Factor graph RTK positioning method based on ambiguity detection, identification and restoration

Abstract

The invention discloses a factor graph RTK positioning method based on ambiguity detection, recognition and repair, which comprises the following steps: detecting an unreliable solution by using an ambiguity domain and a state domain, recognizing possible cycle slip through forward and backward repair of window information, and finally adding a cycle slip repair factor to adjust a factor graph so as to ensure reliable and correct fixation of ambiguity. And therefore, the RTK positioning robustness in a complex environment is improved. In a complex urban environment, the method can basically realize continuous position estimation with centimeter-level precision. Besides, when the available satellites are few, the ambiguity fixing and positioning effects of the method are far better than those of the existing method, which shows that the method has better robust robust capability, and the RTK positioning capability in a complex environment is effectively improved.

Description

Technical Field

[0001] The present invention belongs to the field of GNSS (Global Navigation Satellite System) positioning and navigation technology, and relates to a factor graph RTK positioning method under complex environments, and specifically to a factor graph RTK positioning method based on ambiguity detection, identification and repair. Background Art

[0002] Satellite positioning technology has always played a crucial role in modern urban transportation systems. Real-time kinematic (RTK) satellite positioning technology has emerged as one of the most important high-precision positioning methods in open areas. However, the complexity of urban environments, along with multipath effects and cycle slips caused by high-rise buildings and tree shading, pose significant challenges to high-precision satellite positioning. Despite significant progress in satellite positioning technology in recent years, achieving continuous, stable, and high-precision positioning in complex urban environments remains a pressing challenge.

[0003] Factor Graph Optimization (FGO), a joint estimation framework based on probabilistic graphical models, has recently attracted widespread attention in fields such as robotics, autonomous driving, and GNSS high-precision positioning. Compared to the recursive estimation of traditional Kalman filtering, which relies on the Markov assumption, FGO significantly improves the estimation accuracy and robustness of nonlinear systems through the joint optimization of multiple state variables within a window and iterative relinearization. This characteristic gives it a unique advantage in complex urban scenarios where GNSS signals are affected by multipath interference and other factors.

[0004] Precise satellite positioning relies on accurate carrier measurements and correctly fixed ambiguities. Once integer ambiguities are resolved, centimeter-level or even millimeter-level positioning accuracy can be achieved. The accuracy of the estimated position based on carrier phase observations depends on the performance of ambiguity resolution. In complex environments, ambiguity fixation poses a significant challenge. Unmodeled errors can severely impact the ambiguity fixation process, multipath can severely impact the reliability of pseudorange observations, and can also cause errors of up to a quarter wavelength in carrier measurements. Furthermore, in urban environments, receiver tracking of the carrier is unstable, making cycle slips more likely to occur.

[0005] Existing factor graph RTK methods do not fully exploit the integer consistency of ambiguities within the window. The associated constraints on ambiguity parameters are still limited to the floating-point solution optimization stage. Essentially, they continue the continue model of the EKF framework, that is, only strong constraints are imposed on floating-point ambiguities between epochs, while the fixed integer ambiguity parameters are only output and transmitted. This fails to fully exploit the constant integer characteristics of ambiguities within the window, affecting the ambiguity fixation effect in complex environments. Therefore, in order to obtain more accurate and reliable trajectories, it is necessary to improve the ambiguity fixation rate and accuracy of the FGO method. Summary of the Invention

[0006] To solve the above problems, the present invention discloses a factor graph RTK positioning method based on ambiguity detection, identification and repair. It uses the ambiguity domain and position domain to check and detect unreliable solutions, then identifies possible cycle slips after forward and backward repair through window information, and finally adds a cycle slip repair factor to adjust the factor graph to ensure the reliable and correct fixation of ambiguity, thereby improving the robustness of RTK positioning in complex environments.

[0007] To achieve the above object, the technical solution of the present invention is as follows:

[0008] A factor graph RTK positioning method based on ambiguity detection, identification and repair includes the following steps:

[0009] Step 1: Based on the double-difference carrier pseudorange observations, after cycle slip detection and outlier detection, the carrier observation factor and pseudorange observation factor are constructed respectively to form a factor graph RTK model. At the same time, the sliding window marginalization method is introduced to transfer the ambiguity constraints.

