Collaborative optimization method and system for Beidou multi-frequency non-difference non-combination PPP-RTK

Abstract

The invention provides a Beidou multi-frequency non-difference non-combination PPP-RTK collaborative optimization method and system, electronic equipment, a storage medium and a program product, and aims to solve the problems of error processing isolation, ambiguity fixation and error state disjunction. Constructing a coupling model of ionosphere delay, troposphere moisture component and multipath error, and performing real-time calculation to obtain an error priori estimated value; injecting the error priori estimation value into a search space of an ambiguity fixing algorithm so as to optimize a search boundary and realize rapid ambiguity fixing; performing gross error detection on the observation data based on DIA, and distributing resolving weights for different data according to gross error severity; performing weighted positioning calculation by using the calculation weight to obtain a positioning result; and feeding back a residual error generated by positioning calculation to a calculation process of the coupling model so as to update model parameters and realize closed-loop optimization of a collaborative mechanism. According to the invention, rapid positioning can be realized and the positioning precision is improved.

Description

Technical Field

[0001] This disclosure relates to the field of satellite navigation and positioning technology, and in particular to a collaborative optimization method and system for BeiDou multi-frequency non-differential non-combined PPP-RTK, electronic equipment, computer-readable storage medium, and computer program product. Background Technology

[0002] PPP-RTK technology, by combining the advantages of Precise Point Positioning (PPP) and Real-Time Kinematic Positioning (RTK), can provide users with high-precision, fast-converging positioning services globally, making it a current research hotspot in the field of satellite navigation. With the support of the BeiDou multi-frequency system (such as B1C, B2a, and B3I), PPP-RTK technology has gained richer observation information and stronger error processing potential.

[0003] However, existing BeiDou PPP-RTK technology implementation schemes typically employ a "step-by-step processing" architecture. Specifically, firstly, for major error sources such as ionospheric delay, tropospheric delay (especially the wet component), and multipath effects, independent models or filtering methods are generally used for individual compensation. For example, Klobuchar or Global Ionospheric Map (GIM) models are used to correct ionospheric errors, Saastamoinen models and mapping functions are used to compensate for tropospheric errors, and moving averages or signal-to-noise ratio-based methods are used to suppress multipath errors. This approach ignores the strong coupling and interaction between error sources in complex observation environments (such as urban canyons), which can lead to a compensation deviation for one error interfering with the correction effect of another error, or even causing accuracy cancellation, thus limiting further improvements in final positioning accuracy.

[0004] Secondly, in the ambiguity resolution stage, the classic LAMBDA (Least-squares Ambiguity Decorrelation Adjustment) algorithm is widely used. However, when searching for and fixing integer ambiguities, this algorithm relies primarily on the geometric structure and general statistical properties of the observation equations to construct its search space, failing to effectively incorporate and utilize high-precision prior error information estimated in real-time under current observation conditions. When significant unmodeled or residual errors exist in the observation environment, the ambiguity search space expands abnormally, leading to low search efficiency and prolonged convergence time required for ambiguity resolution. This makes it difficult to meet the urgent needs of applications such as autonomous driving and real-time deformation monitoring for "second-level" or even "instantaneous" high-precision positioning.

[0005] Furthermore, in terms of data quality control, a "detect-and-remove" strategy based on Data Integrity Analysis (DIA) is commonly adopted. This involves first detecting gross errors or outliers in the observation data using statistical tests (such as the chi-square test), and then directly removing the identified outliers from subsequent processing. This "one-size-fits-all" static processing model fails to differentiate the severity of gross errors (such as transient minor interference versus persistent severe bias), resulting in the discarding of a large amount of observation data that still contains valid information. This leads to low data utilization (typically less than 70%), wasting valuable observation resources and potentially indirectly impairing the accuracy and reliability of positioning results due to a reduction in the number of available satellites or deterioration in observation geometry.

[0006] In summary, the shortcomings of existing technologies—isolated error processing, disconnect between ambiguity fixation and error state, and rigid quality control mechanisms—are interconnected and collectively limit the performance ceiling of BeiDou PPP-RTK technology in complex scenarios. Therefore, a collaborative optimization method that integrates error modeling, ambiguity fixation, and quality control throughout the entire process is urgently needed to systematically address these issues. Summary of the Invention

[0007] To address at least some of the problems in existing technologies, such as isolated error processing, disconnect between ambiguity fixation and error state, and rigid quality control mechanisms, this disclosure provides a collaborative optimization method and system for BeiDou multi-frequency non-differential non-combined PPP-RTK, as well as electronic equipment, computer-readable storage media, and computer program products. By establishing an error coupling model, injecting prior error values ​​into the ambiguity fixation algorithm, and dynamically allocating solution weights based on gross error detection results, the collaborative linkage and closed-loop optimization of error correction, ambiguity fixation, and quality control are achieved. This effectively overcomes the shortcomings of traditional technologies, such as isolated error processing, slow ambiguity convergence, and low data utilization, thereby achieving a comprehensive performance leap in BeiDou PPP-RTK system, achieving centimeter-level positioning accuracy and minute-level rapid convergence in complex environments such as urban canyons.

[0008] Firstly, this disclosure provides a collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK, the method comprising: Based on BeiDou multi-frequency observation signals, a coupled model of ionospheric delay, tropospheric wet component and multipath error is constructed and solved in real time to obtain the prior estimate of the error. The prior error estimate is injected into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing. Data integrity analysis (DIA) is used to detect gross errors in the observation data and to assign solution weights to different data based on the severity of the gross errors. The weighted positioning solution is performed using the aforementioned weights to obtain the positioning result. The residuals generated by the positioning calculation are fed back to the calculation process of the coupled model to update the model parameters and realize the closed-loop optimization of the collaborative mechanism.

[0009] Furthermore, the construction of a coupled model of ionospheric delay, tropospheric wet component, and multipath error, and the real-time solution thereof, includes: Based on the differences between code phase and carrier phase observations at BeiDou B1C, B2a, and B3I frequencies, a coupled observation equation including ionospheric delay, tropospheric wet component, multipath error, and ambiguity parameters is established. Kalman filtering is used to perform real-time recursive solution of the coupled observation equations to estimate the coupling coefficients and prior values ​​of the ionospheric delay, tropospheric wet component, and multipath error.

[0010] Furthermore, the coupled observation equation is as follows: ; in, P B1C For B1C frequency point code phase observations, L B2a 、L B3I These are the carrier phase observations at frequencies B2a and B3I, respectively. This represents the geometric distance between the receiver and the satellite. I f Ionospheric delay at each frequency; T w This refers to the tropospheric moisture component; M f For multipath error at each frequency point; N f λ f For each frequency point ambiguity item, N f For ambiguity parameters, λ f For carrier wavelength, f=B1C / B2a / B3I , εp , εL These are the code phase and carrier phase observation noise, respectively; and the ionospheric delay coefficient for the B2a frequency point is set to a preset optimization coefficient.

[0011] Furthermore, the state vector of the Kalman filter includes ionospheric delay, tropospheric wet component and multipath error parameters, and its initial variance matrix is ​​set according to the characteristics of each error source.

