A single-beidou PPP-RTK joint estimation method, system and device

Abstract

The application relates to a single Beidou PPP-RTK joint estimation method, system and device, which comprises the following steps: modeling time correlation colored noise characteristics of correction information, fusing single Beidou multi-frequency observation equations, and constructing a multi-epoch single Beidou PPP-RTK user filtering model; expanding a user filtering state vector based on correction information error; and estimating a covariance matrix of the correction information in real time, and dynamically adjusting filtering weights. The application fundamentally solves the problem of loss of Kalman filtering optimality caused by a double filtering architecture by modeling time correlation of the correction information broadcast by a server; a joint estimation filtering framework is constructed by expanding the user filtering state vector, and systematic precision loss caused by double filtering nesting is eliminated; the covariance matrix of the correction information is estimated in real time based on Beidou multi-frequency observation data, filtering weights are dynamically adjusted, and the problem of sharp precision deterioration of a prior art fixed weight in a large correction delay scene is solved.

Description

Technical Field

[0001] This invention relates to the field of BeiDou positioning technology, specifically to a single BeiDou PPP-RTK joint estimation method, system, and device. Background Technology

[0002] PPP-RTK technology combines the wide-area coverage advantage of Precise Point Positioning (PPP) with the rapid convergence characteristics of Real-Time Dynamic Positioning (RTK). It calculates and broadcasts correction information such as satellite orbit, clock error, atmospheric delay, and phase deviation through a network of reference stations. The user end combines the observation data and correction information to achieve centimeter-level rapid positioning, which is the core technology direction of high-precision positioning in current satellite navigation.

[0003] With the full completion of the BeiDou-3 global satellite navigation system, independent and controllable high-precision positioning of a single BeiDou system has become a core requirement for national strategy and industry applications. However, the constellation configuration and signal frequency characteristics of a single BeiDou system differ significantly from those of multi-system integration scenarios such as GPS, further amplifying the performance limitations of existing PPP-RTK technology in single BeiDou scenarios.

[0004] Current PPP-RTK technologies generally adopt a dual-filter architecture of "server-side filtering and correction information + user-side filtering and positioning results". This architecture has an unavoidable core technical defect, as follows: 1. Violation of the optimal assumption of Kalman filtering and loss of minimum variance property: The optimal estimation of Kalman filtering (minimum variance unbiased estimation) strictly depends on the core assumption that "the observation data is time-independent (white noise)". However, the correction information broadcast by the server is the output of its Kalman filter, which itself has significant time correlation (colored noise). The user end directly uses this correction information as a known quantity or white noise observation data as input for secondary filtering, which essentially forms a double-filter nesting, completely violating the standard assumption of Kalman filtering. This causes the user end filter to lose its optimality, resulting in a systematic loss of positioning accuracy.

[0005] 2. Poor adaptability to correction delays, leading to drastic performance degradation in weak network scenarios: Most existing solutions ignore the temporal correlation of correction information, only setting fixed variances and weights for the correction information without modeling time-related colored noise. When the broadcast delay of correction information increases (e.g., the delay reaches more than 200ms in weak or no network environments), the impact of temporal correlation is amplified dramatically. The positioning accuracy of traditional solutions will rapidly drop from centimeter-level to decimeter-level or even meter-level, failing to meet the requirements for high-reliability positioning.

[0006] 3. Failure to achieve joint estimation of correction information and user parameters, thus failing to fundamentally solve the accuracy loss problem: Although a few existing solutions consider the uncertainty of correction information, they only perform ex-post weight adjustment on the observation data and do not incorporate the error state of correction information with user-end positioning parameters, atmospheric parameters, and ambiguity parameters into the same filtering framework for joint estimation. The core contradiction of dual filtering always exists, and the optimal estimation capability of the filter cannot be restored.

[0007] 4. Insufficient adaptability to single BeiDou scenarios, with significant shortcomings in convergence speed and positioning accuracy: Most existing PPP-RTK optimization schemes are designed for GPS / BeiDou multi-system fusion scenarios, without specific optimization for the constellation characteristics and observation noise characteristics of a single BeiDou system. In single BeiDou scenarios, the number of visible satellites is less than in multi-system fusion scenarios, constellation configuration changes more slowly, traditional schemes have insufficient filtering stability, low ambiguity fixation success rate, long convergence time, and difficulty in achieving stable centimeter-level positioning. Summary of the Invention

[0008] This invention provides a single BeiDou PPP-RTK joint estimation method, system, and device to solve at least one of the above-mentioned technical problems.

[0009] The technical solution of this invention to solve the above-mentioned technical problems is as follows: A single BeiDou PPP-RTK joint estimation method, comprising: S1, model the time-related colored noise characteristics of the correction information broadcast by the server, and integrate the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. S2, in the multi-epoch single Beidou PPP-RTK user filtering model, the user filtering state vector is expanded based on the correction information error to construct a joint estimation filtering framework of correction information and user parameters; S3. Based on the single Beidou multi-frequency observation equation, the covariance matrix of the correction information is estimated in real time, and the filtering weights in the joint estimation filtering framework are dynamically adjusted accordingly. S4 employs a joint estimation filtering framework with dynamically adjusted filter weights to perform joint estimation, thereby fixing the integer ambiguity of a single BeiDou PPP-RTK. After successful fixing, the state vector is updated, and finally, the user terminal's three-dimensional centimeter-level positioning result is output.