[0010] Step 2: Use the partial ambiguity method to solve the integer ambiguity, combine the ratio value test in the ambiguity domain and the chi-square residual test in the state domain to divide the correct fixed set and the set to be repaired, and divide the continuous tracking arc segments according to the reliable solution;

[0011] Step 3: Repair the floating point and wrong fixed ambiguities within the arc segment. That is, use the ambiguities of the correct fixed set to repair the ambiguities of the to-be-repaired set in both the forward and backward directions. At the same time, use the chi-square test to verify the correctness of the correction.

[0012] Step 4: Detect the ambiguity difference between epochs based on the corrected ambiguity value, recover the cycle slips that occurred in the observation value, and add the cycle slip repair factor to the factor graph.

[0013] The specific steps are:

[0014] Step 1: Construct the factor graph RTK positioning model. First, consider the double-difference pseudo-range carrier observation equation as shown below:

[0015]

[0016] Where, the superscript s denotes the corresponding satellite, the subscript r denotes the corresponding receiver, the subscript f denotes the corresponding frequency, ρ denotes the geometric distance between the receiver and the satellite, c denotes the speed of light, t denotes the clock error, I and T denote the ionospheric delay and tropospheric delay, respectively, δρ denotes other residual errors such as relativistic effects, ε denotes the model error, λ denotes the wavelength, and N denotes the integer ambiguity.

[0017] Construct the factor graph carrier pseudorange factor according to the observation equation:

[0018]

[0019] in, represents the pseudorange constraint residual at time t, represents two differences between the reference station and the reference star, It is obtained through the double-difference pseudorange observation equation, represents the carrier constraint residual at time t, It is obtained through the double-difference carrier observation equation. In order to better resist the influence of multipath, the variance is determined by the combination of altitude angle and signal-to-noise ratio.

[0020] Typically, the core issue in RTK solutions is the continuous tracking of carrier ambiguities, especially for high-elevation satellites, which often lasts for multiple GNSS periods. This is similar to tracking feature points in visual positioning. The double-difference ambiguity constraints between epochs will also be an important component of high-precision positioning solutions. Its variance is set to be very small to ensure:

[0021]

[0022] in, represents the inter-epoch ambiguity constraint at time t, represents the double-difference ambiguity.

[0023] In order to achieve real-time estimation of the carrier position, the present invention adopts a sliding window method to manage the scale of the nonlinear optimization problem. However, the continuous tracking of carrier phase ambiguity, especially for high-elevation satellites, usually lasts for multiple GNSS periods, which may exceed the window length. The present invention uses marginalization to convert the measurements associated with the old state (which would otherwise be discarded outside the sliding window) into prior constraints to fully utilize the continuously tracked carrier phase observations for data association between the previous and next GNSS periods. The factors related to the marginalized state are converted into prior factors. The sliding window combined with the marginalization strategy balances real-time performance and information utilization. Combined with the factors related to the marginalized state, the incremental equation for the remaining state vector can be obtained using Schur complement:

[0024]

[0025] Where Λ represents the information matrix, δxr Represents the increments of the marginalized states and the remaining states, and as a whole represents the increment equation of the remaining state vector.

[0026] It is worth noting that the linearization point of the marginalized state is fixed in its corresponding observation factor, which will lead to a certain degree of accuracy loss. Therefore, the sliding window method is a strategy to balance efficiency and accuracy.

[0027] Step 2: Use the ambiguity domain and state domain to reliably check and distinguish the resolved integer ambiguities.

[0028] First, a pre-processed cycle slip detection algorithm is used to roughly divide the window into arc segments, reducing the number of possible cycle slips in a single segment and improving the repair success rate. Correctly fixed solutions are then screened, with the fixed solutions at each moment divided into two datasets: a correctly fixed set and a set to be fixed. This goal is achieved in two ways. First, an AR ratio test is used to verify the solution in the ambiguity domain. A strict threshold of 2.5 is used to reduce the possibility of false fixes, but this is overly optimistic in complex scenarios and can still result in false fixes. Second, a chi-square test is used to further verify the fixed results in the position domain to ensure correct fixation. Fixation solutions that pass these two tests are considered to be correctly fixed ambiguity sets.

