Single-Beidou multi-frequency positioning error correction method and device and medium

Abstract

The invention relates to the technical field of satellite navigation positioning, and discloses a single-Beidou multi-frequency positioning error correction method and device and a medium, and the method comprises the steps: building a single-Beidou multi-frequency positioning observation model which comprises a pseudo-range observation equation and a carrier wave observation equation; performing double-difference processing on the observed value, and eliminating common errors such as satellite clock error and receiver clock error; the troposphere delay and the ionosphere delay are accurately corrected, and improved Kalman filtering is adopted for parameter estimation in ionosphere delay correction; self-adaptive carrier phase smoothing processing is carried out on the double-difference pseudo-range observation value, and a multi-dimensional self-adaptive threshold cycle slip detection and repair algorithm based on dynamic programming is adopted; and performing multi-frequency ambiguity fixation by using an LAMBDA method, and performing robust adaptive filtering by using an IGG weight function. Compared with the prior art, the method has the advantages of remarkably improving the positioning precision, enhancing the environmental adaptability, improving the system reliability, supporting multi-frequency processing and the like.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a method, device and medium for correcting single BeiDou multi-frequency positioning errors. Background Technology

[0002] The BeiDou Navigation Satellite System (BDS), my country's independently developed global satellite navigation system, plays a crucial role in high-precision positioning applications. With the continuous improvement of the BeiDou system and the expansion of its application areas, the requirements for positioning accuracy are becoming increasingly stringent. However, in practical applications, BeiDou multi-frequency positioning suffers from various error sources, which severely impact positioning accuracy and reliability.

[0003] Existing BeiDou multi-frequency positioning technology mainly employs traditional error correction methods, including tropospheric delay correction, ionospheric delay correction, carrier phase smoothing pseudorange technology, and ambiguity fixing. However, these traditional methods suffer from the following technical problems in practical applications: First, the modeling accuracy of tropospheric and ionospheric delays is not high, especially in the case of long baselines. Traditional modeling methods cannot accurately describe the spatial variation characteristics of atmospheric delays, resulting in unsatisfactory correction effects.

[0004] Secondly, existing carrier phase smoothing pseudorange techniques lack adaptability. Fixed smoothing parameters cannot adapt to changes in different observation environments and signal quality, and are prone to generating large errors in environments with poor signal quality or high dynamics.

[0005] Furthermore, traditional cycle slip detection and repair methods lack an adaptive mechanism for threshold setting. Fixed thresholds are prone to missed detections or false alarms under different environmental conditions, affecting the continuity and reliability of carrier phase observation.

[0006] Finally, existing ambiguity fixation methods are not efficient in multi-frequency situations, especially when observation conditions are poor, the success rate of ambiguity fixation is low, which affects the improvement of positioning accuracy.

[0007] Therefore, there is an urgent need for a more accurate and adaptive single-BeiDou multi-frequency positioning error correction method to solve the above-mentioned technical problems and improve positioning accuracy and reliability. Summary of the Invention

[0008] In view of the aforementioned existing problems, the present invention is proposed.

[0009] Therefore, this invention provides a single BeiDou multi-frequency positioning error correction method, which can solve the technical problems in the prior art such as low accuracy of tropospheric delay and ionospheric delay modeling, lack of adaptability of carrier phase smoothing pseudorange technology, lack of adaptive mechanism for cycle slip detection threshold setting, and low efficiency of multi-frequency ambiguity fixing.

[0010] To address the aforementioned technical problems, this invention provides the following technical solution: a single BeiDou multi-frequency positioning error correction method, comprising: establishing a single BeiDou multi-frequency positioning observation model, including pseudorange observation equations and carrier observation equations; performing double-difference processing on the observation values ​​to eliminate common errors of satellite clock bias and receiver clock bias; using a combination of zenith delay correction and mapping function to correct the tropospheric delay in the double-difference observation values; using Kalman filtering of a first-order Markov model to estimate the ionospheric delay parameter to correct the ionospheric delay in the double-difference observation values; performing adaptive carrier phase smoothing processing on the double-difference pseudorange observation values; using a multidimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming to perform cycle slip detection and repair on the carrier phase observation values; fixing the multi-frequency ambiguity of the processed carrier phase observation values, and obtaining the positioning result using the LAMBDA method (i.e., least squares ambiguity decorrelation adjustment method); performing robust adaptive filtering on the observation values, and using an IGG weight function to remove abnormal observation values.

