation equation is constructed based on the corrected real-time position of the current epoch. The elevation Kalman gain and the elevation residual vector of the current epoch are calculated using the virtual observation equation.

[0046] In step 7, the updated real-time position of the current epoch is obtained by jointly solving the real-time position of the current epoch, the elevation Kalman gain of the current epoch, and the elevation residual vector of the current epoch, and the state covariance matrix of the current epoch is updated.

[0047] In some embodiments of the present invention, the positioning method can be executed by a server or by a terminal device with certain processing capabilities. In some embodiments, the positioning method can be used to locate a receiver based on non-cooperative signals from low-Earth orbit satellites.

[0048] In some embodiments of the present invention, non-cooperative low-Earth orbit satellite signals can be received and processed, a set of Doppler observation equations can be constructed and linearized, and the initial position of the receiver can be calculated based on the linearized Doppler linear observation equations.

[0049] In one example, the receiver can first acquire the initial accumulated m non-cooperative signals from low-Earth orbit (LEO) satellites. The initially accumulated signals refer to the non-cooperative LEO satellite signals received by the receiver over a period of time after power-on or activation of the positioning function. For example, if the receiver is powered on or activates the positioning function at time 0, the m non-cooperative LEO satellite signals received during the time period from 0 to t0 are recorded as the initially accumulated signals. m is a positive integer.

[0050] The method can process the initially accumulated m non-cooperative signals from low-Earth orbit satellites, acquire the Doppler observations for each non-cooperative signal, construct a set of Doppler observation equations, linearize these equations, and finally calculate the receiver's initial position based on the linearized Doppler observation equations. The specific implementation process of this method for determining the receiver's initial position will be described in detail later and will not be repeated here.

[0051] In some embodiments of the present invention, the elevation information of the receiver can also be obtained, and the initial position of the receiver can be corrected using this elevation information. This elevation information is used to characterize the height of the receiver above the ground. The method of obtaining the elevation information is not limited here.

[0052] Next, the corrected initial position can be modeled as a virtual observation. This virtual observation, combined with the initial solution of the linearized Doppler linear observation equation, is used to update the receiver's initial position, serving as the receiver's precise initial position. Simultaneously, the state covariance matrix can be initialized to provide initial input conditions for the next positioning calculation.

[0053] After determining the receiver's precise initial position, the receiver can continuously receive and process non-cooperative LEO satellite signals to achieve real-time positioning. For each received satellite signal, an augmented observation equation system can be constructed and linearized based on the newly added observations of the current epoch. Simultaneously, the Doppler Kalman gain of the current epoch is calculated by combining the state covariance matrix of the previous epoch. Each epoch corresponds to one receiver positioning operation.

[0054] Subsequently, the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch are determined based on the Doppler Kalman gain of the current epoch. The real-time position of the current epoch is then determined based on the updated Doppler parameters to be estimated for the current epoch.

[0055] In other words, after initial positioning and initialization of the state covariance matrix are completed, the receiver's positioning process can enter the real-time recursive update stage. At this time, the LEO satellite opportunity signal acquisition platform can continuously receive opportunity signals in real time, extract the corresponding Doppler observations from the opportunity signals, and use them to update and converge the receiver's positioning state epoch by epoch.

[0056] When implementing recursive updates, the Doppler Kalman gain for the current epoch can be determined first based on the state covariance matrix of the transition epoch and the Doppler observations of the current epoch, to optimize the weighting of newly added Doppler observations on parameter estimation. Then, the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch are determined based on the Doppler Kalman gain of the current epoch. Finally, the real-time position of the receiver at the current epoch is determined using the Doppler parameters to be estimated for the current epoch.

[0057] Having determined the receiver's real-time position in the current epoch, elevation information can be used to update this position, thus obtaining the receiver's precise real-time position in the current epoch. If the receiver is a fixed terminal, its elevation information can be fixed, and therefore the elevation information acquired in the initial stage can be reused in each epoch. Conversely, if the receiver is a mobile terminal, its elevation information can change, therefore the elevation information for the current epoch needs to be acquired again in each epoch.

[0058] In some embodiments of the invention, updating the real-time position of the current epoch using elevation information can be achieved by first correcting the real-time position of the current epoch using the elevation information; then, constructing a virtual observation equation based on the corrected real-time position of the current epoch; and using this virtual observation equation to calculate the elevation Kalman gain and the elevation residual vector of the current epoch. Finally, the updated real-time position of the current epoch is obtained by jointly solving the real-time position, the elevation Kalman gain, and the elevation residual vector of the current epoch, and the state covariance matrix of the current epoch is updated.