[0029]

[0030] Among them, V represents the residual, D z represents its variance. In the formula, the threshold T is set based on the significance level α = 0.001. If the test passes, the fixed result is considered correct and the error distribution conforms to the model. The current epoch is classified into the correct fixed set and recorded as A1. At the same time, arcs are further divided according to the ambiguity value. That is, within an arc, the same satellite can have a maximum of two different reliable ambiguity values. If the test fails, the fixed result is still considered not completely correct, and the current epoch is classified into the pending repair set.

[0031]

[0032] Where X represents the entire positioning set, and A1 represents the correct fixed positioning set that passes the chi-square test.

[0033] Step 3: Use the ambiguity of the correct fixed set to perform forward and backward repair on the ambiguity of the to-be-repaired set.

[0034] Next, the floating and incorrect fixed ambiguities are repaired within the arc. This involves using the ambiguities of the correct fixed set to perform both forward and backward repairs on the ambiguities of the set to be repaired. Satellites in each epoch can be divided into two types: continuously tracked satellites, where fix issues in that epoch due to observation quality can be recovered using historical reliable fixed solutions, corresponding to forward repair. Newly emerged satellites or satellites that cannot be continuously tracked due to cycle slips and other factors require time to converge or recover, corresponding to backward repair. As mentioned in the introduction, three main situations can severely impact ambiguity fixation in complex environments. The first two situations, namely, frequent satellite changes and poor observation quality, such as the simultaneous loss of some tracked satellites when a satellite rises in a given epoch, pose challenges to solving the floating solution, as the ambiguities of the newly emerged satellite are difficult to converge immediately. This can lead to unfixed or incorrectly fixed ambiguities for the satellites in that epoch. In these situations, forward repair becomes effective, correctly fixing the ambiguities of the same satellites that existed in the previous, unaffected epochs. Considering that forward repair may result in incorrect repair when a cycle slip occurs, the impact of retaining the wrong positioning solution may be catastrophic, so the ambiguity is fixed first and then the positioning solution is solved by back substitution:

[0035]

[0036] Where W is the weight matrix and G is the coefficient matrix. The repaired solutions are judged by the chi-square test, and only the repair results that pass the test are retained. They are also considered to be reliable positioning solutions and are recorded as A2.

[0037]

[0038] For undetected cycle slips, incorrect measurement constraints will be introduced in the current epoch, resulting in the inability to correctly fix the ambiguity of this epoch and some subsequent epochs until the impact of the cycle slip is gradually weakened and the ambiguity can be correctly fixed again. For the cycle slip detected by preprocessing, the satellite will be equivalent to a newly risen satellite, and the ambiguity will take some time to converge again. At this time, backward repair will play a role. The ambiguity will be correctly fixed again after a period of time after the cycle slip occurs. The correct ambiguity in the latter part of the window can be used to repair the erroneous ambiguity caused by the cycle slip. It is worth noting that backward repair also helps the first two situations, that is, the newly risen satellite will converge quickly after repair, and more fixed satellites in complex environments will greatly improve the reliability of the solution, although this repair may have some delays. The successfully repaired solution is considered a reliable positioning solution and is recorded as A3:

[0039]

[0040] Step 4: After splitting the epoch ambiguity of the detected cycle slip into two segments in the factor graph, a cycle slip factor is added between the ambiguities according to the number of cycle slips to ensure that the ambiguity is correctly and continuously tracked.

[0041] After completing the ambiguity repair, although the positioning solution for that epoch may be correct, there are still constraints that need to be fixed in the optimization, such as unmodeled errors such as cycle slips and multipath. The purpose of this step is to repair the incorrect constraints or weaken their impact.

[0042] After the forward and backward ambiguity repair is completed in the previous step, the ambiguity values are stored in A1, A2, and A3. It is known that the ambiguity values of the epochs before and after the cycle slip will have a whole-cycle jump. By performing consistency checks on the ambiguities in these reliable positioning sets, the cycle slip can be easily detected. At the same time, based on the whole-cycle ambiguity difference of adjacent epochs, the number of cycle slips can be obtained. The present invention introduces this into the observation equation to repair the cycle slip. This ensures that the satellite that has a cycle slip can still be continuously tracked, and no longer needs to be regarded as a newly rising satellite after the cycle slip, which improves the model strength of the factor graph RTK solution. At the same time, for undetected cycle slips, repairing the erroneous ambiguity constraints will greatly improve the reliability of the subsequent positioning solution.

[0043]

[0044] Among them, e cycle Represents the added cycle slip constraint factor, δN t,t-1 Indicates the number of cycle slips identified by this method.

