UPD estimation method and system based on soft constraint hierarchical modeling

Abstract

A UPD estimation method and system based on soft constraint hierarchical modeling, comprising: collecting double-frequency observation data of global IGS stations, and calculating wide-lane float ambiguity and ionosphere-free combination ambiguity float solution; estimating wide-lane UPD based on wide-lane float ambiguity and correcting, completing wide-lane integer ambiguity fixing; under the condition of wide-lane integer ambiguity fixing, combining ionosphere-free combination ambiguity float solution, and solving narrow-lane float ambiguity; according to the global ionospheric spatial distribution characteristics and disturbance law, dividing the observation network into multiple regional partitions; introducing regional common mode items in each partition, and taking the total electron content of the ionosphere extracted based on the global ionospheric map as prior information, constructing a multi-level joint solving framework containing satellite narrow-lane UPD, station narrow-lane UPD and regional common mode items through a soft constraint mode, and solving the narrow-lane float ambiguity in the network to estimate the UPD product. The present application realizes the cross-regional uniformity and high time stability of the UPD product.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, specifically to a UPD estimation method and system based on soft-constraint hierarchical modeling. Background Technology

[0002] Global Navigation Satellite Systems (GNSS) are widely used in high-precision positioning scenarios such as UAV navigation, autonomous driving, aerial surveying, and geological disaster monitoring. In recent years, PPP-RTK technology, which combines Precise Point Positioning (PPP) with Real-Time Kinematics (RTK), has attracted increasing attention due to its advantages such as no need for a reference station, global coverage, low communication costs, and centimeter-level positioning accuracy. The key to PPP-RTK lies in achieving integer-cycle fixation of carrier phase ambiguity, and the core of achieving this goal is generating and providing a reliable Uncalibrated Phase Delay (UPD) product. UPD, as a precise correction information, is used to eliminate system bias between the satellite and the receiver, allowing the ambiguity parameters to be fixed to integers, thereby achieving centimeter-level accuracy.

[0003] However, the UPD generation strategies used in current mainstream PPP-RTK systems have shortcomings. One type of method relies on the global IGS network to generate a unified global UPD product. While this provides good cross-regional consistency, in areas with strong ionospheric activity and frequent space environment disturbances (such as low-latitude regions or during geomagnetic storms), the sparse observation network and difficulty in accurately modeling regional errors lead to low ambiguity fixation rates, long convergence times, and poor positioning stability. Another type of method is based on regional or local CORS networks to generate local UPD correction information. This type of method can absorb ionospheric common-mode errors within the region to some extent, improving positioning accuracy and convergence speed. However, because different regions use different benchmark definitions, there is a lack of unified standards among UPD products. Users often need to re-initialize when operating across regions or switching service sources, which seriously affects the continuity and reliability of positioning results. Therefore, existing UPD generation and application strategies still have significant bottlenecks in terms of global adaptability, robustness to disturbed environments, and cross-regional stability, making it difficult to meet the high-precision, continuous, and stable PPP-RTK application requirements in complex environments. Summary of the Invention

[0004] This invention discloses a UPD estimation method based on soft-constraint hierarchical modeling, mainly used to solve problems such as difficulty in fixing ambiguity, discontinuous positioning, and poor service stability in current PPP-RTK systems under complex spatial environments with strong ionospheric disturbances and inconsistent regional network products. Based on regional hierarchical modeling and soft-constraint fusion solution technology, this invention enhances the adaptability of the solution process to spatial disturbances and achieves cross-regional uniformity and high temporal stability of UPD products, building upon the constructed UPD observation model.

