Low-orbit satellite Doppler positioning method for edge device

Abstract

The application relates to a low-orbit satellite Doppler positioning method for edge devices, wherein a cloud end extracts migratable features in historical observation through global high-precision joint calculation and encapsulates the migratable features into feature packages to be issued to an edge end; the edge end receives real-time observation, calls corresponding feature packages, constructs branches A and B to execute parallel damping iterative calculation, optimally outputs positioning results according to normalized decision costs, monitors the degree of performance degradation based on a sliding window statistic, and triggers feature package updating on demand. The low-orbit satellite Doppler positioning method for edge devices realizes decoupling of cloud learning and edge execution through an asymmetric computing architecture of cloud-edge cooperation, reuses historical environment knowledge in the form of a migratable feature library, balances the weights of prior constraints and real-time observation through a double-branch parallel optimization mechanism, guarantees environment adaptability through a performance degradation triggering updating mechanism, reduces the algorithm power requirement and storage cost of the edge end, and improves real-time performance, accuracy and long-term stability on the edge device.

Description

Technical Field

[0001] This invention relates to the field of low-Earth orbit satellite positioning technology, specifically to a low-Earth orbit satellite Doppler positioning method for edge devices. Background Technology

[0002] Low Earth Orbit (LEO) satellites have a low orbital altitude and high operating speed, exhibiting significant radial velocity variations relative to ground or low-altitude targets. Therefore, they can generate significant Doppler shift observations. In environments where global navigation satellite systems are interfered with, denied, or unavailable, autonomous positioning based on LEO satellite Doppler observations has strong engineering application prospects and can be applied to scenarios such as UAVs, low-altitude platforms, IoT terminals, and emergency nodes.

[0003] Currently, there are two main types of solutions for the aforementioned low-Earth orbit satellite Doppler positioning problem. The first type uses convex optimization techniques such as semidefinite relaxation to transform the non-convex problem into a globally solvable problem. The second type directly uses Gauss-Newton or least squares methods for local iterative solutions at the edge device. However, in practical applications, the first type of scheme requires a large number of high-dimensional matrix operations, making it difficult to run in real time on resource-constrained platforms such as airborne MCUs and low-power FPGAs. The second type of scheme is prone to update explosion or falling into local optima under complex multipath and NLOS conditions due to residual abnormalities and ill-conditioned Jacobian matrices. In addition, neither type of scheme utilizes stable prior information from historical observations, resulting in fragmented temporal information. Even if historical priors are introduced, overfitting may still occur during sudden environmental changes, leading to inverted accuracy. Therefore, a low-Earth orbit satellite Doppler positioning method for edge devices is proposed to solve the above problems. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a low-Earth orbit satellite Doppler positioning method for edge devices. It has advantages such as low computational requirements and improved robustness under multipath and NLOS conditions. It solves the problems of the first type of scheme requiring a large number of high-dimensional matrix operations, which is difficult to run in real time on resource-constrained platforms such as airborne MCUs and low-power FPGAs. The second type of scheme is prone to update explosion or falling into local optima under complex multipath and NLOS conditions due to residual anomalies and ill-conditioned Jacobian matrices. In addition, neither type of scheme utilizes stable prior information from historical observations, resulting in fragmented temporal information. Even if historical priors are introduced, overfitting may still occur during sudden environmental changes, leading to inverted accuracy.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a low-Earth orbit satellite Doppler positioning method for edge devices, characterized by comprising the following steps: S1. Collect regional historical Doppler observations and ephemeris data, perform global high-precision joint calculations in the cloud, and obtain historical reference trajectories. Based on historical reference trajectories Statistically analyze the historical residuals of each observation link, and extract a transferable feature library based on the historical residuals; S2. Encapsulate the transferable feature library into a feature package. And distribute it to the edge; S3. The edge device receives real-time Doppler observations and ephemeris data for the current epoch, and retrieves the corresponding local feature packets based on feature matching. Based on feature packets The portable feature library it carries is used to construct branches. and branches And perform damping iterative calculations separately to obtain the branches. and branches Based on the candidate solutions of each branch and the observation data used, the branches are determined respectively. and branches The cost of normalized judgments; Based on the included protection margin Comparison criteria for branches and branches The normalized decision cost is used to select the best solution, and the candidate solution of the best solution branch is output as the final localization output. ; S4. Update the sliding window statistics based on the positioning results, and calculate the branch. Better than or no worse than branches proportion and average optimal cost ; If the ratio is satisfied Not less than the proportional threshold or average optimal cost Not less than the average cost threshold If any of the features expires, the edge device sends a feature update request to the cloud and returns to step S1; otherwise, it returns to step S3 to continue the positioning for the next epoch.

[0006] Furthermore, the feature package in step S2 At least includes area identifiers Time window indicator Version number Feature validity period And a transferable feature library, namely: ; in, For the region Time window The corresponding feature packet; This serves as the initial state seed. To stabilize the observation subset rules; This is the weight vector; This is the prior information matrix; This is the initial damping factor; For branch switching parameter set; The feature package Further introduce the seed covariance matrix Outlier threshold parameter set Timestamp and integrity verification fields; in, This is the set of threshold parameters for outlier observations.

[0007] Furthermore, the branches in step S3 and branches Furthermore, the corresponding residual vector, Jacobian matrix, and weight matrix are introduced; Branches The optimization objective function is: ; in, For branches In real-time epoch The observation set used consists of the currently visible satellite set. stable observation subset rules distributed from the cloud Joint decision; This represents the difference between the actual observed value and the theoretical predicted value. For the first The state vector to be estimated for each epoch; in addition, For branches The total cost function; For the first Link weight; For the loss function, the squared loss function or... Loss function; The a priori constraint strength coefficient; This serves as the initial state seed. This is the prior information matrix; In the In the next iteration, the objective function is locally linearized to obtain the damped Gaussian-Newton update: ; in, For branches In the State update amount for each iteration; This is the damping factor for this iteration; It is the identity matrix; This represents finding the inverse of a matrix. For branches The residual vector; For branches The Jacobian matrix; For branches The weight matrix; And update the status: ; in, and Representing branches In the Second and third The state estimate for the next iteration; Branches The optimization objective function is: ; in, Let B be the cost function for branch B. For branches The weights; For branches In the Damping factor for the next iteration; The corresponding damped Gauss-Newton update is: ; in, For branches The amount of state updates; Let be the Jacobian matrix for branch B; Here is the weight matrix for branch B; Let be the residual vector of branch B; The update status is: ; in, and These represent the state estimates for the two iterations before and after branch B, respectively.