[0045] Another important unmodeled error is multipath, which can produce large gross errors, especially in pseudoranges. After the repair is complete, the present invention also performs a consistency check on the pseudorange and carrier to eliminate affected pseudorange observations. The geometric term is eliminated by differentially taking the double-difference pseudorange and carrier observations, i.e., the integer ambiguity estimate that includes pseudorange and carrier observation errors and unmodeled errors. When the difference between the estimated ambiguity value and the correct fixed set exceeds a threshold, it is considered that the pseudorange is affected by multipath and has gross errors, which should be eliminated to prevent them from affecting the optimization process.

[0046] The beneficial effects of the present invention include:

[0047] The factor graph RTK positioning method based on ambiguity detection, identification, and repair proposed in this paper leverages the time-invariant and constant properties of ambiguities within a window to improve the accuracy of ambiguity fixation in complex environments, while ensuring reliable ambiguity tracking and positioning robustness. In complex urban environments, this method can achieve continuous position estimation with centimeter-level accuracy. Furthermore, when available satellites are limited, this method achieves significantly better ambiguity fixation and positioning results than existing methods, demonstrating superior robustness and effectively improving RTK positioning capabilities in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1It is an implementation flow chart of the present invention;

[0049] Figure 2 This is a comparison chart of positioning results in a simulation environment using the method of the present invention to add cycle slips;

[0050] Figure 3 is a comparison diagram of ambiguity resolution results of a simulation environment in which cycle slips are added using the method of the present invention;

[0051] Figure 4 This is a comparison chart of positioning results in a complex urban measurement environment using the method described in the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0053] As shown in the figure, this embodiment of the present invention discloses a factor graph RTK positioning method based on ambiguity detection, identification and repair, and the specific steps are as follows:

[0054] Step 1: Construct the factor graph RTK positioning model. First, consider the double-difference pseudo-range carrier observation equation as shown below:

[0055]

[0056] Where, the superscript s denotes the corresponding satellite, the subscript r denotes the corresponding receiver, the subscript f denotes the corresponding frequency, ρ denotes the geometric distance between the receiver and the satellite, c denotes the speed of light, t denotes the clock error, I and T denote the ionospheric delay and tropospheric delay, respectively, δρ denotes other residual errors such as relativistic effects, ε denotes the model error, λ denotes the wavelength, and N denotes the integer ambiguity.

[0057] Construct the factor graph carrier pseudorange factor according to the observation equation:

[0058]

[0059] in, represents the pseudorange constraint residual at time t, represents two differences between the reference station and the reference star, It is obtained through the double-difference pseudorange observation equation, represents the carrier constraint residual at time t, It is obtained through the double-difference carrier observation equation. In order to better resist the influence of multipath, the variance is determined by the combination of altitude angle and signal-to-noise ratio.

[0060] Typically, the core issue in RTK solutions is the continuous tracking of carrier ambiguities, especially for high-elevation satellites, which often lasts for multiple GNSS periods. This is similar to tracking feature points in visual positioning. The double-difference ambiguity constraints between epochs will also be an important component of high-precision positioning solutions. Its variance is set to be very small to ensure:

[0061]

[0062] in, represents the inter-epoch ambiguity constraint at time t, represents the double-difference ambiguity.

[0063] In order to achieve real-time estimation of the carrier position, the present invention adopts a sliding window method to manage the scale of the nonlinear optimization problem. However, the continuous tracking of carrier phase ambiguity, especially for high-elevation satellites, usually lasts for multiple GNSS periods, which may exceed the window length. The present invention uses marginalization to convert the measurements associated with the old state (which would otherwise be discarded outside the sliding window) into prior constraints to fully utilize the continuously tracked carrier phase observations for data association between the previous and next GNSS periods. The factors related to the marginalized state are converted into prior factors. The sliding window combined with the marginalization strategy balances real-time performance and information utilization. Combined with the factors related to the marginalized state, the incremental equation for the remaining state vector can be obtained using Schur complement:

[0064]

[0065] Where Λ represents the information matrix, δx r Represents the increments of the marginalized states and the remaining states, and as a whole represents the increment equation of the remaining state vector.

[0066] It is worth noting that the linearization point of the marginalized state is fixed in its corresponding observation factor, which will lead to a certain degree of accuracy loss. Therefore, the sliding window method is a strategy to balance efficiency and accuracy.