[0005] First, dual-frequency observation data from global IGS stations were collected, and narrow-lane ambiguity floating-point values ​​were generated using a combination of wide-lane and ionospheric-free data. Then, based on the global ionospheric distribution characteristics, the observation network was divided into multiple regional partitions, and a regional ionospheric common-mode term was introduced into each partition to explicitly model regional-scale background errors. Simultaneously, the total ionospheric electron content (VTEC) extracted from the Global Ionospheric Map (GIM) published by IGS was used as regional prior information and embedded into the UPD estimation process using a soft-constraint approach, constructing a multi-level joint solution framework including "satellite bias + receiver bias + regional common-mode + weak constraints." During the solution process, the soft-constraint weights were adaptively adjusted according to the inter-regional residual consistency level, thereby enhancing model dominance during ionospheric calm periods and improving observation dominance during geomagnetic storm active periods, achieving intelligent adaptation to different spatiotemporal conditions. The final output UPD product significantly outperforms existing methods in terms of continuity, consistency, and stability, especially in low-latitude or spatially disturbed regions, maintaining centimeter-level ambiguity fixation capability and significantly improving PPP-RTK positioning performance.

[0006] Firstly, this invention proposes a UPD estimation method based on soft-constraint hierarchical modeling, comprising: collecting dual-frequency observation data from global IGS stations, and calculating the wide-lane floating-point ambiguity and the ionosphere-free combined ambiguity floating-point solution respectively; estimating the wide-lane UPD based on the wide-lane floating-point ambiguity and correcting it to fix the wide-lane integer ambiguity; under the condition of fixed wide-lane integer ambiguity, solving the narrow-lane floating-point ambiguity by combining the ionosphere-free combined ambiguity floating-point solution; dividing the observation network into multiple regional partitions according to the global ionospheric spatial distribution characteristics and disturbance patterns; introducing a regional common mode term in each partition, and using the total electron content of the ionosphere extracted from the global ionospheric map as prior information, constructing a multi-level joint solution framework including satellite-end narrow-lane UPD, station-end narrow-lane UPD, and regional common mode term through soft constraints, and performing network solution on the narrow-lane floating-point ambiguity to estimate the UPD product.

[0007] In some examples, the division of the observation network into multiple regional zones includes: dividing global IGS stations into the low-latitude equatorial ionization anomaly zone, the mid-latitude stable zone, and the high-latitude polar zone according to latitude; within each latitudinal zone, further dividing it into multiple regions according to longitude, including the Africa-Atlantic region, the Americas-Pacific boundary region, the Indian Ocean-East Africa region, the Western Pacific-Asia region, and the Eastern Pacific-International Date Line region.

[0008] In some examples, the introduction of the regional common mode term is achieved by extending the narrow alley observation equation to the following form:

[0009]

[0010] in, It is a measuring station r For satellite s Narrow alleyway observation, It is the narrow alley UPD at the station end. It is a satellite-end narrow-lane UPD. It is the observation noise term; It is the first k Regional common modulus terms for each region, express k A set of stations in each partition.

[0011] In some examples, the soft constraint is implemented for each region common modulus term. This is achieved by introducing a pseudo-observation equation that constrains it to prior values ​​derived from the global ionospheric map. Nearby, represented as:

[0012]

[0013] In the formula, For pseudo-observation residuals, The first obtained from the global ionospheric map k Ionospheric background reference values ​​for each region.

[0014] In some examples, the prior value The VTEC is obtained by weighting the GIMVTEC values ​​of all stations within the zone to obtain the regional average VTEC, and then converting it into a delay value based on the narrow lane frequency.

[0015] In some examples, the weights of the pseudo-observation equations in the solution can be adaptively adjusted; the adjustment of the weights is based on the consistency level of the bidirectional mean-removed residuals within the partitions, and the higher the consistency, the greater the weight and the stronger the soft constraint.

[0016] In some examples, the estimated wide lane UPD uses the least squares method and fixes the solution benchmark by specifying a reference satellite with a UPD of zero.

[0017] In some examples, the narrow-lane floating-point ambiguity is calculated using the following relation:

[0018]

[0019] in, For the floating-point fuzziness of the narrow alley, For the fixed width of the alley, , These are the equivalent wavelength and ambiguity floating-point solutions for the ionosphere-free combination, respectively. For the narrow alley equivalent wavelength, , These are the wavelengths of the two original carrier frequencies.