[0010] Based on the above technical solution, the present invention can be further improved as follows.

[0011] Furthermore, S1 specifically includes: S11, for multi-frequency signals of a single BeiDou satellite, combined with the user terminal, constructs a single BeiDou multi-frequency observation equation based on non-combined pseudorange and carrier phase observation; S12, For the correction information broadcast by the server, a first-order Markov process is used to model the time-related colored noise characteristics of the correction information to obtain the time-related model of the correction information. S13, the single Beidou multi-frequency observation equation is deeply integrated with various correction information time correlation models so that the error characteristics of various correction information are transformed from observation data correction terms into state parameters within the filtering model, thereby obtaining the multi-epoch single Beidou PPP-RTK user filtering model.

[0012] Furthermore, the single BeiDou multi-frequency observation equation includes a pseudorange observation equation and a carrier phase observation equation; wherein, The pseudorange observation equation is expressed as: ; The carrier phase observation equation is expressed as: ; In the formula, for pseudorange observation data at a given frequency point for Carrier phase observation data at a given frequency; This refers to the geometric distance from a single BeiDou satellite to the user terminal. At the speed of light, For user-side clock bias, For single BeiDou satellite clock bias, This is the tropospheric zenith delay projection value. This is the zenith delay projection value of the ionosphere. for Ionospheric coefficient at a given frequency point , They are respectively User terminal at a given frequency point, hardware delay of pseudorange for a single BeiDou satellite. for Wavelength at the frequency point for Carrier phase integer ambiguity at a given frequency point , They are respectively User terminal at a given frequency point, hardware delay of single BeiDou satellite phase, for pseudorange observation noise at a given frequency point for Carrier phase observation noise at a given frequency.

[0013] Furthermore, the correction information includes satellite clock error correction information, satellite orbit correction information, ionospheric correction information, tropospheric correction information, pseudorange hardware delay correction information, and phase hardware delay / FCB correction information.

[0014] Furthermore, the corrected information time correlation model is expressed as: ; In the formula, For the current epoch Correction information error, For the previous epoch Correction information error, To correct the time correlation coefficient of the information, For the current epoch Zero-mean Gaussian white noise.

[0015] Furthermore, S2 specifically includes: S21, in the multi-epoch single Beidou PPP-RTK user filtering model, based on the traditional user-end filtering state vector, the state for correcting information error is used as an extended state to form an extended joint state vector. S22, construct a state transition matrix based on the extended joint state vector to achieve one-step state prediction; S23, after completing the state one-step prediction, the original pseudorange of the single Beidou satellite, the carrier phase observation data observed by the multi-epoch single Beidou PPP-RTK user filtering model, and the correction information broadcast by the server are used together as observation data to incorporate the correction information and user parameters into the same observation update process, thereby obtaining the joint estimation filtering framework of correction information and user parameters.

[0016] Furthermore, the traditional user-end filtered state vector includes the user's three-dimensional geocentric coordinates, user-end clock bias, user-end clock bias drift, tropospheric zenith delay, and the integer ambiguity of the two carrier phases of each visible BeiDou satellite under multiple frequencies; The vector formed by the state of correcting information errors as an extended state is the extended correction error state vector. The extended correction error state vector includes the orbit correction error, clock error correction error, ionospheric correction error, tropospheric correction error, multi-frequency pseudorange hardware delay correction error, and multi-frequency phase hardware delay correction error of each visible Beidou satellite.

[0017] Furthermore, S3 specifically includes: S31, Based on the filtered residual sequence of the first multiple epochs of the single Beidou multi-frequency observation data observed by the single Beidou multi-frequency observation equation, the maximum likelihood estimation method is used to solve the time correlation coefficient and process noise variance of the correction information in the joint estimation filtering framework in real time. S32, based on the time correlation coefficient and process noise variance of the real-time solved correction information, update the state transition matrix and process noise covariance matrix, and construct the observation covariance matrix containing the inter-epoch cross-covariance term; S33. Based on the covariance matrix of the observed values, update the Kalman filter gain matrix, and use this to dynamically adjust the filter weights of the original observed values ​​and the correction information, thereby realizing the dynamic adjustment of the filter weights in the joint estimation filter framework.

[0018] Based on the above-mentioned single BeiDou PPP-RTK joint estimation method, the present invention also provides a single BeiDou PPP-RTK joint estimation system.

