A three-dimensional displacement high-precision monitoring method based on a Beidou carrier phase

Abstract

This invention discloses a high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase, belonging to the field of satellite positioning and surveying technology. It includes simultaneously acquiring multi-source datasets from a monitoring station and at least one reference station; real-time calculation of the error propagation control factor; dynamic filtering and weight pre-allocation of the raw BeiDou carrier phase observation data from the monitoring station; collaborative calculation based on the error propagation control factor to generate intermediate displacement estimates; using the error propagation control factor for spatiotemporal displacement prediction; filtering the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence; and feedback optimization of the error propagation control factor calculation process using auxiliary sensor data. By dynamically filtering, weighting, and collaboratively calculating the observation data through real-time calculation of the error propagation control factor, and performing feedback optimization based on the calculation results, it is possible to achieve proactive control and adaptive adjustment of monitoring errors, improving the accuracy and reliability of monitoring results.

Description

Technical Field

[0001] This invention relates to the field of satellite positioning and mapping technology, and in particular to a high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase. Background Technology

[0002] Carrier phase differential technology based on the BeiDou Navigation Satellite System is one of the core methods for achieving millimeter-level high-precision positioning and displacement monitoring. This technology synchronously observes satellite signals from both the monitoring station and the reference station, using differential processing to eliminate most common errors, thereby accurately retrieving the three-dimensional coordinate changes of the monitoring station relative to the reference station. Due to its advantages of all-weather operation, automation, and high precision, it has been widely used in the health monitoring and deformation early warning of large structures such as bridges, dams, slopes, and high-rise buildings.

[0003] In existing technologies, high-precision three-dimensional displacement monitoring methods based on BeiDou carrier phase typically employ a relative positioning model. This method first performs double-difference processing on the raw observation data from the monitoring station and the reference station to eliminate satellite clock errors, receiver clock errors, and most orbital and atmospheric delay errors. Subsequently, a stochastic model is established based on parameters such as satellite elevation angle and signal-to-noise ratio to weight the observation values. Finally, the double-difference observation equations are solved using algorithms such as Kalman filtering or least squares to obtain the displacement time series between epochs.

[0004] However, existing technical solutions have some inherent technical shortcomings in practical applications. On the one hand, their weighting methods for observations are relatively simplistic, relying mainly on general indicators such as signal-to-noise ratio and elevation angle. They fail to fully consider the varying impacts of satellite geometry on the error propagation of different coordinate components at specific times, and are also ill-suited to effectively address non-model-based errors such as multipath effects in complex environments. On the other hand, the entire data processing flow is typically open-loop, meaning the establishment of the error model and the data processing are unidirectional. There is a lack of mechanisms to use the quality of the final solution to correct and optimize the front-end error model, resulting in poor adaptability to dynamically changing observation environments and difficulty in ensuring the accuracy and reliability of long-term monitoring. Summary of the Invention

[0005] To address the aforementioned issues, this invention provides a high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase. By dynamically filtering, weighting, and collaboratively solving the observation data through real-time calculation of the error propagation control factor, and performing feedback optimization based on the solution results, it is possible to achieve proactive control and adaptive adjustment of monitoring errors, thereby improving the accuracy and reliability of monitoring results.

[0006] The above objectives can be achieved through the following approach:

[0007] A high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase includes: simultaneously acquiring raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data from a monitoring station and at least one reference station to obtain a multi-source dataset; calculating an error propagation control factor reflecting the sensitivity to error propagation under current observation conditions in real time based on the multi-source dataset; dynamically filtering and pre-allocating weights on the raw BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate an optimal observation set; performing collaborative calculation on the optimal observation set according to the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor; performing spatiotemporal displacement prediction using the error propagation control factor and filtering the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence; generating an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and performing feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

[0008] Optionally, the step of synchronously acquiring the original BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data of the monitoring station and at least one reference station to obtain a multi-source dataset includes: synchronously acquiring the original BeiDou carrier phase observation data of the monitoring station and the original BeiDou carrier phase observation data of at least one reference station to obtain an original observation dataset; acquiring satellite ephemeris data and performing time synchronization processing on the original observation dataset to generate time-synchronized observation data; acquiring auxiliary sensor data of the monitoring station and fusing the time-synchronized observation data with the auxiliary sensor data to generate a multi-source dataset.

[0009] Optionally, the step of calculating the error propagation control factor reflecting the error propagation sensitivity under the current observation conditions in real time based on the multi-source dataset includes: extracting satellite geometric configuration parameters and signal propagation environment parameters under the current observation conditions based on the multi-source dataset; calculating the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters; and performing eigenvalue decomposition on the error propagation sensitivity matrix to generate the error propagation control factor.

[0010] Optionally, calculating the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters includes: constructing a geometric accuracy factor matrix based on the satellite geometric configuration parameters; constructing a multipath error influence matrix and an observation noise influence matrix based on the signal propagation environment parameters; and fusing the geometric accuracy factor matrix, the multipath error influence matrix, and the observation noise influence matrix to generate the error propagation sensitivity matrix.

[0011] Optionally, the step of dynamically filtering and pre-allocating weights on the raw BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate an optimal observation set includes: using the error propagation control factor to calculate the confidence index of each observation value in the raw BeiDou carrier phase observation data of the monitoring station; dynamically filtering the raw BeiDou carrier phase observation data of the monitoring station based on the confidence index to obtain a preliminary filtered observation set; and pre-allocating weights on the observation values ​​in the preliminary filtered observation set according to the error propagation control factor to generate an optimal observation set.

[0012] Optionally, the step of performing collaborative calculation on the preferred observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor includes: performing collaborative calculation on the preferred observation set based on the error propagation control factor to obtain a preliminary displacement estimate; and using the error propagation control factor to enhance and correct the preliminary displacement estimate to generate an intermediate displacement estimate.

[0013] Optionally, the step of using the error propagation control factor to perform spatiotemporal displacement prediction and filtering the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence includes: using the error propagation control factor to establish a spatiotemporal displacement prediction model and predicting the intermediate displacement estimate sequence to obtain a displacement prediction value; and based on the displacement prediction value and the corresponding confidence index, filtering the intermediate displacement estimate to output a reliable three-dimensional displacement sequence.

