Multi-point positioning system station distribution optimization method based on airspace traffic flow characteristics

Abstract

The invention discloses a multi-point positioning system station distribution optimization method based on airspace traffic flow characteristics. The method comprises the following steps: obtaining a visual area corresponding to each positioning point in an airspace; determining a preliminary site selection area of the ground base station; screening out ground base stations meeting conditions; calculating the 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 for optimizing a station distribution scheme; and solving the target function by using a genetic algorithm, and finally obtaining an optimal station distribution scheme of the multi-point positioning system. And calculating the coverage ranges of different height layers in the airspace for the optimal station distribution scheme to obtain a final coverage range, and the like. According to the method, by combining the airspace flow density characteristic and the actual topographic condition, the site selection area range is effectively reduced. The airspace traffic change can be dynamically adapted, the efficient configuration of system resources and the stability of airspace coverage are ensured, and the overall positioning precision and coverage effectiveness of the system are effectively improved.

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 the international civil aviation industry, the number of aircraft and flights has increased, and the demand for air traffic monitoring and management has continued to increase. Traditional radar monitoring systems have limited coverage and insufficient monitoring effects when facing complex terrain and airspace environments. To solve this problem, the international civil aviation field has introduced a multi-point positioning system (MLAT) based on the time difference of arrival of target signals (TDOA). The system receives signals from the same target through multiple ground base stations and calculates the arrival time difference to accurately locate the target.

[0003] According to the different application scopes, multilateration systems can be divided into surface multilateration systems (ASM) and wide area multilateration systems (WAM), which are used for monitoring airport surfaces and airway targets respectively. These systems not only make up for the limited coverage of traditional radar surveillance systems, but also solve the defects of the Automatic Dependent Surveillance-Broadcast (ADS-B) system when positioning fails. Due to its advantages such as simple target identification, strong compatibility, high refresh rate, high monitoring accuracy, wide coverage and strong anti-interference, multilateration systems have been widely used around the world.

[0004] In my country, the field multi-point positioning system has been applied in many medium and large airports, but the application of the wide-area multi-point positioning system is relatively small. With the growth of air transport volume, the existing surveillance technology has exposed the problem of insufficient coverage. At the same time, the airspace traffic density is unevenly distributed, and the traffic flow and surveillance needs in different regions vary significantly. If these traffic characteristics are ignored during the station layout process, it may lead to uneven distribution of surveillance resources, insufficient surveillance accuracy or waste of resources in some areas. Therefore, optimizing the station layout based on the airspace traffic density characteristics is crucial to improving the system positioning accuracy and station layout 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] In order to achieve the above object, the multi-point positioning system station layout optimization method based on airspace traffic flow characteristics provided by the present invention comprises the following steps performed in sequence:

[0007] Step 1: Taking each positioning point in the airspace as the reference point and the actual radiation distance of the ground base station antenna in the multi-point positioning system as the line of sight, perform visibility analysis on each azimuth 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 of ​​the ground base station;

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

[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 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 site layout plan, aiming to minimize the CRLB value to optimize the ground base station layout;

[0012] Step 6: Combined with the qualified ground base stations screened out in step 3, the objective function obtained in step 5 is solved by using a genetic algorithm, 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 taking each positioning point in the airspace as a reference point and the actual radiation distance of the ground base station antenna in the multi-point positioning system as the line of sight, performing visibility analysis on each azimuth angle, and obtaining the visible area corresponding to each positioning point in the airspace is:

[0015] Take each positioning point in the airspace as a reference point, and 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 above calculated ground base station antenna height exceeds the ground base station antenna limit height, it indicates that the location is not suitable as a ground base station and it is eliminated; then the visibility of the remaining terrain shielding points is judged. The visibility requirement must not only meet the requirement of unobstructed sight, but also meet 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 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 working distance of the optional ground base station antenna as the radius to draw a circle, and the inside 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 a plurality of rectangular frames, and then each rectangular frame is divided into a plurality of grid units, the terrain characteristics and signal coverage of each grid unit are analyzed, and the ground base stations that meet the conditions are screened out according to the signal coverage analysis results. The method for eliminating the ground base stations that do not meet the conditions is:

[0019] First, the preliminary site selection area obtained in step 2 is divided into multiple regular rectangular frames. The size of the rectangular frame should be determined according to the actual terrain characteristics and the distribution requirements of the ground base stations to ensure that the layout of the ground base stations in each rectangular frame can fully cover the aircraft as the target point in the area; then the side length of the grid unit is determined according to the positioning tolerance range of the ground base station, and then the above rectangular frame is divided into grid units according to the side length, and the center point of each grid unit is used as a potential ground base station. Then, in each grid unit, the influence of terrain factors on signal propagation is considered, and the shielding angle between the ground base station antenna and the positioning point is calculated; by calculating these shielding angles, those ground base stations with sufficient signal visibility are screened out to ensure the effective coverage capability of the ground base station;

[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 points 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 weighted 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 scale among sub-regions, the flow density of all sub-regions is normalized, with the aim of converting the flow density of different sub-regions into comparable weight coefficients ω i , calculated as:

[0026]

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

[0028] In step 5, the CRLB value (Cramer-Rao lower bound) 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, and 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 station layout 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 measured by TDOA 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. According to the above Jacobian matrix J and the noise covariance matrix R, the covariance matrix ∑ of the target point position error is calculated 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 method of solving the objective function obtained in step 5 by using a genetic algorithm in combination with the qualified ground base stations screened out in step 3, and finally obtaining the optimal station layout plan of the multi-point positioning system is:

[0043] 6.1. After obtaining the preliminary selected deployment sites in step 3, randomly generate the initial population, 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:

[0044] (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;

[0045] (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;

[0046] (3) All ground base stations must be located strictly within the selected deployment area to avoid deployment beyond the specified area;

[0047] 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;

[0048] 6.3. For each station layout scheme 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.

[0049] 6.4. The CRLB value of each sub-region is calculated according to the weighting coefficient ω i The weighted sum is performed 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.

[0050] 6.5. Based on the fitness value, the roulette wheel selection algorithm is used to select the station layout scheme with better performance from the current population to enter the next generation; individuals with greater fitness will have a higher probability of being selected, and individuals with less fitness will be eliminated. This mechanism helps to retain individuals with higher fitness and promote the evolution of the population towards a better solution;

[0051] 6.6. Keep several individuals with the best fitness in the population directly to the next generation to ensure that the optimal solution will not be lost during the evolution process. This is to avoid the loss of the local optimal solution and ensure the stability of the global optimal solution;

[0052] 6.7. Use multi-point crossover operation to generate new ground base station location combinations. The crossover operation is performed between the selected parent individuals. Through the crossover operation, the child individuals inherit some characteristics of the parent, thereby 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 , perform random mutation operations 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 according to 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 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 is:

[0057] 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;

[0058] 7.2. Taking each ground base station in the optimal station layout as the center, divide every 5° into an azimuth angle θ in the range of 0° to 360° i , where θ i (i=1,2,...72), used to calculate the shielding 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 Indicates the azimuth angle θ i The altitude of the upper terrain obstruction point, d s R is 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 minimum visible elevation angle of the current azimuth;

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

[0061] 7.5. Each altitude layer H l All azimuth angles θ i The apparent distance d v,i All are projected onto the horizontal plane, and then the visible range boundaries of all azimuths are connected to obtain the complete coverage 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 is verified.

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

[0064] (1) The present invention effectively narrows the scope of the site selection area by combining the characteristics of airspace traffic density and actual terrain conditions, avoiding the problems of large amount of calculation 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 allocation 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 station layout optimization method of the multi-point positioning system based on airspace traffic flow characteristics provided by the present invention.

[0067] Figure 2 It 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 It is a 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 It is a 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 is 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: Taking each positioning point in the airspace as the reference point and the actual radiation distance of the ground base station antenna in the multi-point positioning system as the line of sight, perform visibility analysis on each azimuth 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, 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 restricted, if the ground base station antenna height calculated above exceeds the restricted 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 determined, and the visibility requirement must not only meet the requirement of unobstructed sight, but also meet the actual effective 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 will be used as an optional ground base station; finally, the ground projection of the airspace is assumed to be a circular area, and a circle is drawn with the projection of each positioning point on the ground as the center and the actual radiation effective distance of the optional ground base station antenna as the radius. 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 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 of ​​the ground base station;

[0079] like Figure 3 As shown in Figure 1, 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 for the ground base station. This method can ensure that the site selection range of the ground base station is narrowed while meeting the airspace coverage requirements, focusing on the most effective coverage area, and greatly reducing the computational cost.

