Three-dimensional modeling method and system based on integration of beidou positioning and gauss spatter

Abstract

The application discloses a three-dimensional modeling method and system based on Beidou positioning and Gaussian spatter fusion, relates to the technical field of vision and three-dimensional reconstruction, and the method comprises the following steps: obtaining the absolute position of a collection platform and a positioning covariance matrix through Beidou differential positioning, and uniformly converting to a station-centered coordinate system; synchronously collecting images, Beidou positioning and inertial data, combining visual features to perform weighted joint optimization, and solving an initial camera pose; generating a three-dimensional Gaussian primitive with a Beidou confidence weight based on the initial pose; constructing a composite loss function, and jointly iteratively optimizing the primitive parameters and the camera pose; in the optimization, splitting the primitive according to the gradient and the Beidou confidence double conditions, and pruning the primitive according to the statistical consistency of the primitive and the Beidou track; and finally outputting a three-dimensional Gaussian scene model with absolute geographic coordinates. The application deeply fuses Beidou positioning and three-dimensional Gaussian spatter, and provides a solution for outdoor scene reconstruction.

Description

Technical Field

[0001] This invention relates to the field of vision and 3D reconstruction technology, specifically to a 3D modeling method and system based on the fusion of BeiDou positioning and Gaussian splashing. Background Technology

[0002] 3D Gaussian splashing, as an explicit 3D scene representation technology, models the scene using a large number of anisotropic Gaussian ellipsoids and combines them with differential rasterization to achieve highly realistic real-time rendering.

[0003] However, existing 3D Gaussian splashing methods have the following shortcomings: the reconstruction results are established in an arbitrary local coordinate system, lacking an absolute geographic benchmark, making it difficult to directly use in engineering applications such as digital twins and smart cities that require real spatial coordinates; in outdoor areas with weak or repetitive textures, pure visual feature matching is prone to failure, leading to model drift or even reconstruction interruption; existing methods only treat positioning as an independent initialization prior, without systematically coupling it with the differentiable rendering optimization process of 3D Gaussian splashing, causing positioning errors to propagate to the geometric model; and they do not probabilistically model the uncertainties caused by differential positioning time delays and satellite configuration changes, making it impossible to adaptively adjust the constraint strength.

[0004] Therefore, there is an urgent need for a 3D modeling method that can deeply integrate BeiDou high-precision positioning with 3D Gaussian splashing and dynamically integrate positioning uncertainties throughout the entire process. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the shortcomings of the existing technology by providing a three-dimensional modeling method and system based on the fusion of Beidou positioning and Gaussian splashing.

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

[0007] The 3D modeling method based on the fusion of BeiDou positioning and Gaussian splashing includes the following steps:

[0008] Step S1: Obtain the three-dimensional absolute position of the acquisition platform in real time through BeiDou differential positioning, simultaneously calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system to construct a spatial absolute reference.

[0009] Step S2: Use the hardware synchronous acquisition system to acquire the image sequence of the outdoor scene, the corresponding BeiDou positioning data and inertial measurement data, and perform weighted joint optimization based on visual feature matching and BeiDou absolute position constraints to solve the initial camera extrinsic parameters of each frame of image;

[0010] Step S3: Generate a set of three-dimensional Gaussian elements based on the initial camera extrinsic parameters and the image. Each three-dimensional Gaussian element specifically includes the spatial mean, covariance matrix, opacity, color, and confidence weight factor dynamically calculated from the BeiDou covariance matrix.

[0011] Step S4: Construct a composite loss function that includes photometric consistency loss, BeiDou position constraint loss weighted by the inverse BeiDou covariance matrix, structural similarity loss, and 3D Gaussian meta-parameter regularization loss, and perform joint iterative optimization of the 3D Gaussian meta-parameters and camera pose;

[0012] Step S5: During the optimization process, 3D Gaussian element splitting is performed based on the dual conditions of the 3D Gaussian element projection gradient and the BeiDou confidence weight, and 3D Gaussian element pruning is performed based on the statistical consistency condition between the 3D Gaussian element position and the BeiDou trajectory point to achieve adaptive density control.

[0013] Step S6: Optimize and output a 3D Gaussian scene model with absolute geographic coordinates.

[0014] Furthermore, step S1 specifically includes the following steps:

[0015] Step S1.1: Through the B1I, B2a, and B3I multi-frequency carrier phase double-difference observations of the BeiDou-3 system, the geodetic coordinates of the acquisition platform in the WGS-84 coordinate system are calculated in real time.

[0016] Step S1.2: Construct the design matrix and observation weight matrix based on the visible satellite geometry, calculate the inverse matrix of the normal equation, and multiply it by the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix.

[0017] Step S1.3: Convert the WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then, using the selected reference origin as the reference, transform it to the station center coordinate system through a rotation matrix to obtain the east, north, and celestial coordinates.

[0018] Furthermore, in step S2, the hardware synchronization acquisition system is implemented through a hardware triggering mechanism to ensure that the synchronization error between the image and the BeiDou positioning timestamp is less than 1 millisecond; the weighted joint optimization adopts an objective function that fuses the visual reprojection error robust kernel function and the BeiDou position Mahalanobis distance constraint, wherein the weight matrix of the Mahalanobis distance is taken as the inverse matrix of the BeiDou covariance matrix.

[0019] Furthermore, step S3 specifically includes the following steps:

[0020] Step S3.1: Based on the initial camera extrinsic parameters and images, generate a three-dimensional Gaussian unit described by the spatial location mean, spatial covariance matrix, opacity, and spherical harmonic function color coefficients;

[0021] Step S3.2: Add a BeiDou confidence weight factor to each three-dimensional Gaussian element. The BeiDou confidence weight factor is an exponential function with the natural constant e as the base, multiplied by the trace of the product of the inverse of the BeiDou covariance matrix and the preset reference covariance matrix at the associated time, which is half of the original value.

[0022] Furthermore, step S4 specifically includes the following steps:

[0023] Step S4.1: Calculate the pixel-level L2 error between the rendered image and the actual captured image as the photometric consistency loss;

[0024] Step S4.2: Construct the BeiDou position constraint loss, which is equal to the sum of the BeiDou confidence weight factor corresponding to each frame image multiplied by the sum of the squared Mahalanobis distance between the difference between the camera translation vector to be optimized and the BeiDou measurement position in that frame and the inverse BeiDou covariance matrix.

