Factor graph optimization solution-based ambiguity fixing method and system for PPP

Abstract

The present application relates to the technical field of precise point positioning, and particularly relates to a PPP ambiguity fixing method and system based on factor graph optimization solution, a PPP observation model is established based on state variables between a receiver and a satellite, wherein the state variables include receiver position parameters, receiver clock bias, troposphere delay parameters and satellite carrier phase ambiguity; state variables of the receiver position parameters, the receiver clock bias and the troposphere delay parameters at different time are set as first variable nodes, the satellite carrier phase ambiguity state variables are set as second variable nodes, GNSS pseudorange observation data and carrier phase observation data are set as factor nodes, a PPP factor graph model is constructed, wherein ionosphere combined ambiguity fixing factors are set between the second variable nodes; optimization calculation is carried out based on the constructed PPP factor graph model to obtain a PPP ambiguity fixing solution. The present application realizes PPP ambiguity fixing based on a factor graph optimization framework, improves the PPP convergence speed and positioning accuracy, and lays a foundation for tight combination of PPP AR and camera / laser radar / IMU SLAM.

Description

Technical Field

[0001] This invention relates to the field of precision single-point positioning technology, and in particular to a method and system for fixing PPP ambiguity based on factor graph optimization solutions. Background Technology

[0002] Since its initial introduction, Precise Point Positioning (PPP) has garnered widespread attention and been applied across various fields due to its ability to achieve absolute centimeter / decimeter-level positioning globally using a single receiver. However, the presence of uncalibrated fractional cycle bias (FCB) results in floating-point ambiguities in carrier phase observations within traditional PPP, failing to leverage the advantages of integer ambiguity resolution (AR), leading to slow convergence and low accuracy. One of the major developments in PPP over the past two decades has been ambiguity resolution techniques. PPP AR can be achieved by estimating the FCB and applying it to users' inter-satellite single-difference PPP. In addition to constructing new models, PPP AR has been extended to multi-frequency, multi-GNSS systems. To utilize more frequencies, non-combined PPP models have been employed, and the feasibility of non-combined PPP AR has been verified. In summary, PPP AR has made significant progress in multi-frequency, multi-GNSS applications. Currently, some IGS (International GNSS Services) analysis centers have begun offering satellite products to facilitate PPP AR implementation for users. To ensure consistency in satellite clock bias and phase deviation products, the IGS Analysis Center has also established a PPP AR working group to study the interoperability of PPP AR products. It is foreseeable that PPP AR will replace traditional PPP in many future applications.

[0003] The application of PPP in robot simultaneous localization and mapping (SLAM) systems is very limited. Typically, robots need to fuse data from multiple sensors, such as inertial measurement units (IMUs), cameras, and LiDAR, to achieve environmental perception and navigation, thus enabling autonomous tasks. Adding GNSS sensors can provide robots with precise global coordinate references, enabling broader applications. The main challenge in tightly integrating GNSS systems with robot camera / LiDAR / IMU sensors lies in the fact that PPP generally uses Kalman or Kalman correlation filtering methods for state estimation, while SLAM employs Factor graph optimization (FGO). Compared to Kalman filtering, FGO can utilize more information, supports multiple linearizations, and enables plug-and-play multi-sensor fusion. The efficiency of FGO in camera / LiDAR / IMU data processing has been demonstrated through various open-source libraries.

[0004] However, the application of FGO in GNSS positioning is very limited. FGO was initially applied to pseudorange-based GNSS positioning gross error removal in complex observation environments. FGO-based pseudorange positioning has also been applied to GNSS / INS integrated navigation systems. These works only used pseudorange observations, neglecting more precise carrier phase observations. Recently, time-differentiated carrier phase observations have been used to construct closed-loop constraints based on FGO to improve relative positioning accuracy, such as in pseudorange-based relative positioning, visual odometry, and GNSS / INS systems. These studies also only used time-differentiated carrier phase observations. Furthermore, FGO has been used to process raw pseudorange and carrier phase observations to achieve real-time kinematic positioning (RTK); RTK models have been built using graph state-space models, and RTK solutions have been implemented using FGO. These studies used complete carrier phase observations but only employed differential positioning modes, resulting in similarly poor improvements in positioning accuracy. Summary of the Invention

[0005] To address this, the present invention provides a PPP ambiguity fixing method and system based on factor graph optimization solution, which improves PPP positioning accuracy by increasing ambiguity fixing factors, thereby solving the problems of low GNSS positioning accuracy and unsatisfactory positioning effect of existing FGO.