[0012] Further, injecting the error prior estimate value into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing includes: Using the error prior estimate value to narrow the ambiguity search range related to ionospheric delay and multipath error in the LAMBDA algorithm; Searching for ambiguity candidate values within the optimized search space and verifying the validity of the candidate values through residual tests.

[0013] Further, detecting gross errors in the observed data based on data integrity analysis DIA and assigning solution weights to different data according to the severity of the gross errors includes: Calculating the residual statistic of the observed data using the chi-square test method and comparing it with a preset critical value to determine gross errors; Classifying the data determined to have gross errors according to the ratio r = T / T0 of its residual statistic T to the preset critical value T0: If 1 < r ≤ α, it is determined as a minor gross error and given the first weight value w1; If r > α, it is determined as a severe gross error and given the second weight value w2; Where, w1 > w2, and α is a preset coefficient greater than 1; Assigning the standard weight value w0 to the data not determined to have gross errors, where w0 > w1.

[0014] In a second aspect, the present disclosure provides a collaborative optimization system for Beidou multi-frequency undifferenced and uncombined PPP-RTK, and the system includes: A modeling module configured to construct a coupling model of ionospheric delay, tropospheric wet component and multipath error based on Beidou multi-frequency observation signals and perform real-time solution to obtain an error prior estimate value; An ambiguity fixing module configured to inject the error prior estimate value into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing; An assignment module configured to detect gross errors in the observed data based on data integrity analysis DIA and assign solution weights to different data according to the severity of the gross errors; A positioning solution module configured to perform weighted positioning solution using the solution weights to obtain a positioning result; A feedback module configured to feedback the residuals generated by the positioning solution to the solution process of the coupling model to update the model parameters and achieve closed-loop optimization of the collaborative mechanism.

[0015] Thirdly, this disclosure provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores one or more computer programs executable by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to execute the above-described collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK.

[0016] Fourthly, this disclosure provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the aforementioned collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK.

[0017] Fifthly, this disclosure provides a computer program product that includes computer-readable code or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK.

[0018] Beneficial effects: This disclosure presents a collaborative optimization method and system for BeiDou multi-frequency non-differential non-combined PPP-RTK, as well as electronic devices, computer-readable storage media, and computer program products. By constructing and real-time solving a coupled model of ionospheric, tropospheric, and multipath errors, collaborative correction of multiple error sources is achieved. This changes the situation where errors interfere with each other or even cancel out accuracy under traditional step-by-step compensation methods, significantly improving the accuracy of error correction and positioning robustness in complex scenarios. The high-precision prior error estimates calculated by the coupled model are used to constrain and optimize the search space of ambiguity fixing algorithms (such as LAMBDA). This directly and significantly reduces the search range, enabling rapid and reliable ambiguity fixing under strong error interference environments, shortening the convergence time from several minutes to tens of seconds, greatly meeting the needs of highly dynamic real-time applications. By dynamically transforming the gross error detection results of the quality control process into differentiated solution weights and integrating them into the positioning solution, a simple "one-size-fits-all" elimination strategy is replaced. This mechanism effectively suppresses the impact of gross errors while preserving the effective information in the observation data to the maximum extent, increasing the data utilization rate to over 90%, thereby improving the availability and reliability of the system while ensuring accuracy.

[0019] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the embodiments of the present disclosure to explain the disclosure and do not constitute a limitation thereof. The above and other features and advantages will become more apparent to those skilled in the art from the detailed description of exemplary embodiments with reference to the accompanying drawings, in which: Figure 1 A flowchart illustrating a collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK provided in Embodiment 1 of this disclosure; Figure 2 This is a schematic diagram of a collaborative optimization system structure for BeiDou multi-frequency non-differential non-combined PPP-RTK provided in Embodiment 2 of this disclosure; Figure 3 This is a schematic diagram of a collaborative processing flow provided in Embodiment 2 of this disclosure; Figure 4 This is a block diagram of a collaborative optimization system for BeiDou multi-frequency non-differential non-combined PPP-RTK provided in Embodiment 3 of this disclosure; Figure 5 This is a block diagram of an electronic device provided in Embodiment 4 of this disclosure. Detailed Implementation

[0021] To enable those skilled in the art to better understand the technical solutions of this disclosure, exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments of this disclosure to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0022] Where there is no conflict, the various embodiments of this disclosure and the features thereof in the embodiments may be combined with each other.

[0023] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0024] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. As used herein, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that when the terms “comprising” and / or “made of” are used in this specification, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Words such as “connected” or “linked” are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0025] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in common dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant art and this disclosure, and will not be interpreted as having an idealized or overly formal meaning unless expressly so defined herein. Those skilled in the art will understand that the specific order of execution of the steps in the methods described above in the specific embodiments should be determined by their function and possible internal logic.

[0026] The collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK according to embodiments of this disclosure can be executed by electronic devices such as terminal devices or servers. Terminal devices can be vehicle-mounted devices, user equipment (UE), mobile devices, user terminals, terminals, cellular phones, cordless phones, personal digital assistants (PDAs), handheld devices, computing devices, vehicle-mounted devices, wearable devices, etc. The method can be implemented by a processor calling computer-readable program instructions stored in memory. Alternatively, the method can be executed by a server.

[0027] Example 1

[0028] Figure 1 This is a flowchart illustrating a collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK provided in Embodiment 1 of this disclosure, with reference to... Figure 1 The method includes: Step S100: Based on the BeiDou multi-frequency observation signal, construct a coupled model of ionospheric delay, tropospheric wet component and multipath error and perform real-time calculation to obtain the prior estimate of the error; Step S200: Inject the prior error estimate into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing; Step S300: Based on Data Integrity Analysis (DIA), gross error detection is performed on the observed data, and solution weights are assigned to different data according to the severity of the gross errors; Step S400: Perform weighted positioning calculation using the calculated weights to obtain the positioning result; Step S500: Feedback the residuals generated by the positioning solution to the solution process of the coupled model to update the model parameters and realize the closed-loop optimization of the collaborative mechanism.

[0029] This embodiment aims to illustrate the implementation process of the collaborative optimization method to verify its feasibility and effectiveness in improving the positioning performance of BeiDou PPP-RTK in complex environments. The embodiment will demonstrate the complete closed-loop process from signal processing to result output, focusing on how "coupled modeling - ambiguity fixing - quality control" dynamically interact to systematically solve three major problems: isolated error compensation, slow ambiguity convergence, and low data utilization.

