Multi-path error correction method in Beidou navigation system

Abstract

The invention relates to the technical field of navigation system error correction, and discloses a multi-path error correction method in a Beidou navigation system, which comprises the following steps of: scanning through an environment perception sensor integrated with a navigation receiver to obtain three-dimensional space data of a surrounding environment of the navigation receiver; generating a set comprising a plurality of candidate paths according to the space reflection source model; establishing a sparse optimization model taking an observation matrix as a core through sparsity priori of a plurality of candidate path signals; solving the sparse optimization model, and identifying a real reflection path which forms dominant influence on the pseudo-range observation value; and a corrected pseudo-range observation value is obtained, and a final positioning result is calculated based on the corrected pseudo-range observation value and is fed back. According to the method, potential reflecting surfaces around a receiver are actively sensed and parameterized through an environment modeling and geometric path prediction mechanism based on three-dimensional space data, and the additional delays of all candidate reflecting paths are calculated according to the optical reflection law.

Description

Technical Field

[0001] The present invention relates to the technical field of navigation system error correction, and in particular to a method for multipath error correction in a Beidou navigation system. Background Art

[0002] As a global spatial information infrastructure, the Beidou Navigation Satellite System (BDS) has become a critical component in supporting the efficient operation of modern society. From intelligent transportation and logistics tracking to personal communications and emergency rescue, the demand for high-precision location-based services is growing. However, in densely populated and complex urban environments, the propagation path of navigation signals is severely affected. Before reaching the receiver, the signal often reflects one or more times from building surfaces. The resulting multipath signal superimposes with the direct signal, causing distortion in pseudorange measurements. This is one of the core obstacles that limit the Beidou Navigation System's ability to achieve high-precision positioning in critical scenarios such as cities.

[0003] Existing navigation systems primarily employ correction strategies based on receiver algorithms. These strategies monitor the carrier-to-noise power density ratio of satellite signals and assign less weight to satellite observations with lower carrier-to-noise power density ratios. Furthermore, in continuous positioning scenarios, Kalman filtering is widely used to smooth pseudorange observation sequences. In multi-sensor fusion frameworks (such as integrated BDS / IMU navigation), kinematic models are used to constrain the drift of positioning results.

[0004] However, existing navigation technology relies on weighting signal quality indicators such as the carrier-to-noise power density ratio of satellite signals, and its logical premise is not completely reliable. The attenuation of signal strength comes from non-multipath factors, such as temporary obstruction by leaves or buildings, while a strong reflection path from a large glass curtain wall may have a very high signal strength, making it difficult to fundamentally identify and quantify the multipath error itself. Secondly, the core of the smoothing algorithm represented by Kalman filtering is to approximate the multipath error as a time-varying random noise. The mirror reflection generated by fixed large buildings will form an approximately constant error with systematic deviation over a considerable period of time. Therefore, the present invention provides a method for correcting multipath errors in the Beidou navigation system to address the shortcomings of the prior art. Summary of the Invention

[0005] In response to the shortcomings of the existing technology, the present invention provides a method for correcting multipath errors in the Beidou navigation system, which solves the problems in the existing navigation system caused by inaccurate multipath error modeling, limited positioning accuracy, poor adaptability to dynamic environments, and high computational complexity that makes it difficult to apply in real time.

[0006] To achieve the above objectives, the present invention is implemented through the following technical solutions: A method for multipath error correction in a Beidou navigation system, comprising the following steps:

[0007] S1. Scanning the environment perception sensor integrated in the navigation receiver to obtain three-dimensional spatial data of the surrounding environment of the navigation receiver, and constructing a spatial reflection source model including geometric parameters of potential reflection surfaces based on the three-dimensional spatial data;

[0008] S2. generating a set of multiple candidate paths based on the spatial reflection source model, and calculating an additional path delay generated by each candidate path in the set of multiple candidate paths compared to the direct propagation path;

[0009] S3. Using the additional path delay, a measurement matrix is ​​constructed to characterize the linear relationship between multiple candidate paths and the residuals of pseudorange observations. Based on the sparsity prior of the multiple candidate path signals, a sparse optimization model with the measurement matrix as the core is established.

[0010] S4. Identify the true reflection path that has a dominant influence on the pseudorange observation value by solving the sparse optimization model, and reconstruct the total error of multiple candidate paths based on the additional path delay corresponding to the identified true reflection path;

[0011] S5. Eliminate the total error of multiple candidate paths from the original pseudo-range observation value of the navigation receiver to obtain a corrected pseudo-range observation value, calculate the final positioning result based on the corrected pseudo-range observation value and provide feedback.

[0012] Preferably, in step S1, constructing a spatial reflection source model including geometric parameters of potential reflection surfaces based on three-dimensional spatial data comprises the following steps:

[0013] Processing the acquired three-dimensional spatial data to simplify it into a set of spatial reflection surfaces consisting of multiple planar structures;

[0014] Parameterizing each spatial reflection surface in the set of spatial reflection surfaces, and determining a position, a normal vector, and a reflection coefficient value representing a signal reflection intensity for each spatial reflection surface in a three-dimensional coordinate system;

[0015] Each spatial reflection surface in the parameterized spatial reflection surface set is integrated to form a structured spatial reflection source constraint model.