[0059] The technical solution provided in this invention integrates the RLS algorithm with elevation-aided information to construct a real-time solution framework. Elevation constraints are modeled as virtual observation equations embedded in the recursive estimation process, significantly improving positioning accuracy in the elevation direction. Simultaneously, utilizing the incremental update mechanism of the RLS algorithm, lightweight solution with low computational complexity and low memory consumption is achieved, with single-epoch solution time reaching millisecond levels. This provides a feasible solution for the real-time and engineering applications of LEO non-cooperative signal positioning terminals.

[0060] Figure 3 This is a flowchart illustrating the method for determining the initial position of a receiver according to an embodiment of the present invention. Figure 3 As shown, the method includes the following steps:

[0061] In step 101, the downlink signal from the non-cooperative low-Earth orbit satellite is received and processed, the Doppler observations of the satellite downlink signal are obtained, and an initial set of Doppler observation equations is established based on the Doppler observations.

[0062] In step 102, the initial Doppler observation equations are linearized at the approximate location of the receiver to obtain the linearized initial Doppler linear observation equations.

[0063] In step 103, the least squares algorithm is used to solve the linearized Doppler linear observation equation to obtain the corrections to the initial parameters to be estimated for the receiver.

[0064] In step 104, the initial position of the receiver is determined based on the corrections to the receiver parameters to be estimated.

[0065] In some embodiments of the invention, when determining the initial position of the receiver, the downlink signal of the non-cooperative low-Earth orbit satellite can be processed first to obtain the Doppler observations of the satellite downlink signal, and an initial set of Doppler observation equations can be established based on the Doppler observations.

[0066] The initial Doppler observation equations can be expressed as:

[0067] ;

[0068] In the formula, For Doppler frequency shift, The downlink carrier wavelength of the LEO satellite. For the LEO satellite velocity vector, and These are the position vectors of the LEO satellite and the receiver terminal, respectively. At the speed of light, For combined clock drift of receiver and satellite, The rate of change of tropospheric delay. The ionospheric delay rate, For Doppler measurement noise, the superscript "ini" indicates that the observed and state parameters correspond to the initialization phase.

[0069] The initial Doppler observation equations can then be linearized at the approximate location of the receiver to obtain the linearized initial Doppler linear observation equations.

[0070] The receiver's probabilistic position can be quickly calculated by the receiver based on the signal delay and satellite position information of the acquired satellites, and can be expressed as follows: , This indicates the approximate location of the receiver. , and The probabilistic location represents the three-dimensional coordinate components in the Earth-centered Earth-fixed coordinate system.

[0071] The linearized initial Doppler linear observation equation can be expressed as follows: ,in This is the difference between the Doppler frequency shift value obtained from initial observations and the theoretical Doppler frequency shift value calculated based on the receiver's current estimated position and satellite orbital parameters. This is the initial state estimation vector obtained based on the solution of the initial Doppler linear observation equation. The coefficient matrix of the initial Doppler linear observation equation represents the measurement noise corresponding to the Doppler observations during the initialization phase. Let be the Jacobian matrix of the initial Doppler linear observation equation.

[0072] The corrections to the initial parameters to be estimated for the receiver obtained by solving the linearized Doppler linear observation equations using the least squares algorithm can be expressed as follows: ,in For the initial parameters to be estimated at the receiver, The vector representation is , , and This represents the coordinate correction for the initial position in the three-dimensional coordinate system. This is the correction amount for clock drift.

[0073] Finally, it can be based on this The initial position of the receiver is determined by this probability position. The initial position of the receiver can be expressed as: ,in This is the initial position of the receiver. since Obtain.

[0074] In some embodiments of the present invention, correcting the initial position using elevation information can be achieved by correcting the height component in the initial position using elevation information to obtain a corrected initial position.

[0075] Since elevation information is defined in the geodetic coordinate system and receiver position is defined in the geocentric coordinate system, when using elevation information to correct the initial position, it is first necessary to convert the initial position of the receiver from the geocentric coordinate system to the geodetic coordinate system.

[0076] In one example, a formula can be used. The receiver's initial position is transformed from the geocentric coordinate system to the geodetic coordinate system. Here, b, l, and h represent the geodetic latitude, geodetic longitude, and geodetic height, respectively. For the first eccentricity, The radius of curvature of the circle is denoted as . 'a' represents the Earth's semi-major axis. , and The initial position represents the three-dimensional coordinate components in the Earth-centered Earth-fixed coordinate system.

[0077] Elevation information h can be used ini By replacing the geodetic height component h in the initial position after coordinate system transformation, we obtain the three-dimensional coordinate components b, l, and h of the corrected initial position in the geodetic coordinate system. ini .

[0078] The corrected initial position can be obtained by transforming the corrected initial position in the geodetic coordinate system back to the geocentric-fixed coordinate system. This can be done using the formula... The transformation of the corrected initial position from the geodetic coordinate system to the geocentric Earth-fixed coordinate system is completed. Among these steps... , and This refers to the three-dimensional coordinate components of the corrected initial position in the Earth-centered Earth-fixed coordinate system.

