A method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor

Abstract

This invention discloses a method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor, belonging to the field of Global Navigation Satellite System (GNSS) technology. The method includes: calculating the fractional-cycle portions of ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity based on GNSS reference station phase observations; sequentially selecting stations according to the number of observed satellites, and using the whole-network phase deviation solution method and the fractional-cycle portions of ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, iteratively calculating the receiver-side UPD value and the satellite-side UPD value and extracting the residual vector of phase deviation; calculating the UPD accuracy factor based on the phase deviation residual vector; updating the ambiguity variance-covariance matrix at the user end using the UPD accuracy factor, and fixing the ambiguity at the user end based on the LAMBDA algorithm. This invention solves the problem of inconsistency between the ambiguity and the accuracy of the ambiguity variance-covariance matrix in existing technologies.

Description

Technical Field

[0001] This invention relates to a method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor, belonging to the field of global navigation satellite system technology. Background Technology

[0002] GNSS (Global Navigation Satellite System), as a key infrastructure providing positioning, navigation, and timing services, has demonstrated wide application value in various fields such as precision agriculture, intelligent transportation, and space environment monitoring. Among these, traditional Precise Point Positioning (PPP) technology, using a single receiver combined with precise ephemeris and clock bias products, can theoretically achieve centimeter-level positioning accuracy. However, PPP technology has a long convergence time, typically exceeding 30 minutes, which severely limits its application in real-time high-precision positioning scenarios. To overcome this limitation, PPP-AR (Precise Point Positioning Ambiguity Fixation) technology has emerged. PPP-AR technology significantly shortens the convergence time and improves positioning accuracy by restoring the integer characteristics of carrier phase ambiguity. In particular, the least squares ambiguity decorrelation adjustment method (LAMBDA) is widely used in GNSS ambiguity fixing, relying on real ambiguities and their corresponding variance-covariance matrices for integer ambiguity search. In recent years, PPP-AR technology has been widely promoted and applied in surveying, geological disaster monitoring, and other fields, becoming one of the core means of GNSS high-precision positioning.

[0003] Despite significant progress in high-precision positioning, PPP-AR technology still suffers from several notable shortcomings. First, when using the LAMBDA method for PPP-AR, real-valued ambiguities are typically obtained by subtracting phase deviations from the PPP floating-point solution ambiguity, while the variance-covariance matrix utilizes the variance-covariance information from the PPP floating-point solution. However, due to phase deviation estimation errors, the accuracy of the real-valued ambiguities obtained after phase deviation subtraction may differ from the variance-covariance matrix of the PPP floating-point solution ambiguity. This inconsistency leads to a decrease in ambiguity fixation success rate, particularly in complex environments such as periods of ionospheric activity or areas with significant multipath effects. Second, with the increasing demand for real-time applications, although the International GNSS Service (IGS) has provided real-time satellite orbit, clock bias, and phase deviation products, driving the development of real-time PPP-AR, the quality and latency of these products significantly impact PPP-AR performance. Delays in real-time products lead to the accumulation of satellite clock bias and orbital errors, further exacerbating the uncertainty in ambiguity fixation. Furthermore, existing methods do not fully account for the uncertainty of UPD (uncalibrated phase delay) correction during user-side processing, which also leads to a decrease in ambiguity fixation success rate, especially when real-time product quality is poor. In complex environments, the performance of traditional PPP-AR methods is further limited, with significantly prolonged convergence time, making it difficult to meet the requirements of real-time centimeter-level positioning. Therefore, existing technologies still have significant bottlenecks in terms of efficiency and robustness in high-precision real-time positioning. Summary of the Invention

[0004] The purpose of this invention is to provide a precise single-point positioning ambiguity fixing method based on a phase deviation accuracy factor. By introducing a phase deviation accuracy factor into the ambiguity variance-covariance matrix, the method solves the problem of inconsistency between the ambiguity and the accuracy of the ambiguity variance-covariance matrix in the prior art, and improves the success rate of ambiguity fixing and positioning robustness in complex environments and under real-time product delays.

[0005] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution:

[0006] This invention provides a method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor, comprising:

[0007] Obtain the phase observation values ​​of the GNSS reference station on the server;

[0008] Based on the phase observations from the GNSS reference station, the fractional part of the floating-point ambiguity is calculated for the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity.

[0009] Based on the number of observed satellites, stations are selected sequentially. Using the phase deviation network solution method and the fractional-cycle parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity, the receiver-end UPD values ​​of all receivers in the reference station network and the satellite-end UPD values ​​of all visible satellites are calculated iteratively, and the residual vector of phase deviation is extracted.