[0025] Step S4.3: Calculate the structural similarity loss between the rendered image and the real image, as well as the norm regularization loss for the 3D Gaussian element opacity gradient and spatial covariance matrix;

[0026] Step S4.4: Multiply the photometric consistency loss, BeiDou position constraint loss, structural similarity loss and regularization loss by preset weight hyperparameters and sum them to form a composite loss function. Then, update the three-dimensional Gaussian meta-parameters and camera pose through iterative optimization.

[0027] Furthermore, step S5 specifically includes the following steps:

[0028] Step S5.1: For any three-dimensional Gaussian primitive, if the projection gradient norm of the three-dimensional Gaussian primitive on the image plane is greater than the preset gradient threshold, and the BeiDou confidence weight factor of the three-dimensional Gaussian primitive is greater than the preset confidence threshold, then a splitting operation is performed on the three-dimensional Gaussian primitive to increase the local primitive density.

[0029] Step S5.2: For any three-dimensional Gaussian element, calculate the Euclidean distance between the spatial mean of the three-dimensional Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, then the three-dimensional Gaussian element is determined to be abnormal and is pruned and deleted. The preset multiple ranges from 2 to 3.

[0030] A 3D modeling system based on the fusion of BeiDou positioning and Gaussian splashing, used to implement any of the 3D modeling methods based on the fusion of BeiDou positioning and Gaussian splashing, including:

[0031] The BeiDou differential positioning and spatial reference module is used to acquire the centimeter-level three-dimensional absolute position of the acquisition platform in real time, calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system.

[0032] The synchronous acquisition and joint initialization module is used to synchronously acquire image sequences and BeiDou positioning data of outdoor scenes in hardware, and perform weighted joint optimization of visual feature matching and BeiDou absolute position constraints;

[0033] The 3D Gaussian element generation and confidence embedding module is used to generate a set of 3D Gaussian elements based on the initial camera extrinsic parameters and embed confidence weight factors dynamically calculated by the BeiDou covariance matrix.

[0034] The BeiDou Enhancement Joint Optimization Module is used to construct a composite loss function that includes photometric loss, BeiDou position constraint loss, structural similarity loss, and regularization term, and to perform joint optimization.

[0035] The adaptive density control module is used to perform 3D Gaussian pixel splitting based on the 3D Gaussian pixel projection gradient and the BeiDou confidence weight, and to perform 3D Gaussian pixel pruning based on the statistical consistency between the 3D Gaussian pixel position and the BeiDou measurement trajectory.

[0036] The model output module is used to output a 3D Gaussian scene model with absolute geographic coordinates.

[0037] Furthermore, the BeiDou differential positioning and space reference module includes:

[0038] The multi-frequency carrier phase double-difference calculation submodule is used to calculate the longitude, latitude and geodetic height of the acquisition platform in the WGS-84 coordinate system in real time by utilizing the double-difference observation of the B1I, B2a and B3I multi-frequency signals of the Beidou-3 system.

[0039] The positioning covariance matrix estimation submodule is used to construct a design matrix based on the visible satellite geometry, construct an observation weight matrix based on the satellite elevation angle and signal-to-noise ratio, calculate the inverse matrix of the normal equation, and multiply it with the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix.

[0040] The station-center coordinate transformation submodule is used to convert WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then transform them to the station-center coordinate system using a rotation matrix with the selected reference origin as the reference, to obtain the east, north and celestial coordinates.

[0041] Furthermore, the BeiDou enhancement joint optimization module includes:

[0042] The photometric loss calculation submodule is used to calculate the pixel-level L2 error between the rendered image and the actual captured image;

[0043] The BeiDou position constraint loss calculation submodule is used to multiply the BeiDou confidence weight factor corresponding to each frame image by the squared Mahalanobis distance weighted by the difference between the translation vector of the camera to be optimized and the BeiDou measurement position in that frame, and then accumulate the result.

[0044] The structural similarity loss calculation submodule is used to calculate the structural similarity loss between the rendered image and the real image;

[0045] The regularization loss calculation submodule is used to calculate the truncation loss for the 3D Gaussian element opacity gradient and the Frobenius norm regularization loss for the spatial covariance matrix.

[0046] The composite loss weighted summation submodule is used to multiply the four losses by preset weight hyperparameters and then sum them to form a composite loss function.

[0047] Furthermore, the adaptive density control module includes:

[0048] The 3D Gaussian element splitting judgment submodule is used to determine whether any 3D Gaussian element simultaneously satisfies the following conditions: the image plane projection gradient norm is greater than a preset gradient threshold and the BeiDou confidence weight factor is greater than a preset confidence threshold. If both conditions are met, a splitting operation is performed on the 3D Gaussian element.

[0049] The 3D Gaussian element pruning judgment submodule is used to calculate the Euclidean distance between the spatial position mean of any 3D Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, the 3D Gaussian element is judged to be abnormal and is pruned and deleted.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] 1. This invention couples the entire process of BeiDou centimeter-level differential positioning from initialization to joint optimization with three-dimensional Gaussian splashing. The final model can directly obtain the absolute coordinates in the WGS-84 coordinate system without the need for post-processing spatial registration.

[0052] 2. This invention utilizes the BeiDou positioning covariance matrix to construct an information matrix and confidence weights, enabling the optimization process to automatically adjust the spatial constraint strength according to the measured positioning accuracy of each frame, automatically weakening low-precision frames, and effectively suppressing the propagation of positioning errors to the reconstruction model.

[0053] 3. The BeiDou absolute position constraint of this invention provides a stable, texture-independent global prior for visual optimization, which significantly reduces reconstruction drift and holes in weak texture areas and improves the integrity and geometric consistency of the model.

[0054] 4. Based on the dual splitting conditions of projection gradient and BeiDou confidence, this invention increases the primitive density in areas with reliable positioning and complex textures; based on the pruning condition of consistency between primitive position and BeiDou trajectory statistics, it automatically deletes erroneous primitives caused by visual errors, making the model more compact and realistic. Attached Figure Description

[0055] Other features, objects, and advantages of the invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings:

[0056] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0057] Figure 2 This is a schematic diagram of a system according to an embodiment of the present invention. Detailed Implementation

[0058] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] like Figure 1 As shown, the 3D modeling method based on the fusion of BeiDou positioning and Gaussian splashing includes the following steps:

[0060] Step S1: Obtain the three-dimensional absolute position of the acquisition platform in real time through BeiDou differential positioning, simultaneously calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system to construct a spatial absolute reference.