[0030] Taking a typical urban canyon vehicle positioning scenario as an example, the implementation process includes steps S100-S500. A mobile platform equipped with a receiver supporting BeiDou tri-frequency (B1C, B2a, B3I) signals is used to collect pseudorange and carrier phase observations, satellite ephemeris, and clock bias products at each frequency point in real time at a sampling rate of 1Hz. The B1C signal operates in the 1575.42 MHz band, with a secondary frequency of 32.736 MHz. It is transmitted from three orbital platforms: MEO (Medium Earth Orbit), IGSO (Inclined Geosynchronous Orbit), and GEO (Geostationary Earth Orbit), providing positioning and navigation services. The B2a signal operates in the 1176.45 MHz band, with a secondary frequency of 20.46 MHz. Transmitted from MEO and IGSO orbital platforms, it is used for navigation, positioning, and communication. The B3I signal operates in the 1268.52 MHz band and is the main carrier signal of the BeiDou system. Transmitted from MEO, IGSO, and GEO orbital platforms, it provides crucial data for navigation, positioning, communication, and timing.

[0031] Coupled modeling and real-time solution are performed in step S100.

[0032] First, using BeiDou three-frequency observations, a state-space model (i.e., a coupled model) is constructed that simultaneously incorporates ionospheric delay, tropospheric wet delay, and multipath effects. This model treats these three error terms as related state parameters, rather than independent variables. Subsequently, a Kalman filter is used to perform real-time recursive solution of the model. The filter dynamically estimates the highest priority objective value and its uncertainty for each error term using a continuous sequence of observations. This process changes the traditional step-by-step independent compensation method, enabling error estimation to reflect the mutual influence between the error terms.

[0033] Step S200 is a fixed ambiguity collaborative optimization.

[0034] The prior estimates of the error and their variance information from the Kalman filter output are injected as constraints into the ambiguity fixing module. Specifically, this prior information is used to construct a more accurate variance-covariance matrix, thereby significantly compressing the search space of the LAMBDA algorithm. The algorithm searches and fixes within the optimized space, effectively resisting the interference of residual errors on ambiguity, enabling reliable ambiguity fixing within tens of seconds in urban multi-path environments, thus solving the problem of slow convergence.

[0035] The dynamic quality control and weighted solution process is implemented in steps S300 and S400.

[0036] In parallel, data integrity analysis (DIA) is performed on the original observation sequence. Outliers are detected using residual-based statistical tests (such as the chi-square test). This process does not simply eliminate outliers; instead, based on the degree to which the test statistic exceeds a threshold, suspected outliers are categorized into "minor" and "serious" levels, and different weighting coefficients are dynamically assigned (e.g., weights of 0.6 and 0.2, with normal data weighted at 1.0). These weights are directly substituted into the non-difference, non-combined PPP-RTK observation equations, and weighted least squares are used for localization. This mechanism suppresses the impact of outliers while maximizing the preservation of observational information, increasing the effective data utilization rate to over 90%.

[0037] Step S500 performs closed-loop feedback optimization.

[0038] The observation residuals generated after the localization calculation are fed back to the Kalman filter in step S100 in real time. These residuals contain information about insufficient fitting by the current model and are used to adaptively update the noise parameters or state equations of the filter, enabling the coupled model to continuously track environmental changes. This forms a closed loop of "perception-correction-feedback," realizing the dynamic online optimization of the entire collaborative mechanism.

[0039] This embodiment achieves joint estimation and compensation of multiple errors through coupled modeling and Kalman filtering, avoiding the accuracy cancellation caused by individual compensation. Injecting high-precision error prior information into the ambiguity search significantly accelerates the fixing speed, reducing the measured convergence time from several minutes in traditional methods to less than half a minute. A gross error hierarchical weight allocation strategy replaces direct rejection, significantly improving data utilization efficiency and system robustness. Ultimately, in the complex scenario described in the embodiment, the system achieves a comprehensive performance improvement with a planar positioning accuracy better than 2 cm, an elevation accuracy better than 5 cm, and a significantly reduced initialization time.

[0040] Furthermore, the construction of a coupled model of ionospheric delay, tropospheric wet component, and multipath error, and the real-time solution thereof, includes: Based on the differences between code phase and carrier phase observations at BeiDou B1C, B2a, and B3I frequencies, a coupled observation equation including ionospheric delay, tropospheric wet component, multipath error, and ambiguity parameters is established. Kalman filtering is used to perform real-time recursive solution of the coupled observation equations to estimate the coupling coefficients and prior values ​​of the ionospheric delay, tropospheric wet component, and multipath error.

[0041] This implementation process aims to illustrate how to construct and solve the multi-error coupling model, providing accurate prior error information for the core collaborative mechanism. By specifying the observation equations and filtering process, it demonstrates how to transform the core idea of ​​"joint processing of multiple errors" into an executable technical solution.

[0042] The coupled observation equations are constructed using raw observations acquired by BeiDou tri-frequency (B1C, B2a, B3I) receivers to build an observation equation system suitable for non-differential, non-combined PPP-RTK processing. This system no longer establishes independent equations for each type of error, but instead establishes a unified state-space model.

[0043] The core form of the observation equation of this model can be expressed as follows: set a delay coefficient for the ionosphere corresponding to each frequency point (reflecting the frequency difference), take the tropospheric wet component delay, the ionospheric delay at the reference frequency, and the multipath error of code and phase at different frequencies as state variables to be estimated, and establish their time-varying coupling relationship in the state equation (for example, using random walk or first-order Gauss-Markov process to describe their dynamic characteristics), thereby forcing joint estimation at the mathematical model level.

[0044] Kalman filter real-time recursive solution

[0045] The above model is implemented by embedding it within an extended Kalman filter. The state vector is explicitly set as: X = [position, receiver clock error, ionospheric delay I, tropospheric wet delay T, multipath error at each frequency M]. f Ambiguity parameter N i ] T The filtering process is as follows: Prediction step: Based on the state estimate of the previous time step and the process model describing the state change (including the coupling relationship between error terms), predict the state and covariance of the current time step.

[0046] Update step: The actual three-frequency observations at the current moment are compared with the predicted observations calculated based on the predicted state to generate innovation. The innovation is then weighted and fed back using Kalman gain to optimally update the state vector and its covariance.

[0047] Through this recursive process, the filter can output the optimal estimates (i.e., prior values) of all state variables and their uncertainty information in real time and synchronously, especially the tropospheric wet component delay, the ionospheric delay at the reference frequency, and the estimates and variances of the multipath errors of the code and phase at different frequencies.

[0048] By constructing coupled observation equations and performing real-time recursive solutions, the problem of accuracy cancellation caused by individual compensation for multiple errors is overcome, resulting in the following key effects: To address error coupling interference and improve correction accuracy: By establishing a unified coupled observation equation and setting multiple errors as correlated states, the Kalman filter automatically considers the physical and statistical correlations between the ionosphere, troposphere, and multipath errors during the solution process. For example, when the multipath error of codes at different frequencies increases due to signal reflection in urban canyons, the filter simultaneously adjusts the estimation weights of the tropospheric wet component delay and the ionospheric delay at the reference frequency during estimation, avoiding misjudgment of the ionospheric delay. This fundamentally overcomes the defects of error propagation and mutual amplification in step-by-step compensation, resulting in a significant improvement in the overall accuracy of error correction.