[0020] Secondly, this invention proposes a UPD estimation system based on soft-constraint hierarchical modeling, comprising: a data acquisition and preprocessing module configured to acquire dual-frequency observation data from global IGS stations and calculate the wide-lane floating-point ambiguity and the ionosphere-free combined ambiguity floating-point solution respectively; a wide-lane ambiguity fixing model configured to estimate the wide-lane UPD based on the wide-lane floating-point ambiguity and perform corrections to fix the wide-lane integer ambiguity; and a narrow-lane ambiguity resolution module configured to, under the condition of fixed wide-lane integer ambiguity, combine the ionosphere-free combined ambiguity floating-point solution with the wide-lane ambiguity floating-point solution. The solution is to calculate the narrow-lane floating-point ambiguity; the network region partitioning module is configured to divide the observation network into multiple regional partitions based on the global ionospheric spatial distribution characteristics and disturbance patterns; the hierarchical joint settlement module is configured to introduce a regional common mode term in each partition, and based on the total electron content of the ionosphere extracted from the global ionospheric map as prior information, construct a multi-level joint settlement framework including satellite-end narrow-lane UPD, station-end narrow-lane UPD, and regional common mode term through soft constraints, and perform network solution on the narrow-lane floating-point ambiguity to estimate the UPD product.

[0021] Thirdly, the present invention proposes a server, including a processor and a memory, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the UPD estimation method based on soft constraint hierarchical modeling.

[0022] Compared with existing technologies, this invention has at least the following advantages: It significantly improves the stability and reliability of UPD products during periods of intense geomagnetic storms or ionospheric activity, enhancing the adaptability of PPP-RTK systems in complex environments; it introduces regional common-mode terms and soft-constraint mechanisms, achieving inter-regional unification of UPD, reducing the frequency of re-initialization during cross-regional operations, and ensuring the continuity of high-precision positioning; it possesses good system compatibility and scalability, allowing for flexible deployment in GNSS augmentation networks of various sizes, and has engineering implementation value. Attached Figure Description

[0023] Figure 1 This is a flowchart of a UPD estimation method based on soft constraint hierarchical modeling in one embodiment of the present invention.

[0024] Figure 2 This is a performance comparison chart of the method of the present invention and the conventional method in one embodiment of the present invention, wherein (a) is the narrow alley UPD estimated by the conventional method, and (b) is the narrow alley UPD estimated by the method of the present invention. Detailed Implementation

[0025] like Figure 1 As shown, a UPD estimation method based on soft-constraint hierarchical modeling is proposed. This method divides the observation network into multiple regional partitions, introduces a regional ionospheric common-mode term within each partition, and incorporates the global GIM model as prior information. This constructs a multi-level joint solution framework comprising "satellite bias + receiver bias + regional common-mode + weak constraints." This effectively enhances the adaptability of the solution process to spatial disturbances and enables continuous splicing and unified representation of UPD products across regions.

[0026] S1: Solve WL / IF ambiguity.

[0027] Let the first Each monitoring station has two carrier frequency points. The first observation The carrier phase and pseudorange of each satellite are denoted as follows: ,in The corresponding wavelength is , The speed of light. Station on frequency The above is the first The original integer ambiguity of a satellite is denoted as The integer ambiguity of a wide-lane (WL) is defined as follows: The wide-lane wavelength is .

[0028] To obtain the wide-lane fuzziness, we first need to construct... (MW) Wide Lane Combination:

[0029]

[0030] In the formula The wide-lane floating-point ambiguity estimate (real number, not an integer) is obtained by combining MW.

[0031] The result obtained is actually the wide-lane floating-point ambiguity, which can be represented as:

[0032]

[0033] in For true wide alley integer solutions (wide alley integer ambiguity); and These are the phase deviations at the receiver end and the satellite end, respectively. As noise, its influence is usually mitigated through moving averages.

[0034] After obtaining the wide lane integer, the PPP ionosphere-free (IF) ambiguity is estimated. The ionosphere-free carrier phase combination is defined as:

[0035]

[0036]

[0037] In the formula: This is a carrier phase combination without ionosphere; , These are the weighting coefficients for the ionosphere-free combination.

[0038] This combination cancels out the first-order ionospheric term, and its floating-point ambiguity term is mathematically equivalent to a linear combination of two-frequency integers:

[0039]

[0040] In PPP Kalman filtering, directly... As a constant state estimate at the arc segment level, the result is estimated in meters. This is the floating-point solution for ionosphere-free ambiguity estimated in PPP filtering. The equivalent wavelength for the ionosphere-free combination.