[0061] Step S2: Use the hardware synchronous acquisition system to acquire the image sequence of the outdoor scene, the corresponding BeiDou positioning data and inertial measurement data, and perform weighted joint optimization based on visual feature matching and BeiDou absolute position constraints to solve the initial camera extrinsic parameters of each frame of image;

[0062] Step S3: Generate a set of three-dimensional Gaussian elements based on the initial camera extrinsic parameters and the image. Each three-dimensional Gaussian element specifically includes the spatial mean, covariance matrix, opacity, color, and confidence weight factor dynamically calculated from the BeiDou covariance matrix.

[0063] Step S4: Construct a composite loss function that includes photometric consistency loss, BeiDou position constraint loss weighted by the inverse BeiDou covariance matrix, structural similarity loss, and 3D Gaussian meta-parameter regularization loss, and perform joint iterative optimization of the 3D Gaussian meta-parameters and camera pose;

[0064] Step S5: During the optimization process, 3D Gaussian element splitting is performed based on the dual conditions of the 3D Gaussian element projection gradient and the BeiDou confidence weight, and 3D Gaussian element pruning is performed based on the statistical consistency condition between the 3D Gaussian element position and the BeiDou trajectory point to achieve adaptive density control.

[0065] Step S6: Optimize and output a 3D Gaussian scene model with absolute geographic coordinates.

[0066] Step S1 specifically includes the following steps:

[0067] Step S1.1: Through the B1I, B2a, and B3I multi-frequency carrier phase double-difference observations of the BeiDou-3 system, the geodetic coordinates of the acquisition platform in the WGS-84 coordinate system are calculated in real time.

[0068] Step S1.2: Construct the design matrix and observation weight matrix based on the visible satellite geometry, calculate the inverse matrix of the normal equation, and multiply it by the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix.

[0069] Step S1.3: Convert the WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then, using the selected reference origin as the reference, transform it to the station center coordinate system through a rotation matrix to obtain the east, north, and celestial coordinates.

[0070] The carrier phase double-difference observation equations for satellite k from rover r and base station b are as follows:

[0071]

[0072] in, This represents the double-difference observations of the carrier phase of satellite k between rover r and base station b. This represents the double difference in geometric distance between the rover and the base station relative to satellite k. This indicates the carrier signal wavelength of the selected BeiDou frequency point. Indicates double-difference integer ambiguity. Represents the speed of light in a vacuum. This indicates the clock bias of a double-difference receiver. Indicates the double difference of ionospheric delay. This represents the double difference of tropospheric delay. Indicates carrier phase observation noise;

[0073] By performing real-time calculations, the geodetic coordinates of the rover under the WGS-84 reference ellipsoid, namely longitude, latitude, and geodetic height, are obtained;

[0074] The uncertainty of the positioning result is represented as a three-dimensional covariance matrix, and the calculation formula is as follows:

[0075]

[0076] in, This represents the three-dimensional position covariance matrix of BeiDou positioning at time t, with a size of 3×3. The unit weight variance factor reflects the overall accuracy level of the observed data. This represents the design matrix, describing the linear relationship between position parameters and double-difference observations. It has m rows corresponding to the number of visible satellites and 3 columns. This represents the observation weight matrix, a diagonal matrix of size m×m. Each diagonal element is determined based on the sine of the elevation angle and the signal-to-noise ratio (SNR) of the corresponding satellite. The higher the elevation angle and the greater the SNR, the larger the weight. This represents the actual transmission delay from the generation of the differential correction at the base station to its reception at the rover. This represents the reference delay time constant, typically taken as 1 second. It represents the time constant characteristic of delay attenuation, calibrated according to the characteristics of the communication link;

[0077] It can be seen that the number of satellites m is determined by the number of BeiDou satellites that are actually locked by the receiver at the current epoch and whose carrier-to-noise ratio exceeds the locking threshold. For each satellite whose elevation angle is higher than the cutoff elevation angle, its elevation angle value and signal-to-noise ratio in dB are substituted into the preset weighting function to calculate the corresponding diagonal weight of the satellite. The diagonal weight is equal to the square of the sine of the elevation angle of the satellite multiplied by the square of the ratio of the signal-to-noise ratio in dB to the reference signal-to-noise ratio. Satellites that fail the cutoff elevation angle or carrier-to-noise ratio test are not included in the solution, and their corresponding weight in the weight matrix is ​​zero.

[0078] The delay attenuation characteristic time constant was determined through statistical analysis after conducting multiple delay measurement experiments under actual communication link conditions. In the outdoor target scenario, the same base station and rover equipment as those used in the engineering implementation, as well as the same communication link type, were used to continuously collect the transmission delay data of the differential correction. The delay value was calculated from the time difference between the time the base station generated the correction and the time the rover successfully received and decoded it. The collection lasted for at least 1 hour, covering different communication load periods. Then, with 1 second as the delay reference time constant, all measured transmission delays were sorted from smallest to largest, and the delay value corresponding to the 95th quantile was taken as the delay attenuation characteristic time constant. After calibration, this constant remained unchanged in all subsequent calculations and was only recalibrated when the communication link type or equipment was changed.

[0079] The aforementioned covariance matrix is ​​dynamically updated based on the satellite geometric distribution, observation signal-to-noise ratio, and differential correction, providing adaptive weights for subsequent optimization.

[0080] First, convert the three-dimensional geodetic coordinates to Earth-centered, Earth-fixed, ECEF rectangular coordinates:

[0081]

[0082] in, Indicates longitude. Indicates latitude, This represents the geodetic height, which is the distance along the ellipsoidal normal to the WGS-84 reference ellipsoid. This represents the semi-major axis of the WGS-84 ellipsoid. This represents the square of the first eccentricity of the WGS-84 reference ellipsoid. Indicates the radius of curvature of the zonal loop. Represents ECEF rectangular coordinates;

[0083] Select a reference origin located within or near the target scene area for reconstruction. The reference origin is typically chosen as the approximate geometric center of the target scene area, or a prominent ground marker within the scene that is easy to preserve long-term. It can be assumed that the geodetic height of the reference origin is 0 or the average geodetic height of the region. The geodetic height only affects the overall translation of the station center coordinate components and does not affect the east and north components or the shape of the subsequent 3D reconstruction. Using a rotation matrix, transform the ECEF coordinate difference between any target point and the reference origin to the station center coordinate system ENU with the reference origin as the origin, obtaining the east, north, and celestial coordinates. The specific formula is as follows:

[0084]

[0085] in, This represents the eastward coordinates in the ENU coordinate system. This represents the north coordinates in the ENU coordinate system. This represents the celestial coordinates in the ENU coordinate system. and This indicates the geodetic longitude and geodetic latitude of the reference origin. The ECEF coordinates represent the reference origin;

[0086] The BeiDou positioning results were unified into a station-centered coordinate system with an absolute geographic reference, which is consistent with the visual local coordinate system reconstructed by 3D Gaussian splashing.

