An Optimization Method for Non-Line-of-Sight Base Station Deployment Based on UWB Positioning

Abstract

The present invention discloses an optimization method for non-line-of-sight base station deployment based on UWB positioning. First, the present invention sets reference points, and conducts rough area division according to the characteristics of the terrain scene and experience, and data collection is carried out for each reference point. Secondly, according to the collected data, a probability distribution graph of ranging error and a histogram of different distance errors are constructed, the error model distribution is obtained by fitting, and the parameter values of the reference points in different regions are statistically analyzed. Then, according to the ranging areas divided by the clustering algorithm, and combined with the function fitting relationship, the variance expression of the ranging error is obtained. Finally, based on the geometric dilution of precision evaluation index, an evaluation index for base station deployment in non-line-of-sight situations is constructed, and an optimization model for base station deployment is established around this evaluation index. The present invention makes up for the deficiencies of the GDOP evaluation index in non-line-of-sight scenarios, and provides certain reference value for the base station deployment strategy in complex non-line-of-sight indoor scenarios.

Description

Technical Field

[0001] The present invention belongs to the field of indoor positioning / base station deployment, and in particular relates to a non-line-of-sight base station deployment optimization method based on UWB positioning. Background Art

[0002] The current positioning technologies include Wi-Fi, Bluetooth, ultrasonic, infrared, Zigbee and other positioning technologies. These technologies have good positioning performance in line-of-sight situations, but due to the non-line-of-sight (NLOS) factors in complex indoor environments, these technologies cannot show accurate positioning perception well. Ultra-wide Band (UWB) has become one of the most promising indoor positioning technologies with its advantages such as high precision, strong penetration and low power consumption. In the non-line-of-sight state in complex indoor environments, the quality of base station deployment is the key to improving the positioning accuracy of UWB. However, for indoor positioning, base station deployment mostly depends on the experience of staff and typical regular deployment methods (square, Y-shaped, diamond, T-shaped, etc.). In addition, most studies are based on the assumption that the ranging error follows a Gaussian distribution with a mean of zero and a constant variance, and the GDOP (geometric dilution of precision factor) base station deployment evaluation index is constructed and optimized. This evaluation index is only applicable to base station deployment in line-of-sight situations. In the UWB positioning base station deployment strategy, it is very necessary to construct appropriate base station deployment evaluation indicators. The evaluation indicators also involve the quality of deployment, positioning accuracy, and cost issues.

[0003] At present, the mainstream base station deployment method is mainly based on personnel experience and some typical rules. Although its deployment is fast and easy to adjust, from an essential point of view, this deployment method is still only a deployment method in a special location, and it is not universal for base station deployment in actual situations. Secondly, the base station deployment optimization model based on the GDOP evaluation index assumes that the ranging error obeys a Gaussian distribution with a mean of zero and a constant variance. It does not consider the influence of factors such as the base station and the target position and non-line-of-sight on the measurement error. Therefore, this evaluation index is not suitable for base station deployment in non-line-of-sight situations. For complex non-line-of-sight indoor environments, for targets to be measured in different areas, the ranging error of each base station does not obey the same distribution, and its probability distribution parameters are also different. Therefore, proposing a new evaluation index to determine the pros and cons of base station deployment in non-line-of-sight scenarios is of great significance to the optimization of base station deployment. Summary of the invention

[0004] In order to solve the above problems, the present invention proposes a non-line-of-sight base station deployment optimization method based on UWB positioning. Specifically, it includes the following steps:

[0005] S1: According to the characteristics of the non-line-of-sight (NLOS) scenario where the base station is deployed, the indoor communication line of sight is blocked due to the complex environment and numerous obstacles, set reference points to explore the distribution of NLOS ranging errors.

[0006] S2: Combine the NLOS scenario in S1, and make a preliminary regional division according to the terrain scenario characteristics and experience. Deploy the base stations at corresponding positions by using typical traditional rules such as squares, rectangles, and rhombuses, so as to make the coverage area of the entire region as large as possible. Place the UWB tags at the set reference points respectively, and collect data at each reference point.

[0007] S3: According to the data collected in S2, since the true coordinates of the base station and the reference points are known, the true distance value between the base station and the reference points is calculated from the true coordinates. The ranging values are obtained by the sensors of each base station and tag. Due to the influence of NLOS, the ranging values of each base station are larger than the true distance value, with positive errors, and obviously the ranging accuracy has been reduced.

