An optimal UWB base station selection method based on multi-factor criterion

Abstract

The application discloses a kind of optimal UWB base station selection method based on multi-factor criterion, belong to wireless positioning and navigation technical field.The application constructs multi-factor characteristics in sliding time window to candidate base station / base station combination: including ranging error characteristics, abnormal point characteristics and geometric dilution of precision characteristics;After each feature is normalized, the integrated evaluation target function is obtained by weight fusion, and under the constraint of meeting the volume threshold of four base station tetrahedron, the optimal four base station combination with the minimum target function is obtained from the combination of N base stations;Subsequently, based on the ranging data of the selected base station, the position solution is completed by trilateration combined with weighted least squares / Huber robust estimation.The application can adaptively eliminate high error, high abnormal or configuration deterioration base station combination, reduce positioning error amplification effect, improve the precision and robustness of UWB positioning, suitable for unmanned vehicle, mobile robot and personnel positioning scene.

Description

Technical Field

[0001] This invention relates to the field of ultra-wideband positioning technology, and specifically to an optimal UWB base station selection method based on multi-factor criteria. Background Technology

[0002] Ultra-wideband (UWB) positioning systems typically consist of multiple fixed base stations and mobile tags. Tags acquire distance information through bidirectional ranging or time difference of arrival (TDOA) with the base stations, and their positions are further determined using trilateration or filtering methods. In practical applications, multiple base stations are often deployed to cover large areas. However, due to factors such as occlusion, multipath propagation, non-line-of-sight (NLOS) errors, and hardware differences, the ranging quality of different base stations varies significantly at different distances and orientations, and this variation changes over time during vehicle or robot movement. Using a fixed set of base stations or selecting base stations based solely on a single metric (e.g., using only GDOP to measure geometric configuration) can easily introduce high-error or high-anomaly ranging links, leading to amplified positioning errors, decreased stability, and even geometric degradation causing positioning failure. Therefore, there is an urgent need for a method that can simultaneously integrate multiple factors such as ranging quality, signal stability, and geometric observability, and can adaptively select the optimal combination of base stations online. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention provides an optimal UWB base station selection method based on multi-factor criteria, which is used to select the optimal four-base station combination in real time in a multi-base station environment and improve positioning accuracy and robustness.

[0004] To achieve the above objectives, the present invention provides the following technical solution: S1. Data Acquisition: Acquire the coordinate information of N base stations in the UWB positioning system, and the ranging observation sequence between the tag to be located and each base station at the current time or within the sliding time window.

[0005] S2. Multi-factor feature construction: Extracting multi-factor features based on the acquired information; The steps include: S2.1 Ranging Error Characteristics: For each measurement point, calculate the absolute error between the measured ranging value and the theoretical ranging value of each base station, forming a ranging error vector, and then using a triplet vector... It means that, among them, Indicates the base station number. Indicates tags and base stations The theoretical distance measurement value, Represented as the true ranging error; defined In the first At the measurement point, the first The deviation between the actual distance between each UWB base station and the tag reflects the ranging accuracy, and is expressed as: in, This represents the actual distance measurement value; The smaller the value, the higher the ranging accuracy. S2.2, Anomaly Characteristics: The number of anomalies detected at each measurement point characterizes the signal quality. An anomaly vector is constructed, using triples... It means that, among them, Indicates the base station number. Indicates tags and base stations The theoretical distance measurement value, This represents the number of outliers at that distance (including outliers with missing signals, jumps, or exceeding the ranging threshold); [Definition] In the first The first base station The number of sampling points that fail when a UWB base station acquires tag signals is represented as: in, Indicates the first Total number of samples at each base station Indicates the first Index of total number of samples at each base station Indicates base station The Each sample value, This is an indicator function (1 for invalid, 0 for valid). The smaller the value, the better the signal stability; S2.3 Constructing the area feature vector: Randomly select 4 base stations from N base stations, and calculate the area of ​​the polygon enclosed by their geometric distribution based on the actual distance measured from the tag to these 4 base stations. Simultaneously, the geometrical precision factor (GDOP) of the base station combination is calculated to quantify the impact of base station spatial layout on positioning error; using triples It means that, among them Indicates the base station number. Indicates tags and base stations The theoretical distance, Represents the geometric precision factor of the combination, and defines... In the first The first base station The geometric precision factor of a combination of UWB base stations is expressed as: in, This represents the Jacobian matrix of the positioning system. For operations on the trace of a matrix, The smaller the size, the better the geometric distribution of the base stations, and the weaker the amplification effect on positioning errors.

