Method and system for improving wide-lane ambiguity fixing success rate of compass dual-frequency positioning

Abstract

This invention discloses a method and system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning, belonging to the field of high-precision positioning technology. It solves the problems of existing methods being unable to adapt to dynamic changes in observation quality, suffering from old information contamination, and difficulties in setting the smoothing window length. The method includes: constructing a MW combined observation model for BeiDou dual-frequency positioning; establishing a time-decay-based weight allocation function to recursively smooth the wide-lane ambiguity floating-point solution sequence; performing integer fixing and reliability verification based on the smoothed wide-lane ambiguity floating-point solution estimate; and dynamically adjusting the exponential weighting factor according to the measurement residual to achieve adaptive smoothing. This invention introduces a time-decaying weight function to give higher weight to recent observations and establishes a recursive update model. Simultaneously, it introduces a residual-driven dynamic decay factor adjustment mechanism, effectively improving the reliability and timeliness of wide-lane ambiguity fixation in BeiDou dual-frequency positioning.

Description

Technical Field

[0001] This invention belongs to the field of high-precision positioning technology, specifically relating to a method and system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. Background Technology

[0002] In the field of high-precision positioning technology for Global Navigation Satellite System (GNSS), the rapid and accurate fixation of carrier phase integer ambiguities is one of the core issues in achieving high-precision positioning. In particular, the Melbourne-Wubbena (MW) combination is widely used in BeiDou dual-frequency wide-lane ambiguity fixation to extract wide-lane ambiguities. The MW combination, by linearly combining pseudorange observations with carrier phase observations, can effectively eliminate first-order error terms such as ionospheric delay and geometric distance, thereby extracting the wide-lane ambiguities.

[0003] However, pseudorange observations themselves have significant observation noise; typically, the estimated noise level of a single-epoch wide-lane ambiguity can reach over 0.5 epochs. Due to this high noise level, directly performing rounding and fixing operations on the wide-lane ambiguity is difficult and has a low success rate.

[0004] To improve this situation, traditional methods typically employ multi-epoch smoothing techniques to reduce noise in wide-lane ambiguity estimates. Common multi-epoch smoothing methods include: Arithmetic average method: This method involves summing all historical wide-lane ambiguity floating-point solutions up to the current epoch with equal weights and then averaging them. While simple and intuitive, this method assigns the same weight to all historical information, making it unsuitable for adapting to dynamic changes in observation quality.

[0005] Recursive averaging: This method sets a fixed smoothing window length M and performs equal-weighted averaging only on the epochs within the window. This method can reduce noise to some extent, but it still cannot dynamically adjust the weights.

[0006] Sliding window averaging: Similar to recursive averaging, but in practice, it usually involves recalculating the arithmetic mean of all data within the window. This method also suffers from the problem of assigning equal weight to historical information, making it unsuitable for adapting to dynamic changes in observation quality.

[0007] Hatch filtering: This is a classic recursive smoothing algorithm, originally used for phase smoothing pseudorange. In wide-lane solutions, Hatch filtering is often used to smooth pseudorange observations in MW combinations, indirectly obtaining a more stable wide-lane ambiguity estimate, but it is difficult to achieve adaptive smoothing.

[0008] Stellar daily filtering: For static or periodically repetitive observation scenarios such as deformation monitoring, by identifying and weakening multipath errors that are strongly correlated with satellite geometry, the success rate of wide-lane ambiguity fixation can be improved to some extent, but adaptive smoothing is still not achieved.

[0009] Although these traditional methods can improve the reliability of wide-lane ambiguity fixation to some extent, they have the following main drawbacks: (1) they assign the same weight to all historical information, which cannot adapt to dynamic changes in observation quality (such as changes in satellite elevation angle, sudden changes in multipath effects, cycle slips, etc.); (2) when observation conditions change abruptly, old information will continue to contaminate the current solution results, resulting in slow convergence speed and decreased reliability; (3) the smoothing window length needs to be preset, making it difficult to balance convergence speed and smoothing effect. In response to the above problems, we propose a method and system for improving the success rate of wide-lane ambiguity fixation using BeiDou dual-frequency positioning. Summary of the Invention

[0010] The purpose of this invention is to address the shortcomings of existing technologies by providing a method and system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. This solves the problems of existing methods being unable to adapt to dynamic changes in observation quality, having old information contamination, and having difficulty in setting the smooth window length.

[0011] This invention is implemented as follows: a method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning, the method comprising: A combined observation model for BeiDou dual-frequency positioning was constructed to calculate the wide-lane ambiguity floating-point solution for each epoch. Design an exponentially weighted recursive smoothing factor and establish a weight allocation function based on time decay; A multi-epoch exponential weighted recursive smoothing model is constructed to recursively smooth the wide-lane ambiguity floating-point solution sequence, and obtain the smoothed wide-lane ambiguity floating-point solution estimate. Based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixed and reliability checks are performed to obtain the smoothed wide-lane ambiguity fixed solution, and the measurement residual is calculated; and The exponential weighting factor is dynamically adjusted based on the measurement residual to achieve adaptive smoothing and improve the success rate of wide-lane ambiguity fixation for BeiDou dual-frequency positioning.

[0012] Preferably, the MW combined observation model for BeiDou dual-frequency positioning is constructed as follows:

[0013] The wide-lane ambiguity floating-point solution for each epoch is calculated as follows:

[0014] in, , These are the carrier phase observations at frequency points 1 and 2, respectively, at the k-th epoch; , These correspond to pseudorange observations; , For the corresponding carrier wavelength, For wide-lane wavelength, The speed of light; , Frequency point 1 and frequency point 2; , These are the ambiguity of the wide alleyway in the k-th epoch and its corresponding floating-point solution.

[0015] Preferably, the exponentially weighted recursive smoothing factor Then the weight coefficient for the k-th epoch is The normalized weights satisfy: .

[0016] Preferably, the multi-epoch exponential weighted recursive smoothing model is expressed as: When the initial epoch k=1, ; Recursive update, when k is greater than or equal to 2, ; in, The estimated value of the wide-lane ambiguity floating-point solution after smoothing in the k-th epoch. Let be the wide-lane ambiguity floating-point solution for the k-th epoch; For smoothing gain.

[0017] Preferably, smoothing gain The following determinations are made: When k is greater than the preset epoch iteration threshold, tending to a constant The value is 0.3.

[0018] Preferably, the method for dynamically adjusting the exponential weighting factor based on the measurement residual includes: The innovation bias is calculated and expressed as:

[0019] Construct residual statistics, which are expressed as follows:

[0020] Where M is the length of the statistical window; Based on the residual statistics, the attenuation factor is dynamically adjusted using the following formula:

[0021] in, The baseline attenuation factor; This is the residual threshold.