[0067] Step 2: Use the ambiguity domain and state domain to reliably check and distinguish the resolved integer ambiguities.

[0068] First, a pre-processed cycle slip detection algorithm is used to roughly divide the window into arc segments, reducing the number of possible cycle slips in a single segment and improving the repair success rate. Correctly fixed solutions are then screened, with the fixed solutions at each moment divided into two datasets: a correctly fixed set and a set to be fixed. This goal is achieved in two ways. First, an AR ratio test is used to verify the solution in the ambiguity domain. A strict threshold of 2.5 is used to reduce the possibility of false fixes, but this is overly optimistic in complex scenarios and can still result in false fixes. Second, a chi-square test is used to further verify the fixed solution in the position domain to ensure correct fixation. Fixation solutions that pass these two tests are considered to be correctly fixed ambiguity sets.

[0069]

[0070] Among them, V represents the residual, D z represents its variance. In the formula, the present invention sets the threshold T based on the significance level α = 0.001. If the test passes, the fixed result is considered correct and the error distribution conforms to the model. The current epoch is classified into the correct fixed set and recorded as A1. At the same time, arcs are further divided according to the ambiguity value. That is, within an arc, the same satellite can have a maximum of two different reliable ambiguity values. If the test fails, the fixed result is still considered not completely correct, and the current epoch is classified into the pending repair set.

[0071]

[0072] Where X represents the entire positioning set, and A1 represents the correct fixed positioning set that passes the chi-square test.

[0073] Step 3: Use the ambiguity of the correct fixed set to perform forward and backward repair on the ambiguity of the to-be-repaired set.

[0074] Next, the floating and incorrect fixed ambiguities are repaired within the arc. This involves using the ambiguities of the correct fixed set to perform both forward and backward repairs on the ambiguities of the set to be repaired. Satellites in each epoch can be divided into two types: continuously tracked satellites, where fix issues in that epoch due to observation quality can be recovered using historical reliable fixed solutions, corresponding to forward repair. Newly emerged satellites or satellites that cannot be continuously tracked due to cycle slips and other factors require time to converge or recover, corresponding to backward repair. As mentioned in the introduction, three main situations can severely impact ambiguity fixation in complex environments. The first two situations, namely, frequent satellite changes and poor observation quality, such as the simultaneous loss of some tracked satellites when a satellite rises in a given epoch, pose challenges to solving the floating solution, as the ambiguities of the newly emerged satellite are difficult to converge immediately. This can lead to unfixed or incorrectly fixed ambiguities for the satellites in that epoch. In these situations, forward repair becomes effective, correctly fixing the ambiguities of the same satellites that existed in the previous, unaffected epochs. Considering that forward repair may result in erroneous repair when a cycle slip occurs, the impact of retaining the erroneous positioning solution may be disastrous. After repairing the ambiguity, the present invention first solves the positioning solution by back-substitution:

[0075]

[0076] Where W is the weight matrix and G is the coefficient matrix. The repaired solutions are judged by the chi-square test, and only the repair results that pass the test are retained. They are also considered to be reliable positioning solutions and are recorded as A2.

[0077]

[0078] For undetected cycle slips, incorrect measurement constraints will be introduced in the current epoch, resulting in the inability to correctly fix the ambiguity of this epoch and some subsequent epochs until the impact of the cycle slip is gradually weakened and the ambiguity can be correctly fixed again. For the cycle slip detected by preprocessing, the satellite will be equivalent to a newly risen satellite, and the ambiguity will take some time to converge again. At this time, backward repair will play a role. The ambiguity will be correctly fixed again after a period of time after the cycle slip occurs. The correct ambiguity in the latter part of the window can be used to repair the erroneous ambiguity caused by the cycle slip. It is worth noting that backward repair also helps the first two situations, that is, the newly risen satellite will converge quickly after repair, and more fixed satellites in complex environments will greatly improve the reliability of the solution, although this repair may have some delays. The successfully repaired solution is considered a reliable positioning solution and is recorded as A3:

[0079]

[0080] Step 4: After splitting the epoch ambiguity of the detected cycle slip into two segments in the factor graph, a cycle slip factor is added between the ambiguities according to the number of cycle slips to ensure that the ambiguity is correctly and continuously tracked.

