A full-system PPP-RTK positioning method considering code bias of ambiguity-like

Abstract

A kind of whole system PPP-RTK positioning method considering class ambiguity code bias, the positioning method includes the following steps: first, the GNSS code observation and carrier phase observation model of multiple constellation, multiple frequency points are established, then class ambiguity code bias ALCB parameter is introduced uniformly in code observation model, so as to obtain the GNSS original observation equation containing class ambiguity code bias ALCB;The eight types of rank defect of the GNSS original observation equation of class ambiguity code bias ALCB are processed specifically, according to full rank PPP-RTK network model and the network model of traditional PPP-RTK, whether the interstation single difference ALCB between user and reference station is significant is judged, two kinds of user end model are obtained;The propagation double difference ambiguity parameter in the filtering solution process of two kinds of user end model is obtained, two kinds of ambiguity fixed user end model;According to the network scene requirement of actual GNSS observation, corresponding selection two kinds of ambiguity fixed user end model, then carry out PPP-RTK real-time positioning solution, obtain positioning result.The application considers the influence of ALCB, and improves the positioning precision.

Description

Technical Field

[0001] This invention relates to an improvement of positioning technology that takes into account ambiguity code deviation, belonging to the field of positioning, and particularly to a full-system PPP-RTK positioning method that takes into account ambiguity code deviation. Background Technology

[0002] Since both IFB and SDB are terms related to the receiver, satellite, and frequency simultaneously, they are similar in form to the ambiguity of the phase observation equation. Therefore, they are collectively referred to as ALCB. Existing PPP-RTK algorithms divide code bias into two parts: satellite code bias (SCB) which is only related to the satellite and receiver code bias (RCB) which is only related to the receiver. However, existing PPP-RTK algorithms do not take into account pseudorange bias (including signal distortion bias in CDMA systems and inter-frequency bias in FDMA systems), resulting in uncompensated systematic bias in pseudorange observation. This leads to difficulties in fixing ambiguities in multiple systems, confusion in parameter estimation, and degradation of the solution accuracy in heterogeneous networks, making it impossible to achieve high-precision real-time positioning for the entire GNSS system.

[0003] Patent application CN202110211637.5, filed on August 30, 2022, discloses a PPP-RTK positioning method and apparatus that takes into account atmospheric residual errors. The PPP-RTK positioning method considering atmospheric residual errors includes: acquiring multiple sets of satellite data received by multiple uniformly distributed base stations, wherein each base station receives one set of satellite data; performing non-differential non-combined PPP calculation on each set of satellite data to estimate multiple atmospheric residual errors; fitting the multiple atmospheric residual errors using a fitting function to obtain an atmospheric residual error correction number; correcting the atmospheric residual errors in the satellite positioning data using the atmospheric residual error correction number; and performing PPP-RTK positioning based on the corrected atmospheric residual errors and the satellite positioning data received by the target object to obtain the positioning result of the target object. This scheme can eliminate the influence of atmospheric residual errors on actual positioning accuracy and convergence time, thereby improving positioning performance. However, the above scheme ignores the influence of ALCB (Atmospheric Residual Error Block), which affects positioning accuracy.

[0004] The information disclosed in this background section is intended only to enhance the understanding of the overall background of this patent application and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this invention is to overcome the problem in the prior art that ignores the influence of ALCB, which affects the positioning accuracy. It provides a full-system PPP-RTK positioning method that takes into account the influence of ALCB and improves the positioning accuracy by considering the ambiguity code deviation.

[0006] To achieve the above objectives, the technical solution of the present invention is: a system-wide PPP-RTK positioning method considering ambiguity-type code deviation, wherein the system-wide PPP-RTK positioning method considering ambiguity-type code deviation includes the following steps:

[0007] The first step is to establish a multi-constellation, multi-frequency GNSS code observation and carrier phase observation model based on CDMA and FDMA systems. Then, the ambiguous code bias ALCB parameter is uniformly introduced into the code observation model to obtain the original GNSS observation equation containing the ambiguous code bias ALCB.

[0008] The second step is to process the eight types of rank deficiencies in the GNSS raw observation equations that include the ambiguous code bias ALCB. Specifically, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and ALCB. The clock bias of the first epoch receiver is selected as the reference and the receiver phase bias is transmitted in the filtering to maintain the reference, thereby eliminating the rank deficiency between the receiver clock bias, ALCB and receiver phase bias, so as to obtain a full-rank PPP-RTK network model that takes into account ALCB.

[0009] The third step is to use the satellite products provided by the PPP-RTK server model that takes ALCB into account and the traditional PPP-RTK server model to locate the user receiver. Before positioning, it is necessary to determine whether the inter-station single difference ALCB between the user and the reference station is significant.

[0010] If the inter-station single difference ALCB is significant, the PPP-RTK user terminal model that takes into account ALCB is used for localization.

[0011] If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for positioning.

[0012] The fourth step is to first perform filtering and solving on the two types of user terminal models mentioned above, then propagate the double-difference ambiguity parameters during the filtering and solving process, and introduce the integer estimability theory in the ambiguity solving stage to convert the non-integer estimable ambiguity into an integer estimable form, thereby obtaining two types of user terminal models with fixed ambiguity.

[0013] Step 5: Based on the network scenario requirements of actual GNSS observation, select two types of user terminal models with fixed ambiguity, and then input multi-system GNSS pseudorange and carrier phase observation data to perform PPP-RTK real-time positioning calculation to obtain high-precision positioning results.

[0014] In the first step, the GNSS primitive observation equation for the ambiguous code bias ALCB is specifically as follows:

[0015] ;

[0016] in, Represents the expectation operator; , They represent the receivers respectively. Tracked satellites In frequency The code and phase observations on the screen, Represents geometric distance, zenith tropospheric delay Through mapping function Mapped to receiver With satellite Slant distance between lines of sight; receiver clock bias Satellite clock bias First-order oblique ionospheric delay and its dispersion coefficient , Indicates signal frequency; and These are respectively the ambiguity code bias and the satellite code bias. and These represent receiver phase deviation and satellite phase deviation, respectively. For phase ambiguity, For the corresponding wavelength, Inter-station single-difference ionospheric constraint.