[0022] Preferably, a piecewise function is used to dynamically adjust the attenuation factor, and the dynamic adjustment of the attenuation factor is based on the following formula:

[0023] in, The baseline attenuation factor; The residual threshold, This is the adjustment coefficient.

[0024] Preferably, when performing integer fixing and reliability verification based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixing adopts rounding or LAMBDA search method, and reliability verification adopts fixed success rate or Ratio value index.

[0025] Preferably, when constructing the MW combination observation model for BeiDou dual-frequency positioning, the BeiDou dual-frequency combination includes frequency point combinations of B1C / B2a, B1I / B3I, B1I / B2I, B1C / B3I, and B1I / B2a.

[0026] On the other hand, the present invention also provides a system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning, wherein the system specifically includes: The observation data acquisition unit is used to acquire raw BeiDou dual-frequency observation data; The preprocessing unit is used for cycle slip detection and repair to generate double-difference observations; The single-epoch solution unit is used to calculate the wide-lane ambiguity floating-point solution for each epoch based on the MW combined model. The exponentially weighted smoothing unit is used to perform exponentially weighted recursive smoothing on the wide-lane ambiguity floating-point solution sequence to obtain the smoothed wide-lane ambiguity floating-point solution estimate. The ambiguity fixing unit is used to fix the integer value and verify the reliability of the smoothed wide-lane ambiguity floating-point solution estimate. The output unit is used to output the fixed width ambiguity and positioning results.

[0027] Compared with the prior art, the embodiments of this application have the following main advantages: This invention introduces a weight function that decays over time, giving higher weight to recent observations and establishing a recursive update model. It also introduces a residual-driven dynamic decay factor adjustment mechanism to achieve adaptive smoothing, effectively improving the reliability and timeliness of ambiguity fixation.

[0028] In this embodiment of the invention, the MW combined observation model for BeiDou dual-frequency positioning first acquires raw observation data based on a GNSS receiver. Then, cycle slip detection and repair ensure the continuity and reliability of carrier phase observations. Furthermore, double-difference observations are generated to effectively eliminate common errors such as satellite clock bias and receiver clock bias, thereby significantly improving the quality and availability of the observation data. Based on this, MW combined observation equations are constructed using epoch-correlated dual-frequency observation data. Linear combination eliminates first-order error terms such as ionospheric delay, accurately extracts wide-lane ambiguity floating-point solutions, and finally outputs high-precision, low-noise wide-lane ambiguity floating-point solutions for each epoch. This lays a solid foundation for subsequent smoothing and ambiguity fixing, effectively improving the accuracy, reliability, and stability of wide-lane ambiguity estimation overall.

[0029] This invention employs an exponentially weighted recursive smoothing mechanism. By introducing a weight function that decays over time, recent observations receive higher weights, while the weights of historical observations decay exponentially. This weight allocation method better adapts to dynamic changes in observation conditions, such as satellite elevation angle variations, multipath effect fluctuations, and signal obstruction. Compared to traditional equal-weight smoothing methods that assign equal weights to all historical information, this invention effectively reduces the contamination of current solution results by older, low-quality observations, significantly improving the reliability of wide-lane ambiguity fixation. Furthermore, this method is not only applicable to double-difference wide-lane ambiguity processing but can also be extended to non-difference and single-difference ambiguity smoothing, and is compatible with various BeiDou dual-frequency point combinations such as B1I / B2I, B1C / B2a, and B1I / B3I, demonstrating broad applicability.

[0030] In this embodiment of the invention, when recursively smoothing the wide-lane ambiguity floating-point solution sequence, a multi-epoch exponential weighted recursive smoothing model is initialized. The wide-lane ambiguity floating-point solution of the first epoch is directly used as the initial smoothing value and the smoothing gain is initialized, laying a stable foundation for subsequent recursive calculations. Secondly, by establishing a recursive update framework, subsequent epochs with k≥2 can be efficiently updated based on historical smoothing values ​​and current information, avoiding the repeated storage and calculation of long-sequence historical data in traditional methods. Furthermore, by determining the relationship between smoothing gain and attenuation factor, two implementation schemes are provided: an accurate recursive form and a steady-state approximation form. The time-varying gain can be selected according to accuracy requirements to achieve better convergence characteristics, or a constant gain can be selected according to real-time requirements to simplify the calculation process. Based on this, a smoothing gain is calculated using a decay factor, and the current observation value is fused with the historical smoothed value epoch by epoch. This gives recent observation values ​​higher weight while effectively suppressing the accumulation of historical noise, generating a high-quality floating-point estimate of the smoothed wide-lane ambiguity. The method has a compact overall process and is computationally efficient. It not only significantly reduces memory usage and computational complexity, but also achieves adaptation to dynamic changes in observation conditions through an exponential weighting mechanism. This invention adopts a recursive smoothing model and achieves exponential weighting through smoothing gain. It does not require explicit calculation and storage of weight coefficients for each epoch, nor does it require saving long-sequence historical observation data. It has low computational complexity and small memory usage, making it suitable for real-time dynamic positioning applications with limited computing resources, and ensuring the real-time performance of positioning solutions.

[0031] This invention introduces a residual-driven adaptive factor adjustment mechanism. By monitoring the residual statistics in real time, the exponentially weighted attenuation factor is dynamically adjusted. When the observation quality decreases or the residual increases, the system automatically reduces the attenuation factor, lowers the weight of historical information, improves the response speed of current information, and avoids the continuous contamination of the current solution by old information. This adaptive adjustment mechanism can respond quickly when the observation conditions change abruptly and maintain smoothness when the observation conditions are stable. It effectively balances the contradiction between real-time performance and reliability, and solves the technical problems of the difficulty in presetting the smoothing window length and the difficulty in balancing convergence speed and smoothing effect in traditional methods. Compared with traditional equal-weight smoothing, it can shorten the ambiguity fixing convergence time and improve the timeliness of Beidou dual-frequency wide-lane ambiguity fixing. Attached Figure Description

[0032] Figure 1 This is a schematic diagram illustrating the implementation process of a method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning according to an embodiment of the present invention.

[0033] Figure 2 A schematic diagram illustrating the implementation process of constructing a MW combined observation model for BeiDou dual-frequency positioning is shown.

[0034] Figure 3A schematic diagram illustrating the implementation process of establishing a time-decay-based weight allocation function is shown.

[0035] Figure 4 The diagram illustrates the implementation flow of the recursive smoothing method for the floating-point solution sequence of wide-lane ambiguity provided in an embodiment of the present invention.

[0036] Figure 5 A schematic diagram of the implementation process of the method for calculating measurement residuals is shown.