[0006] S3. Feature normalization and objective function construction: Perform feature normalization on the obtained multi-factor features, and establish an objective function based on the normalized features; S3.1. Perform range normalization on each type of feature to unify the value range to [0, 1]. Range normalization maps error characteristics and outlier characteristics to a unified evaluation direction where smaller values ​​are better; S3.2 Integrate the three types of normalized features into a three-dimensional feature vector to fully describe the comprehensive performance of the base station combination; Let the base station combination be ,in , , and If we represent four different base stations, then the three-dimensional feature vector of this combination is defined as: In the formula, Indicate combination The corresponding normalized ranging error, Indicate combination The corresponding normalized outliers, Indicate combination The corresponding normalized GDOP features; S3.3 Construct the objective function based on the three-dimensional feature vector; The objective function is a normalized weighted fusion of features, expressed as: in, , and These represent the weight coefficients of each item. and , and ≥0.

[0007] S4. Geometric Degradation Constraint: To avoid UWB positioning failures caused by base stations being collinear or coplanar, the volume of the tetrahedron formed by the selected base station combination needs to be optimized. Greater than the threshold , is represented as: In the formula, The three-dimensional coordinates of the four base stations, For determinant operations, ≥0, requirement > To avoid positioning degradation caused by base stations being colinear or coplanar.

[0008] S5. Optimal combination optimization: Among the candidate combinations that meet the volume constraints, the optimal four-base station combination with the minimum objective function is obtained through traversal search. Based on the traversal search, a pruning strategy is introduced, that is, when the normalized GDOP or normalized outlier features of the combination exceed the threshold, it is directly removed.

[0009] S6. Positioning Solution: Based on the optimal four-base station combination, linearized trilateration is adopted. A linear equation system is constructed through squared distance difference and solved by least squares. When there is NLOS or abnormal ranging, weighted least squares or Huber robust estimation is introduced to improve the stability of the solution. Specifically, the location of the tag to be estimated is determined by squared distance difference and linear least squares, where the coordinates of the four positioning base stations are known and denoted as a two-dimensional vector: in, Indicates the first The coordinates of each base station Indicates the first The x-coordinate of each base station Indicates the first The vertical coordinates of each base station; The label position to be estimated is represented as: in, Indicates the position of the label to be estimated. Let x be the x-coordinate of the label position to be estimated. The vertical coordinate of the label position to be estimated; Furthermore, the Euclidean norm and inner product are expressed as: in, Represents any vector, Represent another arbitrary vector; The UWB ranging model including noise is represented as follows: in, Indicates tag to base station The measured distance (including noise). Indicates the first The noise term of each base station ranging value includes NLOS bias and random error; Based on geometric relationships, we have: Its inner product expansion is as follows ,Right now Select a reference base station Eliminate the quadratic term by performing a difference operation, i.e., using subtract the equation The equations are: eliminate After sorting, we get: Multiplying both sides of the rearranged equation by -1 and dividing by 2 gives the information about the position of the undetermined label. The linear equation is: Expanding to coordinate form, we get: Furthermore, the three linear equations obtained after difference elimination (the three equations obtained by difference between base station 1 and base station 2, base station 3, and base station 4 respectively) are written in matrix form: ,in, The coefficient matrix, If the vector is a constant, then: Indicates the first A constant vector of base stations; at this time The equation number is 3, therefore there is no exact solution under noisy ranging. Least squares estimation is used to solve it: the residual is defined as... The least squares estimation objective function is: right Taking the derivative and setting the gradient to zero, we have: get ,like If the column is full, then The invertible, least squares estimation of the closed-form solution of the objective function is: in, This is the least squares estimate of the label location.

[0010] Beneficial effects of the present invention This invention effectively suppresses the bias caused by single-index selection by integrating multiple factors such as ranging error, outliers and GDOP, and improves the reliability of optimal base station combination determination.