[0080] Step 3: Divide the preliminary site selection area obtained in step 2 into multiple rectangular boxes, and then divide each rectangular box into multiple grid units, analyze the terrain characteristics and signal coverage of each grid unit, and screen out qualified ground base stations based on the signal coverage analysis results, and eliminate ground base stations that do not meet the conditions;

[0081] like Figure 4 As shown, first, the preliminary site selection area obtained in step 2 is divided into multiple regular rectangular frames. The size of the rectangular frame should be determined according to the actual terrain characteristics and the distribution requirements of the ground base stations to ensure that the layout of the ground base stations in each rectangular frame can fully cover the aircraft as the target point in the area; then the side length of the grid unit is determined according to the positioning tolerance range of the ground base station (that is, the area within which the ground base station is arranged without affecting the positioning accuracy), and then the above rectangular frame is divided into grid units according to the side length, and the center point of each grid unit is used as a potential ground base station 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 the optimization of ground base stations. Then, in each grid unit, the influence of terrain factors on signal propagation is considered, and the shielding angle between the ground base station antenna and the positioning point is calculated; the shielding angle reflects the influence of terrain or obstacles on the line of sight, and is used to determine whether there is a good line of sight condition between the ground base station antenna and the target point. By calculating these shielding angles, those ground base stations with sufficient signal visibility are screened out to ensure the effective coverage capability of the ground base station;

[0082] 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 points are retained to ensure positioning accuracy and system stability.

[0083] 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;

[0084] like Figure 5 As shown, first, the airspace is divided into multiple sub-areas, each of which is defined as an independent spatial unit, in order 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 scale among sub-regions, the flow density of all sub-regions is normalized, with the aim of converting the flow density of different sub-regions into comparable weight coefficients ω i , calculated as:

[0088]

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

[0090] Step 5: Based on the weighted coefficients obtained in step 4, the Cramer-Rao lower bound (CRLB) value 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 site layout plan, aiming 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 measured by TDOA 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. According to the above Jacobian matrix J and the noise covariance matrix R, the covariance matrix ∑ of the target point position error is calculated 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 out in step 3, the objective function obtained in step 5 is solved by using a genetic algorithm, and finally the optimal station layout plan of the multi-point positioning system is obtained;

[0105] 6.1, such as Figure 6 As shown in FIG. 1 , after obtaining the preliminary selected deployment sites in step 3, an initial population is randomly generated, and 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 beyond 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 scheme 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 performed 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.

[0112] 6.5. Based on the fitness value, the roulette wheel selection algorithm is used to select the station layout scheme with better performance from the current population to enter the next generation; individuals with greater fitness will have a higher probability of being selected, and individuals with less fitness will be eliminated. This mechanism helps to retain individuals with higher fitness and promote the evolution of the population towards a better solution;

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

[0114] 6.7. Use multi-point crossover operation to generate new ground base station location combinations. The crossover operation is performed between the selected parent individuals. Through the crossover operation, the child individuals inherit some characteristics of the parent, thereby 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 , perform random mutation operations 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 according to 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, such as 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 in the range of 0° to 360° i (i=1,2,...72), used to calculate the shielding 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 Indicates the azimuth angle θ i The altitude of the upper terrain obstruction point, d s R is 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 minimum visible elevation angle of the current azimuth;