[0037] Figure 6 A schematic diagram of the system structure for improving the success rate of wide-lane ambiguity fixation using BeiDou dual-frequency positioning is shown. Implementation

[0038] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs; the terminology used herein in the specification of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application; the terms "comprising" and "having," and any variations thereof, in the specification, claims, and foregoing drawings of this application are intended to cover non-exclusive inclusion. The terms "first," "second," etc., in the specification, claims, or foregoing drawings of this application are used to distinguish different objects, not to describe a particular order.

[0039] Existing methods cannot adapt to dynamic changes in observation quality, suffer from contamination by old information, and face difficulties in setting the smoothing window length. To address these issues, we propose a method and system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. In short, the method first constructs a BeiDou dual-frequency positioning MW combined observation model, calculates the wide-lane ambiguity floating-point solution for each epoch, establishes a time-decay-based weight allocation function, recursively smooths the sequence of wide-lane ambiguity floating-point solutions, and obtains the smoothed wide-lane ambiguity floating-point solution estimate. Based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixing and reliability verification are performed. The exponential weighting factor is dynamically adjusted according to the measurement residuals to achieve adaptive smoothing. This invention introduces a time-decaying weight function to give higher weight to recent observations and establishes a recursive update model. Simultaneously, it introduces a residual-driven dynamic decay factor adjustment mechanism to achieve adaptive smoothing, effectively improving the reliability and timeliness of ambiguity fixation.

[0040] This invention provides a method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. Figure 1 The diagram illustrates the implementation process of a method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. The method specifically includes: S10, construct the MW combined observation model for BeiDou dual-frequency positioning, and calculate the wide-lane ambiguity floating-point solution for each epoch; In embodiments of the present invention, such as Figure 2 As shown, the method for constructing the MW combined observation model for BeiDou dual-frequency positioning specifically includes: S101 is based on a GNSS receiver that receives information from BeiDou satellites and analyzes the information to obtain raw BeiDou dual-frequency observation data; S102, acquire BeiDou dual-frequency raw observation data, perform cycle slip detection and repair on the BeiDou dual-frequency raw observation data to ensure carrier phase continuity; S103, based on cycle slip detection and repair results, double-difference observations are generated to eliminate common errors such as clock error; S104, The MW combined observation equation for constructing the MW combined observation model based on the BeiDou dual-frequency raw observation data associated with epoch frequency points, wherein the BeiDou dual-frequency raw observation data associated with epoch frequency points includes, but is not limited to, the carrier phase observation value, frequency point frequency, and pseudorange observation value of the epoch frequency points. S105, solves the wide-lane ambiguity floating-point solution based on the MW combined observation equation, and outputs the wide-lane ambiguity floating-point solution for each epoch; According to one implementation, in BeiDou dual-frequency high-precision positioning, the rapid and accurate fixation of carrier phase integer ambiguity is one of the core issues in achieving high-precision positioning. Wide-lane ambiguity (WL) is a linear combination between two carrier phase observations of different frequencies, and its wavelength is longer and easier to fix. The Melbourne-Wubbena (MW) combination is a commonly used classic method at present. By linearly combining pseudorange and carrier phase observations, it eliminates first-order error terms such as ionospheric delay and geometric distance, thereby extracting wide-lane ambiguity. When constructing the MW combination observation model for BeiDou dual-frequency positioning, the original carrier phase and pseudorange observation data are obtained from the BeiDou receiver. However, these data may contain anomalies such as cycle slips, which will seriously affect subsequent high-precision processing. Therefore, cycle slip detection and repair of these original observation data are required to ensure the continuity and accuracy of the carrier phase observations. Then, by constructing double-difference observations, the common errors at the satellite end and the receiver end are eliminated or significantly reduced. Cycle slip detection and repair are performed on the original BeiDou observation data to form double-difference observations to eliminate errors at the satellite end and the receiver end.

[0041] The MW combined observation equation of the MW combined observation model is expressed as:

[0042] In this embodiment of the invention, the MW combined observation model (i.e., the wide-lane ambiguity calculation formula) for BeiDou dual-frequency positioning is constructed as follows:

[0043] The wide-lane ambiguity floating-point solution for each epoch is calculated as follows:

[0044] in, , These are the carrier phase observations at frequency points 1 and 2, respectively, at the k-th epoch; , These correspond to pseudorange observations; , For the corresponding carrier wavelength, For wide-lane wavelength, The speed of light; , Frequency point 1 and frequency point 2; , These are the ambiguity of the wide alleyway in the k-th epoch and its corresponding floating-point solution.

[0045] In this embodiment of the invention, the original BeiDou observation data includes, but is not limited to, dual-frequency carrier phase and pseudorange observations and frequency information. The MW (Melbourne-Wubbena) combination constructs a wide-lane ambiguity observation model through a linear combination of pseudorange and carrier phase. The significance of this combination lies in using a specific weighted combination of dual-frequency observations to eliminate frequency-independent error terms such as the first-order ionospheric delay, geometric distance, and tropospheric delay, thereby directly extracting wide-lane ambiguity information. The wide-lane ambiguity floating-point solutions calculated at each epoch are then formed into a time series, which serves as the input data for subsequent exponentially weighted recursive smoothing.

[0046] In this embodiment of the invention, the MW combined observation model for BeiDou dual-frequency positioning first acquires raw observation data based on a GNSS receiver. Then, cycle slip detection and repair ensure the continuity and reliability of carrier phase observations. Furthermore, double-difference observations are generated to effectively eliminate common errors such as satellite clock bias and receiver clock bias, thereby significantly improving the quality and availability of the observation data. Based on this, MW combined observation equations are constructed using epoch-correlated dual-frequency observation data. Linear combination eliminates first-order error terms such as ionospheric delay, accurately extracts wide-lane ambiguity floating-point solutions, and finally outputs high-precision, low-noise wide-lane ambiguity floating-point solutions for each epoch. This lays a solid foundation for subsequent smoothing and ambiguity fixing, effectively improving the accuracy, reliability, and stability of wide-lane ambiguity estimation overall.

[0047] S20, design an exponentially weighted recursive smoothing factor and establish a weight allocation function based on time decay; In GNSS positioning, observation conditions (such as satellite elevation angle, multipath effect, and signal obstruction) change over time, leading to inconsistent observation noise levels at different epochs. If all historical observations are assigned the same weight, old data will contaminate the current smoothing result, thus reducing the success rate of fixation. This invention addresses this by using an exponentially weighted recursive smoothing factor to control weight decay, ensuring that recent high-quality observations have higher weights and older low-quality observations have lower weights, thereby more accurately reflecting the current true ambiguity state. In this embodiment, the exponentially weighted recursive smoothing factor is designed as follows: [Define the exponentially weighted recursive smoothing factor...] Then the weight coefficient for the k-th epoch is The normalized weights satisfy:

[0048] Equivalent time constant: ,in The sampling interval is... The larger the value, the slower the historical information decays. Recursive smoothing does not require explicit calculation of weights; instead, it smooths the gain. accomplish; In this embodiment of the invention, a reference attenuation factor can be set. =0.7, corresponding to the time constant Approximately 2.8s, smoothing window length M=10, residual threshold =0.15 weeks.

