Inter-station Anomaly Ambiguity Detection Method Based on Tropospheric Residual Estimation

Abstract

The present invention discloses a method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation, including: proposing to use the zenith tropospheric estimation residuals corresponding to each measurement equation obtained after ambiguity fixing and back substitution, and introducing statistical tests to screen for possible ambiguous outliers; since the original zenith tropospheric residuals exhibit a non-standard normal distribution with long tails and sharp peaks, the present invention proposes to use the Box-Cox transformation to transform the residuals into a standard normal distribution, that is, to make the sum of squared residuals satisfy the chi-square distribution; combining the altitude angle threshold and the chi-square critical value for judgment, preferably selecting satellite pairs with low observation data noise and correct ambiguity fixing, and re-estimating the zenith tropospheric delay; using the newly calculated zenith tropospheric delay to obtain the double-difference tropospheric delay reference value for each satellite, and re-performing ambiguity tests on the satellites excluded in the initial screening, effectively improving the discrimination ability of the satellite ambiguity fixing situation and improving the service quality of network RTK.

Description

Technical Field

[0001] The present invention belongs to the technical field of GNSS (Global Navigation Satellite System) positioning and navigation, and relates to an abnormal ambiguity inspection method, specifically to a method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation. Background Art

[0002] Network RTK (Real-Time Kinematic) is a high-precision real-time positioning technology based on the Global Navigation Satellite System (GNSS). Through data communication between multiple reference stations distributed over a wide area and a mobile receiver, real-time, continuous, and high-precision measurement of the receiver's position is achieved.

[0003] The advantage of network RTK lies in its ability to provide high-precision real-time positioning services over a large area without the need to use a self-set reference station. It conducts data interaction and processing among multiple reference stations in the reference station network to achieve high-precision differential measurement. Network RTK is widely used in fields such as land surveying and mapping, geological exploration, mechanical navigation, vehicle navigation, and UAV navigation, and plays an important role in application scenarios that require high-precision positioning.

[0004] However, in network RTK, to provide high-precision differential information to users, the key is to ensure that the basic ambiguities between reference stations can be accurately fixed. Therefore, improving and ensuring the success rate of ambiguity fixing is one of the important challenges in the research of network RTK technology.

[0005] In terms of ambiguity fixing rate and positioning accuracy, methods relying on Ratio value inspection and Bayesian posterior probability inspection have problems of insufficient accuracy in the case of long baselines and multiple satellites. This method is difficult to accurately detect ambiguity fixing errors and cannot judge the ambiguity fixing situation of a single satellite.

[0006] In addition, although the currently adopted network element closure inspection method is commonly used, it only belongs to a necessary but not sufficient condition. This method cannot ensure that the ambiguities that meet the conditions are definitely fixed correctly, nor can it determine that the ambiguities that do not meet the conditions are definitely fixed incorrectly. Moreover, this method depends on the common view of satellites between baselines, so it cannot cover all satellites for ambiguity inspection. Summary of the Invention

[0007] To solve the above problems, the present invention discloses a method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation, and designs a set of detection and rejection processes for satellite ambiguity fixing anomalies according to statistical principles. Through this method, it is possible to effectively detect situations where there are anomalies in ambiguities, ensure the accuracy of ambiguities between reference stations, and thus improve the service quality of network RTK.

[0008] To achieve the above object, the technical solution of the present invention is as follows:

[0009] A method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation, comprising the following steps:

[0010] Step 1, propose a method that uses ambiguity-fixed back substitution to obtain the residuals of the zenith tropospheric estimates corresponding to each measurement equation, and introduce statistical tests to screen for possible ambiguity outliers;

[0011] Step 2, use the Box-Cox transformation to transform the residuals with a long-tailed and peaked non-standard normal distribution into a standard normal distribution, so that the sum of squared residuals satisfies the chi-square distribution;

[0012] Step 3, combine the elevation angle threshold and the chi-square critical value to judge, and preferably select satellite pairs with low observation data noise and correct ambiguity fixing, and re-estimate the zenith tropospheric delay;

[0013] Step 4, use the newly calculated zenith tropospheric delay to obtain the double-difference tropospheric delay reference value for each satellite, and re-perform ambiguity testing on the satellites excluded in the initial screening;

[0014] The specific steps are as follows:

[0015] In Step 1, use ambiguity-fixed back substitution into the measurement equation to calculate the residuals of the zenith tropospheric estimates.