[0049] Providing high-precision, real-time error prior information: The recursive nature of Kalman filtering enables it to dynamically and optimally estimate the instantaneous values ​​and confidence levels (variance) of each error term using historical and current observation data. These output "error prior estimates" are not merely numerical values, but also include valuable uncertainty quantification information. This provides subsequent steps (such as ambiguity fixing) with high-quality prior constraints far exceeding those offered by traditional models (such as those using global mean ionospheric models) or individual filtering.

[0050] Enhancing the system's adaptability in dynamic and complex environments: Because the filter's state equation can model the dynamic changes in error (such as random walks), the entire error estimation system can continuously track environmental changes, such as a sudden increase in ionospheric scintillation or rapid changes in the multipath environment. This real-time adaptive capability is not available in static or step-by-step models, providing a fundamental guarantee for maintaining high-precision positioning in complex scenarios.

[0051] Furthermore, the coupled observation equation is as follows: ; in, P B1C For B1C frequency point code phase observations, L B2a 、L B3I These are the carrier phase observations at frequencies B2a and B3I, respectively. This represents the geometric distance between the receiver and the satellite. I f Ionospheric delay at each frequency;T w This refers to the tropospheric moisture component; M f For multipath error at each frequency point; N f λ f For each frequency point ambiguity item, N f For ambiguity parameters, λ f For carrier wavelength, f=B1C / B2a / B3I , εp , εL These are the code phase and carrier phase observation noise, respectively; and the ionospheric delay coefficient for the B2a frequency point is set to a preset optimization coefficient.

[0052] This section aims to reveal the core mathematical expression of the multi-error coupling model—the coupled observation equation—and explain its construction method in detail, especially the optimization design for the B2a frequency point. This provides an accurate input model for the aforementioned Kalman filter solution and is a key step in realizing the "co-processing" idea into a computable algorithm.

[0053] In this embodiment, the non-differential, non-combined PPP-RTK coupled observation equation system is constructed as follows. For the three frequency points B1C, B2a, and B3I of the BeiDou system, their code phase (pseudorange) observation equation and carrier phase observation equation can be uniformly expressed as: ; Core optimization features (for B2a frequency): In the standard model, the ionospheric delay coefficient γ at the B2a frequency is... B2a It is calculated from its theoretical frequency value. This embodiment performs preset optimization, specifically by: in the observation equation, the ionospheric delay term coefficient γ in the B2a frequency point (whether it is the code phase PB2a or the carrier phase LB2a equation) is adjusted. B2a Set to a calibrated optimization coefficient γ B2a-opt The γ B2a-opt It can be predetermined in one of the following ways: Based on a large amount of historical measured data, the calibration is obtained by inversion through minimizing the solution residuals or closure errors.

[0054] At the standard theoretical value γ B2a-theory Based on this, an empirical small-scale bias correction, namely γ, is introduced. B2a-opt =γ B2a-theory +δ, where δ is the optimization factor. Preferably, the coefficient value can be set to 1.023; this optimization directly corrects the inaccurate ionospheric mapping relationship at the B2a frequency point caused by hardware deviation, frequency deviation, or unmodeled effects.

[0055] By refining the coupled observation equations and introducing targeted frequency coefficient optimization, the error cancellation problem can be solved, thus constructing a precise joint estimation foundation and suppressing error coupling at its source. The provided observation equation set, for the first time within the non-differential, non-combined PPP-RTK framework, explicitly and parametrically incorporates ionospheric delay, tropospheric wet component, and multipath error into the same set of observation equations. This provides a rigorous mathematical model foundation for the synchronous and correlated estimation of multiple state variables using Kalman filtering, ensuring a mathematical representation of the physical correlation between errors and serving as a fundamental prerequisite for avoiding accuracy cancellation caused by "step-by-step compensation."

[0056] By optimizing the B2a frequency coefficients, the overall consistency of the model is significantly improved: The characteristics of the three BeiDou frequency signals differ, and the B2a frequency may exhibit slight systematic deviations from the theoretical model in practical applications. This is achieved by optimizing the γ... B2a Set to the preset optimization coefficient γ B2a-opt In this embodiment, the ionospheric response characteristics at this frequency point were actively calibrated. This fine-tuning significantly improved the internal consistency among the observation equations at the three frequencies, making the coupled model built based on them more reflective of the actual physical observation relationships. Its direct effect is a substantial reduction in model error, making the state variables such as ionospheric delay and tropospheric delay estimated by Kalman filtering more accurate and reliable, thus providing higher-quality prior information for subsequent ambiguity fixing.

[0057] Enhancing the robustness and scene adaptability of the algorithm: Optimized coefficient γ B2a-opt This can be viewed as a calibration for a specific type of receiver or a typical operating environment (such as a city). This gives the coupling model a certain degree of adaptability, enabling it to better adapt to different hardware or complex radio wave environments, and improving the stability and accuracy maintenance of the entire PPP-RTK system in various practical scenarios.

[0058] Furthermore, the state vector of the Kalman filter includes ionospheric delay, tropospheric wet component and multipath error parameters, and its initial variance matrix is ​​set according to the characteristics of each error source.

[0059] Definition and construction of state vectors

[0060] To achieve joint estimation of multiple errors, the state vector (X) of the extended Kalman filter constructed in this embodiment is explicitly defined as: X=[X pos X clk , I, T, M B1C M B2a M B3I , N B1C , N B2a , NB3I ] T , Among them, X pos Receiver's three-dimensional position parameters, X clk : Receiver clock bias parameter, I: Ionospheric delay state quantity (e.g., in the vertical direction or along the signal path), T: Tropospheric wet component delay state quantity, M B1C M B2a M B3I : These correspond to the multipath and higher-order residual error state quantities at three frequency points, respectively; N B1C N B2a N B3I Carrier phase integer ambiguity parameters at three frequency points.

[0061] This definition, for the first time, places the three key error terms of ionosphere, troposphere, and multipath alongside traditional parameters such as position and ambiguity, and incorporates them into a unified state vector for synchronous estimation. This is a direct manifestation of "coupled modeling" at the algorithm level.

[0062] Differentiation setting of the initial variance matrix

[0063] The initial state variance matrix P0 of the Kalman filter is crucial to the filter's convergence speed and initial estimation accuracy. This embodiment differentiates the settings based on the different physical characteristics and variation patterns of each error source: Ionospheric delay (I): Due to its relatively slow change and spatial correlation, it is given a moderate initial variance, for example, set to (0.5-1.0)m. 2 This provides the filter with reasonable initial uncertainty, enabling it to converge quickly to the true value using subsequent observations.

[0064] Tropospheric moisture content (T): Its variation is generally more gradual than that of the ionosphere, but its absolute amount is smaller. Therefore, a small initial variance is set, for example, (0.05-0.2)m. 2 This reflects its high initial predictability.

[0065] Multipath error (M f Multipath effects vary dramatically and are difficult to predict in complex environments. Therefore, a relatively large initial variance is set for it, such as (0.3-0.6)m. 2 This characterizes its high degree of uncertainty, allowing the filter to quickly adapt to its changes during the update process.

[0066] Position, clock bias, and ambiguity: The initial variance of these parameters is set conventionally based on the receiver's prior information (such as single-point positioning results, clock bias model, and floating-point ambiguity solution).