[0017] In the second step, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and the ALCB, specifically:

[0018] Introduce the first virtual observation equation that includes these two types of parameters: ;

[0019] Assuming two sites , Two satellites were observed simultaneously. , Each satellite transmits two frequencies. , The signal, the virtual observation equation is expressed in the following matrix form: ;

[0020] in, and Representing observed values ​​and unknown parameters respectively, column vectors The elements are arranged in the following order: ;

[0021] column vector The items are arranged in the following order:

[0022] ;

[0023] Indicates the Kronecker product. Given a 4x4 identity matrix, and considering the rank deficiency of the design matrix in the above equations, the ambiguity code deviation of the first receiver is chosen as the benchmark, and other parameters are renormalized to obtain the following matrix equation: ;

[0024] in, Here is the renormalized vector of estimable parameters, whose elements are arranged in the following order:

[0025] ;

[0026] .

[0027] In the second step, the receiver clock bias of the first epoch is selected as the reference, and the receiver phase bias is maintained by passing the reference during filtering, thus eliminating the rank deficiency among the receiver clock bias, ALCB, and receiver phase bias. Specifically:

[0028] Introduce a second virtual observation equation containing the parameters to be analyzed: ;

[0029] Then, the second virtual observation equation is expanded using matrix form:

[0030] ;

[0031] Observation vector The elements in the file are arranged in the following order:

[0032] ;

[0033] Parameter vector The elements in the array are arranged as follows:

[0034] .

[0035] The full-rank form of the second virtual observation equation is as follows:

[0036] ;

[0037] Renormalized parameter vector The elements in the array are arranged in the following order:

[0038] ; .

[0039] The obtained full-rank PPP-RTK network model that takes into account ALCB is as follows:

[0040] ;

[0041] ;

[0042] in, This represents the epoch indicator. For CDMA systems, since different satellites have the same wavelength, the wavelength can be estimated in the following form: ;

[0043] Ambiguity estimable form For GLONASS, wavelength is represented. ,in The fundamental frequency is represented, and the ambiguity can be estimated in the form of: ,in , The frequency designation provides explicit formulas for ionospherically independent combinations (IF) and geometrically independent combinations, as follows:

[0044] .

[0045] In the third step, if the inter-station single difference ALCB is significant, a PPP-RTK user-end model that takes into account ALCB is used for localization, specifically:

[0046] ;

[0047] in, Indicates from satellite to user receiver unit vector, Indicates user positioning error. It is the ionospheric delay at the user's location obtained from the product interpolation derived from the network.

[0048] If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for localization, as detailed below:

[0049] .

[0050] In the fourth step, filtering and solving are first performed on the two types of user-end models mentioned above. Then, double-difference ambiguity parameters are propagated during the filtering and solving process. In the ambiguity solving stage, integer estimability theory is introduced to convert non-integer estimable ambiguities into integer estimable forms, thereby obtaining two types of user-end models with fixed ambiguities. Specifically, double-difference ambiguity parameters are propagated during the filtering process, and integer estimability theory is introduced during the ambiguity solving stage to convert non-integer estimable ambiguities into integer estimable forms, thereby achieving reliable fixation of GLONASS ambiguities. Assuming there are m GLONASS satellites, each transmitting on two FDMA signals, the ambiguity of the FDMA signal in the full-rank model can be represented in matrix form: ;

[0051] Its detailed expression is as follows:

[0052] .

[0053] The integer ambiguity is fixed, and based on the theory of integer estimability, the ambiguity matrix is ​​transformed into an equivalent transformation, mapping the original non-integer estimable ambiguity parameters to a set of integer estimable ambiguity parameters. Specifically, a lower triangular transformation matrix is ​​introduced to transform the original ambiguity matrix... Replace with an equivalent lower triangular matrix Thus, a matrix equation that can be used for integer ambiguity resolution is obtained. The elements of the matrix are constructed as follows:

[0054] ;

[0055] .

[0056] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0057] 1. In the present invention, a full-system PPP-RTK positioning method considering ambiguous code bias, a multi-constellation, multi-frequency GNSS code observation and carrier phase observation model is first established based on CDMA and FDMA systems. Then, the ambiguous code bias (ALCB) parameter is uniformly introduced into the code observation model to obtain the original GNSS observation equation containing the ALCB. The eight types of rank deficiencies in the above-mentioned original GNSS observation equation with ALCB are specifically addressed. Based on the full-rank PPP-RTK network model and the traditional PPP-RTK network model, the user receiver is treated as an intra-network receiver to determine the relationship between the user and the reference receiver. Whether the inter-station single-difference ALCB is significant is determined, resulting in two types of user-end models. In the filtering and solving process of these two types of user-end models, the double-difference ambiguity parameters are propagated. Based on the integer estimability theory, a lower triangular transformation matrix constructed from the satellite frequency channel number is introduced to map the original non-integer estimable ambiguity of GLONASS to an integer estimable form, resulting in two types of user-end models with fixed ambiguity. According to the network scenario requirements of actual GNSS observations, the two types of user-end models with fixed ambiguity are selected accordingly. Then, multi-system GNSS pseudorange and carrier phase observation data are input for PPP-RTK real-time positioning calculation, obtaining high-precision positioning results. The advantages of this design are as follows:

[0058] First, by modeling and estimating ALCB in a unified manner in real time, the systematic adverse effects of ALCB on code observations and ambiguity estimation are eliminated from the root, effectively ensuring the integer characteristics of ambiguity and significantly improving the success rate and speed of ambiguity fixation. The convergence speed of the new model is improved by 24.3% to 76.7%, and the 3D positioning accuracy is improved by 4.7% to 69.7%.

[0059] Secondly, it achieves unified modeling and calculation of ALCB for CDMA and FDMA systems, avoiding parameter estimation bias caused by ALCB aliasing in traditional algorithms, making the calculation of core parameters such as ionospheric delay, receiver clock error, and phase deviation more accurate; and it can maintain stable positioning results in both homogeneous and heterogeneous receiver networks, effectively reducing the dispersion of positioning errors and achieving stable output of centimeter-level high-precision positioning.

[0060] Thirdly, in response to the novel rank deficiency generated by the observation equation after the introduction of ALCB, a dedicated benchmark selection and parameter renormalization strategy was designed, and a full-rank estimable model was successfully constructed. This enabled the synchronous joint estimation of parameters such as ALCB, satellite code bias, receiver clock bias, and phase ambiguity, solving the problems of parameter estimation confusion and inestimation in traditional algorithms. It ensured the physical meaning and accuracy of all positioning parameter solutions, laying the core parameter foundation for high-precision positioning.