[0016] First, consider the matrix form of the observation equation shown in Equation (1):

[0017]

[0018] In the formula, L is a column vector composed of combined carrier observations; Α is a column vector composed of zenith tropospheric mapping values, that is where b and k are two different reference stations, r represents the reference star, n is the number of double-differenced satellites; B is a column vector composed of combined wavelengths; is the floating-point solution of the ambiguity; is the zenith tropospheric value corresponding to the floating-point ambiguity; V is the residual of the floating-point solution.

[0019] After searching and fixing through the LAMBDA method, the fixed solution of the ambiguity is obtained as The fixed solution of the zenith troposphere can be obtained through Equation (2)

[0020]

[0021] In the formula, is the covariance matrix corresponding to the floating-point solution of the zenith troposphere and the floating-point solution of the ambiguity; is the variance matrix corresponding to the float solution of the ambiguity.

[0022] Substitute the fixed solution of the ambiguity and the fixed solution of the zenith troposphere into Equation (1) to obtain the fixed solution residual

[0023]

[0024] where represents the residual error of estimating the zenith troposphere in each measurement equation. If there is a fixed anomaly in the ambiguity, this value will absorb the float bias brought by the abnormal fixation. Using this property combined with statistical tests, satellites with large observation value noise or fixed ambiguity anomalies can be screened out.

[0025] Step 2. Use the Box-Cox transformation to transform the residuals with a long-tailed and peaked non-standard normal distribution into a standard normal distribution, and use the chi-square test to check for outliers.

[0026] The standard deviation of the residuals obtained in Equation (3) depends on the noise of the observation value L. Since the observation equation is a double-difference equation, the correlation between the residuals introduced thereby needs to be considered. In the present invention, the sine altitude angle model is used to obtain the noise matrix R of the observation equation, and further the normalized fixed solution residual can be obtained from Equation (4)

[0027]

[0028] At this time, although the envelope of the distribution of the normalized fixed solution residuals still shows a bell-shaped curve, it has the characteristics of a long-tailed and peaked shape, which will lead to the confusion between normal values and outliers near the critical value in the chi-square test, resulting in a large number of false alarms. Therefore, it is necessary to transform to make the distribution of the residuals close to the standard normal distribution.

[0029] The present invention adopts the Box-Cox transformation to perform a generalized power transformation on the normalized residuals, and its expression is as shown in Equation (5):

[0030]

[0031] where λ is the undetermined parameter, y is the data before transformation, and y (λ) represents the data after transformation. In the present invention, the search method is used to determine the undetermined parameter λ. Traverse all possible λ in the range of [-5, 5] with a step size of 0.01. After transforming the original data according to Equation (5), use the Shapiro-Wilk normal distribution test to find the maximum likelihood probability that the transformed data follows the standard normal distribution, and the value with the maximum probability is the required λ.

[0032] In the weak ionosphere combination adopted in the present invention, the λ values obtained by fitting the normalized residuals of all satellites (27,204, 27,206, and 28,040 data respectively) using three baselines are 0.316, 0.298, and 0.314 respectively. Therefore, taking the average value of the three, 0.31, as the normal distribution transformation parameter, the standardized fixed solution residuals can be obtained. The transformation formula (6):

[0033]

[0034] The sum of squares of the standardized fixed solution residuals follows a chi-square distribution. Thus, the chi-square test can be used to determine whether there are outliers in the residual vector:

[0035]

[0036] In the formula, χ 2 is the chi-square value calculated from the residuals; represents the chi-square critical value with a degree of freedom of υ and a significance level of 0.01.