[0016] Preferably, in step S2, calculating the additional path delay generated by each candidate path in the set of multiple candidate paths compared to the direct propagation path includes the following steps:

[0017] For any visible satellite position S kand the preliminary position Rest of the navigation receiver to determine the geometric length of its direct propagation path;

[0018] Traverse all the reflection surfaces P in the spatial reflection source model j , according to the law of reflection of light, calculate the satellite position S k Via the reflecting surface P j Reflection point R on p The geometric length of the indirect propagation path to the receiver's preliminary location Rest;

[0019] Additional path delay ΔL i The additional path delay is obtained by subtracting the geometric length of the direct propagation path from the geometric length of the indirect propagation path. The calculation formula for the additional path delay is:

[0020]

[0021] Where, is the position of the kth satellite S k To the reflection point R p The path vector, From the reflection point R p To the receiver estimated position R est The path vector, is the satellite position S k To the receiver estimated position R est The direct path vector, ||·|| is the modulus of the vector, ΔL i is the candidate reflection path P j Additional path delay relative to the direct path.

[0022] Preferably, in step S3, establishing a sparse optimization model with the observation matrix as the core includes the following steps:

[0023] The pseudorange prediction value calculated by the standard positioning algorithm is subtracted from the pseudorange observation value obtained by the navigation receiver to obtain the pseudorange residual vector composed of the unmodeled multipath error;

[0024] A LASSO model is constructed as a sparse optimization model. The objective function of the sparse optimization model is to minimize the fitting error of the pseudorange residual and the sparsity of the model solution.

[0025] The objective function of the sparse optimization model is expressed as:

[0026]

[0027] Where X is an M×1 matrix to be solved, A is the measurement matrix, λ is the regularization parameter that balances the fitting accuracy and solution sparsity, ΔP is the pseudorange residual vector, represents the square of the L2 norm of the vector, and ||·||1 represents the L1 norm of the vector.

[0028] Preferably, in step S4, reconstructing the total error amount of multiple candidate paths includes the following steps:

[0029] The sparse optimization model is iteratively solved using a fast iterative shrinkage threshold algorithm or an alternating direction multiplier method to obtain a sparse solution vector.

[0030] Identifying the candidate paths corresponding to the non-zero elements in the sparse solution vector as the real reflection paths that have a dominant influence on the pseudorange observation values;

[0031] The total error amount of multiple candidate paths is obtained by multiplying the sparse solution vector and the pseudorange measurement matrix.

[0032] Preferably, in step S5, calculating the final positioning result based on the corrected pseudorange observation value and providing feedback includes the following steps:

[0033] For each true reflection path identified by the sparse optimization model, a confidence score is calculated based on the signal quality indicators of the corresponding satellite and the stability of its appearance in consecutive positioning epochs;

[0034] The final positioning result is compared with the trajectory predicted by the kinematic model. If unreasonable trajectory jumps occur, it is determined that there is a deviation in the error correction;

[0035] Based on the comparison between the confidence score and the trajectory predicted by the kinematic model, the reflection coefficient value of the corresponding reflecting surface in the spatial reflection source model is adaptively adjusted, or the regularization parameter in the sparse optimization model is adjusted.

[0036] Preferably, the reflection point R o The position is determined by the satellite position S j , the initial position of the receiver Rest and the reflecting surface P j The plane equation n·(x-x0)=0 is determined together, where n is the normal vector of the reflecting surface, and x and x0 are both points on the reflecting surface.

[0037] Preferably, the sparse optimization model is iteratively solved using a fast iterative shrinkage threshold algorithm, and the fast iterative shrinkage threshold algorithm is expressed as:

[0038] X k+1 =S ηθ (X k -ηA T (AX k -ΔP));

[0039] Where, X k+1 With X kare the sparse solution vectors for the k+1th and kth iterations respectively, A is the observation matrix, A T is the transpose of the observation matrix, ΔP is the pseudorange residual vector, η is the iteration step size, λ is the regularization parameter, and S is the soft threshold shrinkage operator

[0040] Preferably, the reflection coefficient value of the corresponding reflection surface in the spatial reflection source model is adaptively adjusted by adopting a recursive low-pass filtering algorithm, and the recursive low-pass filtering algorithm is:

[0041]

[0042] Where, γ j (t) is the updated reflection coefficient value of the reflecting surface at the current epoch, γ j (t-1) is the historical reflection coefficient value of the reflecting surface in the previous epoch, α is the smoothing coefficient that determines the update rate, and the function The value of is determined by the actual reflection path intensity related to the reflecting surface currently solved and C k Decide.

