A method for monitoring the integrity of precision satellite orbit and clock products

Abstract

This invention, belonging to the field of satellite navigation, discloses a method for monitoring the integrity of precision satellite orbit and clock products. This method constructs a test statistic for product failures based on carrier phase observations from a ground integrity monitoring network and corrections provided by precision satellite orbit and clock products. By statistically analyzing multi-station and multi-epoch residuals, the product integrity information (UDRE) is estimated. The UDRE accurately reflects changes in product accuracy while ensuring integrity, and the UDRE estimate is at the centimeter level, meeting the requirements of high-precision positioning technology for monitoring the integrity of precision satellite orbit and clock products.

Description

Technical Field

[0001] The present invention belongs to the field of satellite navigation, and in particular relates to a method for monitoring the integrity of precision satellite orbit and clock error products. Background Art

[0002] Precision satellite orbit and clock products provide accurate satellite time and space reference information for the Global Navigation Satellite System (GNSS). The server broadcasts the precision satellite orbit and clock products generated by the ground tracking network to users. Users calculate the satellite position and satellite clock based on the broadcast ephemeris and add the ephemeris correction and clock correction provided by the product to obtain high-precision satellite position and satellite clock. Precision satellite orbit and clock products play an indispensable role in achieving high-precision and fast-convergence positioning services with high-precision positioning technology. Once the precision satellite orbit and clock products are abnormal, it will directly lead to errors in the positioning results, which will in turn cause risks. Therefore, the integrity of precision satellite orbit and clock products must be monitored to ensure the application of high-precision positioning technology in life-safety-related fields such as autonomous driving and transportation.

[0003] Currently, many organizations and commercial companies have begun releasing precise satellite orbit and clock products, including the International GNSS Service (IGS) Real-Time Service (RTS), Japan's Quasi-Zenith Satellite System (QZSS) Centimeter-Level Augmentation Service (CLAS), Trimble's CenterPoint RTX service, NovAtel's TerraStar-X service, Fugro's Marinestar G4+ service, and GEO++'s SSRPOST service. Generally, IGS-RTS orbit accuracy can reach 5 cm, and clock accuracy can reach 300 ps. While most products have achieved a high level of accuracy, few methods exist for monitoring the integrity of satellite orbit and clock products.

[0004] The Satellite-Based Augmentation System (SBAS) has developed methods for monitoring the integrity of its own satellite orbit and clock products for civil aviation. However, with the continuous improvement in the accuracy of these products, the increasing diversity of product sources, and the widespread application of high-precision positioning technology in various fields, the SBAS monitoring methods are no longer able to meet the integrity monitoring needs of high-precision positioning. The integrity monitoring methods for SBAS satellite orbit and clock products currently have the following main problems: 1) Overconservativeness: The test statistics for product errors are constructed based on pseudorange observations. Due to the accuracy of pseudorange observations, the estimated value of its integrity index is at the meter level, which is not suitable for high-precision positioning technology using carrier phase observations; 2) Poor accuracy: The errors caused by other error sources, such as the ionosphere and troposphere, are not effectively eliminated in the test statistics of product errors, and cannot accurately reflect the accuracy changes of satellite orbit and clock products; 3) Poor compatibility: This method is only applicable to the integrity monitoring of SBAS's own products, and its effectiveness for products from other sources has not been fully verified. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a method for monitoring the integrity of precision satellite orbit and clock products to solve the problems in the prior art. To achieve the above technical objectives, the technical solution adopted by the present invention is:

[0006] A method for monitoring the integrity of precision satellite orbit and clock products comprises the following steps:

[0007] S1. Construct the test statistic of product failure based on the carrier phase observation value: m and carrier phase Φ c Do the difference and get the test statistic dΦ;

[0008] S2. Satellite elevation angle weighting of the test statistic of product failure: set a cutoff elevation angle, and the test statistic dΦ below the cutoff elevation angle is excluded from the UDRE solution;

[0009] If the number of integrity monitoring stations with an elevation angle of the test statistic dΦ higher than the cutoff elevation angle does not exceed 5, the UDRE is considered as not being monitored; the test statistic dΦ with an elevation angle higher than the cutoff elevation angle is weighted;

[0010] S3. Abnormal integrity monitoring station removal: If an integrity monitoring station is misjudged as a satellite failure, the abnormal integrity monitoring station will be removed.