[0049] Specifically, the Exponentially Weighted Recursive Smoothing Factor is a parameter used for dynamically weighted smoothing of multi-epoch (multiple time points) observation data. The Exponentially Weighted Recursive Smoothing Factor assigns weights to historical observations that decay over time and updates the smoothing results epoch-by-epoch based on a recursive formula. This suppresses observation noise while rapidly responding to changes in current observations, thereby improving the accuracy and real-time performance of data smoothing. In this embodiment of the invention, the constant between 0 and 1 in the Exponentially Weighted Recursive Smoothing Factor is called the Exponential Weighting Factor or Smoothing Factor, used to control the decay rate of historical observations. It should be noted that the Exponentially Weighted Recursive Smoothing Factor can also be understood as a decay factor.

[0050] Figure 3 The diagram illustrates the implementation process of establishing a time-decay-based weight allocation function. Specifically, establishing the time-decay-based weight allocation function includes: S201 defines an exponentially weighted recursive smoothing factor, establishes a weight allocation function based on the exponentially weighted recursive smoothing factor, and determines the weight coefficient for the k-th epoch based on the weight allocation function. The core of exponentially weighted recursive smoothing is that the weight of historical observations decays exponentially with time (or epoch), meaning the weight of more recent epochs is larger, and the weight of more distant epochs is smaller. For the k-th epoch, a corresponding weight coefficient is defined. By defining the exponentially weighted recursive smoothing factor, establishing the weight allocation function, and determining the weight coefficient for the k-th epoch, the exponential decay of the weight of historical observations over time is achieved. This ensures that the weight of more recent epochs is larger, and the weight of more distant epochs is smaller, accurately reflecting the timeliness of the observation data. In wide-lane ambiguity fixing for BeiDou dual-frequency positioning, recent wide-lane ambiguity floating-point solutions are often influenced by current observation conditions and better represent the current situation. Giving them higher weights allows the smoothing results to more closely follow actual changes, thereby improving the responsiveness of wide-lane ambiguity fixing to current observations and enhancing the reliability of the fixing results. Specifically, when determining the weight coefficients for the k-th epoch based on the weight allocation function, the weight coefficients for the k-th epoch are: In this embodiment of the invention, the weight allocation function is used to determine the weight of each epoch observation data in the overall calculation when processing multi-epoch observation data. In the method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning, the aim is to smooth the wide-lane ambiguity floating-point solution sequence. By reasonably allocating the weights of the wide-lane ambiguity floating-point solutions of each epoch, the influence of recent observations on the smoothing results is made greater, thereby better adapting to the dynamic changes in observation conditions and improving the reliability of wide-lane ambiguity fixation. Using a targeted weight allocation method can better adapt to the dynamic changes in observation conditions, such as real-time changes in satellite elevation angles and sudden changes in multipath effects. By focusing on recent data, the impact of these dynamic changes on wide-lane ambiguity can be captured more effectively, thereby improving the reliability of wide-lane ambiguity fixation. S202: Obtain the weight coefficients for the k-th epoch. Perform weight normalization on these coefficients. Since the original weights for the k-th epoch increase (or decrease) exponentially with k, they need to be normalized so that the sum of weights within a certain window (or infinite epochs) is 1. This facilitates subsequent smoothing calculations. By performing weight normalization, the sum of weights within a certain window (or infinite epochs) is made 1, transforming the weights into relative proportions. This avoids computational complexity and accuracy issues caused by excessively large or small weight values. This allows for simpler and more efficient calculations in subsequent smoothing operations, reducing computational load, improving computational efficiency, and also reducing computational errors, ensuring the accuracy of the smoothing results. S203, to more intuitively describe the decay rate of historical information, an equivalent time constant is introduced. This transforms exponential decay into an equivalent time constant on a time scale, thus quantifying the decay rate. A larger equivalent time constant results in slower historical information decay and a longer equivalent smoothing window; conversely, a smaller equivalent time constant results in faster historical information decay and a more sensitive system response. By quantifying the decay rate, the equivalent time constant can be flexibly adjusted according to different observation environments and needs, thereby achieving precise control over the smoothing effect. When observation conditions are relatively stable, the equivalent time constant can be appropriately increased to allow historical information to play a greater role and improve the stability of the smoothing results. When observation conditions change abruptly, the equivalent time constant can be decreased, enabling the system to respond more quickly to changes in the current observation data and ensuring the timeliness and accuracy of wide-lane ambiguity fixation. S204, to avoid explicitly calculating and storing the weight coefficients for each epoch, adopts a recursive approach to achieve exponential weighted smoothing, and uses smoothing gain for recursive updates, thereby simplifying the computation and eliminating the need to calculate and store the weight coefficients for each epoch separately, significantly reducing computational load and memory requirements. In scenarios with limited computational resources, such as real-time dynamic positioning, this simplified calculation method improves computational efficiency, ensuring the system can process large amounts of observation data in real time and obtain smoothed results for wide-lane ambiguities promptly. When a new wide-lane ambiguity floating-point solution is added, only a simple calculation based on the current smoothing gain and the smoothing result of the previous epoch is needed to obtain the new smoothed result, without recalculating the weights for all epochs or performing complex calculations. This real-time update capability allows the system to track changes in wide-lane ambiguity in a timely manner, improving the timeliness of wide-lane ambiguity fixation. S205, Auxiliary Parameter Configuration and Threshold Constraints: To balance smoothing effect and response speed, auxiliary parameters such as smoothing window length and residual threshold are set. The smoothing window length limits the number of epochs participating in smoothing, preventing the introduction of outdated information from excessively long historical data. The residual threshold is used to determine the consistency of ambiguity after smoothing; if the residual exceeds the threshold, the smoothing process is reset or abnormal epochs are removed. By setting auxiliary parameters such as smoothing window length and residual threshold, a balance can be struck between smoothing effect and response speed. The smoothing window length limits the number of epochs participating in smoothing, preventing the introduction of outdated information from excessively long historical data. When observation conditions change, excessively long historical data may contain information inconsistent with the current situation, affecting the accuracy of the smoothing results. By reasonably setting the smoothing window length, only the most recent and relevant epoch data can be considered, improving the adaptability of the smoothing results to the current situation. S206, Parameter Verification and Optimization: This section verifies the accuracy, stability, and response speed of the smoothed wide-lane ambiguity floating-point solution. Based on the verification results, parameters are iteratively optimized to ensure that the exponentially weighted recursive smoothing can both suppress noise and promptly track the true changes in ambiguity. Specifically, verifying the accuracy, stability, and response speed of the smoothed wide-lane ambiguity floating-point solution allows for a comprehensive evaluation of the effectiveness of the exponentially weighted recursive smoothing method. Accuracy verification ensures that the smoothing result accurately reflects the true value of the wide-lane ambiguity, reducing the impact of noise. Stability verification guarantees that the smoothing result will not fluctuate significantly under different observation conditions, maintaining a certain level of reliability. Response speed verification ensures that the system can promptly track changes in wide-lane ambiguity and adapt to dynamic changes in observation conditions.