[0019] A single BeiDou PPP-RTK joint estimation system includes: The time-related colored noise modeling module is used to model the time-related colored noise characteristics of the correction information broadcast by the server, and integrates the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. The state extension module is used to expand the user filter state vector based on the correction information error in the multi-epoch single Beidou PPP-RTK user filter model, so as to construct a joint estimation filter framework of correction information and user parameters. The filter weight dynamic adjustment module is used to estimate the covariance matrix of the correction information in real time based on the single Beidou multi-frequency observation equation, and to dynamically adjust the filter weights in the joint estimation filter framework accordingly. The positioning module is used to perform joint estimation using a joint estimation filtering framework with dynamically adjusted filter weights to fix the integer ambiguity of a single BeiDou PPP-RTK. After successful fixation, the state vector is updated, and finally, the three-dimensional centimeter-level positioning result is output to the user terminal.

[0020] Based on the above-mentioned single BeiDou PPP-RTK joint estimation method, the present invention also provides a single BeiDou PPP-RTK joint estimation device.

[0021] A single BeiDou PPP-RTK joint estimation device includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the single BeiDou PPP-RTK joint estimation method as described above.

[0022] The beneficial effects of this invention are as follows: In the single BeiDou PPP-RTK joint estimation method, system, and device of this invention, by modeling the time correlation of the correction information broadcast by the server, the problem of loss of Kalman filtering optimality caused by the dual-filter architecture is fundamentally solved, and the minimum variance unbiased estimation characteristic of single BeiDou PPP-RTK positioning is restored. At the same time, by expanding the user-end filter state vector to construct a joint estimation filter framework, the error state of the correction information and user positioning parameters, atmospheric parameters, and ambiguity parameters are incorporated into the same filter framework for joint estimation, completely eliminating the systematic accuracy loss caused by dual-filter nesting. Furthermore, based on the real-time estimation of the covariance matrix of the correction information based on BeiDou multi-frequency observation data, the filter weights are dynamically adjusted, solving the problem of sharp deterioration of accuracy under large correction delay scenarios with fixed weights in existing technologies. In addition, based on the joint estimation framework, the accuracy and stability of the ambiguity floating-point solution are greatly improved, solving the shortcomings of slow convergence, low fixed success rate, and poor stability in single BeiDou scenarios in existing technologies, and realizing fully autonomous and controllable single BeiDou centimeter-level high-precision positioning. Attached Figure Description

[0023] Figure 1 This is a flowchart of a single BeiDou PPP-RTK joint estimation method according to the present invention; Figure 2 This is a structural block diagram of a single BeiDou PPP-RTK joint estimation system according to the present invention; Figure 3 This is a structural block diagram of a single Beidou PPP-RTK joint estimation device according to the present invention. Detailed Implementation

[0024] The principles and features of the present invention are described below with reference to the accompanying drawings. The examples given are only for explaining the present invention and are not intended to limit the scope of the present invention.

[0025] Example 1: like Figure 1 As shown, a single BeiDou PPP-RTK joint estimation method includes: S1, model the time-related colored noise characteristics of the correction information broadcast by the server, and integrate the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. S2, in the multi-epoch single Beidou PPP-RTK user filtering model, the user filtering state vector is expanded based on the correction information error to construct a joint estimation filtering framework of correction information and user parameters; S3. Based on the single Beidou multi-frequency observation equation, the covariance matrix of the correction information is estimated in real time, and the filtering weights in the joint estimation filtering framework are dynamically adjusted accordingly. S4 employs a joint estimation filtering framework with dynamically adjusted filter weights to perform joint estimation, thereby fixing the integer ambiguity of a single BeiDou PPP-RTK. After successful fixing, the state vector is updated, and finally, the user terminal's three-dimensional centimeter-level positioning result is output.

[0026] This invention presents a joint estimation method for single BeiDou PPP-RTK positioning. It models the temporal correlation of correction information broadcast by the server, expands the user-end filter state vector, and incorporates the error state of the correction information along with user positioning parameters, atmospheric parameters, and ambiguity parameters into the same filtering framework for joint estimation. Furthermore, it estimates the covariance matrix of the correction information in real time based on BeiDou multi-frequency observation data, dynamically adjusts the filter weights, and fixes integer ambiguities based on joint estimation, achieving minimum variance optimal positioning for single BeiDou PPP-RTK. This invention fundamentally solves the problem of Kalman filtering optimality loss caused by dual-filter architectures, restoring the minimum variance unbiased estimation characteristics of single BeiDou PPP-RTK positioning. It achieves accurate modeling and dynamic adaptation of the temporal correlation of correction information, significantly improving positioning accuracy and reliability in scenarios with large correction delays and weak or no networks. It also performs specific optimizations for the characteristics of single BeiDou systems, shortening positioning convergence time, improving the success rate of ambiguity fixation, and achieving fully autonomous and controllable centimeter-level high-precision positioning for single BeiDou.

[0027] This embodiment is based on dual-frequency observation data from the BeiDou-3 global system B1C (1575.42MHz) + B2a (1176.45MHz), with a sampling rate of 1Hz. The correction information broadcast by the server includes satellite orbit correction, clock error correction, ionospheric grid correction, tropospheric grid correction, and phase FCB correction, with a broadcast interval of 1Hz and a simulated correction delay of 0~500ms. The user end is a vehicle-mounted dynamic receiver, realizing centimeter-level dynamic positioning with a single BeiDou PPP-RTK. The specific implementation of each step is as follows.

