A network RTK ambiguity real-time checking method based on particle filtering and VMF3-FC troposphere product

Abstract

This invention addresses the pain points of low ambiguity resolution success rate and degraded service performance in network RTK under complex scenarios. Utilizing the high-precision real-time tropospheric product VMF3-FC, combined with the smooth changes in tropospheric variations and the linear relationship between ambiguity particles and satellite observations, a real-time ambiguity correction method for network RTK based on particle filtering and VMF3-FC tropospheric products is proposed. First, the filtering results of baseline resolution are used to predict the value range of ambiguity particles in real time. Then, the high-precision real-time tropospheric product is used to assign weights to all particles within the range, and the optimal floating-point solution is calculated by combining the particle values ​​and weights. Finally, all ambiguities are corrected based on the rounded value of the optimal particle and the geometric constraints of the station network. This method can effectively detect ambiguity errors in the network RTK system and correct them through additional geometric constraints, significantly improving the service performance of network RTK in complex scenarios.

Description

Technical Field

[0001] This invention relates to the field of GNSS ground-based augmentation services, and more particularly to a real-time network RTK ambiguity correction method based on particle filtering and VMF3-FC (Vienna Mapping Function 3 with Frequency Components) tropospheric products. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) provide all-weather, high-precision positioning, navigation, and timing services globally via satellite signals. They are widely used in engineering construction and daily life, serving as an indispensable infrastructure for economic development and social progress. High-precision positioning technologies based on GNSS systems mainly include Real-Time Kinematic (RTK), Precise Point Positioning (PPP), and PPP-RTK. To achieve robust, reliable, and rapid precise positioning, these technologies typically rely on a dense ground reference network. Using the known precise coordinates of reference stations and GNSS observations, they estimate and broadcast regional error correction information in real time to enhance positioning—this is known as a ground-based augmentation system.

[0003] Network-based real-time kinematics (RTK) is a core technology in current ground-based augmentation systems. Primarily operating within a Kalman filter framework, it generates high-precision virtual observations and broadcasts them to users by resolving ambiguities in the station network and regional atmospheric grids, enabling large-scale, high-precision real-time dynamic positioning. However, as network RTK service scenarios become increasingly complex, factors such as ionospheric disturbances and long-baseline spatial errors significantly degrade service performance. Therefore, it is necessary to construct an effective ambiguity checking and correction framework to improve service performance in complex scenarios.

[0004] In network-based real-time kinematics (RTK), reliable fixation of integer ambiguities on the server side is crucial for ensuring high-precision positioning services. Incorrect ambiguity fixation directly introduces decimeter-level errors into the regional atmospheric modeling process, resulting in virtual observations with gross errors and severely impacting user positioning. To improve the success rate of ambiguity fixation in network RTK, some researchers have adopted methods such as adding ionospheric constraints to enhance the accuracy of ambiguity parameter estimation, while also considering the time-varying characteristics of complex space weather in stochastic models. Although this method can effectively mitigate the impact of ionospheric disturbances on ambiguity resolution on the network RTK server side, it cannot guarantee the correctness of the resolution results, nor can it identify unreliable ambiguities in the results.

[0005] Furthermore, constructing indices such as ratio and F-distribution to test the significance of ambiguity candidate groups can avoid incorrect fixation of some ambiguities. However, in practical applications, even if the ambiguity passes the test and meets the network RTK closure condition, errors in baseline ambiguity resolution can still occur, and there is a lack of effective methods to identify such cases.

[0006] In contrast, with fixed station coordinates, tropospheric parameters are more independent, and the time-varying characteristics of the space troposphere are stable. Existing products can achieve centimeter-level accuracy in real-time tropospheric modeling, which is sufficient to serve as a high-precision reference value for checking and evaluating the solution quality of network RTK systems.

[0007] Enhancing the robustness and reliability of network RTK systems, especially in terms of ambiguity accuracy verification and correction, is key to improving their comprehensive service capabilities across various scenarios. Summary of the Invention

[0008] The purpose of this invention is to address the problem of degraded service performance in current network RTK systems due to the lack of effective and reliable ambiguity correction methods. By fully combining the integer characteristics of ambiguity and the advantages of particle filtering discretization, this invention provides a real-time ambiguity correction method for network RTK based on particle filtering and VMF3-FC tropospheric products without affecting the original filtering framework of network RTK, thereby improving the overall service capabilities of network RTK systems.

[0009] This invention combines the integer characteristics of ambiguity with its linear relationship to tropospheric delay, using high-precision tropospheric products as a reference to construct a discretized particle filter ambiguity checking module independent of the network RTK Kalman filter solution framework, which checks the correctness of integer ambiguity in real time. Based on this, it fully considers the random error characteristics of GNSS observations and tropospheric products, provides the reliability of the particle filter checking results, and attempts to correct unreliable results. This allows for further marking of satellite availability without affecting the original filtering system of the network RTK, thereby improving the overall service capability of the network RTK system.

[0010] The technical solution of this invention is as follows:

[0011] A real-time ambiguity detection method for network RTK based on particle filtering and VMF3-FC tropospheric products includes the following steps:

[0012] Step S1: Continuously receive and decode GNSS observation data from each base station in the network RTK, and preprocess the observation data;

[0013] Step S2: Construct a baseline closed loop and perform baseline solution, using Kalman filtering to estimate the ionosphere, troposphere, and ambiguity floating-point solutions in real time;

[0014] Step S3: Obtain the fixed ambiguity solution using the LAMBDA algorithm and update the parameter state of the particle filter. Combine this with the VMF3-FC real-time high-precision tropospheric product to perform a step-by-step ambiguity check from wide lane to narrow lane.

[0015] Step S4: Correct the baseline ambiguity group that fails the check, construct the least squares equations to eliminate the ionosphere and add baseline and tropospheric constraints, and recheck the corrected integer ambiguity.