[0006] According to the design scheme provided by the present invention, on the one hand, a method for fixing PPP ambiguity based on factor graph optimization solution is provided, comprising:

[0007] A PPP observation model is established based on the state variables between the receiver and the satellite, where the state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity.

[0008] The state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times are set as the first variable node, the satellite carrier phase ambiguity state variable is set as the second variable node, and GNSS pseudorange observation data and carrier phase observation data are set as factor nodes. A PPP factor graph model is constructed, wherein an ionospheric combination ambiguity fixed factor is set between the second variable nodes.

[0009] Optimization calculations are performed based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

[0010] As a method for fixing PPP ambiguity based on factor graph optimization solutions in this invention, the PPP observation model is further expressed as follows: , ,in, Indicates the receiver position parameters. These represent the receiver clock bias and tropospheric delay parameters, respectively. This indicates the first jump of satellite s in the cycle. A degree of ambiguity, This is the size of the sliding window.

[0011] As a PPP ambiguity fixing method based on factor graph optimization solution of the present invention, the PPP factor graph optimization model is further constructed, which also includes: obtaining prior factors from standard single-point positioning, so as to obtain the first variable node information at the initial time using the prior factors; and in the factor nodes, setting the pseudorange factor as a one-sided factor related to the first variable node at the current time, and setting the carrier phase factor as a two-sided factor related to both the first variable node and the second variable node.

[0012] As a PPP ambiguity fixing method based on factor graph optimization solution of the present invention, further, an ionosphere-eliminating combined ambiguity fixing factor is set between the second variable nodes, including:

[0013] First, the satellite carrier phase integer ambiguity is decomposed into wide-lane ambiguity and narrow-lane ambiguity;

[0014] Next, the wide-lane ambiguity is calculated using HMW combination, and the narrow-lane ambiguity is obtained based on the wide-lane ambiguity and floating-point deambiguity.

[0015] Then, the carrier phase ambiguity is tested and fixed based on wide-lane ambiguity and narrow-lane ambiguity, and a new deionization combined ambiguity fixing factor is formed in the PPP factor graph optimization model by constructing strong constraints.

[0016] As a method for fixing PPP ambiguity based on factor graph optimization solutions in this invention, further, strong constraints are applied. Represented as: ,in, and Indicates two different satellites. Indicates the ambiguity of inter-satellite single differences. They represent , Ambiguity, This indicates inter-satellite phase delay.

[0017] As a PPP ambiguity fixing method based on factor graph optimization solution of the present invention, further, the carrier phase ambiguity is tested and fixed based on wide-lane ambiguity and narrow-lane ambiguity, including:

[0018] The ambiguity of wide lanes was fixed using the rounding method, and the ambiguity of narrow lanes was fixed using the least squares reduction correlation adjustment algorithm. The ambiguity fixing was verified by testing the PPP positioning accuracy.

[0019] As a method for fixing PPP ambiguity based on factor graph optimization solutions in this invention, further optimization calculations are performed based on the constructed PPP factor graph model to obtain a fixed PPP ambiguity solution, including:

[0020] First, we assume that the GNSS observation data are independent of each other and follow a Gaussian distribution with zero mean. The problem of calculating the maximum a posteriori estimate in the optimization of the PPP factor graph model is transformed into the problem of minimizing the sum of a series of residuals, where each observation data corresponds to a residual.

[0021] Then, based on prior information, carrier phase or pseudorange observation data, and carrier phase or pseudorange observation data residual function, the maximum a posteriori estimate of the state vector is obtained by using the Bayesian method, so as to obtain the fixed solution of PPP ambiguity based on the maximum a posteriori estimate.