[0014] Optionally, the step of generating an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and performing feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index, includes: calculating a displacement estimation residual sequence based on the reliable three-dimensional displacement sequence; performing statistical analysis on the displacement estimation residual sequence in conjunction with the auxiliary sensor data to generate an accuracy convergence discrimination index; and performing feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

[0015] Optionally, the step of combining the auxiliary sensor data to perform statistical analysis on the displacement estimation residual sequence and generating an accuracy convergence discrimination index includes: performing a normality test on the displacement estimation residual sequence to generate residual distribution characteristic parameters; comparing the consistency between the auxiliary sensor data and the reliable three-dimensional displacement sequence to generate a sensor consistency index; and fusing the residual distribution characteristic parameters and the sensor consistency index to generate an accuracy convergence discrimination index.

[0016] Based on the same inventive concept, this invention also provides a high-precision three-dimensional displacement monitoring system based on BeiDou carrier phase. The system includes: a multi-source data acquisition module, used to simultaneously acquire raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data from the monitoring station and at least one reference station to obtain a multi-source dataset; an error propagation control factor calculation module, used to calculate, in real time, an error propagation control factor reflecting the sensitivity to error propagation under current observation conditions based on the multi-source dataset; and a preferred observation set generation module, used to dynamically filter and weight the raw BeiDou carrier phase observation data from the monitoring station using the error propagation control factor. The system performs a re-allocation to generate an optimal observation set; a displacement intermediate estimate generation module is used to perform collaborative calculation on the optimal observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor; a displacement sequence output module is used to perform spatiotemporal displacement prediction using the error propagation control factor and filter the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence; a feedback optimization module is used to generate an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and to perform feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

[0017] Compared with the prior art, the present invention has the following advantages:

[0018] This invention enhances the robustness of the monitoring system by performing pre-emptive quantitative assessment and proactive intervention on the observation data. By calculating the error propagation control factor in real time, this method can accurately identify satellite signals that negatively affect the solution accuracy before the solution is calculated, and filter or reduce their weight, thereby avoiding the degradation of the solution results caused by poor satellite geometry or harsh signal propagation environment, and ensuring the stable operation of the monitoring system under complex observation conditions.

[0019] This invention improves the accuracy and reliability of displacement monitoring through targeted optimization of the solution process and results. The method not only utilizes an error propagation control factor for collaborative calculation during the solution process but also strengthens the correction of the generated initial displacement, directly suppressing uncertainties in the most error-sensitive direction. Combined with spatiotemporal prediction filtering, random errors are further smoothed, resulting in a more continuous and accurate three-dimensional displacement sequence in the final output.

[0020] This invention achieves adaptive adjustment of the monitoring system error model by constructing a closed-loop feedback optimization mechanism. The method uses the final output reliable displacement sequence and auxiliary sensor data to back-evaluate the quality of the solution process, and optimizes the calculation process of the error propagation control factor based on the evaluation results. This adaptive capability enables the system to continuously learn and adapt to changing observation environments, ensuring accuracy convergence and long-term reliability of results during long-term monitoring. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating the high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase according to an embodiment of the present invention.

[0022] Figure 2 This is a schematic diagram of the structure of a high-precision three-dimensional displacement monitoring system based on BeiDou carrier phase according to an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0024] Reference Figure 1 One embodiment of the present invention proposes a high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase. By dynamically filtering, weighting and co-solving the observation data through real-time calculation of error propagation control factors, and performing feedback optimization based on the solution results, it is possible to achieve active control and adaptive adjustment of monitoring errors, thereby improving the accuracy and reliability of monitoring results.

[0025] The method described in this embodiment specifically includes:

[0026] Simultaneously acquire raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data from the monitoring station and at least one reference station to obtain a multi-source dataset;

[0027] Based on the multi-source dataset, the error propagation control factor, which reflects the sensitivity to error propagation under the current observation conditions, is calculated in real time.

[0028] The error propagation control factor is used to dynamically filter and pre-allocate weights on the raw BeiDou carrier phase observation data of the monitoring station to generate an optimal observation set;

[0029] Based on the error propagation control factor, the preferred observation set is co-calculated to generate an intermediate displacement estimate enhanced by the error propagation control factor;

[0030] The error propagation control factor is used to predict the spatiotemporal displacement, and the intermediate displacement estimate sequence is filtered to output a reliable three-dimensional displacement sequence.

[0031] Based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, an accuracy convergence discrimination index is generated, and the calculation process of the error propagation control factor is optimized by feedback based on the accuracy convergence discrimination index.

[0032] Optionally, the step of synchronously acquiring the original BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data of the monitoring station and at least one reference station to obtain a multi-source dataset includes: synchronously acquiring the original BeiDou carrier phase observation data of the monitoring station and the original BeiDou carrier phase observation data of at least one reference station to obtain an original observation dataset; acquiring satellite ephemeris data and performing time synchronization processing on the original observation dataset to generate time-synchronized observation data; acquiring auxiliary sensor data of the monitoring station and fusing the time-synchronized observation data with the auxiliary sensor data to generate a multi-source dataset.

[0033] Specifically, the process begins with synchronized data acquisition, followed by time standardization, and finally, the fusion of heterogeneous data. The first step in this method aims to synchronously acquire raw observation data. The system uses Network Time Protocol (NTP) or a dedicated time server to send synchronized acquisition commands to the BeiDou receivers at monitoring stations deployed on the target and at least one reference station fixed in a stable area. The receivers, following a preset sampling frequency (typically between 1 Hz and 20 Hz), synchronously begin acquiring raw carrier phase observation data from the BeiDou satellite system. Simultaneously, a satellite altitude cutoff angle higher than 10 degrees is set to filter out satellite data from low altitudes and with poor signal quality. This raw BeiDou carrier phase observation data refers to the phase difference measurement of the carrier signal between the receiver antenna phase center and the satellite phase center, including integer counts and fractional parts less than a full cycle. It is the core observation for high-precision relative positioning. The acquired data is stored in the receiver-independent exchange format RINEX, forming a raw observation dataset containing multi-epoch observations.