[0041] S2: LSQ solves wide lane UPD (Uncalibrated Phase Delay, phase deviation caused by receiver / satellite hardware).

[0042] Before calculating the NL ambiguity, the UPD of the wide lane needs to be calculated first. and This part of the deviation is Therefore, by removing the integer unknowns, only the fractional part is used to establish the network solution equations:

[0043]

[0044] In the formula: This is a function that takes the decimal part, with a range of [0,1].

[0045] Solve the equations of all stations simultaneously, for and Perform least squares estimation and add a reference star constraint, i.e., set the upd of a certain reference star to 0. The solution result is converted to floating-point values. Make corrections to achieve near-integer values:

[0046]

[0047] In the formula: The wide aisle ambiguity is corrected by UPD and is close to an integer.

[0048] After further threshold and variance tests, the integer width of the alley can be fixed.

[0049] S3: Solve NL floating-point ambiguity.

[0050] In the wide lane integer Under fixed conditions, the combined ambiguity parameters of the IF filter obtained by PPP filtering are... Construct narrow alley (NL) floating-point ambiguity. The relationship between IF combinations and WL integers can be written as:

[0051]

[0052] in For the floating-point fuzziness of the narrow alley, The equivalent wavelength for the narrow alleyway.

[0053] S4: Modeling region division.

[0054] The primary objective of this invention's modeling is to minimize the interference of ionospheric spatiotemporal inhomogeneities on NL-UPD estimation during the network computation stage, thus reducing the common-mode error term. The introduction and constraints provide physical support. The core of the partitioning is based on the spatial distribution characteristics of the ionosphere, the laws of disturbance activity, and the characteristics of the observation network.

[0055] Considering the significant spatial differences in the ionosphere along the latitudinal direction, global stations are first divided into three basic zones according to latitude: the low-latitude equatorial ionization anomaly zone ( ): Ionospheric activity is intense and disturbances are frequent; mid-latitude stable zone ( The ionosphere changes relatively smoothly; high-latitude polar regions ( ): The spatial gradient is large but the regularity is strong.

[0056] Ionospheric activity also exhibits a clear "hotspot" distribution along the longitude direction. Therefore, each latitudinal zone is further subdivided by longitude, with the key intervals as follows: Africa–Atlantic region (including SAA). Significant ionospheric anomalies and frequent disturbances are observed in the SAA region; the Americas-Pacific boundary region. Strong diurnal variation, significant cross-regional disturbances, and large TEC fluctuations; Indian Ocean-East Africa region. Significant ionospheric voids and unstable structures exist; Western Pacific–Asia region TEC changes at a high rate and has a large regional gradient; Eastern Pacific – International Date Line region Located near the International Date Line, it exhibits the strongest diurnal variation gradient, with a steep diurnal variation curve for TEC, and possesses independent perturbation characteristics.

[0057] Let the number of regions obtained by the division be . , No. Each region is defined as:

[0058]

[0059] In the formula, , Indicates geographical longitude. Indicates geographical latitude.

[0060] area Contains One GNSS station:

[0061]

[0062] S5: Layered modeling strategy.

[0063] In traditional NL-UPD network solutions, the ionospheric background delay is not explicitly characterized, and its regional non-uniformity is often implicitly absorbed into the satellite-end narrow-lane UPD. ) or narrow lane UPD at the station end ( In this context, the UPD product exhibits significant drift and cross-regional inconsistency in low-latitude regions with strong ionospheric disturbances. The hierarchical modeling strategy of this invention introduces a regional common-mode term into the observation equation. And using GIM (Global Ionospheric Map) as a soft constraint, a "UPD ( , + Regional ionospheric background item ( The solution structure is used to achieve cross-regional consistency and stability of UPD products.

[0064] The basic observation equations for solving the NL-UPD network are:

[0065]

[0066] in: It is a measuring station r For satellite s NL observations; It is the deviation at the station end; It is a satellite-end deviation; This is the observation noise term.