[0051] In this embodiment of the invention, when establishing a weight allocation function method based on time decay, an exponentially weighted recursive smoothing factor is defined and a weight allocation function is established so that the weight of historical observations decays exponentially over time. This ensures that more recent epochs receive larger weights and more distant epochs receive smaller weights, thereby better adapting to dynamic changes in observation conditions and effectively improving the reliability of wide-lane ambiguity fixation. Secondly, by normalizing the weight coefficients, the sum of weights within the window is made equal to 1, facilitating subsequent smoothing calculations. Simultaneously, an equivalent time constant is introduced to transform exponential decay into a time scale, intuitively quantifying the decay rate of historical information and providing a theoretical basis for the reasonable setting of the smoothing window length. By implementing exponentially weighted smoothing through a recursive approach and using smoothing gain for recursive updates, the explicit calculation and storage of weight coefficients for each epoch are avoided, significantly simplifying the computation and reducing memory usage, making it particularly suitable for real-time dynamic positioning applications. In addition, by setting auxiliary parameters such as the smoothing window length and residual threshold, the smoothing effect and response speed are effectively balanced. This not only suppresses observation noise but also tracks the real changes in ambiguity in a timely manner, avoiding the introduction of outdated information from excessively long historical data. Finally, through parameter verification and optimization iteration, it is ensured that exponentially weighted recursive smoothing can effectively suppress noise and quickly respond to sudden changes in observation conditions, providing reliable technical support for BeiDou dual-frequency high-precision positioning.

[0052] S30, construct a multi-epoch exponential weighted recursive smoothing model, and use the multi-epoch exponential weighted recursive smoothing model to recursively smooth the wide-lane ambiguity floating-point solution sequence to obtain the smoothed wide-lane ambiguity floating-point solution estimate; The multi-epoch exponential weighted recursive smoothing model is expressed as follows: First, when the initial epoch k=1, ; Then, recursively update, when k is greater than or equal to 2, ; in, The estimated value of the wide-lane ambiguity floating-point solution after smoothing in the k-th epoch; Let be the wide-lane ambiguity floating-point solution for the k-th epoch; To smooth the gain, it is related to the attenuation factor. The relationship is determined as follows: ,in

[0053] in, This is the attenuation factor.

[0054] According to another implementation, smoothing gain With decay factor The relationship is determined as follows: When k is greater than the preset epoch iteration threshold (i.e., when k is relatively large), in this embodiment, the preset epoch iteration threshold can be 10-20. tending to a constant It can be 0.3.

[0055] Figure 4 This diagram illustrates the implementation flow of a recursive smoothing method for wide-lane ambiguity floating-point solution sequences provided in an embodiment of the present invention. The recursive smoothing method for wide-lane ambiguity floating-point solution sequences specifically includes: S301, Construct a multi-epoch exponentially weighted recursive smoothing model. Initialize the multi-epoch exponentially weighted recursive smoothing model. When the initial epoch k=1, directly use the wide-lane ambiguity floating-point solution of the first epoch as the initial smoothing value. Simultaneously, the smoothing gain is initialized. The multi-epoch exponentially weighted recursive smoothing model utilizes multi-epoch observation data and an exponentially weighted recursive smoothing method to reduce noise in the wide-lane ambiguity floating-point solution, improve its stability, and obtain a more reliable smoothed estimate. The smoothing gain is a key parameter controlling the fusion ratio between the current observation and historical smoothed values. Initializing the smoothing gain at the initial epoch provides the necessary parameter settings for subsequent recursive updates. A suitable initial smoothing gain ensures a reasonable processing method for the observation data in the initial stage, laying the foundation for subsequent dynamic adjustment of the smoothing gain based on the attenuation factor. S302, Establishing the recursive update framework: For subsequent epochs where k≥2, establish the recursive update equation:

[0056] in, The estimated value of the wide-lane ambiguity floating-point solution after smoothing in the k-th epoch; Let be the wide-lane ambiguity floating-point solution for the k-th epoch; To smooth the gain, the recursive update equation can dynamically calculate the estimated floating-point solution of the smoothed wide-lane ambiguity in the current epoch based on the observation value of the current epoch and the smoothed value of the previous epoch. This dynamic smoothing method can reflect changes in the observed data in a timely manner, enabling the smoothing result to better track the true state of the wide-lane ambiguity. S303 defines the relationship between the smoothing gain and the attenuation factor (i.e., the exponentially weighted recursive smoothing factor). There is a close relationship between the smoothing gain and the attenuation factor; by determining this relationship, the weighting of the current observation and historical smoothed values ​​can be precisely controlled during the smoothing process. The attenuation factor determines the rate of decay of historical observations, while the smoothing gain is the specific manifestation of this attenuation in the calculation. By clarifying the relationship between them, the smoothing intensity can be reasonably adjusted according to different observation conditions and requirements. S304, Calculating smoothing gain based on attenuation factor. Calculating smoothing gain based on attenuation factor ensures consistency in the smoothing process across different epochs and observation data. Once the attenuation factor is determined, the calculation of the smoothing gain is also determined, thus making the smoothing results comparable and consistent across different epochs. S305: Obtain the smoothing gain. Based on the smoothing gain, fuse the current observation and historical smoothed values ​​epoch-by-epoch to generate a smoothed wide-lane ambiguity floating-point solution estimate. By obtaining the smoothing gain and fusing the current observation and historical smoothed values, noise in the wide-lane ambiguity floating-point solution can be effectively suppressed. The historical smoothed values ​​contain observation information from multiple previous epochs and have a certain smoothing effect on noise, while the current observation reflects the latest observation. By reasonably allocating the weights of the two through the smoothing gain, the impact of noise can be reduced while retaining the latest observation information.

[0057] In one embodiment of the present invention, the method for determining the relationship between smoothing gain and attenuation factor includes: S3031, Smoothing Gain and Attenuation Factor The relationship is determined as follows: ,in

[0058] in, The attenuation factor is used in this embodiment, which is suitable for scenarios where observation conditions change slowly or require dynamic adaptation. The smoothing effect is gradually optimized through a recursive relationship. If the observation environment changes frequently, this embodiment is preferred to dynamically adapt to changes in observation conditions.