[0043] A multipath error correction system in a BeiDou navigation system is also provided, comprising:

[0044] An environment modeling unit is used to obtain three-dimensional spatial data through scanning by an environment perception sensor integrated in the navigation receiver, and to construct a spatial reflection source model including geometric parameters of potential reflection surfaces;

[0045] a path prediction unit, configured to generate a set of multiple candidate paths based on geometric constraints in the spatial reflection source model constructed by the environment modeling unit, and calculate, for each candidate path in the set, an additional path delay generated compared to a direct propagation path;

[0046] a model building unit, configured to extract the additional path delay of each candidate path calculated by the path prediction unit, assemble the additional path delay into an observation matrix representing the linear relationship between all candidate paths and the residuals of the pseudorange observations, and establish a sparse optimization model;

[0047] an error solving unit, configured to solve the sparse optimization model established by the model building unit to invert a sparse solution vector representing a true reflection path, and reconstruct a total multipath error using the sparse solution vector and the measurement matrix;

[0048] The positioning correction unit is used to subtract the total multipath error reconstructed by the error solving unit from the original pseudorange observation value of the navigation receiver to generate a corrected pseudorange observation value, and calculate the final positioning result based on the corrected pseudorange observation value.

[0049] The present invention provides a method for correcting multipath errors in a Beidou navigation system. It has the following beneficial effects:

[0050] 1. This invention introduces an environmental modeling and geometric path prediction mechanism based on three-dimensional spatial data. By actively sensing and parameterizing potential reflective surfaces around the receiver, the additional delay of all candidate reflection paths is calculated based on the laws of optical reflection. This design, based on the physical roots of multipath generation, can proactively and accurately construct a set of candidate paths containing key error information. Compared to existing methods that primarily rely on signal strength statistics or signal correlation domain processing, this invention solves the problem of only being able to passively and fuzzily estimate multipath effects when the physical structure of the reflector source is difficult to perceive.

[0051] 2. This paper transforms the multipath tracing problem into an optimization problem based on a sparse prior. By constructing an observation matrix driven by additive path delays and solving it using the LASSO model, this method efficiently retrieves the few true reflection paths that dominate the observed values ​​from a vast number of geometric candidate paths, and quantitatively reconstructs the total multipath error based on these paths.

[0052] 3. The present invention constructs a closed-loop feedback correction system that integrates positioning result evaluation and dynamic updating of model parameters. After completing an error correction, the system comprehensively evaluates the confidence of the identified path and the rationality of the final positioning result. It also uses algorithms such as recursive low-pass filtering to feedback the evaluation results for adaptive adjustment of the reflection coefficient value in the spatial reflection source model. Compared with the open-loop correction or simple multi-sensor data fusion strategies commonly used in the prior art, the present invention solves the problem that once the model parameters are set, they are difficult to change, making it difficult to cope with dynamically changing environments or correct initial model deviations. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 is a flow chart of the method steps of the present invention;

[0054] Figure 2 This is a flow chart of the environment-pathway joint modeling of the present invention;

[0055] Figure 3 This is a system architecture diagram of the present invention. DETAILED DESCRIPTION

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the drawings in the present specification. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0057] Please see the attached Figure 1 -Attached Figure 2 The embodiment of the present invention provides a method for correcting multipath errors in a BeiDou navigation system, comprising the following steps:

[0058] S1. Scanning the environment perception sensor integrated in the navigation receiver to obtain three-dimensional spatial data of the surrounding environment of the navigation receiver, and constructing a spatial reflection source model including geometric parameters of potential reflection surfaces based on the three-dimensional spatial data;

[0059] S2. generating a set of multiple candidate paths based on the spatial reflection source model, and calculating an additional path delay generated by each candidate path in the set of multiple candidate paths compared to the direct propagation path;

[0060] S3. Using the additional path delay, a measurement matrix is ​​constructed to characterize the linear relationship between multiple candidate paths and the residuals of pseudorange observations. Based on the sparsity prior of the multiple candidate path signals, a sparse optimization model with the measurement matrix as the core is established.

[0061] S4. Identify the true reflection path that has a dominant influence on the pseudorange observation value by solving the sparse optimization model, and reconstruct the total error of multiple candidate paths based on the additional path delay corresponding to the identified true reflection path;

[0062] S5. Eliminate the total error of multiple candidate paths from the original pseudo-range observation value of the navigation receiver to obtain a corrected pseudo-range observation value, calculate the final positioning result based on the corrected pseudo-range observation value and provide feedback.

[0063] Regarding step S1, in this embodiment, to accurately correct multipath errors in the Beidou navigation system, the primary task is to provide an accurate and efficient digital description of the physical environment that causes signal reflections. Therefore, the method proposed in this invention begins with the perception and modeling of the navigation receiver's surroundings. By constructing a spatial reflection source model that can be understood and processed by a computer, it transforms a complex physical problem into a structured geometric and mathematical problem.

[0064] The specific implementation method of acquiring the three-dimensional spatial data of the surrounding environment of the navigation receiver and constructing a spatial reflection source model including the geometric parameters of the potential reflection surface based on the three-dimensional spatial data is as follows:

[0065] The system actively acquires 3D spatial data of its surroundings through environmental perception sensors integrated into the navigation receiver itself or connected externally. Typically, these sensors can be laser radar (LiDAR), time-of-flight (ToF) cameras, or structured light cameras. Specifically, LiDAR emits laser beams and measures their return time to obtain high-precision 3D point cloud data. This point cloud data can accurately depict the outline and position of potential reflective surfaces such as buildings, walls, and billboards.