[0008] To analyze the ranging error (measured distance minus true distance) in more detail, calculate the error from the ranging of the UWB tag and the true coordinates, and construct the probability distribution function (PDF) of the ranging error and the histogram of different distance errors. According to the probability distribution function of the ranging error and the histogram of different distance errors, it can be fitted by the Gamma curve, and its error model distribution is:

[0009]

[0010] where \(x\) is the ranging error, \(\alpha\) and \(\beta\) are the shape parameter and scale parameter of the Gamma distribution respectively, and \(\Gamma(\cdot)\) is the Gamma function, and its function expression is:

[0011]

[0012] Using the properties of the Gamma function, the mathematical expectation of the Gamma distribution can be obtained as:

[0013]

[0014] Also

[0015]

[0016] Then the variance of the Gamma distribution is:

[0017]

[0018] From the above analysis, it can be seen that to obtain the variance of the Gamma distribution, the most important parameters are the shape parameter \(\alpha\) and the scale parameter \(\beta\). Therefore, the ranging errors of the reference points at different positions are fitted by the Gamma distribution to obtain the corresponding \(\alpha\) and \(\beta\) parameter values.

[0019] S4: Statistically analyze the parameter values α and β of the reference points at different positions in S3, and it will be found that the parameter values in each region are different. Since the regional division is a preliminary division based on scene characteristics and experience, its role is to explore the distribution parameters of ranging errors in each region. Based on the preliminary regional division in S2, use the K-means algorithm of the unsupervised learning method to cluster the distribution parameters obtained in each region, and accurately divide the ranging regions.

[0020] S5: According to the ranging region results divided by the K-means clustering algorithm in S4, examine the terrain and scene of complex indoor non-line-of-sight. Fixed obstacles will occupy a certain space. Due to conditional restrictions and geometric position constraints, when deploying base stations in this scenario, the base station coordinates are constrained on the three sides close to the wall, so that the base station position is not affected by fixed obstacles, and the communication range is large and easy to cover.

[0021] Move the base station coordinates and measure the distance to the reference points in each region to obtain the parameter values of each ranging error distribution, and construct the functional fitting relationship between the base station and the parameter values of each region. Combine the functional fitting relationship to obtain the variance expression of the ranging error, and this variance expression form is consistent with the gamma distribution form. It is expressed as follows:

[0022]

[0023] Among them, i is the serial number of the base station constraint condition.

[0024] S6: Construct an evaluation index for base station deployment in non-line-of-sight situations.

[0025] Based on the geometric dilution of precision (GDOP) evaluation index, combine the variance expression of the ranging error to construct the COV evaluation index for base station deployment in non-line-of-sight situations. Its physical meaning is that considering different ranging error distributions, if the value of the objective function at a certain moment is smaller, it means that the positioning error is smaller, and further indicates that the base station deployment method at this moment is better.

[0026] S7: According to the COV evaluation index proposed in S6, establish an optimization model for base station deployment around this evaluation index. Determine the independent variables, constraint conditions, and objective function of the model according to the actual scenario, and solve the optimal solution of the model.

[0027] (1) Independent variables

[0028] The selected independent variables are the coordinate positions of each base station.

[0029] (2) Constraint conditions

[0030] Due to the particularity of the scenario, the geometric constraint conditions of the base stations analyzed in S5 are used as the constraint conditions for the base station deployment optimization model. The functional relationship between the fitting function of the ranging error distribution parameter values in each region obtained through S5 and the base station constraint conditions is obtained.

[0031] (3) Objective function

[0032] For the non-line-of-sight scenario, the COV evaluation index proposed by the present invention is to weigh the average positioning accuracy of the base stations for the target tags under this base station layout method. Based on the COV evaluation index, the aim is to minimize the average COV in all regions. For the N regions divided in this scenario, the objective function can be set as:

[0033]

[0034] where the independent variable X = [x1, y1, z1, x2, y2, z2,..., x4, y4, z4] T is the coordinate vector of each base station. Set the 16 test points in S2 as sample points.

[0035] Through the above-set independent variable, constraint conditions and objective function, an optimization model for UWB base station deployment in the non-line-of-sight situation can be constructed. Similarly, within the base station deployment constraint area and target area, a heuristic optimization algorithm can be used to iteratively optimize the objective function. When the value of the objective function is the smallest, the independent variable is determined as the optimal deployment position of the base station.

[0036] Advantages of the present invention:

[0037] 1. The present invention mainly proposes a method and strategy for UWB base station deployment in the non-line-of-sight situation, and proposes an objective function COV as an evaluation index to judge the pros and cons of base station deployment in the known non-line-of-sight scenario, making up for the deficiency of the GDOP evaluation index applied to the non-line-of-sight scenario.