[0079] Figure 4 This is a flowchart illustrating the method for determining the updated initial position and initial state covariance matrix provided in an embodiment of the present invention. Figure 4 As shown, the method includes the following steps:

[0080] In step 301, the corrected initial position is modeled as a virtual observation and jointly constructed with the geocentric position coordinates to form the initial virtual pseudorange observation equation.

[0081] In step 302, the initial virtual pseudorange observation equation is linearized at the initial position of the receiver to obtain the initial elevation-aided linear observation equation.

[0082] In step 303, the least squares solution is performed on the initial elevation auxiliary linear observation equation to obtain the correction value of the initial estimated parameter after receiver elevation correction and the updated initial position.

[0083] In step 304, the state covariance matrix for the initialization phase is calculated based on the coefficient matrix of the initial Doppler linear observation equation and the coefficient matrix of the initial elevation-assisted linear observation equation.

[0084] In some embodiments of the present invention, the modified initial position can be modeled as a virtual observation and jointly constructed with the geocentric position coordinates to form an initial virtual pseudorange observation equation. The geocentric position coordinates can be [0 0 0], and the jointly constructed initial virtual pseudorange observation equation can be expressed as follows: ,in For the corrected initial position and the Earth's center The virtual pseudo-distance between them This represents the measurement error of the virtual pseudorange observations after elevation correction.

[0085] The initial virtual pseudorange observation equation can then be linearized at the receiver's initial position to obtain the initial elevation-aided linear observation equation. This initial elevation-aided linear observation equation can be expressed as:

[0086] ;

[0087] in, This is the initial virtual pseudorange increment. This is the coefficient matrix of the initial elevation-aided linear observation equation. This is the correction value for the initial parameters to be estimated at the receiver. , and This represents the coordinate correction of the initial position in the geocentric-geofixed coordinate system for three-dimensional positioning. The superscript "ini" indicates that the observed measurements and state parameters correspond to the initialization phase. Similarly, this... The vector representation of can be .

[0088] By performing a least-squares solution on the initial elevation-aided linear observation equation, the corrected values ​​of the initial estimated parameters after receiver elevation correction can be obtained. and obtain the updated initial position. .in, since Obtain.

[0089] Finally, formulas can also be used for calculation. The state covariance matrix during the initialization phase, where, Let the initial state covariance matrix be... Let be the initial Doppler state covariance matrix. The initial elevation state covariance matrix, The coefficient matrix of the initial Doppler linear observation equation is... This is the coefficient matrix of the initial elevation auxiliary linear observation equation.

[0090] By adopting the technical solution provided in the embodiments of the present invention, the positioning accuracy can be improved without significantly increasing the computational complexity by introducing elevation information to correct the initial position of the receiver during the initial positioning stage of LEO satellites.

[0091] After initial positioning is completed, the receiver's positioning process can enter the real-time recursive update stage. As before, in the real-time recursive update stage, the Doppler Kalman gain of the current epoch can be determined first, then the Doppler observation residual vector of the current epoch can be determined based on the Doppler Kalman gain of the current epoch, and then the Doppler parameters to be estimated for the current epoch can be determined. Finally, the real-time position of the current epoch can be determined based on the Doppler parameters to be estimated for the current epoch.

[0092] The step of determining the Doppler Kalman gain for the current epoch may include: acquiring the Doppler observations of the satellite signal at the k-th epoch; constructing an augmented observation equation set based on the Doppler observations at the k-th epoch and linearizing it to obtain the Doppler linear observation equations for the k-th epoch. .in, The coefficient matrix of the k-th epoch represents the difference between the Doppler shift value obtained from the observation at the k-th epoch and the theoretical Doppler shift value calculated based on the receiver's current estimated position and satellite orbit parameters. Let be the Jacobian matrix of the Doppler linear observation equation for the k-th epoch. The correction value for the receiver's parameters to be estimated. The noise is the observation noise of the k-th epoch Doppler observation, where k is a positive integer greater than 1.

[0093] Use formula The Doppler Kalman gain for the k-th epoch is calculated by combining the state covariance matrix of the (k-1)-th epoch and the Doppler coefficient matrix of the k-th epoch. For the Doppler-Kalman gain of the k-th epoch, Let be the state covariance matrix of the (k-1)th epoch. Doppler observation noise for the k-th epoch The covariance matrix.

[0094] Furthermore, the step of determining the Doppler observation residual vector for the current epoch based on the Doppler Kalman gain can include using the formula... The Doppler residual vector for the k-th epoch is calculated using the state estimate from the (k-1)-th epoch and the newly added observation from the k-th epoch. This is the difference between the Doppler frequency shift value obtained from the observation at the k-th epoch and the theoretical Doppler frequency shift value calculated based on the receiver's current estimated position and satellite orbital parameters. Let be the coefficient matrix of the Doppler linear observation equation for the k-th epoch. This is the correction number for the parameter to be estimated in the (k-1)th epoch of the receiver.