[0011] This invention avoids geometric degradation by using tetrahedral volume threshold constraints, thereby reducing the risk of amplified positioning errors and solution failures.

[0012] This invention, through a sliding time window and a robust solution strategy, can maintain high positioning accuracy and stability in dynamic occlusion and multipath environments, making it suitable for real-time applications. Attached Figure Description

[0013] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the system framework of the present invention; Figure 3 A schematic diagram is constructed for multi-factor features; Figure 4 A schematic diagram illustrating the comprehensive objective function evaluation and optimal combination selection; Figure 5 This is a schematic diagram of the tetrahedral volume constraint. Figure 6 This is a schematic diagram of trilateration / least squares solution; Figure 7 This is a schematic diagram illustrating a specific implementation scenario using the algorithm described in this paper; Figure 8 This is a schematic diagram of the mean RMSE curve results for each base station ranging in this embodiment of the invention; Figure 9 This is a schematic diagram of the abnormality rate curves of data from each base station in an embodiment of the present invention; Figure 10 This is a schematic diagram of the mean curve results of various combinations of GDOP in the embodiments of the present invention; Figure 11 This is a comparison chart of the mean error in the embodiments of the present invention; Figure 12 This is a comparison chart of root mean square error in embodiments of the present invention. Detailed Implementation

[0014] The present invention will be further described in detail below with reference to specific embodiments.

[0015] like Figure 1 and Figure 2 As shown, this invention provides an optimal UWB base station selection method based on multi-factor criteria, comprising the following steps: S1. Data Acquisition: Acquire the coordinate information of N base stations in the UWB positioning system, and the ranging observation sequence between the tag to be positioned and each base station at the current time or within the sliding time window; S2. Multi-factor feature construction: Extracting multi-factor features based on the acquired information, such as... Figure 3 As shown; S3. Feature Normalization and Objective Function Construction: Perform feature normalization on the obtained multi-factor features, and establish an objective function based on the normalized features, such as... Figure 4 As shown; S4. Geometric Degradation Constraint: To avoid UWB positioning failures caused by base stations being collinear or coplanar, the tetrahedral volume formed by the selected base station combination needs to be optimized. Greater than the threshold ,like Figure 5 As shown; S5. Optimal combination optimization: Among the candidate combinations that meet the volume constraints, the optimal four-base station combination with the smallest objective function is obtained through traversal search. A pruning strategy is introduced on the basis of traversal search, that is, when the normalized GDOP or normalized outlier feature of the combination exceeds the threshold, it is directly removed. S6. Positioning Solution: Based on the optimal four-base station combination, linearized trilateration is employed. A system of linear equations is constructed using squared distance differences and solved using least squares. When NLOS or abnormal ranging occurs, weighted least squares or Huber robust estimation is introduced to improve the stability of the solution. Figure 6 As shown.

[0016] like Figure 7 As shown, this embodiment takes an indoor / semi-occluded scenario with an unmanned vehicle as an example. N=6 UWB base stations are deployed within a 10 m × 100 m rectangular area. The vehicle carries a UWB tag and obtains ranging data by sampling at 100 Hz. The system uses a sliding time window (e.g., 300 frames) to statistically analyze the ranging residuals and the number of failed samples for each base station, and calculates the GDOP and volume constraints for 15 (C(N,4)) four-base station combinations. A target function is constructed after range normalization for the three types of features, with weighting coefficients set such as α=0.4, β=0.3, and γ=0.3. When enhanced environmental occlusion leads to an increased proportion of outliers, β can be increased to modulate signal stability. This ensures... > (In this example) From the combinations with a range of 0.2 m³, the combination with the smallest objective function is selected, and a system of linear equations is established using trilateration. The tag coordinates are obtained using least squares. If the residual exceeds the threshold (0.8 m in this example), Huber robust weights are used to iterate and solve the problem again. Through the above steps, a better ranging link and geometric configuration can be obtained without increasing hardware costs, thereby significantly improving positioning accuracy and robustness.