[0038] 2. For large non-line-of-sight indoor scenarios such as underground garages, data is collected through a series of scenario experiments. First, the distribution parameters of the ranging error in the non-line-of-sight situation are obtained based on the experimental data, and the distribution parameters are clustered through the K-means algorithm, and then the non-line-of-sight scenario areas are refined. Secondly, for the geometric constraints of the scenario base stations, on the basis of the above clustering, the relationship between the geometric positions of the base stations and the distribution parameters is fitted. And according to the data results, the evaluation index applicable to the base station deployment in the non-line-of-sight situation is extended and the optimal base station coordinates are solved. The objective function, experimental content, optimization method and steps proposed by the present invention can provide a certain reference value for the base station deployment strategy in complex non-line-of-sight indoor scenarios. Description of the drawings

[0039] Figure 1 It is a schematic plan view of the underground garage scenario;

[0040] Figure 2 It is a flowchart for optimizing the deployment of UWB non-line-of-sight base stations;

[0041] Figure 3 It is a plan view of the non-line-of-sight ranging experiment;

[0042] Figure 4 It is a schematic diagram of fitting with the gamma curve;

[0043] Figure 5 It is the process of the K-menas clustering algorithm;

[0044] Figure 6 It is the workflow for identifying the base station location constraints and probability distribution parameters;

[0045] Figure 7(a) is an iterative curve graph of the taboo optimization objective function;

[0046] Figure 7(b) is the optimal base station deployment based on the taboo optimization algorithm;

[0047] Figure 8(a) is an iterative curve graph of the particle swarm objective function;

[0048] Figure 8(b) is the optimal base station deployment based on the particle swarm algorithm;

[0049] Figure 9(a) is an iterative curve graph of the genetic algorithm objective function;

[0050] Figure 9(b) is the optimal base station deployment based on the genetic algorithm;

[0051] Figure 10 It is a schematic diagram of the convergence curve of the experimental results;

[0052] Figure 11 It is a bar chart of the experimental result errors. Specific implementation manners

[0053] The present invention will be further described below with reference to the accompanying drawings.

[0054] The present invention includes the following steps:

[0055] S1: In an indoor scenario where the positioning area is large and there are many obstacles, the base station signals of UWB are affected by non-line-of-sight. For the target to be measured in different areas, the ranging errors obtained by each base station do not follow the same distribution. Therefore, according to the characteristics of the scenario, reference points need to be set to explore the distribution of non-line-of-sight ranging errors. In the embodiment of the present invention, the non-line-of-sight environment of an underground garage is used as the research object. The size of this scenario is 42.0 m in length, 37.8 m in width, and 2.5 m in height, which includes 3 channel doors, 12 evenly distributed columns, and fixed objects such as a high-voltage room with a length of 21.4 m and a width of 8.4 m. In addition, various vehicles parked in the designated parking spaces are used as fixed obstacles. To better quantify the ground size, each dotted line interval is 4.2 m. The schematic plan view of the underground garage scenario and its various size parameters are as Figure 1 shown.

[0056] S2: Combined with Figure 2 the UWB non-line-of-sight base station deployment optimization flowchart. First, combined with the non-line-of-sight underground garage scenario in S1, Figure 1 area division, reference point setting, and non-line-of-sight error distribution exploration are carried out. To obtain the ranging error distribution in different areas, according to the characteristics of the underground garage scenario and the trajectory routes of pedestrians and motor vehicles, the present invention first divides 4 areas and divides 16 test reference points through the previous tiling partition. Four base stations are placed at the corresponding positions by the relatively optimal square deployment method in the typical rules: A1(0,0), A2(33.6,0), A3(0,33.6), A4(33.6,33.6); the UWB tags are respectively placed at the 16 set test reference points and the height is set to 1 m. 500 groups of data are collected at each point, and the non-line-of-sight conditions include fixed columns and motor vehicles on the parking spaces. The non-line-of-sight ranging experiment plan view is as Figure 3 shown.