[0022] Furthermore, the present invention also provides a PPP ambiguity fixing system based on factor graph optimization solutions, comprising: an observation module, an optimization module, and an output module, wherein,

[0023] The observation module is used to establish a PPP observation model based on the state variables between the receiver and the satellite. The state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity.

[0024] The optimization module is used to set the state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times as the first variable node, the satellite carrier phase ambiguity state variable as the second variable node, and GNSS pseudorange observation data and carrier phase observation data as factor nodes to construct a PPP factor graph model. Among them, an ionospheric combination ambiguity fixed factor is set between the second variable nodes.

[0025] The output module is used to perform optimization calculations based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

[0026] The beneficial effects of this invention are:

[0027] This invention achieves PPP ambiguity fixation based on a factor graph optimization framework, improving PPP convergence speed and positioning accuracy, and laying the foundation for tight integration of PPP AR with camera / LiDAR / IMU SLAM. Further experiments were conducted using over 200 MGEX stations. The results showed that the average accuracy of static PPP in the E, N, and U directions improved from 1.07, 0.51, and 2.49 cm to 0.6, 0.4, and 2.38 cm, representing improvements of 44%, 22.5%, and 4.4%, respectively. For simulated dynamic PPP, the average accuracy in the E, N, and U directions improved from 2.58, 2.15, and 7.3 cm to 1.64, 1.7, and 7.33 cm, representing improvements of 36.9%, 21.1%, and -0.4%, respectively. Furthermore, dynamic PPP was validated using real dynamic data collected from a mobile vehicle. After initial fixation, the PPP accuracy in the E, N, and U directions improved from 3.7, 2.1, and 10.1 cm to 1.6, 2.0, and 9.0 cm, representing improvements of 32%, 5%, and 11%, respectively. This demonstrates the effectiveness of the proposed scheme and its promising application prospects. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the PPP factor graph optimization solution model in the embodiment;

[0029] Figure 2 This is a timing diagram of GPS satellite WL FCB selected as the reference satellite in the embodiment.

[0030] Figure 3 This is a timing diagram illustrating the selection of the G10 satellite as the reference GPS satellite NL FCB in the embodiment.

[0031] Figure 4 This is a schematic diagram of the posterior residual distributions estimated by GPS WL (left) and NL (right) FCB in the example.

[0032] Figure 5 This is a schematic diagram illustrating the errors in three directions for the floating-point and fixed solutions at each station of DOY183 in the embodiment;

[0033] Figure 6 This is a schematic diagram of the errors in three directions for the simulated dynamic floating-point solution and the fixed solution of the DOY183 station CUT0 in the embodiment;

[0034] Figure 7 Examples of vehicle platform and motion trajectory in the embodiments;

[0035] Figure 8 This is a schematic diagram of the number of visible satellites and the sky map during the experiment in the embodiment;

[0036] Figure 9 This is a schematic diagram of the dynamic PPP error timing based on Kalman filtering and factor graph optimization in the embodiment. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of this invention clearer and more understandable, the invention will be further described in detail below with reference to the accompanying drawings and technical solutions.

[0038] For the receiver Observed satellites The corresponding original pseudorange and carrier phase observation equations can be expressed as:

[0039] Among them, subscript Refers to carrier frequency, superscript Refers to satellite; Indicates satellite and receiver Geometric distance between ; , These represent the clock biases of the receiver and the satellite, respectively. Indicates tropospheric delay; Indicates the ionospheric delay at the first carrier frequency. It is a carrier frequency correlation factor; , These represent the hardware delays of the receiver and the satellite, respectively. , These represent wavelength in meters and integer ambiguity in cycles, respectively. , These represent the uncalibrated phase delays associated with the receiver and the satellite, respectively. , These represent pseudorange and on-board measurement noise, respectively.

[0040] In dual-frequency GNSS PPP, an ionospheric de-delay combination is typically used to eliminate the effects of first-order ionospheric delay. Specifically, this involves... Multiply by formula (1)

[0041] ( )

[0042] Precise orbits are generally provided by the IGS analysis center. and clock difference products It is used to correct satellite orbit and clock errors. Furthermore, uncalibrated phase delay (UPD) is inextricably linked to integer ambiguity. Therefore, equation (2) can be reparameterized and written as follows:

[0043] ( )

[0044] in

[0045] ( )

[0046] ( )

[0047] ( )

[0048] ( )

[0049] Estimable parameters include receiver position. Receiver clock bias tropospheric parameters and ambiguity The above model is a traditional PPP floating-point solution model, in which the ambiguity parameters have lost their integer properties.