[0008] Furthermore, the damping factor Further introduce an adaptive update mechanism; Let the first The cost reduction for the next iteration is: ; in, Indicates that branch A is in the 1st... The cost difference before and after the next iteration; like Then reduce the damping factor: ; in, This is the damping attenuation coefficient, with a value between 0 and 1.

[0009] like Then increase the damping factor: ; in, This is the damping amplification factor, which takes a value greater than 1; Further, an iteration termination condition is introduced: If satisfied ,or ,or If any of the conditions are met, the iteration will terminate. in, This represents the maximum number of iterations. The threshold for state update amount; The threshold for cost variation.

[0010] Furthermore, the aforementioned in the first In the next iteration, when the prior information matrix is ​​not enabled, the branch... The update can be in a simplified form: ; in, This represents finding the increment that minimizes the objective function. ; For linearization increment terms; The square of the L2 norm of the update quantity; The corresponding state is then updated as follows: .

[0011] Furthermore, the branches in S3 and branches The normalized decision cost is further introduced by introducing the normalized residual cost of the corresponding branch; Let the first The normalization decision cost for each branch is: ; in, For branches The cost of normalized residuals; For branches Number of observations used; Let be the dimension of the state; For branches The candidate output state; The final output will be: like ,but ;like ,but ; in, For final positioning output; Provide protection margin for branch switching, and .

[0012] Furthermore, the branches in S3 and branches Another implementation of the normalized decision cost is a direct comparison of the original root mean square error, namely: ; in, For branches The root mean square residual; Indicates the first candidate state The square of the observation residuals; like Then output branch The optimal solution; if Then output branch The optimal solution.

[0013] Furthermore, the proportion in step S4 For length is The winning percentage of branch B within the sliding window, i.e.:

[0014] in, Indicates that recently The proportion of branches B that are better than or no worse than branches A within each epoch; For the epoch index in the sliding window; For indicator functions; Average optimal cost For length is The average cost of the sliding window, i.e.:

[0015] in, Indicates recent The average optimal cost within each epoch; This represents the smaller of the two branches at each epoch; If satisfied ,or ,or If any of the above conditions are met, the edge device sends a feature update request to the cloud. in, For branches Winning percentage threshold; The average cost threshold; The current time; The generation time of the current feature version; This refers to the validity period of the feature.

[0016] Compared with existing technologies, this invention provides a low-Earth orbit satellite Doppler positioning method for edge devices, which has the following advantages: 1. This low-Earth orbit satellite Doppler positioning method for edge devices constructs an asymmetric computing execution architecture that combines cloud and edge collaboration by performing global high-precision joint calculation to extract features in the cloud and only performing lightweight damped iterative calculation at the edge. The cloud is responsible for computationally intensive historical data processing, while the edge only undertakes low-complexity iterative updates, which significantly reduces the computing power requirements and storage overhead of the edge. At the same time, the feature library extracted once in the cloud can serve multiple edge devices in the same area, realizing resource reuse. 2. This low-Earth orbit satellite Doppler positioning method for edge devices extracts robust statistical features such as median, robust scale, availability, and outlier ratio by statistically analyzing the historical residuals of each observation link based on historical reference trajectories. This constructs a transferable feature extraction mechanism based on historical reference trajectories. This mechanism quantifies historical environmental knowledge into stable observation subset rules and robust statistical weights, enabling historical experience learned offline in the cloud to be transferred to online calculation at the edge in the form of lightweight parameters. This solves the technical problem that historical observation data cannot be effectively transferred and utilized in traditional methods. 3. This low-Earth orbit satellite Doppler positioning method for edge devices achieves a lightweight damped iterative mechanism by adopting a weighted least squares framework at the edge, combined with adaptive damping factor adjustment and triple iterative termination condition determination. Each iteration only requires local linearization and single-step Gauss-Newton update. The damping factor is adaptively adjusted according to the cost change direction to balance convergence speed and numerical stability. Combined with the triple termination condition, it avoids invalid iterations while ensuring accuracy, making the single-epoch solution time extremely low and adaptable to the computing power constraints of edge devices. 4. This low-Earth orbit satellite Doppler positioning method for edge devices achieves a dual-branch parallel optimization mechanism by constructing a parallel solution dual-branch architecture and combining normalized residual cost comparison with a hysteresis decision criterion with protection margin. Branch A adopts a stable subset of observations and introduces prior regularization constraints, while branch B adopts all observations and does not rely on historical priors. After parallel solution of the two branches, the output is optimized based on the normalized decision cost, so that the system can obtain high-precision results when the prior is valid and automatically switch to the backup branch when the prior fails. The protection margin avoids frequent switching and achieves an adaptive balance between historical priors and real-time observations. 5. This low-Earth orbit satellite Doppler positioning method for edge devices introduces sliding window statistics at the edge to monitor the performance degradation of the system in real time and constructs a performance degradation-triggered update mechanism. The winning ratio of branch B and the average optimal cost characterize performance changes from the two dimensions of relative superiority and absolute quality, respectively. With the expiration of validity period as a fallback condition, any trigger will request an update of the feature package from the cloud, forming a closed-loop adaptive process of "online monitoring - performance degradation - trigger update - feature regeneration", so that the feature library always maintains a match with the current environment. Attached Figure Description

