A multi-point positioning system station arrangement optimization method based on spatial traffic flow characteristics

Abstract

The application discloses a multi-point positioning system station arrangement optimization method based on airspace traffic flow characteristics. The method comprises the following steps: obtaining a visible area corresponding to each positioning point in the airspace; determining a preliminary site selection area of a ground base station; screening out a ground base station meeting a condition; calculating a flow density and obtaining a weighting coefficient; obtaining a global CRLB value of the airspace and taking the global CRLB value as a target function of an optimal station arrangement scheme; solving the target function by using a genetic algorithm, and finally obtaining the optimal station arrangement scheme of the multi-point positioning system; and calculating a coverage range of different height layers in the airspace for the optimal station arrangement scheme, and obtaining a final coverage range. By combining the airspace flow density characteristics and the actual terrain conditions, the application effectively reduces the site selection area range. The application can dynamically adapt to airspace flow changes, ensures efficient configuration of system resources and stability of airspace coverage, and effectively improves the overall positioning precision and coverage effectiveness of the system.

Description

Technical Field

[0001] The present invention belongs to the technical field of multi-point positioning, and in particular relates to a multi-point positioning system station layout optimization method based on airspace traffic flow characteristics. Background Art

[0002] With the rapid development of international civil aviation, the number of aircraft and flight frequencies has increased, leading to a growing demand for air traffic monitoring and management. Traditional radar surveillance systems have limited coverage and inadequate surveillance effectiveness in complex terrain and airspace environments. To address this issue, the international civil aviation sector has introduced the multilateration (MLAT) system, which uses the time difference of arrival (TDOA) of target signals. This system uses multiple ground base stations to receive signals from the same target and calculate the time difference of arrival to accurately locate the target.

[0003] Based on their scope of application, multilateration systems can be categorized as surface multilateration (ASM) and wide-area multilateration (WAM), used for monitoring airport surfaces and en-route targets, respectively. These systems not only address the limited coverage of traditional radar surveillance systems but also overcome the shortcomings of Automatic Dependent Surveillance-Broadcast (ADS-B) systems when positioning fails. Multilateration systems have gained widespread adoption worldwide due to their advantages, including simple target identification, strong compatibility, high refresh rate, high surveillance accuracy, wide coverage, and strong anti-interference capabilities.

[0004] In my country, surface multilateration systems have been implemented at several medium- and large-scale airports, but wide-area multilateration systems are relatively unused. With the growth of air traffic volume, existing surveillance technologies are facing coverage deficiencies. Furthermore, airspace traffic density is unevenly distributed, with significant variations in traffic flow and surveillance requirements across different regions. Ignoring these traffic characteristics during station deployment can lead to uneven allocation of surveillance resources, insufficient surveillance accuracy, or waste of resources in some areas. Therefore, optimizing station deployment based on airspace traffic density characteristics is crucial for improving system positioning accuracy and efficiency. Summary of the Invention

[0005] In order to solve the above problems, the purpose of the present invention is to provide a multi-point positioning system station optimization method based on airspace traffic flow characteristics.

[0006] To achieve the above-mentioned object, the present invention provides a method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics, comprising the following steps performed in sequence:

[0007] Step 1: Using each positioning point in the airspace as a reference point and the actual radiation range of the ground base station antenna in the multilateration system as the line of sight, perform visibility analysis for each azimuth angle to obtain the visible area corresponding to each positioning point in the airspace.

[0008] Step 2: Calculate the intersection of the visible areas of all positioning points in the airspace, and take the intersection of the visible areas of all positioning points as the preliminary site selection area for the ground base station;

[0009] Step 3: Divide the preliminary site selection area obtained in step 2 into multiple rectangular boxes, then divide each rectangular box into multiple grid cells. Analyze the terrain characteristics and signal coverage of each grid cell, and screen out qualified ground base stations based on the signal coverage analysis results, and eliminate those that do not meet the requirements.

[0010] Step 4: Divide the airspace into several sub-areas, then calculate the flow density of each sub-area according to its flow characteristics and perform normalization to obtain the weighting coefficient;

[0011] Step 5: Based on the weighting coefficients obtained in Step 4, calculate the CRLB value (Cramer-Rao lower bound) of each sub-region. Then, perform a weighted sum of the CRLB values ​​of each sub-region to generate a global weighted information matrix. The inverse of this matrix is ​​then taken to extract its diagonal elements, ultimately yielding the global CRLB value. This serves as the objective function for optimizing the base station layout, aiming to minimize the CRLB value to optimize the ground base station layout.

[0012] Step 6: Combined with the qualified ground base stations screened in step 3, the genetic algorithm is used to solve the objective function obtained in step 5, and finally the optimal station layout plan of the multi-point positioning system is obtained;

[0013] Step 7: Calculate the coverage of different altitude layers in the airspace for the optimal station layout solution obtained in step 6 to obtain the final coverage to verify the effectiveness of the optimal station layout solution.