[0010] Calculate the UPD accuracy factor based on the residual vector of the phase deviation;

[0011] The ambiguity variance-covariance matrix of the user terminal is updated using the UPD precision factor, and the ambiguity of the user terminal is fixed based on the LAMBDA algorithm.

[0012] Furthermore, based on the phase observations from the GNSS reference station, the fractional-cycle portions of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity of the floating-point ambiguity are calculated, including:

[0013] Based on the non-differential non-combined observation model, the floating-point ambiguity is estimated from the phase observations of the GNSS reference station;

[0014] The floating-point ambiguity includes integer ambiguity and receiver-side and satellite-side phase deviation;

[0015] The floating-point ambiguity is linearly combined and transformed into ultra-wide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity.

[0016] Round the ultrawide ambiguity, wide ambiguity, and narrow ambiguity to obtain the integer parts of the ultrawide ambiguity, wide ambiguity, and narrow ambiguity respectively.

[0017] By subtracting the integer parts of the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity from the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, the fractional part of the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity is obtained.

[0018] Furthermore, based on the number of observed satellites, stations are selected sequentially. Utilizing the phase deviation network-wide solution method and the fractional-cycle portions of ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, the receiver-side UPD values ​​of all receivers in the reference station network and the satellite-side UPD values ​​of all visible satellites are iteratively calculated, including:

[0019] Set the receiver UPD value of the station with the most observed satellites to 0, and subtract the receiver UPD value from the fractional-week parts of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity to obtain the initial UPD value of the satellite.

[0020] Select the remaining stations in descending order of the number of observed satellites, and repeat the following steps until all stations have been processed:

[0021] For the known satellites at each station:

[0022] The satellite-end UPD value is obtained by subtracting the fractional-week portions of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, and then taking the average value as the receiver-end UPD value.

[0023] For the unknown satellites at each station:

[0024] The satellite-side UPD value of the unknown satellite is obtained by subtracting the receiver-side UPD value from the fractional-week parts of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity.

[0025] The satellite-end UPD values ​​of the same satellite obtained from various stations are weighted and averaged to obtain the satellite-end UPD value of the satellite.

[0026] If the difference between the satellite-end UPD values ​​obtained in two adjacent iterations is less than a preset threshold, the loop is exited, and the receiver-end UPD values ​​of all receivers in the reference station network and the satellite-end UPD values ​​of all visible satellites are obtained.

[0027] Furthermore, the receiver-side UPD value is expressed as:

[0028] ;

[0029] In the formula, This represents the receiver-side UPD value, i.e., the [number]th [unit]. UPD value of each receiver Indicates the first The total number of satellites that a receiver can observe. Indicates the first One satellite, Indicates floating-point ambiguity. Indicates the ambiguity of the integer period. This represents the UPD value at the satellite end, i.e., the first... The UPD value of each satellite.

[0030] Furthermore, the satellite-end UPD value is expressed as:

[0031] ;

[0032] In the formula, This represents the UPD value at the satellite end, i.e., the first... UPD value of each satellite Indicates that the first can be observed The total number of receivers for each satellite. Indicates the first One receiver, Indicates the first The satellite in the The UPD value is calculated at each receiver. Indicates the first satellite No. UPD value calculated at each receiver The corresponding weights.

[0033] Furthermore, the residual vector of the phase deviation is distributed across each satellite, wherein the residual vector of the phase deviation is expressed as:

[0034] ;

[0035] In the formula, The residual vector representing the phase deviation. This indicates the total number of receivers in the base station network. This represents the total number of all visible satellites in the reference station network. Indicates the first The receiver observed the first Phase deviation residuals of each satellite Indicates the first The receiver observed the first The floating-point ambiguity of each satellite, Indicates the first The receiver observed the first Integer ambiguity of a single satellite express OK The identity matrix of columns, Indicates the Kronecker product. express A column vector with row 1 and column 1. express A column vector with row 1 and column 1. express OK The identity matrix of columns, This represents the satellite-side UPD vector of all visible satellites in the reference station network. This represents the receiver-side UPD vector of all receivers in the base station network. This indicates transpose.

[0036] Furthermore, based on the residual vector of the phase deviation, the UPD accuracy factor is calculated, including:

[0037] The root mean square (RMS) of all elements in the residual vector of the phase deviation is used to obtain the UPD accuracy factor.