[0061] Fourthly, a full-system observation model adapted to CDMA and FDMA was constructed, and a dual-scenario adapted server and user models were designed based on whether the inter-station single-difference ALCB was significant. This model can be flexibly applied to various practical application scenarios such as homogeneous / heterogeneous receiver networks, short / long baselines, and single / dual-frequency observation. At the same time, ALCB is regarded as an arc-stable parameter. Combined with anomaly detection and re-initialization strategies, it can adapt to complex situations such as time-varying characteristics of ALCB and satellite signal anomalies, which greatly improves the anti-interference ability and robustness of the model in actual engineering scenarios.

[0062] Therefore, this invention takes into account the influence of ALCB and improves positioning accuracy.

[0063] 2. In this invention, a full-system PPP-RTK positioning method considering ambiguity code bias, a dedicated GLONASS ambiguity fixing strategy is designed based on the integer estimability theory. Through a lower triangular transformation matrix, the non-integer estimability ambiguity under the FDMA system is mapped to an integer estimability form, achieving reliable integer fixing of GLONASS ambiguity for the first time. This overcomes the technical bottleneck of traditional algorithms being unable to directly fix GLONASS ambiguity, enabling GPS+GLONASS multi-constellation joint positioning, fully leveraging the advantages of multi-constellation observation, and improving the continuity and reliability of positioning. Therefore, this invention improves the continuity and reliability of positioning.

[0064] 3. This invention provides a system-wide PPP-RTK positioning method that considers ambiguity code deviation. It effectively estimates and eliminates ALCB differences between receivers, maintaining excellent positioning convergence performance and accuracy even in heterogeneous networks. This overcomes the limitations of traditional PPP-RTK algorithms in scenarios with multiple receiver models and antenna configurations, and is well-suited to the actual construction and application needs of heterogeneous networks in current engineering projects. Therefore, this invention offers high positioning accuracy and strong convergence performance.

[0065] 4. In this invention, a system-wide PPP-RTK positioning method considering ambiguity code bias, the proposed solution does not require the introduction of complex observation combinations or external ionospheric products. The model solution process is highly compatible with traditional PPP-RTK algorithms, requiring no significant modifications to existing GNSS positioning hardware and directly adapting to the upgrade and deployment of existing continuously operating reference station networks. Simultaneously, it supports the extended application of system-wide GNSS, reserving adaptation space for subsequent fusion positioning of constellations such as BDS and Galileo, possessing broad engineering promotion value and industrial application potential. Therefore, this invention has good compatibility and wide applicability. Attached Figure Description

[0066] Figure 1 This is a flowchart of the present invention.

[0067] Figure 2This is a graph showing the original values, simulated values, and estimated statistical characteristics of the satellite ambiguity class code deviation at the HKLT station in this invention.

[0068] Figure 3 This is a comparison chart of the estimation results and statistical distribution of the ambiguity class code bias of some satellites at the HKLT station under different ionospheric weighting strategies in this invention.

[0069] Figure 4 This is a distribution map of the average ambiguity class code deviation of GPS satellites at user station MC06 under different frequency conditions in this invention.

[0070] Figure 5 This is a distribution diagram of the average ambiguity class code deviation of GLONASS satellite at user station MC06 under different frequency conditions in this invention.

[0071] Figure 6 This is a graph showing the changes in positioning error under different ambiguity processing strategies when using dual-frequency GPS and GLONASS observation data at user station MC06 in this invention.

[0072] Figure 7 This is a graph showing the changes in positioning error at user station MC06 in this invention, using single-frequency GPS and GLONASS observation data, under different ambiguity processing strategies.

[0073] Figure 8 This is a time variation diagram of the ambiguity class code deviation and the difference between receivers in the GPS and GLONASS observation signals at some stations, according to the present invention.

[0074] Figure 9 This is a diagram showing the three-dimensional positioning error results under different model conditions at the MABN site using dual-frequency GPS and GLONASS observation data.

[0075] Figure 10 This is a diagram showing the three-dimensional positioning error results under different model conditions when using dual-frequency GPS and GLONASS observation data at the VTSP site, according to the present invention.

[0076] Figure 11 This is a comparison chart of the ambiguity deconvergence performance of different models under two conditions: considering and not considering ambiguity class code deviation, in multiple user stations.

[0077] Figure 12 This invention presents statistical charts of 3D positioning errors for different models under two conditions: considering and not considering ambiguity class code deviation, across multiple user stations. Detailed Implementation

[0078] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0079] See Figures 1 to 12 A system-wide PPP-RTK localization method considering ambiguity code deviation, comprising the following steps:

[0080] The first step is to establish a multi-constellation, multi-frequency GNSS code observation and carrier phase observation model based on CDMA and FDMA systems. Then, the ambiguous code bias ALCB parameter is uniformly introduced into the code observation model to obtain the original GNSS observation equation containing the ambiguous code bias ALCB.

[0081] The second step is to process the eight types of rank deficiencies in the GNSS raw observation equations that include the ambiguous code bias ALCB. Specifically, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and ALCB. The clock bias of the first epoch receiver is selected as the reference and the receiver phase bias is transmitted in the filtering to maintain the reference, thereby eliminating the rank deficiency between the receiver clock bias, ALCB and receiver phase bias, so as to obtain a full-rank PPP-RTK network model that takes into account ALCB.

[0082] The third step is to use the satellite products provided by the PPP-RTK server model that takes ALCB into account and the traditional PPP-RTK server model to locate the user receiver. Before positioning, it is necessary to determine whether the inter-station single difference ALCB between the user and the reference station is significant.

[0083] If the inter-station single difference ALCB is significant, the PPP-RTK user terminal model that takes into account ALCB is used for localization.

[0084] If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for positioning.

[0085] The fourth step is to first perform filtering and solving on the two types of user terminal models mentioned above, then propagate the double-difference ambiguity parameters during the filtering and solving process, and introduce the integer estimability theory in the ambiguity solving stage to convert the non-integer estimable ambiguity into an integer estimable form, thereby obtaining two types of user terminal models with fixed ambiguity.

[0086] Step 5: Based on the network scenario requirements of actual GNSS observation, select two types of user terminal models with fixed ambiguity, and then input multi-system GNSS pseudorange and carrier phase observation data to perform PPP-RTK real-time positioning calculation to obtain high-precision positioning results.

[0087] In the first step, the GNSS primitive observation equation for the ambiguous code bias ALCB is specifically as follows:

[0088] ;

[0089] in, Represents the expectation operator; , They represent the receivers respectively. Tracked satellites In frequency The code and phase observations on the screen, Represents geometric distance, zenith tropospheric delay Through mapping function Mapped to receiver With satellite Slant distance between lines of sight; receiver clock bias Satellite clock bias First-order oblique ionospheric delay and its dispersion coefficient , Indicates signal frequency; and These are respectively the ambiguity code bias and the satellite code bias. and These represent receiver phase deviation and satellite phase deviation, respectively. For phase ambiguity, For the corresponding wavelength, Inter-station single-difference ionospheric constraint.