[0034] The system acquires precise satellite ephemeris data covering the observation period from data centers such as the International GNSS Service Organization (IGS). Satellite ephemeris data is a data file describing the precise three-dimensional coordinates of a satellite in space at a specific point in time, along with satellite clock correction parameters; it is a necessary input for calculating the geometric distance between the satellite and the station. The processing module matches the acquired precise satellite ephemeris data with the original observation dataset, using either BeiDou Time (BDT) or Global Positioning System Time (GPST) as a unified time reference. Sub-millisecond time alignment correction is performed on each observation epoch in the original observation dataset to generate time-synchronized observation data. This step ensures that any observation value from any station has a unified and accurate time label, laying the foundation for subsequent inter-station differential calculations.

[0035] The system acquires data from auxiliary sensors installed at the monitoring station in parallel, such as physical quantities measured by inclinometers, accelerometers, or temperature and humidity sensors. Auxiliary sensor data refers to supplementary information acquired through non-GNSS measurement methods that reflects the attitude, dynamic response, or environmental changes of the monitored target. The data fusion module aligns these auxiliary sensor data streams with the time-synchronized observation data according to their respective timestamps. Using algorithms such as linear interpolation or nearest neighbor matching, it matches one or a set of corresponding auxiliary sensor readings for each GNSS observation epoch and integrates them into a unified data structure. This data structure is the multi-source dataset, whose state at any epoch t can be represented as:

[0036] ,

[0037] in, A record representing a multi-source dataset in epoch t. The vector representing the time-synchronized observation data of all observable satellites at this epoch is obtained through the aforementioned steps. This represents the auxiliary sensor data vector aligned with epoch t, ​​the specific content of which is determined by the type of auxiliary sensor configured. This formula represents the aggregation of two heterogeneous data sets along the time dimension to form a more comprehensive state description vector, rather than a direct mathematical summation. The final output multi-source dataset provides comprehensive input information for subsequent real-time calculation of the error propagation control factor.

[0038] Optionally, the step of calculating the error propagation control factor reflecting the error propagation sensitivity under the current observation conditions in real time based on the multi-source dataset includes: extracting satellite geometric configuration parameters and signal propagation environment parameters under the current observation conditions based on the multi-source dataset; calculating the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters; and performing eigenvalue decomposition on the error propagation sensitivity matrix to generate the error propagation control factor.

[0039] Specifically, data for the current epoch is extracted in real time from multi-source datasets. Based on satellite ephemeris data and the approximate coordinates of the monitoring station, the azimuth and elevation angles of all visible BeiDou satellites relative to the station are calculated. This set of angles constitutes the satellite geometric configuration parameters. These parameters are the geometric basis for positioning accuracy, describing the satellite's distribution in the sky and directly affecting the amplification effect of errors. Simultaneously, the module extracts observations such as signal-to-noise ratio (SNR) and pseudorange-carrier phase combination from the raw BeiDou carrier phase observation data. Combined with historical data and auxiliary sensor data, such as accelerometer vibration data, it assesses the propagation path quality of each satellite signal, obtaining signal propagation environment parameters. These parameters are primarily used to quantify the impact of non-geometric factors such as multipath effects and receiver observation noise on signal quality.

[0040] Based on the satellite geometric configuration parameters and signal propagation environment parameters extracted in the previous step, the system constructs an error propagation sensitivity matrix. .matrix The diagonal elements represent the variance of the coordinate solutions in the three directions of east, north, and elevation, while the off-diagonal elements represent the correlation between the coordinate solutions in different directions.

[0041] In order to propagate the sensitivity matrix from the error The system extracts intuitive and usable control information and performs eigenvalue decomposition on it. Eigenvalue decomposition is a standard linear algebraic operation that decomposes a matrix into eigenvalues ​​and eigenvectors. Its physical meaning lies in finding the principal direction and magnitude of the error distribution. The decomposition process is represented as follows:

[0042] ,

[0043] By solving this characteristic equation, the matrix can be obtained. A set of eigenvalues and the corresponding feature vector Here, the feature vector It is a three-dimensional unit vector that indicates the three principal axes of the error ellipsoid in space, i.e., the directions in which the error is most or least sensitive. The corresponding eigenvalues... It is a scalar whose magnitude represents the variance of the positioning error along the principal axis, i.e., the magnitude of the error. A larger eigenvalue means higher positioning uncertainty along its corresponding eigenvector direction, and greater sensitivity to error propagation. This set consists of eigenvalues ​​and eigenvectors. The resulting set constitutes the error propagation control factor as defined in this invention, which provides a quantitative control basis with clear physical direction significance for subsequent data screening, weighting, and calculation.

[0044] Optionally, calculating the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters includes: constructing a geometric accuracy factor matrix based on the satellite geometric configuration parameters; constructing a multipath error influence matrix and an observation noise influence matrix based on the signal propagation environment parameters; and fusing the geometric accuracy factor matrix, the multipath error influence matrix, and the observation noise influence matrix to generate the error propagation sensitivity matrix.

[0045] Specifically, this process takes three key influencing factors—geometric configuration, multipath effect, and observation noise—and unifies them under a single mathematical framework by constructing their respective influence matrices, ultimately generating an error propagation sensitivity matrix.

[0046] The system constructs a design matrix H based on the satellite geometric configuration parameters extracted in the previous step, namely the unit direction vector of each visible satellite relative to the monitoring station. Each row of this design matrix H corresponds to one satellite, and each row contains the components of that satellite's unit direction vector on the three coordinate axes: East (E), North (N), and Elevation (U). This matrix mathematically establishes a linear relationship between changes in observation values ​​and changes in station coordinates. Based on this, the system's geometric accuracy factor matrix... This can be expressed as:

[0047] ,

[0048] in, This is the geometric precision factor matrix, whose diagonal elements are the squared contributions of the traditional position precision attenuation factor PDOP, horizontal precision attenuation factor HDOP, and elevation precision attenuation factor VDOP. It intuitively reflects the error amplification effect caused solely by the geometric shape of the satellite sky distribution under ideal observation conditions. The design matrix is ​​calculated from the satellite's geometric configuration parameters. for The transpose of .