[0067] These variance values ​​are not fixed and can be dynamically adjusted based on local historical data, real-time ionospheric activity indices (such as TECU), or environmental classifications (open / canyon).

[0068] By employing precise state modeling and scientific initialization, the slow convergence and accuracy issues caused by improper error handling are directly resolved, ensuring rapid and stable convergence of the filter. By setting differentiated initial variances that conform to the physical characteristics of different error states, optimal "start-up prior" information is provided for the Kalman filter. This avoids convergence oscillations or slow convergence caused by improper initial variance settings (such as uniformly setting large or small values). The filter's rapid and stable convergence ensures the output of high-quality error prior estimates within a very short time after positioning begins. This directly provides crucial input conditions for achieving "rapid ambiguity fixing," fundamentally solving the slow convergence problem. Improving the accuracy and reliability of multi-error joint estimation: clearly defining the components I, T, and M... f The state vector forces the filter to comprehensively consider the constraints of all observation equations on all state variables in each recursive update. For example, when the multipath effect (M... f When a sudden increase occurs, the filter automatically assesses whether this will affect the estimation of the ionosphere (I) or troposphere (T), and performs optimal allocation based on the covariance relationship between states, thereby effectively suppressing misallocation and mutual interference between errors. This greatly improves the overall accuracy and reliability of error estimation in complex environments.

[0069] Enhancing the system's adaptability and robustness to dynamic environments: A differentiated and dynamically adjustable initial variance strategy enables the system to possess "context-aware" initialization capabilities. When the ionosphere is active or enters a region with severe multipath propagation, the system can correspondingly increase I or M. f The initial variance gives the filter a stronger "learning" ability to track rapid changes. This adaptive initialization mechanism significantly improves the robustness and continuous high-precision positioning capability of the entire PPP-RTK system in dynamically changing environments.

[0070] Furthermore, the step of injecting the prior error estimate into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing includes: The prior error estimate is used to narrow the ambiguity search range related to ionospheric delay and multipath error in the LAMBDA algorithm. A search for fuzzy candidate values ​​is performed within the optimized search space, and the validity of the candidate values ​​is verified by residual test.

[0071] This section aims to demonstrate how the "error prior estimate" obtained in the previous step can be substantially used to accelerate and stabilize the ambiguity fixing process. It shows how the "cooperative" mechanism is transferred from the error estimation stage to the ambiguity resolution stage, which is a key operation to solve the problem of slow convergence.

[0072] The shape and size of the search space in the traditional LAMBDA algorithm are mainly determined by the variance-covariance matrix (Q matrix) of the observation equation. This matrix is ​​usually constructed based on a general model of observation noise and fails to reflect the specific error situation at present. The core operation of this embodiment is to dynamically reconstruct the Q matrix for ambiguity search using the prior error estimates and covariance information output by the Kalman filter.

[0073] Optimization method: Extract the ionospheric delay (I) and multipath error (M) from the Kalman filter. B1C M B2a M B3I The variance components corresponding to the state variables. These variance values ​​quantify the uncertainty of the current estimation of these error terms. This variance information is used as a correction factor and projected back onto the variance of the double-difference ambiguity parameters obtained by linearizing the observation equation. Specifically, the variance of ambiguity components that are strongly correlated with the error terms with high current estimation accuracy (small variance) is reduced.

[0074] Example of effect: In urban canyon scenarios, if the filter's estimation variance of multipath error is small (indicating a relatively accurate grasp of it), the associated ambiguity search range will be significantly tightened. For example, the search boundary of ±0.4 cycles set in traditional methods due to multipath uncertainty can be dynamically reduced to ±0.25 cycles based on prior information. This optimization is real-time and dynamic, adjusting as the environment changes.

[0075] Within the search space optimized and narrowed in the above manner, the standard LAMBDA algorithm is executed to perform an integer least squares search to obtain a set of optimal ambiguity candidate vectors.

[0076] Residual Test: To ensure the reliability of the fixed results, a rigorous residual test is performed on the best candidate group (integer solutions) obtained from the search. The fixed integer ambiguities are substituted back into the original unequal or double-difference observation equations to calculate the corresponding location parameters and residuals. The sum of squared residuals after standardization is then calculated.

[0077] Judgment criterion: If the statistic is less than a preset significance threshold (e.g., a threshold determined by an F-test or chi-square test), the ambiguity is considered successfully and reliably fixed. This step effectively prevents erroneous fixing when the search space is small but may still contain incorrect candidates, ensuring "accuracy" under the premise of "speed".

[0078] Through the above steps, precise compression of the search space can be achieved, accelerating convergence fundamentally. By injecting real-time and high-precision error prior information (especially its uncertainty) into the process of constructing the ambiguity search space, this embodiment realizes targeted and adaptive compression of the search range. This is not a blind reduction but an intelligent optimization based on the "degree of knowledge" of the error at the current moment. In a complex environment, this operation can reduce the volume of the ambiguity search space by more than 50% on average, enabling the LAMBDA algorithm to avoid long searches in a vast and ambiguous solution space. As a result, the time to first fix (TTFF) is stably shortened from the order of 5 - 10 minutes in traditional methods to within 30 seconds, achieving an order-of-magnitude improvement.

[0079] Improve the success rate and reliability of ambiguity fixing: The reduced search space not only means faster search speed but also significantly reduces the probability that incorrect integer candidate solutions fall within the search range. Combining with strict residual posterior tests, this method ensures the correctness of the fixed results while pursuing speed. In actual tests, in a medium multipath environment, the ambiguity fixing success rate is increased from ~85% in traditional methods to over 99%, significantly enhancing the robustness of the system while maintaining high precision.

[0080] Complete the key value transfer from "error modeling" to "positioning solution": This step is the core hub in the "collaborative optimization" chain. It successfully converts the information advantage (high-precision prior values) generated in the upstream "error coupling modeling" link into the performance advantage (fast and reliable fixing) in the downstream "positioning solution" link. This verifies the effectiveness of the data flow closed-loop in the described trinity architecture, demonstrating that the modules do not work independently but form a synergistic effect with performance multiplication through information injection and feedback.

[0081] Furthermore, the gross error detection is performed on the observed data based on the data integrity analysis DIA, and solution weights are assigned to different data according to the severity of the gross error, including: The chi-square test method is used to calculate the residual statistic of the observed data and compare it with a preset critical value to determine the gross error; The data determined to be gross errors are classified according to the ratio r = T / T0 of its residual statistic T to the preset critical value T0: If 1 < r ≤ α, it is determined to be a minor gross error and is assigned the first weight value w1; If r > α, it is determined to be a severe gross error and is assigned the second weight value w2; where w1 > w2, and α is a preset coefficient greater than 1; The data not determined to be gross errors are assigned the standard weight value w0, where w0 > w1.

[0082] To achieve a dynamic quality control mechanism that allocates solution weights based on the severity of gross errors, this embodiment innovates the traditional "hard rejection" strategy into a refined "soft weighting" strategy, thereby maximizing the utilization rate of effective information while suppressing the impact of outlier data.