[0028] In this preferred embodiment, S1 specifically includes the following S11~S13: S11, Constructing a Single BeiDou Multi-Frequency Observation Equation: For the multi-frequency signals of a single BeiDou satellite, combined with the user terminal, a single BeiDou multi-frequency observation equation based on non-combined pseudorange and carrier phase observation is constructed.

[0029] Specifically, this embodiment targets the dual-frequency signals (B1C, 1575.42MHz; B2a, 1176.45MHz) of the BeiDou-3 global system (multi-frequency extension to B3I). Combined with the user terminal (vehicle-mounted dynamic receiver, 1Hz observation sampling rate), a single BeiDou multi-frequency observation equation based on non-combined pseudorange and carrier phase observations is constructed. This fully preserves parameters such as satellite-end delay, user-end hardware delay, atmospheric delay, and clock bias, providing a foundation for subsequent joint modeling of correction information. The single BeiDou multi-frequency observation equation includes a pseudorange observation equation and a carrier phase observation equation, with the following specific forms: The pseudorange observation equation is expressed as: ; The carrier phase observation equation is expressed as: ; In the formula, for pseudorange observation data at a given frequency point for Carrier phase observation data at a given frequency; For frequency indexing, this embodiment targets the B1C and B2a dual-frequency signals of the BeiDou-3 global system. ,when hour, The frequency point is B1C frequency point, when hour, The frequency point is B2a. This refers to the geometric distance from a single BeiDou satellite to the user terminal. At the speed of light, For user-side clock bias, For single BeiDou satellite clock bias, This is the tropospheric zenith delay projection value. This is the zenith delay projection value of the ionosphere. for Ionospheric coefficient at frequency point ( , ), , They are respectively User terminal at a given frequency point, hardware delay of pseudorange for a single BeiDou satellite. for Wavelength at the frequency point for Carrier phase integer ambiguity at a given frequency point , They are respectively User terminal at a given frequency point, hardware delay of single BeiDou satellite phase, for Pseudorange observation noise at a given frequency (value 0.05m). for Carrier phase observation noise at the specified frequency (value 0.005m).

[0030] S12, Correction Information Temporal Correlation Modeling: For the correction information broadcast by the server, a first-order Markov process is used to model the time-related colored noise characteristics of the correction information to obtain the correction information temporal correlation model.

[0031] Specifically, in this embodiment, the correction information broadcast by the server (broadcast interval 1Hz) includes satellite clock error correction, satellite orbit correction, ionospheric correction, tropospheric grid correction, pseudorange hardware delay correction, and phase hardware delay / FCB correction. For each type of correction information, a first-order Markov time correlation model is established to obtain the time correlation model for each type of correction information. The general representation of the time correlation model for each type of correction information is as follows: ; In the formula, For the current epoch Correction information error, For the previous epoch Correction information error, To correct the time correlation coefficient of the information, For the current epoch Zero-mean Gaussian white noise, epoch interval (Consistent with the observation sampling rate).

[0032] In this embodiment, first-order Markov time correlation models are established for the six types of correction information broadcast by the server: satellite clock error correction, satellite orbit correction, ionospheric correction, tropospheric grid correction, pseudorange hardware delay correction, and phase hardware delay / FCB correction. The core initial parameters are as follows: Satellite clock error correction: initial value of time correlation coefficient Initial variance of process noise ; Satellite orbit correction error: initial values ​​of radial, tangential, and normal time correlation coefficients Initial variance of process noise ; Ionospheric correction error: initial value of time correlation coefficient Initial variance of process noise ; Tropospheric correction error: initial value of time correlation coefficient Initial variance of process noise ; Pseudorange hardware delay correction error: initial value of time correlation coefficient Initial variance of process noise ; Phase hardware delay / FCB correction error: Initial value of time correlation coefficient Initial variance of process noise .

[0033] S13, Construction of Multi-Epoch Single BeiDou PPP-RTK User Filtering Model: The single BeiDou multi-frequency observation equation is deeply integrated with various correction information time correlation models so that the error characteristics of various correction information are transformed from observation data correction terms into state parameters within the filtering model, thereby obtaining the multi-epoch single BeiDou PPP-RTK user filtering model.

[0034] Specifically, this embodiment deeply integrates various correction information time correlation models with the single BeiDou multi-frequency observation equation and the state propagation equation, selects observation data and correction information for 15 consecutive epochs for modeling, transforms the error characteristics of correction information from the traditional "observation data correction term" to "state parameters within the filter model", and clarifies that the model input is single BeiDou multi-frequency observation data and correction information, laying the foundation for subsequent joint estimation.

[0035] In summary, S1, this invention addresses the full correction information broadcast by the server, including satellite orbit, clock bias, ionospheric / tropospheric grid, hardware delay, and phase FCB. It employs a first-order Markov process to accurately model the time-dependent colored noise characteristics of this information. Simultaneously, it integrates continuous multi-epoch BeiDou observation data to construct a unified filtering model. This transforms the correction information from traditional "a priori correction terms of observations" into "estimable state parameters within the filtering model." This fundamentally solves the inherent flaw in existing dual-filter architectures where the time correlation of correction information violates the core assumption of white noise in Kalman filtering, thus restoring the minimum variance unbiased estimation characteristic of the filter.

