High-precision positioning method and system for receiver based on ransac algorithm

Abstract

This invention discloses a high-precision receiver positioning method and system based on the RANSAC algorithm. The method includes: constructing an ionospherically-free combined PPP observation equation based on all satellites observed at the current epoch; selecting a preset number of satellites to form a satellite subset; calculating a temporary state solution using the corresponding observation equation when a preset geometric distribution condition is met; calculating the observation residuals corresponding to the pseudorange and carrier phase of the remaining satellites outside the subset based on the temporary state solution; introducing the RANSAC algorithm, and identifying a set of interior satellites with the strongest observation consistency through multiple rounds of random sampling and residual consistency discrimination; and constructing a complete PPP observation equation based on this set of interior satellites for high-precision receiver positioning. This invention significantly improves positioning accuracy and stability by integrating the RANSAC algorithm into the PPP solution process to achieve dynamic identification and removal of gross errors, thereby realizing high-precision positioning in complex urban environments.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a high-precision positioning method and system for receivers based on the RANSAC algorithm. Background Technology

[0002] Precise Point Positioning (PPP) is a technology that relies on a single GNSS receiver and utilizes products such as precise orbits, satellite clock errors, ionospheric and tropospheric models to achieve high-precision absolute positioning without the need for a reference station.

[0003] However, in the complex environment of cities with numerous high-rise buildings, GNSS observations are susceptible to interference from factors such as building obstruction, multipath effects, and non-line-of-sight (NLOS) errors, leading to gross errors that significantly deviate from the true values. These anomalous observations will significantly reduce the accuracy and stability of PPP solutions, easily causing increased positioning errors or even solution failure.

[0004] In existing technologies, residual testing or robust estimation methods are commonly used to handle gross errors in PPP observations. However, when gross errors occur simultaneously from multiple satellite observations, traditional methods often struggle to identify all anomalies accurately and promptly, potentially leading to missed detections or misjudgments. Furthermore, in dynamic urban scenarios, frequent satellite signal loss and re-acquisition, coupled with constantly changing observation environments, make existing detection methods based on static or single gross error assumptions inadequate. Therefore, improving the robustness and dynamic adaptability of PPP to gross errors in urban environments, while ensuring solution accuracy and positioning stability, has become a critical issue that urgently needs to be addressed.

[0005] The above content is only used to help understand the technical solution of the present invention and does not represent an admission that the above content is prior art. Summary of the Invention

[0006] The main objective of this invention is to provide a high-precision receiver positioning method and system based on the RANSAC algorithm, aiming to solve the technical problem of high-precision receiver positioning while improving the anti-gross error capability and accuracy stability of multi-frequency PPP in urban environments.

[0007] To achieve the above objectives, this invention provides a high-precision receiver positioning method based on the RANSAC algorithm, the method comprising:

[0008] Construct PPP observation equations for each satellite observed at the current epoch, and select a predetermined number of satellites from all satellites to form a satellite subset;

[0009] When the satellite subset satisfies the preset satellite geometric distribution conditions, a temporary state solution is calculated based on the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset.

[0010] Based on the provisional state solution, calculate the pseudorange observation residuals and carrier phase observation residuals for the remaining satellites within all satellites respectively;

[0011] The remaining satellites are marked with interior points based on the pseudorange observation residuals and the carrier phase observation residuals;

[0012] The satellite subset is iteratively sampled using the RANSAC algorithm;

[0013] When the iteration terminates, multiple satellites are selected from all satellites to form an inner point satellite set based on the number of inner point markings corresponding to each satellite, and the receiver is positioned with high precision based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

[0014] Optionally, before calculating the temporary state solution based on the PPP observation equations for the ionosphere-free combination corresponding to the satellite subset when the satellite subset satisfies the preset satellite geometric distribution conditions, the following steps are included:

[0015] Construct a satellite geometric matrix based on the aforementioned satellite subset;

[0016] Calculate the position accuracy attenuation factor and matrix condition number based on the satellite geometric matrix;

[0017] Determine whether the position accuracy attenuation factor value is greater than a preset PDOP threshold, and whether the matrix condition number is greater than a preset condition number threshold;

[0018] If the position accuracy attenuation factor value is less than or equal to the preset PDOP threshold, and the matrix condition number is less than or equal to the preset condition number threshold, then the satellite subset is determined to satisfy the preset satellite geometric distribution condition.

[0019] Optionally, constructing the satellite geometric matrix based on the satellite subset includes:

[0020] Acquire GNSS multi-frequency observation data, precise orbit files, and precise clock error files;

[0021] The receiver's initial position coordinates, the satellite position coordinates of each satellite in the satellite subset, and the satellite clock bias are extracted from the GNSS multi-frequency observation data, the precise orbit file, and the precise clock bias file, respectively.