[0087] In step S2, the hardware synchronous acquisition system is implemented through a hardware triggering mechanism to ensure that the synchronization error between the image and the BeiDou positioning timestamp is less than 1 millisecond; the weighted joint optimization adopts an objective function that fuses the visual reprojection error robust kernel function and the BeiDou position Mahalanobis distance constraint, wherein the weight matrix of the Mahalanobis distance is taken as the inverse matrix of the BeiDou covariance matrix.

[0088] An acquisition platform integrating a high-resolution RGB camera, a BeiDou positioning antenna, and an inertial measurement unit (IMU) is used to synchronously acquire image sequences and BeiDou positioning data of an outdoor target scene through a hardware-triggered synchronization mechanism. The trigger signal simultaneously controls the camera's exposure time and the BeiDou receiver's observation epoch marker, ensuring that the timestamp of each image frame is strictly aligned with the timestamp of the BeiDou positioning data, with a synchronization error of less than 1 millisecond. After acquisition, an image sequence is obtained, where each image frame corresponds to a BeiDou positioning position in the station-centered coordinate system obtained in step S1, its positioning covariance matrix, and attitude prior information provided by the IMU.

[0089] Visual feature points, including SIFT and SuperPoint, are extracted from the acquired image sequences and cross-frame matching is performed to obtain the correspondence between two-dimensional feature points across multiple frames. The BeiDou absolute position obtained in step S1 is used as a spatial constraint to construct a weighted joint optimization objective function, and the camera rotation matrix and translation vector of the j-th frame image are solved. The specific formula is as follows:

[0090]

[0091] in, Let the camera rotation matrix of the j-th frame be represented. Let j represent the camera translation vector of the j-th frame. Indicates the index number of the visual feature point. This represents the two-dimensional pixel coordinates of the k-th visual feature point in its image frame. This represents the coordinates of the three-dimensional spatial point corresponding to the k-th feature point in the station-centered coordinate system. The camera projection function, determined by a pre-calibrated camera intrinsic parameter matrix, maps points in three-dimensional space onto a two-dimensional image plane. This represents the robust kernel function Huber, used to suppress the excessive influence of mismatched feature points on the optimization objective. The input unit is the square of the pixel error. This represents the BeiDou constraint balance factor, used to adjust the relative weights between the visual reprojection error term and the BeiDou position constraint term. This indicates the camera antenna position in the station-centered coordinate system corresponding to the j-th frame image, calculated by BeiDou RTK and transformed in step S1. This represents the information matrix of the BeiDou positioning in the j-th frame, which is the inverse matrix of the positioning covariance matrix of that frame.

[0092] The BeiDou constraint balance factor is used to adjust the relative importance of the visual reprojection error term and the BeiDou position constraint term. The value is determined based on the average number of visual feature points and the nominal accuracy of BeiDou positioning. When visual feature points are abundant, such as an average of more than 500 matching feature points per frame and BeiDou positioning accuracy at the centimeter level, it is set to 1.0 to give the two terms similar weights in optimization. If visual feature points are scarce in weak texture areas, such as less than 100 matching feature points per frame, the factor can be adjusted to 1.5 to 2.0 to appropriately enhance the weight of BeiDou constraints and compensate for the lack of visual information.

[0093] The weighted joint optimization objective function simultaneously minimizes the visual reprojection error and the Mahalanobis distance between the camera position and the BeiDou positioning. It utilizes the inverse matrix of the positioning covariance as the weight of the spatial constraints, so that frames with high positioning accuracy, i.e., larger element values ​​of the inverse matrix of the covariance matrix, provide stronger geometric constraints, while frames with low positioning accuracy automatically weaken the constraint contribution. After optimization, an initial camera pose sequence with an absolute geographic reference is obtained.

[0094] Step S3 specifically includes the following steps:

[0095] Step S3.1: Based on the initial camera extrinsic parameters and images, generate a three-dimensional Gaussian unit described by the spatial location mean, spatial covariance matrix, opacity, and spherical harmonic function color coefficients;

[0096] Step S3.2: Add a BeiDou confidence weight factor to each three-dimensional Gaussian element. The BeiDou confidence weight factor is an exponential function with the natural constant e as the base, multiplied by the trace of the product of the inverse of the BeiDou covariance matrix and the preset reference covariance matrix at the associated time, which is half of the original value.

[0097] Using the initial camera pose and corresponding multi-view images obtained in step S2, sparse point clouds are generated as initialization seeds through methods such as motion reconstruction structures, a set of three-dimensional Gaussian primitives is generated, and each three-dimensional Gaussian primitive is extended and parameterized.

[0098] The standard parameterization of 3D Gaussian primitives includes: a spatial position mean, used to describe the center position of the ellipsoid; a spatial covariance matrix, used to describe the shape, size, and orientation of the ellipsoid; opacity, used to control the visibility weight of the primitives during rendering; and color expressed using spherical harmonic coefficients, used to achieve view-dependent color effects. Based on this, this invention embeds a BeiDou confidence weight factor into each 3D Gaussian primitive, forming an extended 3D Gaussian primitive parameterization, the specific formula of which is:

[0099]

[0100] in, Indicates the index number of a three-dimensional Gaussian unit. This represents the mean vector of the spatial location of the i-th three-dimensional Gaussian element. Let i represent the spatial covariance matrix of the i-th three-dimensional Gaussian element. This represents the opacity of the i-th 3D Gaussian element. Let represent the spherical harmonic coefficient vector of the i-th 3D Gaussian element, used to express view-dependent color. This represents the BeiDou confidence weight factor for the i-th 3D Gaussian element. Let represent the parameter set of the i-th three-dimensional Gaussian element;

[0101] The BeiDou confidence weighting factor is dynamically calculated from the BeiDou positioning covariance matrix at the acquisition time associated with the three-dimensional Gaussian elements. The specific formula is as follows:

[0102]

[0103] in, This represents the index of the BeiDou positioning data acquisition time associated with the i-th 3D Gaussian element. Indicates the time of data collection The BeiDou positioning three-dimensional position covariance matrix, size 3×3. This represents the preset reference covariance matrix, which is usually taken as a diagonal matrix composed of the squared values ​​of the system's nominal design accuracy. The trace operation represents the sum of the elements on the main diagonal of a matrix, which characterizes the total variance of the location.