[0083] The specific implementation process includes: Gross error detection based on chi-square test: At each solution epoch, using the current state estimate (e.g., position, clock bias, error term) and observation model, the predicted residuals (innovation) of all observations (pseudorange and carrier phase at each frequency) are calculated. These residuals are standardized to construct an overall chi-square test statistic. This statistic follows a chi-square distribution with degrees of freedom equal to the number of redundant observations. By comparing the calculated statistic with a predetermined critical value based on a significance level (e.g., 0.05), a comprehensive determination of whether gross errors exist in the current observation set is achieved.

[0084] Quantification rules for gross error classification: When the overall test indicates the presence of gross errors, it is necessary to locate and classify the specific gross error observations. An adjustable threshold coefficient α (e.g., α=1.2) is introduced to quantify the classification. Minor gross error: the normalized residual v of a certain observation. norm Satisfying 1<|v norm |≤α. Such gross errors are usually caused by transient changes in observation noise, slight multipath scintillation, or minor atmospheric disturbances from low-elevation satellites, and the observations still contain a great deal of useful geometric and error information.

[0085] Serious gross error: The normalized residual v of a certain observation. norm Satisfy | v norm |>α. Such gross errors are usually caused by satellite signal loss, severe obstruction, transient receiver failure, or unmodeled cycle slips, resulting in extremely low data reliability.

[0086] Differentiated weight allocation and solution fusion: Based on the above classification results, a weight w is dynamically assigned to each observation, and then directly substituted into weighted least squares or robust estimation based on equivalent weights for location solution: Normal data: weight w0=1.0, fully involved in the solution.

[0087] Minor gross errors: assign a reduced weight, for example, w1=0.6. This means that the information from the observation participates in the solution with 60% strength, suppressing the influence of its outliers while retaining its effective information components.

[0088] Severe gross errors: Assign extremely low weights, such as w2=0.2 or lower, so that their impact on the solution results is negligible, almost eliminating them but preserving the consistency of the program logic.

[0089] The above-described specific implementation methods precisely address the pain point of data loss caused by the disconnect between DIA quality control and the solution process, and bring about performance improvements in the following aspects: By shifting from "hard rejection" to "soft weighting," data utilization is significantly improved: By introducing a hierarchical weighting mechanism, this method completely changes the binary logic of "rejecting anything that is abnormal" in traditional quality control. Data judged as having "minor gross errors" is no longer simply discarded, but is reused through weight reduction. Real-world testing shows that this strategy can significantly increase the effective data utilization rate from approximately 60% with traditional methods to over 90%. Especially in complex urban areas with limited satellite visibility, this improvement directly translates into better observation geometry and higher positioning availability.

[0090] Enhancing the robustness and accuracy of the positioning solution: Traditional direct elimination methods, while removing outliers, may also disrupt the geometry of the observation network, especially in cases of critically visible satellites, potentially leading to solution failure or a sharp drop in accuracy. The weight allocation strategy in this embodiment is a continuous and smooth robustness mechanism. It can gently resist the influence of gross errors without causing drastic oscillations in the solution system. In environments with intermittent interference, the system output positioning results are more continuous and stable, with significantly reduced fluctuations in accuracy in both horizontal and vertical directions.

[0091] Achieving deep integration between quality control and the solution process: This method directly transforms the results of quality control (gross error levels) into input parameters (weights) for the solution process, turning the quality control module from a "pre-filter" into a "real-time regulator." This deep integration ensures real-time consistency between anomaly handling and parameter estimation. For example, a minor gross error caused by a brief occlusion can automatically have its weight restored to its normal value after subsequent epoch signal recovery, achieving dynamic and intelligent management of observation data quality and forming an indispensable link in the collaborative optimization closed loop.

[0092] This disclosure systematically solves the core bottlenecks of traditional BeiDou PPP-RTK technology, namely isolated error processing, slow ambiguity convergence, and low data utilization, by constructing a three-in-one collaborative optimization and closed-loop feedback mechanism of "error coupling modeling - ambiguity fixing - quality control". It utilizes a multi-error coupling model and Kalman filtering to achieve collaborative high-precision error estimation, and dynamically injects prior information to compress the ambiguity search space, thereby shortening the fixed convergence time from several minutes to within 30 seconds. Simultaneously, by employing a gross error classification and dynamic weight allocation strategy, instead of simple elimination, the effective data utilization rate is increased to over 90%. Ultimately, centimeter-level real-time positioning with a horizontal accuracy of ≤2cm and an elevation accuracy of ≤5cm is achieved in complex urban environments, significantly improving the system's accuracy, speed, and robustness.

[0093] Example 2

[0094] Embodiment 2 of this disclosure provides a collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK, proposing a "three-in-one collaborative mechanism of error coupling modeling, ambiguity fixing, and quality control." This breaks through the "step-by-step processing" logic of traditional BeiDou PPP-RTK technology. Based on the characteristics of BeiDou multi-frequency signals (B1C / B2a / B3I), it achieves integrated optimization of multi-error collaborative correction, rapid ambiguity fixing, and efficient data utilization. The closed-loop architecture of the "error coupling modeling, ambiguity fixing, and quality control" three-in-one collaborative linkage is as follows: Figure 2 As shown, it includes: Beidou multi-frequency signal receiving module: As input, it is responsible for receiving raw observation data from three frequency points: B1C, B2a, and B3I.

[0095] Multi-error coupling modeling module: One of the core processing modules, it receives observation data, performs joint multi-error calculation, and outputs key prior error values.

[0096] The ambiguity fixing optimization module and the DIA quality control and solution linkage module both receive prior error values ​​from the error modeling module in parallel. The former uses this information to optimize the search and output ambiguity parameters; the latter uses this information for gross error detection and weight allocation.

[0097] Positioning result output module: Receives results from the ambiguity fixing module and the quality control module, performs fusion calculation, and finally outputs the positioning result.

[0098] The prior error value is the core link of the collaboration. It is generated by the error modeling module and simultaneously injected into the subsequent two modules, driving the entire system to achieve fast, accurate, and robust positioning calculation.

[0099] Specifically, the method includes: Step 1: BeiDou multi-frequency signal acquisition Satellite observation data in urban canyon environments are collected using a BeiDou multi-frequency receiver (supporting B1C / B2a / B3I frequencies), including code phase observations, carrier phase observations, and satellite ephemeris data for each frequency. The data sampling rate is set to 1Hz to ensure the real-time performance and completeness of the observation data.

[0100] Step 2: Multi-error coupling modeling and real-time solution

[0101] Based on the characteristics of the acquired BeiDou multi-frequency signals, a coupling equation for "ionospheric delay - tropospheric wet component - multipath error" is established, and the coupling coefficient is calculated in real time using Kalman filtering, as detailed below: Coupling equation construction: Considering the code phase / carrier phase difference of BeiDou B1C / B2a / B3I frequency points, the coupling equation is designed as shown in equation (1): ; in, For B1C frequency point code phase observations, These are the carrier phase observations at frequencies B2a and B3I, respectively. This represents the geometric distance between the receiver and the satellite. Ionospheric delay at each frequency (optimize the ionospheric delay coefficient for the B2a frequency, with the coefficient value set to 1.023). This refers to the tropospheric moisture component; For multipath error at each frequency point; For each frequency point ambiguity item ( For ambiguity parameters, (carrier wavelength); These are the code phase and carrier phase observation noise, respectively.

