GNSS positioning method based on anisotropic troposphere and ionosphere DCB separation and related device

Abstract

The application discloses a GNSS positioning method based on anisotropic troposphere and ionosphere DCB separation and related equipment, which can be applied to the technical field of satellite navigation and location service. The application constructs an anisotropic troposphere slant delay model based on an observation-state framework, estimates zenith delay parameters and horizontal gradient parameters on a service side, extracts slant ionosphere delay based on precise point positioning state, establishes a vertical ionosphere delay model of regional ionosphere, performs satellite and receiver hardware delay estimation and separation operation based on the slant ionosphere delay and the vertical ionosphere delay model to obtain hardware delay, generates troposphere delay correction and ionosphere delay correction, and then performs low-bandwidth coding broadcasting. After receiving the low-bandwidth coded data broadcasted, the user side applies a troposphere and ionosphere constraint PPP-B2b-RTK resolving positioning, so that GNSS fast and high-precision positioning can be realized.

Description

Technical Field

[0001] This application relates to the field of satellite navigation and location services technology, and in particular to a GNSS positioning method and related equipment based on anisotropic tropospheric and ionospheric DCB separation. Background Technology

[0002] In related technologies, with the widespread application of Global Navigation Satellite Systems (GNSS), high-precision positioning technologies such as Real-time Dynamic Differential (RTK) and Precise Point Positioning (PPP) have been gradually applied to scenarios requiring sub-meter or even centimeter-level positioning accuracy, such as unmanned surface vessels (USVs) and autonomous vehicles. Traditional RTK requires setting up a reference station near the user and transmitting original observation corrections, resulting in a large amount of communication data; traditional PPP relies on the user to obtain precise orbit and clock error correction products in real time, leading to long convergence times and high dependence on communication. Therefore, in scenarios such as marine USVs, it is difficult to achieve fast and high-precision positioning under low-cost, low-bandwidth communication conditions.

[0003] In summary, the technical problems existing in the relevant technologies need to be improved. Summary of the Invention

[0004] The main objective of this application is to propose a GNSS positioning method and related equipment based on the separation of anisotropic troposphere and ionosphere DCB, which can achieve rapid and high-precision GNSS positioning.

[0005] To achieve the above objectives, one aspect of this application proposes a GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation, the method comprising the following steps:

[0006] Construct a non-combined GNSS observation model and a state model to form an observation-state framework;

[0007] Based on the observation-state framework, an anisotropic tropospheric oblique delay model is constructed, and the zenith delay parameter and horizontal gradient parameter are estimated on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient.

[0008] Based on precise single-point positioning, the oblique ionospheric delay is extracted and a vertical ionospheric delay model of the regional ionospheric is established.

[0009] Hardware delay estimation and separation operations for satellite and receiver are performed based on oblique ionospheric delay and vertical ionospheric delay models to obtain hardware delay;

[0010] Generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter;

[0011] Ionospheric delay corrections are generated based on the vertical ionospheric delay model and hardware delay.

[0012] The tropospheric delay correction, the ionospheric delay correction, and the hardware delay are encoded and broadcast using low-bandwidth encoding.

[0013] The PPP-B2b-RTK solution is obtained by applying tropospheric and ionospheric constraints to the user end based on the low-bandwidth encoded data after broadcast.

[0014] In some embodiments, the non-combined GNSS observation model includes a pseudorange observation model and a carrier phase observation model;

[0015] The pseudorange observation model is as follows:

[0016] ;

[0017] In the formula, This represents the pseudorange observation value between receiver r and satellite s at frequency point f; The distance between receiver r and satellite s is represented by r; c represents the speed of light. These represent receiver clock bias and satellite clock bias, respectively. Indicates tropospheric slack delay. Indicates ionospheric slack delay; Both represent pseudorange hardware latency; Indicates pseudorange noise;

[0018] The carrier phase observation model is as follows:

[0019] ;

[0020] In the formula, This represents the carrier phase observation value between receiver r and satellite s at frequency point f; Indicates wavelength. Indicates the ambiguity of the integer period. Both represent phase hardware delay. This represents phase noise.

[0021] In some embodiments, constructing an anisotropic tropospheric oblique delay model and estimating the zenith delay parameter and horizontal gradient parameter on the server side includes:

[0022] An anisotropic tropospheric oblique delay model is constructed based on the horizontal gradient. The mapping function in the anisotropic tropospheric oblique delay model is used to characterize the nonlinear characteristics of the tropospheric delay in the low elevation angle direction as a function of the elevation angle.

[0023] After constructing a stochastic model of the anisotropic tropospheric parameters in the anisotropic tropospheric slant delay model, a Kalman filter is incorporated.

[0024] The server obtains the zenith delay parameters and horizontal gradient parameters of each receiver.

[0025] In some embodiments, the anisotropic tropospheric slack delay model is as follows:

[0026] ;

[0027] In the formula, Indicates receiver The upper elevation angle is azimuth angle is satellite Corresponding anisotropic tropospheric oblique elongation; Indicates receiver The zenith static delay; Indicates receiver The zenith wet delay; These represent the northward tropospheric gradient and the eastward tropospheric gradient, respectively. These represent the static mapping function and the wet delay mapping function, respectively. This represents the gradient mapping function.

[0028] In some embodiments, the step of extracting the oblique ionospheric delay based on precise single-point positioning and establishing a vertical ionospheric delay model of the regional ionosphere includes:

[0029] Oblique ionospheric delay is extracted based on non-combined precise single-point positioning state;

[0030] An ionospheric projection model under the thin-layer assumption is established to map the oblique ionospheric delay to the physical quantity of vertical ionospheric delay;

[0031] Based on the mapped physical quantities, a vertical ionospheric delay model of the regional ionosphere is established using trigonometric series.

[0032] In some embodiments, generating the tropospheric delay correction based on the zenith delay parameter and the horizontal gradient parameter includes:

[0033] Calculate the tropospheric slant delay in any satellite direction based on the zenith delay parameter and the horizontal gradient parameter;

[0034] The tropospheric slant delay is compared with the standard tropospheric delay to obtain the tropospheric delay correction.

[0035] In some embodiments, the step of applying tropospheric and ionospheric constraints to the PPP-B2b-RTK solution at the user end based on the broadcast low-bandwidth coded data to obtain the PPP-B2b-RTK positioning result includes:

[0036] Atmospheric and hardware delay corrections are applied to user-end observations based on the low-bandwidth coded data after broadcast.

[0037] Construct a state vector with residual priors and perform Kalman filtering;

[0038] After applying atmospheric and hardware delay corrections, the ambiguity of the carrier phase observations is reconstructed.