[0050] Therefore, this invention provides a method for fixing PPP ambiguity based on factor graph optimization solutions, comprising the following:

[0051] A PPP observation model is established based on the state variables between the receiver and the satellite, where the state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity.

[0052] The state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times are set as the first variable node, the satellite carrier phase ambiguity state variable is set as the second variable node, and GNSS pseudorange observation data and carrier phase observation data are set as factor nodes. A PPP factor graph model is constructed, wherein an ionospheric combination ambiguity fixed factor is set between the second variable nodes.

[0053] Optimization calculations are performed based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

[0054] Prior factors are obtained from standard single-point positioning to obtain the information of the first variable node at the initial time. In the factor nodes, the pseudorange factor is set as a one-sided factor related to the first variable node at the current time, and the carrier phase factor is set as a two-sided factor related to both the first variable node and the second variable node.

[0055] Among them, an anti-ionization combined ambiguity fixing factor is set between the second variable nodes, which can be designed to include:

[0056] First, the satellite carrier phase ambiguity is decomposed into wide-lane ambiguity and narrow-lane ambiguity;

[0057] Next, the wide lane ambiguity is calculated using HMW combination, and the narrow lane ambiguity is obtained based on the wide lane ambiguity estimation and floating-point deambiguity.

[0058] Then, the carrier phase ambiguity is tested and fixed based on wide-lane ambiguity and narrow-lane ambiguity, and a new deionization combined ambiguity fixing factor is formed in the PPP factor graph optimization model by constructing strong constraints.

[0059] The ambiguity of the wide lane can be fixed using the rounding method, and the ambiguity of the narrow lane can be fixed using the least squares reduction correlation adjustment algorithm. The fixing of the ambiguity of the wide lane and the narrow lane can be tested and verified by PPP positioning accuracy.

[0060] To achieve fixed PPP ambiguity, i.e., to restore the integer property of ambiguity, the following steps are taken: Decomposed into:

[0061]

[0062] In the formula For the wide alley (WL) ambiguity, The narrow alleyway (NL) ambiguity is used. Typically, the WL ambiguity is calculated using the Hatch-Melbourne-Wübbena (HMW) combination. Once the WL ambiguity is determined, the NL ambiguity can be derived, and its fixability can be tested. Only when both the WL and NL ambiguities are fixable can the ionosphere-suppressing combination ambiguity be fixed.

[0063] The WL ambiguity can be obtained by the following formula.

[0064] (8)

[0065] in The wavelength of WL ambiguity. WL ambiguity can be further decomposed into...

[0066] (9)

[0067] (10)

[0068] (11)

[0069] Phase delay not corrected when correcting WL ambiguity and Subsequently, due to the longer wavelength of WL, its ambiguity can be easily fixed as an integer.

[0070] With WL fuzziness And floating-point defuzzification The NL ambiguity can then be calculated based on (7). As shown in the following formula

[0071] (12)

[0072] in

[0073] (13)

[0074] (14)

[0075] After correcting the uncorrected phase delay of NL ambiguity and Subsequently, the NL ambiguity can also be solved into an integer value using the LAMBDA algorithm.

[0076] The uncorrected phase delay can be estimated in advance on the server using a set of reference stations according to formulas (9) and (12). The estimated satellite uncorrected phase delay is sent to the user, who needs to perform inter-satellite single-difference to eliminate the receiver's uncorrected phase delay.

[0077] (15)

[0078] in, and This indicates two different satellites. The ambiguity representing the inter-satellite single difference can be fixed directly using rounding for WL ambiguity, while NL ambiguity requires the LAMBDA algorithm. Once the WL and NL ambiguities are fixed and verified, a strong constraint can be constructed for the ionospheric combined floating-point ambiguity.

[0079] (16)

[0080] In this way, PPP ambiguity can be fixed at the user end.