[0011] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the establishment of the single BeiDou multi-frequency positioning observation model includes establishing a pseudorange observation equation. Establish the carrier observation equation: in, Let u be the pseudorange observation of satellite s at frequency i. For carrier phase observations, For geometric distance, At the speed of light, For receiver clock bias, For satellite clock bias, For tropospheric atmospheric delay, For atmospheric delay of the ionosphere, The hardware delay of the code at frequency i at the receiver end. For the code hardware delay at frequency i at the satellite end, For carrier wavelength, For carrier phase ambiguity parameters, This is pseudorange observation noise. This is carrier phase observation noise.

[0012] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the double-difference processing includes establishing a double-difference pseudorange observation equation. Establish the double-difference carrier observation equation: in, These are double-difference pseudorange observations. These are double-difference carrier phase observations. This indicates a double-difference operator, where inter-station differences are performed first, followed by inter-satellite differences. It is a double-difference geometric distance. For double-difference tropospheric delay, For double-difference ionospheric delay, r and b represent the base station and rover station, and a and n represent the reference satellite and non-reference satellite, For carrier wavelength, For double-difference carrier phase ambiguity parameters, This is noise from double-difference pseudorange observations. This is double-difference carrier phase observation noise.

[0013] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the correction of the tropospheric delay in the double-difference observations is calculated using the following formula: in, For tropospheric delay, For the zenith tropospheric dry delay, For the zenith tropospheric wet delay, For the dry delay mapping function, This is a wet delay mapping function.

[0014] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the correction of ionospheric delay in the double-difference observations includes using a Kalman filter with a first-order Markov model. Establish the state transition equation: Establish the observation equation: in, Let be the ionospheric delay state vector at the k-th epoch. Let be the ionospheric delay state vector of the (k-1)th epoch. Here is the state transition matrix. For process noise, For the observation vector, For the observation matrix, To observe noise; The state transition matrix adopts a first-order Markov model: in, It is the reciprocal of the relevant time constant. The sampling interval is denoted as .

[0015] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the adaptive carrier phase smoothing process is calculated using the following formula: in, The smoothed pseudo-distance of the k-th epoch. The smooth pseudo-range of the (k-1)th epoch. These are the original pseudorange observations. For carrier phase observations, The carrier phase observation value at epoch k-1. This is an adaptive smoothing factor.

[0016] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the adaptive smoothing factor includes: Where k is the current epoch number, The basic smoothing window length is determined by the ratio of the pseudorange observation noise standard deviation to the carrier phase observation noise standard deviation.

[0017] As a preferred embodiment of the single BeiDou multi-frequency positioning error correction method described in this invention, the cycle slip detection and repair of the carrier phase observation values ​​includes: a multi-dimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming, and the establishment of a state transition model. Define the cost function: The Viterbi algorithm is used to find the threshold sequence that minimizes the cost function. in, Let k be the state vector of the kth epoch. Carrier-to-noise ratio, The rate of change of Doppler frequency shift, The standard deviation of the carrier phase. Let cost function be , , These are the weighting coefficients. This represents the probability of a missed detection. This represents the probability of a false alarm. To calculate the cost, The threshold sequence that minimizes the cost function. This is an epochal index.

[0018] The present invention provides a computer device, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps of a single BeiDou multi-frequency positioning error correction method.

[0019] The present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of a single BeiDou multi-frequency positioning error correction method.