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

[0123] 7.5. Each altitude layer H l All azimuth angles θ i The apparent distance d v,iAll are projected onto the horizontal plane, and then the visible range boundaries of all azimuths are connected to obtain the complete coverage 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 is 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: Taking each positioning point in the airspace as the reference point and the actual radiation distance of the ground base station antenna in the multi-point positioning system as the line of sight, perform visibility analysis on each azimuth 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 of ​​the ground base station; Step 3: Divide the preliminary site selection area obtained in step 2 into multiple rectangular boxes, and then divide each rectangular box into multiple grid units, analyze the terrain characteristics and signal coverage of each grid unit, and screen out qualified ground base stations based on the signal coverage analysis results, and eliminate ground base stations that do not meet the conditions; 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 weighted coefficients obtained in step 4, the CRLB value 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 site layout plan, aiming to minimize the CRLB value to optimize the ground base station layout; Step 6: Combined with the qualified ground base stations screened out in step 3, the objective function obtained in step 5 is solved by using a genetic algorithm, 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 is characterized in that: In step 1, the method of taking each positioning point in the airspace as a reference point and the actual radiation distance of the ground base station antenna in the multi-point positioning system as the line of sight, performing visibility analysis on each azimuth angle, and obtaining the visible area corresponding to each positioning point in the airspace is: Take each positioning point in the airspace as a reference point, and 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 above calculated ground base station antenna height exceeds the ground base station antenna limit height, it indicates that the location is not suitable as a ground base station and it is eliminated; then the visibility of the remaining terrain shielding points is judged. The visibility requirement must not only meet the requirement of unobstructed sight, but also meet 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 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 working distance of the optional ground base station antenna as the radius to draw a circle, and the inside 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 is 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 is characterized in that: In step 3, the preliminary site selection area obtained in step 2 is divided into a plurality of rectangular frames, and then each rectangular frame is divided into a plurality of grid units, the terrain characteristics and signal coverage of each grid unit are analyzed, and the ground base stations that meet the conditions are screened out according to the signal coverage analysis results. The method for eliminating the ground base stations that do not meet the conditions is: First, the preliminary site selection area obtained in step 2 is divided into multiple regular rectangular frames. The size of the rectangular frame should be determined according to the actual terrain characteristics and the distribution requirements of the ground base stations to ensure that the layout of the ground base stations in each rectangular frame can fully cover the aircraft as the target point in the area; then the side length of the grid unit is determined according to the positioning tolerance range of the ground base station, and then the above rectangular frame is divided into grid units according to the side length, and the center point of each grid unit is used as a potential ground base station. Then, in each grid unit, the influence of terrain factors on signal propagation is considered, and the shielding angle between the ground base station antenna and the positioning point is calculated; by calculating these shielding angles, those ground base stations with sufficient signal visibility are screened out to ensure the effective coverage capability of the ground base station; 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 points 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 weighted 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 scale among sub-regions, the flow density of all sub-regions is normalized, with the aim of converting the flow density of different sub-regions into comparable weight coefficients ω i , calculated as: in, is the sum of the flow densities of 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 is 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, and 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 station layout 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; x1, y1, and z1 are the three-dimensional coordinates of the target point; 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 measured by TDOA 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. According to the above Jacobian matrix J and the noise covariance matrix R, the covariance matrix ∑ of the target point position error is calculated 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 is characterized in that: In step 6, the method of solving the objective function obtained in step 5 by using a genetic algorithm in combination with the qualified ground base stations screened out in step 3, and finally obtaining the optimal station layout plan of the multi-point positioning system is: 6.

1. After obtaining the preliminary selected deployment sites in step 3, randomly generate the initial population, 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 beyond 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 scheme 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 performed 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 the fitness value, the roulette wheel selection algorithm is used to select the station layout scheme with better performance from the current population to enter the next generation; individuals with greater fitness will have a higher probability of being selected, and individuals with less fitness will be eliminated. This mechanism helps to retain individuals with higher fitness and promote the evolution of the population towards a better solution; 6.

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

7. Use multi-point crossover operation to generate new ground base station location combinations. The crossover operation is performed between the selected parent individuals. Through the crossover operation, the child individuals inherit some characteristics of the parent, thereby 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 , perform random mutation operations 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 according to 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 is characterized in that: In step 7, the method of calculating 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 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 in the range of 0° to 360° i , where θ i (i=1,2,...72), used to calculate the shielding 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 Indicates the azimuth angle θ i The altitude of the upper terrain obstruction point, d s R is 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 minimum visible elevation angle of the current azimuth; 7.

4. Based on the above shielding angle α i Calculate each azimuth angle θ i The apparent distance Then each azimuth angle θ i The apparent distance d v,i Projected onto the horizontal plane, forming the visible range of the current azimuth; 7.

5. Each altitude layer H l All azimuth angles θ i The apparent distance d v,i All are projected onto the horizontal plane, and then the visible range boundaries of all azimuths are connected to obtain the complete coverage 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 is verified.

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