[0039] Calculate the inter-satellite single-difference ambiguity based on the reconstructed ambiguity;

[0040] After performing an integer search and fixing the ambiguity based on the inter-satellite single-difference ambiguity, the coordinate solution is updated;

[0041] The PPP-B2b-RTK positioning result is obtained based on the updated coordinate solution.

[0042] To achieve the above objectives, another aspect of this application proposes a GNSS positioning device based on anisotropic tropospheric and ionospheric DCB separation, the device comprising:

[0043] The first module is used to construct a non-combined GNSS observation model and a state model to form an observation-state framework;

[0044] The second module is used to construct an anisotropic tropospheric oblique delay model based on the observation-state framework and estimate the zenith delay parameter and horizontal gradient parameter on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient.

[0045] The third module is used to extract the oblique ionospheric delay based on the precise single-point positioning state and to establish a vertical ionospheric delay model of the regional ionospheric.

[0046] The fourth module is used to perform hardware delay estimation and separation operations between the satellite and the receiver based on the oblique ionospheric delay and vertical ionospheric delay models, so as to obtain the hardware delay.

[0047] The fifth module is used to generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter.

[0048] The sixth module is used to generate ionospheric delay corrections based on the vertical ionospheric delay model and hardware delay.

[0049] The seventh module is used to perform low-bandwidth encoding and broadcasting of the tropospheric delay correction, the ionospheric delay correction, and the hardware delay;

[0050] The eighth module is used to perform PPP-B2b-RTK calculations at the user end based on the low-bandwidth encoded data after broadcast, applying tropospheric and ionospheric constraints, and to obtain PPP-B2b-RTK positioning results.

[0051] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the method described above.

[0052] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the methods described above.

[0053] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer program product, including a computer program that, when executed by a processor, implements the aforementioned method.

[0054] The embodiments of this application include at least the following beneficial effects: This application provides a GNSS positioning method and related equipment based on the separation of anisotropic tropospheric and ionospheric DCB. This scheme constructs an anisotropic tropospheric oblique delay model based on the constructed observation-state framework and estimates the zenith delay parameter and horizontal gradient parameter at the server end. Simultaneously, it extracts the oblique ionospheric delay based on the precise single-point positioning state and establishes a vertical ionospheric delay model of the regional ionosphere. Then, it estimates the hardware delay of the satellite and receiver based on the oblique ionospheric delay and the vertical ionospheric delay model. The hardware delay is obtained through separation operations, and tropospheric delay corrections are generated based on zenith delay parameters and horizontal gradient parameters. Ionospheric delay corrections are also generated based on the vertical ionospheric delay model and hardware delay. Then, the tropospheric delay corrections, ionospheric delay corrections, and hardware delays are encoded and broadcast using low-bandwidth encoding. After receiving the broadcast low-bandwidth encoded data, the user terminal applies PPP-B2b-RTK solutions with tropospheric and ionospheric constraints to obtain PPP-B2b-RTK positioning results, thereby enabling fast and high-precision GNSS positioning. Attached Figure Description

[0055] Figure 1 This is a flowchart of a GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation provided in an embodiment of this application;

[0056] Figure 2This is a schematic diagram of the marine real-time dynamic precise single-point positioning server business process provided in the embodiments of this application;

[0057] Figure 3 This is a schematic diagram of the marine real-time dynamic precise single-point positioning user terminal service process provided in the embodiments of this application;

[0058] Figure 4 This is a comparison curve between the estimated zenith tropospheric delay (ZTD) of the reference station and the final ZTD product of the IGS provided in the embodiments of this application;

[0059] Figure 5 This is a comparison diagram of the STEC sequences extracted from the base station WUH2 and the user station JFNG before and after removing the satellite end and combining DCB, provided in the embodiments of this application.

[0060] Figure 6 This is a comparison diagram of the single-difference STEC distribution between stations before and after DCB correction provided in the embodiments of this application;

[0061] Figure 7 This is a comparison chart of static positioning results on the user terminal provided in the embodiments of this application;

[0062] Figure 8 This is a schematic diagram of the structure of a GNSS positioning device based on the separation of the anisotropic troposphere and ionosphere DCB provided in the embodiments of this application. Detailed Implementation

[0063] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0064] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0065] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0066] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0067] Before providing a detailed description of the embodiments of this application, some of the nouns and terms used in the embodiments of this application will be explained first. The nouns and terms used in the embodiments of this application shall be interpreted as follows:

[0068] PPP-B2B-RTK integrates PPP reference data with RTK differential technology to achieve a high-precision, highly flexible positioning solution. PPP uses a globally distributed network of reference stations (such as satellite orbit and clock bias parameters provided by IGS) combined with ionospheric pseudorange and phase observations to eliminate errors such as satellite clock bias and ionospheric delay, achieving centimeter-level absolute positioning. RTK, building on PPP, transmits reference station correction information to the rover station via a real-time data link, dynamically eliminating equipment errors (such as tropospheric delay and multipath effects), further improving positioning accuracy and stability.

[0069] Zenith hydrostatic delay (ZHD) is a type of atmospheric tropospheric delay that primarily affects the accuracy of radio navigation and positioning. It belongs to the hydrostatic branch of tropospheric delay and, together with zenith wet delay (ZWD), constitutes the total delay (ZTD). The calculation of zenith hydrostatic delay is based on atmospheric hydrostatic properties and is related to vertical profile parameters such as temperature and pressure.

[0070] In related technologies, with the widespread application of Global Navigation Satellite Systems (GNSS), high-precision positioning technologies such as Real-time Dynamic Differential (RTK) and Precise Point Positioning (PPP) have been gradually applied to scenarios requiring sub-meter or even centimeter-level positioning accuracy, such as unmanned surface vessels (USVs) and autonomous vehicles. Traditional RTK requires setting up a reference station near the user and transmitting original observation corrections, resulting in a large amount of communication data; traditional PPP relies on the user to obtain precise orbit and clock error correction products in real time, leading to long convergence times and high dependence on communication. Therefore, in scenarios such as marine unmanned surface vessels, achieving fast and high-precision positioning under low-cost, low-bandwidth communication conditions faces the following two major challenges:

[0071] (1) Accurate modeling of tropospheric delay is difficult. Tropospheric signal delay is one of the main errors affecting satellite ranging accuracy. In the marine environment, the water vapor content in the atmosphere is abundant and varies drastically. Tropospheric delay is highly non-uniform in space, exhibits significant anisotropy, and changes rapidly over time. Traditional tropospheric models are mostly based on isotropic assumptions and historical meteorological data, which cannot accurately express the differences in tropospheric delay in different directions and at different times over a specific user station, making it difficult to meet the needs of rapid positioning for satellite navigation in the marine environment.