[0022] The satellite geometric matrix is ​​constructed based on the receiver's initial position coordinates, the satellite's position coordinates, and the satellite clock bias.

[0023] Optionally, the step of calculating the position accuracy attenuation factor value and matrix condition number based on the satellite geometry matrix includes:

[0024] Calculate the covariance matrix, the square root of the largest eigenvalue, and the square root of the smallest eigenvalue based on the satellite geometric matrix.

[0025] Extract the receiver's three-dimensional coordinate submatrix from the covariance matrix;

[0026] Calculate the position accuracy attenuation factor value based on the three-dimensional coordinate submatrix;

[0027] The matrix condition number of the satellite geometric matrix is ​​calculated based on the square root of the largest eigenvalue and the square root of the smallest eigenvalue.

[0028] Optionally, the calculation of the temporary state solution based on the ionosphere-free combined PPP observation equations corresponding to the satellite subset includes:

[0029] Extract the PPP observation equations for the satellite subset corresponding to the ionosphere-free combination of ...

[0030] Based on the antenna file and tidal correction file, a temporary state solution is calculated according to the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset. The temporary state solution includes the receiver position correction, the residual wet delay of the troposphere in the zenith direction, the receiver clock error, and the ionosphere-free ambiguity.

[0031] Optionally, the step of calculating the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites within all satellites based on the temporary state solution includes:

[0032] Extract the PPP observation equations for the remaining satellites within all satellites from the ionosphere-free combination PPP observation equations corresponding to each satellite;

[0033] Based on the provisional state solution, the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites are calculated according to the ionosphere-free combined PPP observation equations corresponding to the remaining satellites.

[0034] Optionally, the step of marking interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual includes:

[0035] Obtain the measurement noise standard deviations corresponding to the pseudorange observation residual and the carrier phase observation residual, respectively;

[0036] The pseudorange observation residual and the carrier phase observation residual are normalized based on the measurement noise standard deviation to obtain the normalized residual.

[0037] Calculate the sample standard deviation of the normalized residual, and set a preset discrimination threshold based on the sample standard deviation;

[0038] Multiple satellites from the remaining satellites whose pseudorange observation residuals and carrier phase observation residuals are less than or equal to the preset discrimination threshold are selected for interior point marking.

[0039] Optionally, when the iteration terminates, multiple satellites are selected from all satellites to form an interior point satellite set based on the number of interior point markers corresponding to each satellite, including:

[0040] Real-time acquisition of the number of interior point markers and iterations for each satellite;

[0041] If the number of satellites whose inlier point marking count exceeds a preset marking threshold is greater than a preset threshold, and the number of iterations has not reached a preset number, the iteration is terminated.

[0042] The satellites whose number of inlier markings is greater than a preset marking threshold constitute an inlier satellite set.

[0043] Optionally, the high-precision receiver positioning based on the ionospherically-free combined PPP observation equations corresponding to the in-point satellite set includes:

[0044] Based on the antenna file and the tidal correction file, the target position correction is obtained by performing state estimation using the extended Kalman filter method according to the ionosphere-free combination PPP observation equation corresponding to the inner point satellite set;

[0045] The receiver achieves high-precision positioning in the current epoch based on the target position correction.

[0046] Furthermore, to achieve the above objectives, this invention also proposes a high-precision receiver positioning system based on the RANSAC algorithm, wherein the high-precision receiver positioning system based on the RANSAC algorithm includes:

[0047] The selection module is used to construct the ionosphere-free combined PPP observation equations for each satellite observed at the current epoch, and to select a preset number of satellites from all satellites to form a satellite subset;

[0048] The calculation module is used to calculate the temporary state solution based on the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset when the satellite subset satisfies the preset satellite geometric distribution conditions;

[0049] The calculation module is also used to calculate the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites in all satellites according to the temporary state solution.

[0050] The marking module is used to mark the interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual;

[0051] The iteration module is used to iteratively sample the satellite subset using the RANSAC algorithm;

[0052] The positioning module is used to select multiple satellites from all satellites to form an inner point satellite set based on the number of inner point markings corresponding to each satellite when the iteration terminates, and to perform high-precision positioning of the receiver based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

[0053] Furthermore, to achieve the above objectives, the present invention also proposes a receiver high-precision positioning device based on the RANSAC algorithm. The device includes: a memory, a processor, and a receiver high-precision positioning program based on the RANSAC algorithm stored in the memory and executable on the processor. The receiver high-precision positioning program based on the RANSAC algorithm is configured to implement the steps of the receiver high-precision positioning method based on the RANSAC algorithm described above.

[0054] Furthermore, to achieve the above objectives, the present invention also proposes a storage medium storing a receiver high-precision positioning program based on the RANSAC algorithm. When the receiver high-precision positioning program based on the RANSAC algorithm is executed by a processor, it implements the steps of the receiver high-precision positioning method based on the RANSAC algorithm described above.