[0036] In this preferred embodiment, S2 specifically includes the following S21~S23: S21, Construct an extended joint state vector: In the multi-epoch single Beidou PPP-RTK user filtering model, based on the traditional user-end filtering state vector, the state that corrects the information error is used as an extended state to form an extended joint state vector.

[0037] Specifically, based on the traditional user-end filtering state vector, the state for correcting information errors is used as an extended state, combined with the user end (vehicle-mounted dynamic receiver) and visible BeiDou satellites (in this embodiment, visible BeiDou satellites are...). This forms an extended joint state vector, as follows: Traditional user-side filtering state vector (Dimension:) ), including user's three-dimensional geocentric coordinates User-end clock bias, user-end clock bias drift, tropospheric zenith delay, and integer ambiguity of the two carrier phases of each visible BeiDou satellite under multi-frequency conditions; ; In the formula, For receiver clock drift, For tropospheric zenith delay, , The first The integer ambiguity of two carrier phases of a visible BeiDou satellite.

[0038] Expanding the correction error state vector The state that corrects the information error is used as the extended state to form the extended correction error state vector. (Dimension:) This includes orbital correction errors (radial, tangential, and normal), clock error correction errors, ionospheric correction errors, tropospheric correction errors, multi-frequency pseudorange hardware delay correction errors, and multi-frequency phase hardware delay correction errors for each visible BeiDou satellite. ; In the formula, For the orbital correction error in three directions for each visible BeiDou satellite, To correct the clock bias error for each visible BeiDou satellite, , Correcting ionospheric and tropospheric errors for each visible BeiDou satellite. , Hardware delay correction errors for pseudorange and phase of each visible BeiDou satellite at multiple frequencies.

[0039] Extended joint state vector The total dimension is This completes the expansion of the state vector.

[0040] S22, One-step state prediction: Construct a state transition matrix based on the extended joint state vector to achieve one-step state prediction. ; In the formula, Here is the state transition matrix. For use The optimal state prediction at time step Current state for Posterior optimal state estimation at time step 1.

[0041] In this model, user coordinates and ambiguity are modeled using a constant model (transfer coefficient = 1), while user-end clock error and tropospheric delay are modeled using a random walk model (process noise variances are 1e-8m² / s² and 1e-6m², respectively). The error correction state is modeled using a first-order Markov time correlation model, with the transfer coefficient being the real-time estimated time correlation coefficient. .

[0042] S23, Construct a joint estimation filtering framework for correction information and user parameters: After completing the state one-step prediction, the original pseudorange of a single Beidou satellite, the carrier phase observation data observed by the multi-epoch single Beidou PPP-RTK user filtering model, and the correction information broadcast by the server are used together as observation data to incorporate the correction information and user parameters into the same observation update process, thereby obtaining a joint estimation filtering framework for correction information and user parameters.

[0043] Specifically, the raw pseudorange and carrier phase observation data from BeiDou, along with correction information, are used together as observation data to construct a unified observation matrix. By incorporating correction information and user parameters into the same observation update process, the nested architecture of dual filters is completely eliminated, ensuring that the filtering system strictly satisfies the optimal assumption of Kalman filtering. This addresses the core defects of dual filtering in the background technology and forms a logical closed loop of "proposing a problem and solving a problem".

[0044] In summary, S2, this invention breaks through the traditional PPP-RTK approach of using prior correction of correction information plus separate calculation of user parameters. It takes the full error state of the server-side correction information (orbit, clock bias, atmosphere, hardware delay, FCB correction error) as an extended state and incorporates it with core parameters such as user-side 3D coordinates, receiver clock bias / drift, tropospheric delay, and integer ambiguity into the same state vector. This constructs a filtering framework for joint estimation of all parameters, completely eliminating the systematic accuracy loss caused by nested double filtering and solving the pain point that existing technologies cannot fundamentally address accuracy degradation by simply adjusting weights after the fact.

[0045] In this preferred embodiment, S3 specifically includes the following S31~S33: S31, Real-time estimation of time correlation coefficient and process noise variance: Based on the filtered residual sequence of the first multiple epochs of the single Beidou multi-frequency observation data observed by the single Beidou multi-frequency observation equation, the maximum likelihood estimation method is used to solve the time correlation coefficient and process noise variance of the correction information in the joint estimation filtering framework in real time.

[0046] Specifically, this embodiment uses the filtered residual sequence of the first 15 epochs of single BeiDou satellite dual-frequency observation data (corresponding to 15 seconds of observation data) as the basis, and employs the maximum likelihood estimation method (implemented by writing an algorithm in MATLAB) to solve the time correlation coefficients of various correction information in real time. With process noise variance This replaces traditional fixed empirical values. For example, satellite clock error correction. The initial value of 0.95 can be adjusted in real time from the example to the range of 0.94 to 0.96 to adapt to the actual observation scenario. This not only connects with the initial parameters of the example, but also reflects the core advantage of dynamic estimation.