[0090] In the second step, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and the ALCB, specifically:

[0091] Introduce the first virtual observation equation that includes these two types of parameters: ;

[0092] Assuming two sites , Two satellites were observed simultaneously. , Each satellite transmits two frequencies. , The signal, the virtual observation equation is expressed in the following matrix form: ;

[0093] in, and Representing observed values ​​and unknown parameters respectively, column vectors The elements are arranged in the following order: ;

[0094] column vector The items are arranged in the following order:

[0095] ;

[0096] Indicates the Kronecker product. Given a 4x4 identity matrix, and considering the rank deficiency of the design matrix in the above equations, the ambiguity code deviation of the first receiver is chosen as the benchmark, and other parameters are renormalized to obtain the following matrix equation: ;

[0097] in, Here is the renormalized vector of estimable parameters, whose elements are arranged in the following order:

[0098] ;

[0099] .

[0100] In the second step, the receiver clock bias of the first epoch is selected as the reference, and the receiver phase bias is maintained by passing the reference during filtering, thus eliminating the rank deficiency among the receiver clock bias, ALCB, and receiver phase bias. Specifically:

[0101] Introduce a second virtual observation equation containing the parameters to be analyzed: ;

[0102] Then, the second virtual observation equation is expanded using matrix form:

[0103] ;

[0104] Observation vector The elements in the file are arranged in the following order:

[0105] ;

[0106] Parameter vector The elements in the array are arranged as follows:

[0107] .

[0108] The full-rank form of the second virtual observation equation is as follows:

[0109] ;

[0110] Renormalized parameter vector The elements in the array are arranged in the following order:

[0111] ; .

[0112] The obtained full-rank PPP-RTK network model that takes into account ALCB is as follows:

[0113] ;

[0114] ;

[0115] in, This represents the epoch indicator. For CDMA systems, since different satellites have the same wavelength, the wavelength can be estimated in the following form: ;

[0116] Ambiguity estimable form For GLONASS, wavelength is represented. ,in The fundamental frequency is represented, and the ambiguity can be estimated in the form of: ,in , The frequency designation provides explicit formulas for ionospherically independent combinations (IF) and geometrically independent combinations, as follows:

[0117] .

[0118] In the third step, if the inter-station single difference ALCB is significant, a PPP-RTK user-end model that takes into account ALCB is used for localization. Specifically:

[0119] ;

[0120] in, Indicates from satellite to user receiver unit vector, Indicates user positioning error. It is the ionospheric delay at the user's location obtained from the product interpolation derived from the network.

[0121] If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for localization, as detailed below:

[0122] .

[0123] In the fourth step, filtering and solving are first performed on the two types of user-end models mentioned above. Then, double-difference ambiguity parameters are propagated during the filtering and solving process. In the ambiguity solving stage, integer estimability theory is introduced to convert non-integer estimable ambiguities into integer estimable forms, thereby obtaining two types of user-end models with fixed ambiguities. Specifically, double-difference ambiguity parameters are propagated during the filtering process, and integer estimability theory is introduced during the ambiguity solving stage to convert non-integer estimable ambiguities into integer estimable forms, thereby achieving reliable fixation of GLONASS ambiguities. Assuming there are m GLONASS satellites, each transmitting on two FDMA signals, the ambiguity of the FDMA signal in the full-rank model can be represented in matrix form: ;

[0124] Its detailed expression is as follows:

[0125] .

[0126] The integer ambiguity is fixed, and based on the theory of integer estimability, the ambiguity matrix is ​​transformed into an equivalent transformation, mapping the original non-integer estimable ambiguity parameters to a set of integer estimable ambiguity parameters. Specifically, a lower triangular transformation matrix is ​​introduced to transform the original ambiguity matrix... Replace with an equivalent lower triangular matrix Thus, a matrix equation that can be used for integer ambiguity resolution is obtained. The elements of the matrix are constructed as follows:

[0127] ;

[0128] .

[0129] The supplementary technical features of this design are as follows:

[0130] In PPP-RTK real-time positioning, it is difficult to model the signal distortion deviation of CDMA system and the inter-frequency code deviation of FDMA system in a unified manner. When post-calibration is used, its time-varying characteristics affect the ambiguity fixation and positioning convergence performance. To address these issues, this invention proposes a GNSS PPP-RTK real-time positioning method based on ambiguity code deviation, which realizes unified modeling and real-time estimation of code deviation, thereby improving the performance of PPP-RTK real-time positioning.

[0131] Example 1:

[0132] A system-wide PPP-RTK localization method considering ambiguity-type code deviation, comprising the following steps:

[0133] The first step is to establish a multi-constellation, multi-frequency GNSS code observation and carrier phase observation model based on CDMA and FDMA systems. Then, the ambiguous code bias ALCB parameter is uniformly introduced into the code observation model to obtain the original GNSS observation equation containing the ambiguous code bias ALCB.

[0134] The second step is to process the eight types of rank deficiencies in the GNSS raw observation equations that include the ambiguous code bias ALCB. Specifically, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and ALCB. The clock bias of the first epoch receiver is selected as the reference and the receiver phase bias is transmitted in the filtering to maintain the reference, thereby eliminating the rank deficiency between the receiver clock bias, ALCB and receiver phase bias, so as to obtain a full-rank PPP-RTK network model that takes into account ALCB.

[0135] The third step is to use the satellite products provided by the PPP-RTK server model that takes ALCB into account and the traditional PPP-RTK server model to locate the user receiver. Before positioning, it is necessary to determine whether the inter-station single difference ALCB between the user and the reference station is significant.

[0136] If the inter-station single difference ALCB is significant, the PPP-RTK user terminal model that takes into account ALCB is used for localization.

[0137] If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for positioning.

[0138] The fourth step is to first perform filtering and solving on the two types of user terminal models mentioned above, then propagate the double-difference ambiguity parameters during the filtering and solving process, and introduce the integer estimability theory in the ambiguity solving stage to convert the non-integer estimable ambiguity into an integer estimable form, thereby obtaining two types of user terminal models with fixed ambiguity.