[0011] S4. Multi-epoch residual statistics: Using a sliding window approach, all observation data within the window are used to estimate the UDRE and obtain the mean of the single-difference test statistic of the satellite. and variance

[0012] S5. Integrity information UDRE estimation: The complete probability distribution of satellite orbit and clock product errors is obtained by relying on the mean and variance of the single-difference test statistics in the multi-epoch residuals, thereby obtaining the protection threshold UDRE at which the product errors meet the integrity requirements.

[0013] Furthermore, in step S1, for the observed carrier phase Φ m :The dual-frequency carrier phase observations of the integrity monitoring station are combined without ionosphericity and parameter correction is performed to calculate the observed carrier phase Φ m .

[0014] Furthermore, the parameter correction includes: tropospheric correction, receiver clock correction and carrier phase ambiguity correction, and the observed carrier phase Φ is calculated. m The following formula is used:

[0015] Φ m =Φ IF -cΔt r -T model -n IF ;

[0016] Where, Φ IF is the ionospheric-free combination of dual-frequency carrier phase observations obtained from the original observations of the integrity monitoring station, Δt r is the receiver clock error, T nodel is the slant tropospheric delay, n IF is the carrier phase ambiguity, and c is the speed of light constant.

[0017] Furthermore, in step S1, for the carrier phase Φ c : The carrier phase Φ is calculated from the satellite coordinates and satellite clock errors provided in the real-time satellite orbit and satellite clock products received by the integrity monitoring station, as well as the known coordinates of the integrity monitoring station. c , expressed by the following formula:

[0018]

[0019] Where, and are the satellite coordinates and satellite clock errors provided by real-time orbit and clock error products, X r are the coordinates of known integrity monitoring stations.

[0020] Furthermore, in step S2, the cutoff height angle is set to 25°, and the weighted processing of the test statistic dΦ is expressed by the following formula:

[0021]

[0022] Where W dΦ is the weight of the test statistic dΦ, E is the altitude angle corresponding to the test statistic dΦ; σ 2 (°) represents the variance of the observation value when the altitude angle is E.

[0023] Furthermore, σ 2 (°) is expressed using the following formula:

[0024]

[0025] Where E is the satellite elevation angle, and a, b, and f are coefficients.

[0026] Furthermore, the step S3 includes:

[0027] S3-1. Calculate the weighted average of the test statistic dΦ for all integrity monitoring stations for the same satellite at a certain moment. and standard deviation , calculated using the following formulas:

[0028]

[0029]

[0030] Where, is the test statistic of integrity monitoring station j on satellite p; n site is the number of integrity monitoring stations that observed the satellite; is the weight of the test statistic of integrity monitoring station j on satellite p;

[0031] S3-2. For all integrity monitoring stations, if Then the integrity monitoring station j is eliminated;

[0032] S3-3. Repeat steps S3-1 and S3-2 at least 3 times.

[0033] Furthermore, the step S4 includes:

[0034] Assume that the sliding window length is obs epochs, in which Site, The integrity monitoring station observes the satellite. For a satellite, within one UDRE update interval, Single-difference test statistics All multi-epoch residuals are counted to obtain the mean of the satellite single-difference test statistic and variance , respectively expressed by the following formulas:

[0035]

[0036]

[0037] Furthermore, in step S5, the satellite's UDRE is calculated using the following formula:

[0038]

[0039] Where, represents the maximum value among the means of the test statistics of all GPS satellites, is the standard deviation of the test statistic dΦ.

[0040] The present invention has the following beneficial effects:

[0041] (1) High Accuracy: This method constructs a test statistic for product failure based on carrier phase observations. Compared with the traditional test statistic based on pseudorange observations, this method has higher accuracy. It also effectively weakens or eliminates the influence of other error sources in the test statistic. Therefore, the UDRE estimated based on the test statistic can accurately reflect the accuracy changes of the product in real time.