[0038] The UPD precision factor is expressed as:

[0039] ;

[0040] In the formula, Indicates the first UPD accuracy factor for each satellite Indicates that the first can be observed The total number of receivers for each satellite. Indicates the first One receiver, Indicates the first The receiver observed the first Phase deviation residuals of each satellite.

[0041] Furthermore, the ambiguity variance-covariance matrix of the user terminal is updated using the UPD precision factor, wherein the updated ambiguity variance-covariance matrix is ​​expressed as:

[0042] ;

[0043] In the formula, This represents the updated ambiguity variance-covariance matrix for the user interface. This represents the ambiguity variance-covariance matrix of the user end, where, Indicates the ambiguity on the user's end. This represents a diagonal matrix composed of UPD precision factors. This indicates the total number of satellites that the receiver can observe.

[0044] Furthermore, the ambiguity variance-covariance matrix of the user terminal is updated using the UPD precision factor, and the ambiguity of the user terminal is fixed based on the LAMBDA algorithm, including:

[0045] The ultra-wide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity are used as the ambiguity at the user end;

[0046] By using an invertible integer transformation matrix to reduce the correlation between the ambiguity of the user terminal and the updated ambiguity variance-covariance matrix, the ambiguity vector and the transformed ambiguity variance-covariance matrix are obtained.

[0047] Perform fuzzy integer search and verification on the fuzzy vector and the transformed fuzzy variance-covariance matrix to obtain integer fuzzy solutions;

[0048] The ambiguity at the user end is fixed based on the integer ambiguity solution.

[0049] Furthermore, the ambiguity vector and the transformed ambiguity variance-covariance matrix are respectively expressed as:

[0050] ;

[0051] In the formula, Represents the ambiguity vector. Indicates the ambiguity on the user's end. Represents an invertible integer transformation matrix. This represents the transformed ambiguity variance-covariance matrix. This represents the ambiguity variance-covariance matrix on the user side. Denotes the transpose of an invertible integer transformation matrix. This indicates transpose.

[0052] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0053] 1. This invention introduces a phase deviation accuracy factor and combines it with GNSS reference station phase observations to fix ambiguity in precise single-point positioning. This allows for accurate calculation and updating of the ambiguity variance-covariance matrix at the user end, which not only improves the accuracy of ambiguity fixing but also enhances robustness in complex environments and under real-time data delays, thereby significantly improving the overall performance and reliability of precise single-point positioning.

[0054] 2. This invention selects stations sequentially based on the number of observed satellites and uses a phase deviation network solution method combined with the fractional cycles of wide-lane and narrow-lane ambiguities for iterative calculation. This enables precise calculation of the receiver-side UPD values ​​of all receivers and the satellite-side UPD values ​​of all visible satellites. It not only considers the influence of the number of observed satellites and prioritizes stations with abundant observation data, but also continuously updates the receiver-side and satellite-side UPD values ​​through a step-by-step approximation method until convergence is achieved. This significantly improves the accuracy and reliability of receiver-side and satellite-side UPD value estimation, providing a solid foundation for subsequent ambiguity fixing, thereby improving the accuracy and efficiency of precise single-point positioning.

[0055] 3. This invention updates the ambiguity variance-covariance matrix of the user terminal by combining the UPD accuracy factor, which greatly improves the search efficiency and success rate of the LAMBDA algorithm in the process of ambiguity fixation, thereby accelerating the convergence speed while ensuring positioning accuracy. Attached Figure Description

[0056] Figure 1 This is a flowchart illustrating a method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor, provided in an embodiment of the present invention.

[0057] Figure 2 This is a schematic diagram illustrating the convergence speed of a precision single-point positioning ambiguity fixing method based on phase deviation accuracy factor provided in an embodiment of the present invention. Detailed Implementation

[0058] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations thereof. In the absence of conflict, the embodiments of the present invention and the technical features in the embodiments can be combined with each other.

[0059] The term "and / or" simply describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A alone, A and B simultaneously, or B alone. Additionally, the character " / " generally indicates that the preceding and following related objects have an "or" relationship.

[0060] Example 1

[0061] like Figure 1 As shown in the figure, this embodiment introduces a method for fixing ambiguity in precise single-point positioning based on phase deviation accuracy factor, characterized by including:

[0062] Step 1: Obtain the phase observation values ​​of the GNSS reference station on the server.

[0063] GNSS (Global Navigation Satellite System) reference stations provide high-precision satellite observation data, including pseudorange and phase observations. This invention calculates floating-point ambiguity by acquiring phase observations.