[0014] In step 1, the method of performing visibility analysis on each azimuth angle using each positioning point in the airspace as a reference point and the actual radiation range of the ground base station antenna in the multilateration system as the line of sight to obtain the visible area corresponding to each positioning point in the airspace is as follows:

[0015] Taking each positioning point in the airspace as a reference point, perform a two-dimensional visibility analysis on each azimuth of all positioning points. If there are multiple terrain shielding points at a certain azimuth of a positioning point, perform a reverse view analysis on each terrain shielding point and calculate the required ground base station antenna height at that location so that it can cover the positioning point. If a certain terrain shielding point requires different ground base station antenna heights for different positioning points, take the maximum value as the final ground base station antenna height at that location. Since the actual ground base station antenna height may be limited, if the ground base station antenna height calculated above exceeds the ground base station antenna limit, Height, it indicates that the location is not suitable for a ground base station and it is eliminated; then the visibility of the remaining terrain shielding points is judged. The visibility requirement not only meets the requirement of unobstructed sight, but also meets the actual working distance of the ground base station antenna. If both are met, the terrain shielding point is considered to be visible to the positioning point and is selected as an optional ground base station; finally, the ground projection of the airspace is set to a circular area, with the projection of each positioning point on the ground as the center of the circle and the actual radiation working distance of the optional ground base station antenna as the radius to draw a circle. The interior of the circular area represents the visible area of ​​the positioning point in the airspace.

[0016] In step 2, the method of calculating the intersection of the visible areas of all positioning points in the airspace and taking the intersection of the visible areas of all positioning points as the preliminary site selection area of ​​the ground base station is:

[0017] The visible areas of all the positioning points obtained in step 1 are superimposed to obtain the common coverage area of ​​each positioning point as the intersection of the visible areas, and the intersection of the visible areas is used as the preliminary site selection area of ​​the ground base station.

[0018] In step 3, the preliminary site selection area obtained in step 2 is divided into multiple rectangular frames, and each rectangular frame is then divided into multiple grid cells. The terrain characteristics and signal coverage of each grid cell are analyzed, and the ground base stations that meet the conditions are screened out based on the signal coverage analysis results. The method for eliminating ground base stations that do not meet the conditions is:

[0019] First, divide the preliminary site selection area obtained in step 2 into multiple regular rectangular boxes. The size of the rectangular boxes should be determined based on the actual terrain characteristics and the distribution requirements of ground base stations, ensuring that the ground base station layout within each rectangular box can fully cover the aircraft serving as the target point in the area. Then, determine the side length of the grid unit based on the positioning tolerance range of the ground base station. Then, divide the above rectangular box into grid units based on this side length, and use the center point of each grid unit as a potential ground base station. Then, within each grid unit, consider the impact of terrain factors on signal propagation and calculate the shielding angle between the ground base station antenna and the positioning point. By calculating these shielding angles, screen out those ground base stations with sufficient signal visibility to ensure the effective coverage capability of the ground base stations.

[0020] Then, a signal coverage analysis is performed on all potential ground base stations to evaluate the signal coverage effect of each potential ground base station. On this basis, those ground base stations that do not meet the conditions due to excessive shielding angles or insufficient signal coverage are eliminated, and ground base stations that can effectively cover the target point are retained to ensure positioning accuracy and system stability.

[0021] In step 4, the method of dividing the airspace into several sub-areas, and then calculating the flow density of each sub-area according to its flow characteristics and performing normalization processing to obtain the weighting coefficient is:

[0022] First, the airspace is divided into multiple sub-areas, each of which is defined as an independent spatial unit;

[0023] Then the traffic density ρ of each sub-area i is calculated by calculating the number of aircraft passing through the sub-area per unit time i , the calculation formula is:

[0024]

[0025] In order to unify the flow density scales among the sub-regions, the flow density of all sub-regions is normalized to convert the flow density of different sub-regions into comparable weight coefficients ω i , calculated as:

[0026]

[0027] in, is the sum of traffic densities in all sub-areas.

[0028] In step 5, based on the weighted coefficients obtained in step 4, the CRLB value (Cramer-Rao lower bound) of each sub-area is calculated, and then the CRLB values ​​of each sub-area are weighted and summed to generate a global weighted information matrix. The diagonal elements of the matrix are extracted by solving the inverse matrix of the matrix, and finally the global CRLB value is obtained as the objective function of the optimization plan. The method for minimizing the CRLB value to optimize the ground base station layout is:

[0029] 5.1. For each sub-area i, first determine the distance d1 from the target point to each receiving station based on the receiving station position and the target point position to quantify the positioning error of the target point. The calculation formula is:

[0030]

[0031] Among them, x, y, and z are the three-dimensional coordinates of the receiving station; x1, y1, and z1 are the three-dimensional coordinates of the target point;

[0032] 5.2. Calculate the TDOA measurement value Δt based on the distance d1 from the target point to each receiving station. i , the formula is:

[0033]

[0034] Where c is the signal propagation speed;

[0035] 5.3. Based on the above TDOA measurement value Δt i , establish the Jacobian matrix J to reflect the geometric sensitivity of the target point position, which is in the form of:

[0036]

[0037] 5.4. Assuming that the noise of TDOA measurement follows a Gaussian distribution with a mean of zero, the covariance matrix of the noise is: in is the TDOA measurement variance of the i-th receiving station;

[0038] 5.5. Based on the above Jacobian matrix J and the noise covariance matrix R, calculate the covariance matrix ∑ of the target point position error x , the formula is: ∑ x =(J T R -1 J) -1 , where J T is the transpose of the Jacobian matrix, R -1 is the inverse of the covariance matrix of the noise;

[0039] 5.6. According to the covariance matrix Σ of the target point position error above x , calculate the information matrix I of the i-th sub-region i , the formula is: It is the covariance matrix ∑ of the target point position error in the sub-region x The inverse matrix of is used to characterize the contribution of the sub-region to the positioning accuracy of the target point;

[0040] 5.7. Information matrix I based on the above i-th sub-region i and the weighting coefficient ω obtained in step 4 i , get the global weighted information matrix I global , the formula is:

[0041] 5.8. For the above global weighted information matrix I global Perform inversion to obtain the global CRLB value, the formula is: The global CRLB value is the diagonal element of the inverse matrix of the global weighted information matrix, which represents the lower bound of the positioning accuracy in the entire airspace and is used as the objective function for optimizing the station layout plan.