[0095] Furthermore, the Doppler parameters to be estimated in the current epoch can be determined based on the Doppler Kalman gain and the Doppler observation residual vector of the current epoch. These Doppler parameters to be estimated in the current epoch can be corrections to the parameters to be estimated in the current epoch.

[0096] In one example, a formula can be used. The Doppler parameters to be estimated in the k-th epoch are determined based on the Doppler Kalman gain and the Doppler observation residual vector in the k-th epoch. Let be the correction value for the parameter to be estimated in the k-th epoch of the receiver. This is the correction value for the correction of the parameter to be estimated in the (k-1)th epoch of the receiver. Wherein, The vector representation of can be .

[0097] Based on this, the step of determining the real-time position of the current epoch based on the Doppler parameters to be estimated at the current epoch may include using the formula The real-time position of the receiver at the k-th epoch is determined based on the corrections to the parameters to be estimated at the k-th epoch of the receiver, where Let be the real-time position of the receiver at the k-th epoch. since Obtain.

[0098] In some embodiments of the present invention, during the real-time recursive update phase of the receiver, the real-time position can still be updated using elevation information to obtain the accurate real-time position of the receiver.

[0099] When updating the receiver's real-time position using elevation information, the real-time position of the receiver at the k-th epoch can be corrected first using the elevation information to obtain the corrected real-time position of the receiver at the k-th epoch. This elevation information can be the elevation information of the receiver at the k-th epoch; if it is a fixed receiver, the elevation information can also be reused from the initial positioning.

[0100] Meanwhile, the specific implementation method for correcting the real-time position of the receiver at the k-th epoch using elevation information is basically the same as the specific implementation method for correcting the initial position of the receiver using elevation information. It also includes steps such as transforming the real-time position of the receiver at the k-th epoch from the geocentric coordinate system to the geodetic coordinate system, replacing the geodetic height component of the real-time position of the receiver at the k-th epoch in the geodetic coordinate system with elevation information, and then transforming the replaced real-time position of the receiver at the k-th epoch back to the geocentric coordinate system. For specific calculation formulas, please refer to the description of correcting the initial position of the receiver using elevation information above; they will not be repeated here.

[0101] Then, based on the real-time position of the receiver at the k-th epoch, a virtual pseudorange observation equation for the k-th epoch can be constructed. This virtual pseudorange observation equation is then linearized at the real-time position of the receiver at the k-th epoch to obtain the elevation-aided linear observation equation for the k-th epoch. ,in For the virtual pseudorange increment of the k-th epoch, Let be the coefficient matrix of the elevation-aided linear observation equation for the k-th epoch. The correction value is the correction value for the parameter to be estimated in the receiver. The measurement error is the virtual pseudorange observation value after elevation correction for the k-th epoch.

[0102] Next, we can use the formula. The elevation Kalman gain for the k-th epoch is calculated based on the state covariance matrix of the (k-1)-th epoch and the coefficient matrix of the elevation-assisted linear observation equation for the k-th epoch. ,in Let be the state covariance matrix of the (k-1)th epoch. Let be the coefficient matrix of the elevation-aided linear observation equation for the k-th epoch. The measurement error at the k-th epoch The covariance matrix.

[0103] Then the formula can be used. Calculate the elevation residual vector at the k-th epoch based on the elevation Kalman gain. ,in, For the virtual pseudorange increment of the k-th epoch, This is the correction value for the correction number of the receiver parameter to be estimated in the (k-1)th epoch.

[0104] The correction values ​​for the receiver parameters to be estimated at the k-th epoch can be updated based on the elevation Kalman gain and the elevation residual vector at the k-th epoch, thus obtaining the corrected values ​​for the receiver parameters to be estimated at the k-th epoch. ,in Let be the correction value for the correction of the receiver parameter to be estimated at the k-th epoch. Let be the correction number for the receiver parameter to be estimated at the k-th epoch. The elevation Kalman gain for the k-th epoch. Let be the elevation residual vector of the k-th epoch.

[0105] Finally, the formula can be used. Determine the real-time position of the receiver after the update at the k-th epoch, where, This represents the real-time position of the receiver after the update at the k-th epoch. Let be the real-time position of the receiver at the k-th epoch. , and The value of Obtain.

[0106] In some embodiments of the present invention, in order to ensure the continuity of information between epochs and to achieve continuous optimization and updating of positioning results, it is also necessary to calculate the state covariance matrix of the current epoch as the input condition for the next epoch.