[0064] Step 2: Based on the phase observations from the GNSS reference station, calculate the fractional part of the ultrawide ambiguity, wide ambiguity, and narrow ambiguity of the floating-point ambiguity.

[0065] Floating-point ambiguity includes integer ambiguity, receiver-side UPD value, and satellite-side UPD value. Wide-lane and narrow-lane ambiguities are obtained by linearly combining floating-point ambiguities of different frequencies. They have different sensitivities to ionospheric delay and can therefore be used to separate and estimate phase deviation. This invention estimates receiver-side and satellite-side UPD values ​​by calculating the fractional-week portions of wide-lane and narrow-lane ambiguities.

[0066] Step 3: Select stations sequentially according to the number of observed satellites. Utilize the whole-network phase deviation solution method and the fractional-cycle parts of ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity. Iteratively calculate the receiver-side UPD values ​​of all receivers in the reference station network and the satellite-side UPD values ​​of all visible satellites, and extract the residual vector of phase deviation.

[0067] The phase deviation network-wide solution method utilizes observation data from multiple stations and satellites to estimate the receiver-side and satellite-side UPD values ​​through iterative calculations. Stations with more observed satellites typically provide more observational information and are therefore prioritized. This invention reduces the uncertainty of ambiguity parameters by iteratively calculating the UPD value, and the extracted phase deviation residual vector is used to evaluate the estimation accuracy of the UPD value.

[0068] Step 4: Calculate the UPD accuracy factor based on the residual vector of the phase deviation.

[0069] The UPD accuracy factor reflects the uncertainty or accuracy of the UPD value estimation. The UPD accuracy factor is calculated based on the statistical properties of the phase deviation residual vector, such as the root mean square error. This invention uses the UPD accuracy factor to update the ambiguity variance-covariance matrix at the user end, thereby improving the reliability and accuracy of ambiguity fixing.

[0070] Step 5: Update the ambiguity variance-covariance matrix of the user terminal using the UPD precision factor, and fix the ambiguity of the user terminal based on the LAMBDA algorithm.

[0071] The LAMBDA (Least-squares AMBiguity Decorrelation Adjustment) algorithm is an efficient method for searching integer ambiguities. It reduces the correlation between ambiguity parameters through decorrelation processing, thereby improving search efficiency and success rate. The updated ambiguity variance-covariance matrix provided in this invention offers more accurate statistical information for the LAMBDA algorithm, making the ambiguity fixing process more stable and reliable. Ultimately, this invention achieves high-precision positioning by fixing the ambiguity at the user end using the LAMBDA algorithm.

[0072] Example 2

[0073] Based on the same inventive concept as Embodiment 1, this embodiment describes the implementation steps of a precise single-point positioning ambiguity fixing method based on phase deviation accuracy factor, including:

[0074] Step 1: Obtain the phase observation values ​​of the GNSS reference station on the server.

[0075] Step 2: Based on the phase observations from the GNSS reference station, calculate the fractional part of the ultrawide ambiguity, wide ambiguity, and narrow ambiguity of the floating-point ambiguity.

[0076] In some embodiments, based on GNSS reference station phase observations, the fractional-cycle portions of the ultrawide ambiguity, wide-lane ambiguity, and narrow-lane ambiguity of the floating-point ambiguity are calculated, including:

[0077] Step 2.1: Based on the non-differential non-combined observation model, estimate the floating-point ambiguity from the phase observations of the GNSS reference station;

[0078] In this embodiment, the floating-point ambiguity includes integer ambiguity, receiver-side phase deviation, and satellite-side phase deviation. Wherein, the... The floating-point ambiguity of a satellite is represented as follows:

[0079] ;

[0080] In the formula, Indicates the first The floating-point ambiguity of each satellite, Indicates the ambiguity of the integer period. This represents the receiver-side UPD value, i.e., the [number]th [unit]. UPD value of each receiver This represents the UPD value at the satellite end, i.e., the first... UPD values ​​of each satellite.

[0081] Step 2.2: Perform linear combination processing on the floating-point ambiguity to transform it into ultra-wide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity.

[0082] In this embodiment, the ultra-wide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity are expressed as follows:

[0083] ;

[0084] In the formula, , and These represent the ambiguity of the ultra-wide alley, the wide alley, and the narrow alley, respectively. , and These represent frequencies of 100 and 110 respectively. , and Upper The receiver observed the first The floating-point ambiguity solution for each satellite, where... , and These represent the first, second, and third signal frequencies transmitted by the corresponding satellite system, respectively.