[0037] Step 3. Combine the elevation angle threshold and the chi-square critical value to judge, and preferably select satellite pairs with low observation data noise and correct fixed ambiguities, and re-estimate the zenith tropospheric delay.

[0038] Considering that the weights of satellites with low elevation angles are small, and even if there are abnormal ambiguities, it is difficult to detect them through the chi-square test. Therefore, in the present invention, on the basis of the chi-square test, an elevation angle threshold condition (E≥30°) is added to ensure that the preferably selected satellites are all satellites with correct fixed ambiguities. Substitute the fixed ambiguities of the preferably selected satellites into the observation equation of formula (1) to obtain:

[0039]

[0040] In the formula, L s is the measured value after correcting the preferably selected ambiguity; is the zenith tropospheric elevation angle mapping function; is the parameter to be estimated for the new zenith tropospheric wet delay; is the double-differenced satellite-to-ground range; is the double-differenced tropospheric dry delay given by the empirical model; is the double-differenced combined carrier observation value; λ is the combined wavelength.

[0041] From formula (8), through least squares fitting, a new estimated value of the zenith tropospheric wet delay can be obtained This value eliminates the influence of abnormal ambiguities and at the same time reduces the influence of large-noise measured values, and is more accurate than the original estimated value of the zenith troposphere

[0042] ​Step 4. Use the newly calculated zenith tropospheric delay to obtain the double-difference tropospheric delay reference value for each satellite, and re-perform ambiguity testing on the satellites excluded in the initial screening.

[0043] Considering that the accuracy of estimating the dry tropospheric delay using the prior model can reach the sub-millimeter level, and about 90% of the tropospheric delay is composed of the dry delay, most of the troposphere can be determined relatively accurately. For the wet delay part, the new zenith tropospheric estimation value is obtained by combining with the zenith tropospheric mapping function. Thus, the double-difference tropospheric delay reference value corresponding to each satellite can be given:

[0044]

[0045] In the formula, the dry delay is estimated using the currently most accurate GPT2W model. The high-precision Saastamoinen model is used for modeling in GPT2W. Generally, the hydrostatic delay (dry delay) of this model is considered to be 2 - 3 mm;

[0046] The new zenith tropospheric wet delay depends on the accuracy of the carrier observations. Considering the five-frequency weak ionosphere combination method adopted in the present invention, the accuracy of the wet delay can be expressed as:

[0047]

[0048] In the formula, is the carrier noise, which can be taken as 0.5 cm; i 1 ,i 2 ,…,i 5 are the five-frequency weak ionosphere combination coefficients; f 1 ,f 2 ,…,f 5 are the frequency points corresponding to the combination coefficients.

[0049] It can be calculated therefrom that under the condition of 0.5 cm carrier noise, the wet tropospheric noise of the BDS-3 system The wet tropospheric noise of the Galileo system According to the error propagation law, the noise of the double-difference tropospheric delay reference value can be determined as

[0050] Finally, extract the double-difference tropospheric delay of the non-preferred satellites through the weak ionosphere combination equation, and compare it with the corresponding double-difference tropospheric reference value. Determine whether to retain the satellite by judging whether the difference between the two is within the 3σ range.