[0020] The beneficial effects of this invention are as follows: By establishing an accurate single-BeiDou multi-frequency positioning observation model and using double-difference processing to eliminate common errors, combined with accurate tropospheric and ionospheric delay correction, positioning accuracy can be significantly improved; by employing adaptive carrier phase smoothing pseudorange technology and a multi-dimensional adaptive threshold cycle slip detection algorithm based on dynamic programming, parameters can be automatically adjusted according to the observation environment and signal quality, significantly improving positioning performance and robustness under different environments; by using IGG weight function robust filtering and the Viterbi algorithm, the stability of the system and the global optimality of threshold selection are guaranteed, effectively reducing the impact of abnormal observations on positioning results and improving the reliability of the system. This invention fully supports BeiDou dual-frequency, tri-frequency, and quad-frequency positioning. The LAMBDA method ensures a high success rate in fixing multi-frequency ambiguities, fully leveraging the advantages of multi-frequency observation. This invention offers good real-time performance and moderate algorithm complexity. The Kalman filter and LAMBDA method used are mature algorithms with high computational efficiency, meeting real-time positioning requirements. This invention also demonstrates strong anti-interference capabilities. The multi-dimensional state model and robust filtering effectively handle observation anomalies and signal interference, reducing the false alarm rate and improving the system's ability to operate in complex environments. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic flowchart of a single BeiDou multi-frequency positioning error correction method provided in one embodiment of the present invention.

[0023] Figure 2 This invention provides a double-difference observation model and error correction schematic diagram for a single BeiDou multi-frequency positioning error correction method according to an embodiment of the present invention.

[0024] Figure 3 The flowchart of an adaptive carrier phase smoothing pseudorange algorithm for a single BeiDou multi-frequency positioning error correction method is provided in one embodiment of the present invention.

[0025] Figure 4 The flowchart of a multi-dimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming is provided for a single Beidou multi-frequency positioning error correction method according to an embodiment of the present invention.

[0026] Figure 5 The flowchart of the multi-frequency ambiguity fixing LAMBDA algorithm for a single BeiDou multi-frequency positioning error correction method provided in one embodiment of the present invention is shown.

[0027] Figure 6 This is a schematic diagram of the robust adaptive filtering IGG weight function of a single BeiDou multi-frequency positioning error correction method provided in one embodiment of the present invention. Detailed Implementation

[0028] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the protection scope of the present invention.

[0029] Example 1, referring to Figure 1 This is the first embodiment of the present invention, which provides a single BeiDou multi-frequency positioning error correction method, including: S1: Establish a single BeiDou multi-frequency positioning observation model, including pseudorange observation equations and carrier observation equations.

[0030] S2: Perform double-difference processing on the observations to eliminate common errors from satellite clock bias and receiver clock bias.

[0031] S3: A method combining zenith delay correction and mapping function is used to correct the tropospheric delay in double-difference observations.

[0032] S4: The ionospheric delay parameter is estimated using a Kalman filter based on a first-order Markov model, and the ionospheric delay in the double-difference observations is corrected.

[0033] S5: Perform adaptive carrier phase smoothing on the double-difference pseudorange observations.

[0034] S6: A multi-dimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming is used to detect and repair cycle slips in carrier phase observations.

[0035] S7: Fix the multi-frequency ambiguity of the processed carrier phase observations and obtain the positioning results using the LAMBDA method.

[0036] S8: Perform robust adaptive filtering on the observations and use the IGG weighting function to remove outlier observations.

[0037] It should be noted that this embodiment achieves comprehensive correction of single-BeiDou multi-frequency positioning errors through the organic combination of eight steps. First, a precise observation model is established. Then, common errors are eliminated through double-difference processing. Next, precise corrections are made for tropospheric and ionospheric delays respectively. Then, pseudorange accuracy is improved through adaptive carrier phase smoothing. Dynamic programming algorithms are used to achieve adaptive detection and repair of cycle slips. The LAMBDA method is used for efficient ambiguity fixing. Finally, robust adaptive filtering is used to eliminate outlier observations. The entire process forms a complete error correction system, with each step working together to improve positioning accuracy and reliability.

[0038] Example 2, refer to Figure 2 - Figure 6 As an embodiment of the present invention, based on the above embodiment, a single BeiDou multi-frequency positioning error correction method is provided.