[0139] Step 5: Based on the network scenario requirements of actual GNSS observation, select two types of user terminal models with fixed ambiguity, and then input multi-system GNSS pseudorange and carrier phase observation data to perform PPP-RTK real-time positioning calculation to obtain high-precision positioning results.

[0140] Example 2:

[0141] Example 2 is basically the same as Example 1, except that:

[0142] In the first step, the GNSS primitive observation equation for the ambiguous code bias ALCB is specifically as follows:

[0143] ;

[0144] in, Represents the expectation operator; , They represent the receivers respectively. Tracked satellites In frequency The code and phase observations on the screen, Represents geometric distance, zenith tropospheric delay Through mapping function Mapped to receiver With satellite Slant distance between lines of sight; receiver clock bias Satellite clock bias First-order oblique ionospheric delay and its dispersion coefficient , Indicates signal frequency; and These are respectively the ambiguity code bias and the satellite code bias. and These represent receiver phase deviation and satellite phase deviation, respectively. For phase ambiguity, For the corresponding wavelength, Inter-station single-difference ionospheric constraint.

[0145] Compared with the traditional GNSS observation model, the above-mentioned primitive GNSS observation equations show that the traditional model only has receiver code bias related to receiver code and frequency. The above equation replaces the receiver code bias in the traditional GNSS observation model with ALCB, which is related to the satellite, receiver, and frequency point simultaneously. This difference in parameter form leads to differences in the rank deficiency type and number of the new observation model compared to the traditional observation model, which in turn leads to differences in the benchmark selection method compared to the full-rank model form.

[0146] Example 3:

[0147] Example 3 is basically the same as Example 1, except that:

[0148] The original GNSS observation equations contain eight types of rank deficiencies: 1) rank deficiency between satellite clock error, satellite code bias, and satellite phase bias; 2) rank deficiency between receiver clock error, ALCB, and receiver phase bias; 3) rank deficiency between satellite clock error and receiver clock error; 4) rank deficiency between satellite code bias and ALCB; 5) rank deficiency between satellite phase bias and receiver phase bias; 6) rank deficiency between ionosphere, satellite code bias, and satellite phase bias; 7) rank deficiency between ambiguity and satellite phase bias; and 8) rank deficiency between ambiguity and receiver phase bias. In fact, traditional observation models also contain eight types of rank deficiencies, differing from the original GNSS observation equations in types 2) and 4). In the traditional observation model, the corresponding types of rank deficiencies are the rank deficiency between receiver clock error, receiver code bias, and receiver phase bias, and the rank deficiency between satellite code bias and receiver code bias, respectively. Apart from these two types, the other rank deficiency types and deficiencies elimination methods are the same in the traditional model as in the original GNSS observation equations.

[0149] Using the ALCB of the first receiver as the reference renormalization parameter, the rank deficiency between the satellite code bias and the ALCB is eliminated, specifically as follows:

[0150] Introduce the first virtual observation equation that includes these two types of parameters: ;

[0151] Assuming two sites , Two satellites were observed simultaneously. , Each satellite transmits two frequencies. , The signal, the virtual observation equation is expressed in the following matrix form: ;

[0152] in, and Representing observed values ​​and unknown parameters respectively, column vectors The elements are arranged in the following order: ;

[0153] column vector The items are arranged in the following order:

[0154] ;

[0155] Indicates the Kronecker product. Given a 4x4 identity matrix, and considering the rank deficiency of the design matrix in the above equations, the ambiguity code deviation of the first receiver is chosen as the benchmark, and other parameters are renormalized to obtain the following matrix equation: ;

[0156] in, Here is the renormalized vector of estimable parameters, whose elements are arranged in the following order:

[0157] ;

[0158] .

[0159] The receiver clock bias at the first epoch is selected as the reference, and the receiver phase bias is propagated in the filtering process to maintain the reference, eliminating the rank deficiency among the receiver clock bias, ALCB, and receiver phase bias. Specifically:

[0160] Introduce a second virtual observation equation containing the parameters to be analyzed: ;

[0161] Then, the second virtual observation equation is expanded using matrix form:

[0162] ;

[0163] Observation vector The elements in the file are arranged in the following order:

[0164] ;

[0165] Parameter vector The elements in the array are arranged as follows:

[0166] .

[0167] The full-rank form of the second virtual observation equation is as follows:

[0168] ;

[0169] Renormalized parameter vector The elements in the array are arranged in the following order:

[0170] ; .

[0171] The obtained full-rank PPP-RTK network model that takes into account ALCB is as follows:

[0172] ;

[0173] ;

[0174] in, This represents the epoch indicator. For CDMA systems, since different satellites have the same wavelength, the wavelength can be estimated in the following form: ;

[0175] Ambiguity estimable form For GLONASS, wavelength is represented. ,in The fundamental frequency is represented, and the ambiguity can be estimated in the form of: ,in , The frequency designation provides explicit formulas for ionospherically independent combinations (IF) and geometrically independent combinations, as follows:

[0176] .

[0177] Example 4:

[0178] Example 4 is basically the same as Example 1, except that:

[0179] By passing ALCB as a constant and calculating the satellite's posterior residual, if the posterior residual exceeds a threshold (generally set to three times the posterior mean error), it is determined that the satellite's ALCB is abnormal.

[0180] Calculate the posterior residuals for each satellite: ;in, The results of PPP-RTK parameter estimation. To design the matrix, A constant vector, This refers to the a posteriori residual;

[0181] Calculate the posterior mean square error: ;in, The prior weight matrix of the observations, For model redundancy;

[0182] Compare the posterior residuals at each frequency point for each satellite. Relationship with three times the standard error: If this value is greater than 0, then an ALCB anomaly exists.

[0183] In the full-rank PPP-RTK network model given by the equation, considering the initial observation scenario including two frequencies, two receivers and multiple satellites, in order to achieve stable estimation of network parameters, the model introduces at least two epochs of observation data in the filtering initialization stage to ensure that all parameters to be estimated can be reliably estimated and used for state updates in subsequent epochs.

[0184] When the inter-station single-difference ALCB is significant, the user-end model is derived from the full-rank model by shifting all satellite-related correction terms—tropospheric delay, satellite code bias, and satellite phase bias—from the right side to the left side, resulting in the following expression:

[0185] ;

[0186] in, Indicates from satellite to user receiver unit vector, Indicates user positioning error. It is the ionospheric delay at the user's location obtained from the product interpolation derived from the network.

[0187] When the inter-station single difference ALCB is not significant, the user-side model derivation is as follows:

[0188] .