[0072] (2) Difficulty in extracting ionospheric hardware delay and correction. Ionospheric delay is another major source of error in GNSS ranging. Dual-frequency observations can eliminate most of the first-order ionospheric delay, but in order to fix integer ambiguity and speed up convergence, the ionospheric delay of each satellite is usually explicitly estimated as a state variable in non-combined PPP models. At this time, the hardware delay (DCB, ionospheric differential code deviation) of the satellite signal will be strongly coupled with the ionospheric delay parameter. The tilted ionospheric delay (STEC) observation value obtained by single-station observations contains both the DCB at the satellite end and the receiver end, making it difficult to accurately separate the ionospheric delay from the hardware delay under real-time conditions. Traditional methods usually require long-term observation data from multiple stations globally or regionally to accurately estimate the satellite and receiver DCB, but in real-time PPP-RTK supported by a single reference station, accurate DCB separation cannot be completed in a short time.

[0073] Therefore, it can be seen that in existing technologies, it is difficult to achieve fast and high-precision positioning under low-cost and low-bandwidth communication conditions in scenarios such as marine unmanned surface vessels.

[0074] In view of this, this application provides a GNSS positioning method and related equipment based on the separation of the anisotropic troposphere and ionosphere DCB, which can achieve rapid and high-precision GNSS positioning.

[0075] The GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation provided in this application relates to the field of satellite navigation and location services technology. This GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation can be applied to terminals, servers, or software running on either terminal or server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited to these. The server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network. The software can be an application implementing the GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation, but is not limited to the above forms.

[0076] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0077] The embodiments of this application will be described in detail below with reference to the accompanying drawings:

[0078] Figure 1 This is an optional flowchart of a GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation provided in the embodiments of this application. Figure 1 The method may include, but is not limited to, steps S110 to S180:

[0079] Step S110: Construct a non-combined GNSS observation model and a state model to form an observation-state framework;

[0080] Step S120: Based on the observation-state framework, construct an anisotropic tropospheric oblique delay model and estimate the zenith delay parameter and horizontal gradient parameter on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient.

[0081] Step S130: Extract the oblique ionospheric delay based on the precise single-point positioning state and establish a vertical ionospheric delay model of the regional ionospheric layer;

[0082] Step S140: Based on the oblique ionospheric delay and vertical ionospheric delay models, perform hardware delay estimation and separation operations for the satellite and receiver to obtain the hardware delay;

[0083] Step S150: Generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter;

[0084] Step S160: Generate ionospheric delay corrections based on the vertical ionospheric delay model and hardware delay;

[0085] Step S170: Perform low-bandwidth encoding and broadcasting of the tropospheric delay correction, ionospheric delay correction, and hardware delay;

[0086] Step S180: Apply PPP-B2b-RTK solution with tropospheric and ionospheric constraints to the user end based on the low-bandwidth encoded data after broadcasting to obtain the PPP-B2b-RTK positioning result.

[0087] Specifically, with Figure 2 and Figure 3 Taking the server-side business process and user-side business process shown as examples, the specific steps of the embodiments of this application are described:

[0088] Understandably, in a single BeiDou PPP-B2b-RTK scenario, pseudorange and carrier phase observations are simultaneously affected by multiple factors such as satellite orbit clock errors, tropospheric, ionospheric, and hardware delays. Without explicit modeling of these errors in a unified observation and state model, it is impossible to specifically separate tropospheric anisotropy effects and ionospheric (DCB) in subsequent steps. Therefore, this embodiment first constructs a complete uncombined GNSS observation model and a Kalman filter state model to form a measurement-state framework, which can then provide a unified framework for subsequent anisotropic tropospheric modeling and ionospheric correction extraction. Specifically, the processing in this embodiment includes, but is not limited to, the following steps:

[0089] (1) Establish pseudorange observation model and carrier phase observation model.

[0090] For the receiver ,satellite Frequency The pseudorange observation model can be expressed as the following formula:

[0091] ;

[0092] In the formula, This represents the pseudorange observation value between receiver r and satellite s at frequency point f; The distance between receiver r and satellite s is represented by r; c represents the speed of light. These represent receiver clock bias and satellite clock bias, respectively. Indicates tropospheric slack delay. Indicates ionospheric slack delay; Both represent pseudorange hardware latency; This represents pseudorange noise.

[0093] The corresponding carrier phase observation model can be expressed as the following formula:

[0094] ;

[0095] In the formula, This represents the carrier phase observation value between receiver r and satellite s at frequency point f; Indicates wavelength. Indicates the ambiguity of the integer period. Both represent phase hardware delay. This represents phase noise.

[0096] By using the pseudorange observation model and the carrier phase observation model described above, errors such as geometric distance, tropospheric, ionospheric, and DCB can be explicitly separated, allowing subsequent anisotropic tropospheric models and ionospheric delay corrections to be directly embedded.

[0097] (2) Construct a system observation model in vector form.

[0098] All satellite and frequency observations can be expressed in vector form as follows:

[0099] ;

[0100] In the formula, For the calendar The observation vector; For the calendar The state vector (including receiver coordinates, clock error, tropospheric parameters, ionospheric parameters, ambiguity, etc.); For the calendar The design matrix; For the calendar Observation noise.

[0101] (3) Establish state transition model and stochastic model.

[0102] Considering the characteristics of receiver position, clock bias, troposphere, and ionosphere changing slowly over time, the random walk model with the following formula is adopted as the random model in this embodiment:

[0103] ;

[0104] In the formula, For the calendar The state transition matrix, For the calendar System noise, For the calendar The covariance.

[0105] (4) Use Kalman filtering for parameter recursive estimation.

[0106] The unknown parameters in the observation equation are estimated in real time through five steps: state prediction, covariance prediction, Kalman gain calculation, state update, and covariance update.

[0107] Through the content of this embodiment, a unified observation-state framework can be established, enabling the simultaneous estimation of tropospheric anisotropy parameters, ionospheric STEC, and related DCB within the same filtering framework.

[0108] Understandably, based on the observation-state framework constructed above, this embodiment constructs an anisotropic tropospheric slant delay model and estimates the zenith delay parameter and horizontal gradient parameter on the server side. Since tropospheric delay is not isotropic at different azimuths and elevation angles in the ocean and complex atmospheric environments, if an isotropic model considering only zenith delay is still used, systematic errors will occur in the low elevation angle direction, affecting the fast convergence and accuracy of PPP-B2b-RTK. Therefore, this embodiment introduces the horizontal gradient on the server side to establish an anisotropic tropospheric slant delay model and jointly estimates it with the PPP state, making the tropospheric correction more refined. Specifically, the processing procedure of this embodiment includes the following steps:

[0109] (1) Construct an anisotropic tropospheric slant delay model based on the horizontal gradient.