[0016] Step S1 includes:

[0017] Step S11: Receive raw GNSS data from each base station in the network RTK in real time;

[0018] Step S12: Decode the raw data in RTCM (Radio Technical Commission for Maritime Services) format to initially remove satellite data with severe frequency missingness and unhealthy receiver identifiers;

[0019] Step S13: Preprocess GNSS observation data;

[0020] GNSS observation data preprocessing includes, but is not limited to, monitoring and removing abnormal data, detecting and repairing cycle slips, setting satellite cutoff elevation angles, setting data cutoff signal-to-noise ratios, setting reference satellite selection strategies, and weighting according to elevation angles.

[0021] The formula for determining the elevation angle is as follows:

[0022] (1)

[0023] in, Indicates the first i The elevation angle of the satellite; It is the prior unit weight error; It is the first i The pre-test standard deviation of satellite observations.

[0024] For each GNSS observation data station in the network RTK, perform data preprocessing according to this step.

[0025] Step S2 includes:

[0026] Step S21: Construct a baseline closed loop;

[0027] First, for all reference stations in the network RTK, baseline closure loops are generated using Delaunay triangulation or manually defined methods. Specifically, for a triangulation network consisting of any three reference stations A, B, and C, three baselines "AB", "BC", and "CA" are constructed in a clockwise spatial direction with a "rover-reference station" relationship, satisfying the closure loop condition.

[0028] Step S22: Establish a full-system, full-frequency baseline solution model;

[0029] Baseline calculation employs a station-satellite double-difference model to solve for integer ambiguities, ionospheric, and tropospheric parameters. The coordinates of the reference station are known but not used for parameter estimation. To further clarify the differences between code division multiple access (CDMA) and frequency division multiple access (FDMA) GNSS systems in their calculation models, the inter-station single-difference GNSS observation equations are first given as follows:

[0030] (2a)

[0031] (2b)

[0032] Among them, superscript and subscript These represent satellite, frequency, base station, and rover, respectively. These represent the inter-station single-difference carrier phase and pseudorange observations after model correction, in meters; These represent the residual tropospheric delay and ionospheric delay of the single-difference inter-station difference, respectively. ,in Representing frequency ; These represent the inter-station single-difference phase and pseudorange receiver clock difference at the receiver end, respectively; This indicates the hardware delay of the single-difference phase between stations; This indicates the hardware delay of the single-difference pseudorange between stations; Indicates wavelength; Indicates the integer ambiguity of the single difference between stations; and These represent the observation noise of the inter-station single-difference phase and pseudorange, respectively.

[0033] For code division multiple access (CDMA) systems, the frequencies of satellite data at the same frequency point are completely consistent. Therefore, the phase and pseudorange hardware delays at the receiver end are eliminated during inter-satellite differential calculation. Thus, the baseline solution model for a CDMA system can be obtained as follows:

[0034] (3a)

[0035] (3b)

[0036] Among them, superscript Indicates connection with satellite For the other satellite undergoing inter-satellite difference, the remaining parameters are defined as the same double difference as in equation (2).

[0037] For frequency division multiple access (FDMA) systems, satellite data at the same frequency point exhibits a linear relationship with the satellite number in terms of frequency, therefore, the phase and pseudorange hardware delays at the receiver cannot be completely eliminated. Furthermore, due to frequency differences, the wavelength coefficients before the ambiguity parameters differ, leading to the following baseline solution model for the FDMA system:

[0038] (4a)

[0039] (4b)

[0040] To further express the ambiguity parameter in double-difference form, equation (4a) can be rewritten as:

[0041] (5)

[0042] Among them, single-difference ambiguity It can be roughly calculated directly from phase and pseudorange observations. Considering the small differences between different satellite wavelengths, the error in single-difference ambiguity does not affect the error in double-difference ambiguity. The solution is as follows. Furthermore, existing research indicates that the inter-frequency deviation of the phase hardware delay is extremely small and its impact on ambiguity can be ignored. For similar receivers, the inter-frequency deviation of the pseudorange hardware delay can also be ignored.

[0043] Step S23: Estimate the floating-point solution of the parameters;

[0044] The station coordinates of the fixed base station and rover are used to solve the floating-point solutions for the double-difference ionosphere, residual troposphere, and ambiguity parameters for each epoch using Kalman filtering; in the frequency division multiple access system, the pseudorange observations are first weighted down before solving.

[0045] Step S3 includes:

[0046] Step S31: Calculation of fuzziness between "wide alley" and "narrow alley";

[0047] First, construct the wide-lane fuzziness. The transformation matrix is ​​used, and the wide-lane ambiguity floating-point solution and covariance matrix are calculated based on the information from the Kalman filter in step S23. The calculation method is existing technology.

[0048] To facilitate subsequent ambiguity checking and correction, the wide-lane ambiguity floating-point solution for the [1,-1] combination was calculated using data from two different frequency bands, along with its corresponding covariance matrix. The wavelength of the wide-lane ambiguity for the [1,-1] combination is approximately 0.8 m, significantly larger than that of the narrow-lane ambiguity. Therefore, it exhibits higher tolerance for spatial errors and is more likely to yield correct integer ambiguity values. Considering the high accuracy of the filtered floating-point solution under the geometric model, a ambiguity screening strategy with controllable failure probability and the LAMBDA algorithm were employed to obtain a fixed solution for the wide-lane ambiguity based on the wide-lane ambiguity floating-point solution and the covariance matrix.

[0049] For narrow-lane ambiguity, it can be directly determined from the floating-point solution of the narrow-lane ambiguity in the Kalman filter. The covariance matrix is ​​calculated using the LAMBDA algorithm to obtain integer values ​​for all satellite ambiguities, which are then fed into the particle filter to update the ambiguity particle states and perform correctness checks on the ambiguity particles. The operational details of the particle filter will be described in sections S33-S34.

[0050] Step S32: Perform wide-lane ambiguity check on a satellite-by-satellite basis;

[0051] Wide-lane ambiguities are characterized by long wavelengths and high resolution success rates, and once successfully resolved, they can be used as constraints to assist in narrow-lane ambiguity resolution. However, due to non-modeling errors, some wide-lane ambiguities in baselines "AB", "BC", and "CA" are affected. , and Although the baseline loop closure condition is met However, there are still cases of calculation errors. In order to prevent incorrect wide-lane ambiguity from affecting the narrow-lane ambiguity calculation, it is necessary to check the integer values ​​of the wide-lane ambiguity obtained in S31.