[0067] To explicitly characterize regional-scale ionospheric trends, the regional common mode term is... Introducing equations, for the region Any station within r and satellite s Narrow alley observations The observation equation is:

[0068]

[0069] in: It is a region The ionospheric background term is shared by all stations in the region; The spatial region is determined by the partitioning modeling in step S4. This equation establishes the relationship between the observations of each station-satellite pair and the parameters to be estimated. A network containing R stations and S satellites will generate S... R such methods.

[0070] If no constraints are added to this observation equation There are free translations between them, which makes the UPD solution non-unique. Therefore, it is necessary to introduce constraints on the degrees of freedom in two directions:

[0071] Satellite-side constraints: Typically, a reference satellite is fixed at the satellite end. ,make It can fix one degree of freedom in one direction.

[0072] Region common mode constraint: Introducing soft constraints That is, the estimated It should be close to the prior value derived from GIM. .

[0073] The GIM model published by international organizations can provide a continuous field of total electron content (VTEC) in the ionosphere. ,in Geographical longitude, Geographical latitude, t This is the epoch time. The region of this partition. Collection of all stations A weighted average is performed to obtain the background ionospheric reference value for this region:

[0074]

[0075] In the formula: It is a partition k The set of stations in the middle; It is the first r The weight of each monitoring station; This is the corresponding location (longitude) of the station. ,latitude )exist The GIM VTEC value at time 1.

[0076] Convert to delay unit:

[0077]

[0078] In the formula This is the carrier frequency corresponding to the narrow lane.

[0079] Using the above Background terms of regional ionosphere Introduce soft constraints. To achieve Close to the estimate ( This constraint, in the least squares / filtering framework, is typically addressed using a "pseudo-observation" technique, which artificially introduces a virtual observation equation to constrain the parameters to be estimated. Specifically, this involves using a common-mode term for each region. Add a pseudo-observation equation to constrain the parameter to its prior value. nearby:

[0080]

[0081] In the formula, These are spurious observation residuals, reflecting the deviation between the model results and prior values. The entire network incorporates... K Such a pseudo-observation equation ( K (Total number of regions).

[0082] when When, it indicates an estimate. Maintain consistency with the GIM background. At this point, in the least squares / filtering process, the above S... R actual observation equations and K pseudo observation equations can be combined to form an augmented observation system:

[0083]

[0084] Its power array is:

[0085]

[0086] in, The matrix P is the weight matrix of the pseudo-observation equation, defined below. Matrix P is the weight matrix corresponding to the actual narrow-lane observation equation, used to reflect the accuracy differences between different station-satellite observations. Considering that GNSS carrier phase observation errors are closely related to satellite elevation angles, and low-elevation-angle observations are more susceptible to ionospheric residual errors, multipath effects, and tropospheric mapping errors, the weight matrix is ​​constructed using a sinusoidal function weighting strategy based on the satellite elevation angle during network solution. Specifically, for narrow-lane observations of satellite s from station r, its weights... With satellite elevation angle The sine function is related, and in a preferred embodiment, it can be expressed as:

[0087]

[0088] The higher the satellite elevation angle, the larger the corresponding weight; the lower the satellite elevation angle, the smaller the corresponding weight. Matrix P is a diagonal matrix, and its diagonal elements are the weights of each station's satellite observations.

[0089] The observation equations for all station-satellite pairs in the region ( Combining these elements and writing them in matrix form, we get the actual observation equation:

[0090] Ax=y+v

[0091] In the formula, A is the actual observation design matrix with dimensions ( ) Each row corresponds to a satellite pair from a station, and within that row, the corresponding stations are... r of The column coefficient is +1, corresponding to satellite s. The column coefficient is -1, corresponding to region k. The column coefficient is -1, and all other elements are 0. y represents all narrow alley observations. The vector formed has a dimension of v is the corresponding observation noise vector, with latitude . . Let be the vector of parameters to be estimated, with dimension . .

