A method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions

Abstract

A method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions includes: acquiring and preprocessing GNSS observation data to obtain an observation sequence; calculating, based on the observation sequence, observations including wide-lane (MW) combined observations, geometrically neutral (GF) combined observations, total electron content along the slant path, and the rate of change of total ionospheric electron content; using a static parameter transfer method, making a preliminary determination of cycle slips by comparing the difference between the MW combined observations of the current epoch and the previous epoch with a preset MW threshold; constructing a GF combined cycle slip detection and repair model based on the GF geometrically neutral (GF) combined observations, their difference components, and the rate of change of total ionospheric electron content; dynamically planning the GF cycle slip detection threshold using the GF combined cycle slip detection and repair model; and performing cycle slip detection and repair based on the preliminary determination and the GF cycle slip detection threshold. This invention reduces the false alarm cycle slip incidence under strong ionospheric disturbance conditions.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and positioning technology, specifically relating to a method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions. Background Technology

[0002] As satellite navigation systems play an increasingly important role in social production and construction, users have higher and higher requirements for satellite positioning accuracy. Currently, the most commonly used high-precision positioning technology is Point Positioning (PPP), a method that uses a single receiver without a reference station and generates positioning data using precise orbit and clock bias products from a GNSS analysis center. PPP primarily relies on pseudorange and carrier phase observations obtained from radio wave transmission at specific frequencies between the satellite and the ground receiving station to locate the target. High-precision positioning, however, depends on multi-frequency carrier phase observations. Since cycle slips exist in carrier phase observations, a single cycle slip can introduce decimeter-level distance errors along the propagation path. Therefore, cycle slip detection and correction are crucial for ensuring positioning accuracy during data processing.

[0003] Current PPP processing widely employs the TurboEdit cycle slip detection algorithm, which combines the Melbourne-Wubbena (MW) wide-lane (WLL) and Geometry-Free (GF) geometry-free (GF) methods. This method typically relies on fixed or empirical thresholds to determine cycle slips. However, due to ionospheric inhomogeneities (such as feather-like extensions F), the space radio wave propagation environment undergoes drastic changes, ionospheric delay exhibits rapid fluctuations, and ionospheric scintillation occurs, leading to significant changes in the statistical characteristics of the MW and GF combined observations. Under ionospheric disturbances, the MW and GF combination cannot effectively handle scenarios where unstable ionospheric fluctuations cause disturbances, greatly increasing the likelihood of false alarm cycle slips and severely impacting the accuracy and reliability of precise point positioning.

[0004] Under the above conditions, existing technologies have the following shortcomings: Traditional MW combining methods detect cycle slips by calculating the difference between the current epoch and the average combining ambiguity of all historical epochs. Under strong ionospheric disturbances, extreme outliers in a single epoch can affect the smoothing results of subsequent epochs through the averaging process, producing a "tailing" effect of "error accumulation," leading to continuous false alarm cycle slips and severely disrupting the continuity of ambiguity estimation. GF combining methods are significantly affected by ionospheric delay. Under rapid TEC fluctuations caused by ionospheric inhomogeneities, commonly used static thresholds cannot adapt, causing GF combining observations to frequently exceed the threshold, generating a large number of false alarms. Although some existing improved methods introduce empirical threshold models for elevation angle and epoch interval, they still suffer from problems such as non-adaptability and limited scene coverage, failing to effectively address the influence of higher-order ionospheric delay terms. Therefore, a GNSS cycle slip detection and repair method that can adapt to the characteristics of ionospheric inhomogeneity disturbances is needed to improve the reliability and positioning accuracy of PPP in complex ionospheric environments. Summary of the Invention

[0005] The purpose of this invention is to provide a method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions. By improving the parameter transfer mechanism of MW combination in the existing TurboEdit cycle slip detection process and constructing a GF combination adaptive statistical threshold model based on ROTI, the false alarm cycle slip occurrence rate under strong ionospheric disturbance conditions is reduced, thereby improving the stability and positioning accuracy of PPP solution.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions includes the following steps: S1. Acquire and preprocess GNSS observation data to obtain an observation sequence; S2. Based on the observation sequence, calculate the MW wide-lane combination observation, GF non-geometric combination observation, oblique path total electron content and ionospheric total electron content change rate index; S3. Using the static parameter transfer method, a preliminary determination of cycle slip is made by comparing the difference between the combined MW observations of the current epoch and the previous epoch with the preset MW threshold. S4. Construct a GF combined cycle slip detection and repair model based on GF non-geometric combination observations, their difference components, and the ionospheric total electron content change rate index; use the GF combined cycle slip detection and repair model to dynamically plan the GF cycle slip detection threshold. S5. Perform cycle slip detection repair based on the preliminary judgment and GF cycle slip detection threshold.