[0059] In another embodiment of the present invention, the method for determining the relationship between smoothing gain and attenuation factor includes: S3031, smooth gain With decay factor The relationship is determined as follows: When k is greater than the preset epoch iteration threshold (i.e., when k is relatively large), in this embodiment, the preset epoch iteration threshold can be 10-20. tending to a constant The value can be 0.3. This embodiment is suitable for scenarios where the observation conditions are relatively stable or where rapid convergence is required. The smoothing intensity is directly controlled by fixing the attenuation factor α. If the observation environment is relatively stable (fixed base station, static measurement), this embodiment is preferred to simplify the calculation and ensure the stability of the smoothing results.

[0060] All the above embodiments adjust the decay rate of historical information by controlling the decay factor α. The ultimate goal is to obtain a low-noise, high-reliability smoothed wide-lane ambiguity floating-point solution estimate, laying the foundation for improving the success rate of subsequent integer fixing and wide-lane ambiguity fixing.

[0061] In this embodiment of the invention, when recursively smoothing a sequence of wide-lane ambiguity floating-point solutions, a multi-epoch exponentially weighted recursive smoothing model is initialized. The wide-lane ambiguity floating-point solution of the first epoch is directly used as the initial smoothing value, and the smoothing gain is initialized, laying a stable foundation for subsequent recursive calculations. Secondly, by establishing a recursive update framework, subsequent epochs with k≥2 can be efficiently updated based on historical smoothing values ​​and current information, avoiding the repeated storage and calculation of long-sequence historical data in traditional methods. Furthermore, by determining the relationship between the smoothing gain and the attenuation factor, two implementation schemes are provided: an accurate recursive form and a steady-state approximation form. The time-varying gain can be selected according to accuracy requirements to achieve better convergence characteristics, or a constant gain can be selected according to real-time requirements to simplify the calculation process. On this basis, the smoothing gain is calculated based on the attenuation factor, and the current observation value and historical smoothing value are fused epoch by epoch, so that recent observation values ​​are given higher weights while effectively suppressing the accumulation of historical noise, generating a high-quality smoothed wide-lane ambiguity floating-point solution estimate. The method has a compact overall process and is computationally efficient, which not only significantly reduces memory usage and computational complexity, but also achieves adaptation to dynamic changes in observation conditions through the exponential weighting mechanism.

[0062] S40, based on the smoothed wide-lane ambiguity floating-point solution estimate, perform integer fixing and reliability verification to obtain the smoothed wide-lane ambiguity fixed solution, and calculate the measurement residual; When performing integer fixing and reliability verification based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixing adopts rounding or LAMBDA search method, and reliability verification adopts fixed success rate or Ratio value index.

[0063] Specifically, the smoothed wide-lane ambiguity Rounding or LAMBDA search is used to obtain integer solutions. And calculate a fixed success rate or ratio value to determine reliability. According to one implementation, when using the rounding method, if: Zhou, on the other hand, considers a fixed success rate and records a fixed time and a fixed success rate.

[0064] In this embodiment of the invention, a method for calculating measurement residuals is provided. Figure 5 This diagram illustrates the implementation flow of a method for calculating measurement residuals. The method specifically includes: S401, obtain the smoothed wide-lane ambiguity floating-point solution estimate; S402, the smoothed wide-lane ambiguity floating-point solution estimate is fixed to an integer value. The purpose of fixing the integer value is to convert the smoothed floating-point solution into an integer solution that is closest to the true wide-lane ambiguity integer value. In one embodiment of the present invention, the integer can be fixed by rounding, which directly rounds the floating-point solution and takes the nearest integer as the fixed solution.

[0065] In another embodiment of the present invention, the integer can be fixed by using the LAMBDA search algorithm, that is, based on the least squares principle, by searching the candidate solution space of integers, the integer solution that minimizes the residual is found as the fixed solution.

[0066] S403: Obtain the wide-lane ambiguity floating-point solution estimate after fixing the integer, and perform a fixed success rate test on the wide-lane ambiguity floating-point solution estimate.

[0067] In this embodiment of the invention, when performing a fixed success rate test on the floating-point solution estimate of the wide-lane ambiguity, the residual (decimal part) after rounding can be calculated, and the fixed reliability can be determined. If: Zhou, on the other hand, considers a fixed success rate and records a fixed time and a fixed success rate.

[0068] S404, perform integer reliability verification on the floating-point solution estimate of the wide-lane ambiguity after fixing the integer. For the LAMBDA search method, the Ratio value can be used for reliability verification. S405: Obtain the floating-point estimate of the wide-lane ambiguity after fixing the integer, calculate the measurement residual on the floating-point estimate of the wide-lane ambiguity after fixing the integer, construct the residual statistics based on the measurement residual, and output the residual statistics and the floating-point estimate of the wide-lane ambiguity after fixing the integer.

[0069] In this embodiment of the invention, when calculating the measurement residual, firstly, based on the estimated value of the smoothed high-precision wide-lane ambiguity floating-point solution, integer fixing is performed using algorithms such as rounding or LAMBDA search, effectively converting non-integer solutions into integer values ​​that conform to physical reality. Secondly, the reliability of the fixed solution is verified through a fixation success rate test and a Ratio value test for the LAMBDA search method, and the credibility of the fixed solution is verified from both probabilistic and statistical perspectives, ensuring that the fixation result has no significant error. Finally, by calculating the measurement residual and constructing residual statistics, not only is the matching degree between the fixed solution and the original observation data quantified, but real-time feedback is also provided for subsequent dynamic adjustment of smoothing parameters or positioning strategies. Simultaneously, the output residual statistics and the fixed solution together constitute the reliable input required for high-precision positioning. This significantly improves the success rate, reliability, and traceability of wide-lane ambiguity fixation, laying a solid foundation for BeiDou dual-frequency high-precision positioning.

[0070] S50, dynamically adjusts the exponential weighting factor according to the measurement residual to achieve adaptive smoothing and improve the success rate of wide-lane ambiguity fixation for Beidou dual-frequency positioning.

[0071] In this embodiment, the method for dynamically adjusting the exponential weighting factor based on the measurement residual includes: The innovation bias is calculated and expressed as:

[0072] A residual statistic is constructed to comprehensively assess the overall stability of the current observation conditions by statistically analyzing multi-epoch residuals, while avoiding the influence of randomness in single-epoch residuals. The residual statistic is expressed as follows:

[0073] Where M is the statistical window length, which can be 10. is the root mean square (i.e., residual statistic) within the sliding window. Information deviation calculated per epoch Statistics every 10 epochs ; Then, the attenuation factor is dynamically adjusted based on the residual statistics.