[0066] After acquiring the original three-dimensional spatial data (such as a 3D point cloud), the system needs to process and simplify this data to improve the efficiency of subsequent calculations and identify key contradictions. In one possible implementation, the system uses a random sampling consensus (RANSAC) algorithm or a Hough transform-based plane detection algorithm to iteratively identify and extract dominant planar structures from the cluttered original point cloud. Through this process, complex building surfaces are simplified into a set of spatial reflective surfaces composed of multiple discrete planes with clear boundaries, which greatly reduces the complexity of the model.

[0067] Next, each spatial reflection surface in the set of spatial reflection surfaces needs to be parameterized to give it clear geometric and physical properties.

[0068] As an option, the determination of geometric parameters is the core of this step. The position and orientation of each identified spatial reflective surface in the three-dimensional coordinate system can be uniquely described by a plane equation. The specific form of the plane equation is:

[0069] n·(x-x0)=0;

[0070] Where n is the unit normal vector representing the orientation of the spatial reflection surface; x0 is the three-dimensional coordinate vector of any known point on the spatial reflection surface; and x is the coordinate vector of any point on the plane. By determining the normal vector n and point x0 of each plane, its geometric shape is completely defined.

[0071] At the same time, in addition to the geometric parameters, it is also necessary to determine the reflection coefficient value that characterizes the signal reflection intensity for each spatial reflection surface. The reflection coefficient value is a dimensionless scalar whose value range is between 0 and 1. It is used to simulate the energy attenuation of the Beidou navigation signal when it comes into contact with surfaces of different materials. In some embodiments, the value can be initially set according to a preset material library. For example, the reflection coefficient value of a glass curtain wall can be set to 0.8, while the reflection coefficient value of an ordinary concrete wall can be set to 0.4. In the absence of prior information, it can also be uniformly set to a default value and dynamically adjusted in subsequent feedback correction steps.

[0072] Finally, all parameterized spatial reflective surfaces—mathematical planes that each carry information about their position, normal, and reflection coefficient—are integrated to form a structured spatial reflective source constraint model. This model can be structured as a list or array containing multiple object instances, each of which fully records the parameters of a reflective surface. This structured model provides a coherent geometric constraint database that can be efficiently queried and called upon by the program for subsequent steps (such as path prediction), completing the transformation from a physical environment to a mathematical model.

[0073] In step S2, after digitizing the navigation receiver's surroundings and constructing a structured spatial reflection source model, this embodiment utilizes the geometric model generated in the previous stage to comprehensively predict and quantify all possible signal propagation paths. Essentially, this process transforms static environmental geometric constraints into a dynamic set of paths suitable for mathematical modeling, and calculates the key physical quantity, "additive path delay," for each potential multipath signal.

[0074] A specific implementation method of generating a set of multiple candidate paths based on the spatial reflection source model and calculating the additional path delay generated by each candidate path in the set compared to the direct propagation path is as follows:

[0075] First, the system needs to prepare the initial data for path geometry deduction. This includes obtaining the precise position vectors of all currently visible Beidou satellites from the broadcast ephemeris decoded by the navigation receiver, denoted as S k At the same time, the system uses the original pseudo-range observation value received by the receiver to calculate a preliminary position of the receiver through the standard single point positioning (SPP) algorithm, which is recorded as R est Although the initial position contains multipath errors that need to be corrected, its accuracy is sufficient to serve as the geometric reference for path prediction. For each visible satellite S in the field of view, k ,The system starts to generate a set of candidate paths based on the established ,spatial reflection source model.

[0076] Specifically, the system will traverse each parameterized spatial reflection surface P in the spatial reflection source model. j For each reflecting surface, the system attempts to calculate a unique reflection point R p In one possible implementation, the reflection point R p The position is determined by the satellite position S k , initial receiver position R est , and the reflection surface P defined by the normal vector and a point on the plane jThe calculation process strictly follows the law of reflection of light, that is, the reflection point must satisfy the geometric constraint that the incident vector and the reflection vector are symmetrical about the plane normal. This process corresponds to the technical content defined in claim 7. If the calculated reflection point falls within the pre-set effective boundary of the reflection surface, then a line from satellite S k Via reflection point R p Arrives at the receiver R est The indirect propagation path (i.e., a candidate reflection path) is considered to be effectively generated.

[0077] After generating the direct propagation path and all valid indirect propagation paths, these paths need to be quantified. The key here is to calculate the additional path delay incurred by each indirect propagation path compared to the direct propagation path. Generally speaking, this delay is due to the additional geometric distance incurred by the signal's detour.