[0051]

[0052] The beneficial effects of the present invention include:

[0053] The method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation proposed by the present invention can effectively detect the situation where there are abnormal ambiguities and improve the accuracy of ambiguity fixing. A detection and rejection process for abnormal satellite ambiguity fixing is designed, which helps to exclude abnormal ambiguity values and ensure the correctness of the ambiguities between reference stations. By preferentially selecting satellite pairs with small observation data noise and correct ambiguity fixing, the zenith tropospheric delay is re-estimated, further improving the accuracy of atmospheric parameter estimation. Through the re-calculated zenith tropospheric delay and ambiguity test, the discrimination ability for satellite ambiguity fixing is effectively improved, and the service quality of network RTK is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is the flowchart of the implementation of the present invention;

[0055] Figure 2 is the sample-population quantile comparison chart before and after applying the transformation of the present invention;

[0056] Figure 3 is the histogram of the chi-square value calculated by the method of the present invention and accumulated by epoch;

[0057] Figure 4 is the comparison chart of the zenith tropospheric estimation before and after satellite selection by the method of the present invention;

[0058] Figure 5 is the effect diagram of detecting incorrect ambiguity fixing caused by abnormal satellite observations by the method of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0059] The present invention will be further clarified below in conjunction with the drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

[0060] As shown in the figure, this embodiment discloses a method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation. The specific steps are as follows:

[0061] Step 1: Use the ambiguity fixing to substitute back into the measurement equation to calculate the residual of the zenith tropospheric estimation value.

[0062] First, consider the matrix form of the observation equation shown in Equation (1):

[0063]

[0064] In the formula, L is the column vector composed of combined carrier observations; Α is the column vector composed of zenith tropospheric mapping values, that is where b and k are two different reference stations, r represents the reference satellite, n is the number of double-differenced satellites; B is the column vector composed of combined wavelengths; is the floating-point solution of the ambiguity; is the zenith tropospheric value corresponding to the floating-point ambiguity; V is the residual of the floating-point solution.

[0065] After searching and fixing by the LAMBDA method, the fixed solution of the ambiguity is The fixed solution of the zenith troposphere can be obtained through Equation (2)

[0066]

[0067] In the formula, is the covariance matrix corresponding to the floating-point solution of the zenith troposphere and the floating-point solution of the ambiguity; is the variance matrix corresponding to the floating-point solution of the ambiguity.

[0068] Substitute the fixed solution of the ambiguity and the fixed solution of the zenith troposphere into Equation (1), and the residual of the fixed solution can be obtained

[0069]

[0070] In the formula, represents the residual error of estimating the zenith troposphere in each measurement equation. If there is a fixed anomaly in the ambiguity, this value will absorb the floating-point deviation brought by the abnormal fixation. Using this property combined with statistical tests, satellites with large observation noise or fixed ambiguity anomalies can be screened out.

[0071] Step 2: Use the Box-Cox transformation to transform the residuals with a long-tailed and peaked non-standard normal distribution into a standard normal distribution, and use the chi-square test to check for outliers.

[0072] The standard deviation of the residuals obtained in Equation (3) depends on the noise of the observation value L. Since the observation equation is a double-difference equation, the correlation between the residuals introduced thereby needs to be considered. In the present invention, the sine elevation angle model is used to obtain the noise matrix R of the observation equation, and further the normalized residual of the fixed solution can be obtained from Equation (4)

[0073]

[0074] At this time, although the envelope of the distribution of the normalized residual of the fixed solution obtained still shows a bell-shaped curve, it has the characteristics of a long tail and a peak, which will lead to confusion between normal values and outliers near the critical value in the chi-square test, resulting in a large number of false alarms. Therefore, it is necessary to transform to make the distribution of the residuals close to the standard normal distribution.

[0075] The present invention uses the Box-Cox transformation to perform a power transformation on the normalized residuals, and its expression is as shown in Equation (5):

[0076]

[0077] In the formula, λ is a parameter to be determined, y is the data before transformation, and y (λ) represents the data after transformation. In the present invention, the parameter λ to be determined is determined by means of search. All possible λ values are traversed within the range of [-5, 5] with a step size of 0.01. After the original data is transformed according to Equation (5), the maximum likelihood probability that the transformed data follows the standard normal distribution is obtained by using the Shapiro-Wilk normal distribution test. The value with the maximum probability is the required λ. The results of the parameter search are shown in Table 1, and the fitting effects of the distributions before and after the transformation are as Figure 2 shown.