[0049] System construction of observation noise impact matrix For BeiDou carrier phase observations, the observation noise is mainly related to the satellite signal strength and elevation angle. The system employs a method based on signal-to-noise ratio (SNR) and satellite elevation angle. A stochastic model is used to calculate the prior variance of each observation link. A commonly used model is... ,in It is the observation noise variance of the i-th satellite. and It is an empirical constant. Let be the elevation angle of the i-th satellite. Using the noise variances of all n observation links as diagonal elements, and setting the remaining elements to zero, we construct an n-order diagonal matrix, which is the observation noise influence matrix. Next, the system constructs a multipath error influence matrix. The system uses multipath combination (MP) and other indicators to evaluate the degree of multipath effect contamination of each satellite signal in real time. These indicators can be extracted from BeiDou multi-frequency pseudorange and carrier phase observation data. The system converts the evaluated multipath effect magnitude into an equivalent variance contribution. And use these as diagonal elements to construct an n-order diagonal matrix, which is the multipath error influence matrix. .

[0050] The fusion here is not a simple matrix addition, but rather a covariance propagation within the framework of least squares adjustment theory. The system first incorporates the multipath error influence matrix... With observation noise influence matrix Adding them together yields the total observation random error covariance matrix. Since both matrices are diagonal matrices and represent independent sources of random error, they can be directly added together.

[0051] Subsequently, the system utilizes the covariance propagation law to propagate the error covariance matrix of the observation space to the coordinate parameter space to be determined through the geometric relationship implicit in the geometric precision factor matrix, thereby generating the final error propagation sensitivity matrix S:

[0052] ,

[0053] in, This is the error propagation sensitivity matrix, which is a 3x3 symmetric matrix. Its diagonal elements represent the estimated variance of displacement in the three directions E, N, and U, while the off-diagonal elements represent the covariance between different directions. Typically represented as a design matrix The generalized inverse, in the case of full rank, is... . for The transpose of the matrix reflects how observation noise and multipath errors are amplified by satellite geometry and affect the covariance of the final coordinate parameters.

[0054] Optionally, the step of dynamically filtering and pre-allocating weights on the raw BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate an optimal observation set includes: using the error propagation control factor to calculate the confidence index of each observation value in the raw BeiDou carrier phase observation data of the monitoring station; dynamically filtering the raw BeiDou carrier phase observation data of the monitoring station based on the confidence index to obtain a preliminary filtered observation set; and pre-allocating weights on the observation values ​​in the preliminary filtered observation set according to the error propagation control factor to generate an optimal observation set.

[0055] Specifically, the system utilizes the previously generated error propagation control factor, i.e., the eigenvalues ​​of the error propagation sensitivity matrix S. and eigenvectors The system uses a set of data to evaluate the contribution of each satellite j's observations in the raw BeiDou carrier phase observation data from the monitoring station to the stability of the current solution. Specifically, the system focuses on the largest eigenvalue. Corresponding eigenvectors These represent the direction and magnitude of the largest error under the current geometric configuration. For each satellite j, its corresponding row vector in the design matrix H... This represents its geometric contribution. The system calculates... In the direction of worst error The projection onto the surface is used to quantify the satellite's contribution to the maximum error. Confidence index It can be defined as:

[0056] ,

[0057] in, It is the confidence index of satellite j, and its value range is usually between 0 and 1. It is the representation of the satellite j-unit direction vector in the station coordinate system, which is directly obtained from its geometric configuration parameters. It is the largest eigenvalue The corresponding eigenvector. k' is a dimensionless adjustment coefficient used to scale the magnitude of the penalty term. The meaning of this formula is that if the line of sight of a satellite coincides with the direction of the largest solution error at a certain height, i.e. and If the absolute value of the inner product is close to 1, then the satellite's observations contribute significantly to instability, and its confidence index... It will decrease.

[0058] The system sets a dynamic or fixed confidence threshold. For example, 0.5. Then, the system iterates through the confidence indices of all satellites in the current epoch. All Below Satellite observations are removed from the observation dataset of the current epoch. This step aims to remove satellites that have a significant negative impact on the solution geometry; for example, in certain configurations, the presence of certain satellites can drastically amplify errors in a particular direction. This filtering operation yields a preliminary filtered observation set that has removed unstable sources of observation.

[0059] For observations that pass the initial screening and are retained in the initial observation set, the system will further refine their weights using the error propagation control factor. The initial weights are primarily based on the signal-to-noise ratio and satellite elevation angle, reflecting the quality of the signal itself. The weight pre-assignment, however, additionally considers the role of each observation in the current overall geometry. The system calculates an adjustment factor for each retained observation j. This factor comprehensively considers its contribution in all principal error directions:

[0060] ,

[0061] in, This is the weight adjustment factor calculated for satellite j. This indicates summing over all eigenvalues ​​i. and It is the i-th pair of eigenvalues ​​and eigenvectors. These are weighting coefficients for different principal error axes, with larger eigenvalues ​​typically assigned greater weight. Ultimately, the system will use the initial weights... Divide by this adjustment factor The new weights after pre-allocation are obtained. .Right now The observation data in the initial screening set will be matched with their corresponding new weights. By combining these, a final optimal observation set is generated, which has optimized data quality and geometric strength.

[0062] Optionally, the step of performing collaborative calculation on the preferred observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor includes: performing collaborative calculation on the preferred observation set based on the error propagation control factor to obtain a preliminary displacement estimate; and using the error propagation control factor to enhance and correct the preliminary displacement estimate to generate an intermediate displacement estimate.