[0092] Meanwhile, the pseudo-observation equation can also be written in matrix form:

[0093]

[0094] in: , dimension K ×1; Unknown parameter vector, dimension is ; The residuals are pseudo-observations with dimension 1. K ×1; Design a matrix for pseudo-observations, with the following dimensions: R represents the number of stations, S represents the number of satellites, and K represents the number of regions. For the k-th row (corresponding to the pseudo-observation equation for region k)... ), this line in parameters The corresponding column (i.e., in the x vector) The location column is set to 1, and all other columns (including all station UPDs, all satellite UPDs, and C for other regions) are set to 0. This allows for matrix multiplication. The result is exactly .

[0095] To prevent overly strong or weak constraints, a weighted form of spurious observations is used, with the weight matrix defined as follows: Weights for each region Adaptive adjustments are made based on the level of consistency of observations within the partition.

[0096] Each region The evaluation can be based on the residuals from two-way mean removal: first calculate the station mean. Star average and global mean Construct two-way mean-removed residuals This eliminates station-end and satellite-end biases and resolves regional common-mode terms, retaining only the "residual" of spatial inconsistencies within the region. This is achieved using regional robust statistics. (or RMS) Quantitative Consistency: The smaller value indicates that the region can be described by a single common modulus term. The large representation exhibits significant small-scale perturbations or gradients; based on this, adaptive soft constraints are set for the region. The intensity.

[0097] The above-described hierarchical modeling and soft-constraint solution achieve effective error stripping, product consistency, and adaptive stable solution. Specifically, this is achieved by introducing a regional common-mode term. will traditionally be , The absorbed regional ionospheric delay background was clearly separated, resulting in a more physically meaningful and "cleaner" estimate of UPD. , Using GIM prior information to... Applying adaptive soft constraints effectively suppresses cross-regional inconsistencies and low-latitude drift in UPD products caused by ionospheric spatial disturbances, enabling continuous splicing and unified representation of global or large-scale UPD products. This is achieved using an adaptive weighting matrix based on bidirectional mean-removed residuals. The settings enable the solution framework to flexibly respond to differences in ionospheric spatial consistency in different regions (such as low-latitude disturbance regions and mid-latitude calm regions), thereby enhancing the robustness and practicality of the model.

[0098] Ultimately, the resulting high-precision, highly consistent UPD products can provide reliable correction information for precision positioning services such as PPP-RTK at the user end. When used by users, combining regional ionospheric and tropospheric constraints can significantly shorten the ambiguity fixation time and improve the convergence speed and final accuracy of positioning.

[0099] The method of this invention is aimed at the server system for UPD product generation and broadcasting. It can run on physical devices or virtualized resources with the ability to access observation data, batch processing / near real-time computing, product packaging and network broadcasting. Typical deployment forms include, but are not limited to, dedicated physical servers (central processing servers), cloud servers / cloud-native computing clusters (elastic computing power platforms), and regional edge computing nodes (regional aggregation and distribution nodes).

[0100] Dedicated physical servers (central processing servers) are deployed in data centers or computer rooms, equipped with multi-core CPUs, ample memory, and high-speed storage. They are used for long-term stable access to IGS / CORS observation data and to complete WL / IF ambiguity processing, UPD network calculation, and product output. They are suitable for continuous broadcasting under fixed public IP or leased line environments.

[0101] Cloud servers / cloud-native computing clusters (elastic computing platforms) are deployed on public or private cloud IaaS / Kubernetes platforms. Through containerization and automated operation and maintenance, they achieve elastic scaling, fault migration, and high availability deployment. They can provide continuous services to the outside world using domain name resolution and load balancing, without relying on a single fixed physical IP.

[0102] Regional edge computing nodes (regional aggregation and distribution nodes) are deployed at regional data aggregation points or operation-side data centers to access regional monitoring station data nearby, receive central processing results, and perform regional consistency monitoring, regional partition statistics, and product forwarding, thereby reducing central bandwidth pressure and improving regional service availability.

[0103] Corresponding to the foregoing method embodiments, the present invention also provides an embodiment of a UPD estimation system based on soft-constraint hierarchical modeling. The system includes: a data acquisition and preprocessing module, a wide-lane ambiguity fixing model, a narrow-lane ambiguity resolution module, a network region partitioning module, and a hierarchical joint settlement module.

[0104] The data acquisition and preprocessing module is configured to acquire dual-frequency observation data from global IGS stations and calculate the wide-lane floating-point ambiguity and the ionosphere-free combined ambiguity floating-point solution, respectively.