[0017] Figure 1 This is a diagram illustrating the overall architecture of the cloud-edge collaborative low-orbit satellite Doppler positioning system of the present invention. Figure 2 This is an overall flowchart of the present invention; Figure 3 This is a flowchart of the online edge-end solution process of the present invention; Figure 4 This is a schematic diagram of the cloud-edge closed-loop update mechanism of the present invention; Figure 5 This is a schematic diagram comparing the prior injection point clouds of the present invention; Figure 6 This is a schematic diagram of the prior injection error curve of the present invention. Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] Example 1: Please refer to Figure 1-6 This embodiment of a low-Earth orbit satellite Doppler positioning method for edge devices includes the following steps: S1. Collect regional historical Doppler observations and ephemeris data, perform global high-precision joint calculations in the cloud, and obtain historical reference trajectories. Based on historical reference trajectories Statistically analyze the historical residuals of each observation link, and extract a transferable feature library based on the historical residuals; S2. Encapsulate the transferable feature library into a feature package. And distribute it to the edge; S3. The edge device receives real-time Doppler observations and ephemeris data for the current epoch, and retrieves the corresponding local feature packets based on feature matching. Based on feature packets The portable feature library it carries is used to construct branches. and branches And perform damping iterative calculations separately to obtain the branches. and branches Based on the candidate solutions of each branch and the observation data used, the branches are determined respectively. and branches The cost of normalized judgments; Based on the included protection margin Comparison criteria for branches and branches The normalized decision cost is used to select the best solution, and the candidate solution of the best solution branch is output as the final localization output. ; S4. Update the sliding window statistics based on the positioning results, and calculate the branch. Better than or no worse than branches proportion and average optimal cost ; If the ratio is satisfied Not less than the proportional threshold or average optimal cost Not less than the average cost threshold If any of the features expires, the edge device sends a feature update request to the cloud and returns to step S1; otherwise, it returns to step S3 to continue the positioning for the next epoch.

[0020] Wherein, the target area number is set as The historical time window number is The real-time epoch number is The cloud in the region Historical time window Retrieve historical observation datasets: ; Indicates the area In the time window Historical datasets within; For the first A collection of Doppler observations from 1 historical epoch; For the first A set of ephemeris and auxiliary information corresponding to each historical epoch; This represents the total number of epochs within the history window. It should be noted that the time window It can be set as a fixed-length window, a sliding window, or a time interval that adapts to task requirements. For the Let the set of currently visible satellites be: (Ephemeris) ; in, Indicates the first The set of satellite indexes that can be observed in each epoch; For satellite indexing; This represents the number of visible satellites at that epoch. No. The satellite in the A single observation for each epoch is: ; in, Indicates the first The satellite in the Observation tuples of each epoch; These are actual Doppler observations; This is a link quality indicator, which can be carrier-to-noise ratio, signal-to-noise ratio, or received power. This refers to the satellite's elevation angle; This refers to the satellite azimuth angle. It should be noted that the settings , , The purpose is to provide auxiliary features for subsequent link quality assessment and selection of stable observation subsets; No. The satellite in the The ephemeris information for each epoch is as follows: ; in, Indicates the first The satellite in the The epochal group of each epoch; This is the satellite position vector; The satellite velocity vector; Represents the three-dimensional real number space; Edge devices in real-time epochs The received real-time input is: ; in, Indicates the first Online input data for each real-time epoch; This represents the set of real-time Doppler observations for that epoch; This represents the set of real-time ephemeris and auxiliary information for that epoch.

[0021] It should be noted that the real-time input and historical input use the same data structure definition. This design ensures that the features extracted from the cloud can be seamlessly applied to the real-time observation data at the edge, avoiding the additional computational overhead and potential mismatch risks caused by data format conversion. At the same time, the introduction of real-time ephemeris enables the edge to independently calculate the satellite position and velocity at the current epoch without relying on the satellite orbit information provided by the cloud, thus ensuring the real-time performance and autonomy of online calculation.

[0022] In addition, the state vector to be estimated at the edge is: ; in, For the first The state vector to be estimated for each epoch; The target position vector; The target velocity vector; For receiver frequency offset or equivalent Doppler common bias term; superscript Indicates transpose; Represents the seven-dimensional real space; It should be noted that incorporating the frequency offset term into the state variables is to absorb the receiver's local oscillator error or other common Doppler biases, thereby enhancing the model's integrity. In a simplified implementation, when the target velocity can be provided by inertial navigation, extrapolated values ​​from the previous epoch, or other sensors, the state vector can be simplified to: ; It should be noted that this simplified state vector only contains position and frequency offset components, and is suitable for scenarios where edge devices have weaker computing power or where external speed priors are available. Target and the The instantaneous geometric distance between the satellites is defined as: ; in, Indicates the target and the first The satellite in the Euclidean distance in each epoch; This represents the second norm, also known as the Euclidean norm. Target and the The unit vector of the line-of-sight direction between the satellites is: ; in, This represents the unit direction vector pointing from the target to the satellite, whose direction reflects the geometric sensitivity of Doppler observations to the target's state; the denominator contains... That is, the aforementioned geometric distance .

[0023] It should be noted that the complete state vector incorporates the target position, velocity, and receiver frequency offset into the parameter space to be estimated. The position component describes the target's spatial coordinates, the velocity component describes the target's motion state, and the frequency offset component absorbs the receiver's local oscillator error and various common Doppler biases. Incorporating the velocity component into the state vector enables this method to maintain high solution accuracy in high dynamic scenarios, while the introduction of the frequency offset component avoids model mismatch caused by receiver clock drift. When the computing power of edge devices is limited or external velocity priors are available, the state vector can be simplified to include only the position component and the frequency offset component. In this case, the velocity component is provided by the external sensor and is not used as a quantity to be estimated, which effectively reduces the computational complexity while ensuring positioning accuracy. The geometric distance is the Euclidean distance between the satellite position and the target position, which is the basis for the subsequent calculation of the line-of-sight direction unit vector. The line-of-sight direction vector reflects the sensitivity of the target position error to the projection onto the satellite direction. Its calculation accuracy directly affects the accuracy of the position-related terms in the Jacobian matrix, and thus determines whether the convergence direction of the iterative update is correct.