[0189] In the fourth step, double-difference ambiguity parameters are propagated in the filtering and solving process of the two types of user-end models. Based on the integer estimability theory, a lower triangular transformation matrix constructed from the satellite frequency channel number is introduced to map the original non-integer estimable ambiguity of GLONASS into an integer estimable form, resulting in two types of user-end models with fixed ambiguity. Specifically, double-difference ambiguity parameters are propagated during the filtering process, and the integer estimability theory is introduced in the ambiguity solving stage to convert the non-integer estimable ambiguity into an integer estimable form, thereby achieving reliable fixation of GLONASS ambiguity. Assuming there are m GLONASS satellites, each transmitting on two FDMA signals, the ambiguity of the FDMA signal in the full-rank model can be expressed in matrix form: ;

[0190] Its detailed expression is as follows:

[0191] .

[0192] The integer ambiguity is fixed, and based on the theory of integer estimability, the ambiguity matrix is ​​transformed into an equivalent transformation, mapping the original non-integer estimable ambiguity parameters to a set of integer estimable ambiguity parameters. Specifically, a lower triangular transformation matrix is ​​introduced to transform the original ambiguity matrix... Replace with an equivalent lower triangular matrix Thus, a matrix equation that can be used for integer ambiguity resolution is obtained. The elements of the matrix are constructed as follows:

[0193] ;

[0194] .

[0195] Example 5:

[0196] Example 5 is basically the same as Example 1, except that:

[0197] To comprehensively evaluate the positioning performance of the proposed model under different network conditions, two continuously operating reference station networks in different regions were selected as the source of experimental data, denoted as Network 1 and Network 2, respectively. Network 1 is a homogeneous network in which all stations use the same receiver and antenna, while Network 2 is a heterogeneous network used to verify the applicability and stability of the method of the present invention under different receiver and antenna configurations.

[0198] Network 1 consists of four stations, all equipped with Trimble NetR9 receivers, indicated by yellow markers in the diagram. The average baseline length between the stations is approximately 30 kilometers. In Network 1, network-end stations are represented by triangles, and user-end stations by circles.

[0199] In contrast, Network 2 is a heterogeneous network, containing various receiver and antenna combinations. Specifically, Network 2 includes ten stations configured with Trimble Alloy receivers (marked in red in the figure), two stations configured with Trimble NetR9 receivers (marked in yellow), and six stations configured with Leica GR30 receivers (marked in blue). The average distance between stations is approximately 60 kilometers. Similarly, in Network 2, network-end stations are marked with triangles, and user-end stations are marked with circles.

[0200] All receivers in the two regional networks mentioned above are able to continuously track dual-frequency GPS and GLONASS satellite observation data with a sampling interval of 30 seconds, thus providing a consistent data basis for subsequent positioning models and parameter estimation.

[0201] In addition, to further evaluate the ability of the model of this invention to extract and estimate the ambiguity class code bias (ALCB), especially for the application scenario of the BDS system in the Asian region, two stations configured with Leica GR50 receivers were selected from the positioning reference station network as auxiliary experimental data sources. Since the BDS GEO satellite has almost continuous visibility in region A, this dataset can be used to support the stability analysis of relevant bias parameters.

[0202] Regarding the data time span, the observation data of Network 1 covers 2019, from 017 to 022, a total of 6 days; the data of Network 2 and the aforementioned Hong Kong reference station both select data from the same period in 2025. The 2019 data was selected for the Network 1 experiment because the number of visible GLONASS satellites during that period is relatively large, which is conducive to the analysis and modeling of inter-frequency code deviation and related parameters.

[0203] Regarding the network-side reference receiver setup, station MC07 is selected as the reference receiver in network 1, which corresponds to receiver 1 in the model derivation; while station VTBE is selected as the reference receiver in network 2, which is used to construct a unified reference framework for the regional network.

[0204] Example 6:

[0205] Example 6 is basically the same as Example 1, except that:

[0206] See Figure 2 and Figure 3 This embodiment aims to verify the ability of the proposed full GNSS PPP-RTK model to extract the Ambiguity Class Code Offset (ALCB) under regional network conditions. A set of verification experiments based on real GNSS observation data was designed. This experiment artificially introduces a known constant offset into the code observation values ​​and estimates it using the model described in this invention to evaluate the accuracy and stability of ALCB extraction. The experimental data is selected from a homogeneous receiver baseline in the SatRef network. Both ends of this baseline use the same type of receiver and antenna configuration and can continuously track BDS GEO satellites, making it suitable for long-term series analysis. To ensure the representativeness and identifiability of the experimental results, the selected data meets the following conditions: first, the original ALCB amplitude is small to avoid interference with the identification of simulated biases; second, the relevant satellites remain continuously visible during the observation period to analyze the long-term stability of the ALCB. The experimental data sampling interval is 30 seconds, and the continuous observation period is six days.

[0207] Figure 2 The original ALCB, the simulated ALCB, and the results estimated by the model of this invention for some satellites during the experimental period are presented. The results show that without the introduction of simulated migration, the estimated ALCB values ​​are concentrated near zero, and their root mean square values ​​are consistent with the code observation noise level; after the introduction of simulated migration, the estimated results of each satellite are highly consistent with the preset migration values, and the time series is stable.

[0208] Figure 3 This paper presents the time series and statistical distribution of ALCB estimates for satellites CO2 and CO3 under different ionospheric weighting conditions. The results show that under different baseline lengths, the ALCB estimates obtained by various weighting strategies are generally consistent, with small variations in estimation accuracy. Even under longer baseline conditions, ALCB extraction remains stable.

[0209] Example 7:

[0210] Example 7 is basically the same as Example 1, except that:

[0211] See Figures 4 to 7This embodiment aims to evaluate the positioning performance of the proposed model under homogeneous receiver network conditions. In the experiment, the Ambiguity Class Code Bias (ALCB) is modeled as a white noise process at the user end, and the estimated ALCB is processed by inter-satellite single-difference to eliminate the receiver clock bias term it contains. The reference satellite is selected as the satellite with the smallest average ALCB at the corresponding frequency. The experiment uses a regional network composed of homogeneous receivers, and user station MC06 is selected as the positioning target. The experimental data was collected on January 17, 2025, and the observation data used includes pseudorange and carrier phase observations from the GPS and GLONASS systems, with a sampling interval of 30 seconds.