[0078] The additional path delay is calculated by subtracting the geometric length of the direct propagation path from the total geometric length of the indirect propagation path. The calculation formula for the additional path delay is:

[0079]

[0080] Where ΔL i represents the additional path delay caused by the i-th candidate reflection path relative to its corresponding direct path, which is a scalar value; S k represents the position of the kth visible satellite in the three-dimensional coordinate system; R p Indicates the position of the reflection point calculated on a specific reflection surface that satisfies the law of reflection; R est Represents the preliminary estimated position of the navigation receiver calculated by the standard positioning algorithm; Indicates the satellite position S k Point to the reflection point R p Path vector of Represents the reflection point R p Pointing to the estimated position R of the receiver est The path vector of Indicates the satellite position S k Pointing to the estimated position R of the receiver est The direct path vector of ; ||·|| represents the Euclidean norm of the vector, that is, the modulus of the calculated vector, and its physical meaning is the geometric length of the path segment.

[0081] In step S3, in this embodiment, after the system has completed the geometric prediction of all potential signal propagation paths and quantified the unique additional path delay for each candidate reflection path, it constructs a mathematical model that describes how these candidate paths interact with the pseudorange observations. The core idea is to leverage the inherent sparsity of multipath signals in physical reality to transform the complex error tracing problem into a constrained, solvable sparse optimization problem.

[0082] By using , a measurement matrix is ​​constructed to characterize the linear relationship between multiple candidate paths and pseudorange observation residuals. And through the sparsity prior of multiple candidate path signals, a sparse optimization model with the measurement matrix as the core is established. The specific implementation method is as follows:

[0083] First, the system needs to obtain a signal that can represent the total amount of the current unmodeled error, namely the pseudorange residual vector. Generally, this vector is obtained by subtracting the pseudorange observation value actually measured by the navigation receiver from the pseudorange prediction value calculated based on the satellite ephemeris and the preliminary position of the receiver. In one possible implementation, the calculation process of the pseudorange residual vector ΔP can be expressed as:

[0084] ΔP=P obs -P pred ;

[0085] Where, P obs is the original pseudorange observation vector output by the navigation receiver, including the multipath error; pred is the theoretical pseudorange value vector calculated using the satellite position, the initial receiver position, and the atmospheric model. Ideally, the residual vector ΔP is mainly composed of the multipath error to be solved.

[0086] The system uses the calculated additional path delay ΔL of each candidate path i , to construct a core observation matrix A. This matrix establishes a linear mapping relationship between the additional delay of all candidate paths and the pseudorange residuals of each satellite channel. Specifically, the observation matrix A is an N×M dimensional matrix, where N is the number of currently visible satellites and M is the total number of candidate reflection paths generated for all visible satellites. The elements in the matrix A ki It is defined as follows: If the i-th candidate path is formed by the reflection of the signal from the k-th satellite, the value of this element is the additional path delay ΔL of the path i ; If the i-th candidate path is not related to the k-th satellite, the value of this element is 0.

[0087] Building on this foundation, we introduce a key physical prior: the sparsity of multipath signals. In most urban scenarios, while there could theoretically be hundreds or thousands of candidate reflection paths, in reality, only a handful of highly energetic, real reflection paths dominate the receiver signal. This phenomenon is known as the sparsity of the multipath channel. This approach shifts the problem-solving goal from fitting all paths to identifying these few critical paths.

[0088] As an option, the system constructs a LASSO model as the sparse optimization model. The objective function of this model is designed to minimize two parts simultaneously: one is the fitting error between the model prediction error and the actual pseudorange residual, and the other is the sparsity of the model solution itself. The objective function of the sparse optimization model is specifically expressed as:

[0089]

[0090] Where X is an M×1 vector to be solved; each element x of the vector i Corresponding to a candidate reflection path, its physical meaning can be understood as the equivalent signal amplitude or intensity of the path; A is the N×M-dimensional observation matrix constructed above; ΔP is the N×1-dimensional pseudorange residual vector calculated above; λ is a non-negative regularization parameter. A larger λ will cause more elements in the solution vector X to become zero, thus obtaining a sparser solution; a smaller λ will focus more on reducing the fitting error. Where, represents the square of the L2 norm of the vector, which is used to measure the mean squared error between the model-predicted multipath error (AX) and the observed pseudorange residual (ΔP); ||·||1 represents the L1 norm of the vector, which is the sum of the absolute values ​​of all elements in the vector. This term, as a penalty term, has the mathematical property of effectively driving many elements in the solution vector X to precisely zero, thereby achieving automatic path selection and model sparsification. In some embodiments, the value of this parameter can be set empirically or adaptively optimized through methods such as cross-validation.

[0091] For step S4, in this embodiment, a sparse solution is inverted from the model through an efficient numerical algorithm, and this solution is used to accurately identify the real reflection path that has a dominant influence on the pseudorange observation value, and finally reconstruct the quantized total multipath error.

[0092] By solving the established sparse optimization objective function. Since the objective function contains a non-smooth L1 norm term, an analytical solution cannot be obtained by simple derivation, so an iterative optimization algorithm is required. As an option, the present invention adopts a proximal gradient descent method such as the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA) or the Alternating Direction Multiplier Method (ADMM). These algorithms are particularly suitable for solving large-scale LASSO problems.