[0042] In step 6, the ground base stations that meet the conditions screened in step 3 are used to solve the target function obtained in step 5 by using a genetic algorithm, and the method for finally obtaining the optimal station arrangement scheme of the multi-point positioning system is:

[0043] 6.1, after obtaining the preliminary screened station arrangement sites in step 3, an initial population is randomly generated, each individual representing a station arrangement scheme; each station arrangement scheme is composed of the positions of multiple ground base stations, and all need to meet the following constraint conditions:

[0044] (1) the minimum distance between ground base stations must meet the preset safety distance requirement to avoid excessive density of ground base stations and ensure reasonable signal coverage;

[0045] (2) the position of each ground base station must be able to cover the predetermined area to ensure full coverage of the key areas in the airspace;

[0046] (3) the positions of all ground base stations must be strictly located within the selected station arrangement range to avoid exceeding the specified area for station arrangement;

[0047] 6.2, each station arrangement scheme is encoded as a set of base station position coordinates (x, y, z), and the position of each ground base station is randomly distributed within the selected airspace range to ensure that the generated station arrangement scheme can be used for subsequent fitness evaluation;

[0048] 6.3, for each station arrangement scheme in the population, the CRLB value of each sub-area in the airspace is calculated, and the CRLB value reflects the positioning accuracy, with a lower value indicating higher positioning accuracy;

[0049] 6.4, the CRLB values of each sub-area are weighted and summed according to the weighting coefficient ω i to obtain the global CRLB value of the entire airspace, which is used as the fitness value of the station arrangement scheme, and a smaller fitness value indicates a better station arrangement scheme;

[0050] 6.5, based on the fitness value, the roulette wheel selection algorithm is used to select better station arrangement schemes from the current population into the next generation; individuals with higher fitness values will have a higher probability of being selected, and individuals with lower fitness values will be eliminated, which helps to retain individuals with higher fitness values and promote the evolution of the population towards better solutions;

[0051] 6.6, a number of individuals with the best fitness values in the population are directly retained to the next generation to ensure that the optimal solution is not lost during the evolution process, which is done to avoid the loss of local optimal solutions and ensure the stability of the global optimal solution;

[0052] 6.7. Use multi-point crossover to generate new ground base station location combinations. The crossover operation is performed between selected parent individuals. Through the crossover operation, the child individuals inherit some of the characteristics of the parent, thus generating a new station layout plan, increasing the diversity of the station layout plan, and further improving the station layout quality.

[0053] 6.8. To prevent the algorithm from falling into a local optimal solution, set the mutation probability P m , random mutation operations are performed on some individuals in the population; the mutation operation regenerates by randomly selecting the location of a base station to increase the diversity of the population, thereby improving the ability to search for the global optimal solution;

[0054] 6.9. Determine whether the maximum number of iterations has been reached. If so, terminate the algorithm and output the current optimal solution. If not, return to step 6.5, select the next generation population based on the fitness value, and continue the iterative process of the genetic algorithm.

[0055] 6.10. After reaching the maximum number of iterations, the final optimal station layout plan is output and the global CRLB value of the corresponding airspace is recorded for actual deployment and optimization of the performance of the multi-point positioning system.

[0056] In step 7, the method of calculating the coverage range of different altitude layers in the airspace for the optimal station layout solution obtained in step 6 to obtain the final coverage range to verify the effectiveness of the optimal station layout solution is:

[0057] 7.1、Select different altitude layers in the airspace to be analyzed r ,These altitude layers will be used to evaluate the coverage effects of different ground base stations at these altitude layers;

[0058] 7.2. Taking each ground base station in the optimal station layout as the center, divide every 5° into an azimuth angle θ within the range of 0° to 360°. i , where θ i (i=1,2,...72), used to calculate the obscuration angle and apparent distance at a specific azimuth;

[0059] 7.3. For each azimuth angle θ i , calculate the shielding angle caused by terrain or obstacles according to the following formula Among them, H a Indicates the altitude of the ground base station antenna, H o represents the azimuth angle θ i The altitude of the upper terrain obstruction point, d s R represents the slant distance from the terrain shielding point to the ground base station antenna. e represents the equivalent earth radius; shielding angle α iUsed to determine the lowest visible elevation angle of the current azimuth;

[0060] 7.4. Based on the above shielding angle α i Calculate each azimuth angle θ i Apparent distance Then each azimuth angle θ i The apparent distance d v,i Projected onto the horizontal plane, forming the visual range of the current azimuth;

[0061] 7.5、Each height layer H l All azimuth angles θ i The apparent distance d v,i All are projected onto the horizontal plane, and then the visual range boundaries of all azimuths are connected to obtain the complete coverage range of the ground base station antenna at the current altitude layer;

[0062] 7.6. For each selected altitude layer H l Repeat the above steps to obtain the coverage of the ground base station at each altitude layer. By comparing the coverage, the effectiveness of the optimal station layout plan at different altitude layers can be verified.