[0081] In recent years, factor graph optimization has become dominant in SLAM backend data processing because it can incorporate more information, allows for repeated linearization, and supports plug-and-play multi-sensor fusion. Figure 1 As shown, PPP AR can be represented using a factor graph based on a probabilistic graphical model. The factor graph provides a convenient framework for factorizing the posterior distribution, thus enabling efficient computation of the maximum a posteriori (MAP) estimation problem.

[0082] The state parameters of PPP AR are defined as follows:

[0083] in These represent receiver position, receiver clock error, and tropospheric delay, respectively, with the same meaning as in the previous section. Indicates the size of the sliding window. For ambiguity. Superscripts indicate different satellites. Due to cycle slips, the same satellite may have multiple ambiguities, therefore subscripts are used. To distinguish ambiguities within the same satellite. Assuming that GNSS observations are independent and follow a zero-mean Gaussian distribution, the MAP problem can be further transformed into minimizing the sum of a series of residuals, where each observation corresponds to a residual.

[0084] In the formula, Prior information representing the state. It is the first Each carrier phase or pseudorange observation value The residual function representing the carrier phase or pseudorange observations. It is Mahalanobis distance.

[0085] The optimization calculation based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity can be designed to include the following:

[0086] First, we assume that the GNSS observation data are independent of each other and follow a Gaussian distribution with zero mean. The problem of calculating the maximum a posteriori estimate in the optimization of the PPP factor graph model is transformed into the problem of minimizing the sum of a series of residuals, where each observation data corresponds to a residual.

[0087] Then, based on prior information, carrier phase or pseudorange observation data and the residual function of carrier phase or pseudorange observation data, the maximum a posteriori estimate of the state vector is obtained by using the Bayesian method, so as to obtain the fixed solution of PPP ambiguity based on the maximum a posteriori estimate.

[0088] Figure 1In this context, prior factors can be obtained from standard point positioning. Pseudorange and carrier phase factors can be obtained from the error equations of the corresponding observation data (e.g., Equation 3). The pseudorange factor is a one-sided factor, dependent only on the position, clock difference, and tropospheric variables at time k. Links, while the carrier phase factor is a two-sided factor, with links at both ends. and ambiguity variables When the carrier phase is continuously tracked and there are no cycle slips, the ambiguity variables remain unchanged, thus allowing the connection of multiple carrier phase factors across continuous arcs. Furthermore, after the WL and NL ambiguities are fixed and verified, a strong constraint condition can be reconstructed for the ambiguities, forming new ambiguity fixing factors, as shown in Equation 16. After defining and constructing the factor graph, open-source factor graph libraries can be used for factor graph optimization to obtain the PPP ambiguity fixing solution.

[0089] Furthermore, based on the above method, this embodiment of the invention also provides a PPP ambiguity fixing system based on factor graph optimization, comprising: an observation module, an optimization module, and an output module, wherein,

[0090] The observation module is used to establish a PPP observation model based on the state variables between the receiver and the satellite. The state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity.

[0091] The optimization module is used to set the state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times as the first variable node, the satellite carrier phase ambiguity state variable as the second variable node, and GNSS pseudorange observation data and carrier phase observation data as factor nodes to construct a PPP factor graph model. Among them, an ionospheric combination ambiguity fixed factor is set between the second variable nodes.

[0092] The output module is used to perform optimization calculations based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

[0093] To verify the effectiveness of this solution, the following explanation is based on experimental data:

[0094] Two datasets were used. First, daily observation data from over 200 MGEX stations were used to estimate the satellite FCB and resolve PPP ambiguities. The data spanned from June 29 to July 4, 2022 (DOY180-186). Second, real-time dynamic data was collected on July 2, 2022, in Zhengzhou, China, using a GNSS receiver on a mobile vehicle platform to evaluate the performance of dynamic PPP AR.

[0095] To perform PPP AR, the satellite FCB was first estimated using 354 selected MGEX stations, with an elevation cutoff angle set at 10°, and using multi-GNSS rapid precision products provided by the German Research Centre for Geosciences (Germany). Satellite phase center deviation and variation were corrected according to IGS antenna files. Other errors, including tropospheric delay interference, phase entanglement effects, and ocean tides, were corrected according to the IGS model. Since the quality of the FCB product directly affects the performance of PPP AR, the FCB product was evaluated first.