[0212] Figure 4 This figure shows the distribution of the average ALCB values ​​of GPS satellites at frequencies P1 and P2 at user station MC06 at 017 day of year 2025. Satellite G18 is used as the reference satellite for frequency P1, and satellite G05 is used as the reference satellite for frequency P2. The figure shows the average ALCB values ​​of each satellite relative to the reference satellite. The inter-satellite differences are very small, with a maximum difference of approximately 0.2 meters, which is below the code observation noise level, and the data is comparable across the two frequencies. Given that the inter-satellite differences in GPS ALCB are smaller than the code observation noise, the influence of ALCB can be ignored when processing GPS data from user station MC06.

[0213] Figure 5 This diagram shows the average ALCB distribution of GLONASS satellites at frequencies P1 and P2 on the same observation day at user station MC06. Satellite R10 was selected as the reference satellite for both frequencies. Unlike GPS, GLONASS exhibits inter-satellite differences at the meter level. Furthermore, the amplitude differs between frequencies, approximately 1 meter on P1 and approximately 2 meters on P2.

[0214] See Figure 6 The figure shows the PPP-RTK positioning error time series of user station MC06 under dual-frequency GPS and GLONASS joint positioning conditions. The figure focuses on the positioning error variation of the eastward component. The upper panel shows the ambiguity floating-point solution results, the middle panel shows the positioning results when only GLONASS ambiguities are fixed, and the lower panel shows the positioning results when GPS and GLONASS ambiguities are jointly fixed. Each panel compares the positioning error variation under conditions considering ALCB and not considering ALCB, and indicates the convergence process of the positioning error over time and the stable state after convergence.

[0215] See Figure 7The figure shows the positioning error time series of user station MC06 under single-frequency PPP-RTK positioning conditions. The figure presents positioning results for two scenarios: the combination of GPS P1 and GLONASS P1, and the combination of GPS P1 and GLONASS P2. The left panel corresponds to the floating-point ambiguity solution results, and the right panel corresponds to the fixed-point ambiguity solution results, used to compare the changes in positioning error under different frequency combination conditions.

[0216] Example 8:

[0217] Example 8 is basically the same as Example 1, except that:

[0218] See Figures 8 to 12 This embodiment aims to evaluate the positioning performance of the proposed model under heterogeneous receiver network conditions. In network 2, the VTBE station is selected as the network-end reference station, and the remaining stations are used as reference stations or user stations. The experimental procedure first analyzes the ambiguity class code deviation (ALCB) of each station in the network, and then calculates and compares the PPP-RTK positioning results of the user stations based on dual-frequency GPS and GLONASS observation data. The experimental data are all derived from continuous multi-day measured observation data, used to analyze the positioning error time series, convergence process, and statistical characteristics under different receiver and antenna configurations.

[0219] See Figure 8 The figure shows the ALCB time series corresponding to GPS P1 and GLONASS P1 observations from the MAWM and MASH stations, as well as the receiver-differential ALCB time series relative to the network reference station VTBE. The ALCB shown in the figure is the receiver-differential value relative to the VTBE station, obtained in an estimable form. It also presents the inter-satellite ALCB variations under homogeneous receiver combinations (MAWM–MASH) and heterogeneous receiver combinations (MAWM–VTBE, MASH–VTBE), corresponding to the GPS and GLONASS systems, respectively.

[0220] See Figure 9 This paper presents the time series results of the 3D positioning error of the MABN user station under the condition of using dual-frequency GPS and GLONASS observation data. The figures show the changes in positioning error for both ambiguity-floating-point and fixed-ambiguity solutions, and compare the time-varying process of positioning error with and without considering ALCB. In the ambiguity-floating-point solution, the model considering ALCB reduces the convergence time from 85.5 minutes to 36.0 minutes, reducing the 3D error to below 0.1 meters. Regarding positioning accuracy, the two models perform similarly after convergence.

[0221] See Figure 10 The figure shows the time series results of the 3D positioning error of the user station VTSP under the condition of using dual-frequency GPS and GLONASS observation data. This station and the network reference station VTBE use the same type of receiver and antenna. The figure shows the changes in 3D positioning error for two models, one considering ALCB and the other not, with ambiguity floating-point solution and fixed ambiguity solution, respectively, to reflect the positioning error performance under the condition of homogeneous equipment. Among them, the model considering ALCB performs slightly worse than the traditional model not considering ALCB.

[0222] See Figure 11 The figure illustrates the positioning convergence process of nine user stations in Network 2 under the condition of using dual-frequency GPS and GLONASS observation data. The nine user stations are divided into three categories according to different receiver and antenna configurations. The figure shows the convergence time distribution of ambiguity floating-point solutions and ambiguity fixed solutions for each category of stations under two models: considering ALCB and not considering ALCB. The convergence time results of the VTSP station are shown separately, while the results of the other user stations are statistically analyzed according to the three categories of stations mentioned above. Figure 10 The results show that the convergence time reduction for the second group of stations ranged from 24.3% to 48.6% under both solution modes, with an average reduction of approximately 41.7%; the convergence time reduction for the third group of stations was approximately 60.7%. These convergence time results cover both ambiguity floating-point solutions and ambiguity fixed-point solutions.

[0223] See Figure 12 The figure shows the statistical results of 3D positioning accuracy for nine user stations in Network 2 under the condition of using dual-frequency GPS and GLONASS observation data. The nine user stations are classified according to different receiver and antenna configurations. The figure shows the distribution of 3D root mean square error (RMSE) for each user station under two models: one considering ALCB and the other not. Specifically, the average variation of 3D RMSE for the second group of stations is approximately 30.4%, with individual station variations ranging from 4.7% to 50.0%; the average variation of 3D RMSE for the third group of stations is approximately 59.4%. Figure 12 The results shown cover user stations under different receiver and antenna configurations, reflecting the statistical characteristics of three-dimensional positioning accuracy of each station under different model conditions.

[0224] The above description is only a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. Any equivalent modifications or changes made by those skilled in the art based on the content disclosed in the present invention should be included within the scope of protection set forth in the claims.