[0104] The preset reference covariance matrix is ​​a diagonal matrix composed of the squared values ​​of the nominal design accuracy of the system. For the Beidou equipment used in this embodiment, its nominal dynamic positioning accuracy in an open environment is 0.008 m + 1 ppm in the horizontal direction and 0.015 m + 1 ppm in the vertical direction. Taking typical values, the horizontal accuracy can be regarded as 0.02 m and the vertical accuracy as 0.03 m. Therefore, the preset reference covariance matrix is ​​determined to be a 3×3 diagonal matrix, and the three elements of its main diagonal are the squared values ​​of the horizontal accuracy, the horizontal accuracy, and the vertical accuracy, respectively, i.e. (0.02², 0.02², 0.03²).

[0105] The weighting factor approaches 1 when the BeiDou positioning conditions are ideal; when the positioning uncertainty increases, such as due to satellite signal blockage, multipath effect and other reasons that cause the trace value to increase, it decays exponentially and approaches 0.

[0106] Step S4 specifically includes the following steps:

[0107] Step S4.1: Calculate the pixel-level L2 error between the rendered image and the actual captured image as the photometric consistency loss;

[0108] Step S4.2: Construct the BeiDou position constraint loss, which is equal to the sum of the BeiDou confidence weight factor corresponding to each frame image multiplied by the sum of the squared Mahalanobis distance between the difference between the camera translation vector to be optimized and the BeiDou measurement position in that frame and the inverse BeiDou covariance matrix.

[0109] Step S4.3: Calculate the structural similarity loss between the rendered image and the real image, as well as the norm regularization loss for the 3D Gaussian element opacity gradient and spatial covariance matrix;

[0110] Step S4.4: Multiply the photometric consistency loss, BeiDou position constraint loss, structural similarity loss and regularization loss by preset weight hyperparameters and sum them to form a composite loss function. Then, update the three-dimensional Gaussian meta-parameters and camera pose through iterative optimization.

[0111] A composite loss function is constructed that integrates photometric consistency constraints, BeiDou positioning constraints, structural similarity constraints, and 3D Gaussian element parameter regularization constraints. Gradient descent is then used to jointly optimize all parameters of the 3D Gaussian elements and the camera pose. The formula for the composite loss function is as follows:

[0112]

[0113] in, Represents the composite loss function. This represents the photometric consistency loss term, used to measure the pixel-level difference between the rendered image and the real image. This represents the BeiDou position constraint loss term, which uses BeiDou positioning information to constrain the absolute spatial position of the camera translation vector. This represents the structural similarity loss term, used to measure the structurally similar consistency between the rendered image and the real image. This represents the regularization loss term, used to impose smoothing constraints on the opacity gradient and covariance matrix of the 3D Gaussian elements. , and These represent the preset weight hyperparameters for each loss;

[0114] in, The corresponding BeiDou position constraint loss is set to 0.1. The corresponding structural similarity loss is set to 0.2. The corresponding regularization loss is set to 0.01. The first weight hyperparameter of the BeiDou position constraint loss is set to 0.1 because the BeiDou position constraint, as a spatial regularization term, should have a lower effect than the data-driven term. This preserves the ability of visual optimization to fit local details while providing sufficient global geometric constraints. The weight hyperparameter of the structural similarity loss is set to 0.2 because the structural similarity index measures structural information on an image patch basis, complementing the pixel-by-pixel photometric loss. A smaller weight helps improve visual structure without introducing additional blur. The third weight hyperparameter of the regularization loss is set to 0.01, used only to suppress anomalous Gaussian cell deformation. An excessively large weight would limit the ability to express scene details. In practical implementation, if the BeiDou positioning conditions are poor, the first weight hyperparameter can be reduced to 0.03 to 0.05 to further weaken the BeiDou constraint. If the scene texture is very rich, the second weight hyperparameter can be appropriately reduced to 0.1 or the third weight hyperparameter increased to 0.02 to encourage richer detail expression.

[0115] The specific formula for photometric uniformity loss is as follows:

[0116]

[0117] in, This represents the set of valid pixels in the training image, excluding sky or invalid regions not covered by the scene. This indicates the number of elements in the set of valid pixels. Represents the pixel coordinates in the image. Indicated in pixels The three-channel RGB color vector is obtained through differentiable alpha blending rendering, with each channel taking values ​​in the range [0,1]. Indicated in pixels The RGB color truth vector is read from the actual captured image, with a value range of [0,1].

[0118] The formula for the rendered three-channel RGB color vector is:

[0119]

[0120] in, This represents the total number of three-dimensional Gaussian elements intersecting with the ray. This represents the cumulative transmittance before the light reaches the i-th element. This indicates that after the i-th 3D Gaussian primitive is projected onto the image plane, at the pixel level... The two-dimensional Gaussian kernel response value at the location;

[0121] The specific formula for BeiDou position constraint loss is as follows:

[0122]

[0123] in, Indicates the image frame index that participated in the optimization. This represents the total number of image frames participating in the joint optimization. The weight factor representing the BeiDou confidence level for the j-th frame image is calculated from the BeiDou covariance matrix at the acquisition time of that frame using the formula in step S3. This represents the camera translation vector for the j-th frame to be optimized, i.e., the spatial position of the camera's optical center. This represents the camera position in frame j after coordinate transformation, measured by BeiDou RTK. This represents the information matrix of the BeiDou positioning in the j-th frame, which is the inverse matrix of the positioning covariance matrix of that frame.