[0096] Figure 2 This displays a time series diagram of the DOY180-186 GPS satellite WL FCB over seven days. It can be seen that the GPS satellite WL FCB changes relatively stably over time, indicating that the WL FCB quality is good.

[0097] Figure 3 The timing diagram of the GPS satellite NL FCB for DOY183 in 2022 is shown. It can be seen that the GPS satellite NL FCB stabilizes only within tens of minutes. This is because the wavelength of the NL FCB is relatively short and easily affected by errors. Another phenomenon is that the NLFCB exhibits a significant system bias of about 0.5 weeks. This is because the GFZ precision product has achieved PPP ambiguity fixation using the integer phase clock method. When the estimated WL FCB differs from the GFZ product's WL FCB by one week, it will result in a NL FCB difference of 0.47 weeks (or 0.53 weeks, depending on the definition range of FCB). It is worth noting that the above deviation does not affect PPP AR, because the one-week deviation of the WL FCB is absorbed by the WL ambiguity, and the resulting NL FCB deviation is also completely absorbed by the new NL FCB. From another perspective, this also indicates that the product estimated in this case is highly consistent with the GFZ product.

[0098] The posterior residuals estimated by FCB can also be used to assess the quality of FCB products. Generally, if the residuals are close to zero, the consistency of the FCB products is high. Figure 4 The residual distribution of the DOY183 WL / NL FCB estimates for 2022 is shown. The root mean square of the WL and NL FCB residuals are 0.072 and 0.040 weeks, respectively, and the percentages of WL and NL FCB residuals less than 0.1 weeks are 84.7% and 97.5%, respectively. These results indicate that the WL and NL FCB estimates are accurate and reliable.

[0099] To verify the positioning performance of PPP AR based on factor graph optimization, some MGEX stations were processed in static mode. It is important to note that, to clearly demonstrate the accuracy improvement, only data from the first three hours of the day were processed. Figure 5 The table shows the errors of the PPP floating-point and fixed solutions for each station in DOY183, 2022, for a total of 242 stations. Table 1 also provides the average absolute error of positioning for all stations for each day from DOY180 to 186. It can be seen that the error of the fixed solution is smaller than that of the floating-point solution, especially in the horizontal direction. Furthermore, the accuracy improvement in the east direction is more significant than that in the north direction. To further confirm this conclusion, all data from all stations and all data from another six days were processed. Table 1 lists the statistical data for these seven days.

[0100] Table 1. Accuracy of Seven-Day Static PPP Floating-Point and Fixed-Point Solutions (Unit: cm)

[0101]

[0102] As can be seen from the table, the accuracy of the fixed-point solution is significantly better than that of the floating-point solution. The average accuracy of PPP in the E, N, and U directions improved from 1.07, 0.51, and 2.49 cm to 0.6, 0.4, and 2.38 cm, respectively, representing improvements of 44%, 22.5%, and 4.4%.

[0103] The MGEX station was also used for the simulated dynamic experiment. Figure 6 The table below shows the time series error of the simulated dynamic PPP at station CUT0 in DOY183 in 2022. It can be seen that the accuracy of the fixed solution is significantly improved in all three directions, with the improvement in the horizontal direction being significantly greater than that in the vertical direction. Furthermore, the convergence time is also significantly shortened due to the fixed ambiguity. To further verify these results, we randomly selected approximately 80 stations (DOY180-DOY186) and processed their data; the statistical results are shown in Table 2.

[0104] Table 2. Statistical values ​​of accuracy of floating-point and fixed solutions for seven-day simulated dynamic PPP (unit: cm)

[0105]

[0106] It can be seen that the fixed-point solution is generally more accurate than the floating-point solution. The accuracy of the simulated dynamic PPP in the E, N, and U directions improves from 2.58, 2.15, and 7.30 cm to 1.64, 1.70, and 7.33 cm, respectively, representing improvements of 36.9%, 21.1%, and -0.4%. Similar to the static solution, the improvement is most significant in the east direction. However, the accuracy in the vertical direction remains almost unchanged. The reason for this phenomenon is currently unclear, but it may be related to the strong correlation between the vertical coordinate components, receiver clock error, and tropospheric wet delay components. Inaccurate tropospheric delay modeling may lead to less significant improvement in vertical accuracy.