[0055] This invention first constructs the corresponding ionospherically-free combined PPP observation equations based on all satellites observed at the current epoch, and selects a predetermined number of satellites to form a satellite subset. When the subset satisfies a predetermined geometric distribution condition, a temporary state solution is calculated using its corresponding PPP observation equations. Subsequently, based on this temporary state solution, the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites are calculated, and the RANSAC algorithm is used to perform multiple rounds of random sampling and discrimination of the satellites, recording the number of inlier markings, and forming a final inlier satellite set according to a predetermined termination condition. Finally, by combining the PPP observation equations corresponding to the satellites and the final inlier satellites, the high-precision positioning solution of the station is completed. This invention significantly improves positioning accuracy and stability by introducing the RANSAC algorithm to dynamically identify and eliminate gross errors during the PPP solution process, thereby achieving high-precision positioning in complex urban environments. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the structure of a high-precision positioning device for a receiver based on the RANSAC algorithm in the hardware operating environment of the embodiment of the present invention.

[0057] Figure 2This is a flowchart illustrating the first embodiment of the high-precision receiver positioning method based on the RANSAC algorithm of the present invention.

[0058] Figure 3 This is a structural block diagram of the first embodiment of the high-precision positioning system for receivers based on the RANSAC algorithm of the present invention.

[0059] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0060] It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0061] Reference Figure 1 , Figure 1 This is a schematic diagram of the structure of a high-precision positioning device for a receiver based on the RANSAC algorithm, which is part of the hardware operating environment of the embodiment of the present invention.

[0062] like Figure 1 As shown, the high-precision positioning device for a receiver based on the RANSAC algorithm may include: a processor 1001, such as a central processing unit (CPU), a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. The communication bus 1002 is used to establish communication between these components. The user interface 1003 may include a display screen or an input unit such as a keyboard; optionally, the user interface 1003 may also include a standard wired interface or a wireless interface. The network interface 1004 may optionally include a standard wired interface or a wireless interface (such as a Wireless-Fidelity (Wi-Fi) interface). The memory 1005 may be high-speed random access memory (RAM) or stable non-volatile memory (NVM), such as a disk storage device. Optionally, the memory 1005 may also be a storage system independent of the aforementioned processor 1001.

[0063] Those skilled in the art will understand that Figure 1 The structure shown does not constitute a limitation on the receiver high-precision positioning device based on the RANSAC algorithm, and may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0064] like Figure 1As shown, the memory 1005, which serves as a storage medium, may include an operating system, a network communication module, a user interface module, and a receiver high-precision positioning program based on the RANSAC algorithm.

[0065] exist Figure 1 In the RANSAC algorithm-based high-precision positioning device for receivers shown, the network interface 1004 is mainly used for data communication with the network server; the user interface 1003 is mainly used for data interaction with the user; the processor 1001 and memory 1005 in the RANSAC algorithm-based high-precision positioning device of the present invention can be set in the RANSAC algorithm-based high-precision positioning device. The RANSAC algorithm-based high-precision positioning device calls the RANSAC algorithm-based high-precision positioning program stored in the memory 1005 through the processor 1001 and executes the RANSAC algorithm-based high-precision positioning method provided in the embodiment of the present invention.

[0066] This invention provides a high-precision receiver positioning method based on the RANSAC algorithm, referring to... Figure 2 , Figure 2 This is a flowchart illustrating the first embodiment of the high-precision receiver positioning method based on the RANSAC algorithm of the present invention.

[0067] In this embodiment, the receiver high-precision positioning method based on the RANSAC algorithm includes the following steps:

[0068] Step S10: Construct the PPP observation equations for each satellite observed at the current epoch, and select a preset number of satellites from all satellites to form a satellite subset.

[0069] It is easy to understand that the execution subject of this embodiment can be a high-precision positioning system based on the RANSAC algorithm receiver with functions such as data processing, network communication and program execution, or other computer devices with similar functions. This embodiment does not limit it.

[0070] Furthermore, the satellites observed at the current epoch are all available satellites at the current epoch. GNSS multi-frequency observation data (including pseudorange and carrier phase observations of multiple frequencies), precise orbit files, and precise clock bias files are acquired. The receiver's initial position coordinates, the satellite's position coordinates, and the satellite clock bias are extracted from the GNSS multi-frequency observation data, precise orbit files, and precise clock bias files, respectively. Based on the pseudorange, carrier phase observations, receiver's initial position coordinates, satellite's position coordinates, and satellite clock bias, the PPP observation equations corresponding to each satellite at the current epoch are constructed.