[0124] The specific formula for the structural similarity loss term is:

[0125]

[0126] in, The structural similarity index function is represented. This represents a three-channel RGB color vector obtained through differentiable alpha blending rendering. This represents the RGB color truth vector read from the actual captured image;

[0127] The specific formula for the regularization loss term is:

[0128]

[0129] in, This represents the total number of 3D Gaussian elements in the scene. This represents the opacity of the i-th 3D Gaussian element at its spatial position. The gradient vector at that point, The L2 norm of the opacity gradient is represented by... This represents the cutoff threshold for the opacity gradient. Let i represent the spatial covariance matrix of the i-th three-dimensional Gaussian element. This represents the arithmetic mean matrix of the covariance matrices of all three-dimensional Gaussian element spaces. Let Frobenius norm be the square of the difference between the covariance matrix of the i-th primitive and the mean covariance matrix. Represents the weighting coefficients of the covariance regularization term;

[0130] The cutoff threshold for the opacity gradient is set to 0.05. Based on the statistical analysis of the typical opacity change rate of the 3D scene surface, in a normal reconstructed scene, the change in opacity from 0 to 1 usually occurs within a depth range of about 0.1 to 0.3 meters, and its gradient norm is generally between 0.05 and 1.0. Setting it to 0.05 allows for normal surface transitions in the scene, while effectively suppressing extremely sharp surfaces caused by discrete sampling errors or noise.

[0131] The weighting coefficient for the covariance regularization term is set to 1.0 × 10⁻⁶. - ³, determined by comparing the magnitudes of the covariance regularization term and the photometric loss term in the initial optimization stage. Typically, in the early stages of 3D Gaussian splash reconstruction, the covariance matrices of each primitive differ significantly, with the value of the covariance regularization term being approximately on the order of 10², while the photometric loss term is approximately 10. - ¹Order of magnitude: To keep the effect of the regularization term within a reasonable range, the weight coefficient needs to be set to approximately 10. - ³;

[0132] By minimizing the total loss through an iterative optimizer such as Adam, the parameters of the 3D Gaussian primitives and the camera pose are updated simultaneously in each iteration, ultimately obtaining a 3D scene representation that combines high visual fidelity and absolute geographic coordinate alignment.

[0133] Step S5 specifically includes the following steps:

[0134] Step S5.1: For any three-dimensional Gaussian primitive, if the projection gradient norm of the three-dimensional Gaussian primitive on the image plane is greater than the preset gradient threshold, and the BeiDou confidence weight factor of the three-dimensional Gaussian primitive is greater than the preset confidence threshold, then a splitting operation is performed on the three-dimensional Gaussian primitive to increase the local primitive density.

[0135] Step S5.2: For any three-dimensional Gaussian element, calculate the Euclidean distance between the spatial mean of the three-dimensional Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, then the three-dimensional Gaussian element is determined to be abnormal and is pruned and deleted. The preset multiple ranges from 2 to 3.

[0136] For any three-dimensional Gaussian primitive, if the following two conditions are met simultaneously, a splitting operation is performed on it to split it into multiple smaller, adjacent primitives along the direction of maximum variance, in order to increase the local spatial resolution.

[0137] Condition 1: The projection gradient norm of the 3D Gaussian primitive on the image plane is greater than the preset gradient threshold; Condition 2: The BeiDou confidence weight factor of the 3D Gaussian primitive is greater than the preset confidence threshold.

[0138] The preset gradient threshold is set to 0.0002. It is obtained by statistically analyzing the projection gradient norm of all primitives before the first round of density control during the 3D Gaussian splash reconstruction process. The 80th percentile of the projection gradient norm of all primitives is taken as the gradient threshold, so that about 20% of the primitives with the largest gradient may enter the splitting candidate.

[0139] The preset confidence threshold is set to 0.3, which is determined based on the decay characteristics of the BeiDou confidence weight factor. When the trace of the BeiDou covariance matrix is ​​about 2.4 times the trace of the reference covariance matrix, the weight factor is about 0.3.

[0140] For any 3D Gaussian primitive, calculate the Euclidean distance between its spatial mean and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance meets the condition, the 3D Gaussian primitive is determined to be a geometric drift product caused by visual error and is pruned and deleted. The specific formula is as follows:

[0141]

[0142] in, This represents the mean spatial location of the i-th three-dimensional Gaussian element. Indicates that in the spatial and temporal dimensions, it is related to The coordinates of the station center of the nearest BeiDou tracking point. Indicates and The corresponding BeiDou positioning covariance matrix, The trace of the covariance matrix is ​​the sum of the variances along the three coordinate axes. This represents the preset confidence level factor, which is dimensionless and typically ranges from 2 to 3, corresponding to statistical confidence intervals of 95% to 99%.

[0143] In the spatial dimension, all BeiDou measurement trajectory points are traversed, and the Euclidean distance between each trajectory point and the mean position of the current 3D Gaussian primitive to be pruned is calculated. In the temporal dimension, only BeiDou measurement trajectory points within a 5-second time window before and after the acquisition time associated with the current 3D Gaussian primitive are considered. Within this spatiotemporal window, the trajectory point with the smallest Euclidean distance is selected as the spatiotemporally nearest BeiDou measurement trajectory point. If there are no BeiDou measurement trajectory points within the window, the current pruning judgment for that primitive is skipped and it is retained until the next optimization cycle.

[0144] If the location of a 3D Gaussian primitive is outside the uncertainty range of the nearest reliable BeiDou measurement point, it is determined that the primitive is an erroneous reconstruction caused by insufficient visual information or mismatch, and should be removed. By utilizing the uncertainty range of BeiDou absolute position and quantization, geometrically erroneous primitives are automatically identified and deleted to ensure the spatial authenticity of the reconstructed model.

[0145] After optimization and convergence, a complete set of 3D geospatial elements with an absolute geographic reference, defined in the station-centered coordinate system, is obtained. This set can be directly used for real-time high-fidelity volume rendering of any specified camera viewpoint to generate a 2D image. Finally, the station-centered coordinates of each vertex of the model are reverse-engineered and transformed back to the WGS-84 geodetic coordinate system via the ECEF coordinate system to obtain the geodetic coordinates of each vertex, which are then output in a standard geospatial data format, such as a GeoTIFF elevation map.

[0146] A 3D modeling system based on the fusion of BeiDou positioning and Gaussian splashing, used to implement any of the 3D modeling methods based on the fusion of BeiDou positioning and Gaussian splashing, including:

[0147] The BeiDou differential positioning and spatial reference module is used to acquire the centimeter-level three-dimensional absolute position of the acquisition platform in real time, calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system.