[0024] Let the center frequency of the signal carrier be... The speed of light is Then the first The satellite in the The theoretically predicted Doppler value for each epoch is: ; in, Indicates the state Next to the Theoretical predictions from Doppler observations by a single satellite; The center frequency of the carrier. The speed of light; It represents the relative radial velocity between the satellite and the target along the line of sight; the negative sign reflects the sign relationship between the Doppler frequency shift and the radial relative motion direction; This refers to the receiver frequency offset or equivalent common offset term. It should be noted that this formula indicates that the Doppler prediction value is mainly determined by the relative velocity in the line-of-sight direction and the receiver frequency offset. Therefore, the actual observation model can be expressed as: ; in, The actual observed Doppler value; Indicates random measurement noise; This represents the system disturbance term caused by multipath, NLOS, local occlusion, and modeling errors; It should be noted that this formula indicates that the actual observation consists of the ideal predicted value and two types of error terms; Definition of the first The observation in the first The residuals for each epoch are: ; in, It represents the difference between the actual observed value and the theoretical prediction value, and is the core error quantity in the subsequent optimization solution; It should be noted that when the model is accurate and the observations are good, the residuals should be close to zero; when there is anomalous propagation or model mismatch, the residuals will increase significantly. By stacking the residuals of all observations for this epoch, we can obtain the residual vector: ; in, For the first The residual vector of each epoch; This indicates omitted terms of the same kind; its dimension is the same as the number of available observations in the current epoch. Consistent.

[0025] It should be noted that the predicted Doppler value establishes a mapping relationship between the state vector and the observation space, and the difference between it and the actual observation value is the residual; the magnitude of the residual directly reflects the degree of deviation between the current state estimate and the true state.

[0026] The actual observation model decomposes the observed values ​​into three parts: predicted values, random measurement noise, and system disturbances. The latter includes factors that are difficult to model accurately, such as multipath, NLOS, and modeling errors.

[0027] The residual vector stacks the residuals of all satellites into a unified vector, which is the core basis for subsequent weighted iteration, cost calculation and branch decision, and is also the fundamental motivation for introducing historical residual statistics and robust weighting mechanism.

[0028] Let the first Observation pairs of state vectors Jacobi behavior Then we have: ; in, Indicates the first The first-order partial derivatives of the residuals with respect to the state vector; This represents the gradient information of the residual function with respect to the state variables; It should be noted that the Jacobian matrix reflects the effect of small changes in the state on the changes in the residual, and is the basis for Gauss-Newton type iterative solutions; In the complete state model, the Jacobian block representation is as follows: ; The first term represents the residual's sensitivity to the target position, the second term represents the residual's sensitivity to the target velocity, and the third term represents the residual's sensitivity to the frequency offset term. in: ; It should be noted that this formula indicates that the partial derivative of the residual with respect to the target velocity is determined only by the carrier frequency, the speed of light, and the line of sight, which means that the change of the target velocity along the line of sight will directly affect the Doppler residual. ; It should be noted that this formula indicates that the effect of the frequency offset term on the residual is linear and the coefficient is constant, which means that changes in the frequency offset term will affect the residual in an equal manner. The partial derivative with respect to the position vector can be written as: ; Among them, the first item The first term represents the first-order effect of relative velocity on position change; the second term represents the higher-order geometric correction caused by changes in the line-of-sight direction. Represents the cube of the distance term; It should be noted that this formula reflects the obvious nonlinear characteristics of the Doppler residual's dependence on position; Stacking all the Jacobians of the observations, we obtain the Jacobian matrix for the current epoch: ; in, For the first The overall Jacobian matrix for each epoch, with the number of rows equal to the number of observations. Correspondingly, the number of columns and the state dimension correspond.

[0029] It should be noted that the overall Jacobian matrix is ​​formed by stacking the Jacobian row vectors of all observation links along the row direction. Its number of rows is equal to the number of available observations in the current epoch, and its number of columns is equal to the dimension of the state vector. This matrix centrally reflects the sensitivity of all observation residuals to all state variables and is the core computational object for solving the state update in the subsequent weighted Gauss-Newton iteration. The condition number of the Jacobian matrix reflects the quality of the observation geometry. A larger condition number indicates a more severe ill-conditioned nature of the observation equation, requiring the introduction of damping factors and prior regularization terms to ensure numerical stability. A smaller condition number indicates a better geometry and faster iterative convergence.

[0030] The historical reference trajectory is as follows: ; in, Indicates that the cloud is in the region Time window The historical reference state sequence obtained above; For the first Reference state estimates for each historical epoch; superscript This indicates either a "reference solution" or an "offline high-precision solution"; It should be noted that this reference trajectory serves as the benchmark for subsequent historical residual statistics and prior feature extraction.

[0031] Based on historical reference trajectories, construct the first... The link is in the 1st Residuals of each historical era: ; in, Indicates the first The link is in the 1st Historical residuals in a historical era; These are historical, actual observation values. These are predicted observations obtained based on a high-precision reference state in the cloud. It should be noted that this residual reflects the error distribution characteristics of the link in the historical environment; Furthermore, define the first The residual sequence of the link within the historical window: ; in, Indicates the first The residual set of each link over the entire historical window is used for subsequent robust statistical analysis.

[0032] It should be noted that the high-precision reference trajectory in the cloud is obtained by offline global joint calculation of all observation data within the historical window, and its accuracy is usually significantly better than the real-time calculation results of a single epoch at the edge. As the benchmark for all subsequent historical residual calculations and prior feature extraction, the quality of this reference trajectory directly affects the reliability of the feature library. The historical residuals constructed based on this reference trajectory reflect the systematic error characteristics of the link under historical conditions, encompassing the combined effects of deterministic or semi-deterministic factors such as multipath, NLOS, atmospheric delay residuals, ephemeris errors, and modeling errors.