[0102] Kalman filter solution: Delaying the ionosphere Tropospheric moisture content Multipath error Using the state vector of the Kalman filter and the residuals of the coupling equations as the observation vector, the initial variance matrix of the filter is set (the initial variance of the ionospheric delay is set to 0.1 m², the initial variance of the tropospheric wet component is set to 0.05 m², and the initial variance of the multipath error is set to 0.08 m²). The coupling coefficients of each error are calculated in real time through recursion to obtain the prior values ​​of the errors (such as the prior value of the ionospheric delay). Multipath error prior value ).

[0103] Step 3: Co-optimization of ARF and error modeling

[0104] The "error prior value" obtained in step 2 is injected into the ambiguity fixing algorithm to optimize the LAMBDA search space and achieve rapid ambiguity fixing, as detailed below: Search space optimization: based on error prior values , The search boundaries of the traditional LAMBDA algorithm are corrected. For example, the search range for ionospheric delay correlation is reduced from ±0.5 weeks to ±0.35 weeks, and the search range for multipath error correlation is reduced from ±0.4 weeks to ±0.28 weeks, resulting in an overall search space reduction of more than 30%.

[0105] Ambiguity fixation verification: A "search first, verify later" process is adopted—candidate ambiguity values ​​are searched within the optimized search space, and then the validity of the candidate values ​​is verified through residual testing (with a residual threshold set to 0.1m). Finally, ambiguity fixation is achieved within 30 seconds, and the fixed ambiguity parameters are output. .

[0106] Collaborative processing flow such as Figure 3As shown. The core path of the process is: Starting point: Observational data is acquired by the "BeiDou multi-frequency signal acquisition" module.

[0107] Core processing: Data enters the "multi-error coupling modeling" module, which calculates and outputs "error prior values".

[0108] Collaborative branch: "Error prior value" is injected into two parallel modules simultaneously: ARF optimization module: Optimizes the search using prior values ​​and outputs "optimization parameters".

[0109] The DIA and solution linkage module receives prior values ​​and optimization parameters, and performs quality control and weighted solution.

[0110] Output results: The "DIA and Solution Linkage" module outputs the final "positioning solution results" (i.e., high-precision positioning data).

[0111] The "residual feedback" path in the diagram, i.e., the "location solution result," serves as residual information and is fed back to the "multi-error coupling modeling" module. This enables dynamic updating and continuous optimization of system parameters.

[0112] Step 4: Dynamic Linkage Between DIA and Solution

[0113] DIA (Different Identification) technology is used to detect gross errors, and the detection results are transformed into solution weights and incorporated into the localization solution process, as detailed below: Gross error detection: The chi-square test was used to detect gross errors in DIA. The significance level was set to 0.05. The residual statistics of each observation data were calculated. If the statistic exceeded the chi-square critical value (the critical value was set to 7.81 when the degrees of freedom was 3), it was judged as gross error data. According to the size of the residual, the gross errors were divided into "minor gross errors" (residuals are 1-1.2 times the critical value) and "serious gross errors" (residuals are greater than 1.2 times the critical value).

[0114] Weighting and calculation: Establish weight mapping relationship - assign a weight of 0.6 to slightly gross data, a weight of 0.2 to severely gross data, and a weight of 1.0 to normal data; substitute the weight values ​​into the BeiDou PPP-RTK positioning calculation equation (such as the non-difference non-combination observation equation), and calculate the final positioning result (longitude, latitude, and elevation) by weighted least squares method.

[0115] Step 5: Output and Feedback of Location Results

[0116] Output the positioning results (positioning accuracy up to centimeter level, planar accuracy ≤2cm, elevation accuracy ≤5cm), and simultaneously feed the positioning residuals back to the Kalman filter module in step 2 to update the variance matrix of the filter state vector, thereby realizing the closed-loop optimization of the collaborative mechanism.

[0117] Test and verification: Based on the urban canyon simulation dataset (containing 100 sets of observation data with different building densities and satellite obstruction rates), this solution was used for calculation. The average ambiguity fixation time was 28 seconds, the data utilization rate reached 92%, the average horizontal positioning accuracy was 1.8 cm, and the average vertical positioning accuracy was 4.2 cm, all of which met the design specifications.

[0118] Example 3

[0119] Embodiment 3 of this disclosure provides a collaborative optimization system for BeiDou multi-frequency non-differential non-combined PPP-RTK, such as... Figure 4 As shown, the system includes: Modeling module 11 is configured to construct a coupled model of ionospheric delay, tropospheric wet component and multipath error based on BeiDou multi-frequency observation signals and perform real-time calculation to obtain the prior estimate of error. The ambiguity fixing module 12 is configured to inject the prior error estimate into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing. The allocation module 13 is configured to perform gross error detection on the observation data based on data integrity analysis (DIA) and assign solution weights to different data according to the severity of the gross errors. The positioning solution module 14 is configured to perform weighted positioning solution using the solution weights to obtain the positioning result; Feedback module 15 is configured to feed back the residuals generated by the positioning solution to the solution process of the coupled model in order to update the model parameters and realize closed-loop optimization of the collaborative mechanism.

[0120] Furthermore, the modeling module 11 is specifically configured as follows: Based on the differences between code phase and carrier phase observations at BeiDou B1C, B2a, and B3I frequencies, a coupled observation equation including ionospheric delay, tropospheric wet component, multipath error, and ambiguity parameters is established. Kalman filtering is used to perform real-time recursive solution of the coupled observation equations to estimate the coupling coefficients and prior values ​​of the ionospheric delay, tropospheric wet component, and multipath error.

[0121] Furthermore, the coupled observation equation is as follows: ; in, P B1C For B1C frequency point code phase observations, L B2a 、L B3I These are the carrier phase observations at frequencies B2a and B3I, respectively. This represents the geometric distance between the receiver and the satellite. If is the ionospheric delay at each frequency point; T w is the wet component of the troposphere; M f is the multipath error at each frequency point; N f λ f is the ambiguity term at each frequency point, N f is the ambiguity parameter, λ f is the carrier wavelength, f=B1C / B2a / B3I , εp 、 εL are the code phase and carrier phase observation noises respectively; and the ionospheric delay coefficient for the B2a frequency point is set to a preset optimization coefficient.

[0122] Furthermore, the state vector of the Kalman filter includes the ionospheric delay, the wet component of the troposphere and the multipath error parameter, and its initial variance matrix is set respectively according to the characteristics of each error source.

[0123] Furthermore, the ambiguity fixing module 12 is specifically set as: using the prior error estimate value to narrow the ambiguity search range related to the ionospheric delay and multipath error in the LAMBDA algorithm; searching for ambiguity candidate values within the optimized search space, and verifying the validity of the candidate values through residual tests.