[0105] The wide-lane ambiguity fixing model is configured to estimate the wide-lane UPD based on the wide-lane floating-point ambiguity and make corrections, thereby completing the fixing of the wide-lane integer ambiguity.

[0106] The narrow alley ambiguity resolution module is configured to calculate the narrow alley floating-point ambiguity by combining the ionosphere-free combined ambiguity floating-point solution under the condition that the wide alley integer ambiguity is fixed.

[0107] The network region division module is configured to divide the observation network into multiple regional partitions based on the spatial distribution characteristics and disturbance patterns of the global ionosphere.

[0108] The hierarchical joint settlement module is configured to introduce a regional common mode term in each partition and use the total electron content of the ionosphere extracted from the global ionospheric map as prior information. It constructs a multi-level joint solution framework including satellite-end narrow lane UPD, station-end narrow lane UPD, and regional common mode term through a soft constraint method. The network solution is used to solve the narrow lane floating point ambiguity to estimate the UPD product.

[0109] This system is based on the same inventive concept as the aforementioned method, and achieves the same technical effect by executing the corresponding steps in the aforementioned method embodiments through its various modules. Each module of the system can be implemented by a processor of a computing device (such as a server) executing corresponding instructions through programming. Its specific software functional logic corresponds to the steps in the aforementioned method embodiments, and will not be elaborated here.

[0110] A computer-readable storage medium. For example, the computer-readable storage medium may be a read-only memory (ROM). Read-only memory (ROM), random access memory (RAM), and compact disc (CD-ROM). Only memory, CD ROM, magnetic tape, floppy disk, and optical data storage devices, etc. This computer-readable storage medium is used to store computer-readable instructions, which, when executed by a computer, can implement one or more steps of the aforementioned UPD estimation method based on soft-constraint hierarchical modeling.

[0111] Application examples such as Figure 2 As shown. The experiment uses global observation data from DOY 144 in 2025. Based on the proposed partitioning method of this invention, the global observation network is divided into 6 regions, and soft-constraint hierarchical modeling is performed. Figure 2 In the graph, the horizontal axis represents the epoch (sampling interval of 15 minutes, including 96 epochs throughout the day), and the vertical axis represents the estimated narrow alleyway UPD (unit: week). Figure 2 Figures (a) and (b) compare the performance of the improved method of this invention with that of the traditional method (ordinary least squares method without regional modeling and without removing regional common mode terms). The results show that the average standard deviation (STD) per satellite using the traditional method is 0.4 weeks, while the STD of the improved method is reduced to 0.26 weeks (an improvement of approximately 35%), resulting in a significant improvement in the stability of the generated UPD product sequence. This method effectively suppresses spatial correlation errors through regional modeling, improving the quality and reliability of satellite navigation precise positioning products.

Claims

1. A UPD estimation method based on soft-constraint hierarchical modeling, characterized in that, include: Dual-frequency observation data from IGS stations worldwide were collected, and the wide-lane floating-point ambiguity and the ionosphere-free combined ambiguity floating-point solutions were calculated respectively. Based on the wide-lane floating-point ambiguity, the wide-lane UPD is estimated and corrected to complete the fixation of the wide-lane integer ambiguity; Under the condition that the wide alley integer ambiguity is fixed, the narrow alley floating-point ambiguity is calculated by combining the ionosphere-free combined ambiguity floating-point solution. Based on the spatial distribution characteristics and disturbance patterns of the global ionosphere, the observation network is divided into multiple regional zones; A regional common mode term is introduced within each partition, and the total electron content of the ionosphere extracted from the global ionospheric map is used as prior information. A multi-level joint solution framework, including satellite-end narrow-lane UPD, station-end narrow-lane UPD, and regional common mode term, is constructed using a soft-constraint approach. The narrow-lane floating-point ambiguity is then solved via a network to estimate the UPD product. The introduction of the regional common mode term is achieved by extending the narrow alley observation equation to the following form: in, It is a measuring station r For satellite s Narrow alleyway observation, It is the narrow alley UPD at the station end. It is a satellite-end narrow-lane UPD. It is the observation noise term; It is the first k The regional common modulus of each region, express k The set of stations in each region; The soft constraint is implemented through the common modulus term for each region. This is achieved by introducing a pseudo-observation equation that constrains it to prior values ​​derived from the global ionospheric map. Nearby, represented as: In the formula, For pseudo-observation residuals, The first obtained from the global ionospheric map k Ionospheric background reference values ​​for each region.