[0033] Definition of the first The historical median residual of the link is: ; in, Indicates the first The median of the historical residuals of a link is used to describe the central location of the residuals of that link. Indicates the epoch index Take the median; It should be noted that the median is less sensitive to outliers than the mean; Definition of the first The robustness metric for each link is: ; in, Indicates the first Robust scaling estimation of link residuals; This represents the absolute deviation of the residuals relative to the median; the coefficient 1.4826 is used to approximately correct the MAD dimension to the standard deviation scale. To prevent positive numbers with a denominator of zero; It should be noted that this definition corresponds to the absolute median difference (MAD) estimation, which can maintain strong stability even when outliers exist.

[0034] Definition of the first The availability of the link within the historical window is: ; in, Indicates the first The frequency of occurrence of a link within a historical window; For indicator functions; It should be noted that the value is 1 when the condition inside the parentheses is true, and 0 otherwise. It should be noted that this quantity reflects the stability and visibility of a certain link in historical observations; Definition of the first The outlier ratio of each link is: ; in, Indicates the first The outlier probability of a link within a historical window; The numerator represents the outlier detection threshold; the numerator represents the number of residuals that exceed the robustness threshold; the denominator represents the total number of times the link actually participated in observations. It should be noted that the larger this ratio is, the more unstable the link is.

[0035] Definition of the first The overall quality score for the link is: ; in, Indicates the first A comprehensive score for each link; Availability; For robustness; The proportion of outliers; This refers to the historical average quality metric of the link. The historical average elevation angle of the link; These are non-negative weighting coefficients used to adjust the importance of different features; It should be noted that the higher the score, the more suitable the link is for stable observation to participate in edge-end solution; Based on this, the stable observation subset rule is defined as follows: ; in, Indicates the area Time window The corresponding stable observation subset; The scoring threshold; This is the minimum availability threshold; The threshold for the maximum outlier ratio; It should be noted that this set is not a fixed satellite numbering list, but rather a stable link selection result determined by statistical characteristics.

[0036] Based on robust scale , define the first The robust statistical weights for each link are: ; in, For the first The weight of each link; This indicates that the smaller the scale, the greater the weight. This represents a clipping function used to restrict the result to a range. Inside; and These are the minimum and maximum weight thresholds, respectively.

[0037] It should be noted that this operation is used to avoid the value from being unstable due to individual link weights being too large or too small; Therefore, the weight vector is constructed as follows: ; in, This represents the link weight vector extracted from the cloud and awaiting distribution; Indicates the total number of links used for modeling or the maximum number of links; And the corresponding diagonal weight matrix: ; in, This indicates that a diagonal matrix is ​​constructed using the elements within the parentheses as diagonal elements. Used for subsequent weighted Gauss-Newton or weighted least squares iterations.

[0038] The cloud uses the optimal state at the end of the historical window or its extrapolated state as the initial state seed for online solution on the edge side, defined as: ; in, Indicates the area Time window The corresponding initial state seed is used to provide a good starting point for real-time iteration at the edge. In a preferred embodiment, the following can be adopted: ; in, This is a high-precision reference state at the end of the historical window.

[0039] Alternatively, a simple motion model can be used for extrapolation: ; in, This is the state extrapolation matrix, used to extrapolate the terminal reference state to the expected real-time time.

[0040] The cloud can also construct a seed covariance matrix based on several state samples at the end of the historical window: ; in, The covariance matrix representing the state seed; Represents covariance operation; This indicates the number of terminal state samples included in the statistics; Here is the regularization constant; It is the identity matrix; It should be noted that this matrix is ​​used to describe the uncertainty of the seed state in each dimension; Further construct the prior information matrix: ; in, Represents the prior information matrix; superscript This represents the inversion of a matrix; the smaller the covariance, the larger the information matrix, indicating a stronger prior in that direction; this matrix can be used as a regularization term at the edge to constrain the state update direction and step size; It should be noted that the complete process described above, from historical residual statistics to the construction of the prior information matrix, constitutes the core content of the cloud-based transferable feature library. The median residual and robust scale characterize the central tendency and dispersion of the error distribution of each link, while availability and outlier ratio reflect the visible stability and frequency of anomalies of the link. Together, these four factors constitute a multi-dimensional quantitative description of the historical behavior of the link. The comprehensive score compresses the above multi-dimensional features into a single sortable scalar, and, together with threshold screening, generates stable observation subset rules, thereby realizing the automatic identification and optimization of reliable links.

[0041] Robust weights further transform the robustness scale of the link into the degree of differentiated contribution in the solution. The smaller the scale, the greater the weight, so that links with high historical accuracy occupy a greater weight in edge iterations.

[0042] The seed state and prior information matrix transform the state information at the end of the historical window into the initial constraints for edge iteration. The seed state provides the starting point for iteration, and the prior information matrix updates the direction and step size through regularization terms to prevent excessive deviation caused by abnormal observations.

[0043] All of the above feature extraction processes are completed offline in the cloud. The extraction results are uniformly packaged in the form of feature packages and sent to the edge, so that historical environmental knowledge can be transferred to online calculation in the form of lightweight parameters, realizing the collaboration between cloud offline learning and edge online inference.

[0044] The feature package in step S2 At least includes area identifiers Time window indicator Version number Feature validity period And a transferable feature library, namely:

[0045] in, For the region Time window The corresponding feature packet; This serves as the initial state seed. To stabilize the observation subset rules; This is the weight vector; This is the prior information matrix; This is the initial damping factor; For branch switching parameter set; The feature package Further introduce the seed covariance matrix Outlier threshold parameter set Timestamp and integrity verification fields; in, This is the set of threshold parameters for outlier observations.