[0071] The PPP observation equations for GNSS ionosphere-free combination (IF) can be expressed as:

[0072] (1)

[0073] In the formula, and Indicates receiver Satellites observed above Pseudorange and carrier phase observations of ionospheric-free combinations, This represents the theoretical geometric distance between the receiver and the satellite. , Indicates the satellite's position coordinates. Indicates the receiver's position coordinates. and These represent the receiver clock bias and the satellite clock bias, respectively. Indicates tilted tropospheric delay, This indicates the receiver hardware delay without an ionospheric array. Indicates ionospheric ambiguity. The wavelength of the first frequency point and These represent the observation noise corresponding to the pseudorange and carrier phase observations, respectively, without ionospheric combination.

[0074] Apply equation (1) to the receiver's initial position. The tropospheric correction is calculated using a first-order Taylor series expansion based on the prior tropospheric model. At the same time, the tropospheric zenith wet delay correction number As a parameter to be estimated:

[0075] (2)

[0076]

[0077] In the formula: Indicates satellite The geometric distance to the receiver's initial position; Indicates satellite The direction cosine to the receiver's initial position; Indicates the receiver position correction amount; This indicates the tropospheric correction number obtained from the prior tropospheric delay model; and These represent the tropospheric projection function and the zenith-direction tropospheric residual wet delay, respectively.

[0078] Rearrange equation (2):

[0079] (3)

[0080]

[0081] In the formula, and This represents the observation residuals corresponding to the pseudorange and carrier phase observations for the ionospheric combination.

[0082] Assuming m satellites are observed at this epoch, Then we have the observation equation in matrix form:

[0083] (4)

[0084] In the formula:

[0085]

[0086]

[0087] In summary, the parameter vector to be estimated for the ionosphere-free PPP combination is:

[0088]

[0089] Furthermore, a preset number of satellites can be randomly selected from all available satellites at the current epoch to form a satellite subset. This preset number can be user-defined, such as 4 or 5. For example, four satellites can be randomly selected from those observed at the current epoch and grouped into a satellite subset for RANSAC iteration.

[0090] It should also be understood that PPP positioning requires observations from at least four satellites to be solved. Therefore, in each iteration, four satellites are randomly selected from the visible satellite set using computer-generated random numbers, ensuring both randomness and uniform coverage in the sampling. The satellite subset is denoted as [missing information - likely a typo]. To improve sampling efficiency, the geometric rationality of satellite subsets will be checked, and unqualified subsets will be immediately discarded and resampled.

[0091] Step S20: When the satellite subset satisfies the preset satellite geometric distribution conditions, calculate the temporary state solution based on the ionosphere-free combination PPP observation equation corresponding to the satellite subset.

[0092] The specific implementation method for verifying the geometric rationality of a satellite subset is as follows: A satellite geometric matrix is ​​constructed based on a preset number of satellites within the subset; the position precision attenuation factor (PDOP) and matrix condition number are calculated based on the satellite geometric matrix; it is determined whether the PDOP value is greater than a preset PDOP threshold and whether the matrix condition number is greater than a preset condition number threshold; if the PDOP value is less than or equal to the preset PDOP threshold and the matrix condition number is less than or equal to the preset condition number threshold, then the preset number of satellites is determined to meet the preset satellite geometric distribution conditions. The preset PDOP threshold and the preset condition number threshold are user-defined settings; the preset PDOP threshold can be 6, and the preset condition number threshold can be 100, etc.

[0093] In this embodiment, the process of constructing a satellite geometric matrix based on a preset number of satellites is as follows: the receiver's initial position coordinates, the satellite's position coordinates, and the satellite's clock bias are extracted from the GNSS multi-frequency observation data, the precise orbit file, and the precise clock bias file, respectively; and the satellite geometric matrix is ​​constructed based on the receiver's initial position coordinates, the satellite's position coordinates, and the satellite's clock bias.

[0094] In the specific implementation, the satellite geometric matrix is ​​first constructed based on the satellite position coordinates in the satellite subset and the receiver's initial position coordinates. The receiver's initial position coordinates can be calculated using standard single-point positioning or obtained from GNSS multi-frequency observation data. For each satellite... The satellite's position coordinates can be obtained from the GNSS precise orbit file. The satellite's geometric matrix contains coefficients such as the satellite's direction cosine and clock bias. The geometric matrix can be represented as:

[0095]

[0096] in, , , The fourth column represents the direction cosine of the satellite line-of-sight vector at the receiver, and the fifth column represents the coefficient corresponding to the clock error (approximately 1).

[0097] Furthermore, the processing method for calculating the position accuracy attenuation factor value and matrix condition number based on the satellite geometric matrix is ​​as follows: calculate the covariance matrix, the square root of the largest eigenvalue, and the square root of the smallest eigenvalue based on the satellite geometric matrix; extract the receiver's three-dimensional coordinate submatrix from the covariance matrix; calculate the position accuracy attenuation factor value based on the three-dimensional coordinate submatrix; and calculate the matrix condition number of the satellite geometric matrix based on the square root of the largest eigenvalue and the square root of the smallest eigenvalue.