[0110] For the receiver of the observation The upper elevation angle is azimuth angle is satellite The anisotropic tropospheric slant delay model is as follows:

[0111] ;

[0112] In the formula, Indicates receiver The upper elevation angle is azimuth angle is satellite Corresponding anisotropic tropospheric oblique elongation; Indicates receiver The zenith static delay; Indicates receiver The zenith wet delay; These represent the northward tropospheric gradient and the eastward tropospheric gradient, respectively. These represent the static mapping function and the wet delay mapping function, respectively. This represents the gradient mapping function.

[0113] This embodiment increases... Two horizontal gradient parameters can describe the anisotropic changes of the troposphere in different orientations, solving the problem of large errors in the low elevation direction of traditional isotropic models.

[0114] In the anisotropic tropospheric oblique delay model, the mapping function adopts a continued fractional mapping function and a CHENHER gradient function.

[0115] The static mapping function and the wet delay mapping function adopt a unified continued fraction form as shown in the following formula:

[0116] ;

[0117] In the formula, a, b, and c are all constant parameters.

[0118] The horizontal gradient mapping function takes the form of a first-order fraction, CHENHER, as shown in the following formula:

[0119] ;

[0120] In the formula, This is an empirical constant.

[0121] By employing the aforementioned mapping function, this embodiment can accurately characterize the nonlinear features of tropospheric delay varying with elevation angle at low elevation angles while ensuring the physical rationality of the model.

[0122] (3) After constructing the stochastic model of the anisotropic tropospheric parameters in the anisotropic tropospheric slant delay model, the model is incorporated into the Kalman filter.

[0123] right The parameters are always slowly varying, and a random walk model is used.

[0124] ;

[0125] In the formula, This represents the zenith wet delay on receiver r corresponding to epoch k; This represents the zenith wet delay on receiver r corresponding to epoch k-1; This indicates the northward tropospheric gradient corresponding to epoch k; This indicates the northward tropospheric gradient corresponding to epoch k-1; This indicates the eastward tropospheric gradient corresponding to epoch k; This indicates the eastward tropospheric gradient corresponding to epoch k-1; , and These represent the zenith wet delay, northward tropospheric noise, and eastward tropospheric noise corresponding to epoch k, respectively.

[0126] The noise variance in this embodiment is set based on the rate of tropospheric change in a marine environment, and is achieved through... The Kalman filter from step S110 is incorporated.

[0127] Through the processing method of this embodiment, high-precision estimates of the zenith wet delay and horizontal gradient of each receiver can be obtained on the server side under a unified filtering framework, thereby laying the foundation for generating high-precision anisotropic tropospheric corrections.

[0128] It is understandable that this embodiment can extract the oblique ionospheric delay (STEC) based on the precise single-point positioning (PPP) state and establish a vertical ionospheric delay (VTEC) model for the regional ionosphere. Since ionospheric delay has significant frequency correlation and spatiotemporal variation characteristics, directly and coarsely modeling it in pseudorange not only makes DCB separation difficult but also weakens the ability of PPP-B2b-RTK to fix integer ambiguities. Therefore, this step uses the PPP solution results to extract the oblique TEC (STEC) and then constructs a regional VTEC model, explicitly parameterizing the temporal and spatial variation characteristics, providing a foundation for subsequent DCB separation and ionospheric correction number generation. The specific process of this embodiment includes the following steps:

[0129] (1) Extract the total tilted electron content (STEC) from the non-combined PPP state.

[0130] This embodiment utilizes the frequency relationship between ionospheric delays at different frequency points to combine the ionospheric quantity of the dual-frequency combination. Convert to STEC on the satellite-receiver path:

[0131] ;

[0132] In the formula, Represents the epoch STEC under; This represents a coefficient related to frequency.

[0133] In practice, this embodiment can use carrier phase smoothing pseudorange to reduce noise and improve STEC observation accuracy.

[0134] (2) Establish the ionospheric projection model under the thin-layer assumption.

[0135] This example uses the "thin layer" assumption of the ionosphere, approximating the ionosphere as a height of... For a spherical shell, the relationship between the oblique TEC and the vertical TEC (VTEC) is as follows:

[0136] ;

[0137] In the formula, Let be the Earth's radius. Introduce the projection function. This is to normalize STEC at different times and altitudes to a unified VTEC physical quantity, which facilitates the establishment of regional ionospheric models.

[0138] (3) A regional VTEC model is established using trigonometric series.

[0139] To describe the ionosphere with geomagnetic latitude and local time To determine the changing characteristics, this embodiment employs a finite-term trigonometric series:

[0140] ;

[0141] In the formula, All of these represent parameters to be estimated.

[0142] This embodiment can compress complex spatiotemporal variations of the ionosphere into a small number of estimable model parameters, creating conditions for broadcasting ionospheric correction information under low bandwidth conditions.

[0143] Understandably, this embodiment, after obtaining the oblique and vertical ionospheric delay models, performs hardware delay estimation and separation operations for the satellite and receiver based on these models to obtain the hardware delay. Since the differential code bias (DCB) in pseudorange observations is highly correlated with ionospheric delay, if the DCB at the satellite and receiver ends cannot be properly separated, the hardware bias will be mistakenly identified as ionospheric variation, leading to severe distortion of the VTEC model and ionospheric correction. Therefore, this embodiment introduces DCB parameters based on the STEC–VTEC model and uses constrained least squares to achieve joint estimation and separation of the satellite and receiver DCB. The specific process includes the following steps:

[0144] (1) Construct the STEC observation equation that includes DCB.

[0145] For each satellite-receiver path, the STEC observation model is constructed using the following formula:

[0146] ;

[0147] In the formula, These are the DCB at the receiver end and the DCB at the satellite end, respectively. Represents the projection function of the i-th path; Indicates the local time in the i-th path With geomagnetic dimension The corresponding vertical ionospheric delay; This represents the pseudorange noise of the i-th path.

[0148] (2) Weighted least squares are used to jointly estimate VTEC parameters and combined DCB.

[0149] The equations for multiple epochs and multiple satellites can be written in matrix form as shown in the following formula:

[0150] ;

[0151] This matrix is ​​composed of STEC, and in the formula, and These represent the correlation coefficient matrix and fitting coefficient matrix after the STEC correction is applied to the multi-epoch and multi-satellite equations in matrix form, respectively. Indicates noise; This includes VTEC model parameters and DCBs for each satellite and receiver. The weighted least squares solution is shown in the following formula:

[0152] ;

[0153] In the formula, This indicates finding the pair of least squares solutions. The matrix obtained by performing the decomposition calculation steps.

[0154] (3) Apply zero-sum constraints to satellite DCB to achieve DCB separation.

[0155] This embodiment applies to systems within the same system. The satellites are subject to zero-mean constraints using the following formula:

[0156] ;

[0157] In the least squares solution, constraints are applied to separate the originally coupled components. It is decomposed into DCB at the satellite end and DCB at the receiver end.