[0107] In one example, a formula can be used. The state covariance matrix of the k-th epoch is updated. Let be the state covariance matrix of the k-th epoch. Let be the Doppler state covariance matrix of the (k-1)th epoch. For the Doppler-Kalman gain of the k-th epoch, Let be the coefficient matrix of the elevation-aided linear observation equation for the k-th epoch. Let be the elevation state covariance matrix of the (k-1)th epoch. The elevation Kalman gain for the k-th epoch. Let be the coefficient matrix of the Doppler linear observation equation for the k-th epoch.

[0108] The technical solution provided in this invention constructs a lightweight real-time positioning calculation framework for low-Earth orbit satellites based on the recursive least squares algorithm, thereby reducing computational complexity while improving response capability. The recursive least squares algorithm has the structural advantage of incremental recursive updates, enabling rapid updates of receiver position parameters at each epoch without recalculating all observation data, significantly reducing computational complexity and memory usage.

[0109] Furthermore, the method improves positioning accuracy and stability by introducing elevation information to assist positioning and constructing an augmented observation model. Specifically, by introducing elevation-assisted information as a virtual observation, an augmented observation model is jointly constructed with Doppler observations and coupled into the estimation process of the recursive least squares algorithm. This method can not only correct the initial position of the receiver through elevation assistance during the initialization stage, but also continuously introduce elevation constraints during the epochal recursion process, further improving positioning accuracy and stability.

[0110] Figure 5 This is a flowchart illustrating another lightweight real-time positioning method for low-Earth orbit opportunity signals coupled with elevation constraints, provided by an embodiment of the present invention. Figure 5 As shown, the method includes the following steps: After the algorithm starts, firstly, low-orbit satellite Doppler observations and elevation information are acquired, and an observation model is constructed; then, the observation equations are linearized, and the initial position is calculated; next, elevation auxiliary information is introduced, and coordinate consistency transformation is required when introducing elevation auxiliary information, and then the initial positioning is completed by combining the coordinate transformed elevation auxiliary information; then, augmented observation equations can be constructed epoch by epoch, with one epoch corresponding to one positioning.

[0111] When constructing the augmented observation equations epoch-by-epoch, parameter updates can be performed based on a recursive least squares algorithm. This includes updating the Kalman gain matrix epoch-by-epoch, calculating and updating the residual vector and estimated parameters epoch-by-epoch, correcting the estimated parameters of the receiver at the current epoch using combined elevation information, and calculating the covariance matrix epoch-by-epoch. After completing these steps, the receiver's position can be calculated in real time.

[0112] After the receiver's position is calculated in real time, it can be determined whether to continue acquiring observations. If so, the method is iteratively executed starting from the step of constructing the augmented observation equation system epoch by epoch; otherwise, the current positioning ends.

[0113] The technical solution provided in this invention employs a recursive least squares algorithm to construct a lightweight positioning solution framework. This framework simplifies the system's algorithm structure, compresses the dimensionality of matrix operations, and can complete the positioning parameter calculation without storing large amounts of historical observation data. This effectively improves the computational complexity during the solution process and significantly reduces memory consumption and CPU utilization. Simultaneously, it fully leverages the incremental recursive characteristics of the recursive algorithm to achieve real-time dynamic calculation of the receiver position during epoch updates. The single-epoch calculation time is stable at the millisecond level, meeting the requirements of real-time positioning.

[0114] Meanwhile, to address the issue of insufficient sensitivity of polar-orbiting Doppler positioning in the elevation direction, the technical solution provided in this embodiment of the invention introduces elevation information and uses the elevation information to construct virtual observation equations to enhance the constraint capability of the positioning model. This can effectively improve the convergence speed of the system in the elevation direction without increasing additional hardware costs, and significantly improve the three-dimensional positioning accuracy and robustness of the positioning system.

[0115] Figure 6 This is a schematic diagram of the lightweight real-time positioning device for low-orbit opportunity signals coupled with elevation constraints provided in an embodiment of the present invention. Figure 6 As shown, the device includes:

[0116] The receiving module 601 is configured to receive and process non-cooperative LEO satellite signals, construct and linearize the Doppler observation equations, and calculate the initial position of the receiver based on the linearized Doppler linear observation equations.

[0117] The elevation correction module 602 is configured to acquire elevation information and use the elevation information to correct the initial position.

[0118] The initial positioning module 603 is configured to model the corrected initial position as a virtual observation, update the initial position of the receiver in conjunction with the initial solution results, and initialize the state covariance matrix.

[0119] The real-time positioning module 604 is configured to continuously receive and process non-cooperative LEO satellite signals. For each epoch of satellite signals, it constructs and linearizes an augmented observation equation set based on the newly added observations of the current epoch, and calculates the Doppler Kalman gain of the current epoch by combining the state covariance matrix of the previous epoch. Each epoch corresponds to one receiver positioning operation.