[0007] Preferably, S2 includes: S21. Based on the dual-frequency pseudorange and carrier phase observations in the observation sequence, the MW wide-lane combined observations are calculated as follows: The observations without geometric combinations of GF are calculated as follows: in, , and At frequency j The pseudorange phase observations, carrier phase observations, and wavelength are shown on the image. j The values ​​are 1 and 2, which correspond to the L1 and L2 frequency bands of the GPS system, respectively. , and The L1 and L2 frequency bands represent the GPS carrier phase, respectively. =1575.42MHz, =1227.60MHz, where c is the speed of light.

[0008] As a preferred embodiment, S2 also includes: S22. Calculate the total electron content (STEC) along the oblique path based on GNSS observation data, and further calculate the rate of change (ROT) of the total electron content along the oblique path between adjacent epochs. Perform statistical processing on the ROT within a preset time window to obtain the ionospheric total electron content change rate index (ROTI), which characterizes the intensity of ionospheric activity. The formula is as follows: Where s represents a specific satellite, i represents the epoch index, and R represents the time interval between adjacent epochs; angle brackets indicate the average value within a certain time window. K =40.3 m 3 / s 2 .

[0009] As a preferred embodiment, in S3, for each epoch i, the difference between the combined MW observations of the current epoch and the previous epoch is calculated: Set MW threshold ,like Then, it records the cycle jump that occurred in the current epoch.

[0010] As a preferred option, in S4, the construction of the GF combined cycle slip detection and repair model includes: The first and second order difference components of GF without geometric combination observations were obtained; GF cycle slip detection parameters were constructed based on the first and second order difference components of GF; the ionospheric disturbance intensity intervals were divided according to the magnitude of the ionospheric total electron content change rate exponent, and the distribution characteristics of the first and second order difference components of GF were statistically analyzed in different intervals; based on the statistical results, the mapping relationship between the GF cycle slip detection threshold and the ionospheric total electron content change rate exponent was established, forming a GF combined cycle slip detection repair model.

[0011] As a preferred option, S4 also includes: Using the rate of change of total ionospheric electron content as the independent variable, the dependent variables are defined as the linear relationship parameters determined by the statistical distributions of the first and second difference components of GF within each interval of 0.05 TECU / min: slope k and intercept b. For any interval of 0.05 TECU / min, the mapping relationship is constructed as follows: : in, std The standard deviation of the data; k and b enclosing and The slope and intercept of the proportional function of the triangular region formed by the horizontal and vertical axes of the two-dimensional statistical distribution. r The index representing the rate of change of total electron content in the ionosphere for any given value; For based on and The GF cycle slip detection threshold was jointly constructed; x and y Representing the corresponding statistical samples respectively and .

[0012] As a preferred embodiment, S4 further includes: for any value of the rate of change exponent of total ionospheric electron content r, constructing a three-dimensional function f(r) to describe the statistical boundary of the GF cycle slip detection threshold.

[0013] Preferably, the three-dimensional function f(r) is expressed as: = Where mean represents the average value, b(r) is the threshold model parameter, and b(ROTI) has the following form: Based on three-dimensional surface fitting, a three-dimensional surface model for the GF cycle slip detection threshold is constructed, as shown in the following equation: In the above formula, (i=1,2,3) are the fitting coefficients; x 1， x2 represents the fitted segmentation points; For epoch i, according to its , And ROTI value, if the GF cycle slip detection threshold is on the surface If the threshold boundary is outside, the GF combination detection flag for that epoch is recorded, i.e., a cycle slip has occurred.

[0014] Preferably, the construction of the three-dimensional function f(r) includes piecewise fitting of the threshold model parameters b(r): When ROTI≤x1 or x1<ROTI≤x2, the intercept b and the ROTI value have a synergistic relationship, and the threshold model parameter b(r) is fitted using a multinomial model; When ROTI > x2, the co-growth trend of b and ROTI gradually disappears, and the threshold model parameter b(r) is set to a constant; ROTI is the rate of change index of total electron content in the ionosphere.