[0063] Specifically, the collaborative solution here refers to the positioning solution process that uses differential processing of synchronous observation data from monitoring stations and base stations. The system employs the weighted least squares method, using an optimized observation set as input. This optimized observation set already includes screened observation values ​​and weights optimized by the error propagation control factor. The solution model is as follows:

[0064] ,

[0065] in, The calculated preliminary displacement estimate is a three-dimensional vector containing displacement components in the east, north, and elevation directions. The design matrix for the observation equations is determined by the geometric relationship between the satellite and the station. It is the residual vector of the inter-station and inter-satellite double-difference carrier phase observations, that is, the observed value minus the theoretical value calculated based on the prior coordinates. This is a diagonal weight matrix, where the elements on the diagonal are the weights pre-assigned to each observation in the preferred observation set. The output of this step is a preliminary three-dimensional displacement estimate that implicitly incorporates error control principles.

[0066] The second step of this method aims to directly affect the solution results, further weakening the displacement estimation components in the direction most sensitive to error under the current observation conditions. The system then uses the preliminary displacement estimate obtained in the previous step... The error is projected onto the principal error axis defined by the error propagation control factor, and then the error sensitivity in each direction, i.e., the eigenvalue, is calculated. The magnitude of the vector is used to differentiate and reduce the projection components, and finally reconstruct the corrected displacement vector. The enhancement and correction process can be expressed as:

[0067] ,

[0068] in, It is the intermediate estimate of the final generated displacement. This represents the summation over all principal error axes, i.e., all pairs of eigenvalues ​​and eigenvectors. It is the transpose of the preliminary displacement estimate dX. It is the unit direction vector of the i-th principal error axis, i.e., the eigenvector. It is along The magnitude of the error in direction, i.e., the eigenvalue. The preliminary displacement estimate was calculated. Projected components in the direction. It is a dimensionless adjustment coefficient, typically ranging from 0.1 to 1.0, used to control the strength of the correction. The core of this formula lies in the reduction factor. ,for The larger the value of the factor, the more sensitive the direction to error, and thus the stronger the suppression of displacement components in that direction. This step ultimately outputs a statistically more reliable intermediate estimate of displacement.

[0069] Optionally, the step of using the error propagation control factor to perform spatiotemporal displacement prediction and filtering the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence includes: using the error propagation control factor to establish a spatiotemporal displacement prediction model and predicting the intermediate displacement estimate sequence to obtain a displacement prediction value; and based on the displacement prediction value and the corresponding confidence index, filtering the intermediate displacement estimate to output a reliable three-dimensional displacement sequence.

[0070] Specifically, the engineering implementation of the reliable three-dimensional displacement sequence in this invention lies in the introduction of time-domain filtering and prediction mechanisms to smooth the random fluctuations of the single-epoch solution results and effectively process epochs with poor solution quality, thereby generating a continuous, reliable and more accurate final displacement time series.

[0071] The system constructs a dynamic spatiotemporal displacement prediction model based on historical intermediate displacement estimates and the associated error propagation control factor sequence. This model not only considers the displacement trend over time but also incorporates the impact of current observation conditions on prediction accuracy. A typical implementation is a Kalman filter with adaptive process noise. Its state prediction equation can be expressed as:

[0072] ,

[0073] in, It is the predicted displacement state value for the current epoch k, i.e., the predicted displacement value. It is the optimal estimated state of the previous epoch k-1. This is the state transition matrix. For static or slowly varying displacement monitoring, it can usually be set as an identity matrix, indicating that the predicted current position is the same as the previous position. More importantly, it is the process noise covariance matrix. The setting is related to the error propagation control factor.

[0074] ,

[0075] Here, Q_k-1 represents the uncertainty of the system model itself from time k-1 to time k. To construct a diagonal matrix function. It is the maximum eigenvalue at time k-1, given by the error propagation control factor at that time. This is a scaling factor. The meaning of this setting is that if the observation conditions at the previous moment were poor and the solution uncertainty was high, then the probability of the displacement actually changing at the next moment is considered higher, thus giving the prediction model greater flexibility.

[0076] The second step of this method is to filter the predicted values ​​to output the final displacement sequence. The filtering step aims to optimize the newly acquired measurement information, specifically the intermediate displacement estimates for the current epoch k. Compared with the displacement prediction value obtained in the previous step Perform optimal fusion. The update equation for the Kalman filter is:

[0077] ,

[0078] ,

[0079] ,

[0080] in, It is the Kalman gain that determines the weighting of the measured and predicted values. It is the covariance matrix of the predicted state, from the previous epoch. and process noise It follows a recursive pattern. In this application, the observation matrix is ​​used because the intermediate displacement estimates directly correspond to the state variables. It is usually an identity matrix. It is the measurement noise covariance matrix, the value of which is derived from the error propagation sensitivity matrix of the current epoch k. Provided directly, or associated with confidence metrics, such as ,in , , For confidence levels in each direction, To construct a diagonal matrix function, This is an adjustment coefficient. This setting allows for adjustments when the current observation quality is poor and the confidence level is low. Increase Kalman gain Decreasing the value makes the system more confident in the predicted value; conversely, increasing the value makes it more confident in the current measurement. Ultimately, this update step yields... This refers to a point in the reliable 3D displacement sequence output at the current epoch. By iterating through such epochs, a continuous, filtered, and optimized reliable 3D displacement sequence is formed.

[0081] Optionally, the step of generating an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and performing feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index, includes: calculating a displacement estimation residual sequence based on the reliable three-dimensional displacement sequence; performing statistical analysis on the displacement estimation residual sequence in conjunction with the auxiliary sensor data to generate an accuracy convergence discrimination index; and performing feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

[0082] Specifically, the system uses the latest generated reliable 3D displacement sequence as the reference true value or best estimate, and then calculates the difference between the intermediate displacement estimate and the reference true value for each epoch. Specifically, for each epoch k in the time series, its displacement estimation residual... It can be calculated as:

[0083] ,

[0084] in, It is the displacement estimation residual vector of the k-th epoch. It is the intermediate displacement estimate obtained after strengthening and correction in the k-th epoch. This is the value in the reliable three-dimensional displacement sequence obtained after time-domain filtering at the k-th epoch. This residual vector... This reflects the random fluctuations or potential systematic biases in the single-epoch solution results before time-domain filtering. By collecting these residual vectors within a certain time window, such as the past 100 epochs, the system generates a sequence of displacement estimation residuals.