[0057] S3: According to the data collected in S2, since the true coordinates of the positions of the base stations and the test reference points are known, the true distance values between the nodes can be calculated from the theoretical coordinates. Due to the influence of non-line-of-sight, the ranging values of each base station are larger than the true distance values, with positive errors, and obviously the ranging accuracy has decreased. To analyze the ranging error (measured distance minus true distance) in more detail, the error is calculated from the ranging of the UWB tag and the true coordinates, and the probability distribution diagram (PDF) of the ranging error and the histogram of different distance errors are constructed. According to the ranging error probability distribution diagram, it can be fitted by the Gamma curve, as Figure 4 shown, and its error model distribution is:

[0058]

[0059] Where x is the ranging error, α and β are the shape parameter and scale parameter of the gamma distribution respectively, and Γ(·) is the gamma function, whose function expression is:

[0060]

[0061] Using the properties of the gamma function, the mathematical expectation of the gamma distribution can be obtained as:

[0062]

[0063] Also

[0064]

[0065] Then the variance of the gamma distribution is:

[0066]

[0067] From the above analysis, it can be seen that to obtain the variance of the gamma distribution, the most important parameters are the shape parameter α and the scale parameter β. Therefore, the ranging errors of the reference test points at different positions are fitted through the gamma distribution to obtain the corresponding α and β parameter values.

[0068] S4: Statistically analyze the parameter values α and β of the internal reference test points at different positions in S3, and it will be found that the parameter values in each region are not the same. Since the regional division of the underground garage is a preliminary division work based on scene characteristics and experience, its role is to explore the distribution parameter situation of the ranging errors in each region. From Figure 2 the UWB non-line-of-sight base station deployment optimization flowchart, it can be seen that based on the first-step regional division work in S2, the present invention performs clustering processing on the distribution parameters obtained in each region through the K-means algorithm of the unsupervised learning method, accurately divides the ranging regions, and further lays a foundation for the subsequent identification of the distribution parameters. The basic idea of K-means is to first determine the points in space and cluster them with these points as the centers, so that the objects close to the center are grouped into one category. K-means updates the values of the cluster centers in an iterative manner. When the objective function converges, the process ends. Finally, the test points with distribution parameters belonging to the same cluster are divided into one region for subsequent parameter identification processing. The K-menas clustering algorithm process is as Figure 5 shown.

[0069] S5: Based on the regional division results of the K-means clustering algorithm in S4, the complex indoor non-line-of-sight terrain and scenes are investigated. Fixed obstructions such as pillars, motor vehicles and doors will occupy a certain space. Due to the restrictions of conditions and geometric positions, the present invention constrains the base station coordinates on three sides close to the wall when deploying base stations in this scenario, so that the base station position is not affected by fixed obstructions, and the communication range is large and easy to cover. The workflow of base station position constraint and probability distribution parameter identification is as follows: Figure 6 As shown. Due to the particularity of the scene, x and y are the horizontal and vertical coordinates of the constrained base station respectively. The base station constraint conditions are:

[0070]

[0071] Secondly, the base station coordinates are moved with a step length of 4.2m between each dotted line and the reference points in each area are measured to obtain the parameter values of each ranging error distribution, and a function fitting relationship between the base station and the parameter values of each area is constructed. The variance expression of the ranging error is obtained by combining the functional relationship, and the variance expression form is consistent with the gamma distribution form. It is expressed as follows:

[0072]

[0073] Wherein, i is the base station constraint condition number.

[0074] S6: Combine Figure 2 The optimization flow chart of UWB non-line-of-sight base station deployment needs to construct the evaluation index of base station deployment in non-line-of-sight situation. The present invention constructs the evaluation index COV of base station deployment in non-line-of-sight situation based on the evaluation index of geometric dilution of precision factor (GDOP). The GDOP definition formula is:

[0075] dX=[(H T H) -1 H T )]dR=MdR

[0076] We can get:

[0077] dZ=[(H T H) -1 H T )]dr

[0078] Among them, there are n base stations, dZ is the target position estimation error value in the non-line-of-sight situation, which is a 3-dimensional vector; dr represents the ranging error of the base station, which is an n-dimensional vector; H is still the coefficient matrix of the direction cosine of the tag to be tested relative to each base station. They are respectively expressed as:

[0079]

[0080] According to the definition of covariance, the covariance matrix can be written as:

[0081] cov(dZ) = E[dZ·dZ T 3×3

[0082] Similarly, when the geometric relationship between the tag to be measured and the base station remains unchanged at a certain moment, we have:

[0083] cov(dZ) = E(dZ·dZ T ) = (H T H) -1 H T E(dr·dr T )H(H T H) -1

[0084] where E(drdr T ) is the covariance of dr. The covariance of dr can be expressed as:

[0085]

[0086] The three components of dZ represent the error values of the position estimation solution. According to the definition of covariance, cov(dZ) can be expanded as:

[0087]

[0088] By combining the above equations, we can obtain:

[0089]

[0090] By analyzing the above equation, the objective function COV can be defined as the sum of the components of cov(dZ). The specific expression is as follows:

[0091]

[0092] This objective function can be used as an evaluation index for base station deployment in the NLOS scenario. Its physical meaning is that considering different ranging error distributions, if the value of the objective function is smaller at a certain moment, it means that the positioning error is smaller, and thus the base station deployment method at that moment is better.