[0039] Furthermore, in this embodiment, step S1 establishes a single BeiDou multi-frequency positioning observation model, including pseudorange observation equations and carrier observation equations, specifically as follows: A single BeiDou multi-frequency positioning observation model is established, including pseudorange observation equations and carrier observation equations. Specifically, the receiver... Regarding satellites In frequency The observation equation on is expressed as: Pseudorange observation equation: Carrier observation equation: in, For receiver In frequency Up to satellite The pseudorange observations are in meters; These are carrier phase observations, in meters. For receiver To satellite The geometric distance between them, in meters; For the speed of light, take a value of m / s; This refers to the receiver clock error, expressed in seconds. Satellite clock bias, in seconds; The delay in tropospheric atmospheric time is expressed in meters. For frequency The atmospheric delay of the ionosphere above, in meters; For the receiver end at frequency The hardware latency of the code is measured in meters. For satellite end in frequency The hardware latency of the code is measured in meters. For frequency The corresponding carrier wavelength, in meters; This is the carrier phase ambiguity parameter, in cycles; This is pseudorange observation noise, in meters; The carrier phase observation noise is expressed in meters.

[0040] Specific parameters and conditions: The BeiDou system supports multiple frequencies, including B1I (1561.098 MHz), B3I (1268.520 MHz), B1C (1575.420 MHz), and B2a (1176.450 MHz), with corresponding carrier wavelengths of approximately 0.1919 m, 0.2367 m, 0.1903 m, and 0.2548 m, respectively.

[0041] The observation model is characterized by its full consideration of the characteristics of the BeiDou system, including various error sources such as satellite clock error, receiver clock error, atmospheric delay, and hardware delay, providing a complete theoretical basis for subsequent error correction.

[0042] Furthermore, in this embodiment, step S2 performs double-difference processing on the observed values ​​to eliminate common errors between satellite clock bias and receiver clock bias, specifically as follows: The observations obtained in step S1 are subjected to double-difference processing to eliminate common errors from satellite clock bias and receiver clock bias. For example... Figure 2 As shown, the double-difference processing adopts the method of first inter-station differential and then inter-satellite differential: Double-difference pseudorange observation equation: Double-difference carrier observation equation: in, These are double-difference pseudorange observations. These are double-difference carrier phase observations. This indicates a double-difference operator, where inter-station differences are performed first, followed by inter-satellite differences. It is a double-difference geometric distance. For double-difference tropospheric delay, For double-difference ionospheric delay, r and b represent the base station and rover station, and a and n represent the reference satellite and non-reference satellite, For carrier wavelength, For double-difference carrier phase ambiguity parameters, This is noise from double-difference pseudorange observations. This is double-difference carrier phase observation noise.

[0043] By using double-difference processing, satellite clock errors, receiver clock errors, and most hardware delays are effectively eliminated, significantly simplifying the observation equations and improving positioning accuracy.

[0044] The satellite with the highest elevation angle and the best signal quality is usually selected as the reference satellite to ensure the stability of the double-difference observations.

[0045] Furthermore, in this embodiment, step S3 uses a combination of zenith delay correction and mapping function to correct the tropospheric delay in the double-difference observations, specifically as follows: The tropospheric delay in the double-difference observations obtained in step S2 is corrected using a combination of zenith delay correction and mapping function: in, For tropospheric delay, For the zenith tropospheric dry delay, For the zenith tropospheric wet delay, For the dry delay mapping function, This is a wet delay mapping function.

[0046] The tropospheric model employs one of the following: the Hopfield model, the Saastamoinen model, or the Black model. The Saastamoinen model is suitable for general accuracy requirements, the Hopfield model for medium accuracy requirements, and the Black model for high accuracy requirements. The dry delay mapping function typically uses the Niell mapping function or the GMF mapping function, while the wet delay mapping function considers the spatiotemporal variation characteristics of water vapor.

[0047] The dry zenith delay is approximately 2.3 meters, while the wet zenith delay varies from 0 to 0.5 meters, with the specific value determined based on meteorological conditions.

[0048] Furthermore, in this embodiment, step S4 uses a Kalman filter based on a first-order Markov model to estimate the ionospheric delay parameter and corrects the ionospheric delay in the double-difference observations, specifically as follows: The ionospheric delay in the double-difference observations obtained in step S2 is corrected, and the ionospheric delay parameters are estimated using a Kalman filter of a first-order Markov model: frequency Formula for calculating ionospheric delay: in, For frequency The ionospheric delay above, measured in meters; The carrier frequency is expressed in Hz. Total electron content, in TECU (Total Electronic Content) electrons / m²).

[0049] Establish the state transition equation: Observation equation: The state transition matrix adopts a first-order Markov model: in, It is the reciprocal of the relevant time constant, with the unit being 1 / s; The sampling interval is expressed in seconds (s).