[0085] The corresponding satellite systems can be GPS, GLONASS, Galileo, and BDS, etc. The specific values ​​for the first, second, and third signal frequencies in these satellite systems are as follows:

[0086] GPS system: First signal frequency L1: 1575.42MHz, second signal frequency L2: 1227.60MHz, third signal frequency L5: 1176.45MHz;

[0087] GLONASS system: First signal frequency L1: ~1602MHz, second signal frequency L2: ~1246MHz, third signal frequency L3: 1202.025MHz;

[0088] Galileo system: First signal frequency is E1: 1575.42MHz, second signal frequency is E5a: 1176.45MHz, third signal frequency is E5b: 1207.14MHz;

[0089] BDS system: First signal frequency B1: 1561.098MHz, second signal frequency B2: 1207.14MHz, third signal frequency B3: 1268.52MHz.

[0090] This embodiment effectively separates ambiguity information of different frequencies by performing linear combination processing on the floating-point ambiguity, laying the foundation for subsequent phase deviation estimation.

[0091] Step 2.3: Perform rounding operations on the ultrawide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity respectively to obtain the integer parts of the ultrawide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity.

[0092] Step 2.4: Subtract the integer parts of the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity from the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity to obtain the fractional part of the ultrawide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity.

[0093] Step 3: Select stations sequentially according to the number of observed satellites. Utilize the phase deviation network solution method and the fractional cycles of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity to iteratively calculate the receiver-side UPD values ​​of all receivers in the reference station network and the satellite-side UPD values ​​of all visible satellites, and extract the residual vector of the phase deviation.

[0094] In this embodiment, when the first station The receiver observed the first When processing data from multiple satellites, the receiver-side UPD values ​​and satellite-side UPD values ​​of all satellites at all stations are combined. The combined receiver-side UPD value and satellite-side UPD value are represented as follows:

[0095] ;

[0096] In the formula, Indicates the first The receiver observed the first The floating-point ambiguity of a satellite, Indicates the first The receiver observed the first Each satellite receives integer ambiguity. express The identity matrix, express The vector, express The identity matrix, express The vector, ⊗ represents the Kronecker product. This represents the phase deviation vector at the receiver end. Represents the satellite-end phase offset vector. This indicates transpose.

[0097] In this embodiment, since the receiver-side UPD value and the satellite-side UPD value are linearly correlated, resulting in a rank deficiency in both values, this embodiment introduces an additional baseline condition for constraint. This baseline condition is expressed as follows:

[0098] ;

[0099] In some embodiments, stations are selected sequentially according to the number of observed satellites. Using the phase deviation network-wide solution method and the fractional-cycle portions of ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, the receiver-side UPD values ​​of all receivers and the satellite-side UPD values ​​of all visible satellites in the reference station network are iteratively calculated, including:

[0100] In some embodiments, since the solution of phase deviation depends on ambiguity rounding, and ambiguity needs to eliminate the influence of phase deviation to have integer characteristics, the above phase deviation processing requires multiple iterations to complete the phase deviation separation between the receiver end and the satellite end.

[0101] Step 3.1: Set the UPD value of the receiver at the station with the most observed satellites to 0, and subtract the receiver UPD value from the fractional-cycle parts of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity to obtain the initial UPD value at the satellite end;

[0102] Step 3.2: Select the remaining stations in descending order of the number of observed satellites, and repeat the following steps until all stations have been processed:

[0103] Step 3.2.1: For the known satellites at each station:

[0104] The satellite-end UPD value is obtained by subtracting the fractional-week portions of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity, and then taking the average value as the receiver-end UPD value.

[0105] In this embodiment, the receiver-side UPD value is represented as:

[0106] ;

[0107] In the formula, This represents the receiver-side UPD value, i.e., the [number]th [unit]. UPD value of each receiver Indicates the first The total number of satellites that a receiver can observe. Indicates the first One satellite, Indicates floating-point ambiguity. Indicates the ambiguity of the integer period. This represents the UPD value at the satellite end, i.e., the first... The UPD value of each satellite.

[0108] Step 3.2.2: For the unknown satellites at each station:

[0109] The satellite-side UPD value of the unknown satellite is obtained by subtracting the receiver-side UPD value from the fractional-week parts of the ultra-wide lane ambiguity, wide lane ambiguity, and narrow lane ambiguity.