[0078] Table 1 Search results of λ parameters for three baseline data

[0079]

[0080] In the present invention, the average value of the three, 0.31, is taken as the normal distribution transformation parameter, and the transformation formula (6) of the standardized fixed solution residuals can be obtained:

[0081]

[0082] The sum of squares of the standardized fixed solution residuals follows the chi-square distribution (as Figure 3 shown), so the chi-square test can be used to determine whether there are outliers in the residual vector:

[0083]

[0084] In the formula, χ 2 is the chi-square value calculated from the residuals; represents the chi-square critical value with υ degrees of freedom and a significance level of 0.01.

[0085] Step 3, combine the elevation angle threshold and the chi-square critical value to judge, and preferably select satellite pairs with small observation data noise and correct ambiguity fixation, and re-estimate the zenith tropospheric delay.

[0086] Considering that the weights of satellites with low elevation angles are small, and it is difficult to detect abnormal ambiguities through the chi-square test even if they occur, the present invention adds an elevation angle threshold condition (E≥30°) on the basis of the chi-square test to ensure that the preferably selected satellites are all satellites with correct ambiguity fixation. Substitute the fixed ambiguities of the preferably selected satellites into the observation equation of Equation (1) to obtain:

[0087]

[0088] In the formula, L s is the preferably ambiguity-corrected measurement value; is the zenith tropospheric elevation angle mapping function; is the parameter to be estimated for the new zenith tropospheric wet delay; is the double-differenced satellite-to-ground range; is the double-differenced tropospheric dry delay given by the empirical model; is the double-differenced combined carrier observation value; λ is the combined wavelength.

[0089] From Equation (8), through least squares fitting, a new estimated value of the zenith tropospheric wet delay can be obtained. This value removes the influence of abnormal ambiguities and at the same time reduces the influence of large-noise observation values, and is more accurate than the original estimated value of the zenith troposphere . Figure 4 shows the comparison results of the estimated values of the zenith troposphere before and after screening with the true value when the ambiguity is wrong by one cycle.

[0090] Step 4: Use the newly calculated zenith tropospheric delay to obtain the double-differenced tropospheric delay reference value for each satellite, and re-perform ambiguity testing on the satellites excluded in the initial screening.

[0091] Considering that the estimation accuracy of the tropospheric dry delay using the prior model can reach the sub-millimeter level, and about 90% of the tropospheric delay is composed of the dry delay, most of the troposphere can be determined more accurately. For the wet delay part, the new zenith tropospheric estimation value is combined with the zenith tropospheric mapping function to obtain. Thus, the double-differenced tropospheric delay reference value corresponding to each satellite can be given:

[0092]

[0093] In the formula, the dry delay is estimated using the currently most accurate GPT2W model. The high-precision Saastamoinen model is used for modeling in GPT2W. Generally, the hydrostatic delay (dry delay) of this model is considered to be 2 - 3 mm;

[0094] The new zenith tropospheric wet delay depends on the accuracy of the carrier observation value. Considering the five-frequency weak ionosphere combination method adopted in the present invention, the accuracy of the wet delay can be expressed as:

[0095]

[0096] In the formula, is the carrier noise, which can be taken as 0.5 cm; i 1 ,i 2 ,…,i 5is the five-frequency weak ionosphere combination coefficient; f 1 , f 2 , …, f 5 are the frequency points corresponding to the combination coefficients.

[0097] From this, it can be calculated that under the condition of a carrier noise of 0.5 cm, the wet tropospheric noise of the BDS-3 system the wet tropospheric noise of the Galileo system According to the error propagation law, the noise of the double-difference tropospheric delay reference value can be determined as

[0098] Finally, the double-difference tropospheric delay of non-preferred satellites is extracted through the weak ionosphere combination equation, and compared with the corresponding double-difference tropospheric reference value. By judging whether the difference between the two is within the 3σ range, it is decided whether to retain the satellite.