[0052] The real-time inversion equation for the troposphere, which eliminates the ionosphere, is constructed as follows:

[0053] (6)

[0054] in, This is a double-difference slant path tropospheric delay; For the BeiDou / GNSS system, there are two different frequencies; These are combined observations of phase deionization. The floating-point solution for the double-difference ambiguity at the first frequency point; It is an integer solution for the double-difference wide-lane ambiguity.

[0055] Using the VMF3-FC high-precision real-time tropospheric product as a reference, and considering that the influence of the erroneous wide-lane ambiguity on the troposphere in equation (6) is approximately 0.5 m, while the accuracy of the VMF3-FC real-time tropospheric product can reach 0.01 m, the success of the wide-lane ambiguity resolution is determined by calculating the degree of conformity between the tropospheric delay of the three baselines and the VMF3-FC product. For the triangulation "ABC", the formula for calculating the degree of conformity of the tropospheric delay is as follows:

[0056] (7)

[0057] in, This serves as a reference value for the tropospheric delay. It is important to note that the accuracy of the double-difference ambiguity floating-point solution at the first frequency point should be as high as possible to avoid significant discrepancies with the integer solution, which could lead to large deviations in the tropospheric inversion values.

[0058] If the wide-lane ambiguity in the baseline loop satisfies the closed-loop condition, and If m is correct, the wide-lane ambiguity is considered correct, and step S33 continues. If the wide-lane ambiguity fails the check, the wide-lane ambiguity correction method in step S4 is used to correct it.

[0059] Step S33: Update the narrow alley ambiguity particle filter parameter state;

[0060] Based on the ambiguity integer value provided in step S31 Integer ambiguity values ​​inherited from the previous epoch of the particle filter Determine the particle sampling range and weights for the current epoch. Typically, the ambiguity integer value provided in step S31... The value is either very close to or equal to the correct value, therefore the sampling range can be controlled within ±10 cycles of the initial value, with a sampling interval of 1 cycle. If it is the first epoch or a cycle slip occurs, the particle sampling range is initialized to... Otherwise, the particle sampling range depends on and Update, take the union of them. The total number of particles is Furthermore, since the integer values ​​of the wide-lane ambiguity have been reliably determined, only the one-dimensional particle filter needs to be updated to perform narrow-lane ambiguity checks, effectively avoiding the problem of reduced computational efficiency in two-dimensional / multi-dimensional cases.

[0061] The weights of all particles within the current epoch's downsampling range are further determined. Combining historical weight information, the particle weighting formula is as follows:

[0062] (8)

[0063] (9)

[0064] in, For particles In the calendar The weights below; For observations The conditional likelihood function; The normalized particle weights are used. Considering the correlation between ambiguity and ionospheric parameters, the likelihood function cannot be determined by the relationship between the observation residual and ambiguity. Therefore, an external high-precision tropospheric model is introduced as a reference. VMF3-FC is a real-time tropospheric product generated based on a numerical weather model, with an accuracy of 0.01 m in the zenith direction. The tropospheric delay retrieved from GNSS observations responds to ambiguity errors of about 0.1 m for 1 week. Therefore, VMF3-FC products can be used to check erroneous ambiguities in network RTK. The conditional likelihood function in equation (8) is defined and replaced based on the difference between the tropospheric model value and the retrieved value. Its normalized form is as follows:

[0065] (10)

[0066] in, and These are the correct fuzziness and the fuzzy particle, respectively, with subscripts. For the calendar year, Indicates the particle order; The tropospheric reference value calculated for the VMF3-FC product; Based on GNSS observations and ambiguity particles The inverted tropospheric values ​​are calculated as follows:

[0067] (11)

[0068] in, This represents the double-difference deionized ionospheric phase observation, in meters; For narrow alley ambiguity integer particles; The ambiguity of the fixed wide alleyway.

[0069] Step S34: Narrow alleyway ambiguity check;

[0070] As shown in equation (11), the GNSS inversion result of the troposphere is proportional to the narrow-lane ambiguity particles. The closer the inversion value matches the reference value, the greater the likelihood that the narrow-lane ambiguity particles are correct. Combining the particle values ​​and weights given in step S33, the particle estimate is calculated. ,variance and decimal deviation for:

[0071] (12)

[0072] (13)

[0073] (14)

[0074] in, Indicates rounding down.

[0075] like 0.3 weeks and At 0.2 weeks, considering the integer property of ambiguity, particle estimation can be directly performed. Rounding down yields the nearest integer value. Additionally, if the rounded value of the particle estimate matches the fixed LAMBDA solution of the Kalman filter, and satisfies... If the closed loop condition is met, then the narrow alley ambiguity is considered to have passed the check.

[0076] If the check is not passed, Greater than 0.3 weeks or If the error is greater than 0.2 weeks, then in step S4, we will attempt to correct the ambiguity of the wide alley and the narrow alley sequentially.

[0077] Step S4 includes:

[0078] Step S41: Wide lane ambiguity correction;

[0079] For the wide-lane ambiguity that failed the loop test in step S32, its correct integer value is... Within the range. Accordingly, any two baselines in the baseline loop are selected, and the possible values ​​of the wide-lane ambiguity of the two baselines are iterated. The wide-lane ambiguity of the third baseline is calculated based on the baseline loop closure condition, resulting in a candidate group of wide-lane ambiguity combinations for the baseline loop. To avoid introducing incorrect wide-lane ambiguity values ​​during the enumeration process, the selection criteria in step S32 are used to screen those that meet the requirements. The minimum wide-lane ambiguity combination is used as the final correction value.

[0080] Step S42: Narrow alleyway ambiguity correction;

[0081] Narrow alleyway ambiguity correction includes two sub-steps:

[0082] Step S421, for satellites whose wide-lane ambiguity fails the check, completes step S33 using the corrected wide-lane ambiguity, i.e., checking the narrow-lane ambiguity. If the check conditions in S33 are met, the narrow-lane ambiguity is considered reliably fixed and can be used to generate virtual observations.