[0093] Specifically, when using the fast iterative shrinkage threshold algorithm, its core is to gradually approach the optimal sparse solution vector through an iterative update calculation process. The iterative update calculation formula is expressed as:

[0094] X k+1 =S ηλ (X k -ηA T (AX k -ΔP));

[0095] Where, X k With X k+1 are the sparse solution vectors for the kth and k+1th iterations respectively; before the iteration begins, X0 can be initialized to a zero vector; A is the observation matrix constructed in the previous steps; A T is the transposed matrix of the observation matrix; λ is the regularization parameter in the sparse optimization model, whose value remains unchanged during this step; S is the soft threshold shrinkage operator; ΔP is the pseudorange residual vector calculated in the previous step; η is the iteration step size, a positive scalar. This parameter controls the update amplitude of each iteration and its value affects the convergence speed and stability of the algorithm. In some embodiments, the step size η can be a fixed value calculated based on the spectral norm of A to ensure convergence.

[0096] The iterative process continues until the preset convergence conditions are met, such as the norm of the difference between the solution vectors of two consecutive iterations is less than a minimum value, or the maximum number of iterations is reached, and finally a stable and converged sparse solution vector is obtained.

[0097] In obtaining the sparse solution vector After that, it needs to be physically interpreted to identify the true reflection path. In one possible implementation, the system traverses the vector All elements of . Due to the effect of sparse optimization, The vast majority of elements in are precisely zero. The indices corresponding to those non-zero elements directly point to the actual reflection paths that are determined to exist in the initial candidate path set and that have a dominant influence on the pseudorange observations. The numerical values ​​of the non-zero elements can be considered as the signal strength or confidence level of the corresponding actual reflection paths.

[0098] Finally, the system reconstructs the total multipath error of the pseudorange observation value of each satellite channel based on the identified real reflection path and its corresponding intensity. Specifically, the total error of multiple candidate paths is obtained by adding the sparse solution vector Multiplying it with the original observation matrix A, the calculation formula is:

[0099]

[0100] Where, is an N×1 dimensional vector representing the total multipath error reconstructed for each of the N visible satellites.

[0101] The above calculation is essentially a linear combination process: it multiplies the additional path delay corresponding to each identified real reflection path (the corresponding column of the observation matrix A) by its corresponding solution strength (the sparse solution vector The reconstructed error vector is then superimposed to obtain the final error estimate for each satellite pseudorange. It is the final output of this step, which will be used to correct the original pseudorange in the next stage.

[0102] Regarding step S5, in this embodiment, the total error of multiple candidate paths is eliminated from the original pseudorange observation values ​​of the navigation receiver to obtain corrected pseudorange observation values, and the specific implementation method of calculating the final positioning result based on the corrected pseudorange observation values ​​and providing feedback is as follows:

[0103] The system performs a direct error removal operation. This operation reconstructs the total multipath error vector for each satellite The original pseudorange observation vector P obtained from the navigation receiver obs As an option, the corrected pseudorange observation vector P corr The generation process can be expressed as:

[0104]

[0105] Where, P obs is the original pseudorange measurement value without any processing, P corr It is a purer pseudo-range measurement value after removing the main multipath error contribution. Then, the system converts this set of corrected pseudo-range observation values ​​Pcorr The data is input into a standard positioning solution engine (eg, weighted least squares method) to calculate the final positioning result of the receiver with significantly improved accuracy.

[0106] After obtaining the final positioning result, a feedback correction process is initiated. This feedback mechanism is the key to ensure that the method maintains long-term robustness and high accuracy in a dynamically changing environment.

[0107] Specifically, the first step of the feedback process is to calculate a confidence score for each true reflection path identified this time. This score combines information from two dimensions. First, it is the signal quality indicator of the corresponding satellite. Generally, the carrier-to-noise power density ratio (C / N0) is used as a measurement standard. A higher C / N0 value usually means a stronger direct signal and a more reliable measurement, thereby giving the reflection path generated by the satellite signal a higher initial credibility. Second, it is the stability of appearance in multiple consecutive positioning epochs. A reflection path that appears continuously and stably in time is more likely to correspond to a fixed physical reflection surface than a path that only flashes briefly, so its confidence should also be higher.

[0108] Based on the calculated confidence score and the comparison with the trajectory predicted by the kinematic model, the parameters in the system model are adaptively adjusted. This adjustment is intended to optimize the error correction performance of the next epoch. When the adjustment target is the reflection coefficient value of the corresponding reflecting surface in the spatial reflection source model, the system uses a recursive low-pass filtering algorithm to achieve smooth and robust updates. The recursive low-pass filtering algorithm is:

[0109]

[0110] Where, γ j (t) is the update of the j-th reflector at the current epoch t, ​​which is the final output of this feedback calculation; γ j (t-1) is the historical reflection coefficient value of the reflecting surface at the previous epoch t-1, reflecting the recursive nature of the update; α is a smoothing coefficient that determines the update rate and ranges from 0 to 1; this parameter balances the stability of historical information and the immediacy of current observations; f(·) is a function whose input is the current solved true reflection path intensity associated with the j-th reflecting surface is the sparse solution vector In , the non-zero element values ​​corresponding to the reflection path generated by the j-th reflection surface.