[0085] The residual sequence is statistically analyzed using auxiliary sensor data to generate accuracy convergence criteria. The system sets predetermined thresholds and continuously monitors these criteria. For example, when the standard deviation of the displacement estimation residual sequence consistently exceeds a preset value for multiple consecutive windows, or when its distribution deviates significantly from a normal distribution, a feedback optimization mechanism is triggered. This feedback optimization directly affects the calculation of the error propagation control factor, specifically adjusting the model parameters used to construct the error propagation sensitivity matrix S. For instance, if the residual sequence shows a deviation strongly correlated with a specific satellite elevation angle range, the system will adjust the observation noise impact matrix. The empirical constants in the computational model. If the residual spectrum matches the spectrum of the multipath effect index, the system will adjust the multipath error influence matrix. The weighted model is used. Through this feedback mechanism, the parameters of the error model are continuously optimized, so that the calculated error propagation control factor can more realistically reflect the actual error situation, thereby guiding subsequent data processing to be more accurate, and ultimately improving the monitoring accuracy and reliability of the entire system.

[0086] Optionally, the step of combining the auxiliary sensor data to perform statistical analysis on the displacement estimation residual sequence and generating an accuracy convergence discrimination index includes: performing a normality test on the displacement estimation residual sequence to generate residual distribution characteristic parameters; comparing the consistency between the auxiliary sensor data and the reliable three-dimensional displacement sequence to generate a sensor consistency index; and fusing the residual distribution characteristic parameters and the sensor consistency index to generate an accuracy convergence discrimination index.

[0087] Specifically, the system performs statistical characteristic analysis on each component of the displacement estimation residual sequence—namely, the residual data in the east, north, and elevation directions—within a set time window, for example, containing 300 to 500 epochs of data. The system calculates the mean of the residual sequence within this time window. and standard deviation Simultaneously, the system employs standard statistical tests, such as the Shapiro-Wilk test or the Kolmogorov-Smirnov test, to assess whether the residual sequence conforms to a normal distribution with zero mean. The test results are typically output as a p-value. A smaller p-value indicates a greater likelihood that the data deviates from a normal distribution. The system will then calculate the mean. Standard deviation These three statistics—the p-value of the normality test, the residual distribution characteristic parameter, and the p-value of the normality test—are combined to assess whether the random error model has been properly handled from the perspective of internal data consistency.

[0088] The system cross-validates reliable 3D displacement sequences within the same time window with data from auxiliary sensors. This step requires different comparison strategies depending on the type of auxiliary sensor. For example, if the auxiliary sensor is a high-frequency accelerometer, the system first performs a second derivative on the reliable 3D displacement sequence to obtain the acceleration sequence extrapolated from GNSS. Then, it performs coherence analysis on this extrapolated acceleration sequence and the acceleration sequence directly measured by the accelerometer within a common frequency band, such as 0.1 Hz to 5 Hz. The coherence analysis calculates the linear correlation between the two time series at various frequencies, outputting a coherence function value between 0 and 1. The system calculates the average coherence coefficient within the target frequency band and uses it as one of the sensor fit indices. If the auxiliary sensor is a high-precision inclinometer, the system can compare the tilt angle calculated from the GNSS baseline vector variation with the tilt angle directly measured by the inclinometer, calculate the root mean square error (RMSE) between the two, and use the reciprocal of the RMSE as a fit index. This index verifies the physical authenticity of the GNSS solution from the perspective of independent external measurement.

[0089] The system weighted and fused the residual distribution characteristic parameters generated in the first two steps with the sensor fit index to form a comprehensive scalar or vector, which is the accuracy convergence discrimination index. :

[0090] ,

[0091] in, This is the final accuracy convergence criterion. w1 and w2 are weighting coefficients, their sum is 1, and they are set according to engineering experience, for example, w1=0.6, w2=0.4. Functions f and g are mapping functions that normalize their respective input parameters to a similar scale (such as 0 to 1). For example, the f function can be designed so that its value is close to 1 when the mean is close to zero, the standard deviation is less than the threshold, and the p-value is greater than the significance level; otherwise, it is close to 0. The g function can directly use the normalized coherence coefficient or the reciprocal of RMSE. When If the value of this indicator remains consistently above a preset convergence threshold, such as 0.85, for a certain period of time, the system determines that the monitoring accuracy has reached convergence. The fluctuation of this indicator also provides direct quantitative evidence for feedback optimization.

[0092] Based on the same inventive concept, such as Figure 2 As shown, the present invention also provides a high-precision three-dimensional displacement monitoring system based on BeiDou carrier phase, the system comprising:

[0093] The multi-source data acquisition module is used to simultaneously acquire the raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data of the monitoring station from the monitoring station and at least one reference station to obtain a multi-source dataset.

[0094] The error propagation control factor calculation module is used to calculate, in real time, the error propagation control factor that reflects the sensitivity of error propagation under the current observation conditions based on the multi-source dataset.

[0095] The preferred observation set generation module is used to dynamically filter and pre-allocate weights on the original BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate a preferred observation set.

[0096] The intermediate displacement estimate generation module is used to perform collaborative calculation on the preferred observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor.

[0097] The displacement sequence output module is used to perform spatiotemporal prediction of displacement using the error propagation control factor, and to filter the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence.

[0098] The feedback optimization module is used to generate an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and to perform feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

[0099] To verify the technical feasibility and practical effectiveness of this invention, it was applied to a structural health monitoring project for a super high-rise building. The building is 500 meters tall and surrounded by tall buildings, making the BeiDou satellite signal susceptible to obstruction and multipath effects, thus posing requirements for the accuracy and reliability of three-dimensional displacement monitoring.

[0100] In this embodiment, a BeiDou receiver is installed on the top of the building (the monitoring point) as a monitoring station (ROV1), and another BeiDou receiver of the same model is installed on the roof of a geologically stable building 2 kilometers away as a reference station (REF1). A triaxial accelerometer is also deployed at the monitoring station (ROV1) as an auxiliary sensor. The data acquisition parameters are set as follows: the BeiDou receiver data sampling frequency is 10 Hz, and the satellite altitude cutoff angle is set to 10 degrees; the accelerometer sampling frequency is 100 Hz. The test selects a 30-minute data segment starting at 14:00 (UTC) on a certain afternoon for processing and analysis. The monitoring objective is to obtain the three-dimensional displacement sequence of the building top during this period and compare it with the traditional differential calculation method that does not adopt the error control strategy of this invention.