[0074] In one embodiment of this invention, the attenuation factor is dynamically adjusted based on the residual statistics. The dynamic adjustment of the attenuation factor is achieved using the following formula:

[0075] Obtain the dynamically adjusted attenuation factor, then substitute the dynamically adjusted attenuation factor into the exponentially weighted recursive smoothing model, recalculate the smoothing gain or recursive relationship, and perform recursive smoothing on the wide-lane ambiguity floating-point solution sequence of subsequent epochs to generate a new smoothed estimate.

[0076] According to another implementation method, the attenuation factor can also be adjusted dynamically using a piecewise function. The dynamic adjustment of the attenuation factor is achieved using the following formula:

[0077] in, The baseline attenuation factor can be 0.7; This is the residual threshold, which can be 0.15 weeks. This is an adjustment factor, which can be 0.5. When the observation quality deteriorates and the residuals increase, the attenuation factor is reduced, i.e., the weight of historical information is decreased, and the response speed of current information is improved; conversely, a larger attenuation factor is maintained to achieve a smoothing effect. (Adjusted) Used for smoothing gain calculation in subsequent epochs, but in practical applications it is recommended to set the reference attenuation factor between 0.6 and 0.8 and adjust it dynamically according to the environment.

[0078] In this embodiment of the invention, the exponential weighting factor is dynamically adjusted according to the measurement residual to achieve adaptive smoothing. When the observation quality deteriorates and the residual increases, the weight of historical information is automatically reduced to enhance the dominant role of the current observation and quickly respond to real changes. When the observation conditions are stable and the residual is small, the weight of historical information is maintained or enhanced to effectively suppress noise interference. Furthermore, through the closed-loop mechanism of "residual feedback-factor adjustment-smoothing optimization", the requirements of smoothing and noise reduction and real-time response are precisely balanced, significantly improving the stability and reliability of the wide-lane ambiguity floating-point solution. This effectively improves the success rate of wide-lane ambiguity fixation and positioning accuracy, while also taking into account computational efficiency and real-time performance. This provides more adaptable and robust key technical support for BeiDou dual-frequency high-precision positioning.

[0079] In this embodiment of the invention, when constructing the MW combined observation model for BeiDou dual-frequency positioning, the BeiDou dual-frequency combination includes, but is not limited to, the frequency point combinations of B1C / B2a, B1I / B3I, B1I / B2I, B1C / B3I, and B1I / B2a. The method of the present invention is not only applicable to double-difference wide-lane ambiguity, but can also be extended to smoothing non-difference and single-difference ambiguities. The method can also be used for wide-lane ambiguity processing of other satellite navigation systems such as GPS and Galileo, and the method is applicable to static or dynamic positioning modes, including short-baseline RTK positioning and medium-long-baseline RTK positioning.

[0080] This invention introduces a weight function that decays over time, giving higher weight to recent observations and establishing a recursive update model. It also introduces a residual-driven dynamic decay factor adjustment mechanism to achieve adaptive smoothing, effectively improving the reliability and timeliness of ambiguity fixation.

[0081] This invention employs an exponentially weighted recursive smoothing mechanism. By introducing a weight function that decays over time, recent observations receive higher weights, while the weights of historical observations decay exponentially. This weight allocation method better adapts to dynamic changes in observation conditions, such as satellite elevation angle variations, multipath effect fluctuations, and signal obstruction. Compared to traditional equal-weight smoothing methods that assign equal weights to all historical information, this invention effectively reduces the contamination of current solution results by older, low-quality observations, significantly improving the reliability of wide-lane ambiguity fixation. Furthermore, this method is not only applicable to double-difference wide-lane ambiguity processing but can also be extended to non-difference and single-difference ambiguity smoothing, and is compatible with various BeiDou dual-frequency point combinations such as B1I / B2I, B1C / B2a, and B1I / B3I, demonstrating broad applicability.

[0082] This invention employs a recursive smoothing model, which achieves exponential weighting through smoothing gain. It eliminates the need to explicitly calculate and store the weight coefficients for each epoch, as well as the need to save long-sequence historical observation data. This results in low computational complexity and small memory footprint, making it suitable for real-time dynamic positioning applications with limited computing resources and ensuring the real-time performance of positioning solutions.

[0083] This invention introduces a residual-driven adaptive factor adjustment mechanism. By monitoring the residual statistics in real time, the exponentially weighted attenuation factor is dynamically adjusted. When the observation quality decreases or the residual increases, the system automatically reduces the attenuation factor, lowers the weight of historical information, improves the response speed of current information, and avoids the continuous contamination of the current solution by old information. This adaptive adjustment mechanism can respond quickly when the observation conditions change abruptly and maintain smoothness when the observation conditions are stable. It effectively balances the contradiction between real-time performance and reliability, and solves the technical problems of the difficulty in presetting the smoothing window length and the difficulty in balancing convergence speed and smoothing effect in traditional methods. Compared with traditional equal-weight smoothing, it can shorten the ambiguity fixing convergence time and improve the timeliness of Beidou dual-frequency wide-lane ambiguity fixing.

[0084] On the other hand, the present invention also provides a system for improving the success rate of wide-lane ambiguity fixation using BeiDou dual-frequency positioning. Figure 6 A schematic diagram of a wide-lane ambiguity fixation success rate improvement system for BeiDou dual-frequency positioning is shown. This system specifically includes: The observation data acquisition unit 100 is used to acquire raw BeiDou dual-frequency observation data. The observation data acquisition unit 100 is responsible for directly acquiring raw observation data (including pseudorange, carrier phase, and corresponding satellite / receiver information) from the BeiDou dual-frequency receiver, and is the input source for system processing. The preprocessing unit 200 is used to perform cycle slip detection and repair to form double-difference observations. The preprocessing unit 200 can perform cycle slip detection and repair on the acquired raw observation data, eliminate carrier phase jump errors caused by signal interruption / loosening, and further generate double-difference observations (eliminating common errors at the satellite end / receiver end), providing clean data for subsequent high-precision calculations.

[0085] The single-epoch solution unit 300 is used to calculate the wide-lane ambiguity floating-point solution for each epoch based on the MW combination model. The single-epoch solution unit 300 calculates the preprocessed double-difference observations based on the MW combination model (Melbourne-Wubbena combination) and outputs the wide-lane ambiguity floating-point solution for each epoch (preliminary but noisy ambiguity estimate).

[0086] The exponentially weighted smoothing unit 400 is used to perform exponentially weighted recursive smoothing on the wide-lane ambiguity floating-point solution sequence to obtain the smoothed wide-lane ambiguity floating-point solution estimate. The exponentially weighted smoothing unit 400 can perform exponentially weighted recursive smoothing on the wide-lane ambiguity floating-point solution sequence, and generate the smoothed wide-lane ambiguity floating-point solution estimate by giving higher weight to recent observations and suppressing the influence of historical low-quality data.