[0111] In some embodiments, if the path strength If the confidence score is high and the trajectory comparison is normal, then the function Will output a higher value, driving γ j (t) moves closer to this value, thus more accurately simulating the reflection ability of the reflecting surface in the next epoch. On the contrary, if there is a jump in the trajectory comparison, the output of the function g(·) may be suppressed, or even cause γ j (t) Callback to enhance system stability.

[0112] The multipath error correction system in a Beidou navigation system described below and the multipath error correction method in a Beidou navigation system described above can correspond to each other.

[0113] Please see the attached Figure 3 The present invention also provides a multipath error correction system in a Beidou navigation system, comprising:

[0114] An environment modeling unit is used to obtain three-dimensional spatial data through scanning by an environment perception sensor integrated in the navigation receiver, and to construct a spatial reflection source model including geometric parameters of potential reflection surfaces;

[0115] a path prediction unit, configured to generate a set of multiple candidate paths based on geometric constraints in the spatial reflection source model constructed by the environment modeling unit, and calculate, for each candidate path in the set, an additional path delay generated compared to a direct propagation path;

[0116] a model building unit, configured to extract the additional path delay of each candidate path calculated by the path prediction unit, assemble the additional path delay into an observation matrix representing the linear relationship between all candidate paths and the residuals of the pseudorange observations, and establish a sparse optimization model;

[0117] an error solving unit, configured to solve the sparse optimization model established by the model building unit to invert a sparse solution vector representing a true reflection path, and reconstruct a total multipath error using the sparse solution vector and the measurement matrix;

[0118] The positioning correction unit is used to subtract the total multipath error reconstructed by the error solving unit from the original pseudorange observation value of the navigation receiver to generate a corrected pseudorange observation value, and calculate the final positioning result based on the corrected pseudorange observation value.

[0119] The system of this embodiment can be used to execute the above method embodiments, and its principles and technical effects are similar, so they will not be repeated here.

[0120] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. A method for multipath error correction in a BeiDou navigation system, characterized in that: The following steps are involved: S1. Scanning the environment perception sensor integrated in the navigation receiver to obtain three-dimensional spatial data of the surrounding environment of the navigation receiver, and constructing a spatial reflection source model including geometric parameters of potential reflection surfaces based on the three-dimensional spatial data; S2. generating a set of multiple candidate paths based on the spatial reflection source model, and calculating an additional path delay generated by each candidate path in the set of multiple candidate paths compared to the direct propagation path; S3. Using the additional path delay, a measurement matrix is ​​constructed to characterize the linear relationship between multiple candidate paths and the residuals of pseudorange observations. Based on the sparsity prior of the multiple candidate path signals, a sparse optimization model with the measurement matrix as the core is established. S4. Identify the true reflection path that has a dominant influence on the pseudorange observation value by solving the sparse optimization model, and reconstruct the total error of multiple candidate paths based on the additional path delay corresponding to the identified true reflection path; S5. Eliminate the total error of multiple candidate paths from the original pseudo-range observation value of the navigation receiver to obtain a corrected pseudo-range observation value, calculate the final positioning result based on the corrected pseudo-range observation value and provide feedback.

2. The method for multipath error correction in a BeiDou navigation system according to claim 1, wherein: In step S1, constructing a spatial reflection source model including geometric parameters of potential reflection surfaces based on three-dimensional spatial data includes the following steps: Processing the acquired three-dimensional spatial data to simplify it into a set of spatial reflection surfaces consisting of multiple planar structures; Parameterizing each spatial reflection surface in the set of spatial reflection surfaces, and determining a position, a normal vector, and a reflection coefficient value representing a signal reflection intensity for each spatial reflection surface in a three-dimensional coordinate system; Each spatial reflection surface in the parameterized spatial reflection surface set is integrated to form a structured spatial reflection source constraint model.

3. The method for correcting multipath errors in a BeiDou navigation system according to claim 1, wherein: In step S2, calculating the additional path delay generated by each candidate path in the set of multiple candidate paths compared to the direct propagation path includes the following steps: For any visible satellite position S k and the preliminary position Rest of the navigation receiver to determine the geometric length of its direct propagation path; Traverse all the reflection surfaces P in the spatial reflection source model j , according to the law of reflection of light, calculate the satellite position S k Via the reflecting surface P j Reflection point R on p The geometric length of the indirect propagation path to the receiver's preliminary location Rest; Additional path delay ΔL i The additional path delay is obtained by subtracting the geometric length of the direct propagation path from the geometric length of the indirect propagation path. The calculation formula for the additional path delay is: Where, is the position of the kth satellite S k To the reflection point R p The path vector, From the reflection point R p To the receiver estimated position R est The path vector, is the satellite position S k To the receiver estimated position R est The direct path vector, ||·|| is the modulus of the vector, ΔL i is the candidate reflection path P j Additional path delay relative to the direct path.