[0158] In single-system scenarios with few reference stations, this embodiment prioritizes the stability of the satellite DCB and treats the receiver DCB as a locally slowly changing parameter. This satisfies the ionospheric correction accuracy and facilitates the generation of satellite DCB products that can be directly used by users.

[0159] It is understandable that, after obtaining the various delay parameters, this embodiment generates tropospheric and ionospheric delay corrections and performs low-bandwidth encoded broadcasting. Due to the limited downlink bandwidth of the PPP-B2b link, directly broadcasting the original tropospheric and ionospheric states of all stations and all epochs to users would result in excessive data volume, failing to meet actual communication requirements. Therefore, this embodiment generates compressed tropospheric and ionospheric corrections on the server side based on the estimated parameters and meets the low-bandwidth broadcasting requirements through parameterization and encoding. The specific process of this embodiment includes the following steps:

[0160] (1) Generate tropospheric delay corrections based on zenith delay parameters and horizontal gradient parameters.

[0161] This embodiment uses the estimation obtained from the above steps. The tropospheric slant delay in any satellite direction is calculated using the following formula. :

[0162] ;

[0163] The tropospheric oblique delay is calculated using the following formula. Compared with standard tropospheric delay By comparison, the tropospheric correction number is obtained. :

[0164] ;

[0165] (2) Generate ionospheric delay corrections based on the vertical ionospheric delay model and hardware delay.

[0166] This embodiment utilizes the VTEC model and the separated DCB from the above steps to achieve a given time... Altitude angle Puncture point corresponding to azimuth angle The ionospheric slant delay is calculated using the following formula. :

[0167] ;

[0168] ionospheric slack delay The ionospheric corrections to be broadcast can be constructed by comparing them with the ionospheric terms in the user's original observations. .

[0169] (3) Parameter compression and low-bandwidth encoding broadcast.

[0170] The aforementioned tropospheric gradient parameters, VTEC trigonometric series coefficients, and a small number of DCB parameters are quantized and differentially encoded. The spatiotemporally continuous correction information is compressed into a small number of key parameters, which are then encapsulated in PPP-B2b short messages in tabular or grid form for low-bandwidth encoding and broadcasting.

[0171] This embodiment can ensure the accuracy and continuity of the correction data, while also meeting the low bandwidth limitation of a single BeiDou PPP-B2b link.

[0172] It is understandable that in this embodiment, after receiving the low-bandwidth encoded data after broadcast, the user terminal applies tropospheric and ionospheric constraints to the PPP-B2b-RTK solution. Since when the user terminal does not fully utilize the tropospheric and ionospheric corrections provided by the server, but instead estimates atmospheric errors entirely on its own, it not only increases the state dimension and prolongs the convergence time, but also significantly reduces the ambiguity fixation rate of PPP-B2b-RTK. Therefore, this embodiment constructs a PPP-B2b-RTK model with atmospheric prior constraints at the user terminal, using the server corrections as strong priors and retaining a small number of residual parameters to achieve fast and high-precision positioning. The specific process of this embodiment includes the following steps:

[0173] (1) Perform atmospheric and DCB corrections on the user-end observations.

[0174] The user terminal receives PPP-B2b precise orbital clock bias and satellite DCB products, as well as the tropospheric correction data between satellite s and user terminal u broadcast in this embodiment. Then, the original observations are corrected using the following formula:

[0175] ;

[0176] In the formula, This represents the corrected observation value between satellite s and user terminal u; This represents the raw observation values ​​between satellite s and user terminal u; This represents the raw carrier phase observation between satellite s and user terminal u; This represents the corrected carrier phase observation between satellite s and user terminal u.

[0177] This embodiment can explicitly eliminate most of the influence of the troposphere and ionosphere in the observation equation.

[0178] (2) Construct a state vector with residual prior and perform Kalman filtering.

[0179] The user-end state vector in this embodiment includes: receiver three-dimensional coordinates, clock error, and residual zenith wet delay. Residual ionospheric delay And integer ambiguity. A zero-mean prior is introduced into the residual term using the following formula:

[0180] ;

[0181] ;

[0182] This embodiment incorporates prior information into the Kalman filter in the form of "virtual observation" or process noise constraints to constrain the fluctuation range of the residuals, thereby improving the solution stability and convergence speed.

[0183] (3) Ambiguity reparameterization and integer fixation.

[0184] In this embodiment, after applying atmospheric and DCB corrections, the ambiguity of the carrier phase observation is reconstructed using the following formula:

[0185] ;

[0186] Calculate the single-difference ambiguity between any two satellites based on the reconstructed ambiguity. For example, for a reference satellite... and satellite The inter-satellite single-difference ambiguity can be calculated using the following formula:

[0187] ;

[0188] In the formula, express It is an integer, used to obtain the integer part of the solution when performing fuzzy fixation.

[0189] At this point, the single-difference ambiguity has basically recovered its integer properties, and the LAMBDA method can be used for integer search and fixation. After the ambiguity is fixed, the coordinate solution is updated again, and PPP-B2b-RTK positioning results with centimeter-level or even higher precision can be quickly obtained.

[0190] As can be seen from the above, this embodiment addresses the problem that single BeiDou PPP-B2b-RTK systems are difficult to accurately model under conditions such as low bandwidth, low elevation angle, and atmospheric inhomogeneity, leading to slow convergence and limited positioning accuracy due to the difficulty in accurately modeling tropospheric anisotropy and ionospheric-DCB coupling. It proposes a combined method of "anisotropic tropospheric modeling + ionospheric VTEC-DCB separation + low bandwidth correction broadcasting + end-side constraint solution". An anisotropic tropospheric oblique delay model with north- and east-west horizontal gradients is introduced within a unified non-combined observation framework. This model is combined with a continued fractional elevation angle mapping and the CHENHER gradient function. A random walk prior is used to incorporate the zenith wet delay and gradient parameters into a Kalman filter for time series estimation. Based on PPP state extraction, tilted TEC (STEC) is extracted. A trigonometric series VTEC regional model with geomagnetic latitude and local time as independent variables is constructed under the ionospheric thin-layer projection. Simultaneously, the satellite-end and receiver-end DCB are incorporated into weighted least squares, and a zero-mean constraint is applied to the satellite DCB to achieve robust separation of ionospheric and hardware code biases. On this basis, the anisotropic tropospheric parameters and VTEC-DCB results obtained from the server are gridded and quantized to meet the bandwidth limitations of PPP-B2b short messages, and tropospheric and ionospheric corrections that can be sent by spatiotemporal interpolation are generated. At the user end, the corrections are incorporated into pseudorange and phase observations to construct a PPP-B2b-RTK with an "atmospheric residual zero-mean prior". The stochastic model achieves integer-cycle fixation through ambiguity reparameterization and inter-satellite single-difference, thereby obtaining a fast, robust, and high-precision solution. Experimental results show that the PPP-B2b-RTK mode of this invention achieves positioning accuracy comparable to PPP-CNT by broadcasting only a small number of tropospheric and ionospheric correction parameters, and significantly accelerates the convergence speed. Under the 20cm convergence criterion, PPP-B2b-RTK can almost achieve instantaneous convergence. In terms of positioning accuracy, the horizontal error of the two sets of inland and marine user stations is within 95% root mean square (RMS) of 5cm and within 10cm in the vertical direction, fully verifying the role of the tropospheric and ionospheric dual-constraint model constructed in this invention in improving the high-precision positioning performance of a single BeiDou satellite. It has significant advantages over the traditional isotropic tropospheric model and the method without DCB separation.