[0046] It should be noted that the feature package is a unified data carrier for transmitting transferable features from the cloud to the edge. The region identifier, time window identifier, and version number are used for accurate matching and retrieval at the edge, and the feature validity period provides a quantitative basis for judging timeliness. The seed state, stable observation subset rules, weight vector, and prior information matrix in the transferable feature library jointly determine the way prior information is applied in the edge solution, while the initial damping factor and branch switching parameters control the iterative numerical stability and branch decision behavior, respectively.

[0047] The structured encapsulation of feature packages enables the environmental knowledge extracted offline from the cloud to be transferred to the online solution at the edge in a lightweight and traceable form, providing a unified entry point for historical environmental prior information at the edge.

[0048] The branch in step S3 and branches Furthermore, the corresponding residual vector, Jacobian matrix, and weight matrix are introduced; Define branch A in the first... The set of observations for each epoch is:

[0049] in, This indicates that branch A is in the real-time epoch. The observation set used; this set consists of the currently visible satellite set. stable observation subset rules distributed from the cloud Joint decision; It should be noted that the corresponding residual vector, Jacobian matrix, and weight matrix are denoted as follows: , and ; in, Let A be the residual vector of branch A. Let A be the Jacobian matrix of branch A. Let be the weight matrix for branch A; Branches The optimization objective function is: ; in, For branches In real-time epoch The observation set used consists of the currently visible satellite set. stable observation subset rules distributed from the cloud Joint decision; This represents the difference between the actual observed value and the theoretical predicted value. For the first The state vector to be estimated for each epoch; in addition, For branches The total cost function; For the first Link weight; For the loss function, the squared loss function or... Loss function; The a priori constraint strength coefficient; This serves as the initial state seed. This is the prior information matrix; In the In the next iteration, the objective function is locally linearized to obtain the damped Gaussian-Newton update: ; in, For branches In the State update amount for each iteration; This is the damping factor for this iteration; It is the identity matrix; This represents finding the inverse of a matrix. For branches The residual vector; For branches The Jacobian matrix; For branches The weight matrix; And update the status: ; in, and Representing branches In the Second and third The state estimate for the next iteration; Define branch B in the first... The set of observations for each epoch is: ; in, Branch B uses the set of all available observations in the current epoch. This branch does not rely on historical prior subsets for filtering and is used as a backup against degradation. Branches The optimization objective function is: ; in, Let B be the cost function for branch B. The weight of branch B can be a unit weight or a basic weight that depends only on real-time link quality indicators. For branch B in the th Damping factor for the next iteration.

[0050] It should be noted that, compared to branch A, branch B does not explicitly introduce historical prior regularization terms; The corresponding damped Gauss-Newton update is: ; in, For branches The amount of state updates; Let be the Jacobian matrix for branch B; Here is the weight matrix for branch B; Let be the residual vector of branch B; The update status is: ; in, and These represent the state estimates for the two iterations before and after branch B, respectively.

[0051] It should be noted that branch A and branch B constitute a pair of complementary solution strategies, corresponding to the two modes of "refined localization under historical prior constraints" and "pure real-time observation-driven anti-degradation backup" respectively. The observation set of branch A is selected by the stable observation subset rule, and only links with good historical statistical characteristics are retained to participate in the solution. Its optimization objective function includes both weighted residual terms and prior regularization terms. The prior regularization term is centered on the seed state and uses the prior information matrix as the constraint strength to ensure that the state update does not deviate excessively from the reliable benchmark provided by the cloud, so as to maintain the solution stability when the number of observations is insufficient or the geometric configuration is poor. Branch B uses all available observations in the current epoch and does not introduce historical prior regularization terms. Its solution results rely entirely on real-time observation data and can provide positioning outputs that are not contaminated by prior biases when environmental characteristics change abruptly or historical priors become outdated.

[0052] The damping factor Further introduce an adaptive update mechanism; Let the first The cost reduction for the next iteration is: ; in, Indicates that branch A is in the 1st... The cost difference before and after the next iteration; if this value is less than or equal to zero, it indicates that the current update effect is not good. like Then reduce the damping factor: ; in, This is the damping attenuation coefficient, with a value between 0 and 1.

[0053] like Then increase the damping factor: ; in, This is the damping amplification factor, which takes a value greater than 1; It should be noted that these two rules can achieve a balance between convergence speed and numerical stability; Further, an iteration termination condition is introduced: If satisfied ,or ,or If any of the conditions are met, the iteration will terminate. in, This is the maximum number of iterations, used to limit the computational load at the edge. The threshold for the state update amount is used; when the update is sufficiently small, it is considered to have approximately converged. The threshold for cost variation is set when the cost function changes sufficiently; if the cost function changes to a sufficiently small value, it is considered that continuing the iteration is not meaningful.

[0054] It should be noted that the adaptive update mechanism of the damping factor is used to dynamically adjust the state update step size during the iteration process; When the cost function decreases effectively, it indicates that the current iteration direction is correct. The damping factor should be appropriately reduced to accelerate convergence. When the cost function does not decrease, it indicates that the current iteration step size is too large or the direction is deviated. The damping factor should be increased to reduce the step size and improve numerical stability. The aforementioned adjustment strategy of "reducing speeds up and increasing stability" achieves a balance between high accuracy and high robustness in the iterative process. The iteration termination condition is determined by jointly considering three dimensions: the maximum number of iterations, the state update threshold, and the cost change threshold. The iteration terminates when any one of these conditions is met. This ensures the accuracy of the solution while avoiding excessive consumption of computing resources at the edge due to excessive iteration, thus adapting to the computing power constraints of edge devices.

[0055] The branch in S3 and branches The normalized decision cost is further introduced by introducing the normalized residual cost of the corresponding branch; Let the first The normalization decision cost for each branch is: ; in, For branches The cost of normalized residuals; For branches Number of observations used; Let be the dimension of the state; For branches The candidate output state; express Only branch A or branch B can be taken; in the denominator It serves to normalize the degrees of freedom, making the costs under different numbers of observations more comparable; The final output will be: like ,but ;like ,but ; in, For final positioning output; Provide protection margin for branch switching, and This is to avoid frequent switching when the performance of the two branches is similar.