[0015] Compared with the prior art, the beneficial effects of the present invention are reflected in: 1. Unlike traditional technologies that use fixed thresholds for cycle slip detection, which suffer from poor adaptability and high false alarm rates under ionospheric inhomogeneities, this invention employs a GF combined adaptive statistical threshold model based on ROTI. This allows the cycle slip detection threshold to be dynamically adjusted according to the intensity of ionospheric activity, significantly reducing the false alarm probability under strong disturbances and fundamentally improving the environmental adaptability of the detection algorithm.

[0016] 2. Unlike traditional techniques that use the difference between the current MW combination ambiguity and the mean of all previous epochs, which is susceptible to tailing effects, this invention introduces a static parameter transfer strategy in MW combination. This avoids the continuous contamination of extreme outliers during long-term averaging, strictly limiting their impact to a single epoch. This effectively suppresses error accumulation and frequent false alarm cycle slips during the average ambiguity smoothing process. Combined with the aforementioned adaptive threshold model, this scheme synergistically reduces false alarm cycle slips in the PPP solution process from both threshold setting and data control perspectives, improving the stability of parameter estimation and observation redundancy. This significantly enhances the positioning accuracy and overall robustness of the GNSS system under strong ionospheric disturbances. Attached Figure Description

[0017] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention; Figure 2 The diagram shows the PPP positioning error distribution between the existing method and the method described in Embodiment 1 of this invention. Detailed Implementation

[0018] To make the technical means, inventive features, objectives, and effects of the invention readily understandable, the invention is further described below with reference to specific illustrations. However, the invention is not limited to the embodiments described below.

[0019] It should be noted that the structures, proportions, sizes, etc., illustrated in the accompanying drawings of this specification are only used to complement the content disclosed in the specification for those skilled in the art to understand and read, and are not intended to limit the conditions under which the present invention can be implemented. Therefore, they have no substantial technical significance. Any modifications to the structure, changes in the proportions, or adjustments to the size, without affecting the effects and objectives that the present invention can produce, should still fall within the scope of the technical content disclosed in the present invention.

[0020] To achieve the above objectives, this invention proposes a GNSS precise single-point positioning cycle slip adaptive detection and repair method that takes into account ionospheric inhomogeneity disturbances. The method employs the following techniques: For the MW combination, static parameter transfer is used instead of average combination ambiguity smoothing. The difference between MW combination observations between adjacent epochs is directly calculated as the cycle slip measurement, thus limiting the impact of instantaneous outliers to a single epoch and suppressing the accumulation of instantaneous gross errors. For the GF combination, a "ROTI adaptive statistical model" (RAS model) is proposed. This model innovatively combines the first-order and second-order differences of the GF combination with the real-time calculated ROTI value to construct a three-dimensional statistical distribution relationship. Through piecewise function fitting, the optimal GF cycle slip detection threshold corresponding to different ROTI levels is dynamically determined, enabling the threshold to adapt to changes in ionospheric disturbances and significantly reducing the false alarm rate. These methods make cycle slip detection more accurate during periods of ionospheric inhomogeneity, achieving the technical effect of reducing positioning errors and possessing advantages of strong robustness and wide applicability.

[0021] Example 1: like Figure 1 The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions, as shown, includes the following steps: S1. Acquire and preprocess GNSS observation data to obtain a continuous and reliable sequence of observations; Acquire GNSS (Global Navigation Satellite System) receiver data from the base station, such as dual-frequency pseudorange observations and dual-frequency carrier phase observations, precise ephemeris and clock bias data.

[0022] Preprocessing includes quality control of the raw observation data, such as removing observation data with satellite elevation angles below a preset threshold, deleting obviously gross observations, and performing time synchronization processing to ensure the continuity and reliability of the input data.

[0023] Download the GPS observation file (.o file), navigation file (.n file), and IGS precise ephemeris clock difference file for the test date, set a reasonable cutoff elevation angle, and read the pseudorange at L1 and L2 frequencies. and carrier phase Observed values.

[0024] S2. Based on the observation sequence, calculate the MW wide-lane combination observation, GF non-geometric combination observation, oblique path total electron content and ionospheric total electron content change rate index; S21. Based on the preprocessed dual-frequency pseudorange and carrier phase observations, construct MW wide-lane combined observations and GF geometric-free combined observations according to the predetermined combination formula, as the basic observations for subsequent cycle slip detection and repair processing.

[0025] The observation values ​​of the MW (Melbourne-Wubbena) wide lane combination are calculated using the following formula.

[0026] Calculate GF (Geometry-Free) observations using the following formula.