[0017] Furthermore, as shown in Table 1, four base stations are randomly selected from the six groups of positioning base stations as the body combination method and configuration number of the positioning configuration. The combination number is used in place of the specific base station combination type for subsequent description. Table 1: Combination Numbering Table Calculate the three types of costs for 15 combinations of four base stations for 10 static points. , , A normalization function is constructed, and the candidate combinations are then used to solve for positioning errors using the actual locations. Finally, the combination with the smallest error is selected as the optimal combination for the static point. The positioning error is statistically analyzed using two metrics: Mean Absolute Error (MAE) and Root Mean Square Error (RMSE), and compared with a random four-base station strategy.

[0018] like Figure 8 The figure shows the RMSE in the simulation experiment, reflecting the mean RMSE variation curves of each base station in this example. Base station A has the highest RMSE, while base stations C and F have relatively lower RMSEs. The overall mean ranging RMSE error remains within the range of 0.5 to 0.6, which is consistent with the statistical law of UWB errors. Under the current settings, the ranging accuracy of each base station is on the same order of magnitude, with relatively mild differences.

[0019] Furthermore, under the condition that the ranging accuracy of each base station is similar, the optimal base station fusion selection strategy is more sensitive to the geometric configuration. The ranging error term mainly plays a constraining role in suppressing the combination of inferior base stations, rather than being a dominant ranking factor.

[0020] Figure 9 The anomaly rate variation curves in this example are presented. As can be seen from the figure, the simulation anomaly rates of base stations D and A are relatively high, while the signal quality of base stations C and F is good. The anomaly rate statistics are consistent with the constructed hybrid error model under the threshold meaning, thus verifying the rationality of anomaly point modeling and discrimination threshold setting. Anomalies affect positioning accuracy by increasing residuals, while lost ranging affects availability by reducing effective solution rate.

[0021] Figure 10 The figure presents the variation of the mean GODOP (Geometric Optimization Distance) for different base station combinations under 10 static positioning points. Since GODOP reflects the geometric amplification effect—meaning that when the ranging noise statistical level is similar—a smaller GODOP indicates a smaller amplification of the same ranging disturbance in the location domain, making the positioning solution less sensitive to noise and small deviations—GDOP is a purely geometric quality index independent of specific noise levels, suitable for prior screening of the geometric observability of base station combinations. The figure shows that the average GDOP of the combinations ranges from approximately 1.8 to 3.5, with significant differences, indicating that even with the same number of base stations, the geometric configuration still has a significant impact on positioning observability.

[0022] In this example, the optimal base station combinations for each static point are shown in Table 2. During the experiment, the optimal combinations were repeated at different locations, indicating that several combinations were repeatedly selected at multiple static points. This demonstrates that under the same error model, this combination simultaneously possesses lower ranging error costs and anomaly risk costs, thus exhibiting a stable advantage across multiple locations.

[0023] Table 2: Optimal base station combination for each static point Figure 11 and Figure 12 The MAE curve and RMSE change curve of the sampling points after the weighted optimal base station selection described in this chapter are described.

[0024] Statistical results show that, at the vast majority of static points, the optimal four-base station selection outperforms the random four-base station strategy in both MAE and RMSE, with some points exhibiting significant gains. This indicates that the fusion selection mechanism can achieve a more reasonable trade-off between geometric advantages and disadvantages and data quality risks, thereby reducing the expected level of positioning errors and suppressing their occurrence. The reasons for this gain are twofold: first, the optimal selection tends towards combinations with low GDOP, weakening the amplification effect of ranging noise into the location domain; second, the optimal selection tends towards combinations with lower anomaly rates, reducing the number of extreme residuals faced by the system, thus improving estimation stability and accuracy consistency.

[0025] The above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the concept and scope of the present invention. Without departing from the design concept of the present invention, all modifications and improvements made by those skilled in the art to the technical solutions of the present invention should fall within the protection scope of the present invention. The technical content for which protection is sought in the present invention has been fully described in the claims.