[0148] The synchronous acquisition and joint initialization module is used to synchronously acquire image sequences and BeiDou positioning data of outdoor scenes in hardware, and perform weighted joint optimization of visual feature matching and BeiDou absolute position constraints;

[0149] The 3D Gaussian element generation and confidence embedding module is used to generate a set of 3D Gaussian elements based on the initial camera extrinsic parameters and embed confidence weight factors dynamically calculated by the BeiDou covariance matrix.

[0150] The BeiDou Enhancement Joint Optimization Module is used to construct a composite loss function that includes photometric loss, BeiDou position constraint loss, structural similarity loss, and regularization term, and to perform joint optimization.

[0151] The adaptive density control module is used to perform 3D Gaussian pixel splitting based on the 3D Gaussian pixel projection gradient and the BeiDou confidence weight, and to perform 3D Gaussian pixel pruning based on the statistical consistency between the 3D Gaussian pixel position and the BeiDou measurement trajectory.

[0152] The model output module is used to output a 3D Gaussian scene model with absolute geographic coordinates.

[0153] The BeiDou differential positioning and space reference module includes:

[0154] The multi-frequency carrier phase double-difference calculation submodule is used to calculate the longitude, latitude and geodetic height of the acquisition platform in the WGS-84 coordinate system in real time by utilizing the double-difference observation of the B1I, B2a and B3I multi-frequency signals of the Beidou-3 system.

[0155] The positioning covariance matrix estimation submodule is used to construct a design matrix based on the visible satellite geometry, construct an observation weight matrix based on the satellite elevation angle and signal-to-noise ratio, calculate the inverse matrix of the normal equation, and multiply it with the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix.

[0156] The station-center coordinate transformation submodule is used to convert WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then transform them to the station-center coordinate system using a rotation matrix with the selected reference origin as the reference, to obtain the east, north and celestial coordinates.

[0157] The BeiDou enhanced joint optimization module includes:

[0158] The photometric loss calculation submodule is used to calculate the pixel-level L2 error between the rendered image and the actual captured image;

[0159] The BeiDou position constraint loss calculation submodule is used to multiply the BeiDou confidence weight factor corresponding to each frame image by the squared Mahalanobis distance weighted by the difference between the translation vector of the camera to be optimized and the BeiDou measurement position in that frame, and then accumulate the result.

[0160] The structural similarity loss calculation submodule is used to calculate the structural similarity loss between the rendered image and the real image;

[0161] The regularization loss calculation submodule is used to calculate the truncation loss for the 3D Gaussian element opacity gradient and the Frobenius norm regularization loss for the spatial covariance matrix.

[0162] The composite loss weighted summation submodule is used to multiply the four losses by preset weight hyperparameters and then sum them to form a composite loss function.

[0163] The adaptive density control module includes:

[0164] The 3D Gaussian element splitting judgment submodule is used to determine whether any 3D Gaussian element simultaneously satisfies the following conditions: the image plane projection gradient norm is greater than a preset gradient threshold and the BeiDou confidence weight factor is greater than a preset confidence threshold. If both conditions are met, a splitting operation is performed on the 3D Gaussian element.

[0165] The 3D Gaussian element pruning judgment submodule is used to calculate the Euclidean distance between the spatial position mean of any 3D Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, the 3D Gaussian element is judged to be abnormal and is pruned and deleted.

[0166] Any combination of one or more computer-readable media may be used. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in connection with an instruction execution system, apparatus, or device.

[0167] The examples described herein are merely preferred embodiments of the invention and are not intended to limit the concept and scope of the invention. Any modifications and improvements made by those skilled in the art to the technical solutions of the invention without departing from the design concept of the invention should fall within the protection scope of the invention.

Claims

1. A 3D modeling method based on the fusion of BeiDou positioning and Gaussian splashing, characterized in that, Includes the following steps: Step S1: Obtain the three-dimensional absolute position of the acquisition platform in real time through BeiDou differential positioning, simultaneously calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system to construct a spatial absolute reference. Step S2: Use the hardware synchronous acquisition system to acquire the image sequence of the outdoor scene, the corresponding BeiDou positioning data and inertial measurement data, and perform weighted joint optimization based on visual feature matching and BeiDou absolute position constraints to solve the initial camera extrinsic parameters of each frame of image; Step S3: Generate a set of three-dimensional Gaussian elements based on the initial camera extrinsic parameters and the image. Each three-dimensional Gaussian element specifically includes the spatial mean, covariance matrix, opacity, color, and confidence weight factor dynamically calculated from the BeiDou covariance matrix. Step S4: Construct a composite loss function that includes photometric consistency loss, BeiDou position constraint loss weighted by the inverse BeiDou covariance matrix, structural similarity loss, and 3D Gaussian meta-parameter regularization loss, and perform joint iterative optimization of the 3D Gaussian meta-parameters and camera pose; Step S5: During the optimization process, 3D Gaussian element splitting is performed based on the dual conditions of the 3D Gaussian element projection gradient and the BeiDou confidence weight, and 3D Gaussian element pruning is performed based on the statistical consistency condition between the 3D Gaussian element position and the BeiDou trajectory point to achieve adaptive density control. Step S6: Optimize and output a 3D Gaussian scene model with absolute geographic coordinates.

2. The method according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S1.1: Through the B1I, B2a, and B3I multi-frequency carrier phase double-difference observations of the BeiDou-3 system, the geodetic coordinates of the acquisition platform in the WGS-84 coordinate system are calculated in real time. Step S1.2: Construct the design matrix and observation weight matrix based on the visible satellite geometry, calculate the inverse matrix of the normal equation, and multiply it by the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix. Step S1.3: Convert the WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then, using the selected reference origin as the reference, transform it to the station center coordinate system through a rotation matrix to obtain the east, north, and celestial coordinates.

3. The method according to claim 2, characterized in that, In step S2, the hardware synchronous acquisition system is implemented through a hardware triggering mechanism to ensure that the synchronization error between the image and the BeiDou positioning timestamp is less than 1 millisecond; the weighted joint optimization adopts an objective function that fuses the visual reprojection error robust kernel function and the BeiDou position Mahalanobis distance constraint, wherein the weight matrix of the Mahalanobis distance is taken as the inverse matrix of the BeiDou covariance matrix.