[0110] Step 3.3: Take a weighted average of the satellite-end UPD values ​​of the same satellite obtained from each station to obtain the satellite-end UPD value of the satellite;

[0111] In this embodiment, the satellite-end UPD value is represented as:

[0112] ;

[0113] In the formula, This represents the UPD value at the satellite end, i.e., the first... UPD value of each satellite Indicates that the first can be observed The total number of receivers for each satellite. Indicates the first One receiver, Indicates the first The satellite in the The UPD value is calculated at each receiver. Indicates the first satellite No. UPD value calculated at each receiver The corresponding weights.

[0114] Step 3.4: If the difference between the satellite-end UPD values ​​obtained in two adjacent iterations is less than a preset threshold, then exit the loop and obtain the receiver-end UPD values ​​of all receivers in the base station network and the satellite-end UPD values ​​of all visible satellites.

[0115] In this embodiment, the difference between the satellite-end UPD values ​​obtained in two adjacent iterations being less than a preset threshold is expressed as follows:

[0116] ;

[0117] In the formula, and They represent the first Second and third The difference in UPD values ​​obtained in each iteration at the satellite end This indicates a preset threshold.

[0118] In some embodiments, the residual vector of the phase deviation is distributed across each satellite, wherein the residual vector of the phase deviation is represented as:

[0119] ;

[0120] In the formula, The residual vector representing the phase deviation. This indicates the total number of receivers in the base station network (the terms "station" and "receiver" are redundant, so this expression is better). This represents the total number of all visible satellites in the reference station network. Indicates the first The receiver observed the first Phase deviation residuals of each satellite Indicates the first The receiver observed the first The floating-point ambiguity of each satellite, Indicates the first The receiver observed the first Integer ambiguity of a single satellite express OK The identity matrix of columns, Indicates the Kronecker product. express A column vector with row 1 and column 1. express A column vector with row 1 and column 1. express OK The identity matrix of columns, This represents the satellite-side UPD vector of all visible satellites in the reference station network. This represents the receiver-side UPD vector of all receivers in the base station network. This indicates transpose.

[0121] Step 4: Calculate the UPD accuracy factor based on the residual vector of the phase deviation.

[0122] In some embodiments, the UPD accuracy factor is calculated based on the residual vector of the phase deviation, including:

[0123] The root mean square (RMS) of all elements in the residual vector of the phase deviation is used to obtain the UPD accuracy factor.

[0124] In this embodiment, the UPD precision factor is expressed as:

[0125] ;

[0126] In the formula, Indicates the first UPD accuracy factor for each satellite Indicates that the first can be observed The total number of receivers for each satellite. Indicates the first One receiver, Indicates the first The receiver observed the first Phase deviation residuals of each satellite.

[0127] Step 5: Update the ambiguity variance-covariance matrix of the user terminal using the UPD precision factor, and fix the ambiguity of the user terminal based on the LAMBDA algorithm.

[0128] In this embodiment, the ambiguity variance-covariance matrix of the user terminal is updated using the UPD precision factor, wherein the updated ambiguity variance-covariance matrix is ​​expressed as follows:

[0129] ;

[0130] In the formula, This represents the updated ambiguity variance-covariance matrix for the user interface. This represents the ambiguity variance-covariance matrix of the user end, where, Indicates the ambiguity on the user's end. This represents a diagonal matrix composed of UPD precision factors. This indicates the total number of satellites that the receiver can observe.

[0131] In some embodiments, the ambiguity variance-covariance matrix of the user terminal is updated using the UPD precision factor, and the ambiguity of the user terminal is fixed based on the LAMBDA algorithm, including:

[0132] Step 5.1: Use the ultra-wide alley ambiguity, wide alley ambiguity, and narrow alley ambiguity as the ambiguity at the user end;

[0133] Step 5.2: Reduce the correlation between the ambiguity of the user terminal and the updated ambiguity variance-covariance matrix using an invertible integer transformation matrix to obtain the ambiguity vector and the transformed ambiguity variance-covariance matrix;

[0134] Step 5.3: Perform fuzzy integer search and verification on the fuzzy vector and the transformed fuzzy variance-covariance matrix to obtain the integer fuzzy solution;

[0135] Step 5.4: Fix the ambiguity of the user terminal based on the integer ambiguity solution.