Claims

1. A full-system PPP-RTK positioning method considering code bias of ambiguity-like, characterized in that: The system-wide PPP-RTK localization method that takes into account ambiguity code bias includes the following steps: The first step is to establish a multi-constellation, multi-frequency GNSS code observation and carrier phase observation model based on CDMA and FDMA systems. Then, the ambiguous code bias ALCB parameter is uniformly introduced into the code observation model to obtain the original GNSS observation equation containing the ambiguous code bias ALCB. The second step is to process the eight types of rank deficiencies in the GNSS raw observation equations that include the ambiguous code bias ALCB. Specifically, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and ALCB. The clock bias of the first epoch receiver is selected as the reference and the receiver phase bias is transmitted in the filtering to maintain the reference, thereby eliminating the rank deficiency between the receiver clock bias, ALCB and receiver phase bias, so as to obtain a full-rank PPP-RTK network model that takes into account ALCB. The third step is to use the satellite products provided by the PPP-RTK server model that takes ALCB into account and the traditional PPP-RTK server model to locate the user receiver. Before positioning, it is necessary to determine whether the inter-station single difference ALCB between the user and the reference station is significant. If the inter-station single difference ALCB is significant, the PPP-RTK user terminal model that takes into account ALCB is used for localization. If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for positioning. The fourth step is to first perform filtering and solving on the two types of user terminal models mentioned above, then propagate the double-difference ambiguity parameters during the filtering and solving process, and introduce the integer estimability theory in the ambiguity solving stage to convert the non-integer estimable ambiguity into an integer estimable form, thereby obtaining two types of user terminal models with fixed ambiguity. Step 5: Based on the network scenario requirements of actual GNSS observation, select two types of user terminal models with fixed ambiguity, and then input multi-system GNSS pseudorange and carrier phase observation data to perform PPP-RTK real-time positioning calculation to obtain high-precision positioning results. 2.The full-system PPP-RTK positioning method considering code bias of ambiguity-like code error according to claim 1, wherein: In the first step, the GNSS primitive observation equation for the ambiguous code bias ALCB is specifically as follows: ； in, Represents the expectation operator; , They represent the receivers respectively. Tracked satellites In frequency The code and phase observations on the screen, Represents geometric distance, zenith tropospheric delay Through mapping function Mapped to receiver With satellite Slant distance between lines of sight; receiver clock bias Satellite clock bias First-order oblique ionospheric delay and its dispersion coefficient , Indicates signal frequency; and These are respectively the ambiguity code bias and the satellite code bias. and These represent receiver phase deviation and satellite phase deviation, respectively. For phase ambiguity, For the corresponding wavelength, Inter-station single-difference ionospheric constraint. 3.The full-system PPP-RTK positioning method considering code bias of ambiguity-like code error according to claim 1, wherein: In the second step, the ALCB of the first receiver is used as the reference renormalization parameter to eliminate the rank deficiency between the satellite code bias and the ALCB, specifically: A first virtual observation equation comprising both types of parameters is introduced: ; Assuming two sites , Two satellites were observed simultaneously. , Each satellite transmits two frequencies. , The signal, the virtual observation equation is expressed in the following matrix form: ; wherein and denote the observed values and unknown parameters, respectively, and the elements of column vector are arranged in the following order: ; Column vector In each of the above, the items are arranged in the following order: ； Indicates the Kronecker product. Given a 4x4 identity matrix, and considering the rank deficiency of the design matrix in the above equations, the ambiguity code deviation of the first receiver is chosen as the benchmark, and other parameters are renormalized to obtain the following matrix equation: ; wherein is the vector of estimated parameters after the reformulation, with the elements arranged in the following order: ； 。 4. The full-system PPP-RTK positioning method considering code bias of ambiguity-like code according to claim 3, characterized in that: In the second step, the receiver clock bias of the first epoch is selected as the reference, and the receiver phase bias is maintained by passing the reference during filtering, thus eliminating the rank deficiency among the receiver clock bias, ALCB, and receiver phase bias. Specifically: Introduce a second virtual observation equation containing the parameters to be analyzed: ; Then, the second virtual observation equation is expanded using matrix form: ； Observation vectors The elements in the vector are ordered as follows: ； Parameter vector The elements in the parameter vector are arranged as follows: 。 5. The full-system PPP-RTK positioning method considering code bias of ambiguity-like code according to claim 4, characterized in that: The full-rank form of the second virtual observation equation is as follows: ； Renormalized parameter vector The elements in the array are arranged in the following order: ； 。 6. The whole-system PPP-RTK positioning method considering ambiguity code deviation according to claim 5, characterized in that: The obtained full-rank PPP-RTK network model that takes into account ALCB is as follows: ； ； in, This represents the epoch indicator. For CDMA systems, since different satellites have the same wavelength, the wavelength can be estimated in the following form: ; Ambiguity estimable form For GLONASS, wavelength is represented. ,in The fundamental frequency is represented, and the ambiguity can be estimated in the form of: ,in , The frequency designation provides explicit formulas for ionospherically independent combinations (IF) and geometrically independent combinations, as follows: 。 7. The whole-system PPP-RTK positioning method considering ambiguity code deviation according to claim 1, characterized in that: In the third step, if the inter-station single difference ALCB is significant, a PPP-RTK user-end model that takes into account ALCB is used for localization, specifically: ； in, Indicates from satellite to user receiver unit vector, Indicates user positioning error. It is the ionospheric delay at the user's location obtained from the product interpolation derived from the network.

8. The full-system PPP-RTK positioning method considering code bias of ambiguity-like code according to claim 7, characterized in that: If the inter-station single difference ALCB is not significant, the traditional PPP-RTK user terminal model is used for localization, as detailed below: 。 9. The full-system PPP-RTK positioning method considering code bias of ambiguity-like code according to claim 8, characterized in that: In the fourth step, filtering and solving are first performed on the two types of user-end models mentioned above. Then, double-difference ambiguity parameters are propagated during the filtering and solving process. In the ambiguity solving stage, integer estimability theory is introduced to convert non-integer estimable ambiguities into integer estimable forms, thereby obtaining two types of user-end models with fixed ambiguities. Specifically, double-difference ambiguity parameters are propagated during the filtering process, and integer estimability theory is introduced during the ambiguity solving stage to convert non-integer estimable ambiguities into integer estimable forms, thereby achieving reliable fixation of GLONASS ambiguities. Assuming there are m GLONASS satellites, each transmitting on two FDMA signals, the ambiguity of the FDMA signal in the full-rank model can be represented in matrix form: ; Its detailed expression is as follows: 。 10. A system-wide PPP-RTK positioning method considering ambiguity code deviation according to claim 9, characterized in that: To achieve fixed ambiguity, an equivalent transformation is performed on the ambiguity matrix based on the theory of integer estimability. This transforms the original non-integer estimable ambiguity parameters into a set of integer estimable ambiguity parameters. Specifically, a lower triangular transformation matrix is ​​introduced to transform the original ambiguity matrix... Replace with an equivalent lower triangular matrix Thus, a matrix equation that can be used for integer ambiguity resolution is obtained. The elements of the matrix are constructed as follows: ； ； wherein .

Images