[0063] Compared with the prior art, the present invention has the following significant advantages:

[0064] (1) By combining the characteristics of airspace traffic density and actual terrain conditions, the present invention effectively narrows the scope of the site selection area, avoiding the problems of large computational complexity and high implementation difficulty caused by the coverage analysis of all possible ground base stations in the traditional method.

[0065] (2) The method of the present invention can dynamically adapt to changes in airspace traffic, ensure the efficient configuration of system resources and the stability of airspace coverage, and effectively improve the overall positioning accuracy and coverage effectiveness of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flow chart of the multi-point positioning system station layout optimization method based on airspace traffic flow characteristics provided by the present invention.

[0067] Figure 2 This is a schematic diagram of the visual range analysis of a positioning point at a certain direction in the present invention.

[0068] Figure 3 This is a schematic diagram of the preliminary site selection area after superimposing the visible areas of each positioning point in the present invention.

[0069] Figure 4 This is a grid diagram of the preliminary site selection area in the present invention.

[0070] Figure 5 Schematic diagram of dividing the airspace into multiple sub-areas in the present invention.

[0071] Figure 6 This is a flow chart of the genetic algorithm used in the present invention.

[0072] Figure 7 Schematic diagram of the coverage area of ​​the ground base station antenna at a certain altitude layer in the present invention. DETAILED DESCRIPTION

[0073] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0074] like Figure 1 As shown, the multi-point positioning system station layout optimization method based on airspace traffic flow characteristics provided by the present invention includes the following steps:

[0075] The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics provided by the present invention comprises the following steps performed in sequence:

[0076] Step 1: Using each positioning point in the airspace as a reference point and the actual radiation range of the ground base station antenna in the multilateration system as the line of sight, perform visibility analysis for each azimuth angle to obtain the visible area corresponding to each positioning point in the airspace.

[0077] like Figure 2 As shown in the figure, each positioning point in the airspace is used as a reference point, and a two-dimensional visibility analysis is performed on each azimuth of all positioning points. If there are multiple terrain shielding points A, B, and C at a certain azimuth of the positioning point, a reverse view analysis is performed on each terrain shielding point A, B, and C to calculate the required ground base station antenna height h at that location. A ,h B ,h C , so that it can cover the positioning point; if a certain terrain shielding point requires different ground base station antenna heights for different positioning points, then the maximum value max(h A ,h B ,h C ) as the final ground base station antenna height at that location; since the actual ground base station antenna height may be limited, if the ground base station antenna height calculated above exceeds the limited height of the ground base station antenna, it indicates that the location is not suitable as a ground base station and will be eliminated; then the visibility of the remaining terrain shielding points is judged, and the visibility requirement not only meets the requirement of unobstructed sight, but also meets the actual effective range of the ground base station antenna. If both are met, the terrain shielding point is considered to be visible to the positioning point and will be used as an optional ground base station; finally, the ground projection of the airspace is set to be a circular area, with the projection of each positioning point on the ground as the center of the circle and the actual radiation effective range of the optional ground base station antenna as the radius to draw a circle, and the interior of the circular area represents the visible area of ​​the positioning point in the airspace.

[0078] Step 2: Calculate the intersection of the visible regions of all positioning points in the airspace, and take the intersection of the visible regions of all positioning points as the preliminary site selection area of the ground base station;

[0079] As shown in Figure 3 , superimpose the visible regions of all positioning points obtained in step 1 to obtain the common coverage area of each positioning point as the intersection of the visible regions, and take the intersection of the visible regions as the preliminary site selection area of the ground base station. This method can ensure that the site selection range of the ground base station is reduced under the premise of meeting the airspace coverage requirement, focusing on the most effective coverage area, and can greatly reduce the calculation cost.

[0080] Step 3: Divide the preliminary site selection area obtained in step 2 into multiple rectangular frames, then divide each rectangular frame into multiple grid cells, analyze the terrain features and signal coverage of each grid cell, and select the ground base station that meets the conditions and eliminate the ground base station that does not meet the conditions according to the signal coverage analysis result;

[0081] As shown in Figure 4 , first, divide the preliminary site selection area obtained in step 2 into multiple regular rectangular frames, the size of the rectangular frame should be determined according to the actual terrain features and ground base station distribution requirements, to ensure that the ground base station layout in each rectangular frame can fully cover the aircraft as the target point in the area; then determine the side length of the grid cell according to the positioning tolerance range of the ground base station (i.e. the area within which the ground base station is arranged without affecting the positioning accuracy); then divide the above rectangular frame into grid cells according to the side length, and take the center point of each grid cell as a potential ground base station as the basis for subsequent site selection analysis. In this way, it is ensured that the entire area can be covered after gridding, and basic data is provided for ground base station optimization. Then, in each grid cell, consider the influence of terrain factors on signal propagation, calculate the shadow angle between the ground base station antenna and the positioning point; the shadow angle reflects the influence of terrain or obstacles on the line of sight, and is used to judge whether the ground base station antenna and the target point have good line-of-sight conditions. By calculating these shadow angles, those ground base stations with sufficient signal visibility are selected to ensure the effective coverage ability of the ground base station;

[0082] Then, perform signal coverage analysis on all potential ground base stations to evaluate the signal coverage effect of each potential ground base station, and on this basis, eliminate those ground base stations that do not meet the conditions due to excessive shadow angle or insufficient signal coverage, and retain the ground base stations that can effectively cover the target points to ensure the positioning accuracy and stability of the system.