[0050] Kalman filter parameters, correlation time constant The value is usually taken as This corresponds to a 1-hour relevant time period; sampling interval Typically 1 second or 30 seconds Let be the ionospheric delay state vector at the k-th epoch. Let be the ionospheric delay state vector of the (k-1)th epoch. Here is the state transition matrix. For process noise, For the observation vector, For the observation matrix, To observe noise.

[0051] Process noise settings, process noise covariance matrix: in, Represents the process noise covariance matrix. This represents the variance of the ionospheric delay variation. The observation noise covariance matrix. The precision is determined by the observation accuracy, typically at the centimeter level.

[0052] Furthermore, in this embodiment, step S5 performs adaptive carrier phase smoothing processing on the double-difference pseudorange observations, specifically as follows: The double-difference pseudorange observations obtained in step S2 are then subjected to carrier phase smoothing, such as... Figure 3 As shown: in, The smoothed pseudo-distance of the k-th epoch. The smooth pseudo-range of the (k-1)th epoch. These are the original pseudorange observations. For carrier phase observations, The carrier phase observation value at epoch k-1. It is an adaptive smoothing factor, with a value range of [0,1].

[0053] Adaptive smoothing factor calculation: Observation quality assessment indicators: in, This is the current epoch number; The basic smoothing window length is determined by the ratio of the standard deviation of pseudorange observation noise to the standard deviation of carrier phase observation noise; This represents the standard deviation of pseudorange observation noise. This represents the standard deviation of carrier phase observation noise.

[0054] when At that time, increase To enhance the smoothing effect; when When, decrease To improve response speed. Threshold Typically, it's set to 0.5. Base smoothing window length. The initial value for smoothed pseudorange is typically set between 100 and 300 epochs, and is dynamically adjusted based on the observation environment. The initial value for smoothed pseudorange is set to the original pseudorange observation value of the first epoch.

[0055] Furthermore, in this embodiment, step S6 employs a dynamic programming-based multidimensional adaptive threshold cycle slip detection and repair algorithm to perform cycle slip detection and repair on the carrier phase observations, specifically as follows: A multidimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming is used to detect and repair cycle slips in carrier phase observations, such as... Figure 4 As shown: Establish a state transition model: in, Let k be the state vector of the kth epoch. For the first Carrier-to-noise ratio of an epoch; This represents the rate of change of Doppler frequency shift. The standard deviation of the carrier phase. This indicates the matrix transpose.

[0056] Define the cost function: in, Let cost function be This represents the probability of a missed detection. This represents the probability of a false alarm. To calculate the cost; , , These are the weighting coefficients.

[0057] The Viterbi algorithm is used to find the threshold sequence that minimizes the cost function. in, The threshold sequence that minimizes the cost function. This is an epochal index.

[0058] Threshold update formula: in, The adaptive threshold for the k-th epoch. Basic threshold; , To adjust the parameters; For reference carrier-to-noise ratio; This represents the maximum Doppler frequency shift rate.

[0059] Base threshold Typically set to 3-5 weeks; adjust parameters. Take a value of 0.2-0.5. Use a value of 0.1-0.3; refer to the carrier-to-noise ratio. Use 45 dB-Hz. Threshold variation range , These represent the minimum and maximum values ​​of the adaptive threshold, and the threshold change between adjacent epochs, respectively. , This represents the maximum change in the threshold between adjacent epochs.

[0060] After detecting cycle slips, multi-frequency combined observations are used to estimate and repair the cycle slip size. Multi-frequency signals are used to construct combined observations with different characteristics. By combining long and short wavelengths, the integer cycle slip variables at each frequency are gradually and accurately estimated, and finally the repair is completed.

[0061] Furthermore, in this embodiment, step S7 fixes the multi-frequency ambiguity of the processed carrier phase observations and obtains the positioning result using the LAMBDA method, specifically as follows: The ambiguity of the carrier phase observations processed in step S6 is fixed, and the LAMBDA method is used to obtain high-precision positioning results, such as... Figure 5 As shown: Ambiguity floating-point solution estimation: in, The floating-point solution vector for ambiguity; For designing the matrix; This is the weight matrix; For the observation vector, This indicates the matrix transpose.