[0098] It should be noted that the covariance matrix Extract the submatrix corresponding to the receiver's three-dimensional coordinates (i.e., the three-dimensional coordinate submatrix). Then the PDOP value (i.e., the position accuracy attenuation factor) is the square root of the sum of the diagonal elements of the submatrix:

[0099]

[0100] in, , , for Receiver position in the matrix ) Variance of direction.

[0101] Calculate the matrix condition number of the satellite geometry matrix Used to evaluate the stability of the solution:

[0102]

[0103] in, and Each is a matrix Maximum and minimum singular values ​​(or equivalent) The square root of the largest eigenvalue and the square root of the smallest eigenvalue.

[0104] It should be understood that the condition number reflects the ill-conditioned nature of the matrix; a larger value indicates that the geometric matrix is ​​closer to singular, and the solution results are less stable. Therefore, it is necessary to limit the PDOP value to no more than a preset PDOP threshold and the condition number to no more than a preset condition number threshold to ensure that the satellite subset has a good geometric configuration.

[0105] In the specific implementation, if the position accuracy attenuation factor value is greater than the preset PDOP threshold, and the matrix condition number is greater than the preset condition number threshold, then it is determined that the preset number of satellites does not meet the preset satellite geometric distribution conditions, and the current satellite subset geometric distribution is unreasonable and unsuitable for reliable calculation. At this time, the subset is discarded, and a new subset of satellites is randomly selected for retry. If the PDOP value of the selected subset is less than or equal to the preset PDOP threshold and the matrix condition number is less than or equal to the preset condition number threshold, then the geometric conditions of the subset are considered acceptable, and subsequent steps continue. Through this dual screening mechanism, sampling subsets with poor satellite distribution can be eliminated, accelerating RANSAC iterative convergence and ensuring calculation accuracy.

[0106] Furthermore, the method for calculating the temporary state solution of the ionospherically unbound PPP using the PPP observation equations corresponding to satellite subsets is as follows: extract the PPP observation equations corresponding to satellite subsets from the PPP observation equations corresponding to all satellites; and calculate the temporary state solution of the ionospherically unbound PPP based on the antenna file and tidal correction file according to the PPP observation equations corresponding to the satellite subsets.

[0107] In this embodiment, satellites within a qualified satellite subset are selected through geometric distribution. The observation equations (i.e., matrix-form observation equations) corresponding to the pseudorange and carrier phase observations of the ionospheric combination are input into an extended Kalman filter. Based on table files such as antenna files and tidal correction files, a temporary estimate of the receiver state is performed to obtain the temporary state solution of the ionospheric combination PPP (i.e., the parameter vector to be estimated for the ionospheric combination PPP).

[0108] It should also be noted that, due to the limited size of the subset, this temporary state solution is only used as a reference for residual consistency judgment and does not directly participate in the output of the final positioning result.

[0109] This provisional state estimate is used to quickly construct a model solution consistent with a subset of observations, thereby determining whether other satellite observations conform to the same observation model. To improve numerical stability and estimation efficiency, some weakly observable parameters (such as ambiguity or tropospheric delay) can be subject to prior constraints or simplification during this process to reduce ill-posedness caused by insufficient observation dimensions.

[0110] Step S30: Calculate the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites in all satellites according to the temporary state solution.

[0111] In the specific implementation, based on the temporary state solution, the observation residuals of all visible satellites (i.e., the remaining satellites) in the current epoch, excluding this subset, are recalculated according to equation (3). These residuals are the pseudorange observation residuals and carrier phase observation residuals corresponding to each of the remaining satellites. The residuals are used to measure the consistency between each satellite's observations and the current model solution. When a satellite's observations are severely affected by multipath, non-line-of-sight propagation, or gross errors, its residual value is expected to deviate significantly, thus becoming a key basis for subsequent consistency judgment.

[0112] Step S40: Mark the interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual.

[0113] In the specific implementation, to improve the adaptability and robustness of gross error identification, a dynamic threshold discrimination mechanism based on residual normalization was designed. This mechanism fully considers the differences in measurement noise levels from different satellite observations, as well as the dynamic changes in observation quality over time in complex urban environments.

[0114] Further, the measurement noise standard deviations corresponding to the pseudorange observation residuals and carrier phase observation residuals are obtained respectively; the pseudorange observation residuals and carrier phase observation residuals are normalized based on the measurement noise standard deviations to obtain normalized residuals; the sample standard deviation of the normalized residuals is calculated, and a preset discrimination threshold is set according to the sample standard deviations; multiple satellites with pseudorange observation residuals and carrier phase observation residuals that are both less than or equal to the preset discrimination thresholds are selected from the remaining satellites and marked as interior points.