[0083] Step S422 further addresses the issue of narrow-lane ambiguity in the particle filter failing to meet the baseline loop ambiguity closure condition or exhibiting excessive variance. GNSS observations and VMF3-FC products contain elevation-angle-related random errors; these errors are more significant at lower satellite elevation angles, leading to biases in the likelihood function in step S33 and degrading the particle filter's performance. To ensure effective verification and avoid the impact of potential errors, a least-squares method with additional geometric constraints is used to adjust the particle filter's parameter estimates, as shown in the following formula:

[0084] (15)

[0085] in, For phase-free ionospheric composite observations under different baselines (“AB”, “BC”, and “CA”), after correcting the width-lane ambiguity, Tropospheric reference values ​​calculated for VMF3-FC products under different baselines. Narrow-lane ambiguity for the first frequency phase data under different baselines. For observation noise, superscript These represent satellite and differential satellite, respectively. Closed-loop constraints and tropospheric model constraints were applied to the ambiguity and tropospheric parameters, respectively, while also considering the error characteristics of GNSS observations and VMF3-FC products. If the narrow-lane ambiguity estimate deviation exceeds 0.3 cycles at a certain moment, the satellite narrow-lane ambiguity is considered unreliable, requiring long-term Kalman filtering to improve the floating-point solution accuracy.

[0086] Step S43: Update the particle filter correction results to the Kalman filter;

[0087] The final result of the current particle filter will serve as a decision reference for the Kalman filter and the entire network RTK system. Ambiguities that fail the check and cannot be successfully corrected will be marked as unavailable, and the duration of their unavailability will be recorded in order to reset the filter parameters of satellites that have been unavailable for a long time (more than 20 epochs).

[0088] For each subsequent epoch, execute S3-S4 until all data has been solved.

[0089] Beneficial effects

[0090] In summary, this invention presents a real-time ambiguity correction method for network RTK based on particle filtering and VMF3-FC tropospheric products. It fully integrates the integer characteristics of ambiguity and utilizes high-precision tropospheric products as a reference to establish a real-time particle filter verification method for ambiguity accuracy. Simultaneously, it fully considers the random error characteristics of GNSS observations and tropospheric products, provides the reliability of the particle filter verification results, and attempts to correct unreliable results, thereby improving the overall service capability of the network RTK system.

[0091] Specifically, compared with the prior art, the present invention has the following advantages:

[0092] Existing network RTK systems typically employ additional ionospheric constraints to improve the accuracy of ambiguity parameter estimation and utilize metrics such as ratio and F-distribution to examine the significance of ambiguity candidate groups, thereby increasing the success rate of ambiguity resolution. However, for cases where the network RTK closed-loop condition is met but baseline ambiguity resolution is incorrect, effective verification and correction methods are still lacking. Reliable fixation of network RTK ambiguities is crucial for ensuring positioning service quality; identifying erroneous values ​​in the resolution results requires the introduction of high-precision external references. This invention leverages the stable time-varying characteristics of the troposphere and utilizes the VMF3-FC high-precision real-time tropospheric product to construct a real-time ambiguity verification and correction system for network RTK. Without affecting the original filter, it effectively identifies unreliable ambiguities in the resolution process and attempts to correct them, significantly improving the comprehensive service capabilities of the network RTK system in various scenarios. Attached Figure Description

[0093] Figure 1 This is a schematic diagram of the real-time ambiguity detection method for network RTK based on particle filtering and VMF3-FC tropospheric products according to the present invention. Detailed Implementation

[0094] The specific embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. The advantages and features of the present invention will become clearer from the following description and claims.

[0095] refer to Figure 1 In a preferred embodiment of the present invention, a network RTK ambiguity real-time correction method based on particle filtering and VMF3-FC tropospheric products includes:

[0096] Step S1: Continuously receive and decode GNSS observation data from each base station in the network RTK, and preprocess the observation data;

[0097] Specifically, step S1 includes:

[0098] Step S11: Receive raw GNSS data from each base station in the network RTK in real time;

[0099] Step S12: Decode the raw RTCM format data and initially remove satellite data with severe frequency missing and unhealthy receiver identifiers;

[0100] Step S13: Preprocess GNSS observation data;

[0101] GNSS observation data preprocessing includes, but is not limited to, monitoring and removing abnormal data, detecting and repairing cycle slips, setting satellite cutoff elevation angles, setting data cutoff signal-to-noise ratios, setting reference satellite selection strategies, and weighting according to elevation angles.

[0102] The formula for determining the elevation angle is as follows:

[0103] (1)

[0104] in, Indicates the first i The elevation angle of the satellite; It is the prior unit weight error; It is the first i The pre-test standard deviation of each satellite observation. For GNSS observation data from all base stations in the network RTK, perform data preprocessing according to this step.

[0105] Step S2: Construct a baseline closed loop and perform baseline solution, using Kalman filtering to estimate the ionosphere, troposphere, and ambiguity floating-point solutions in real time;

[0106] Specifically, step S2 includes:

[0107] Step S21: Construct a baseline closed loop;

[0108] First, for all reference stations in the network RTK, baseline closure loops are generated using Delaunay triangulation or manually defined methods. For a triangulation network consisting of any three reference stations A, B, and C, three baseline relationships, “AB”, “BC”, and “CA”, are constructed in a clockwise spatial direction according to the “rover-reference station” relationship, satisfying the closure loop condition.

[0109] Step S22: Establish a full-system, full-frequency baseline solution model;

[0110] Typically, baseline resolution uses a station-satellite double-difference model to solve for integer ambiguities, ionospheric, and tropospheric parameters, with the reference station coordinates known but not used for parameter estimation. To further clarify the differences between code division multiple access (CDMA) and frequency division multiple access (FDMA) GNSS systems in their resolution models, the inter-station single-difference GNSS observation equation is first given as follows:

[0111] (2a)

[0112] (2b)

[0113] Among them, superscript and subscript These represent satellite, frequency, base station, and rover, respectively. These represent the inter-station single-difference carrier phase and pseudorange observations after model correction, in meters; These represent the residual tropospheric delay and ionospheric delay of the single-difference inter-station difference, respectively. ,in Representing frequency ; These represent the inter-station single-difference phase and pseudorange receiver clock difference at the receiver end, respectively; This indicates the hardware delay of the single-difference phase between stations; This indicates the hardware delay of the single-difference pseudorange between stations; Indicates wavelength; Indicates the integer ambiguity of the single difference between stations; and These represent the observation noise of the inter-station single-difference phase and pseudorange, respectively.