[0042] (2) High Availability: This invention determines product integrity information (UDRE) through variance inflation and incorporates a historical empirical model of product errors, effectively ensuring product integrity. While ensuring integrity, the invention estimates UDRE at the centimeter level, significantly improving system availability compared to the meter-level UDRE of traditional methods.

[0043] (3) Good compatibility: The precision satellite orbit and clock error product integrity monitoring of the present invention is applicable to products provided by all current institutions or organizations. When users change the products they use, they do not need to change the integrity monitoring algorithm, which reduces its cost in actual application. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is a flow chart of the method of the present invention;

[0045] Figure 2 UDRE error envelope effect diagram of the G09 satellite and the G15 satellite in a specific embodiment of the present invention (June 10, 2021);

[0046] Figure 3This is the Stanford integrity map (full year 2021) of the satellite orbits and satellite clock products of the G09 satellite and G15 satellite in the specific embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following is a combination of the embodiments of the present invention Figure 1-Figure 3 , the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only part of the embodiments of the present invention, rather than all the embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0048] In view of the shortcomings of the traditional satellite orbit and clock product integrity monitoring method of SBAS, the present invention aims to propose a method for monitoring the integrity of precision satellite orbit and clock products, which estimates the integrity information User Differential Range Error (UDRE) of the product through the ground integrity monitoring network and broadcasts it to the user, so that the user knows the accuracy of the precision satellite orbit and clock products currently in use. Specifically, this method constructs a test statistic for product failure based on the carrier phase observation value of the ground integrity monitoring network, which has higher accuracy than the pseudorange observation value of the traditional method. At the same time, by combining the carrier phase observation value or using a high-precision model for correction, the influence of other error sources in the test statistic is further weakened or eliminated, so that it can accurately reflect the accuracy change of the product in real time. This method proposes an altitude angle weighted model suitable for UDRE solution to weaken the influence of atmospheric delay and multipath effect on the accuracy of the test statistic. In addition, the integrity risk caused by the integrity monitoring network is further eliminated by eliminating abnormal integrity monitoring stations, making the product integrity information UDRE more accurate and reasonable, and can meet the integrity monitoring needs of high-precision positioning for precise satellite orbit and clock error products.

[0049] like Figure 1 The specific steps of the technical solution adopted by the present invention are as follows:

[0050] S1. Construct product fault test statistics based on carrier phase observations:

[0051] First, the dual-frequency carrier phase observations of the integrity monitoring station are combined in an ionosphere-free manner, thereby eliminating the influence of ionospheric errors on the satellite orbit and the test statistic dΦ of the satellite clock product; the ionosphere-free combination of the dual-frequency carrier phase observations is corrected for the troposphere, the receiver clock error, and the carrier phase ambiguity, and then the observed carrier phase Φ is obtained. m , as shown in formula (1);

[0052] Among them, the tropospheric error is corrected using the GPT2w model, which is the most publicly available and widely used empirical model of tropospheric delay with the highest nominal accuracy. The carrier phase ambiguity n IF and the receiver clock difference Δt r Obtained through PPP estimation.

[0053] Calculate the carrier phase Φ c : Calculated from the satellite coordinates and satellite clock errors provided in the real-time satellite orbits and clock products received by the integrity monitoring station, and the known coordinates of the integrity monitoring station, as shown in formula (2).

[0054] The observed carrier phase Φ m and carrier phase Φ c Do the difference and get the test statistic dΦ, as shown in formula (3):

[0055] Φ m =Φ IF -cΔt r -T model -n IF (1)

[0056]

[0057]

[0058] Where dΦ represents the test statistic of the precise orbit and clock error products, Φ IF is the ionospheric-free combination of dual-frequency carrier phase observations obtained from the original observations of the integrity monitoring station, Δt r is the receiver clock error, T model is the slant tropospheric delay obtained from the GPT2w model, n IF is the carrier phase ambiguity of the ionospheric-free combination, and are the satellite coordinates and satellite clock errors provided by real-time orbit and clock error products, X r are the coordinates of known integrity monitoring stations.