[0083] Step 4: Divide the airspace into several sub-areas, then calculate the traffic density of each sub-area according to its traffic characteristics and perform normalization processing to obtain a weighting coefficient;

[0084] As shown in Figure 5 As shown, first, the airspace is divided into multiple sub-areas, each of which is defined as an independent spatial unit. The purpose is to conduct a detailed analysis of the traffic density in the airspace. Each sub-area should have an appropriate size to effectively reflect the traffic distribution in the airspace.

[0085] Then the traffic density ρ of each sub-area i is calculated by calculating the number of aircraft passing through the sub-area per unit time i , the calculation formula is:

[0086]

[0087] In order to unify the flow density scales among the sub-regions, the flow density of all sub-regions is normalized to convert the flow density of different sub-regions into comparable weight coefficients ω i , calculated as:

[0088]

[0089] in, is the sum of traffic densities in all sub-areas.

[0090] Step 5: Based on the weighting coefficients obtained in Step 4, the Cramer-Rao Lower Bound (CRLB) value of each sub-region is calculated. The CRLB values ​​of each sub-region are then weighted and summed to generate a global weighted information matrix. The diagonal elements of this matrix are extracted by solving its inverse matrix. The final global CRLB value is used as the objective function for optimizing the base station layout. The goal is to minimize the CRLB value to optimize the ground base station layout.

[0091] 5.1. For each sub-area i, first determine the distance d1 from the target point to each receiving station based on the receiving station position and the target point position to quantify the positioning error of the target point. The calculation formula is:

[0092]

[0093] Among them, (please add the definition of each parameter after the equal sign)

[0094] 5.2. Calculate the TDOA measurement value Δt based on the distance d1 from the target point to each receiving station. i , the formula is:

[0095]

[0096] Where c is the signal propagation speed;

[0097] 5.3. Based on the above TDOA measurement value Δt i , establish the Jacobian matrix J to reflect the geometric sensitivity of the target point position, which is in the form of:

[0098]

[0099] 5.4. Assuming that the noise of TDOA measurement follows a Gaussian distribution with a mean of zero, the covariance matrix of the noise is: in is the TDOA measurement variance of the i-th receiving station;

[0100] 5.5. Based on the above Jacobian matrix J and the noise covariance matrix R, calculate the covariance matrix ∑ of the target point position error x , the formula is: ∑ x =(J T R -1 J) -1 , where J T is the transpose of the Jacobian matrix, R -1 is the inverse of the covariance matrix of the noise;

[0101] 5.6. According to the covariance matrix ∑ of the target point position error above x , calculate the information matrix I of the i-th sub-region i , the formula is: It is the covariance matrix ∑ of the target point position error in the sub-region x The inverse matrix of is used to characterize the contribution of the sub-region to the positioning accuracy of the target point;

[0102] 5.7. Information matrix I based on the above i-th sub-region i and the weighting coefficient ω obtained in step 4 i , get the global weighted information matrix I global , the formula is:

[0103] 5.8. For the above global weighted information matrix I global Perform inversion to obtain the global CRLB value, the formula is: The global CRLB value is the diagonal element of the inverse matrix of the global weighted information matrix, which represents the lower bound of the positioning accuracy in the entire airspace and is used as the objective function for optimizing the station layout plan.

[0104] Step 6: Combined with the qualified ground base stations screened in step 3, the genetic algorithm is used to solve the objective function obtained in step 5, and finally the optimal station layout plan of the multi-point positioning system is obtained;

[0105] 6.1、As Figure 6 As shown in Figure 3, after obtaining the preliminary selected deployment sites in step 3, an initial population is randomly generated, where each individual represents a deployment plan. Each deployment plan consists of the locations of multiple ground base stations, and all must meet the following constraints:

[0106] (1) The minimum distance between ground base stations must meet the preset safety distance requirements to avoid overcrowding of ground base stations and ensure reasonable signal coverage;

[0107] (2) Each ground base station must be located in a way that covers the intended area, ensuring full coverage of key areas within the airspace;

[0108] (3) All ground base stations must be located strictly within the selected deployment area to avoid deployment outside the specified area;

[0109] 6.2. Encode each station layout plan as a set of base station location coordinates (x, y, z). The location of each ground base station is randomly distributed within the selected station layout range to ensure that the generated station layout plan can be used for subsequent fitness evaluation;

[0110] 6.3. For each station layout plan in the population, calculate the CRLB value of each sub-area in the airspace. The CRLB value reflects the positioning accuracy. The lower the value, the higher the positioning accuracy.

[0111] 6.4. The CRLB value of each sub-region is calculated according to the weighting coefficient ω i The weighted sum is used to obtain the global CRLB value of the entire airspace and used as the fitness value of the station layout plan. The smaller the fitness value, the better the station layout plan.