[0114] For code division multiple access (CDMA) systems, the frequencies of satellite data at the same frequency point are completely consistent. Therefore, the phase and pseudorange hardware delays at the receiver end are eliminated during inter-satellite differential calculation. Thus, the baseline solution model for a CDMA system can be obtained as follows:

[0115] (3a)

[0116] (3b)

[0117] Among them, superscript Indicates connection with satellite For the other satellite undergoing inter-satellite difference, the remaining parameters are defined as the same double difference as in equation (2).

[0118] For frequency division multiple access (FDMA) systems, satellite data at the same frequency point exhibits a linear relationship with the satellite number in terms of frequency, therefore, the phase and pseudorange hardware delays at the receiver cannot be completely eliminated. Furthermore, due to frequency differences, the wavelength coefficients before the ambiguity parameters differ, leading to the following baseline solution model for the FDMA system:

[0119] (4a)

[0120] (4b)

[0121] To further express the ambiguity parameter in double-difference form, equation (4a) can be rewritten as:

[0122] (5)

[0123] Among them, single-difference ambiguity It can be roughly calculated directly from phase and pseudorange observations. Considering the small differences between different satellite wavelengths, the error in single-difference ambiguity does not affect the error in double-difference ambiguity. The solution is as follows. Furthermore, existing research indicates that the inter-frequency deviation of the phase hardware delay is extremely small and its impact on ambiguity can be ignored. For similar receivers, the inter-frequency deviation of the pseudorange hardware delay can also be ignored.

[0124] Step S23: Estimate the floating-point solution of the parameters;

[0125] The station coordinates of the fixed base station and rover are used to solve the floating-point solutions for the double-difference ionosphere, residual troposphere, and ambiguity parameters for each epoch using Kalman filtering; in the frequency division multiple access system, the pseudorange observations are first weighted down before solving.

[0126] Step S3: Obtain the fixed ambiguity solution using the LAMBDA algorithm and update the parameter state of the particle filter. Combine this with the VMF3-FC real-time high-precision tropospheric product to perform a step-by-step ambiguity check from wide lane to narrow lane.

[0127] Specifically, step S3 includes:

[0128] Step S31: Calculation of fuzziness between "wide alley" and "narrow alley";

[0129] First, construct the wide-lane fuzziness. The transformation matrix is ​​used, and the wide-lane ambiguity floating-point solution and covariance matrix are calculated based on the information from the Kalman filter in step S23. The calculation method is existing technology.

[0130] To facilitate subsequent ambiguity checking and correction, the wide-lane ambiguity floating-point solution for the [1,-1] combination was calculated using data from two different frequency bands, along with its corresponding covariance matrix. The wavelength of the wide-lane ambiguity for the [1,-1] combination is approximately 0.8 m, significantly longer than that of the narrow-lane ambiguity. Therefore, it exhibits higher tolerance for spatial errors and is more likely to yield correct integer ambiguity values. Considering the high accuracy of the filtered floating-point solution under the geometric model, a ambiguity screening strategy with controllable failure probability and the LAMBDA algorithm were employed to obtain a fixed solution for the wide-lane ambiguity based on the wide-lane ambiguity floating-point solution and the covariance matrix.

[0131] For narrow-lane ambiguity, it can be directly determined from the floating-point solution of the narrow-lane ambiguity in the Kalman filter. The covariance matrix is ​​calculated using the LAMBDA algorithm to obtain integer values ​​for all satellite ambiguities, which are then fed into the particle filter to update the ambiguity particle states and perform correctness checks on the ambiguity particles. The operational details of the particle filter will be described in sections S33-S34.

[0132] Step S32: Perform wide-lane ambiguity check on a satellite-by-satellite basis;

[0133] Wide-lane ambiguities are characterized by long wavelengths and high resolution success rates, and once successfully resolved, they can be used as constraints to assist in narrow-lane ambiguity resolution. However, due to non-modeling errors, some wide-lane ambiguities in baselines "AB", "BC", and "CA" are affected. , and Although the baseline loop closure condition is met However, there are still cases of calculation errors. In order to prevent incorrect wide-lane ambiguity from affecting the narrow-lane ambiguity calculation, it is necessary to check the integer values ​​of the wide-lane ambiguity obtained in S31.

[0134] Using the VMF3-FC high-precision real-time tropospheric product as a reference, the real-time tropospheric inversion equation without ionosphere is constructed as follows:

[0135] (6)

[0136] in, This is a double-difference slant path tropospheric delay; For the BeiDou / GNSS system, there are two different frequencies; These are combined observations of phase deionization. The floating-point solution for the double-difference ambiguity at the first frequency point; It is an integer solution for the double-difference wide-lane ambiguity.

[0137] Considering that the influence of the erroneous wide-lane ambiguity on the troposphere in equation (6) is approximately 0.5 m, while the accuracy of the VMF3-FC real-time tropospheric product can reach 0.01 m, the success of the wide-lane ambiguity resolution is determined by calculating the degree of conformity between the tropospheric delay of the three baselines and the VMF3-FC product. For the triangulated network "ABC", the formula for calculating the degree of conformity of the tropospheric delay is as follows:

[0138] (7)

[0139] in, This serves as a reference value for the tropospheric delay. It is important to note that the accuracy of the double-difference ambiguity floating-point solution at the first frequency point should be as high as possible to avoid significant discrepancies with the integer solution, which could lead to large deviations in the tropospheric inversion values.