[0059] S2. Satellite altitude angle weighting of the test statistic for product failures: Altitude angle is closely related to atmospheric delay and multipath effects. The lower the altitude angle, the longer the signal propagation path, and the worse the quality of the observation. Although we have eliminated atmospheric delay from the test statistic dΦ of the satellite clock product as much as possible, the impact of multipath effects cannot be ignored. Therefore, we adopted a satellite altitude angle weighting method to weaken the influence of altitude angle: First, the cutoff altitude angle is set to 25°. The test statistic dΦ below this cutoff altitude angle is excluded from the UDRE solution;

[0060] If the number of integrity monitoring stations with an elevation angle of the test statistic dΦ higher than the cutoff elevation angle (25°) does not exceed 5, the UDRE is considered to be unmonitored. Otherwise, the test statistic dΦ with an elevation angle higher than the cutoff elevation angle (25°) is weighted and expressed using the following formula (4):

[0061]

[0062] Where W dΦ is the weight of the test statistic dΦ, E is the altitude angle corresponding to the test statistic dΦ, σ 2 (°) represents the variance of the observation value when the elevation angle is E, as shown in formula (5).

[0063]

[0064] Where, σ 2 () is the variance of the observation value, E is the satellite elevation angle, a and b are based on experience, usually 3 and 4 mm; f is 100 when the observation value type is pseudorange observation value, and is 1 when the observation value type is carrier phase observation value; when the ionosphere-free combination is used, σ 2 () should be tripled.

[0065] S3. Abnormal integrity monitoring stations are eliminated: Due to hardware failure, atmospheric anomalies, or the influence of the surrounding environment, the errors in the test statistic dΦ that are not related to the satellite orbit and clock products cannot be effectively eliminated. There is a possibility that the abnormality of the integrity monitoring station will be misjudged as a satellite failure. Therefore, abnormal integrity monitoring stations need to be eliminated. The specific process is as follows:

[0066] S3-1. Calculate the weighted average of the test statistic dΦ of all integrity monitoring stations for the same satellite at a certain moment. and standard deviation , as shown in (6) and (7):

[0067]

[0068]

[0069] in, is the test statistic of integrity monitoring station j on satellite p; n site is the number of integrity monitoring stations that observed the satellite; is the weight of the test statistic of integrity monitoring station j on satellite p.

[0070] S3-2. For all integrity monitoring stations, if Then the integrity monitoring station j is eliminated.

[0071] S3-3. Repeat steps S3-1 and S3-2 at least 3 times.

[0072] S4. Multi-epoch residual statistics: In order to make the estimated value of UDRE more stable, this method uses a sliding window method and uses all observation data within the window to participate in the estimation of UDRE. Assume that the sliding window length is obs epochs, in which Site, If a satellite is observed by an integrity monitoring station, then for a satellite, a total of Single-difference test statistics , statistics of all multi-epoch residuals can be used to obtain the mean of the single-difference test statistics of the satellite and variance , as shown in formula (8) and formula (9).

[0073]

[0074]

[0075] S5. Integrity Information UDRE Estimation: Product errors are generally assumed to follow a normal distribution. Under normal distribution conditions, 99.9% of errors should be within the range of μ ± 3.29. Therefore, the complete probability distribution of satellite orbit and clock product errors can be obtained by calculating the mean and variance of multi-epoch residuals, thereby obtaining the protection threshold UDRE that ensures that product errors meet the integrity requirement (99.9%). The satellite UDRE calculation method is shown in Equation (10).

[0076]

[0077] in, Represents the maximum value among the means of the test statistic for all GPS satellites, obtained from the long-term empirical distribution of the test statistic.