[0136] In this embodiment, the ambiguity vector and the transformed ambiguity variance-covariance matrix are respectively represented as:

[0137] ;

[0138] In the formula, Represents the ambiguity vector. Indicates the ambiguity on the user's end. Represents an invertible integer transformation matrix. This represents the transformed ambiguity variance-covariance matrix. This represents the ambiguity variance-covariance matrix on the user side. Denotes the transpose of an invertible integer transformation matrix. This indicates transpose.

[0139] like Figure 2 The convergence rate example shown illustrates the impact of introducing a phase deviation accuracy factor on the convergence time of the PPP-AR fixed solution under different delay conditions, and compares the convergence time during periods of ionospheric activity and inactivity. As can be seen from the figure, from... Figure 2 It can be seen that the present invention accelerates the convergence speed under different environments and product delays.

[0140] Example 3

[0141] Based on the same inventive concept as other embodiments, this embodiment describes a computer-readable storage medium having computer instructions stored thereon, which, when executed by a processor, implement the steps of the methods of Embodiment 1 or 2 described above.

[0142] Example 4

[0143] Based on the same inventive concept as other embodiments, this embodiment introduces a computer program product, including computer instructions that, when executed by a processor, implement the steps of the methods described in Embodiment 1 or 2 above.

[0144] In summary, by introducing a phase deviation accuracy factor and combining it with GNSS reference station phase observations for precise single-point positioning ambiguity fixation, this invention can accurately calculate and update the ambiguity variance-covariance matrix at the user end. This not only improves the accuracy of ambiguity fixation but also enhances robustness in complex environments and under real-time data delays, thereby significantly improving the overall performance and reliability of precise single-point positioning.

[0145] This invention selects stations sequentially based on the number of observed satellites and uses a phase deviation network solution method combined with the fractional cycles of wide-lane and narrow-lane ambiguities for iterative calculation. This enables precise calculation of the receiver-side UPD values ​​of all receivers and the satellite-side UPD values ​​of all visible satellites. It not only considers the influence of the number of observed satellites and prioritizes stations with abundant observation data, but also continuously updates the receiver-side and satellite-side UPD values ​​through a stepwise approximation method until convergence is achieved. This significantly improves the accuracy and reliability of receiver-side and satellite-side UPD value estimation, providing a solid foundation for subsequent ambiguity fixing, thereby improving the accuracy and efficiency of precise point positioning.

[0146] This invention updates the ambiguity variance-covariance matrix of the user terminal by combining the UPD accuracy factor, which greatly improves the search efficiency and success rate of the LAMBDA algorithm in the process of ambiguity fixation, thereby accelerating the convergence speed while ensuring positioning accuracy.

[0147] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0148] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0149] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0150] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0151] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A precise point positioning ambiguity resolution method based on phase bias precision factor, characterized in that, The method comprises the following steps: acquiring GNSS reference station phase observation values of a service end; based on the GNSS reference station phase observation values, calculating decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity of floating point ambiguity; selecting stations in turn according to the number of observed satellites, using a phase bias whole-network solution method and the decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity, and iteratively calculating receiver end UPD values of all receivers in the reference station network and satellite end UPD values of all visible satellites and extracting a residual vector of phase bias; calculating a UPD accuracy factor according to the residual vector of phase bias; updating a user end ambiguity variance-covariance matrix using the UPD accuracy factor, and fixing user end ambiguity based on a LAMBDA algorithm; the residual vector of phase bias is expressed as: ； wherein denotes the residual vector of phase bias, denotes the total number of receivers in the reference station network, denotes the total number of all visible satellites in the reference station network, denotes the phase bias residual observed by the receiver for the satellite, denotes the float ambiguity observed by the receiver for the satellite, denotes the integer ambiguity observed by the receiver for the satellite, denotes a row column identity matrix, denotes the Kronecker product, denotes a column vector of rows 1 column, denotes a column vector of rows 1 column, denotes a row column identity matrix, denotes the receiver-end UPD vector of all receivers in the reference station network, denotes the transpose; the UPD accuracy factor is expressed as: ； wherein represents the UPD accuracy factor of the th satellite, represents the total number of receivers that can observe the th satellite, represents the th receiver, represents the th receiver observing the phase bias residual of the th satellite.

2. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 1, characterized in that, based on the GNSS reference station phase observation values, calculating decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity of floating point ambiguity, comprising: estimating floating point ambiguity from the GNSS reference station phase observation values based on a non-difference non-combined observation model; the floating point ambiguity comprises integer ambiguity, receiver end and satellite end phase bias; performing linear combination processing on the floating point ambiguity to transform it into ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity; respectively performing rounding operations on ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity to obtain integer parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity; subtracting the integer parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity from ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity to obtain decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity.

3. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 2, characterized in that, selecting stations in turn according to the number of observed satellites, using a phase bias whole-network solution method and the decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity, and iteratively calculating receiver end UPD values of all receivers in the reference station network and satellite end UPD values of all visible satellites, comprising: setting the receiver end UPD value of the station with the most observed satellites to 0, subtracting the receiver end UPD value from the decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity to obtain satellite end UPD initial values; selecting the remaining stations in turn according to the descending order of the number of observed satellites, and repeating the following steps until all stations are processed: for known satellites in each station: subtracting the satellite end UPD value from the decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity, and then taking an average value as the receiver end UPD value; for unknown satellites in each station: subtracting the receiver end UPD value from the decimal fraction parts of ultra-wide lane ambiguity, wide lane ambiguity and narrow lane ambiguity to obtain satellite end UPD values of unknown satellites; performing weighted averaging on satellite end UPD values of the same satellite obtained by each station to obtain the satellite end UPD value of the satellite; If the difference between the satellite-end UPD values obtained in two adjacent iterations is less than a preset threshold, the loop is exited, and the receiver-end UPD values of all receivers in the reference station network and the satellite-end UPD values of all visible satellites are obtained.

4. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 3, characterized in that, The receiver-end UPD value is expressed as: ； wherein, represents the receiver-end UPD value, i.e. the UPD value of the receiver, represents the total number of satellites that can be observed by the receiver, represents the total number of satellites that can be observed by the receiver, represents the float ambiguity, represents the integer ambiguity, represents the satellite-end UPD value, i.e. the UPD value of the satellite.

5. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 3, characterized in that, The satellite-end UPD value is expressed as: ； In the formula, represents the satellite end UPD value, i.e. the UPD value of the i-th satellite represents the UPD value of the i-th satellite represents the total number of receivers that can observe the i-th satellite represents the total number of receivers that can observe the i-th satellite represents the j-th receiver represents the j-th receiver represents the UPD value calculated at the j-th receiver of the i-th satellite represents the UPD value calculated at the j-th receiver of the i-th satellite represents the UPD value calculated at the j-th receiver of the i-th satellite represents the i-th satellite represents the i-th satellite represents the UPD value calculated at the j-th receiver of the i-th satellite represents the UPD value calculated at the j-th receiver of the i-th satellite represents the corresponding weight value.

6. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 1, characterized in that, The residual vector of the phase bias is distributed on each satellite.

7. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 1, characterized in that, According to the residual vector of the phase bias, a UPD precision factor is calculated, including: The root mean square (RMS) of all elements in the residual vector of the phase bias is calculated to obtain the UPD precision factor.

8. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 2, characterized in that, The ambiguity variance-covariance matrix at the user end is updated using the UPD precision factor, and the ambiguity at the user end is fixed based on the LAMBDA algorithm, including: ； wherein, denotes the updated ambiguity variance-covariance matrix of the user end, denotes the ambiguity variance-covariance matrix of the user end, wherein, denotes the ambiguity of the user end, denotes a diagonal matrix consisting of UPD precision factors, denotes the total number of satellites observable by the receiver.

9. The precise point positioning ambiguity resolution method based on phase bias precision factor according to claim 8, characterized in that, The ambiguity variance-covariance matrix at the user end is updated using the UPD precision factor, and the ambiguity at the user end is fixed based on the LAMBDA algorithm, including: The super-wide-lane ambiguity, wide-lane ambiguity, and narrow-lane ambiguity are taken as the ambiguity at the user end. The ambiguity at the user end and the updated ambiguity variance-covariance matrix are decorrelated through an invertible integer conversion matrix to obtain an ambiguity vector and a converted ambiguity variance-covariance matrix. Integer ambiguity search and verification are performed on the ambiguity vector and the converted ambiguity variance-covariance matrix to obtain an integer ambiguity solution. The ambiguity at the user end is fixed according to the integer ambiguity solution.

10. The ambiguity fixing method based on phase bias precision factor for precise point positioning according to claim 9, characterized in that, The ambiguity vector and the converted ambiguity variance-covariance matrix are expressed as: ； wherein denotes the ambiguity vector, denotes the ambiguity at the user end, denotes the invertible integer conversion matrix, denotes the converted ambiguity variance-covariance matrix, denotes the ambiguity variance-covariance matrix at the user end, denotes the transpose of the invertible integer conversion matrix, denotes the transpose.

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