[0140] If the wide-lane ambiguity in the baseline loop satisfies the closed-loop condition, and If m is correct, then the wide-lane ambiguity is considered correct, and step S33 is performed. If the wide-lane ambiguity fails the check, an attempt is made to correct it; the correction method will be described in detail in S4.

[0141] Step S33: Update the narrow alley ambiguity particle filter parameter state;

[0142] Based on the ambiguity integer value provided in step S31 Integer ambiguity values ​​inherited from the previous epoch of the particle filter Determine the particle sampling range and weights for the current epoch. Typically, the ambiguity integer value provided in step S31... The value is either very close to or equal to the correct value, therefore the sampling range can be controlled within ±10 cycles of the initial value, with a sampling interval of 1 cycle. If it is the first epoch or a cycle slip occurs, the particle sampling range is initialized to... Otherwise, the particle sampling range depends on and Update, take the union of them. The total number of particles is Furthermore, since the integer values ​​of the wide-lane ambiguity have been reliably determined, only the one-dimensional particle filter needs to be updated to perform narrow-lane ambiguity checking, effectively avoiding the problem of reduced computational efficiency in two-dimensional / multi-dimensional cases.

[0143] The weights of all particles within the current epoch's downsampling range are further determined. Combining historical weight information, the particle weighting formula is as follows:

[0144] (8)

[0145] (9)

[0146] in, For particles In the calendar The weights below; For observations The conditional likelihood function; The normalized particle weights are used. Considering the correlation between ambiguity and ionospheric parameters, the likelihood function cannot be determined by the relationship between the observation residual and ambiguity. Therefore, an external high-precision tropospheric model is introduced as a reference. VMF3-FC is a real-time tropospheric product generated based on a numerical weather model, with an accuracy of 0.01 m in the zenith direction. The tropospheric delay retrieved from GNSS observations responds to ambiguity errors of about 0.1 m for 1 week. Therefore, VMF3-FC products can be used to check erroneous ambiguities in network RTK. The conditional likelihood function in equation (8) is defined and replaced based on the difference between the tropospheric model value and the retrieved value. Its normalized form is as follows:

[0147] (10)

[0148] in, and These are the correct fuzziness and the fuzzy particle, respectively, with subscripts. For the calendar year, Indicates the particle order; The tropospheric reference value calculated for the VMF3-FC product; Based on GNSS observations and ambiguity particles The inverted tropospheric values ​​are calculated as follows:

[0149] (11)

[0150] in, This represents the double-difference deionized ionospheric phase observation, in meters; For narrow alley ambiguity integer particles; The ambiguity of the fixed wide alleyway.

[0151] Step S34: Narrow alleyway ambiguity check;

[0152] As shown in equation (11), the GNSS inversion result of the troposphere is proportional to the narrow-lane ambiguity particles. The closer the inversion value matches the reference value, the greater the likelihood that the narrow-lane ambiguity particles are correct. Combining the particle values ​​and weights given in step S33, the particle estimate is calculated. ,variance and decimal deviation for:

[0153] (12)

[0154] (13)

[0155] (14)

[0156] in, Indicates rounding down.

[0157] like 0.3 weeks and At 0.2 weeks, considering the integer property of ambiguity, particle estimation can be directly performed. Rounding down yields the nearest integer value. Additionally, if the rounded value of the particle estimate matches the fixed LAMBDA solution of the Kalman filter, and satisfies... If the closed loop condition is met, then the narrow alley ambiguity is considered to have passed the check.

[0158] If the check is not passed, Greater than 0.3 weeks or If the error is greater than 0.2 weeks, then in step S4, we will attempt to correct the ambiguity of the wide alley and the narrow alley sequentially.

[0159] Step S4: Correct the baseline ambiguity group that fails the check, construct the least squares equations to eliminate the ionosphere and add baseline and tropospheric constraints, and recheck the corrected integer ambiguity.

[0160] Specifically, step S4 includes:

[0161] Step S41: Wide lane ambiguity correction;

[0162] For the wide-lane ambiguity that failed the loop test in step S32, its correct integer value is... Within the range. Accordingly, any two baselines in the baseline loop are selected, and the possible values ​​of the wide-lane ambiguity of the two baselines are iterated. The wide-lane ambiguity of the third baseline is calculated based on the baseline loop closure condition, resulting in a candidate group of wide-lane ambiguity combinations for the baseline loop. To avoid introducing incorrect wide-lane ambiguity values ​​during the enumeration process, the selection criteria in step S32 are used to screen those that meet the requirements. The minimum wide-lane ambiguity combination is used as the final correction value.

[0163] Step S42: Narrow alleyway ambiguity correction;

[0164] Narrow alleyway ambiguity correction includes two sub-steps:

[0165] Step S421 primarily targets satellites whose wide-lane ambiguity fails the check. It uses the corrected wide-lane ambiguity to complete step S33, which checks the narrow-lane ambiguity. If the check conditions in S33 are met, the narrow-lane ambiguity is considered reliably fixed and can be used to generate virtual observations.

[0166] Step S422 further addresses the issue of narrow-lane ambiguity in the particle filter failing to meet the baseline loop ambiguity closure condition or exhibiting excessive variance. GNSS observations and VMF3-FC products contain elevation-angle-related random errors; these errors are more significant at lower satellite elevation angles, leading to biases in the likelihood function in step S33 and degrading the particle filter's performance. To ensure effective verification and avoid the impact of potential errors, a least-squares method with additional geometric constraints is used to adjust the particle filter's parameter estimates, as shown in the following formula:

[0167] (15)

[0168] in, For phase-free ionospheric composite observations under different baselines (“AB”, “BC”, and “CA”), after correcting the width-lane ambiguity, Tropospheric reference values ​​calculated for VMF3-FC products under different baselines. Narrow-lane ambiguity for the first frequency phase data under different baselines. For observation noise, superscript These represent the satellite and the differential satellite, respectively. Closed-loop constraints and tropospheric model constraints were applied to the ambiguity and tropospheric parameters, respectively, while also considering the error characteristics of GNSS observations and VMF3-FC products. If the narrow-lane ambiguity estimate deviation is greater than 0.3 cycles at a certain moment, the narrow-lane ambiguity of that satellite is considered unreliable, and long-term Kalman filtering is required to improve the accuracy of the floating-point solution.