[0120] The real-time positioning module 604 is further configured to determine the Doppler observation residual vector and the Doppler parameters to be estimated for the current epoch based on the Doppler Kalman gain of the current epoch, and to determine the real-time position of the current epoch based on the updated Doppler parameters to be estimated for the current epoch.

[0121] The elevation correction module 602 is further configured to use the elevation information to correct the real-time position of the current epoch, construct a virtual observation equation based on the corrected real-time position of the current epoch, and use the virtual observation equation to calculate the elevation Kalman gain and the elevation residual vector of the current epoch.

[0122] The real-time positioning module 604 is further configured to jointly calculate the updated real-time position of the current epoch based on the real-time position of the current epoch, the elevation Kalman gain of the current epoch, and the elevation residual vector of the current epoch, and update the state covariance matrix of the current epoch.

[0123] The technical solution provided in this invention integrates the RLS algorithm with elevation-aided information to construct a real-time solution framework. Elevation constraints are modeled as virtual observation equations embedded in the recursive estimation process, significantly improving positioning accuracy in the elevation direction. Simultaneously, utilizing the incremental update mechanism of the RLS algorithm, lightweight solution with low computational complexity and low memory consumption is achieved, with single-epoch solution time reaching millisecond levels. This provides a feasible solution for the real-time and engineering applications of LEO non-cooperative signal positioning terminals.

[0124] On the other hand, the present invention provides a computer device including a memory and a processor, wherein the memory stores a computer program, characterized in that the processor implements the above-mentioned lightweight real-time positioning method for low-orbit opportunity signals with coupled elevation constraints when executing the computer program.

[0125] On another front, the present invention provides a computer-readable storage medium storing a computer program, characterized in that it constructs a lightweight real-time positioning method for low-orbit opportunity signals with coupled elevation constraints when the computer is executed by a processor. The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A lightweight real-time positioning method for coupling elevation-constrained low earth orbit opportunistic signals, characterized in that, The method comprises: Step 1, receiving and processing non-cooperative LEO satellite signals, constructing a Doppler observation equation set and linearizing, solving the initial position of the receiver based on the linearized Doppler linear observation equation; Step 2, obtaining elevation information, and correcting the initial position using the elevation information; Step 3, modeling the corrected initial position as a virtual observation, updating the initial position of the receiver jointly with the initial solving result, and initializing the state covariance matrix; Step 4, continuously receiving and processing non-cooperative LEO satellite signals, constructing an augmented observation equation set based on the new observation of the current epoch for each epoch of satellite signals and linearizing, and calculating the Doppler Kalman gain of the current epoch combined with the state covariance matrix of the previous epoch; wherein each epoch corresponds to a receiver positioning operation; Step 5, determining the Doppler observation residual vector of the current epoch and the Doppler estimated parameter of the current epoch based on the Doppler Kalman gain of the current epoch, and determining the real-time position of the current epoch based on the updated Doppler estimated parameter of the current epoch; Step 6, correcting the real-time position of the current epoch using the elevation information, constructing a virtual observation equation based on the corrected real-time position of the current epoch, and calculating the elevation Kalman gain of the current epoch and the elevation residual vector of the current epoch using the virtual observation equation; Step 7, jointly solving the updated real-time position of the current epoch based on the real-time position of the current epoch, the elevation Kalman gain of the current epoch and the elevation residual vector of the current epoch, and updating the state covariance matrix of the current epoch.

2. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 1 comprises: receiving and processing non-cooperative low-orbit satellite downlink signals, obtaining Doppler observations of the satellite downlink signals, and establishing an initial Doppler observation equation set based on the Doppler observations; The initial Doppler observation equation set is: ； where is the Doppler shift, is the LEO satellite downlink signal carrier wavelength, is the LEO satellite velocity vector, is the position vector of the receiver terminal, are the position vectors of the LEO satellite and the receiver terminal, respectively, is the speed of light, is the combined clock bias of the receiver and the satellite, is the tropospheric delay rate of change, is the ionospheric delay rate of change, is the Doppler measurement noise, the superscript ini indicates that the observation and the state parameter correspond to the initialization phase, is the initial accumulated number of epochs of low earth orbit satellite non-cooperative signals.

3. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 2, wherein, The step 1 further comprises: linearizing the initial Doppler observation equations at the approximate position of the receiver yields linearized initial Doppler linear observation equations ;​ wherein, is a rough position of the receiver, , and are three-dimensional coordinate components of the rough position in a geocentric geodetic coordinate system, is a difference between a Doppler shift value observed in an initial stage and a theoretical Doppler shift value calculated based on a current estimated position of the receiver and satellite orbit parameters, is an initial state estimation vector obtained based on a solution of an initial Doppler linear observation equation, denotes a measurement noise corresponding to the Doppler observation in the initialization stage, a coefficient matrix of the initial Doppler linear observation equation is a Jacobian matrix of the initial Doppler linear observation equation; solving the linearized initial Doppler linear observation equation using a least square algorithm to obtain the correction of the initial estimated parameters of the receiver ; wherein is the correction of the initial estimated parameters of the receiver, is represented by a vector , , and is the coordinate correction of the three-dimensional position of the initial position in the Earth-Centered Earth-Fixed coordinate system, is the clock drift correction determining an initial position of the receiver based on the corrections to the initial parameters to be estimated for the receiver is wherein is the initial position of the receiver.

4. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 2 comprises: Using the formula Converting the initial position of the receiver from the geocentric coordinate system to the geodetic coordinate system, wherein b, l, h respectively represent the geodetic latitude, geodetic longitude and geodetic height, is the first eccentricity, is the radius of curvature of the prime vertical circle, , and is the three-dimensional coordinate component of the initial position in the geocentric coordinate system; Using the height information h ini Replacing the geodetic height h; Using the formula Converting the b, l, h ini Convert to the geocentric and geodetic coordinate system to obtain the corrected initial position.

5. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 3 comprises: The corrected initial position is modeled as a virtual observation, and an initial virtual pseudo-range observation equation is constructed in combination with the geocentric position coordinates wherein is a virtual pseudo-range between the corrected initial position and the geocentric , is a measurement error of the virtual pseudo-range observation value after the height correction, , and are three-dimensional coordinate components of the corrected initial position in the geocentric and geodetic coordinate system. linearizing the initial virtual pseudo-range observation equation at an initial position of the receiver to obtain an initial elevation-aided linear observation equation ; wherein, is an initial virtual pseudo-range increment, is a coefficient matrix of the initial elevation auxiliary linear observation equation, is a correction value of a correction of a correction number of an initial to-be-estimated parameter of a receiver, , and is a coordinate correction amount of a three-dimensional position of the corrected initial position in a geocentric geodetic coordinate system, and a superscript ini indicates that the observation and the state parameter correspond to an initialization stage. least squares solution of the initial height-aided linear observation equation to obtain the correction value of the initial to-be-estimated parameter correction number of the receiver height after correction and the updated initial position wherein, , , is the initial position of the receiver The state covariance matrix of the initialization phase is calculated based on the coefficient matrix of the initial Doppler linear observation equation and the coefficient matrix of the initial elevation auxiliary linear observation equation using the formula wherein is the initial state covariance matrix, is the initial Doppler state covariance matrix, is the initial elevation state covariance matrix, is the coefficient matrix of the initial Doppler linear observation equation, is the coefficient matrix of the initial elevation auxiliary linear observation equation.

6. The coupled altitude-constrained low earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 4 comprises: Doppler observation of the kth epoch satellite signal, constructing an augmented observation equation set based on the Doppler observation of the kth epoch and linearizing the same to obtain a Doppler linear observation equation of the kth epoch wherein, is a difference between a Doppler shift value obtained by observation of the kth epoch and a theoretical Doppler shift value calculated based on a current estimated position of the receiver and satellite orbit parameters, the coefficient matrix of the kth epoch is a Jacobian matrix of the Doppler linear observation equation of the kth epoch, is a correction number of a parameter to be estimated by the receiver, is observation noise of the Doppler observation of the kth epoch, and k is a positive integer greater than 1. The Doppler Kalman gain for the kth epoch is calculated using the formula , combining the state covariance matrix for the (k-1)th epoch and the Doppler coefficient matrix for the kth epoch, where, is the Doppler Kalman gain for the kth epoch, is the state covariance matrix for the (k-1)th epoch, is the Doppler observation noise covariance matrix for the kth epoch.

7. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 6, wherein, The step 5 comprises: The Doppler residual vector at epoch k is calculated using the formula where is the state estimate at epoch k-1 and is the new observation at epoch k. is the difference between the observed Doppler shift at epoch k and the theoretical Doppler shift calculated based on the current estimated position of the receiver and the satellite orbit parameters, is the coefficient matrix of the linear Doppler observation equation at epoch k, is the correction to the receiver's estimated parameters at epoch k-1. using the formula determining Doppler parameters to be estimated at the kth epoch based on the Doppler Kalman gain at the kth epoch and the Doppler observation residual vector at the kth epoch, wherein, a correction to the receiver parameters to be estimated at the kth epoch, a correction to the correction to the receiver parameters to be estimated at the k-1th epoch; using the formula determining a real-time position of the receiver at the kth epoch based on the corrections to the parameters to be estimated for the receiver at the kth epoch, wherein updating the real-time position of the receiver at the kth epoch, updating the real-time position of the receiver at the k-1th epoch.

8. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 6 comprises: correcting the real-time position of the receiver at the kth epoch using the elevation information to obtain the corrected real-time position of the receiver at the kth epoch; constructing a virtual pseudo-range observation equation of the kth epoch based on the corrected real-time position of the receiver at the kth epoch, linearizing the virtual pseudo-range observation equation of the kth epoch at the real-time position of the receiver at the kth epoch to obtain an elevation auxiliary linear observation equation of the kth epoch wherein is a virtual pseudo-range increment of the kth epoch, is a coefficient matrix of the elevation auxiliary linear observation equation of the kth epoch, is a correction value of a correction of a parameter to be estimated of the receiver, is a measurement error of the corrected virtual pseudo-range observation value of the kth epoch, and k is a positive integer greater than 1. Using the formula The elevation Kalman gain at epoch k is calculated based on the state covariance matrix at epoch k-1 and the coefficient matrix of the elevation auxiliary linear observation equation at epoch k where is the state covariance matrix at epoch k-1, is the coefficient matrix of the elevation auxiliary linear observation equation at epoch k, is the measurement error at epoch k covariance matrix of using the formula calculating the elevation residual vector of the kth epoch based on the elevation Kalman gain of the kth epoch wherein, is a virtual pseudo-range increment of the kth epoch, is a correction value of the correction of the receiver parameters to be estimated of the k-1th epoch.

9. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 1, wherein, The step 7 comprises: update the correction number of the receiver estimated parameter at the kth epoch based on the elevation Kalman gain at the kth epoch and the elevation residual vector at the kth epoch to obtain a modified value of the correction number of the receiver estimated parameter at the kth epoch wherein, is the modified value of the correction number of the receiver estimated parameter at the kth epoch, is the correction number of the receiver estimated parameter at the kth epoch, is the elevation Kalman gain at the kth epoch, is the elevation residual vector at the kth epoch, and k is a positive integer greater than 1. Using the formula the real-time position of the receiver updated at the kth epoch is determined, where, the real-time position of the receiver updated at the kth epoch is determined, the real-time position of the receiver at the kth epoch is determined, , and the values of are obtained.

10. The coupled altitude-constrained low Earth opportunity signal lightweight real-time positioning method according to claim 9, wherein, The step 7 further comprises: Using the formula Update the state covariance matrix for the kth epoch; wherein, is the state covariance matrix for the kth epoch, is the Doppler state covariance matrix for the (k-1)th epoch, is the Doppler Kalman gain for the kth epoch, is the coefficient matrix for the elevation auxiliary linear observation equation for the kth epoch, is the elevation state covariance matrix for the (k-1)th epoch, is the elevation Kalman gain for the kth epoch, is the coefficient matrix for the Doppler linear observation equation for the kth epoch.

11. A coupled elevation-constrained low earth opportunity signal lightweight real-time positioning apparatus, characterized by, The device comprises: a receiving module configured to receive and process non-cooperative LEO satellite signals, construct a Doppler observation equation set and linearize, and solve the initial position of the receiver based on the linearized Doppler linear observation equation; an elevation correction module configured to obtain elevation information and correct the initial position using the elevation information; an initial positioning module configured to model the corrected initial position as a virtual observation, update the initial position of the receiver jointly with the initial solving result, and initialize the state covariance matrix; a real-time positioning module configured to continuously receive and process non-cooperative LEO satellite signals, construct an augmented observation equation set based on the new observation of the current epoch for each epoch of satellite signals and linearize, and calculate the Doppler Kalman gain of the current epoch combined with the state covariance matrix of the previous epoch; wherein each epoch corresponds to a receiver positioning operation; a real-time positioning module configured to continuously receive and process non-cooperative LEO satellite signals, construct an augmented observation equation set based on the new observation of the current epoch for each epoch of satellite signals and linearize, and calculate the Doppler Kalman gain of the current epoch combined with the state covariance matrix of the previous epoch; wherein each epoch corresponds to a receiver positioning operation; The real-time positioning module is further configured to determine a Doppler observation residual vector of the current epoch and Doppler parameters to be estimated of the current epoch based on the Doppler Kalman gain of the current epoch, determine a real-time position of the current epoch based on the updated Doppler parameters to be estimated of the current epoch; The height correction module is further configured to correct the real-time position of the current epoch by using the height information, construct a virtual observation equation based on the corrected real-time position of the current epoch, and calculate a height Kalman gain of the current epoch and a height residual vector of the current epoch by using the virtual observation equation; The real-time positioning module is further configured to jointly solve the updated real-time position of the current epoch based on the real-time position of the current epoch, the height Kalman gain of the current epoch and the height residual vector of the current epoch, and update a state covariance matrix of the current epoch.

12. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that, The processor executes the computer program to implement the low-orbit opportunistic signal lightweight real-time positioning method coupled with height constraint as claimed in any one of claims 1 to 10.

13. A computer readable storage medium having stored thereon a computer program, characterized in that, The computer is executed by the processor to implement the low-orbit opportunistic signal lightweight real-time positioning method coupled with height constraint as claimed in any one of claims 1 to 10.

Images