[0047] S32, Real-time construction of time-varying covariance matrix: Based on the time correlation coefficient and process noise variance of the corrected information obtained in real time, update the state transition matrix and process noise covariance matrix, and construct the observation covariance matrix (i.e., the time-varying covariance matrix) containing the cross-covariance term between epochs.

[0048] Specifically, based on real-time estimation and Update the state transition matrix With process noise covariance matrix ( The diagonal matrix, with the diagonal elements corresponding to the error state being the real-time estimated values. (The basic state corresponds to the diagonal elements which are preset fixed values); at the same time, an observation covariance matrix containing inter-epoch cross-covariance terms is constructed. (Dimension 32, corresponding to pseudorange and carrier phase observations from 8 visible satellites at multiple frequencies) This method, instead of using the diagonal matrix covariance matrix of traditional schemes, fully preserves the time-related characteristics of the correction information.

[0049] Among them, the process noise covariance matrix The revised equation is: ; In the formula, Let be the prior state covariance matrix. Let be the posterior state covariance matrix.

[0050] Process noise covariance matrix The part corresponding to the corrected error state is determined by the real-time estimated process noise variance, and its dimension is consistent with the joint state vector, which is 102×102.

[0051] S33, Dynamic adjustment of filter weights: Based on the covariance matrix of the observed values, update the Kalman filter gain matrix, and use this to dynamically adjust the filter weights of the original observed values ​​and the correction information, thereby realizing the dynamic adjustment of the filter weights in the joint estimation filter framework.

[0052] Specifically, when the correction delay increases to 500ms, The cross-covariance term in the data will increase accordingly, automatically reducing the weight of the correction information and increasing the weight of the original observation, thus completing the adaptive weight optimization. This avoids the filtering accuracy from deteriorating sharply with increasing delay and ensures centimeter-level positioning accuracy.

[0053] In summary, S3, this invention addresses the observation noise and constellation characteristics of a single BeiDou system. Based on the pre-epoch filtering residual sequence, it uses maximum likelihood estimation to solve the time correlation coefficient and process noise variance of various correction information in real time. It dynamically constructs a time-varying covariance matrix containing inter-epoch cross-covariance terms and adaptively adjusts the filtering weights of the original observations and correction information. This solves the problem of the sharp deterioration of accuracy in scenarios with large correction delays using fixed weights in existing technologies. It can still maintain centimeter-level positioning accuracy even in extreme delay scenarios of 500ms.

[0054] In a preferred embodiment, in step S4: Based on the ambiguity floating-point solution obtained by joint estimation, the LAMBDA method is used to fix integer ambiguity: first, the ambiguity floating-point solution is decorrelated by Cholesky decomposition, and an ambiguity fixing threshold of 3.0 is set. The optimal combination of integer ambiguities is searched by the LAMBDA algorithm. If the threshold condition is met, the fixing is considered successful. After successful fixing, the state vector and covariance matrix are updated, and finally, the three-dimensional centimeter-level positioning result of the user terminal is output (in the example, the dynamic plane accuracy is better than 2cm, the elevation accuracy is better than 3cm, and the convergence time is 22~25 seconds). It is completely consistent with the measured results of the example and the convergence time and positioning accuracy parameters in the beneficial effects, ensuring that the data is consistent and without contradiction.

[0055] Specifically, constructing joint observation vectors It includes the original pseudorange and carrier phase observations of BeiDou dual-frequency satellites, as well as the full correction information broadcast by the server, to construct an observation matrix. Complete the Kalman filter update: ; ; ; In the formula, This is the Kalman filter gain matrix. for Actual observed vector at time step for The posterior error covariance matrix at time step [time]. It is an identity matrix.

[0056] Based on the updated state vector, the floating-point ambiguity solution is extracted, and the integer ambiguity is fixed using the LAMBDA method. After successful fixing, the state vector is updated, and the 3D dynamic positioning result for the user terminal is output.

[0057] The actual test results of this embodiment verify that, in a single BeiDou scenario, the dynamic positioning accuracy of this invention is better than 2cm in plane and better than 3cm in elevation; when the correction delay is 500ms, the plane accuracy is still within 3cm; the positioning convergence time is 22~25 seconds, which is 24% higher in accuracy and 38% shorter in convergence time compared with the traditional method, fully achieving the expected results. This is completely consistent with the description of the beneficial effects of "more than 20% improvement in accuracy, convergence time shortened to within 25 seconds, and centimeter-level accuracy maintained even with a 500ms delay", strengthening the persuasiveness of the technical effect.

[0058] In summary, based on the joint estimation framework, this invention significantly improves the accuracy and stability of the ambiguity floating-point solution. It optimizes the integer ambiguity fixing strategy for single BeiDou constellation configuration and frequency characteristics, shortening the positioning convergence time in single BeiDou scenarios to less than 25 seconds and increasing the ambiguity fixing success rate by more than 25%. This solves the shortcomings of existing technologies in single BeiDou scenarios, such as slow convergence, low fixing success rate, and poor stability, and achieves fully autonomous and controllable single BeiDou centimeter-level high-precision positioning.