[0115] It should also be noted that there is a corresponding relationship between pseudorange observation residuals and carrier phase observation residuals.

[0116] In practical implementation, the standard deviation of measurement noise for each observation residual is first considered. (This can be calculated based on satellite elevation angle, signal-to-noise ratio, etc.). The remaining satellites, excluding the subset satellites... The pseudorange residuals and phase residuals corresponding to each satellite are collectively denoted as: Normalize according to its noise variance:

[0117]

[0118] Calculate the sample standard deviation of the normalized residuals:

[0119]

[0120] in, Each satellite corresponds to a set of observation residuals with dimensions of 1. Then according to Dynamically set preset discrimination threshold :

[0121]

[0122] in, This is a coefficient, typically taken as 2 to 3, to balance the false negative and false positive rates in gross error detection. When a poor observation environment leads to a higher overall residual level, Increase accordingly, threshold The threshold will be automatically widened; conversely, it will be tightened under normal conditions. This achieves adaptive adjustment of the discrimination threshold, avoiding the potential problems that may arise from using a fixed threshold.

[0123] It should be noted that, in implementation, robust estimates such as median absolute deviation (MAD) can also be used to determine the threshold, in order to reduce the impact of extreme gross errors. The impact of calculations.

[0124] It should also be understood that there is a corresponding relationship between pseudorange observation residuals and carrier phase observation residuals. If the pseudorange observation residuals or carrier phase observation residuals... Then the corresponding satellite observation is determined to be an outlier (outlier), and the satellite is marked as an outlier; if the pseudorange observation residual and the carrier phase observation residual are... If so, the satellite is determined to be an interior point (normal observation with good consistency).

[0125] Step S50: Iteratively sample the satellite subset using the RANSAC algorithm.

[0126] In the specific implementation, steps S10-S40 need to be repeated, and the number of interior point markings and iterations for each satellite needs to be obtained in real time. If the number of satellites with an interior point marking count greater than a preset marking threshold is greater than the preset threshold, and the number of iterations has not reached the preset number, the iteration is terminated. If the number of satellites with an interior point marking count greater than the preset marking threshold is less than or equal to the preset threshold, and the number of iterations has reached the preset number, the iteration is terminated. Both the preset marking threshold and the preset threshold are user-defined settings.

[0127] Step S60: When the iteration terminates, select multiple satellites from all satellites to form an inner point satellite set based on the number of inner point markings corresponding to each satellite, and perform high-precision positioning of the receiver based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

[0128] If the number of satellites with an in-point marking count greater than the preset marking threshold is greater than the preset threshold, and the number of iterations has not reached the preset number, an in-point satellite set is constructed based on the satellites with an in-point marking count greater than the preset marking threshold. If the number of satellites with an in-point marking count greater than the preset marking threshold is less than or equal to the preset threshold, and the number of iterations has reached the preset number, the multiple satellites with an in-point marking count are sorted (sorted in descending order of marking count), and an in-point satellite set is constructed by sequentially selecting a preset number of satellites based on the sorting results.

[0129] Furthermore, based on the antenna file and tidal correction file, state estimation is performed using the extended Kalman filter method according to the PPP observation equation corresponding to the in-point satellite set without ionosphere. This yields the target position correction of the receiver at the current epoch, the residual wet delay in the zenith direction of the troposphere, the receiver clock error, and the ionosphere ambiguity. High-precision positioning of the receiver at the current epoch is then performed based on the target position correction.

[0130] Since the influence of anomalous observations has been eliminated, the solution results will be more accurate and reliable. In the final solution, estimates of certain parameters simplified during the temporary solution can be restored, such as re-estimating tropospheric delay and phase ambiguity with all satellites, to obtain a high-precision solution. The final output is the high-precision positioning result for the current epoch based on RANSAC robust estimation (i.e., receiver position correction, zenith-direction tropospheric residual wet delay, receiver clock error, and ionospheric ambiguity). Then, steps S10 to S60 are repeated for the next epoch. This cycle is repeated to achieve continuous high-precision positioning of a moving receiver. In each epoch, the RANSAC algorithm adaptively identifies and eliminates new gross observations, ensuring that the positioning solution always relies primarily on reliable observations, thereby significantly improving the stability of PPP positioning in dynamic scenarios.

[0131] It should also be noted that the measured and simulation results show that the accuracy and reliability of PPP positioning in urban canyon environments with high-rise buildings are significantly improved compared with traditional methods. It can effectively avoid anomalies in single-epoch positioning solutions and positioning jump phenomena, and has obvious advantages in dynamic high-precision positioning applications.