[0169] Step S43: Update the particle filter correction results to the Kalman filter;

[0170] The final result of the current particle filter will serve as a decision reference for the Kalman filter and the entire network RTK system. Ambiguities that fail the check and cannot be successfully corrected will be marked as unavailable, and the duration of their unavailability will be recorded in order to reset the filter parameters of satellites that have been unavailable for a long time (more than 20 epochs).

[0171] For each subsequent epoch, execute S3-S4 until all data has been solved.

[0172] In summary, this invention presents a real-time ambiguity correction method for network RTK based on particle filtering and VMF3-FC tropospheric products. It fully integrates the integer characteristics of ambiguity and utilizes high-precision tropospheric products as a reference to establish a real-time particle filter verification method for ambiguity accuracy. Simultaneously, it fully considers the random error characteristics of GNSS observations and tropospheric products, provides the reliability of the particle filter verification results, and attempts to correct unreliable results, thereby improving the overall service capability of the network RTK system.

[0173] Specifically, compared with the prior art, the present invention has the following advantages:

[0174] Existing network RTK systems typically employ additional ionospheric constraints to improve the accuracy of ambiguity parameter estimation and utilize metrics such as ratio and F-distribution to examine the significance of ambiguity candidate groups, thereby increasing the success rate of ambiguity resolution. However, for cases where the network RTK closed-loop condition is met but baseline ambiguity resolution is incorrect, effective verification and correction methods are still lacking. Reliable fixation of network RTK ambiguities is crucial for ensuring positioning service quality; identifying erroneous values ​​in the resolution results requires the introduction of high-precision external references. This invention leverages the stable time-varying characteristics of the troposphere and utilizes the VMF3-FC high-precision real-time tropospheric product to construct a real-time ambiguity verification and correction system for network RTK. Without affecting the original filter, it effectively identifies unreliable ambiguities in the resolution process and attempts to correct them, significantly improving the comprehensive service capabilities of the network RTK system in various scenarios.

[0175] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A real-time ambiguity detection method for network RTK based on particle filtering and VMF3-FC tropospheric products, characterized in that, Includes the following steps: Step S1: Continuously receive and decode GNSS observation data from each base station in the network RTK, and preprocess the observation data; Step S2: Construct a baseline closed loop and perform baseline solution, using Kalman filtering to estimate the ionosphere, troposphere, and ambiguity floating-point solutions in real time; Step S3: Use the LAMBDA algorithm to obtain the fixed ambiguity solution and update the parameter state of the particle filter; combine the VMF3-FC real-time high-precision tropospheric product to perform "wide-lane-narrow-lane" ambiguity step-by-step check; Step S4: Correct the baseline ambiguity group that fails the check, construct the least squares equations to eliminate the ionosphere and add baseline and tropospheric constraints, and recheck the corrected integer ambiguity.

2. The method as described in claim 1, characterized in that, Step S1 includes: Step S11: Receive raw GNSS data from each base station in the network RTK in real time; Step S12: Decode the raw RTCM format data and initially remove satellite data with severe frequency missing and unhealthy receiver identifiers; Step S13: Preprocess GNSS observation data; GNSS observation data preprocessing includes monitoring and removing abnormal data, detecting and repairing cycle slips, setting satellite cutoff elevation angles, setting data cutoff signal-to-noise ratios, setting reference satellite selection strategies, and weighting according to elevation angles. The formula for determining the elevation angle is as follows: (1) in, Indicates the first i The elevation angle of the satellite; It is the prior unit weight error; It is the first i The pre-test standard deviation of satellite observations; For each GNSS observation data station in the network RTK, perform data preprocessing according to this step.

3. The method as described in claim 1, characterized in that, Step S2 includes: Step S21: Construct a baseline closed loop; First, for all reference stations in the network RTK, baseline closure loops are generated using Delaunay triangulation or manual definition. Specifically, for a triangular network consisting of any three reference stations A, B, and C, three baselines "AB", "BC", and "CA" are constructed in a clockwise direction in space with a "rover-reference station" relationship to satisfy the closure loop condition. Step S22: Establish a full-system, full-frequency baseline solution model; The baseline solution uses a station-satellite double-difference model to solve for integer ambiguity, ionospheric and tropospheric parameters. The coordinates of the reference station are known and are not used as parameter estimates. The equation for single-difference GNSS observations between stations is given first as follows: (2a) (2b) Among them, superscript and subscript These represent satellite, frequency, base station, and rover, respectively. These represent the inter-station single-difference carrier phase and pseudorange observations after model correction, in meters; These represent the residual tropospheric delay and ionospheric delay of the single-difference inter-station difference, respectively. ,in Representing frequency ; These represent the inter-station single-difference phase and pseudorange receiver clock difference at the receiver end, respectively; This indicates the hardware delay of the single-difference phase between stations; This indicates the hardware delay of the single-difference pseudorange between stations; Indicates wavelength; Indicates the integer ambiguity of the single difference between stations; and These represent the observation noise of the inter-station single-difference phase and pseudorange, respectively; For code division multiple access systems, the baseline solution model is: (3a) (3b) Among them, superscript For the difference star, the remaining parameters are defined as double difference as in equation (2); For frequency division multiple access systems, the baseline solution model is: (4a) (4b) Equation (4a) can be rewritten as: (5) Among them, single-difference ambiguity Calculated from phase and pseudorange observations; Step S23: Estimate the floating-point solution of the parameters; The station coordinates of the fixed base station and rover are used to solve the floating-point solutions for estimating the double-difference ionosphere, residual troposphere, and ambiguity parameters at each epoch using Kalman filtering; in the frequency division multiple access system, the pseudorange observations are first weighted down before solving.