[0081] After completing the ambiguity repair, although the positioning solution for that epoch may be correct, there are still constraints that need to be fixed in the optimization, such as unmodeled errors such as cycle slips and multipath. The purpose of this step is to repair the incorrect constraints or weaken their impact.

[0082] After the forward and backward ambiguity repair is completed in the previous step, the ambiguity values are stored in A1, A2, and A3 by the present invention. The ambiguity values of the epochs before and after the cycle jump will have a whole-cycle jump. By performing consistency checks on the ambiguities in these reliable positioning sets, the cycle jump will be easily detected. At the same time, based on the whole-cycle ambiguity difference of adjacent epochs, the number of cycle jumps can be obtained. The present invention introduces this into the observation equation to repair the cycle jump. This ensures that the satellite that has a cycle jump can still be tracked continuously, and no longer needs to be regarded as a newly rising satellite after the cycle jump, which improves the model strength of the factor graph RTK solution. At the same time, for undetected cycle jumps, repairing the erroneous ambiguity constraints will greatly improve the reliability of the subsequent positioning solution.

[0083] Figure 2 This paper compares the positioning results of this method and existing factor graph algorithms in a simulated cycle slip experiment. Adding a cycle to the observations is equivalent to adding a cycle slip to the edge epochs. In other words, the epochs immediately entering and leaving the gray background are most affected by the added cycle slips. The positioning error graph shows that while FGO exhibits some robustness against cycle slips, it still exhibits positioning errors approaching the meter level. The proposed method, on the other hand, effectively resists all added cycle slips, achieving centimeter-level positioning results throughout the entire time period. Figure 3 Comparison of positioning results between this method and existing factor graph algorithms in complex on-board vehicle experiments. The proposed method achieves superior positioning accuracy compared to FGO due to its robustness against multipath and cycle slips in complex environments. The ambiguity-based DIA method essentially eliminates large positioning jumps, achieving reliable continuous positioning capabilities.

[0084] It should be noted that the above content merely illustrates the technical idea of the present invention and cannot be used to limit the scope of protection of the present invention. For ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications all fall within the scope of protection of the claims of the present invention.

Claims

1. A factor graph RTK positioning method based on ambiguity detection, identification and repair, characterized in that: include: Step 1: Based on the double-difference carrier pseudorange observations, after cycle slip detection and outlier detection, the carrier observation factor and pseudorange observation factor are constructed respectively to form a factor graph RTK model. At the same time, the sliding window marginalization method is introduced to transfer the ambiguity constraints. Step 2: Use the partial ambiguity method to solve the integer ambiguity, combine the ratio value test in the ambiguity domain and the chi-square residual test in the state domain to divide the correct fixed set and the set to be repaired, and divide the continuous tracking arc segments according to the reliable solution; Step 3: Repair the floating point and wrong fixed ambiguities within the arc segment. That is, use the ambiguities of the correct fixed set to repair the ambiguities of the to-be-repaired set in both the forward and backward directions. At the same time, use the chi-square test to verify the correctness of the correction. Step 4: Detect the ambiguity difference between epochs based on the corrected ambiguity value, recover the cycle slips that occurred in the observation value, and add the cycle slip repair factor to the factor graph.

2. The factor graph RTK positioning method based on ambiguity detection, identification and repair according to claim 1, characterized in that: The construction process of the factor graph RTK positioning model described in step 1 first considers the double-difference pseudorange carrier observation equation shown in the following formula: Where, the superscript s indicates the corresponding satellite, the subscript r indicates the corresponding receiver, the subscript f indicates the corresponding frequency, ρ indicates the geometric distance between the receiver and the satellite, c indicates the speed of light, t indicates the clock error, I and T indicate the ionospheric delay and tropospheric delay, respectively, δρ indicates other residual errors such as relativistic effects, ε indicates the model error, λ indicates the wavelength, and N indicates the integer ambiguity. Construct the factor graph carrier pseudorange factor according to the observation equation: in, represents the pseudorange constraint residual at time t, represents two differences between the reference station and the reference star, It is obtained through the double-difference pseudorange observation equation, represents the carrier constraint residual at time t, It is obtained through the double-difference carrier observation equation, and the variance is determined by the combination of altitude angle and signal-to-noise ratio; The double-difference ambiguity constraint between epochs is an important component of high-precision positioning solution. Its variance is set to be very small to ensure: in, represents the inter-epoch ambiguity constraint at time t, represents the double-difference ambiguity, To achieve real-time carrier position estimation, this paper employs a sliding window approach to manage the scale of the nonlinear optimization problem. Marginalization is used to convert measurements associated with the old state into prior constraints, fully leveraging continuously tracked carrier phase observations for data correlation between previous and subsequent GNSS periods. Factors associated with the marginalized state are converted into prior factors. The sliding window, combined with the marginalization strategy, balances real-time performance and information utilization. Incorporating factors associated with the marginalized state and utilizing Schur complements, the incremental equation for the remaining state vector is derived: Where Λ represents the information matrix, δx r Represents the increments of the marginalized states and the remaining states, and as a whole represents the increment equation of the remaining state vector.