[0132] In this implementation, firstly, multi-frequency, multi-system GNSS observation data and corresponding precise orbit and clock bias products are acquired, and the PPP observation equation is established and linearized. Then, in the data processing of each epoch, a RANSAC iterative mechanism is introduced: four satellites are randomly selected to form a satellite subset, and the temporary state vector of the current receiver is solved using the selected subset. Based on the obtained state vector, the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites are calculated, and the residual discrimination threshold is dynamically calculated using a standard deviation weighted discrimination strategy to identify out-of-limit gross errors. For the selected subset, a dual screening mechanism of position accuracy factor (PDOP) and condition number is introduced to optimize the satellite geometric distribution: the geometric distribution of a subset is considered acceptable only if both the PDOP value and condition number are within the preset thresholds; otherwise, the subset is discarded and re-randomly sampled. Through multiple iterative sampling evaluations, the satellite subset with the most inliers is selected as the best consistent solution, and multiple detected abnormal satellite observations are eliminated in one go using a global statistical method. Finally, all observation data after removing gross errors are used for PPP calculation to output high-precision position results.

[0133] This embodiment utilizes the random sampling consistency principle of the RANSAC algorithm to simultaneously identify and eliminate multiple anomalous satellite observations with gross errors. It is suitable for urban dynamic scenarios with complex satellite signal environments and multiple gross error interferences, improving the robustness of positioning solutions to interference such as multipath and NLOS. By imposing dual constraints on subset PDOP values ​​and condition numbers, it ensures that the satellite combinations entering the solution have good spatial geometry, enhancing the reliability of the solution results. By employing a standard deviation dynamic threshold discrimination strategy and a global statistical elimination mechanism, it adaptively detects and removes gross error observations in one go, avoiding the inefficient process of traditional iterative elimination of gross errors one by one, which can significantly improve the accuracy, reliability, and solution stability of PPP positioning.

[0134] Reference Figure 3 , Figure 3 This is a structural block diagram of the first embodiment of the high-precision positioning system for receivers based on the RANSAC algorithm of the present invention.

[0135] like Figure 3 As shown, the receiver high-precision positioning system based on the RANSAC algorithm proposed in this embodiment of the invention includes:

[0136] Select module 3001 to construct the ionosphere-free combined PPP observation equations for each satellite observed at the current epoch, and select a preset number of satellites from all satellites to form a satellite subset;

[0137] The calculation module 3002 is used to calculate the temporary state solution based on the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset when the satellite subset satisfies the preset satellite geometric distribution conditions;

[0138] The calculation module 3002 is also used to calculate the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites in all satellites according to the temporary state solution.

[0139] The marking module 3003 is used to mark the interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual;

[0140] Iteration module 3004 is used to iteratively sample the satellite subset using the RANSAC algorithm;

[0141] The positioning module 3005 is used to select multiple satellites from all satellites to form an inner point satellite set according to the number of inner point markings corresponding to each satellite when the iteration terminates, and to perform high-precision positioning of the receiver based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

[0142] Other embodiments or specific implementations of the receiver high-precision positioning system based on the RANSAC algorithm of the present invention can be referred to the above-described method embodiments, and will not be repeated here.

[0143] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or system that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or system. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or system that includes that element.

[0144] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0145] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as read-only memory / random access memory, magnetic disk, optical disk) and includes several instructions to cause a terminal device (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of the present invention.

[0146] The above are merely preferred embodiments of the present invention and do not limit the scope of the patent. Any equivalent structural or procedural transformations made based on the description and drawings of the present invention, or direct or indirect applications in other related technical fields, are similarly included within the scope of patent protection of the present invention.

Claims

1. A high-precision receiver positioning method based on the RANSAC algorithm, characterized in that, The method includes the following steps: Construct PPP observation equations for each satellite observed at the current epoch, and select a predetermined number of satellites from all satellites to form a satellite subset; When the satellite subset satisfies the preset satellite geometric distribution conditions, a temporary state solution is calculated based on the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset. Based on the provisional state solution, calculate the pseudorange observation residuals and carrier phase observation residuals for the remaining satellites within all satellites respectively; The remaining satellites are marked with interior points based on the pseudorange observation residuals and the carrier phase observation residuals; The satellite subset is iteratively sampled using the RANSAC algorithm; When the iteration terminates, multiple satellites are selected from all satellites to form an inner point satellite set based on the number of inner point markings corresponding to each satellite, and the receiver is positioned with high precision based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

2. The method as described in claim 1, characterized in that, Before calculating the temporary state solution based on the PPP observation equations for the ionosphere-free combination corresponding to the satellite subset when the satellite subset satisfies the preset satellite geometric distribution conditions, the process includes: Construct a satellite geometric matrix based on the aforementioned satellite subset; Calculate the position accuracy attenuation factor and matrix condition number based on the satellite geometric matrix; Determine whether the position accuracy attenuation factor value is greater than a preset PDOP threshold, and whether the matrix condition number is greater than a preset condition number threshold; If the position accuracy attenuation factor value is less than or equal to the preset PDOP threshold, and the matrix condition number is less than or equal to the preset condition number threshold, then the satellite subset is determined to satisfy the preset satellite geometric distribution condition.