4. The network RTK ambiguity real-time correction method based on particle filtering and VMF3-FC tropospheric products as described in claim 3, characterized in that, Step S3 includes: Step S31: Solving the ambiguity between the "wide alley" and "narrow alley"; First, construct the wide-lane fuzziness. Transform the matrix, and calculate the wide-lane ambiguity floating-point solution and covariance matrix based on the information from the Kalman filter in step S23; The wide-lane ambiguity floating-point solution of the [1,-1] combination is calculated using two different frequency band data, and its corresponding covariance matrix is ​​also calculated. For narrow-lane ambiguity, the floating-point solution of narrow-lane ambiguity in the Kalman filter is used directly. The covariance matrix is ​​calculated using the LAMBDA algorithm to calculate the integer values ​​of all satellite ambiguities, and then fed into the particle filter to update the ambiguity particle state and perform ambiguity particle correctness checks. Step S32: Perform wide-lane ambiguity check on a satellite-by-satellite basis; The real-time inversion equation for the troposphere, which eliminates the ionosphere, is constructed as follows: (6) in, This is a double-difference slant path tropospheric delay; For the BeiDou / GNSS system, there are two different frequencies; These are combined observations of phase deionization. The floating-point solution for the double-difference ambiguity at the first frequency point; For the double-difference wide-lane ambiguity integer solution; The VMF3-FC high-precision real-time tropospheric product is introduced as a reference. The success of wide-lane ambiguity resolution is determined by calculating the degree of conformity between the tropospheric delay of the three baselines and the VMF3-FC product. For the triangular network "ABC", the formula for calculating the degree of agreement of the tropospheric delay is as follows: (7) in, This is a reference value for the tropospheric delay. If the wide-lane ambiguity in the baseline loop satisfies the closed-loop condition, and If m, then the wide alley ambiguity is considered correct, and step S33 continues; if the wide alley ambiguity fails the check, then step S4 wide alley ambiguity correction method is used to correct it. Step S33: Update the narrow alley ambiguity particle filter parameter state; Based on the ambiguity integer value provided in step S31 Integer value of ambiguity inherited from the previous epoch of the particle filter The particle sampling range and weights for the current epoch are determined, with the sampling range controlled within ±10 cycles of the initial value and a sampling interval of 1 cycle. If it is the first epoch or a cycle slip occurs, the particle sampling range is initialized to... Otherwise, the particle sampling range depends on and Update, take the union of them. The total number of particles is Update the one-dimensional particle filter to perform narrow-lane ambiguity checking; Determine the weights of all particles within the current epoch's downsampling range; combining historical weight information, the particle weighting formula is: (8) (9) in, For particles In the calendar The weights below; For observations The conditional likelihood function; The particle weights are normalized; the VMF3-FC product is introduced to check the erroneous ambiguity in the network RTK; the conditional likelihood function in equation (8) is defined and replaced based on the difference between the tropospheric model value and the inversion value, and its normalized form is: (10) in, and These are the correct fuzziness and the fuzzy particle, respectively, with subscripts. For the calendar year, Indicates the particle order; The tropospheric reference value calculated for the VMF3-FC product; Based on GNSS observations and ambiguity particles The inverted tropospheric values ​​are calculated as follows: (11) in, This represents the double-difference deionized ionospheric phase observation, in meters; For narrow alley ambiguity integer particles; The width ambiguity is fixed; Step S34: Narrow alleyway ambiguity check; Calculate the particle estimate by combining the particle value and weight given in step S33. ,variance and decimal deviation for: (12) (13) (14) in, Indicates rounding down; like 0.3 weeks and 0.2 weeks, direct particle estimation Rounding down yields the nearest integer value; simultaneously, if the rounded value of the particle estimate is consistent with the fixed LAMBDA solution of the Kalman filter, and satisfies... If the closed-loop condition is met, then the narrow alley ambiguity is considered to have passed the check. If the check is not passed, Greater than 0.3 weeks or If the error is greater than 0.2 weeks, then in step S4, we will attempt to correct the ambiguity of the wide alley and the narrow alley sequentially.

5. The network RTK ambiguity real-time correction method based on particle filtering and VMF3-FC tropospheric products as described in claim 4, characterized in that, Step S4 includes: Step S41: Wide lane ambiguity correction; For the wide-lane ambiguity that failed the loop test in step S32, its correct integer value is... Within the range; accordingly, select any two baselines in the baseline loop, traverse the possible values ​​of the wide-lane ambiguity of the two baselines, and calculate the wide-lane ambiguity of the third baseline according to the baseline loop closure condition to obtain the candidate group of wide-lane ambiguity combinations of the baseline loop; according to the check conditions in step S32, screen those that meet the requirements. The minimum wide-lane ambiguity combination is used as the final correction value; Step S42: Narrow alleyway ambiguity correction; Narrow alleyway ambiguity correction includes two sub-steps: Step S421 is for satellites whose wide-lane ambiguity fails the check. Step S33 is completed using the corrected wide-lane ambiguity, that is, the narrow-lane ambiguity is checked. If the check conditions in S33 are met, the narrow-lane ambiguity is considered to be reliably fixed and can be used to generate virtual observations. Step S422 addresses the issue of narrow-lane ambiguity in the particle filter not meeting the baseline loop ambiguity closure condition or having excessive variance; it employs a least-squares method with additional geometric constraints to adjust the parameter estimates of the particle filter, as shown in the following formula: (15) in, These are phase-free, ionospheric combination observations after subtracting the correct wide-lane ambiguity from different baselines. Tropospheric reference values ​​calculated for VMF3-FC products under different baselines. Narrow-lane ambiguity for the first frequency phase data under different baselines. For observation noise, superscript These represent satellite and differential satellite, respectively. If the narrow-lane ambiguity estimation deviation is greater than 0.3 cycles at a certain moment, the narrow-lane ambiguity is unreliable and requires long-term Kalman filtering to improve the accuracy of the floating-point solution. Step S43: Update the particle filter correction results to the Kalman filter; The final result of the current particle filter will serve as a decision reference for the Kalman filter and the entire network RTK system; ambiguities that fail the check and cannot be successfully corrected will be marked as unusable, and the duration of their unavailability will be recorded in order to reset the filtering parameters of satellites that have been unusable for a long time. For each subsequent epoch, execute S3-S4 until all data has been solved.

Images