[0107] On July 2, 2022, a vehicle-mounted experiment was conducted in Zhengzhou, China, to evaluate the performance of dynamic PPP AR. The vehicle was equipped with a Huace P5 receiver and a Harxon HX-CGX611 antenna for receiving GNSS signals, and a high-precision GNSS / INS navigation system POS320 with a fiber optic gyroscope for calculating the reference true trajectory. Additionally, an industrial camera was used to record the observation environment. Figure 8 As shown, all sensors are mounted on a high-strength steel frame and precisely calibrated to achieve millimeter-level spatial synchronization and microsecond-level time synchronization. Sensor parameters are shown in Table 3. The vehicle traveled for 7485 seconds between GPS time 534616 and 542100 (i.e., UTC 04:30:16 to 06:35:00), with a sampling rate of 1Hz. Figure 7 It also displays the ground truth trajectories of GNSS / INS compact motion calculated using Novatel Inertial Explorer (IE) commercial software, with centimeter-level accuracy.

[0108] Table 3 Sensor-related information

[0109]

[0110] from Figure 7 It can be seen that the observation environment is good, with almost no tall trees or buildings on both sides of the road. From Figure 8 As can be seen, satellite signal reception is good, averaging approximately 24 satellites. It is worth noting that only GPS / GLONASS / Galileo satellites were used in the processing, not BDS satellites. Furthermore, although GPS / GLONASS / Galileo satellites were used, only the GPS satellites underwent ambiguity fixing to clearly demonstrate PPP AR performance.

[0111] Figure 9 The time series diagrams of errors for dynamic PPP floating-point and fixed solutions are shown. It can be seen that the PPP AR error is significantly reduced compared to the floating-point solution. Starting from second 535560, the ambiguity was successfully fixed, and the accuracy improved significantly. Table 4 lists the statistical values ​​of the absolute PPP deviation for all epochs and epochs after second 535560. After the initial fixation, the PPP accuracy in the E, N, and U directions improved from 3.7, 2.1, and 10.1 cm to 1.6, 2.0, and 9.0 cm, respectively, representing improvements of 32%, 5%, and 11%. The improvement in accuracy was most significant in the east direction. Another interesting phenomenon is that the improvement based on median statistics is more significant than that based on average statistics, at 53%, 6%, and 21%, respectively. This phenomenon indicates that the fixed solution has less fluctuation and is more reliable.

[0112] Table 4. Statistical values ​​of accuracy for dynamic PPP floating-point and fixed-point solutions (unit: cm)

[0113]

[0114] The above data further demonstrates that the proposed solution can fix PPP ambiguity, improve PPP convergence speed and positioning accuracy, and has good application prospects.

[0115] Unless otherwise specifically stated, the relative steps, numerical expressions, and values ​​of the components and steps described in these embodiments do not limit the scope of the invention.

[0116] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0117] The units and method steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations are not considered to be beyond the scope of this invention.

[0118] Those skilled in the art will understand that all or part of the steps in the above methods can be implemented by a program instructing related hardware, and the program can be stored in a computer-readable storage medium, such as a read-only memory, a disk, or an optical disk. Optionally, all or part of the steps in the above embodiments can also be implemented using one or more integrated circuits. Accordingly, each module / unit in the above embodiments can be implemented in hardware or as a software functional module. This invention is not limited to any particular combination of hardware and software.