[0093] S7: According to the COV evaluation index mentioned in S6, establish an optimization model for base station deployment around this evaluation index. Determine the independent variables, constraint conditions, and objective function of the model according to the actual scenario, and solve the optimal solution of the model. Three aspects need to be considered:

[0094] (1) Independent variables

[0095] The selected independent variables are the coordinate positions of each base station. In the present invention, 4 base stations are selected, and their coordinates in the three-dimensional space are set as S i = [x i , y​i , z i T , where \(i = 1, 2, 3, 4\), and the corresponding independent variables are \([x_1, y_1, z_1, x_2, y_2, z_2, \cdots, x_4, y_4, z_4]\) T 。

[0096] (2) Constraint conditions

[0097] Due to the particularity of the scenario, the geometric constraint conditions of the base stations analyzed in S5 are used as the constraint conditions for the base station deployment optimization model. The functional relationship between the fitting function of the ranging error distribution parameters in each area obtained through S5 and the function of the base station constraint conditions is obtained.

[0098] (3) Objective function

[0099] For the non-line-of-sight scenario, the COV evaluation index proposed by the present invention is to balance the average positioning accuracy of the base stations for the target tags in this station layout method. Based on the COV evaluation index, the aim is to minimize the average COV in all areas. For the N areas divided in this scenario, the objective function can be set as:

[0100]

[0101] where the independent variable \(X = [x_1, y_1, z_1, x_2, y_2, z_2, \cdots, x_4, y_4, z_4]\) T 。Set the 16 test points in S2 as sample points.

[0102] Through the above-set independent variables, constraint conditions, and objective function, an optimization model for UWB base station deployment in the non-line-of-sight scenario can be constructed. Similarly, within the constraint area and target area of the base station deployment, a heuristic optimization algorithm can be used to iteratively optimize the objective function, and when the value of the objective function is the smallest, the independent variable is determined as the optimal deployment position of the base station.

[0103] Optimization experiment:

[0104] According to the COV objective function proposed in the previous section, an optimization model for base station deployment is established around this objective function. Similarly, according to the actual scenario of the underground garage, determine the independent variable, constraint conditions, and objective function of the model, and then solve the optimal solution of the model.

[0105] Three aspects need to be considered:

[0106] (1) Independent variable

[0107] The selected independent variable is the coordinate position of each base station. In this case, 4 base stations are selected. Due to the limitation of pipelines at high places in the underground garage scenario this time, the height is uniformly set to 2m during station layout, that is, its coordinates in the three-dimensional space are S i = [x i , y​i , 2] T , where \(i = 1, 2, 3, 4\), and the corresponding independent variables are \([x_1, y_1, 2, x_2, y_2, 2, \cdots, x_4, y_4, 2]\) T 。

[0108] (2) Constraint conditions

[0109] There is a certain quantitative relationship between the ranging error distribution parameters and the constraint conditions, as shown in Table 1 specifically.

[0110] Table 1 Quantitative relationship diagram of parameter identification

[0111]

[0112] (3) Objective function

[0113] For the non-line-of-sight scenario, the COV objective function proposed by the present invention is to balance the average positioning accuracy of the base station for the target tag in this station layout mode. Based on the COV evaluation index, the aim is to minimize the average COV of all regions. For the three regions divided in this scenario, the objective function can be set as follows:

[0114]

[0115] where the independent variable \(X = [x_1, y_1, 2, x_2, y_2, 2, \cdots, x_4, y_4, 2]\) T 。Set Figure 3 The 16 test points are used as sample points. Among them, Region 1 contains 8 sample points, Region 2 contains 4 sample points, and Region 3 contains 4 sample points.

[0116] Through the above-set independent variables, constraint conditions, and objective function, an optimization model for UWB base station deployment in the non-line-of-sight scenario can be constructed. Similarly, within the constraint region and target region of the base station deployment, a heuristic optimization algorithm is used to iteratively optimize the objective function. When the value of the objective function is the smallest, the independent variable is determined as the optimal deployment position of the base station. The tabu algorithm, particle swarm algorithm, and genetic algorithm are used to solve the deployment optimization model to obtain the corresponding optimal base station positions, and experimental verification and comparative analysis are carried out. Furthermore, conclusions are drawn. The optimal base station coordinates based on the tabu optimization algorithm are shown in Table 2, and the optimal base station coordinates based on the particle swarm algorithm are shown in Table 2.