[0101] At 14:00:00 UTC, the system started, and the BeiDou receivers at the monitoring station (ROV1) and the base station (REF1) synchronously began acquiring raw carrier phase observation data for the B1I and B3I frequency points via Network Time Protocol (NTP). Simultaneously, the accelerometers began recording the three-axis acceleration data from the monitoring station. The system obtained precise ephemeris data covering this time period from the International GNSS Service (IGS) data center. At 14:00:10.0 epoch, the two receivers observed a total of 9 BeiDou satellites. The system time-aligned and fused the raw observation data, matched satellite ephemeris data, and synchronized accelerometer readings for this epoch, generating the multi-source dataset Dt for that epoch.

[0102] The system calculates the error propagation control factor in real time based on a multi-source dataset from epoch 14:00:10.0. First, it extracts satellite geometric parameters, namely the azimuth and elevation angles of each satellite, and signal propagation environment parameters, such as the signal-to-noise ratio (SNR) and multipath effect index (MP) of each satellite signal. For example, at this time, satellite C41 has an elevation angle of 12.5 degrees, an SNR of 38.2 dB-Hz, and a MP value of 0.75 meters, indicating poor signal quality. Next, it constructs an error propagation sensitivity matrix S. A design matrix H is constructed based on the satellite geometric parameters, and an observation weight matrix W is constructed based on the signal propagation environment parameters. The observations of satellite C41 are given a lower initial weight due to its poor signal quality. The formula is used to calculate the initial weight. The error propagation sensitivity matrix for the current epoch is calculated, and the specific values ​​are as follows (unit: mm²):

[0103] ,

[0104] Performing eigenvalue decomposition on matrix S yields three eigenvalues ​​and their corresponding eigenvectors; this set is the error propagation control factor: the largest eigenvalue. , corresponding feature vector This indicates that the most unstable direction in the current solution is mainly along the vertical direction, with the variance of the error amplification reaching 9.50 mm²; intermediate eigenvalues , corresponding feature vector Minimum eigenvalue Feature vector .

[0105] Calculate the confidence index of each satellite observation. For the C30 satellite at a high elevation angle, its unit direction vector is... Nearly orthogonal The confidence level was calculated using the formula. For the C41 satellite at low elevation angles, its unit direction vector is... Almost parallel, The confidence level was calculated. Set a confidence threshold. .because The system removes observation data from the C41 satellite from the current epoch calculation, forming a preliminary filtered observation set. For the remaining eight satellite observations, their contributions along the principal error axes are calculated using the formula... The weights were reallocated. For example, the weight of C30 satellites, which contribute significantly to the solution of geometric strength, was moderately increased. The final result was a preferred observation set containing only 8 satellites with optimized weights.

[0106] Based on the optimized observation set, the system uses the weighted least squares method to perform inter-station double-difference calculations to obtain preliminary displacement estimates. This result outperforms the traditional solution using all nine satellites without weighted optimization. An enhanced correction to dX is applied using an error propagation control factor. dX is projected along the three principal error axes and reduced according to the magnitude of the corresponding eigenvalues. For example, in the direction of maximum error... Shadow component is This component is multiplied by a reduction factor. (where the adjustment coefficient is) (Set to 0.5). After reducing and reconstructing the three directional components respectively, the intermediate displacement estimate enhanced by the error propagation control factor is finally generated. It can be seen that the vertical component, which has the greatest uncertainty, was significantly suppressed from 18.3 mm to 4.5 mm.

[0107] The system employs a Kalman filter to filter the intermediate displacement estimate sequence. At epoch 14:00:10.0: the filter's state prediction value is derived from the optimal estimate of the previous epoch (14:00:09.9). Given; in the update step, the noise covariance matrix is ​​measured. The sensitivity matrix is ​​directly propagated from the error at the current epoch. Settings. Due to vertical component The gain is very large, resulting in a Kalman gain. It becomes very small in the vertical direction. Therefore, when fusing predicted and measured values... At this point, the system relies more heavily on the predicted values. Ultimately, the updated optimal estimate, i.e., the output reliable 3D displacement, is... This value smooths out the jumps in the single-epoch solution and forms a point in a reliable three-dimensional displacement sequence.

[0108] After running for 10 minutes, the system generates a sequence of displacement estimation residuals. Analysis revealed that the standard deviation of the vertical residual sequence was 2.5 mm, exceeding the preset threshold of 1.5 mm. Furthermore, coherence analysis of the vertical acceleration calculated by GNSS and the actual acceleration measured by auxiliary sensors (accelerometers) showed that the coherence coefficient was only 0.4 in the 0.1-1 Hz frequency band, lower than the ideal value of 0.7. The system integrates this information to generate an accuracy convergence criterion. The error rate was below the convergence threshold of 0.85, indicating that the current error model failed to fully reflect the true error characteristics. The system triggered a feedback optimization mechanism. Based on the analysis of residuals and auxiliary data, the problem was determined to stem primarily from insufficient model estimation of low-elevation satellite multipath effects and observation noise. The system automatically converted the observation noise influence matrix... The empirical constant in the model is increased by 10% to more strictly suppress the weighting of low-elevation satellites in subsequent calculations. This adjustment will be applied to the calculation of the error propagation control factor for all subsequent epochs, thus forming a closed-loop adaptive optimization process.

[0109] It should be noted that the above descriptions are merely exemplary embodiments of the present invention and should not be construed as limiting the scope of the invention. All equivalent changes and modifications made in accordance with the teachings of this invention are still within the scope of this invention. Those skilled in the art will readily conceive of other embodiments of the invention upon considering the disclosure of the specification and practical truths. This application is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or conventional techniques in the art not described herein.