[0099]

[0100] Figure 5 shows the result of detecting ambiguity anomalies using the method described in the present invention after adding a one-week cycle slip lasting 100 epochs to the carrier observations of the B23 satellite. It should be noted that in the first few epochs of adding the cycle slip, due to the existence of filtering, the fixed ambiguity solution did not directly increase by one week, but the anomalies in the observations were still detected by this method.

[0101] It should be noted that the above content only illustrates the technical idea of the present invention and cannot be used to limit the protection scope of the present invention. For those of ordinary skill in the art in this technical field, without departing from the principle of the present invention, several improvements and refinements can still be made, and these improvements and refinements all fall within the protection scope of the claims of the present invention.

Claims

1. A method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation, characterized in that, it includes: Step 1: Propose a method that uses ambiguity-fixed back substitution to obtain the residuals of the zenith tropospheric estimates corresponding to each measurement equation, and introduce statistical tests to screen for possible abnormal ambiguity values; The calculation method of the zenith tropospheric estimate residuals first considers the matrix form of the observation equation shown in Equation (1): In the formula, \(L\) is a column vector composed of combined carrier observations; \(\varLambda\) is a column vector composed of zenith tropospheric mapping values, that is where \(b\) and \(k\) are two different reference stations, \(r\) represents the reference satellite, \(n\) is the number of double-differenced satellites; \(B\) is a column vector composed of combined wavelengths; is the floating-point solution of the ambiguity; is the zenith tropospheric value corresponding to the floating-point ambiguity; \(V\) is the residual of the floating-point solution; After the ambiguity is fixed by searching through the LAMBDA method, the fixed solution of the ambiguity is obtained as The fixed solution of the zenith troposphere is obtained through Equation (2) In the formula, is the covariance matrix corresponding to the zenith tropospheric floating solution and the ambiguity floating solution; is the variance matrix corresponding to the ambiguity floating solution; The fixed ambiguity solution and the fixed zenith troposphere solution are substituted into Equation (1) to obtain the fixed solution residual In the formula, represents the residual error of estimating the zenith troposphere in each measurement equation. If there is a fixed ambiguity anomaly, this value will absorb the floating-point deviation caused by the abnormal fixation. Using this property and combining statistical tests, satellites with large observation value noise or fixed ambiguity anomalies can be screened out; Step 2: Use the Box-Cox transformation to transform the residuals with a long-tailed and peaked non-standard normal distribution into a standard normal distribution, so that the sum of the squared residuals satisfies the chi-square distribution; Step 3: Combine the elevation angle threshold and the chi-square critical value to judge, and preferably select satellite pairs with low observation data noise and correct ambiguity fixation, and re-estimate the zenith tropospheric delay; Step 4: Use the newly calculated zenith tropospheric delay to obtain the double-difference tropospheric delay reference value for each satellite, and re-perform ambiguity tests on the satellites excluded in the initial screening.

2. The method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation according to claim 1, characterized in that, Step 2 uses the Box-Cox transformation to transform the residuals with a long-tailed and peaked non-standard normal distribution into a standard normal distribution, and uses the chi-square test to check for outliers; the residual standard deviation obtained in Equation (3) depends on the noise of the observed value L, and since the observation equation is a double-difference equation, the correlation between the residuals introduced thereby needs to be considered; the noise matrix R of the observation equation is obtained using the sine altitude angle model, and further the unitized fixed solution residuals are obtained from Equation (4). Although the envelope of the distribution of the unitized fixed solution residuals obtained at this time still presents a bell-shaped curve, it has the characteristics of a long tail and a peak, which will lead to the confusion of normal values and abnormal values near the critical value in the chi-square test, resulting in a large number of false alarms; therefore, it is necessary to transform the distribution of the residuals to be close to the standard normal distribution; Adopt the Box-Cox transformation to perform a power transformation on the unitized residuals, and its expression is shown in Equation (5): where λ is a parameter to be determined, y is the data before transformation, and y (λ) represents the data after transformation; the parameter λ to be determined is found by searching. All possible values of λ are traversed within the range of [-5, 5] with a step size of 0.