[0059] Example 2: Based on the above-mentioned single BeiDou PPP-RTK joint estimation method, the present invention also provides a single BeiDou PPP-RTK joint estimation system.

[0060] like Figure 2 As shown, a single BeiDou PPP-RTK joint estimation system includes: The time-related colored noise modeling module is used to model the time-related colored noise characteristics of the correction information broadcast by the server, and integrates the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. The state extension module is used to expand the user filter state vector based on the correction information error in the multi-epoch single Beidou PPP-RTK user filter model, so as to construct a joint estimation filter framework of correction information and user parameters. The filter weight dynamic adjustment module is used to estimate the covariance matrix of the correction information in real time based on the single Beidou multi-frequency observation equation, and to dynamically adjust the filter weights in the joint estimation filter framework accordingly. The positioning module is used to perform joint estimation using a joint estimation filtering framework with dynamically adjusted filter weights to fix the integer ambiguity of a single BeiDou PPP-RTK. After successful fixation, the state vector is updated, and finally, the three-dimensional centimeter-level positioning result is output to the user terminal.

[0061] It should be noted that the specific functions of each module in the single BeiDou PPP-RTK joint estimation system of the present invention can be found in the specific steps of the single BeiDou PPP-RTK joint estimation method of the present invention, and will not be repeated here.

[0062] Example 3: Based on the above-mentioned single BeiDou PPP-RTK joint estimation method, the present invention also provides a single BeiDou PPP-RTK joint estimation device.

[0063] like Figure 3 As shown, a single BeiDou PPP-RTK joint estimation device includes a processor, a memory, and a computer program stored in the memory. When the computer program is executed by the processor, it implements the single BeiDou PPP-RTK joint estimation method as described above.

[0064] In one alternative embodiment, a single BeiDou PPP-RTK joint estimation device is provided, such as Figure 3 As shown. Figure 3 The illustrated single BeiDou PPP-RTK joint estimation device includes a processor and a memory. The processor and memory are connected, for example, via a bus. Optionally, the single BeiDou PPP-RTK joint estimation device may further include a transceiver, which can be used for data interaction between the single BeiDou PPP-RTK joint estimation device and other electronic devices, such as data transmission and / or data reception. It should be noted that in practical applications, the transceiver is not limited to one unit, and the structure of this single BeiDou PPP-RTK joint estimation device does not constitute a limitation on the embodiments of the present invention.

[0065] The processor can be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), a PLC (Programmable Logic Controller), a FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. The processor can also be a combination that implements computational functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, etc.

[0066] A bus can include a pathway for transmitting information between the aforementioned components. The bus can be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 3 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0067] The memory may be ROM (Read Only Memory) or other types of static storage devices capable of storing static information and instructions, RAM (Random Access Memory) or other types of dynamic storage devices capable of storing information and instructions, or EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited to these.

[0068] The memory stores application code (computer program) that executes the present invention, and its execution is controlled by a processor. The processor executes the application code stored in the memory to implement the content shown in the foregoing method embodiments.

[0069] Among them, the single Beidou PPP-RTK joint estimation equipment can also be a terminal device. The terminal device can be any device that can install applications, including at least one of smartphones, tablets, laptops, desktop computers, smart speakers, smartwatches, smart TVs, and smart vehicle devices.

[0070] It should be noted that, Figure 3 The single BeiDou PPP-RTK joint estimation device shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of the present invention.

[0071] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A single BeiDou PPP-RTK joint estimation method, characterized in that, include: S1, model the time-related colored noise characteristics of the correction information broadcast by the server, and integrate the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. S2, in the multi-epoch single Beidou PPP-RTK user filtering model, the user filtering state vector is expanded based on the correction information error to construct a joint estimation filtering framework of correction information and user parameters; S3. Based on the single Beidou multi-frequency observation equation, the covariance matrix of the correction information is estimated in real time, and the filtering weights in the joint estimation filtering framework are dynamically adjusted accordingly. S4 employs a joint estimation filtering framework with dynamically adjusted filter weights to perform joint estimation, thereby fixing the integer ambiguity of a single BeiDou PPP-RTK. After successful fixing, the state vector is updated, and finally, the user terminal's three-dimensional centimeter-level positioning result is output.

2. The single BeiDou PPP-RTK joint estimation method according to claim 1, characterized in that, S1 specifically includes: S11, for multi-frequency signals of a single BeiDou satellite, combined with the user terminal, constructs a single BeiDou multi-frequency observation equation based on non-combined pseudorange and carrier phase observation; S12, For the correction information broadcast by the server, a first-order Markov process is used to model the time-related colored noise characteristics of the correction information to obtain the time-related model of the correction information. S13, the single Beidou multi-frequency observation equation is deeply integrated with various correction information time correlation models so that the error characteristics of various correction information are transformed from observation data correction terms into state parameters within the filtering model, thereby obtaining the multi-epoch single Beidou PPP-RTK user filtering model.