Claims

1. A high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase, characterized in that, The method includes: Simultaneously acquire raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data from the monitoring station and at least one reference station to obtain a multi-source dataset; Based on the multi-source dataset, the error propagation control factor, which reflects the sensitivity to error propagation under the current observation conditions, is calculated in real time. The error propagation control factor is used to dynamically filter and pre-allocate weights on the raw BeiDou carrier phase observation data of the monitoring station to generate an optimal observation set; Based on the error propagation control factor, the preferred observation set is co-calculated to generate an intermediate displacement estimate enhanced by the error propagation control factor; The error propagation control factor is used to predict the spatiotemporal displacement, and the intermediate displacement estimate sequence is filtered to output a reliable three-dimensional displacement sequence. Based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, an accuracy convergence discrimination index is generated, and the calculation process of the error propagation control factor is optimized by feedback based on the accuracy convergence discrimination index.

2. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 1, characterized in that, The simultaneous acquisition of raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data from the monitoring station and at least one reference station yields a multi-source dataset including: The raw observation data of BeiDou carrier phase from the monitoring station and the raw observation data of BeiDou carrier phase from at least one reference station are collected simultaneously to obtain the raw observation dataset. Acquire satellite ephemeris data and perform time synchronization processing on the original observation dataset to generate time-synchronized observation data; The auxiliary sensor data of the monitoring station is acquired, and the time-synchronized observation data is fused with the auxiliary sensor data to generate a multi-source dataset.

3. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 2, characterized in that, The error propagation control factor, which reflects the sensitivity to error propagation under the current observation conditions and is calculated in real time based on the multi-source dataset, includes: Based on the multi-source dataset, satellite geometric configuration parameters and signal propagation environment parameters under the current observation conditions are extracted; Calculate the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters; The error propagation sensitivity matrix is ​​decomposed into eigenvalues ​​to generate an error propagation control factor.

4. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 3, characterized in that, The calculation of the error propagation sensitivity matrix based on the satellite geometric configuration parameters and signal propagation environment parameters includes: Based on the aforementioned satellite geometric configuration parameters, a geometric accuracy factor matrix is ​​constructed; Based on the aforementioned signal propagation environment parameters, a multipath error influence matrix and an observation noise influence matrix are constructed. The geometric accuracy factor matrix, the multipath error influence matrix, and the observation noise influence matrix are combined to generate an error propagation sensitivity matrix.

5. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 3, characterized in that, The process of dynamically filtering and pre-assigning weights to the raw BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate an optimal observation set includes: Using the aforementioned error propagation control factor, the confidence index of each observation value in the original BeiDou carrier phase observation data of the monitoring station is calculated; Based on the confidence index, the raw BeiDou carrier phase observation data of the monitoring station are dynamically filtered to obtain a preliminary filtered observation set; The observations in the preliminary screening observation set are pre-weighted according to the error propagation control factor to generate the preferred observation set.

6. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 5, characterized in that, The step of performing collaborative calculations on the preferred observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor includes: Based on the error propagation control factor, the preferred observation set is co-calculated to obtain a preliminary displacement estimate; The initial displacement estimate is enhanced and corrected using the error propagation control factor to generate an intermediate displacement estimate.

7. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 6, characterized in that, The process of using the error propagation control factor to perform spatiotemporal displacement prediction, filtering the intermediate displacement estimate sequence, and outputting a reliable three-dimensional displacement sequence includes: Using the error propagation control factor, a displacement spatiotemporal prediction model is established, and the intermediate displacement estimate sequence is predicted to obtain the displacement prediction value. Based on the predicted displacement value and the corresponding confidence index, the intermediate displacement estimate is filtered to output a reliable three-dimensional displacement sequence.

8. The method for high-precision three-dimensional displacement monitoring based on BeiDou carrier phase according to claim 7, characterized in that, The process of generating an accuracy convergence criterion based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and then optimizing the calculation process of the error propagation control factor based on the accuracy convergence criterion, includes: Based on the reliable three-dimensional displacement sequence, calculate the displacement estimation residual sequence; Based on the auxiliary sensor data, statistical analysis is performed on the displacement estimation residual sequence to generate an accuracy convergence discrimination index. The calculation process of the error propagation control factor is optimized by feedback based on the accuracy convergence criterion.

9. A high-precision three-dimensional displacement monitoring method based on BeiDou carrier phase according to claim 8, characterized in that, The step of combining the auxiliary sensor data to perform statistical analysis on the displacement estimation residual sequence and generating accuracy convergence criteria includes: The displacement estimation residual sequence is subjected to a normality test to generate residual distribution characteristic parameters; The consistency of the auxiliary sensor data with the reliable three-dimensional displacement sequence is compared to generate a sensor consistency index. By integrating the residual distribution characteristic parameters with the sensor consistency index, an accuracy convergence discrimination index is generated.

10. A high-precision three-dimensional displacement monitoring system based on BeiDou carrier phase, characterized in that, The system includes: The multi-source data acquisition module is used to simultaneously acquire the raw BeiDou carrier phase observation data, satellite ephemeris, and auxiliary sensor data of the monitoring station from the monitoring station and at least one reference station to obtain a multi-source dataset. The error propagation control factor calculation module is used to calculate, in real time, the error propagation control factor that reflects the sensitivity of error propagation under the current observation conditions based on the multi-source dataset. The preferred observation set generation module is used to dynamically filter and pre-allocate weights on the original BeiDou carrier phase observation data of the monitoring station using the error propagation control factor to generate a preferred observation set. The intermediate displacement estimate generation module is used to perform collaborative calculation on the preferred observation set based on the error propagation control factor to generate an intermediate displacement estimate enhanced by the error propagation control factor. The displacement sequence output module is used to perform spatiotemporal prediction of displacement using the error propagation control factor, and to filter the intermediate displacement estimate sequence to output a reliable three-dimensional displacement sequence. The feedback optimization module is used to generate an accuracy convergence discrimination index based on the reliable three-dimensional displacement sequence and the auxiliary sensor data, and to perform feedback optimization on the calculation process of the error propagation control factor based on the accuracy convergence discrimination index.

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