Claims

1. A method for selecting the optimal UWB base station based on multi-factor criteria, characterized in that, Includes the following steps: S1. Obtain the coordinate information of N base stations in the UWB positioning system and the ranging observation sequence between the tag to be positioned and each base station at the current time or within the sliding time window. S2. Extract multi-factor features based on the acquired information, including: ranging error features, outlier features, and area feature vectors; S3. Perform feature normalization on the obtained multi-factor features, and establish an objective function based on the normalized features; S4. In order to avoid UWB positioning failure caused by base stations being collinear or coplanar, the volume of the tetrahedron formed by the selected base station combination needs to be greater than the threshold. S5. Among the candidate combinations that satisfy the volume constraints, the optimal four-base station combination with the minimum objective function is obtained by traversing the search. A pruning strategy is introduced during the traversal search, that is, when the combined normalized geometric precision factor or normalized outlier features exceed the threshold, they are directly removed. S6. Based on the optimal four-base station combination, linearized trilateration is adopted, and a system of linear equations is constructed by squared distance difference and solved by least squares. When NLOS or outlier ranging exists, weighted least squares or Huber robust estimation is introduced to improve the stability of the solution and complete the final position calculation.

2. The optimal UWB base station selection method based on multi-factor criteria according to claim 1, characterized in that: Step S2 includes: S2.1 Ranging Error Characteristics: For each measurement point, calculate the absolute error between the measured ranging value and the theoretical ranging value of each base station, forming a ranging error vector, and then using a triplet vector... It means that, among them, Indicates the base station number. Indicates tags and base stations The theoretical distance measurement value, Represented as the true ranging error; defined In the first At the measurement point, the first The deviation between the actual distance between each UWB base station and the tag reflects the ranging accuracy, and is expressed as: in, This represents the actual distance measurement value; The smaller the value, the higher the ranging accuracy. S2.2, Anomaly Characteristics: The number of anomalies detected at each measurement point characterizes the signal quality. An anomaly vector is constructed, using triples... It means that, among them, Indicates the base station number. Indicates tags and base stations The theoretical distance measurement value, This represents the number of outliers at that distance; definition In the first The first base station The number of sampling points that fail when a UWB base station acquires tag signals is represented as: in, Indicates the first Total number of samples at each base station Indicates the first Index of total number of samples at each base station Indicates base station The Each sample value, For indicator functions, The smaller the value, the better the signal stability; S2.3 Constructing the area feature vector: Randomly select 4 base stations from N base stations, and calculate the area of ​​the polygon enclosed by their geometric distribution based on the actual distance measured from the tag to these 4 base stations. Simultaneously, the geometrical precision factor (GDOP) of the base station combination is calculated to quantify the impact of base station spatial layout on positioning error; using triples It means that among them Indicates the base station number. Indicates tags and base stations The theoretical distance, Represents the geometric precision factor of the combination, and defines... In the first The first base station The geometric precision factor of a combination of UWB base stations is expressed as: in, This represents the Jacobian matrix of the positioning system. For operations on the trace of a matrix, The smaller the size, the better the geometric distribution of the base stations, and the weaker the amplification effect on positioning errors.

3. The optimal UWB base station selection method based on multi-factor criteria according to claim 1, characterized in that: The steps in S3 include: S3.

1. Perform range normalization on each type of feature to unify the value range to [0, 1]. S3.

2. The three normalized features are integrated into a three-dimensional feature vector to fully describe the overall performance of the base station combination. The three-dimensional feature vector of this combination is defined as follows: In the formula, Indicate combination The corresponding normalized ranging error, Indicate combination The corresponding normalized outliers, Indicate combination The corresponding normalized GDOP features; S3.

3. Based on the three-dimensional feature vectors, construct the objective function, expressed as: in, , and These represent the weight coefficients of each item. and , and ≥0.

4. The optimal UWB base station selection method based on multi-factor criteria according to claim 1, characterized in that: The expression for S4 is as follows: In the formula, The three-dimensional coordinates of the four base stations, For determinant operations, ≥0, require the tetrahedron volume Threshold To avoid positioning degradation caused by base stations being colinear or coplanar.

5. The optimal UWB base station selection method based on multi-factor criteria according to claim 1, characterized in that: S6 includes the following steps: Construct a system of linear equations using the squared distance difference method: In the formula, The coefficient matrix, If the vector is a constant, then: In the formula, The three-dimensional coordinates of the four base stations, The x-coordinates of the four base stations are: The vertical coordinates of the four base stations are: Let be a constant vector of three base stations, where , Indicates the first A constant vector for each base station, This represents the measured distance from the tag to base station 1. Indicates tag to base station The measured distance Indicates the first The coordinates of each base station; Solve using the least squares method: in, This is the least squares estimate of the label location.

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