[0112] 6.5. Based on fitness values, a roulette wheel selection algorithm is used to select the best-performing station layout solutions from the current population for the next generation. Individuals with higher fitness have a higher probability of being selected, while individuals with lower fitness are eliminated. This mechanism helps retain individuals with higher fitness and promotes the evolution of the population towards a more optimal solution.

[0113] 6.6. The individuals with the best fitness in the population are directly retained to the next generation to ensure that the optimal solution will not be lost during the evolution process. This is done to avoid the loss of local optimal solutions and ensure the stability of the global optimal solution.

[0114] 6.7. Use multi-point crossover to generate new ground base station location combinations. The crossover operation is performed between selected parent individuals. Through the crossover operation, the child individuals inherit some of the characteristics of the parent, thus generating a new station layout plan, increasing the diversity of the station layout plan, and further improving the station layout quality.

[0115] 6.8. To prevent the algorithm from falling into a local optimal solution, set the mutation probability P m , random mutation operations are performed on some individuals in the population; the mutation operation regenerates by randomly selecting the location of a base station to increase the diversity of the population, thereby improving the ability to search for the global optimal solution;

[0116] 6.9. Determine whether the maximum number of iterations has been reached. If so, terminate the algorithm and output the current optimal solution. If not, return to step 6.5, select the next generation population based on the fitness value, and continue the iterative process of the genetic algorithm.

[0117] 6.10. After reaching the maximum number of iterations, the final optimal station layout plan is output and the global CRLB value of the corresponding airspace is recorded for actual deployment and optimization of the performance of the multi-point positioning system.

[0118] Step 7: Calculate the coverage of different altitude layers in the airspace for the optimal station layout solution obtained in step 6 to obtain the final coverage to verify the effectiveness of the optimal station layout solution.

[0119] 7.1、If Figure 7 As shown, different altitude layers h in the airspace to be analyzed are selected. r ,These altitude layers will be used to evaluate the coverage effects of different ground base stations at these altitude layers;

[0120] 7.2. Taking each ground base station in the optimal station layout as the center, divide every 5° into an azimuth angle θ within the range of 0° to 360°. i (i=1,2,...72), used to calculate the obscuration angle and apparent distance at a specific azimuth;

[0121] 7.3. For each azimuth angle θ i , calculate the shielding angle caused by terrain or obstacles according to the following formula Among them, H a Indicates the altitude of the ground base station antenna, H o represents the azimuth angle θ i The altitude of the upper terrain obstruction point, d s R represents the slant distance from the terrain shielding point to the ground base station antenna. e represents the equivalent earth radius; shielding angle α i Used to determine the lowest visible elevation angle of the current azimuth;

[0122] 7.4. Based on the above shielding angle α i Calculate each azimuth angle θ i Apparent distance Then each azimuth angle θ i The apparent distance d v,i Projected onto the horizontal plane, forming the visual range of the current azimuth;

[0123] 7.5、Each height layer H l All azimuth angles θ i The apparent distance d v,iAll are projected onto the horizontal plane, and then the visual range boundaries of all azimuths are connected to obtain the complete coverage range of the ground base station antenna at the current altitude layer;

[0124] 7.6. For each selected altitude layer H l Repeat the above steps to obtain the coverage of the ground base station at each altitude layer. By comparing the coverage, the effectiveness of the optimal station layout plan at different altitude layers can be verified.

Claims

1. A method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics, characterized by: The method comprises the following steps performed in sequence: Step 1: Using each positioning point in the airspace as a reference point and the actual radiation range of the ground base station antenna in the multilateration system as the line of sight, perform visibility analysis for each azimuth angle to obtain the visible area corresponding to each positioning point in the airspace. Step 2: Calculate the intersection of the visible areas of all positioning points in the airspace, and take the intersection of the visible areas of all positioning points as the preliminary site selection area for the ground base station; Step 3: Divide the preliminary site selection area obtained in step 2 into multiple rectangular boxes, then divide each rectangular box into multiple grid cells. Analyze the terrain characteristics and signal coverage of each grid cell, and screen out qualified ground base stations based on the signal coverage analysis results, and eliminate those that do not meet the requirements. Step 4: Divide the airspace into several sub-areas, then calculate the flow density of each sub-area according to its flow characteristics and perform normalization to obtain the weighting coefficient; Step 5: Based on the weighting coefficients obtained in Step 4, calculate the CRLB value of each sub-area. Then, perform a weighted sum of the CRLB values ​​of each sub-area to generate a global weighted information matrix. The inverse of this matrix is ​​then calculated to extract its diagonal elements. Finally, the global CRLB value is obtained as the objective function for optimizing the base station layout. The goal is to minimize the CRLB value to optimize the ground base station layout. Step 6: Combined with the qualified ground base stations screened in step 3, the genetic algorithm is used to solve the objective function obtained in step 5, and finally the optimal station layout plan of the multi-point positioning system is obtained; Step 7: Calculate the coverage of different altitude layers in the airspace for the optimal station layout solution obtained in step 6 to obtain the final coverage to verify the effectiveness of the optimal station layout solution.

2. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 1, the method of performing visibility analysis on each azimuth angle using each positioning point in the airspace as a reference point and the actual radiation range of the ground base station antenna in the multilateration system as the line of sight to obtain the visible area corresponding to each positioning point in the airspace is as follows: Taking each positioning point in the airspace as a reference point, perform a two-dimensional visibility analysis on each azimuth of all positioning points. If there are multiple terrain shielding points at a certain azimuth of a positioning point, perform a reverse view analysis on each terrain shielding point and calculate the required ground base station antenna height at that location so that it can cover the positioning point. If a certain terrain shielding point requires different ground base station antenna heights for different positioning points, take the maximum value as the final ground base station antenna height at that location. Since the actual ground base station antenna height may be limited, if the ground base station antenna height calculated above exceeds the ground base station antenna limit, Height, it indicates that the location is not suitable for a ground base station and it is eliminated; then the visibility of the remaining terrain shielding points is judged. The visibility requirement not only meets the requirement of unobstructed sight, but also meets the actual working distance of the ground base station antenna. If both are met, the terrain shielding point is considered to be visible to the positioning point and is selected as an optional ground base station; finally, the ground projection of the airspace is set to a circular area, with the projection of each positioning point on the ground as the center of the circle and the actual radiation working distance of the optional ground base station antenna as the radius to draw a circle. The interior of the circular area represents the visible area of ​​the positioning point in the airspace.

3. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 2, the method of calculating the intersection of the visible areas of all positioning points in the airspace and taking the intersection of the visible areas of all positioning points as the preliminary site selection area of ​​the ground base station is: The visible areas of all the positioning points obtained in step 1 are superimposed to obtain the common coverage area of ​​each positioning point as the intersection of the visible areas, and the intersection of the visible areas is used as the preliminary site selection area of ​​the ground base station.

4. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 3, the preliminary site selection area obtained in step 2 is divided into multiple rectangular frames, and each rectangular frame is then divided into multiple grid cells. The terrain characteristics and signal coverage of each grid cell are analyzed, and the ground base stations that meet the conditions are screened out based on the signal coverage analysis results. The method for eliminating ground base stations that do not meet the conditions is: First, divide the preliminary site selection area obtained in step 2 into multiple regular rectangular boxes. The size of the rectangular boxes should be determined based on the actual terrain characteristics and the distribution requirements of ground base stations, ensuring that the ground base station layout within each rectangular box can fully cover the aircraft serving as the target point in the area. Then, determine the side length of the grid unit based on the positioning tolerance range of the ground base station. Then, divide the above rectangular box into grid units based on this side length, and use the center point of each grid unit as a potential ground base station. Then, within each grid unit, consider the impact of terrain factors on signal propagation and calculate the shielding angle between the ground base station antenna and the positioning point. By calculating these shielding angles, screen out those ground base stations with sufficient signal visibility to ensure the effective coverage capability of the ground base stations. Then, a signal coverage analysis is performed on all potential ground base stations to evaluate the signal coverage effect of each potential ground base station. On this basis, those ground base stations that do not meet the conditions due to excessive shielding angles or insufficient signal coverage are eliminated, and ground base stations that can effectively cover the target point are retained to ensure positioning accuracy and system stability.

5. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1 is characterized in that: In step 4, the method of dividing the airspace into several sub-areas, and then calculating the flow density of each sub-area according to its flow characteristics and performing normalization processing to obtain the weighting coefficient is: First, the airspace is divided into multiple sub-areas, each of which is defined as an independent spatial unit; Then the traffic density ρ of each sub-area i is calculated by calculating the number of aircraft passing through the sub-area per unit time i , the calculation formula is: In order to unify the flow density scales among the sub-regions, the flow density of all sub-regions is normalized to convert the flow density of different sub-regions into comparable weight coefficients ω i , calculated as: in, is the sum of traffic densities in all sub-areas.

6. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 5, the CRLB value of each sub-area is calculated based on the weighted coefficient obtained in step 4, and then the CRLB values ​​of each sub-area are weighted and summed to generate a global weighted information matrix. The diagonal elements of the matrix are extracted by solving the inverse matrix of the matrix, and finally the global CRLB value is obtained as the objective function of the optimization plan. The method for minimizing the CRLB value to optimize the ground base station layout is: 5.

1. For each sub-area i, first determine the distance d1 from the target point to each receiving station based on the receiving station position and the target point position to quantify the positioning error of the target point. The calculation formula is: Among them, x, y, and z are the three-dimensional coordinates of the receiving station respectively; x i 、y i 、z i are the three-dimensional coordinates of the target point respectively; 5.

2. Calculate the TDOA measurement value Δt based on the distance d1 from the target point to each receiving station. i , the formula is: Where c is the signal propagation speed; 5.

3. Based on the above TDOA measurement value Δt i , establish the Jacobian matrix J to reflect the geometric sensitivity of the target point position, which is in the form of: 5.

4. Assuming that the noise of TDOA measurement follows a Gaussian distribution with a mean of zero, the covariance matrix of the noise is: in is the TDOA measurement variance of the i-th receiving station; 5.

5. Based on the above Jacobian matrix J and the noise covariance matrix R, calculate the covariance matrix ∑ of the target point position error x , the formula is: ∑ x =(J T R -1 J) -1 ,in, J T is the transpose of the Jacobian matrix, R -1 is the inverse of the covariance matrix of the noise; 5.

6. According to the covariance matrix ∑ of the target point position error above x , calculate the information matrix I of the i-th sub-region i , the formula is: It is the covariance matrix ∑ of the target point position error in the sub-region x The inverse matrix of is used to characterize the contribution of the sub-region to the positioning accuracy of the target point; 5.