[0078] This invention provides a method for monitoring the integrity of precision satellite orbit and clock products. This method constructs a test statistic for product failures based on carrier phase observations from a ground-based integrity monitoring network and corrections provided by precision satellite orbit and clock products. By analyzing multi-station, multi-epoch residuals, the product integrity information (UDRE) is estimated. The UDRE accurately reflects changes in product accuracy while ensuring integrity. With centimeter-level UDRE estimates, it meets the requirements of high-precision positioning technology for monitoring the integrity of precision satellite orbit and clock products.

[0079] A specific embodiment of the present invention is given below:

[0080] S1: Construct a test statistic for product failure based on carrier phase observations:

[0081] The integrity monitoring network is composed of 100 IGS stations evenly distributed around the world. The dual-frequency carrier phase observations of the integrity monitoring stations are combined without ionospheric interference, thereby eliminating the residual error of satellite orbit and clock products caused by ionospheric error. Orb+Clk The carrier phase of the integrity monitoring station is corrected by the troposphere-free combination, the receiver clock error is corrected, and the carrier phase ambiguity is corrected to obtain the observed carrier phase Φ m Among them, the tropospheric error is corrected using the GPT2w model, which is the most publicly available and widely used empirical model of tropospheric delay with the highest nominal accuracy. The carrier phase ambiguity n IF and the receiver clock difference Δt r It is obtained by PPP estimation. And the carrier phase Φ is calculated c The satellite coordinates and satellite clock errors provided in the final IGS satellite orbit and satellite clock products received by the integrity monitoring station are calculated, as well as the known coordinates of the integrity monitoring station. m and calculate the pseudorange Φ c The test statistic dΦ is obtained by performing the difference. The duration of this embodiment is set to the whole year of 2021.

[0082] S2. Satellite altitude angle weighting of the test statistic of product failure: According to the satellite altitude angle, the weight of each test statistic is calculated using the altitude angle weighting model shown in formula (4).

[0083] S3. Abnormal integrity monitoring station removal: When an integrity monitoring station is misjudged as a satellite failure, the abnormal integrity monitoring station is removed. Specifically:

[0084] S3-1. For the same satellite, all test statistics of the previous 10 epochs (300s in total) including the current time constitute a sequence, and the weighted average of the sequence is calculated. and standard deviation , as shown in (6) and (7):

[0085] S3-2. For all stations, if Then eliminate station j.

[0086] S3-3. Repeat steps S3-1 and S3-2 at least three times or until all measuring stations are inspected.

[0087] S4. Multi-epoch residual statistics: In the first 10 epochs (300 seconds in total) including the current moment, the test statistics of all stations that passed the test in step 3 constitute the error sequence. The mean of the satellite multi-station multi-epoch test statistics can be obtained by statistics. and variance , as shown in formula (8) and formula (9).

[0088] S5. Integrity information UDRE estimation: Based on the error experience model of the IGS final satellite orbit and clock products in the past three years, we can get Therefore, the UDRE of satellite p can be estimated according to formula (10).

[0089] This example uses the integrity monitoring results of the G09 and G15 satellites on June 10, 2021 as an example to illustrate the error envelope effect of this method. Figure 2 As shown in the figure, the UDRE estimated by the precision satellite orbit and clock error product integrity monitoring method can accurately reflect the accuracy changes of the product and can well envelop the product error. Figure 3 The final IGS satellite orbits and Stanford integrity charts of the G09 and G15 satellites for the entire year of 2021 are shown. The Stanford integrity chart is a statistical chart widely used in the industry to evaluate the integrity of algorithms. Figure 3 As shown in the figure, the integrity risk probability of G09 and G15 is less than 0.1%, and the UDRE estimation value is between 0-10cm. This shows that this method improves the availability of the system while ensuring the integrity of the system, and can meet the needs of high-precision positioning technology for integrity monitoring of precise satellite orbit and clock products.