[0117] The tabu optimization algorithm curve and the optimal base station deployment coordinates are shown in Figures 7(a) and 7(b).

[0118] Table 2 Optimal base station coordinates based on the tabu optimization algorithm

[0119]

[0120] Secondly, the particle swarm optimization algorithm is adopted, and the relevant parameters of the particle swarm algorithm are set as shown in Table 3.

[0121] Table 3 Parameter Values of Particle Swarm Algorithm

[0122]

[0123] The particle swarm iteration curve and the optimal base station deployment coordinates are shown in Figures 8(a), 8(b) and Table 4.

[0124] Table 4 Optimal Base Station Coordinates Based on Particle Swarm Algorithm

[0125]

[0126] The genetic algorithm is adopted. Set the positioning base stations to 4. The deployable area of the set base stations, the area of the target to be measured, the constraint conditions and the sampling point area are the same. Set the maximum number of iterations to 500, the population size to 60, the selection probability to 0.9, the crossover probability of the single-point crossover method to 0.6, and the mutation probability to 0.01. The particle swarm iteration curve and the optimal base station deployment coordinates are shown in Figures 9(a) and 9(b), and the optimal base station coordinates based on the genetic algorithm are shown in Table 5.

[0127] Table 5 Optimal Base Station Coordinates Based on Genetic Algorithm

[0128]

[0129] In addition, in the face of this complex indoor non-line-of-sight environment, the complexity of the system model calculation is also analyzed. By collecting the calculation time of the three algorithms, the configuration of the experimental computer processor is 11th Gen Intel(R) Core(TM) i5-1135G7, and the on-board memory is 16.0GB. The calculation time of the solution is shown in Table 6.

[0130] Table 6 Comparison Table of Calculation Time

[0131]

[0132] By Figure 10It can be seen that the convergence results of the tabu optimization algorithm and the particle swarm optimization algorithm are both better than those of the genetic algorithm, and both can obtain the optimal solution of 1.6540. Among them, the tabu optimization algorithm has a faster convergence speed. Secondly, the particle swarm algorithm can start from a higher objective value and finally converge to the optimal solution of 1.6540. Its span is relatively large, indicating its strong global search ability, but its convergence speed is lower than that of the tabu optimization algorithm and the genetic algorithm. And it can be seen from Table 6 that the solution time of the tabu algorithm is shorter, which also highlights its great advantage in the real-time performance of the algorithm. Therefore, it can be seen from the iteration curve and the system complexity that the tabu algorithm has great advantages in both the line-of-sight experimental scenario and the non-line-of-sight underground garage experimental scenario in the base station deployment optimization.

[0133] Experimental Verification of the Optimal Deployment Positioning Error of the Base Station

[0134] Similarly, in order to analyze the positioning accuracy of the optimal base station deployment under non-line-of-sight of the three optimization algorithms proposed in the present invention, 4 static target test points are selected in the known non-line-of-sight scenario of the underground garage, and the target tags are placed at the 4 test points for data collection and positioning solution. 1000 times of data collection and positioning solution are carried out at each position, and the average coordinates are obtained and compared with the true value coordinates to obtain the positioning error, and the positioning accuracy of the optimal base station deployment obtained by the three algorithms is analyzed and evaluated. The coordinates of the test points are shown in Table 7.

[0135] Table 7 True Coordinates of the Test Points

[0136]

[0137] The error analysis values of the static target test points are shown in Table 8. The solved coordinates are reserved to 2 decimal places, and the positioning error is reserved to 4 decimal places.

[0138] Table 8 Error Analysis Values of the Static Target Test Points

[0139]

[0140] Conclusion:

[0141] Based on the proposed non-line-of-sight base station deployment COV evaluation index, the tabu algorithm, the particle swarm algorithm and the genetic algorithm are used to solve the base station deployment optimization model, and the corresponding optimal base station positions are obtained. Static test points are used for the comparison and analysis of the positioning accuracy. From Table 8 and Figure 11 it can be seen that for the known non-line-of-sight indoor scenario of the underground garage, compared with the other two optimization algorithms, the tabu optimization algorithm has a higher positioning accuracy for the optimal base station deployment solved. In Area 1 and Area 2, the positioning error is basically about 0.2 m; even in the more complex Area 3, the positioning error can be maintained at about 0.55 m, which meets the positioning accuracy of a single UWB sensor in the face of complex non-line-of-sight situations. The results of the positioning experiment verification are also in line with Figure 10The COV iterative change curve graph has been mutually verified.