7. Information matrix I based on the above i-th sub-region i and the weighting coefficient ω obtained in step 4 i , get the global weighted information matrix I global , the formula is: 5.

8. For the above global weighted information matrix I global Perform inversion to obtain the global CRLB value, the formula is: The global CRLB value is the diagonal element of the inverse matrix of the global weighted information matrix, which represents the lower bound of the positioning accuracy in the entire airspace and is used as the objective function for optimizing the station layout plan.

7. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 6, the method of solving the objective function obtained in step 5 by using a genetic algorithm based on the qualified ground base stations screened in step 3 to finally obtain the optimal station layout plan of the multi-point positioning system is as follows: 6.

1. After obtaining the preliminary selected deployment sites in step 3, randomly generate an initial population, where each individual represents a deployment plan. Each deployment plan consists of the locations of multiple ground base stations, and all must meet the following constraints: (1) The minimum distance between ground base stations must meet the preset safety distance requirements to avoid overcrowding of ground base stations and ensure reasonable signal coverage; (2) Each ground base station must be located in a way that covers the intended area, ensuring full coverage of key areas within the airspace; (3) All ground base stations must be located strictly within the selected deployment area to avoid deployment outside the specified area; 6.

2. Encode each station layout plan as a set of base station location coordinates (x, y, z). The location of each ground base station is randomly distributed within the selected airspace to ensure that the generated station layout plan can be used for subsequent fitness evaluation; 6.

3. For each station layout plan in the population, calculate the CRLB value of each sub-area in the airspace. The CRLB value reflects the positioning accuracy. The lower the value, the higher the positioning accuracy. 6.

4. The CRLB value of each sub-region is calculated according to the weighting coefficient ω i The weighted sum is used to obtain the global CRLB value of the entire airspace and use it as the fitness value of the station layout plan. The smaller the fitness value, the better the station layout plan. 6.

5. Based on fitness values, a roulette wheel selection algorithm is used to select the best-performing station layout solutions from the current population for the next generation. Individuals with higher fitness have a higher probability of being selected, while individuals with lower fitness are eliminated. This mechanism helps retain individuals with higher fitness and promotes the evolution of the population towards a more optimal solution. 6.

6. The individuals with the best fitness in the population are directly retained to the next generation to ensure that the optimal solution will not be lost during the evolution process. This is done to avoid the loss of local optimal solutions and ensure the stability of the global optimal solution. 6.

7. Use multi-point crossover to generate new ground base station location combinations. The crossover operation is performed between selected parent individuals. Through the crossover operation, the child individuals inherit some of the characteristics of the parent, thus generating a new station layout plan, increasing the diversity of the station layout plan, and further improving the station layout quality. 6.

8. To prevent the algorithm from falling into a local optimal solution, set the mutation probability P m , random mutation operations are performed on some individuals in the population; the mutation operation regenerates by randomly selecting the location of a base station to increase the diversity of the population, thereby improving the ability to search for the global optimal solution; 6.

9. Determine whether the maximum number of iterations has been reached; If the maximum number of iterations is reached, the algorithm is terminated and the current optimal solution is output; if the maximum number of iterations is not reached, return to step 6.5, select the next generation population based on the fitness value, and continue the iterative process of the genetic algorithm; 6.

10. After reaching the maximum number of iterations, the final optimal station layout plan is output and the global CRLB value of the corresponding airspace is recorded for actual deployment and optimization of the performance of the multi-point positioning system.

8. The method for optimizing the station layout of a multi-point positioning system based on airspace traffic flow characteristics according to claim 1, characterized in that: In step 7, the method of calculating the coverage range of different altitude layers in the airspace for the optimal station layout solution obtained in step 6 to obtain the final coverage range to verify the effectiveness of the optimal station layout solution is: 7.1、Select different altitude layers h in the airspace to be analyzed r ,These altitude layers will be used to evaluate the coverage effects of different ground base stations at these altitude layers; 7.

2. Taking each ground base station in the optimal station layout as the center, divide every 5° into an azimuth angle θ within the range of 0° to 360°. i , where θ i (i=1,2,...72), used to calculate the obscuration angle and apparent distance at a specific azimuth; 7.

3. For each azimuth angle θ i , calculate the shielding angle α caused by terrain or obstacles according to the following formula i : in, H a Indicates the altitude of the ground base station antenna, H o represents the azimuth angle θ i The altitude of the upper terrain shielding point, d s R represents the slant distance from the terrain shielding point to the ground base station antenna. e represents the equivalent earth radius; shielding angle α i Used to determine the lowest visible elevation angle of the current azimuth; 7.

4. Based on the above shielding angle α i Calculate each azimuth angle θ i Apparent distance Then each azimuth angle θ i The apparent distance d v,i Projected onto the horizontal plane, forming the visual range of the current azimuth; 7.5、Each height layer H l All azimuth angles θ i The apparent distance d v,i All are projected onto the horizontal plane, and then the visual range boundaries of all azimuths are connected to obtain the complete coverage range of the ground base station antenna at the current altitude layer; 7.

6. For each selected altitude layer H l Repeat the above steps to obtain the coverage of the ground base station at each altitude layer. By comparing the coverage, the effectiveness of the optimal station layout plan at different altitude layers can be verified.

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