[0090] The embodiments described above are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various deformations, modifications, and substitutions made to the technical solutions of the present invention by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A method for monitoring the integrity of precision satellite orbit and clock products, characterized in that: The following steps are involved: S1. Construct the test statistic of product failure based on the carrier phase observation value: m and carrier phase Φ c Do the difference and get the test statistic dΦ; S2. Satellite elevation angle weighting of the test statistic of product failure: set a cutoff elevation angle, and the test statistic dΦ below the cutoff elevation angle is excluded from the UDRE solution; If the number of integrity monitoring stations with an elevation angle of the test statistic dΦ higher than the cutoff elevation angle does not exceed 5, the UDRE is considered as not being monitored; the test statistic dΦ with an elevation angle higher than the cutoff elevation angle is weighted; S3. Abnormal integrity monitoring station removal: If an integrity monitoring station is misjudged as a satellite failure, the abnormal integrity monitoring station will be removed. S4. Multi-epoch residual statistics: Using a sliding window approach, all observation data within the window are used to estimate the UDRE, and the mean of the single-difference test statistic of satellite p is obtained. and variance S5. Integrity information UDRE estimation: The complete probability distribution of satellite orbit and clock product errors is obtained by relying on the mean and variance of the single-difference test statistics in the multi-epoch residuals, thereby obtaining the protection threshold UDRE at which the product errors meet the integrity requirements.

2. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 1, characterized in that: In step S1, for the observed carrier phase Φ m :The dual-frequency carrier phase observations of the integrity monitoring station are combined without ionosphericity and parameter correction is performed to calculate the observed carrier phase Φ m .

3. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 2, wherein: Parameter correction includes: tropospheric correction, receiver clock correction and carrier phase ambiguity correction, and the observed carrier phase Φ is calculated. m The following formula is used: F m =Φ IF -cΔt r -T model -n IF ; Where, Φ IF is the ionospheric-free combination of dual-frequency carrier phase observations obtained from the original observations of the integrity monitoring station, Δt r is the receiver clock error, T model is the slant tropospheric delay, n IF is the carrier phase ambiguity, and c is the speed of light constant.

4. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 1, wherein: In step S1, for the carrier phase Φ c : The carrier phase Φ is calculated from the satellite coordinates and satellite clock errors provided in the real-time satellite orbit and satellite clock products received by the integrity monitoring station, as well as the known coordinates of the integrity monitoring station. c , expressed by the following formula: Where, and are the satellite coordinates and satellite clock errors provided by real-time orbit and clock error products, X r are the coordinates of known integrity monitoring stations.

5. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 1, wherein: In step S2, the cutoff height angle is set to 25°, and the weighted processing of the test statistic dΦ is expressed by the following formula: Where W dΦ is the weight of the test statistic dΦ, E is the altitude angle corresponding to the test statistic dΦ; σ 2 (E°) represents the variance of the observation value when the altitude angle is E.

6. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 5, characterized in that: σ 2 (E°) is expressed using the following formula: Where E is the satellite elevation angle, a and b are based on experience, usually 3 and 4 mm; f is 100 when the observation type is pseudorange observation, and 1 when the observation type is carrier phase observation; when the ionosphere-free combination is used, σ 2 (E) should be tripled.

7. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 1, characterized in that: The step S3 includes: S3-1. Calculate the weighted average of the test statistic dΦ for all integrity monitoring stations for the same satellite at a certain moment. and standard deviation The following formulas are used for calculation: Where, is the test statistic of integrity monitoring station j on satellite p; n site is the number of integrity monitoring stations that observed the satellite; is the weight of the test statistic of integrity monitoring station j on satellite p; S3-2. For all integrity monitoring stations, if Then the integrity monitoring station j is eliminated; S3-3. Repeat steps S3-1 and S3-2 at least 3 times.

8. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 7, characterized in that: The step S4 includes: Assume that the sliding window length is n obs epochs, there are n Site,k The integrity monitoring stations observe satellite p. For satellite p, there are Single-difference test statistics All multi-epoch residuals are counted to obtain the mean of the satellite p single-difference test statistic and variance They are expressed using the following formulas:

9. The method for monitoring the integrity of precision satellite orbit and clock products according to claim 8, characterized in that: In step S5, the UDRE of satellite p is calculated using the following formula: Where, represents the maximum value among the means of the test statistics of all GPS satellites, is the standard deviation of the test statistic dΦ.

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