[0119] Finally, it should be noted that the above-described embodiments are merely specific implementations of the present invention, used to illustrate the technical solutions of the present invention, and not to limit it. The scope of protection of the present invention is not limited thereto. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that any person skilled in the art can still modify or easily conceive of changes to the technical solutions described in the foregoing embodiments within the technical scope disclosed in the present invention, or make equivalent substitutions for some of the technical features; and these modifications, changes, or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for fixing PPP ambiguity based on factor graph optimization solutions, characterized in that, Include: A PPP observation model is established based on the state variables between the receiver and the satellite, where the state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity. The state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times are set as the first variable node, the satellite carrier phase ambiguity state variable is set as the second variable node, and GNSS pseudorange observation data and carrier phase observation data are set as factor nodes. A PPP factor graph model is constructed, wherein an ionospheric combination ambiguity fixed factor is set between the second variable nodes. Optimization calculations are performed based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

2. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 1, characterized in that, The PPP observation model is represented as follows: Where, x * ,y * ,z * Indicates the receiver position parameters. dT represents the receiver clock error and the tropospheric delay parameter, respectively. This represents the ms-th ambiguity of satellite s under cycle jump, where n is the size of the sliding window.

3. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 1 or 2, characterized in that, The PPP factor graph optimization model also includes: obtaining prior factors from standard single-point positioning to obtain the information of the first variable node at the initial time using the prior factors; and in the factor nodes, setting the pseudorange factor as a one-sided factor related to the first variable node at the current time, and setting the carrier phase factor as a two-sided factor related to both the first variable node and the second variable node.

4. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 1, characterized in that, A fixed factor for ionization-free combined ambiguity is set between the second variable nodes, including: First, the satellite carrier phase integer ambiguity is decomposed into wide-lane ambiguity and narrow-lane ambiguity; Next, the wide-lane ambiguity is calculated using HMW combination, and the narrow-lane ambiguity is obtained based on the wide-lane ambiguity and floating-point deambiguity. Then, the carrier phase ambiguity is tested and fixed based on wide-lane ambiguity and narrow-lane ambiguity, and a new deionization combined ambiguity fixing factor is formed in the PPP factor graph optimization model by constructing strong constraints.

5. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 1 or 4, characterized in that, Strong constraints Represented as: Here, s1 and s2 represent two different satellites. Indicates the ambiguity of inter-satellite single differences. Let s1 and s2 represent the ambiguity respectively, and d s1,s2 This indicates inter-satellite phase delay.

6. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 4, characterized in that, The carrier phase ambiguity is tested and fixed based on wide-lane ambiguity and narrow-lane ambiguity, including: The ambiguity of wide lanes was fixed using the rounding method, and the ambiguity of narrow lanes was fixed using the least squares reduction correlation adjustment algorithm. The ambiguity fixing was verified by testing the PPP positioning accuracy.

7. The PPP ambiguity fixing method based on factor graph optimization solution according to claim 1, characterized in that, Optimization calculations are performed based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity, including: First, we assume that the GNSS observation data are independent of each other and follow a Gaussian distribution with zero mean. The problem of calculating the maximum a posteriori estimate in the optimization of the PPP factor graph model is transformed into the problem of minimizing the sum of a series of residuals, where each observation data corresponds to a residual. Then, based on prior information, carrier phase or pseudorange observation data, and carrier phase or pseudorange observation data residual function, the maximum a posteriori estimate of the state vector is obtained by using the Bayesian method, so as to obtain the fixed solution of PPP ambiguity based on the maximum a posteriori estimate.

8. A PPP fuzzyness fixing system based on factor graph optimization solution, characterized in that, It includes: an observation module, an optimization module, and an output module, among which, The observation module is used to establish a PPP observation model based on the state variables between the receiver and the satellite. The state variables include receiver position parameters, receiver clock error, tropospheric delay parameters, and satellite carrier phase ambiguity. The optimization module is used to set the state variables of receiver position parameters, receiver clock error and tropospheric delay parameters at different times as the first variable node, the satellite carrier phase ambiguity state variable as the second variable node, and GNSS pseudorange observation data and carrier phase observation data as factor nodes to construct a PPP factor graph model. Among them, an ionospheric combination ambiguity fixed factor is set between the second variable nodes. The output module is used to perform optimization calculations based on the constructed PPP factor graph model to obtain a fixed solution for PPP ambiguity.

9. An electronic device, characterized in that, include: At least one processor, and a memory coupled to said at least one processor; The memory stores a computer program that can be executed by the at least one processor to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed, enables the implementation of the method as described in any one of claims 1 to 7.

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