[0087] The ambiguity fixing unit 500 is used to fix the integer value and verify the reliability of the smoothed wide-lane ambiguity floating-point solution estimate. Output unit 600 is used to output the fixed wide-lane ambiguity and positioning results. The exponential weighted smoothing module also includes a dynamic adjustment submodule, which is used to adjust the exponential weighting factor in real time according to the measurement residual. Output unit 600 can integrate all processing results and provide the final fixed solution of wide-lane ambiguity and the corresponding positioning results to users or downstream applications (such as high-precision navigation and surveying and positioning), completing the entire process from raw observation to high-precision output.

[0088] It should be noted that the observation data acquisition unit 100, preprocessing unit 200, single epoch calculation unit 300, exponential weighted smoothing unit 400, ambiguity fixing unit 500, and output unit 600 in the BeiDou dual-frequency positioning wide-lane ambiguity fixing success rate improvement system in this embodiment of the invention correspond to the steps in the BeiDou dual-frequency positioning wide-lane ambiguity fixing success rate improvement method, and will not be elaborated here.

[0089] In summary, this invention provides a method and system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning. By introducing a weight function that decays over time, this invention gives higher weight to recent observations and establishes a recursive update model. At the same time, it introduces a residual-driven dynamic decay factor adjustment mechanism to achieve adaptive smoothing, effectively improving the reliability and timeliness of ambiguity fixation.

[0090] It should be noted that, for the sake of simplicity, the foregoing embodiments are all described as a series of actions. However, those skilled in the art should understand that the present invention is not limited to the described order of actions, as some steps may be performed in other orders or simultaneously according to the present invention. Furthermore, those skilled in the art should also understand that the embodiments described in the specification are preferred embodiments, and the actions and modules involved are not necessarily essential to the present invention.

[0091] It should be understood that the disclosed apparatus can be implemented in other ways, given the several embodiments provided in this application. For example, the apparatus embodiments described above are merely illustrative; the division of units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or communication connections shown or discussed may be through some interfaces; the indirect coupling or communication connections between devices or units may be telecommunications or other forms.

[0092] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the scope of protection of the invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on these embodiments, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art can still combine, add, delete, or otherwise adjust the features of the various embodiments of the present invention according to the circumstances without conflict or creative effort, thereby obtaining different technical solutions that do not fundamentally depart from the concept of the present invention. These technical solutions also fall within the scope of protection of the present invention.

Claims

1. A method for improving the success rate of wide-lane ambiguity fixing in Beidou dual-frequency positioning, characterized in that, The method includes: A combined observation model for BeiDou dual-frequency positioning was constructed to calculate the wide-lane ambiguity floating-point solution for each epoch. Design an exponentially weighted recursive smoothing factor and establish a weight allocation function based on time decay; A multi-epoch exponential weighted recursive smoothing model is constructed to recursively smooth the wide-lane ambiguity floating-point solution sequence, and obtain the smoothed wide-lane ambiguity floating-point solution estimate. Based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixed and reliability checks are performed to obtain the smoothed wide-lane ambiguity fixed solution, and the measurement residual is calculated; and The exponential weighting factor is dynamically adjusted based on the measured residuals to achieve adaptive smoothing.

2. The method of claim 1, wherein the method is characterized by, The MW combined observation model for BeiDou dual-frequency positioning is constructed as follows: The wide-lane ambiguity float solution of each epoch is calculated as follows: wherein, , are the carrier phase observations of the kth epoch frequency 1 and frequency 2, respectively; , are the corresponding pseudo-range observations; , is the corresponding carrier wavelength, is the wide-lane wavelength, is the speed of light; , are the frequency of frequency 1 and frequency 2, respectively; , are the kth epoch wide-lane ambiguity and its corresponding float solution, respectively.

3. The method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning as described in claim 1, characterized in that, The exponentially weighted recursive smoothing factor The weight coefficient of the kth epoch is , The normalized weight satisfies: 。 4. The method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning as described in claim 1, characterized in that, The multi-epoch exponential weighted recursive smoothing model is constructed as follows: at the initial epoch k = 1, ; Recursive update, k is greater than or equal to 2, ; wherein, is the smoothed wide-lane ambiguity float solution estimate at epoch k; is the wide-lane ambiguity float solution at epoch k; is the smoothing gain, determined as follows: wherein wherein, is the damping factor.

5. The method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning as described in claim 4, characterized in that, Smooth gain is determined as follows: when k is greater than a preset epoch iteration threshold, Tends to constant is 0.

3.

6. The method of claim 5, wherein the method is characterized by, The method for dynamically adjusting the exponential weighting factor based on the measurement residual includes: The innovation bias is calculated and expressed as: Constructing a residual statistics, the residual statistics is expressed as: Wherein, M is the length of the statistics window; The attenuation factor is dynamically adjusted according to the residual statistics, and the dynamic adjustment of the attenuation factor adopts the following formula: Wherein, is a reference attenuation factor; is a residual threshold.

7. The method of claim 6, wherein the method is characterized by, The attenuation factor is dynamically adjusted using a piecewise function, and the dynamic adjustment of the attenuation factor is based on the following formula: wherein, is a reference decay factor; is a residual threshold, is an adjustment coefficient.

8. The method of claim 1, wherein the method is characterized by, When performing integer fixing and reliability verification based on the smoothed wide-lane ambiguity floating-point solution estimate, integer fixing adopts rounding or LAMBDA search method, and reliability verification adopts fixed success rate or Ratio value index.

9. The method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning as described in claim 8, characterized in that, When constructing the MW combined observation model for BeiDou dual-frequency positioning, the BeiDou dual-frequency combination includes the frequency point combinations of B1C / B2a, B1I / B3I, B1I / B2I, B1C / B3I, and B1I / B2a.

10. A system for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning, used to implement the method for improving the success rate of wide-lane ambiguity fixation in BeiDou dual-frequency positioning as described in any one of claims 1-9, characterized in that, The BeiDou dual-frequency positioning wide-lane ambiguity fixation success rate improvement system includes: The observation data acquisition unit is used to acquire raw BeiDou dual-frequency observation data; The preprocessing unit is used for cycle slip detection and repair to generate double-difference observations; The single-epoch solution unit is used to calculate the wide-lane ambiguity floating-point solution for each epoch based on the MW combined model. The exponentially weighted smoothing unit is used to perform exponentially weighted recursive smoothing on the wide-lane ambiguity floating-point solution sequence to obtain the smoothed wide-lane ambiguity floating-point solution estimate. The ambiguity fixing unit is used to fix the integer value and verify the reliability of the smoothed wide-lane ambiguity floating-point solution estimate. The output unit is used to output the fixed width ambiguity and positioning results.

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