2. The UPD estimation method according to claim 1, characterized in that, The division of the observation network into multiple regional partitions includes: Based on latitude, global IGS stations are divided into the low-latitude equatorial ionization anomaly zone, the mid-latitude stable zone, and the high-latitude polar zone. Within each latitudinal zone, multiple regions are further divided according to longitude. These regions include the Africa-Atlantic region, the Americas-Pacific boundary region, the Indian Ocean-East Africa region, the Western Pacific-Asia region, and the Eastern Pacific-International Date Line region.

3. The UPD estimation method according to claim 1, characterized in that, The prior value The VTEC values ​​of all stations within the zone are obtained by weighted averaging to obtain the regional average VTEC, which is then converted into a delay value based on the narrow lane frequency.

4. The UPD estimation method according to claim 3, characterized in that, The weights of the pseudo-observation equations in the solution can be adaptively adjusted. The adjustment of the weights is based on the consistency level of the bidirectional mean-removed residuals within the partition. The higher the consistency, the greater the weight and the stronger the soft constraint.

5. The UPD estimation method according to claim 1, characterized in that, The estimated wide lane UPD is calculated using the least squares method, and the solution benchmark is fixed by specifying the UPD of a reference satellite as zero.

6. The UPD estimation method according to claim 1, characterized in that, The narrow-lane floating-point ambiguity is calculated using the following relation: in, For the floating-point fuzziness of the narrow alley, For the fixed width of the alley, , These are the equivalent wavelength and ambiguity floating-point solutions for the ionosphere-free combination, respectively. For the narrow alley equivalent wavelength, , These are the wavelengths of the two original carrier frequencies.

7. A UPD estimation system based on soft-constraint hierarchical modeling, characterized in that, include: The data acquisition and preprocessing module is configured to acquire dual-frequency observation data from global IGS stations and calculate the wide-lane floating-point ambiguity and the ionosphere-free combined ambiguity floating-point solution, respectively. A wide-lane ambiguity fixing model is configured to estimate the wide-lane UPD based on the wide-lane floating-point ambiguity and correct it to complete the fixing of the wide-lane integer ambiguity. The narrow alley ambiguity resolution module is configured to calculate the narrow alley floating-point ambiguity by combining the ionosphere-free combined ambiguity floating-point solution under the condition that the wide alley integer ambiguity is fixed. The network region division module is configured to divide the observation network into multiple regional partitions based on the spatial distribution characteristics and disturbance patterns of the global ionosphere. The hierarchical joint settlement module is configured to introduce a regional common mode term within each partition and, based on the total electron content of the ionosphere extracted from the global ionospheric map as prior information, construct a multi-level joint solution framework including satellite-end narrow-lane UPD, station-end narrow-lane UPD, and regional common mode term using a soft-constraint approach. It then performs network-based solution of the narrow-lane floating-point ambiguity to estimate the UPD product. The introduction of the regional common mode term is achieved by extending the narrow alley observation equation to the following form: in, It is a measuring station r For satellite s Narrow alleyway observation, It is the narrow alley UPD at the station end. It is a satellite-end narrow-lane UPD. It is the observation noise term; It is the first k The regional common modulus of each region, express k The set of stations in each region; The soft constraint is implemented through the common modulus term for each region. This is achieved by introducing a pseudo-observation equation that constrains it to prior values ​​derived from the global ionospheric map. Nearby, represented as: In the formula, For pseudo-observation residuals, The first obtained from the global ionospheric map k Ionospheric background reference values ​​for each region.

8. A server, characterized in that, It includes a processor and a memory, the memory storing a computer program, and when the processor executes the computer program, it implements the UPD estimation method based on soft constraint hierarchical modeling as described in any one of claims 1 to 6.

Images