[0056] It should be noted that the normalized decision cost corrects the degree of freedom of the residual cost by adjusting the denominator, which eliminates the problem of incomparability of costs caused by the difference in the number of observations in different branches, so that the decision results of branch A and branch B only reflect the quality of observations rather than the number of observations. If the normalized cost plus δ for branch A is still less than that for branch B, then choose branch A; otherwise, choose branch B. The introduction of this is equivalent to setting an insensitive interval, which only occurs when branch A has a sufficiently significant advantage. This avoids frequent switching caused by observation noise interference when the performance of the two branches is similar, thus ensuring the timing continuity and stability of the positioning output.

[0057] The proportion in step S4 For length is The winning percentage of branch B within the sliding window, i.e.:

[0058] in, Indicates that recently The proportion of branches B that are better than or no worse than branches A within each epoch; For the epoch index in the sliding window; For indicator functions; It should be noted that the larger this quantity is, the more likely the historical prior branch is to fail; Average optimal cost For length is The average cost of the sliding window, i.e.:

[0059] in, Indicates recent The average optimal cost within each epoch; This represents the smaller of the two branches at each epoch; It should be noted that this indicator is used to reflect whether the overall solution quality of the system continues to decline; If satisfied ,or ,or If any of the above conditions are met, the edge device sends a feature update request to the cloud. in, For branches Winning percentage threshold; The average cost threshold; The current time; The generation time of the current feature version; For the validity period of the feature; After receiving the update request, the cloud re-executes historical data aggregation, reference trajectory solving, and feature extraction to form a new version of the feature library, which is then distributed to the edge, realizing the following closed-loop update process: ; in, Represents historical datasets; Indicates a historical reference trajectory; Indicates the current feature packet; Indicates the current output status on the edge side; This indicates that an update event has been triggered; This indicates the updated feature package.

[0060] It should be noted that, and The degree of system performance degradation is characterized from both "relative" and "absolute" dimensions. The frequency with which branch B, which does not depend on historical priors, is better than or equal to branch A within the sliding window is measured. A continuously increasing proportion of this means that the consistency between historical prior information and the current environment is continuously decreasing, and the prior constraints may have become invalid. The absolute level of the overall solution quality of the system is measured. A continuous increase in this indicator indicates that even when choosing between the two branches, the positioning accuracy is still deteriorating, which may be due to the overall deterioration of the environment or a systematic decline in ephemeris quality.

[0061] The two indicators complement each other: the former senses the relative validity of prior information, while the latter senses the absolute reliability of the system output. The three triggering conditions adopt "OR" logic to ensure that any performance degradation sign can trigger an update in a timely manner. Among them, the expiration date serves as a fallback mechanism to ensure that the feature library is not used indefinitely.

[0062] Example 2: Please refer to Figure 1-6 Based on Example 1, a low-Earth orbit satellite Doppler positioning method for edge devices, in step S3, branch Another optional iterative update method: In the first In the next iteration, when the prior information matrix is ​​not enabled, the branch... The update can be in a simplified form: ; in, This represents finding the increment that minimizes the objective function. ; For linearization increment terms; The square of the L2 norm of the update quantity; The corresponding state is then updated as follows: .

[0063] It should be noted that in this simplified update method, branch A no longer explicitly introduces the prior information matrix as a regularization constraint, and the objective function degenerates into a standard damped least squares form containing only the weighted sum of squared residuals and the damping regularization term. At this point, historical prior information only indirectly affects the solution results through the stable observation subset rules and weight vectors. That is, historical knowledge is only used to select which observations participate in the solution and the contribution weight of each observation, and is not forcibly applied as a constraint term for state update during the iteration process. This simplified method significantly reduces the computational load and is suitable for scenarios where edge devices have more limited computing power or where real-time requirements are extremely high and it is difficult to bear the additional matrix operation overhead brought about by the participation of the prior information matrix in each iteration. As a parallel alternative to Implementation Example 1, this simplified method can be flexibly selected according to the actual computing resources at the edge.

[0064] Example 3: Please refer to Figure 1-6 Based on Example 2, a low-Earth orbit satellite Doppler positioning method for edge devices, branch S3 and branches Another implementation of the normalized decision cost is a direct comparison of the original root mean square error, namely: ; in, For branches The root mean square residual; Indicates the first candidate state The square of the observation residuals; like Then output branch The optimal solution; if Then output branch The optimal solution.

[0065] It should be noted that in this simplified decision-making method, the branch decision is directly based on the comparison of the original root mean square residuals, omitting the degree-of-freedom correction term in the normalized cost calculation in Example 1, as well as the branch switching protection margin. Hysteresis comparison criteria; This method is simpler to implement and has less computational overhead. It is suitable for scenarios where edge devices have extremely limited computing resources or extremely high real-time requirements, and cannot afford the additional computational overhead caused by normalization cost calculation and comparison with protection margin. However, it should be noted that since this method does not normalize the degrees of freedom, when the difference in the number of observations between branch A and branch B is large, the branch with fewer observations may obtain an artificially low RMS value due to the smaller denominator, which may lead to a decision biased towards the branch with fewer observations. Meanwhile, due to the lack of protection margin, frequent switching is likely to occur due to observation noise interference when the residual performance on both sides is similar. This simplified decision method, as a parallel alternative to the third embodiment, forms a scheme selection with different complexity levels with the normalized cost decision method of the first embodiment. It can be flexibly selected according to the balance between actual computing resources and positioning accuracy requirements at the edge.

[0066] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, 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 a process, method, article, or apparatus. Without further limitations, 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 said element.