[0062] Ambiguity covariance matrix: in, Let be the covariance matrix of the floating-point solution for ambiguity.

[0063] Using the downcorrelation transform Z-transform: in, This is the transformed ambiguity vector; This is the decorrelation transformation matrix.

[0064] Integer Least Squares Search: in, The ambiguity is a fixed integer. A candidate integer vector; This is the transformed covariance matrix.

[0065] The ambiguity fixation test uses the Ratio test: in, To fix the ambiguity test ratio, The candidate solution that minimizes the objective function; To find the second smallest candidate solution for the objective function, Let represent the Euclidean norm of a vector. When hour, To verify the threshold, the result of fixed ambiguity is accepted.

[0066] The LAMBDA algorithm significantly improves search efficiency through downcorrelation transformation, and can quickly find the optimal integer solution in the case of multiple frequencies.

[0067] The test threshold is typically set between 2.0 and 3.0. A higher threshold ensures the reliability of the fixation results, while a lower threshold increases the fixation success rate. A layer-by-layer search strategy is adopted, first searching for fuzzy parameters with low relevance, and then searching for parameters with higher relevance.

[0068] Furthermore, in this embodiment, step S8 performs robust adaptive filtering on the observations, using the IGG weight function to remove outlier observations, specifically as follows: The observations obtained in step S7 are robustly processed to remove outlier observations, such as... Figure 6 As shown: Standardized residual calculation: in, For the first Standardized residuals of each observation; These are actual observed values; To predict the observed values; is the standard deviation of the observed values.

[0069] IGG weight function: when hour, ; when hour, ; when hour: in, The weight of the l-th observation; This is the first threshold, typically set to 1.5; This is the second threshold, usually set to 3.0.

[0070] Adaptive factor calculation: when At the same time, increase the process noise variance: in, As an adaptive factor, This represents the prior value of the unit weight variance; This represents the posterior value of the unit weighted variance; The process noise covariance matrix is... The noise covariance matrix of the adaptive process; The threshold is adaptive and is usually set to 1.5.

[0071] The IGG weight function automatically adjusts the observation weights based on the residual size, maintaining the original weights for small residuals, reducing the weights for medium residuals, and completely eliminating large residuals. By comparing the prior and posterior unit weight variances, it dynamically adjusts process noise, improving the filter's adaptability to model errors. It also incorporates various statistical testing methods, such as... Tests such as t-tests can be used to improve the accuracy of outlier detection.

[0072] Example 3 is the third embodiment of the present invention, which differs from the previous two embodiments in that: This embodiment also provides an electronic device suitable for single BeiDou multi-frequency positioning error correction, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the single BeiDou multi-frequency positioning error correction method proposed in the above embodiment.

[0073] This embodiment also provides a storage medium on which a computer program is stored. When the program is executed by a processor, it implements the single BeiDou multi-frequency positioning error correction method proposed in the above embodiment.

[0074] The storage medium proposed in this embodiment and the method for correcting single BeiDou multi-frequency positioning errors proposed in the above embodiments belong to the same inventive concept. Technical details not described in detail in this embodiment can be found in the above embodiments, and this embodiment has the same beneficial effects as the above embodiments.

[0075] Based on the above description of the implementation methods, those skilled in the art can clearly understand that the present invention can be implemented using software and necessary general-purpose hardware, and of course, it can also be implemented using hardware. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as a computer floppy disk, read-only memory (ROM), random access memory (RAM), flash memory, hard disk, or optical disk, etc., including several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of the various embodiments of the present invention.

[0076] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for correcting errors in single-BeiDou multi-frequency positioning, characterized in that: include, Establish a single BeiDou multi-frequency positioning observation model, including pseudorange observation equations and carrier observation equations; The observations are double-differenced to eliminate common errors from satellite clock bias and receiver clock bias. A method combining zenith delay correction and mapping function is used to correct the tropospheric delay in double-difference observations; The ionospheric delay parameter is estimated using a first-order Markov model Kalman filter, and the ionospheric delay in the double-difference observations is corrected. Adaptive carrier phase smoothing is applied to the double-difference pseudorange observations; A multidimensional adaptive threshold cycle slip detection and repair algorithm based on dynamic programming is adopted to perform cycle slip detection and repair on carrier phase observations; The processed carrier phase observations are fixed with multi-frequency ambiguity, and the LAMBDA method is used to obtain the positioning results. Robust adaptive filtering is applied to the observations, and outlier observations are removed using the IGG weighting function.