3. The factor graph RTK positioning method based on ambiguity detection, identification and repair according to claim 1, characterized in that: Step 2: Use the ambiguity domain and state domain to reliably check and distinguish the resolved integer ambiguities. First, pre-processed cycle slip detection is used to roughly divide the window into arc segments, reducing the number of possible cycle slips in a single segment and improving the repair success rate. At the same time, the correct fix results are screened, and the fixed solution at each moment is divided into two data sets: the correct fixed set and the unfixed set. This goal is achieved here from two aspects. First, the AR ratio test is used to verify the solution in the ambiguity domain. A relatively strict 2.5 threshold is used to reduce the possibility of false fixes. However, due to its overoptimism in complex scenarios, false fixes may still occur. Second, the chi-square test is used to further verify the fix results in the position domain to ensure the correct fix. Fix results that pass these two tests are considered to be the correctly fixed ambiguity set. Among them, V represents the residual, D z represents its variance; in the formula, the present invention sets the threshold T according to the significance level α = 0.001; if the test passes, it is considered that the result after fixation is correct, the error distribution conforms to the modeling, and the current epoch is classified into the correct fixed set, which is recorded as A1; at the same time, the arc is further divided according to the ambiguity value, that is, the same satellite in an arc has at most two different reliable ambiguity values; if the test fails, it is considered that the result after fixation is still not completely correct, and the current epoch is classified into the set to be repaired Where X represents the entire positioning set, and A1 represents the correct fixed positioning set that passes the chi-square test.

4. The factor graph RTK positioning method based on ambiguity detection, identification and repair according to claim 1, characterized in that: In step 3, the ambiguity of the set to be repaired is repaired twice, forward and backward, using the ambiguity of the correct fixed set; After repairing the ambiguity, the present invention first back-substitutes to solve the positioning solution: δX=(G T WG) -1 G T W(Δ▽L-λΔ▽N fixed -Δ▽ρ0) Where W is the weight matrix and G is the coefficient matrix. The repaired solution is judged by the chi-square test, and only the repair results that pass the test are retained. They are also considered to be reliable positioning solutions and are recorded as A2. The solution that is successfully repaired is considered a reliable positioning solution and is recorded as A3:

5. The factor graph RTK positioning method based on ambiguity detection, identification and repair according to claim 1, characterized in that: After splitting the epoch ambiguity of the detected cycle slip into two segments in the factor graph as described in step 4, a cycle slip factor is added between the ambiguities according to the number of cycle slips to ensure that the ambiguities are correctly and continuously tracked; After completing the ambiguity repair, although the positioning solution for this epoch may be correct, there are still constraints to be repaired in the optimization. The purpose of this step is to repair the incorrect constraints or weaken their influence. After the forward and backward ambiguity repair is completed in the previous step, the ambiguity values are stored in A1, A2, and A3. The present invention obtains the cycle slip number based on the ambiguity difference between adjacent epochs and introduces it into the observation equation to repair the cycle slip. This ensures that satellites with cycle slips are still continuously tracked, improving the model strength of the factor graph RTK solution. Among them, e cycle Represents the added cycle slip constraint factor, δN t,t-1 Indicates the number of cycle slips identified by this method; The geometric terms are eliminated by differentiating the double-difference pseudorange and carrier observation values, that is, the integer ambiguity estimate containing pseudorange and carrier observation errors and unmodeled errors; when the difference between the estimated ambiguity value and the correct fixed set exceeds the threshold, it is considered that the pseudorange is affected by the multipath effect and there is a gross error, which should be eliminated to prevent it from affecting the optimization process.

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