[0067] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A low-Earth orbit satellite Doppler positioning method for edge devices, characterized in that, Includes the following steps: S1. Collect regional historical Doppler observations and ephemeris data, perform global high-precision joint calculations in the cloud, and obtain historical reference trajectories. Based on historical reference trajectories Statistically analyze the historical residuals of each observation link, and extract a transferable feature library based on the historical residuals; S2. Encapsulate the transferable feature library into a feature package. And distribute it to the edge; S3. The edge device receives real-time Doppler observations and ephemeris data for the current epoch, and retrieves the corresponding local feature packets based on feature matching. Based on feature packets The portable feature library it carries is used to construct branches. and branches And perform damping iterative calculations separately to obtain the branches. and branches Based on the candidate solutions of each branch and the observation data used, the branches are determined respectively. and branches The cost of normalized judgments; Based on the included protection margin Comparison criteria for branches and branches The normalized decision cost is used to select the best solution, and the candidate solution of the selected branch is output as the final localization output. ; S4. Update the sliding window statistics based on the positioning results, and calculate the branch. Better than or no worse than branches proportion and average optimal cost ; If the ratio is satisfied Not less than the proportional threshold or average optimal cost Not less than the average cost threshold If any of the features expires, the edge device sends a feature update request to the cloud and returns to step S1; otherwise, it returns to step S3 to continue the positioning for the next epoch.

2. The low-Earth orbit satellite Doppler positioning method for edge devices according to claim 1, characterized in that: The feature package in step S2 At least includes area identifiers Time window indicator Version number Feature validity period And a transferable feature library, namely: ； in, For the region Time window The corresponding feature packet; This serves as the initial state seed. To stabilize the observation subset rules; This is the weight vector; This is the prior information matrix; This is the initial damping factor; For branch switching parameter set; The feature package Further introduce the seed covariance matrix Outlier threshold parameter set Timestamp and integrity verification fields; in, This is the set of threshold parameters for outlier observations.

3. The low-Earth orbit satellite Doppler positioning method for edge devices according to claim 1, characterized in that: The branch in step S3 and branches Furthermore, the corresponding residual vector, Jacobian matrix, and weight matrix are introduced; Branches The optimization objective function is: ； in, For branches In real-time epoch The observation set used consists of the currently visible satellite set. stable observation subset rules distributed from the cloud Joint decision; This represents the difference between the actual observed value and the theoretical predicted value. For the first The state vector to be estimated for each epoch; in addition, For branches The total cost function; For the first Link weight; For the loss function, the squared loss function or... Loss function; The a priori constraint strength coefficient; This serves as the initial state seed. This is the prior information matrix; In the In the next iteration, the objective function is locally linearized to obtain the damped Gaussian-Newton update: ； in, For branches In the State update amount for each iteration; This is the damping factor for this iteration; It is the identity matrix; This represents finding the inverse of a matrix. For branches The residual vector; For branches The Jacobian matrix; For branches The weight matrix; And update the status: ； in, and Representing branches In the Second and third The state estimate for the next iteration; Branches The optimization objective function is: ； in, Let B be the cost function for branch B. For branches The weights; For branches In the Damping factor for the next iteration; The corresponding damped Gauss-Newton update is: ； in, For branches The amount of state updates; Let be the Jacobian matrix for branch B; Here is the weight matrix for branch B; Let be the residual vector of branch B; The updated status is: ； in, and These represent the state estimates for the two iterations before and after branch B, respectively.

4. The low-Earth orbit satellite Doppler positioning method for edge devices according to claim 3, characterized in that: The damping factor Further introduce an adaptive update mechanism; Let the first The cost reduction for the next iteration is: ； in, Indicates that branch A is in the th... The cost difference before and after the next iteration; like Then reduce the damping factor: ; in, This is the damping attenuation coefficient, with a value between 0 and 1; like Then increase the damping factor: ; in, This is the damping amplification factor, with a value greater than 1; Further, an iteration termination condition is introduced: If satisfied ,or ,or If any of the conditions are met, the iteration will terminate. in, This represents the maximum number of iterations. The threshold for state update amount; The threshold for cost variation.

5. The low-Earth orbit satellite Doppler positioning method for edge devices according to claim 3, characterized in that: In the first In the next iteration, when the prior information matrix is ​​not enabled, the branch... The update can be done in a simplified form: ； in, This represents finding the increment that minimizes the objective function. ; For linearization increment terms; The square of the L2 norm of the update quantity; The corresponding state is then updated as follows: .

6. A low-Earth orbit satellite Doppler positioning method for edge devices according to any one of claims 1, characterized in that: The branch in S3 and branches The normalized decision cost is further introduced by introducing the normalized residual cost of the corresponding branch; Let the first The normalization decision cost for each branch is: ； in, For branches The cost of normalized residuals; For branches Number of observations used; Let be the dimension of the state; For branches The candidate output states; The final output will be: like ,but ;like ,but ; in, For final positioning output; For branch switching protection margin, and .

7. A low-Earth orbit satellite Doppler positioning method for edge devices according to claim 6, characterized in that: The branch in S3 and branches Another implementation of the normalized decision cost is a direct comparison of the original root mean square error, namely: ； in, For branches The root mean square residual; Indicates the first candidate state The square of the observation residuals; like Then output branch The optimal solution; if Then output branch The optimal solution.

8. The low-Earth orbit satellite Doppler positioning method for edge devices according to claim 1, characterized in that: The proportion in step S4 For length is The winning percentage of branch B within the sliding window, i.e.: ； in, Indicates that recently The proportion of branches B that are better than or no worse than branches A within each epoch; For the epoch index in the sliding window; For indicator functions; Average optimal cost For length is The average cost of the sliding window, i.e.: ； in, Indicates recent The average optimal cost within each epoch; This represents the smaller of the two branches at each epoch; If satisfied ,or ,or If any of the above conditions are met, the edge device sends a feature update request to the cloud. in, For branches Winning percentage threshold; The average cost threshold; The current time; The generation time of the current feature version; This refers to the validity period of the feature.

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