4. The method according to claim 3, characterized in that, Step S3 specifically includes the following steps: Step S3.1: Based on the initial camera extrinsic parameters and images, generate a three-dimensional Gaussian unit described by the spatial location mean, spatial covariance matrix, opacity, and spherical harmonic function color coefficients; Step S3.2: Add a BeiDou confidence weight factor to each three-dimensional Gaussian element. The BeiDou confidence weight factor is an exponential function with the natural constant e as the base, multiplied by the trace of the product of the inverse of the BeiDou covariance matrix and the preset reference covariance matrix at the associated time, which is half of the original value.

5. The method according to claim 4, characterized in that, Step S4 specifically includes the following steps: Step S4.1: Calculate the pixel-level L2 error between the rendered image and the actual captured image as the photometric consistency loss; Step S4.2: Construct the BeiDou position constraint loss, which is equal to the sum of the BeiDou confidence weight factor corresponding to each frame image multiplied by the sum of the squared Mahalanobis distance between the difference between the camera translation vector to be optimized and the BeiDou measurement position in that frame and the inverse BeiDou covariance matrix. Step S4.3: Calculate the structural similarity loss between the rendered image and the real image, as well as the norm regularization loss for the 3D Gaussian element opacity gradient and spatial covariance matrix; Step S4.4: Multiply the photometric consistency loss, BeiDou position constraint loss, structural similarity loss and regularization loss by preset weight hyperparameters and sum them to form a composite loss function. Then, update the three-dimensional Gaussian meta-parameters and camera pose through iterative optimization.

6. The method according to claim 5, characterized in that, Step S5 specifically includes the following steps: Step S5.1: For any three-dimensional Gaussian primitive, if the projection gradient norm of the three-dimensional Gaussian primitive on the image plane is greater than the preset gradient threshold, and the BeiDou confidence weight factor of the three-dimensional Gaussian primitive is greater than the preset confidence threshold, then a splitting operation is performed on the three-dimensional Gaussian primitive to increase the local primitive density. Step S5.2: For any three-dimensional Gaussian element, calculate the Euclidean distance between the spatial mean of the three-dimensional Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, then the three-dimensional Gaussian element is determined to be abnormal and is pruned and deleted. The preset multiple ranges from 2 to 3.

7. A 3D modeling system based on the fusion of BeiDou positioning and Gaussian splashing, used to implement the 3D modeling method based on the fusion of BeiDou positioning and Gaussian splashing as described in any one of claims 1-6, characterized in that, include: The BeiDou differential positioning and spatial reference module is used to acquire the centimeter-level three-dimensional absolute position of the acquisition platform in real time, calculate the covariance matrix reflecting the positioning uncertainty, and uniformly transform the geodetic coordinates to the station center coordinate system. The synchronous acquisition and joint initialization module is used to synchronously acquire image sequences and BeiDou positioning data of outdoor scenes in hardware, and perform weighted joint optimization of visual feature matching and BeiDou absolute position constraints. The 3D Gaussian element generation and confidence embedding module is used to generate a set of 3D Gaussian elements based on the initial camera extrinsic parameters and embed confidence weight factors dynamically calculated by the BeiDou covariance matrix. The BeiDou Enhancement Joint Optimization Module is used to construct a composite loss function that includes photometric loss, BeiDou position constraint loss, structural similarity loss, and regularization term, and to perform joint optimization. The adaptive density control module is used to perform 3D Gaussian pixel splitting based on the 3D Gaussian pixel projection gradient and the BeiDou confidence weight, and to perform 3D Gaussian pixel pruning based on the statistical consistency between the 3D Gaussian pixel position and the BeiDou measurement trajectory. The model output module is used to output a 3D Gaussian scene model with absolute geographic coordinates.

8. The system according to claim 7, characterized in that, The BeiDou differential positioning and space reference module includes: The multi-frequency carrier phase double-difference calculation submodule is used to calculate the longitude, latitude and geodetic height of the acquisition platform in the WGS-84 coordinate system in real time by utilizing the double-difference observation of the B1I, B2a and B3I multi-frequency signals of the Beidou-3 system. The positioning covariance matrix estimation submodule is used to construct a design matrix based on the visible satellite geometry, construct an observation weight matrix based on the satellite elevation angle and signal-to-noise ratio, calculate the inverse matrix of the normal equation, and multiply it with the unit weight variance factor and the exponential decay factor with the differential correction transmission delay as the independent variable to obtain the dynamic three-dimensional position covariance matrix. The station-center coordinate transformation submodule is used to convert WGS-84 geodetic coordinates to geocentric rectangular coordinates, and then transform them to the station-center coordinate system using a rotation matrix with the selected reference origin as the reference, to obtain the east, north and celestial coordinates.

9. The system according to claim 8, characterized in that, The BeiDou enhanced joint optimization module includes: The photometric loss calculation submodule is used to calculate the pixel-level L2 error between the rendered image and the actual captured image; The BeiDou position constraint loss calculation submodule is used to multiply the BeiDou confidence weight factor corresponding to each frame image by the squared Mahalanobis distance weighted by the difference between the translation vector of the camera to be optimized and the BeiDou measurement position in that frame, and then accumulate the result. The structural similarity loss calculation submodule is used to calculate the structural similarity loss between the rendered image and the real image; The regularization loss calculation submodule is used to calculate the truncation loss for the 3D Gaussian element opacity gradient and the Frobenius norm regularization loss for the spatial covariance matrix. The composite loss weighted summation submodule is used to multiply the four losses by preset weight hyperparameters and then sum them to form a composite loss function.

10. The system according to claim 9, characterized in that, The adaptive density control module includes: The 3D Gaussian element splitting judgment submodule is used to determine whether any 3D Gaussian element simultaneously satisfies the following conditions: the image plane projection gradient norm is greater than a preset gradient threshold and the BeiDou confidence weight factor is greater than a preset confidence threshold. If both conditions are met, a splitting operation is performed on the 3D Gaussian element. The 3D Gaussian element pruning judgment submodule is used to calculate the Euclidean distance between the spatial position mean of any 3D Gaussian element and the nearest BeiDou measurement trajectory point in space and time. If the Euclidean distance is greater than a preset multiple multiplied by the square root of the trace of the covariance matrix of the BeiDou trajectory point corresponding to the nearest BeiDou measurement trajectory point in space and time, the 3D Gaussian element is judged to be abnormal and is pruned and deleted.

Images