01. After transforming the original data according to Equation (5), the maximum likelihood probability that the transformed data follows the standard normal distribution is obtained using the Shapiro-Wilk normal distribution test. The value of λ corresponding to the maximum probability is the desired value; For the weak ionosphere combination, the λ values obtained by fitting the unitized residuals of all satellites using three baselines are 0.316, 0.298, and 0.314 respectively. Therefore, the mean value of the three, 0.31, is taken as the normal distribution transformation parameter to obtain the standardized fixed solution residuals Transformation formula (6): The sum of the squares of the standardized fixed solution residuals follows the chi-square distribution, and the chi-square test is used to judge whether there are abnormal values in the residual vector: where χ 2 is the chi-square value for residual calculation; represents the chi-square critical value with a degree of freedom of υ and a significance level of 0.

01.

3. The method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation according to claim 1, characterized in that, The combination of the elevation angle threshold and the chi-square critical value judgment described in Step 3 preferably selects satellite pairs with low observation data noise and correct ambiguity fixation, and re-estimates the zenith tropospheric delay; Considering that the weights of low-elevation satellites are small, and it is difficult to detect ambiguity anomalies even if they occur through the chi-square test, so on the basis of the chi-square test, add an elevation angle threshold condition of E≥30° to ensure that the selected satellites are all satellites with correct ambiguity fixation; substitute the fixed ambiguities of the selected satellites into the observation equation of Equation (1) to obtain: Where, L s is the preferably ambiguity-corrected measurement value; is the zenith troposphere elevation angle mapping function; is the parameter to be estimated for the new zenith troposphere wet delay; is the double-differenced satellite-to-ground range; is the double-differenced troposphere dry delay given by the empirical model; is the double-differenced combined carrier observation value; λ is the combined wavelength; From Equation (8), through least squares fitting, a new estimated value of the zenith tropospheric wet delay is obtained. This value eliminates the influence of abnormal ambiguities and, at the same time, reduces the influence of large-noise observations, and is more accurate than the original estimated value of the zenith troposphere. More accurate.

4. The method for detecting abnormal ambiguities between reference stations based on tropospheric residual estimation according to claim 1, characterized in that, The use of the newly calculated zenith tropospheric delay to obtain the double-difference tropospheric delay reference value for each satellite and re-perform ambiguity tests on the satellites excluded in the initial screening described in Step 4; Considering that the estimation accuracy of the tropospheric dry delay using the prior model reaches the sub-millimeter level, and about 90% of the tropospheric delay is composed of the dry delay, most of the troposphere is thus determined more accurately. For the wet delay part, a new zenith tropospheric estimate is adopted obtained by combining with the zenith tropospheric mapping function; thus, the reference values of the double-differenced tropospheric delay corresponding to each satellite are given: where the dry delay is estimated using the currently most accurate GPT2W model. The high-precision Saastamoinen model is used for modeling in GPT2W. Generally, the hydrostatic delay of this model is considered to be 2-3 mm; The accuracy of the wet delay is expressed as: In the formula, is the carrier noise, taking 0.5 cm; i 1 , i 2 , …, i 5 are the five-frequency weak ionosphere combination coefficients; f 1 , f 2 , …, f 5 are the frequency points corresponding to the combination coefficients. It is calculated that under the condition of carrier noise of 0.5 cm, the wet tropospheric noise of the BDS-3 system the wet tropospheric noise of the Galileo system According to the error propagation law, the noise of the double-difference tropospheric delay reference value is defined as Finally, extract the double-difference tropospheric delay of non-preferred satellites through the weak ionospheric combination equation, compare it with the corresponding double-difference tropospheric reference value, and decide whether to retain the satellite by judging whether the difference between the two is within 3σ.

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