2. The single BeiDou multi-frequency positioning error correction method as described in claim 1, characterized in that: The establishment of the single BeiDou multi-frequency positioning observation model includes establishing pseudorange observation equations. Establish the carrier observation equation: in, Let u be the pseudorange observation of satellite s at frequency i. For carrier phase observations, For geometric distance, At the speed of light, For receiver clock bias, For satellite clock bias, For tropospheric atmospheric delay, For atmospheric delay of the ionosphere, The hardware delay of the code at frequency i at the receiver end. For the code hardware delay at frequency i at the satellite end, For carrier wavelength, For carrier phase ambiguity parameters, This is pseudorange observation noise. This is carrier phase observation noise.

3. The single BeiDou multi-frequency positioning error correction method as described in claim 2, characterized in that: The double-difference processing includes establishing a double-difference pseudorange observation equation. Establish the double-difference carrier observation equation: in, These are double-difference pseudorange observations. These are double-difference carrier phase observations. This indicates a double-difference operator, where inter-station differences are performed first, followed by inter-satellite differences. It is a double-difference geometric distance. For double-difference tropospheric delay, For double-difference ionospheric delay, r and b represent the reference station and rover station, respectively, and a and n represent the reference satellite and non-reference satellite, respectively. For carrier wavelength, For double-difference carrier phase ambiguity parameters, This is noise from double-difference pseudorange observations. This is double-difference carrier phase observation noise.

4. The single BeiDou multi-frequency positioning error correction method as described in claim 3, characterized in that: The correction for the tropospheric delay in the double-difference observations is calculated using the following formula: in, For tropospheric delay, For the zenith tropospheric dry delay, For the zenith tropospheric wet delay, For the dry delay mapping function, This is a wet delay mapping function.

5. The single BeiDou multi-frequency positioning error correction method as described in claim 4, characterized in that: The correction for ionospheric delay in the double-difference observations includes using a Kalman filter based on a first-order Markov model. Establish the state transition equation: Establish the observation equation: in, Let be the ionospheric delay state vector at the k-th epoch. Let be the ionospheric delay state vector of the (k-1)th epoch. Here is the state transition matrix. For process noise, For the observation vector, For the observation matrix, To observe noise; The state transition matrix adopts a first-order Markov model: in, It is the reciprocal of the relevant time constant. The sampling interval is denoted as .

6. The single BeiDou multi-frequency positioning error correction method as described in claim 5, characterized in that: The adaptive carrier phase smoothing process is calculated using the following formula: in, The smoothed pseudo-distance of the k-th epoch. The smooth pseudo-range of the (k-1)th epoch. These are the original pseudorange observations. For carrier phase observations, The carrier phase observation value at epoch k-1. This is an adaptive smoothing factor.

7. The single BeiDou multi-frequency positioning error correction method as described in claim 6, characterized in that: The adaptive smoothing factor includes, Where k is the current epoch number, The basic smoothing window length is determined by the ratio of the pseudorange observation noise standard deviation to the carrier phase observation noise standard deviation.

8. The single BeiDou multi-frequency positioning error correction method as described in claim 7, characterized in that: The cycle slip detection and repair of carrier phase observations includes establishing a state transition model based on a multidimensional adaptive threshold cycle slip detection and repair algorithm using dynamic programming. Define the cost function: The Viterbi algorithm is used to find the threshold sequence that minimizes the cost function. in, Let k be the state vector of the kth epoch. Carrier-to-noise ratio, The rate of change of Doppler frequency shift, The standard deviation of the carrier phase. Indicates matrix transpose. Let cost function be , , These are the weighting coefficients. This represents the probability of a missed detection. This represents the probability of a false alarm. To calculate the cost, The threshold sequence that minimizes the cost function. This is an epochal index.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the single Beidou multi-frequency positioning error correction method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the single Beidou multi-frequency positioning error correction method according to any one of claims 1 to 7.

Images