[0191] The embodiments of this application are illustrated below using practical scenarios:

[0192] This embodiment selects the Chinese IGS stations WUH2 (Wuhan, inland) and JFNG (Ezhou, near the lake) as the server-side base station and user-side rover station to simulate the near-shore steady-state tropospheric environment and complex water vapor environment. Simultaneously, PTGG (Manila) and PIMO (near Manila) in the IGS Philippines region are selected as the second set of base stations and user stations to simulate the scenario of drastic atmospheric changes over tropical oceans. The distances between the two sets of base stations and user stations are 12.96 km and 11.77 km, respectively, both meeting the localization requirements for PPP-RTK correction data applications. The experiment uses dual-frequency observation data (B1I / B3I) from a single BeiDou-3 satellite system with a sampling rate of 1 Hz. The server-side base station calculation is implemented using an improved non-combined PPP algorithm in the Wuhan University MADIS software, while the user-side positioning uses a self-developed PPP-RTK calculation software. Both the server and user ends receive precise orbit and clock corrections provided by the BeiDou B2b satellite-based augmentation signal to reduce dependence on ground communication links. Based on this, the following processing is performed on the server and the user end respectively according to the method of the embodiments of this application.

[0193] I. Precise Modeling and Forecasting of Tropospheric Delay at the Server: The server-side base station first calculates the anisotropic tropospheric delay parameters. For the Wuhan regional station WUH2, observation data from 00:00 to 24:00 on May 11, 2024 were selected, and tropospheric calculations were performed under two configurations: known (fixed) and unknown (floating) base station coordinates. In both cases, the process noise standard deviation for the zenith wet delay (ZWD) and the northward and lateral tropospheric gradients (GNGE) were set to 5 mm / s. and 1mm / This allows for a certain range of daily drift in tropospheric wet delay and gradient. The results show that, regardless of whether the base station coordinates are fixed, the estimated zenith tropospheric delay (ZTD) matches well with the final ZTD product from the International GNSS Service (IGS): when the coordinates are fixed, the average difference is approximately 1.2 cm, and the RMS is approximately 3.5 cm; when the coordinates are floating, the average difference is approximately 1.5 cm, and the RMS is approximately 3.8 cm, both within the accuracy range of the IGS product. Figure 4Comparison curves of epoch-by-epoch ZTD solutions and IGS products for two stations in the Wuhan area are presented, showing that the trends of the two are highly consistent, with residuals generally within ±5cm. For the PTGG station in the Manila area (near the coast), the same method was used for ZTD solution, and the results show that its RMS deviation from the IGS reference is approximately 4.6cm. In contrast, inland stations such as WUH2 in the Wuhan area have relatively stable water vapor, resulting in a ZTD accuracy RMS of approximately 2–4cm. Nearshore stations such as PIMO in the Manila area exhibit more drastic ZTD changes, but their RMS is still better than 5cm. These findings verify the effectiveness of the anisotropic tropospheric modeling of this invention. Based on this, to generate tropospheric corrections for user applications, the base station further performs short-term predictions using the calculated ZTD and gradient: a first-order autoregressive model is used to extrapolate the ZTD time series to predict the ZTD change over the next 5 minutes; the gradient parameter, due to its small value and slow change, can be approximately kept constant for 5 minutes. The server outputs the current epoch ZTD correction value and the linear change rate for the next 5 minutes every 5 minutes and broadcasts it to the client.

[0194] II. Server-Side Ionospheric DCB Separation and Correction Number Generation: Simultaneously with tropospheric parameter calculation, the server-side reference station uses non-combined PPP filtering to estimate the ionospheric parameters for each satellite and extracts the STEC observation sequence formed by pseudorange-carrier combination. Considering the sensitivity of ionospheric delay to time variations, the reference station uses a relatively short sliding time window (e.g., 30 minutes) to fit the STEC data to the IGG-DCB model, updating the model parameters and DCB estimates every 5 minutes. Taking the data from the WUH2 station on May 11, 2024 (Yearly Day 132) as an example, a strong geomagnetic storm occurred that day (Dst index minimum < -400 nT, Kp index maximum 9), and the ionosphere was in a highly unstable state. Without external prior DCB correction, the server directly applied the IGG-DCB model to solve the STEC data of the single WUH2 station. It was found that due to insufficient differentiation between satellite and receiver DCB, the obtained STEC correction sequence had a significant negative bias, and the STEC measurements from the user station JFNG were also scattered and inconsistent (e.g., Figure 5 (As shown in the upper left). Subsequently, after correcting the WUH2 observations using the BeiDou satellite DCB product released by CAS, a new model was created. The results showed that the STEC values ​​of high-elevation satellites tended to converge, but still deviated from zero overall. Figure 5 (Top right), indicating that the receiver DCB has not yet separated. Finally, using the combined DCB solution strategy proposed in this embodiment, the combined DCB values ​​of each satellite and receiver are estimated using 30 minutes of data from the WUH2 station, and these are directly used as constant terms to correct the STEC sequence. After processing, the STEC sequences of both WUH2 and JFNG stations are shifted to above zero, and the STEC values ​​of the same satellite at the two stations are almost identical ( Figure 5(Lower left, lower right) The STEC sequences of low-elevation stars also converge to the same level as those of high-elevation stars. Further comparison of the inter-station single-difference STEC between WUH2 and JFNG shows that the original single-difference STEC scatter points are discrete, with a mean deviation of approximately 2.5 TECU; after applying combined DCB correction, the scatter points of the single-difference STEC are evenly distributed near zero. Figure 6 The mean value is close to 0 TECU, and the standard deviation has decreased from 2.1 TECU to 1.1 TECU. This indicates that the server has effectively eliminated the satellite-side DCB, and the remaining ionospheric residuals mainly reflect the regional VTEC model error. When low elevation angle observations are not filtered, the instantaneous error of the inter-station single-difference STEC can reach about 10 TECU during periods of strong disturbance (equivalent to a 2m delay, corresponding to about 2m pseudorange error in the B1 band), which may lead to non-convergence of user-side filtering. Therefore, in this embodiment, a cutoff of 30° is set for the satellite elevation angle when generating ionospheric corrections to discard low-altitude observations with excessive errors, thereby controlling the root mean square error of the single-difference STEC throughout the day to within 1.7 TECU (about 0.27m delay). For cases where the satellite DCB prior is insufficient, the server can also run a long-term solution strategy in parallel: continuously collect base station observations, use 24-hour data to solve the satellite and receiver DCB, and use the results to generate the STEC corrections in the next 24-hour cycle to maintain the stability of the corrections in the long term. Finally, the server generates ionospheric correction parameters every 5 minutes, including: ionospheric model polynomial coefficients, a set of reference point coordinates and time labels (for model solving and extrapolation), and integrates the receiver DCB residuals (if any) estimated in the previous cycle into the correction numbers.