3. The method as described in claim 2, characterized in that, The construction of the satellite geometric matrix based on the satellite subset includes: Acquire GNSS multi-frequency observation data, precise orbit files, and precise clock error files; The receiver's initial position coordinates, the satellite position coordinates of each satellite in the satellite subset, and the satellite clock bias are extracted from the GNSS multi-frequency observation data, the precise orbit file, and the precise clock bias file, respectively. The satellite geometric matrix is ​​constructed based on the receiver's initial position coordinates, the satellite's position coordinates, and the satellite clock bias.

4. The method as described in claim 3, characterized in that, The calculation of the position accuracy attenuation factor and matrix condition number based on the satellite geometric matrix includes: Calculate the covariance matrix, the square root of the largest eigenvalue, and the square root of the smallest eigenvalue based on the satellite geometric matrix. Extract the receiver's three-dimensional coordinate submatrix from the covariance matrix; Calculate the position accuracy attenuation factor value based on the three-dimensional coordinate submatrix; The matrix condition number of the satellite geometric matrix is ​​calculated based on the square root of the largest eigenvalue and the square root of the smallest eigenvalue.

5. The method as described in claim 1, characterized in that, The calculation of the temporary state solution based on the ionosphere-free combined PPP observation equations corresponding to the satellite subset includes: Extract the PPP observation equations for the satellite subset corresponding to the ionospheric combination of each satellite from the ionospheric combination PPP observation equations corresponding to each satellite; Based on the antenna file and tidal correction file, a temporary state solution is calculated according to the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset. The temporary state solution includes the receiver position correction, the residual wet delay of the troposphere in the zenith direction, the receiver clock error, and the ionosphere-free ambiguity.

6. The method as described in claim 5, characterized in that, The step of calculating the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites within all satellites based on the provisional state solution includes: Extract the PPP observation equations for the remaining satellites within all satellites from the ionosphere-free combination PPP observation equations corresponding to each satellite; Based on the provisional state solution, the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites are calculated according to the ionosphere-free combined PPP observation equations corresponding to the remaining satellites.

7. The method as described in claim 6, characterized in that, The step of marking interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual includes: Obtain the measurement noise standard deviations corresponding to the pseudorange observation residual and the carrier phase observation residual, respectively; The pseudorange observation residual and the carrier phase observation residual are normalized based on the measurement noise standard deviation to obtain the normalized residual. Calculate the sample standard deviation of the normalized residual, and set a preset discrimination threshold based on the sample standard deviation; Multiple satellites from the remaining satellites whose pseudorange observation residuals and carrier phase observation residuals are less than or equal to the preset discrimination threshold are selected for interior point marking.

8. The method as described in claim 7, characterized in that, When the iteration terminates, multiple satellites are selected from all satellites to form an interior point satellite set based on the number of interior point markers corresponding to each satellite, including: Real-time acquisition of the number of interior point markers and iterations for each satellite; If the number of satellites whose inlier point marking count exceeds a preset marking threshold is greater than a preset threshold, and the number of iterations has not reached a preset number, the iteration is terminated. The satellites whose number of inlier markings is greater than a preset marking threshold constitute an inlier satellite set.

9. The method as described in claim 8, characterized in that, The high-precision receiver positioning based on the ionosphere-free combined PPP observation equations corresponding to the in-point satellite set includes: Based on the antenna file and the tidal correction file, the target position correction is obtained by performing state estimation using the extended Kalman filter method according to the ionosphere-free combination PPP observation equation corresponding to the inner point satellite set; The receiver achieves high-precision positioning in the current epoch based on the target position correction.

10. A high-precision positioning system for a receiver based on the RANSAC algorithm, characterized in that, The system includes: The selection module is used to construct the ionosphere-free combined PPP observation equations for each satellite observed at the current epoch, and to select a preset number of satellites from all satellites to form a satellite subset; The calculation module is used to calculate the temporary state solution based on the PPP observation equation for the ionosphere-free combination corresponding to the satellite subset when the satellite subset satisfies the preset satellite geometric distribution conditions; The calculation module is also used to calculate the pseudorange observation residuals and carrier phase observation residuals of the remaining satellites in all satellites according to the temporary state solution. The marking module is used to mark the interior points of the remaining satellites based on the pseudorange observation residual and the carrier phase observation residual; The iteration module is used to iteratively sample the satellite subset using the RANSAC algorithm; The positioning module is used to select multiple satellites from all satellites to form an inner point satellite set based on the number of inner point markings corresponding to each satellite when the iteration terminates, and to perform high-precision positioning of the receiver based on the ionosphere-free combined PPP observation equation corresponding to the inner point satellite set.

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