4. The method for correcting multipath errors in a BeiDou navigation system according to claim 1, wherein: In step S3, the establishment of a sparse optimization model with the observation matrix as the core includes the following steps: The pseudorange prediction value calculated by the standard positioning algorithm is subtracted from the pseudorange observation value obtained by the navigation receiver to obtain the pseudorange residual vector composed of the unmodeled multipath error; A LASSO model is constructed as a sparse optimization model. The objective function of the sparse optimization model is to minimize the fitting error of the pseudorange residual and the sparsity of the model solution. The objective function of the sparse optimization model is expressed as: Where X is an M×1 matrix to be solved, A is the measurement matrix, λ is the regularization parameter that balances the fitting accuracy and solution sparsity, ΔP is the pseudorange residual vector, represents the square of the L2 norm of the vector, and ||·||1 represents the L1 norm of the vector.

5. The method for correcting multipath errors in a BeiDou navigation system according to claim 1, wherein: In step S4, reconstructing the total error amount of multiple candidate paths includes the following steps: The sparse optimization model is iteratively solved using a fast iterative shrinkage threshold algorithm or an alternating direction multiplier method to obtain a sparse solution vector. Identifying the candidate paths corresponding to the non-zero elements in the sparse solution vector as the real reflection paths that have a dominant influence on the pseudorange observation values; The total error amount of multiple candidate paths is obtained by multiplying the sparse solution vector and the pseudorange measurement matrix.

6. The method for correcting multipath errors in a BeiDou navigation system according to claim 1, wherein: In step S5, calculating the final positioning result based on the corrected pseudorange observation value and providing feedback includes the following steps: For each true reflection path identified by the sparse optimization model, a confidence score is calculated based on the signal quality indicators of the corresponding satellite and the stability of its appearance in consecutive positioning epochs; The final positioning result is compared with the trajectory predicted by the kinematic model. If unreasonable trajectory jumps occur, it is determined that there is a deviation in the error correction; Based on the comparison between the confidence score and the trajectory predicted by the kinematic model, the reflection coefficient value of the corresponding reflecting surface in the spatial reflection source model is adaptively adjusted, or the regularization parameter in the sparse optimization model is adjusted.

7. The method for correcting multipath errors in a BeiDou navigation system according to claim 3, wherein: The reflection point R P The position is determined by the satellite position S k , the initial position of the receiver Rest and the reflecting surface P j The plane equation n·(x-x0)=0 is determined together, where n is the normal vector of the reflecting surface, and x and x0 are both points on the reflecting surface.

8. The method for correcting multipath errors in a BeiDou navigation system according to claim 5, wherein: The fast iterative shrinkage threshold algorithm is used to iteratively solve the sparse optimization model. The fast iterative shrinkage threshold algorithm is expressed as: X k+1 =S ηλ (X k -ηA T (AX k -ΔP)); Where, X k+1 With X k are the sparse solution vectors for the k+1th and kth iterations respectively, A is the observation matrix, A T is the transpose of the observation matrix, ΔP is the pseudorange residual vector, η is the iteration step size, λ is the regularization parameter, and S is the soft threshold shrinkage operator.

9. The method for correcting multipath errors in a BeiDou navigation system according to claim 6, wherein: The reflection coefficient value of the corresponding reflection surface in the spatial reflection source model is adaptively adjusted by using a recursive low-pass filtering algorithm, and the recursive low-pass filtering algorithm is: Where, γ j (t) is the updated reflection coefficient value of the reflecting surface at the current epoch, γ j (t-1) is the historical reflection coefficient value of the reflecting surface in the previous epoch, α is the smoothing coefficient that determines the update rate, and the function The value of is determined by the actual reflection path intensity related to the reflecting surface currently solved and C k Decide.

10. A multipath error correction system in a BeiDou navigation system, applied to a multipath error correction method in a BeiDou navigation system according to any one of claims 1 to 9, characterized in that: include: An environment modeling unit is used to obtain three-dimensional spatial data through scanning by an environment perception sensor integrated in the navigation receiver, and to construct a spatial reflection source model including geometric parameters of potential reflection surfaces; a path prediction unit, configured to generate a set of multiple candidate paths based on geometric constraints in the spatial reflection source model constructed by the environment modeling unit, and calculate, for each candidate path in the set, an additional path delay generated compared to a direct propagation path; a model building unit, configured to extract the additional path delay of each candidate path calculated by the path prediction unit, assemble the additional path delay into an observation matrix representing the linear relationship between all candidate paths and the residuals of the pseudorange observations, and establish a sparse optimization model; an error solving unit, configured to solve the sparse optimization model established by the model building unit to invert a sparse solution vector representing a true reflection path, and reconstruct a total multipath error using the sparse solution vector and the measurement matrix; The positioning correction unit is used to subtract the total multipath error reconstructed by the error solving unit from the original pseudorange observation value of the navigation receiver to generate a corrected pseudorange observation value, and calculate the final positioning result based on the corrected pseudorange observation value.

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