[0027] In the formula , and At frequency j The pseudorange phase observation (m), carrier phase observation (cycle), and wavelength (m) are measured. j The values ​​are 1 and 2, which correspond to the L1 and L2 frequency bands of the GPS system, respectively. (m), and The L1 and L2 frequency bands represent the GPS carrier phase, respectively. =1575.42MHz, =1227.60MHz. c is the speed of light.

[0028] S22. Calculate the total electron content (STEC) along the oblique path based on GNSS observation data, and further calculate the rate of change of STEC (ROT) between adjacent epochs. Perform statistical processing on ROT within a preset time window to obtain the ROTI index, which characterizes the intensity of ionospheric activity. The ROTI value is used to reflect the severity of ionospheric disturbances on the current satellite signal propagation path.

[0029] Calculate the total electron content along the oblique path (STEC) and the rate of change index of total electron content in the ionosphere (ROTI value) using the following formulas.

[0030] Where s represents a specific satellite, i represents the epoch index, and R represents the time interval between adjacent epochs; angle brackets indicate the average value within a certain time window (5 minutes in this embodiment). STEC is the total electron content along the slant path (TECU). K =40.3 m 3 / s 2 ROTI is the standard deviation of the rate of change of TEC (total electron content), and ROT is the rate of change of TEC.

[0031] S3. Using the static parameter transfer method, a preliminary determination of cycle slip is made by comparing the difference between the combined MW observations of the current epoch and the previous epoch with the preset MW threshold. An improved MW combination cycle slip detection and repair model employs a static parameter transfer method: The MW combination observation value for the current epoch i is calculated and directly subtracted from the previous epoch. This difference is used as the cycle slip detection criterion for the MW combination and compared with a set threshold. If the difference exceeds the threshold, the epoch is considered to have a potential cycle slip. This scheme avoids the tailing phenomenon caused by extreme values ​​during long-term averaging. After the improvement, extreme outliers are limited to a single epoch, and the problem of frequent false alarm cycle slips is suppressed.

[0032] For each epoch i, calculate Set the MW threshold. ,like If the MW combination detection flag is recorded for that epoch, then a cycle slip has occurred.

[0033] S4. Construct a GF combined cycle slip detection and repair model based on GF non-geometric combination observations, their difference components, and the ionospheric total electron content change rate index. The ionospheric disturbance intensity range is divided according to the magnitude of the rate of change of total electron content in the ionosphere, and the distribution characteristics of the first-order difference component and the second-order difference component of GF are statistically analyzed in different ranges. Based on the statistical results, the mapping relationship between the GF cycle slip detection threshold and the rate of change of total electron content in the ionosphere is established, forming a GF combined cycle slip detection repair model. Improved GF combined cycle slip detection and repair model (RAS model): Introducing ROTI as an ionospheric perturbation index, the RAS model is constructed, specifically including: S41. Construct the first-order epoch difference component and the second-order epoch difference component of GF based on the GF observations without geometric combination; this enhances the sensitivity to higher-order ionospheric delay variations and carrier phase anomalies, and provides multidimensional statistical characteristics for the subsequent establishment of an adaptive threshold model. First-order GF difference component GF second-order difference component A RAS model was constructed by combining the statistical distribution relationship between ROTI and GF cycle slip detection.

[0034] S42. Divide the ionospheric disturbance intensity into intervals according to the magnitude of the ROTI index, and statistically analyze the distribution characteristics of the first and second difference components of the GF combination in different ROTI intervals; construct the mapping relationship between the GF cycle slip detection threshold and ROTI based on the statistical distribution results, so that the cycle slip judgment threshold of the GF combination can dynamically change with the ionospheric disturbance intensity, forming a threshold model that adapts to different ROTI distribution regions.

[0035] S421. Using ROTI as the independent variable, its dependent variable is defined as the sum of the values ​​of ROTI within each interval of 0.05 TECU / min. and The linear relationship parameters determined by the statistical distribution are: slope k and intercept b. Based on this, a linear relationship is constructed for any ROTI interval with an interval of 0.05 TECU / min. : In the formula, std The standard deviation of the data; k and b enclosing and The slope and intercept of the proportional function of the triangular region formed by the horizontal and vertical axes of the two-dimensional statistical distribution. r ROTI (TECU / min) represents any value. For based on and The jointly constructed GF cycle slip detection threshold (m); x and y Representing the corresponding statistical samples respectively and .