[0142] Supplementary description:

[0143] Furthermore, the calculation method of the geometric dilution of precision (GDOP) described in S6 is obtained based on the Taylor series iterative algorithm under the TOA ranging method. Assume that the three-dimensional coordinates of the tag to be measured are (x, y, z), and the known base station coordinates in space are (x i , y i , z i ), i = 1, 2, 3...n, and the ranging value from the tag to be measured to the i-th base station is expressed as r i . Then, the ranging equation set for TOA is expressed as follows:

[0144]

[0145] To solve this equation using the Taylor series iterative algorithm, a tag position coordinate for initial calculation is required to perform the Taylor series expansion. Assume that the deviation between the true tag position p = (x, y, z) and the initial calculated tag coordinates is (△x, △y, △z). Then, the ranging value can be expressed as:

[0146]

[0147] The ranging value at the approximate value of the initial tag position can be expressed as:

[0148]

[0149] The following relationship exists between the true tag position coordinates and the initial calculated position coordinates:

[0150]

[0151] So, there is:

[0152]

[0153] Perform Taylor expansion on it at , and omit the terms of the second order and later to obtain:

[0154]

[0155] Its partial derivative at p' is:

[0156]

[0157] Let Its geometric meaning represents the cosine of the x direction of the initial calculated coordinates relative to the known point i. Therefore, it can be sorted out as:

[0158]

[0159] Let There is:

[0160] △r i = a xi △x - a yi △y - a zi △z

[0161] When the number of positioning base stations is greater than or equal to 4, it can be written as a system of equations as follows:

[0162]

[0163] Written in matrix form as:

[0164] △R = H△X

[0165] Where

[0166]

[0167] Then it can be obtained:

[0168] △X = (H T H) -1 H T △R

[0169] Among them, H is the coefficient matrix of the direction cosine of the tag to be measured relative to each base station, which is related to the relative positions of the tag to be measured and each base station. (a xi , a yi , a zi ) is the unit vector from the n×3 - dimensional point to the i - th base station. When n = 4, △X can be obtained by the following formula:

[0170] △X = H -1 △R

[0171] When n > 4, it can be written as:

[0172] H T △R = H T H△X

[0173] Also, H T H is a 3×3 matrix, and it can be obtained:

[0174] △X = (H T H) -1 H T △R

[0175] The ranging value often contains an error - free term, and its model can be expressed by the following formula:

[0176] △R = R τ - RL +dR

[0177] In the formula, R τ is the true distance vector between the tag to be measured and each base station, R L is the ranging value vector after linearization, and dR is the net error value of the ranging value. △X can be expressed as:

[0178] △X = X τ - X L + dX

[0179] In the above formula, X τ is the true position of the tag to be measured, X L is the approximate position after linearization, and dX is the error value of the position estimation.

[0180] By combining the above equations, we can get:

[0181] X τ - X L = (H T H) -1 H T (R τ - R L )

[0182] Then

[0183] dX = [(H T H) -1 H T )]dR = MdR

[0184] Among them, in most cases, the relative positions of the tag to be measured and the base station at a certain moment remain unchanged. Therefore, M is determined by (H T H) -1 H T ). Equation (2.58) means that there is a linear relationship between the ranging error and the positioning error caused by it. In the line-of-sight case, the ranging errors dR are independent of each other and follow a Gaussian distribution of random variables with a mean of zero and a variance of a fixed value . At a certain moment, the geometric relationship between the tag to be measured and the base station remains unchanged. Therefore, dX also follows a Gaussian random distribution with a mean of zero. According to the definition of covariance, the covariance matrix can be written as:

[0185] cov(dX) = E(dXdX T )

[0186] Furthermore, we have:

[0187] cov(dX) = E(dX · dX T ) = (H T H) -1 H T E(dR · dRT )H(H T H) -1

[0188] E(dRdR T ) is the covariance of dR and can be expressed as:

[0189]

[0190] where I n×n is the n×n identity matrix. By combining, we can get:

[0191]

[0192] The three components of dX represent the error values of the calculated values of X τ =(x, y, z). According to the definition of covariance, cov(dX) expands to:

[0193]

[0194] Therefore, the components of the matrix (H T H) -1 can be expressed by the variance of the ranging value error and the components of cov(dX). Also, from the definition formula of GDOP, it can be known that GDOP is expressed by the ratio of the sum of the components of cov(dX) and σ r . Secondly, (H T H) -1 can be expressed as:

[0195]

[0196] where G ij represents the covariance between the i-th observable and the j-th observable. The expression of the GDOP geometric dilution of precision can be obtained:

[0197]

Claims

1. An optimization method for non-line-of-sight base station deployment based on UWB positioning, characterized in that The specific steps include: S1: Reference points are set based on the complex non-line-of-sight scenario environment where base stations are deployed and obstacles that block the line of sight of communication. S2: Combined with the non-line-of-sight scenario in S1, preliminary regional division is performed according to the terrain scenario, and base stations are deployed using typical traditional rules; UWB tags are placed at the set reference points, and data is collected at each reference point; S3: According to the data collected by S2, the real coordinates of the base station and the reference point are obtained, and the real distance between the base station and the reference point is calculated from the real coordinates; The error is calculated from the ranging and true coordinates of the UWB tag, and the probability distribution diagram of the ranging error and the histogram of errors at different distances are constructed, and fitted by the gamma curve; The ranging errors of reference points at different positions are fitted by a gamma distribution to obtain the parameter values of the shape parameter and the scale parameter ; S4: Based on the preliminary area division in S2, perform clustering on the parameter values obtained for each area through unsupervised learning to accurately divide the ranging area; S5: Deploy base stations according to the ranging area divided by S4, and constrain the base station coordinates to the three sides close to the wall; Move the base station coordinates and measure the distances to the reference points in each area to obtain the parameter values of the ranging error distributions in each area , and construct a functional fitting relationship between the base station and the parameter values of each area; The variance expression of the ranging error is obtained by combining the function fitting relationship, and the variance expression form is consistent with the variance form of the gamma distribution; S6: Based on the geometric dilution of precision factor GDOP evaluation index and combined with the variance expression of ranging error, the base station deployment evaluation index COV under non-line-of-sight conditions is constructed; S7: Based on the COV evaluation index proposed in S6, a base station deployment optimization model is established. The model independent variables, constraints and objective functions are determined according to the non-line-of-sight scenario, and the optimal solution of the model is solved to obtain the optimal deployment location of the base station. In S4, the unsupervised learning adopts K-means algorithm; In S6, the specific process of constructing the base station deployment evaluation index COV in the non-line-of-sight situation is as follows: According to the GDOP definition: Among them, there are base stations, is the target position estimation error value in the non-line-of-sight scenario, which is a three-dimensional vector; represents the ranging error of the base station, which is dimensional vector; is the coefficient matrix of the direction cosine of the tag to be measured with respect to each base station, which are respectively expressed as: According to the definition of covariance, the covariance matrix is written as: Similarly, the geometric relationship between the tag to be tested and the base station remains unchanged, and we have: Among them, is 's covariance, The covariance of is expressed as: The three components represent the error values of the position estimation solution value; by the definition of covariance, Expanded as: Lianlide: By analyzing the above formula, the objective function COV is defined as the sum of each component, and the specific expression is as follows: This objective function is used as an evaluation index for base station deployment in non-line-of-sight situations.

2. The method for optimizing the deployment of non-line-of-sight base stations based on UWB positioning according to claim 1, wherein In S2, the base stations are deployed by adopting typical traditional rules, including deploying the base stations by adopting square, rectangular and diamond traditional rules.

3. The optimization method for non-line-of-sight base station deployment based on UWB positioning according to claim 2, wherein, In S3, the error model distribution obtained by fitting the gamma curve is: wherein, is the ranging error, are respectively the shape parameter and the scale parameter of the gamma distribution, is the gamma function, and its functional expression is: Using the properties of the gamma function, the mathematical expectation of the gamma distribution is obtained as: again Then the variance of the gamma distribution is: 。 4. The optimized method for non-line-of-sight base station deployment based on UWB positioning according to claim 1, wherein In S7, the independent variable: the coordinate position of each base station is selected as the independent variable; The constraint conditions: using the base station geometric constraint conditions analyzed in S5 as the constraint conditions of the base station deployment optimization model; The functional relationship between the fitting function of the ranging error distribution parameter value in each area and the geometric constraint condition of the base station is obtained through S5; The objective function: For the non-line-of-sight scenario, based on the COV evaluation metric, for the regions divided in this scenario, the objective function is set as: wherein, the independent variable is the three-dimensional spatial coordinates of 4 selected base stations; The heuristic optimization algorithm is used to iteratively optimize the objective function. When the objective function value is the minimum, the independent variable is determined to be the optimal deployment position of the base station.

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