[0195] III. User-side Corrected Constraint Positioning and Effect Verification: The user station receives and parses the tropospheric and ionospheric correction information sent by the server, and improves the PPP solution according to the method in this embodiment. First, the user station uses the precise ephemeris and clock bias provided by the BeiDou B2b signal to perform non-combined PPP filtering with an update interval of 30 seconds, dynamically estimating its own position, clock bias, tropospheric parameters, etc. In the traditional PPP mode (i.e., without any corrections, referred to as PPP-B2b), the user station faces large unknown errors in the early stages of the solution because it needs to estimate the ZTD and the ionospheric parameters of each satellite itself, resulting in slow positioning convergence. In the PPP-RTK mode of this embodiment, each time the user station receives a batch of corrections, it immediately updates the PPP filter as follows: First, it uses the latest predicted ZTD residual value of the user station from the server as a measurement to perform a Kalman update on the user station's ZTD parameters, thereby instantly eliminating more than 90% of the tropospheric error. Second, for each satellite, it subtracts the STEC correction value provided by the server (calculated from the broadcast polynomial coefficients) from the observation equation, and eliminates the hardware bias of the user receiver through single-difference of the reference satellite, thus constraining the ionospheric residual. Based on this, the PPP filter continues to iterate and attempts to fix the unfixed carrier ambiguity with LAMBDA at each epoch. Since the tropospheric and ionospheric errors have been significantly reduced, the convergence accuracy of the floating-point solution of the user station ambiguity improves rapidly, and usually only a few epochs of observation fusion are needed to meet the fixing conditions. Once the dual-frequency ambiguity of at least four satellites is successfully fixed, the positioning solution can jump to the centimeter level. Figure 7The figure shows a comparison of positioning error curves for JFNG and PIMO user stations under static conditions using different correction strategies. In the PPP-B2b mode (orbit clock correction only), the horizontal error of both stations fluctuates within decimeters for the first 45 minutes and struggles to converge stably to within 10cm. In the PPP-CNT mode (using CNES real-time precise orbit clock correction), the convergence speed is improved, but it still takes approximately 30–60 minutes to achieve 5cm accuracy. In the PPP-B2b-RTK mode (this invention), both stations immediately achieve accuracy within 5cm at the initial positioning calculation, and the error subsequently stabilizes at 2–3cm. Further statistical analysis shows that compared to PPP-B2b, this invention shortens the positioning convergence time by approximately 90%, improves positioning accuracy by about an order of magnitude, and is almost unaffected by strong ionospheric disturbances in the region. To evaluate the dynamic application effect, this embodiment also simulated a frequent start-stop scenario for unmanned surface vessels (USVs): the JFNG and PIMO stations were repeatedly restarted at different time periods, each for 45 minutes. During this period, 1Hz dynamic positioning results were recorded and the filter was reset to verify the reconvergence performance. The results show that in the first epoch after each restart, the method of this embodiment can output a fixed solution (if there are many low elevation angle observations, it is fixed within 2-3 epochs), without positioning failure or large deviation jumps. The horizontal RMS error of each segment of dynamic positioning is about 3cm and the vertical RMS is about 6cm, which fully meets the accuracy requirements of USV navigation and positioning. In summary, the experiments show that the GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation proposed in this embodiment achieves positioning performance close to dual-frequency RTK under single-system low bandwidth conditions, and has significant practical value and promotion prospects.

[0196] Please see Figure 8 This application also provides a GNSS positioning device based on anisotropic tropospheric and ionospheric DCB separation, the device comprising:

[0197] The first module is used to construct a non-combined GNSS observation model and a state model to form an observation-state framework;

[0198] The second module is used to construct an anisotropic tropospheric oblique delay model based on the observation-state framework and estimate the zenith delay parameter and horizontal gradient parameter on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient.

[0199] The third module is used to extract the oblique ionospheric delay based on the precise single-point positioning state and to establish a vertical ionospheric delay model of the regional ionospheric.

[0200] The fourth module is used to perform hardware delay estimation and separation operations between the satellite and the receiver based on the oblique ionospheric delay and vertical ionospheric delay models, so as to obtain the hardware delay.

[0201] The fifth module is used to generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter.

[0202] The sixth module is used to generate ionospheric delay corrections based on the vertical ionospheric delay model and hardware delay.

[0203] The seventh module is used for low-bandwidth encoding and broadcasting of tropospheric delay corrections, ionospheric delay corrections, and hardware delays;

[0204] The eighth module is used to perform PPP-B2b-RTK calculations at the user end based on the low-bandwidth encoded data after broadcast, applying tropospheric and ionospheric constraints, and to obtain PPP-B2b-RTK positioning results.

[0205] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0206] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0207] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0208] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0209] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0210] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0211] It is understood that the content of the above method embodiments is applicable to the embodiments of this program product. The specific functions implemented by the embodiments of this program product are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0212] This application provides a GNSS positioning method and related equipment based on anisotropic tropospheric and ionospheric DCB separation. By constructing an anisotropic tropospheric oblique delay model based on a built observation-state framework, and estimating zenith delay and horizontal gradient parameters at the server end, the method extracts oblique ionospheric delay based on precise single-point positioning and establishes a regional ionospheric vertical ionospheric delay model. Hardware delay estimation and separation operations are performed on the satellite and receiver based on the oblique and vertical ionospheric delay models to obtain the hardware delay. Tropospheric delay corrections are generated based on the zenith delay and horizontal gradient parameters, and ionospheric delay corrections are generated based on the vertical ionospheric delay model and hardware delay. The tropospheric delay corrections, ionospheric delay corrections, and hardware delay are then broadcast using low-bandwidth encoding. After receiving the broadcast low-bandwidth encoded data, the user end applies PPP-B2b-RTK calculations with tropospheric and ionospheric constraints to obtain the PPP-B2b-RTK positioning result, thereby achieving rapid and high-precision GNSS positioning.