[0036] S422. Analyze the relationship between the intercept b and ROTI, based on the distributions of b and ROTI and their co-current trend. For any ROTI value *r*, a three-dimensional function *f(r)* is constructed. This function describes the statistical boundary of the GF cycle slip detection parameters, where the GF cycle slip detection threshold is constructed based on the first-order and second-order difference components. The three-dimensional function *f(r)* corresponding to any ROTI can be expressed as: = , where mean represents the average. b(ROTI) has the following form: Based on three-dimensional surface fitting, a three-dimensional surface model for the GF cycle slip detection threshold is constructed, as shown in the following equation: In the above formula, (i=1,2,3) are the fitting coefficients, and x1,x2 represent the fitting segmentation points; Preferably, the construction of the three-dimensional function f(r) includes piecewise fitting of the threshold model parameter b(r) to achieve dynamic programming of the GF cycle slip detection threshold: When ROTI≤x1 and x1<ROTI≤x2, there is a clear synergistic relationship between the intercept b and the ROTI value, and b(r) is fitted using a two-segment quadratic polynomial model; When ROTI > x2, the co-growth trend of b and ROTI gradually disappears, and the data volume in this interval is relatively sparse, so b(r) is set to a constant.

[0037] When ROTI is low, a relatively strict threshold is used to improve cycle slip detection accuracy; when ROTI is high, the threshold is appropriately relaxed to reduce the risk of false alarms caused by severe ionospheric fluctuations. This model can reduce false alarms and make cycle slip detection more accurate.

[0038] The RAS model dynamically programs threshold boundaries to map high ROTI values ​​to high thresholds and filters cycle slips based on the 3σ statistical principle. This model appropriately discards data under low ionospheric disturbances and retains more observations under high disturbances, achieving balanced optimization of cycle slip detection under different ionospheric activity intensities and reducing the impact of outliers and process noise in navigation and positioning solutions.

[0039] For each epoch i, according to its , And ROTI value, using GF cycle slip threshold three-dimensional surface model To determine cycle slips, if the aforementioned observation parameters within a given epoch are outside the threshold boundary of the surface, then the GF combination detection flag for that epoch is recorded, indicating that a cycle slip has occurred.

[0040] S5. Perform cycle slip detection repair based on the preliminary judgment and GF cycle slip detection threshold.

[0041] A combined MW and GF improved scheme was used for cycle slip detection and repair.

[0042] Based on the observations from the MW and GF combinations, the threshold models in S3 and S4 above are used to jointly determine and repair cycle slips. If the observed value is greater than the threshold, a cycle slip is determined to have occurred; if the observed value is less than the threshold, a cycle slip is determined to have not occurred. Comparative experiments are conducted to verify the improvement of cycle slip detection and repair on PPP positioning. The determination is based on the detection of a cycle slip.

[0043] like Figure 2 As shown, the improved cycle slip detection method has achieved remarkable optimization results in non-differential and non-combined PPP positioning tests, with a reduction in positioning errors in all three directions.

[0044] For 69 sets of satellite observation data during the occurrence of ionospheric inhomogeneities, positioning experiments were conducted using three different schemes, and the corresponding positioning errors were compared. Scheme 1 uses the traditional empirical threshold model, Scheme 2 uses the MW static transfer threshold model, and Scheme 3 uses the proposed combined MW static transfer threshold and GF RAS threshold model. The 3D positioning errors of each scheme are visualized using color bars, and the RMS statistics of all positioning errors are given on the east, north, and celestial axes. The statistical distribution of positioning errors shows that Scheme 3 has a more concentrated distribution of error points and fewer high-error anomalies. In the east, north, and celestial directions, the average RMS values ​​of Scheme 3 are 0.241m, 0.240m, and 0.652m, respectively, all lower than the corresponding results of Schemes 1 and 2. These results demonstrate that the improved algorithm proposed in this paper can effectively improve the GNSS navigation and positioning accuracy during the occurrence of inhomogeneities, exhibiting good universality and reliability.

Claims

1. A method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions, characterized in that, Includes the following steps: S1. Acquire and preprocess GNSS observation data to obtain an observation sequence; S2. Based on the observation sequence, calculate the MW wide-lane combination observation, GF non-geometric combination observation, oblique path total electron content and ionospheric total electron content change rate index; S3. Using the static parameter transfer method, a preliminary determination of cycle slip is made by comparing the difference between the combined MW observations of the current epoch and the previous epoch with the preset MW threshold. S4. Construct a GF combined cycle slip detection and repair model based on GF non-geometric combination observations, their difference components, and the ionospheric total electron content change rate index; use the GF combined cycle slip detection and repair model to dynamically plan the GF cycle slip detection threshold. S5. Perform cycle slip detection repair based on the preliminary judgment and GF cycle slip detection threshold.

2. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 1, characterized in that, S2 include: S21. Based on the dual-frequency pseudorange and carrier phase observations in the observation sequence, the MW wide-lane combined observations are calculated as follows: The observations without geometric combinations of GF are calculated as follows: in, , and At frequency j The pseudorange phase observations, carrier phase observations, and wavelength are shown on the image. j The values ​​are 1 and 2, which correspond to the L1 and L2 frequency bands of the GPS system, respectively. , and The L1 and L2 frequency bands represent the GPS carrier phase, respectively. =1575.42MHz, =1227.60MHz, where c is the speed of light.

3. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 2, characterized in that, S2 also includes: S22. Calculate the total electron content (STEC) along the oblique path based on GNSS observation data, and further calculate the rate of change (ROT) of the total electron content along the oblique path between adjacent epochs. Perform statistical processing on the ROT within a preset time window to obtain the ionospheric total electron content change rate index (ROTI), which characterizes the intensity of ionospheric activity. The formula is as follows: Where s represents a specific satellite, i represents the epoch index, and R represents the time interval between adjacent epochs; angle brackets indicate the average value within a certain time window. K =40.3 m 3 / s 2 .

4. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 1, characterized in that, In S3, for each epoch i, calculate the difference between the combined MW observations of the current epoch and the previous epoch: The preset MW threshold is ,like Then, it records the cycle jump that occurred in the current epoch.

5. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 1, characterized in that, In S4, the construction of the GF combined cycle slip detection and repair model includes: The first and second order difference components of GF without geometric combination observations were obtained; GF cycle slip detection parameters were constructed based on the first and second order difference components of GF; the ionospheric disturbance intensity intervals were divided according to the magnitude of the ionospheric total electron content change rate exponent, and the distribution characteristics of the first and second order difference components of GF were statistically analyzed in different intervals; based on the statistical results, the mapping relationship between the GF cycle slip detection threshold and the ionospheric total electron content change rate exponent was established, forming a GF combined cycle slip detection repair model.

6. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 5, characterized in that, S4 also includes: Using the rate of change of total ionospheric electron content as the independent variable, the dependent variable is defined as the first difference component of GF within each interval of 0.05 TECU / min. The second-order difference component with GF The linear relationship parameters determined by the statistical distribution are: slope k and intercept b; for any interval of 0.05 TECU / min between the exponential intervals of the rate of change of total ionospheric electron content, the mapping relationship is constructed as follows: ： in, std The standard deviation of the data; k and b enclosing and The slope and intercept of the proportional function of the triangular region formed by the horizontal and vertical axes of the two-dimensional statistical distribution. r The index representing the rate of change of total electron content in the ionosphere for any given value; For based on and The GF cycle slip detection threshold was jointly constructed; x and y Representing the corresponding statistical samples respectively and .

7. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 6, characterized in that, S4 also includes: for any value of the exponent of the rate of change of total electron content in the ionosphere r, constructing a three-dimensional function f(r) to describe the statistical boundary of the GF cycle slip detection threshold.

8. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 7, characterized in that, The three-dimensional function f(r) is expressed as: = Where mean represents the average value, b(r) is the threshold model parameter, and b(ROTI) is: Based on three-dimensional surface fitting, a three-dimensional surface model for the GF cycle slip detection threshold is constructed: in, (i=1,2,3) are the fitting coefficients; x 1， x2 represents the fitting segmentation point, and ROTI is the rate of change index of total electron content in the ionosphere. For epoch i, if the GF cycle slip detection threshold is on the surface Outside the threshold boundary, the GF combination detection flag of that epoch is recorded to determine that a cycle slip has occurred.

9. The method for GNSS cycle slip repair and navigation accuracy improvement under ionospheric inhomogeneity conditions according to claim 7, characterized in that, The construction of the three-dimensional function f(r) involves piecewise fitting of the threshold model parameters b(r): When ROTI≤x1 or x1<ROTI≤x2, the intercept b and the ROTI value have a synergistic relationship, and the threshold model parameter b(r) is fitted using a multinomial model; When ROTI > x2, the co-growth trend of b and ROTI gradually disappears, and the threshold model parameter b(r) is set to a constant; Wherein, ROTI is the rate of change index of total electron content in the ionosphere, x 1， x2 represents the fitted segmentation point.

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