[0124] Furthermore, the allocation module 13 is specifically set as: using the chi-square test method to calculate the residual statistic of the observed data, and comparing it with a preset critical value to determine gross errors; grading the data determined to be gross errors according to the ratio r = T / T0 of its residual statistic T to the preset critical value T0: if 1 < r ≤ α, it is determined to be a minor gross error and given the first weight value w1; if r > α, it is determined to be a serious gross error and given the second weight value w2; where, w1 > w2, and α is a preset coefficient greater than 1; giving the data not determined to be gross errors the standard weight value w0, where w0 > w1.

[0125] The collaborative optimization system of the Beidou multi-frequency non-differential non-combination PPP-RTK in the embodiments of the present disclosure is used to implement the collaborative optimization method of the Beidou multi-frequency non-differential non-combination PPP-RTK in Embodiment 1 and Embodiment 2 of the method, so the description is relatively simple. For specific details, reference can be made to the relevant descriptions in the previous method embodiments, which will not be elaborated here.

[0126] Figure 5 This is a block diagram of an electronic device provided in Embodiment 4 of this disclosure.

[0127] Reference Figure 5 This disclosure provides an electronic device comprising: at least one processor 701; at least one memory 702; and one or more I / O interfaces 703 connected between the processor 701 and the memory 702; wherein the memory 702 stores one or more computer programs executable by the at least one processor 701, the one or more computer programs being executed by the at least one processor 701 to enable the at least one processor 701 to execute the above-described collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK.

[0128] This disclosure also provides a computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the aforementioned collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK. The computer-readable storage medium can be volatile or non-volatile.

[0129] This disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code. When the computer-readable code is run in the processor of an electronic device, the processor in the electronic device executes the above-described collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK.

[0130] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0131] As is known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0132] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0133] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0134] The computer program product described herein can be implemented specifically through hardware, software, or a combination thereof. In one alternative embodiment, the computer program product is specifically embodied in a computer storage medium; in another alternative embodiment, the computer program product is specifically embodied in a software product, such as a software development kit (SDK), etc.

[0135] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer-readable program instructions.

[0136] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0137] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0138] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0139] Example embodiments have been disclosed herein, and while specific terminology has been used, it is for illustrative purposes only and should be construed as such, and is not intended to be limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in connection with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in connection with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of this disclosure as set forth by the appended claims.

Claims

1. A collaborative optimization method for BeiDou multi-frequency non-differential non-combined PPP-RTK, characterized in that, The method includes: Based on the Beidou multi-frequency observation signals, constructing a coupling model of ionospheric delay, tropospheric wet component and multipath error and performing real-time calculation to obtain a prior error estimate value; Injecting the prior error estimate value into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing; Performing gross error detection on the observation data based on the data integrity analysis DIA, and assigning calculation weights to different data according to the severity of the gross error; Performing weighted positioning calculation using the calculation weights to obtain a positioning result; Feeding back the residuals generated by the positioning calculation to the calculation process of the coupling model to update the model parameters and achieve closed-loop optimization of the cooperation mechanism.

2. The method according to claim 1, characterized in that, The constructing a coupling model of ionospheric delay, tropospheric wet component and multipath error and performing real-time calculation includes: Based on the differences between the code phase and carrier phase observation values of the Beidou B1C, B2a, and B3I frequency points, establishing a coupling observation equation including ionospheric delay, tropospheric wet component, multipath error and ambiguity parameters; Using Kalman filtering to perform real-time recursive calculation on the coupling observation equation to estimate the coupling coefficients and prior values of the ionospheric delay, tropospheric wet component and multipath error.

3. The method according to claim 2, characterized in that, The coupling observation equation is: ； in, P B1C For B1C frequency point code phase observations, L B2a 、L B3I These are the carrier phase observations at frequencies B2a and B3I, respectively. This represents the geometric distance between the receiver and the satellite. I f Ionospheric delay at each frequency; T w This refers to the tropospheric moisture component; M f For multipath error at each frequency point; N f λ f For each frequency point ambiguity item, N f For ambiguity parameters, λ f For carrier wavelength, f = B1C / B2a / B3I , εp , εL These are the code phase and carrier phase observation noise, respectively; and the ionospheric delay coefficient for the B2a frequency point is set to a preset optimization coefficient.

4. The method according to claim 3, characterized in that, The state vector of the Kalman filtering includes ionospheric delay, tropospheric wet component and multipath error parameters, and its initial variance matrix is set respectively according to the characteristics of each error source.

5. The method according to claim 1, characterized in that, The injecting the prior error estimate value into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing includes: Using the prior error estimate value to narrow the ambiguity search range related to ionospheric delay and multipath error in the LAMBDA algorithm; Searching for ambiguity candidate values within the optimized search space and verifying the effectiveness of the candidate values through residual tests.

6. The method according to claim 1, characterized in that, The performing gross error detection on the observation data based on the data integrity analysis DIA and assigning calculation weights to different data according to the severity of the gross error includes: Using the chi-square test method to calculate the residual statistic of the observation data and comparing it with a preset critical value to determine gross errors; Classifying the data determined to be gross errors according to the ratio r = T / T0 of its residual statistic T to the preset critical value T0: If 1 < r ≤ α, it is determined to be a minor gross error and given the first weight value w1; If r > α, it is determined to be a serious gross error and given the second weight value w2; where w1 > w2, and α is a preset coefficient greater than 1; Assigning the standard weight value w0 to the data not determined to be gross errors, where w0 > w1.

7. A collaborative optimization system for BeiDou multi-frequency non-differential non-combined PPP-RTK, characterized in that, The system includes: A modeling module configured to construct a coupling model of ionospheric delay, tropospheric wet component and multipath error based on the Beidou multi-frequency observation signals and perform real-time calculation to obtain a prior error estimate value; An ambiguity fixing module configured to inject the prior error estimate value into the search space of the ambiguity fixing algorithm to optimize the search boundary and achieve fast ambiguity fixing; The allocation module is configured to detect gross errors in the observation data based on Data Integrity Analysis (DIA) and assign solution weights to different data based on the severity of the gross errors. The positioning solution module is configured to perform weighted positioning solution using the solution weights to obtain the positioning result; The feedback module is configured to feed back the residuals generated by the positioning solution to the solution process of the coupled model in order to update the model parameters and realize the closed-loop optimization of the collaborative mechanism.

8. An electronic device, characterized in that, include: At least one processor; as well as A memory communicatively connected to the at least one processor; wherein, The memory stores one or more computer programs that can be executed by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the collaborative optimization method of BeiDou multi-frequency non-differential non-combined PPP-RTK as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the collaborative optimization method of BeiDou multi-frequency non-differential non-combined PPP-RTK as described in any one of claims 1-6.

10. A computer program product, characterized in that, Includes computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device executes the collaborative optimization method of BeiDou multi-frequency non-differential non-combined PPP-RTK as described in any one of claims 1-6.

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