[0213] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0214] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0215] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0216] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0217] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0218] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0219] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0220] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0221] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0222] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0223] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A GNSS positioning method based on anisotropic tropospheric and ionospheric DCB separation, characterized in that, The method includes the following steps: Construct a non-combined GNSS observation model and a state model to form an observation-state framework; Based on the observation-state framework, an anisotropic tropospheric oblique delay model is constructed, and the zenith delay parameter and horizontal gradient parameter are estimated on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient. Based on precise single-point positioning, the oblique ionospheric delay is extracted and a vertical ionospheric delay model of the regional ionospheric is established. Hardware delay estimation and separation operations for satellite and receiver are performed based on oblique ionospheric delay and vertical ionospheric delay models to obtain hardware delay; Generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter; Ionospheric delay corrections are generated based on the vertical ionospheric delay model and hardware delay. The tropospheric delay correction, the ionospheric delay correction, and the hardware delay are encoded and broadcast using low-bandwidth encoding. Based on the low-bandwidth encoded data after broadcast, PPP-B2b-RTK solution with tropospheric and ionospheric constraints is applied at the user end to obtain PPP-B2b-RTK positioning results; The anisotropic tropospheric slant delay model is as follows: ； In the formula, Indicates receiver The upper elevation angle is azimuth angle is satellite Corresponding anisotropic tropospheric oblique elongation; Indicates receiver The zenith static delay; Indicates receiver The zenith wet delay; These represent the northward tropospheric gradient and the eastward tropospheric gradient, respectively. These represent the static mapping function and the wet delay mapping function, respectively. This represents the gradient mapping function.

2. The method according to claim 1, characterized in that, The non-combined GNSS observation model includes a pseudorange observation model and a carrier phase observation model; The pseudorange observation model is as follows: ； In the formula, This represents the pseudorange observation value between receiver r and satellite s at frequency point f; The distance between receiver r and satellite s is represented by r; c represents the speed of light. These represent receiver clock bias and satellite clock bias, respectively. Indicates tropospheric slack delay. Indicates ionospheric slack delay; Both represent pseudorange hardware latency; Indicates pseudorange noise; The carrier phase observation model is as follows: ； In the formula, This represents the carrier phase observation value between receiver r and satellite s at frequency point f; Indicates wavelength. Indicates the ambiguity of the integer period. Both represent phase hardware delay. This represents phase noise.

3. The method according to claim 1, characterized in that, The construction of the anisotropic tropospheric oblique delay model and the estimation of zenith delay parameters and horizontal gradient parameters on the server side include: An anisotropic tropospheric oblique delay model is constructed based on the horizontal gradient. The mapping function in the anisotropic tropospheric oblique delay model is used to characterize the nonlinear characteristics of the tropospheric delay in the low elevation angle direction as a function of the elevation angle. After constructing a stochastic model of the anisotropic tropospheric parameters in the anisotropic tropospheric slant delay model, a Kalman filter is incorporated. The server obtains the zenith delay parameters and horizontal gradient parameters of each receiver.

4. The method according to claim 1, characterized in that, The process of extracting the oblique ionospheric delay based on precise single-point positioning and establishing a vertical ionospheric delay model for the regional ionosphere includes: Oblique ionospheric delay is extracted based on non-combined precise single-point positioning state; An ionospheric projection model under the thin-layer assumption is established to map the oblique ionospheric delay to the physical quantity of vertical ionospheric delay; Based on the mapped physical quantities, a vertical ionospheric delay model of the regional ionosphere is established using trigonometric series.

5. The method according to claim 1, characterized in that, The step of generating the tropospheric delay correction based on the zenith delay parameter and the horizontal gradient parameter includes: Calculate the tropospheric slant delay in any satellite direction based on the zenith delay parameter and the horizontal gradient parameter; The tropospheric slant delay is compared with the standard tropospheric delay to obtain the tropospheric delay correction.

6. The method according to claim 1, characterized in that, The PPP-B2b-RTK solution, which applies tropospheric and ionospheric constraints to the user end based on the broadcast low-bandwidth encoded data, yields the PPP-B2b-RTK positioning result, including: Atmospheric and hardware delay corrections are applied to user-end observations based on the low-bandwidth coded data after broadcast. Construct a state vector with residual priors and perform Kalman filtering; After applying atmospheric and hardware delay corrections, the ambiguity of the carrier phase observations is reconstructed. Calculate the inter-satellite single-difference ambiguity based on the reconstructed ambiguity; After performing an integer search and fixing the ambiguity based on the inter-satellite single-difference ambiguity, the coordinate solution is updated; The PPP-B2b-RTK positioning result is obtained based on the updated coordinate solution.

7. A GNSS positioning device based on anisotropic tropospheric and ionospheric DCB separation, characterized in that, The device includes: The first module is used to construct a non-combined GNSS observation model and a state model to form an observation-state framework; The second module is used to construct an anisotropic tropospheric oblique delay model based on the observation-state framework and estimate the zenith delay parameter and horizontal gradient parameter on the server side. The zenith delay parameter includes the zenith static delay and the zenith wet delay, and the horizontal gradient parameter includes the northward tropospheric gradient and the dynamic tropospheric gradient. The third module is used to extract the oblique ionospheric delay based on the precise single-point positioning state and to establish a vertical ionospheric delay model of the regional ionospheric. The fourth module is used to perform hardware delay estimation and separation operations between the satellite and the receiver based on the oblique ionospheric delay and vertical ionospheric delay models, so as to obtain the hardware delay. The fifth module is used to generate tropospheric delay corrections based on the zenith delay parameter and the horizontal gradient parameter. The sixth module is used to generate ionospheric delay corrections based on the vertical ionospheric delay model and hardware delay. The seventh module is used to perform low-bandwidth encoding and broadcasting of the tropospheric delay correction, the ionospheric delay correction, and the hardware delay; The eighth module is used to perform PPP-B2b-RTK calculations with tropospheric and ionospheric constraints on the user end based on the low-bandwidth encoded data after broadcast, and to obtain PPP-B2b-RTK positioning results. The anisotropic tropospheric slant delay model is as follows: ； In the formula, Indicates receiver The upper elevation angle is azimuth angle is satellite Corresponding anisotropic tropospheric oblique elongation; Indicates receiver The zenith static delay; Indicates receiver The zenith wet delay; These represent the northward tropospheric gradient and the eastward tropospheric gradient, respectively. These represent the static mapping function and the wet delay mapping function, respectively. This represents the gradient mapping function.

8. An electronic device, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method as described in any one of claims 1 to 6.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by a processor, it implements the method of any one of claims 1 to 6.

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