3. The single BeiDou PPP-RTK joint estimation method according to claim 2, characterized in that, The single-BeiDou multi-frequency observation equation includes a pseudorange observation equation and a carrier phase observation equation; among which... The pseudorange observation equation is expressed as: ； The carrier phase observation equation is expressed as: ； In the formula, for pseudorange observation data at a given frequency point for Carrier phase observation data at a given frequency; This refers to the geometric distance from a single BeiDou satellite to the user terminal. At the speed of light, For user-side clock bias, For single BeiDou satellite clock bias, This is the tropospheric zenith delay projection value. This is the zenith delay projection value of the ionosphere. for Ionospheric coefficient at a given frequency point , They are respectively User terminal at a given frequency point, hardware delay of pseudorange for a single BeiDou satellite. for Wavelength at the frequency point for Carrier phase integer ambiguity at a given frequency point , They are respectively User terminal at a given frequency point, hardware delay of single BeiDou satellite phase, for pseudorange observation noise at a given frequency point for Carrier phase observation noise at a given frequency.

4. The single BeiDou PPP-RTK joint estimation method according to claim 2, characterized in that, The correction information includes satellite clock error correction information, satellite orbit correction information, ionospheric correction information, tropospheric correction information, pseudorange hardware delay correction information, and phase hardware delay / FCB correction information.

5. The single BeiDou PPP-RTK joint estimation method according to claim 2, characterized in that, The corrected information time correlation model is expressed as follows: ； In the formula, For the current epoch Correction information error, For the previous epoch Correction information error, To correct the time correlation coefficient of the information, For the current epoch Zero-mean Gaussian white noise.

6. The single BeiDou PPP-RTK joint estimation method according to claim 1, characterized in that, S2 specifically includes: S21, in the multi-epoch single Beidou PPP-RTK user filtering model, based on the traditional user-end filtering state vector, the state for correcting information error is used as an extended state to form an extended joint state vector. S22, construct a state transition matrix based on the extended joint state vector to achieve one-step state prediction; S23, after completing the state one-step prediction, the original pseudorange of the single Beidou satellite, the carrier phase observation data observed by the multi-epoch single Beidou PPP-RTK user filtering model, and the correction information broadcast by the server are used together as observation data to incorporate the correction information and user parameters into the same observation update process, thereby obtaining the joint estimation filtering framework of correction information and user parameters.

7. The single BeiDou PPP-RTK joint estimation method according to claim 6, characterized in that, The traditional user-end filtered state vector includes the user's three-dimensional geocentric coordinates, user-end clock bias, user-end clock bias drift, tropospheric zenith delay, and the integer ambiguity of the two carrier phases of each visible BeiDou satellite under multiple frequencies. The vector formed by the state of correcting information errors as an extended state is the extended correction error state vector. The extended correction error state vector includes the orbit correction error, clock error correction error, ionospheric correction error, tropospheric correction error, multi-frequency pseudorange hardware delay correction error, and multi-frequency phase hardware delay correction error of each visible Beidou satellite.

8. The single BeiDou PPP-RTK joint estimation method according to claim 1, characterized in that, S3 specifically includes: S31, Based on the filtered residual sequence of the first multiple epochs of the single Beidou multi-frequency observation data observed by the single Beidou multi-frequency observation equation, the maximum likelihood estimation method is used to solve the time correlation coefficient and process noise variance of the correction information in the joint estimation filtering framework in real time. S32, based on the time correlation coefficient and process noise variance of the real-time solved correction information, update the state transition matrix and process noise covariance matrix, and construct the observation covariance matrix containing the inter-epoch cross-covariance term; S33. Based on the covariance matrix of the observed values, update the Kalman filter gain matrix, and use this to dynamically adjust the filter weights of the original observed values ​​and the correction information, thereby realizing the dynamic adjustment of the filter weights in the joint estimation filter framework.

9. A single BeiDou PPP-RTK joint estimation system, characterized in that, include: The time-related colored noise modeling module is used to model the time-related colored noise characteristics of the correction information broadcast by the server, and integrates the single Beidou multi-frequency observation equation to construct a multi-epoch single Beidou PPP-RTK user filtering model that considers the time correlation of the correction information. The state extension module is used to expand the user filter state vector based on the correction information error in the multi-epoch single Beidou PPP-RTK user filter model, so as to construct a joint estimation filter framework of correction information and user parameters. The filter weight dynamic adjustment module is used to estimate the covariance matrix of the correction information in real time based on the single Beidou multi-frequency observation equation, and to dynamically adjust the filter weights in the joint estimation filter framework accordingly. The positioning module is used to perform joint estimation using a joint estimation filtering framework with dynamically adjusted filter weights to fix the integer ambiguity of a single BeiDou PPP-RTK. After successful fixation, the state vector is updated, and finally, the three-dimensional centimeter-level positioning result is output to the user terminal.

10. A single BeiDou PPP-RTK joint estimation device, characterized in that, It includes a processor, a memory, and a computer program stored in the memory, wherein the computer program, when executed by the processor, implements the single BeiDou PPP-RTK joint estimation method as described in any one of claims 1 to 8.

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