Airborne distributed MIMO radar position deployment method under task reinforcement background

Abstract

The invention discloses an airborne distributed MIMO (Multiple Input Multiple Output) radar node position deployment method under a task reinforcement background, which is applied to the field of radar signal processing, and aims to solve the problem of airborne distributed MIMO radar station distribution under the condition that task reinforcement is not considered in the prior art. And the radar is classified into a cluster F and a cluster W. Secondly, aiming at the aircraft groups W and F, calculating the flight cost at the beginning and end positions; and for the cluster F, calculating the arrival boundary cost of the cluster F. And then calculating the total flight cost by using the starting and ending position cost and the arrival boundary in combination with a weighting factor. And then the detection probability of each target point in the radar task area is calculated by using a Markom function. And finally, establishing a multi-target optimization model about radar position deployment by using the total flight cost and the detection probability, and solving the optimization model to obtain the airborne distributed MIMO radar node position optimization deployment method under the task reinforcement background.

Description

Technical Field

[0001] The invention belongs to the field of radar signal processing, and in particular relates to a radar node deployment technology. Background Art

[0002] With the development of modern airborne radar technology, airborne radar systems have the characteristics of unmanned operation, clustering and high efficiency. These characteristics make airborne radar systems play a vital role on the battlefield and are often used to perform tasks such as searching, detecting and tracking enemy targets. However, due to the harsh and complex battlefield environment, the airborne radars in the combat group will inevitably be damaged when performing tasks. In this case, the command center needs to send new airborne radars to the battlefield to provide mission reinforcement for the damaged airborne radar group. The key to solving the mission reinforcement problem lies in measuring the mission requirements of the two radar groups and allocating radar system resources.

[0003] In order to solve the resource allocation problem of fixed platforms, Y. Wang et al. adopted an improved algorithm based on multi-objective particle swarm optimization (MOPSO) to allocate radar position resources, thereby improving the detection and positioning performance of different mission areas, but did not consider the resource allocation problem of airborne radar. In order to solve the resource allocation problem of dynamic platforms, P. Sujit et al. focused on the airborne platform operating under time constraints, and enhanced the system's ability to search and monitor unknown areas by controlling the path resources of the airborne platform. In addition, J. Yan et al. also considered the limitations on aircraft performance and used the Cramer-Rao lower bound as a measure of tracking performance. The study allocated maneuvering resources to improve the tracking performance of the airborne radar system. However, the existing work did not consider the situation where the airborne radar may be damaged during the mission execution state and a new airborne radar is needed to provide reinforcement. In addition, no radar resource allocation method has been proposed for this situation. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a method for deploying airborne distributed MIMO radar nodes in the context of mission reinforcement. Based on a multi-objective particle swarm optimization method, an optimized deployment scheme of airborne distributed MIMO radar nodes in the context of mission reinforcement is obtained.

[0005] The technical solution adopted by the present invention is: a method for deploying airborne distributed MIMO radar node positions in the context of mission reinforcement, comprising:

[0006] S1. The radars in the mission execution state are assigned to the fleet W, and the radars in the mission support state are assigned to the fleet F;

[0007] S2. Calculate the flight cost of the start and end positions for the fleets W and F;

[0008] S3. For cluster F, the cost of reaching the boundary of cluster F;

[0009] S4. Calculate the total cost of the flight using the cost of the start and end positions and the cost of reaching the boundary, combined with a weighting factor;

[0010] S5. Calculate the detection probability of each target point in the radar mission area using the Malkum function;

[0011] S6. Establish a multi-objective optimization model for radar position deployment with maximizing coverage and minimizing total flight cost as the optimization objectives;

[0012] S7. Using the optimization method based on multi-objective particle swarm, solve the multi-objective optimization model established in step S6; and obtain the optimal deployment plan.

[0013] Beneficial effects of the present invention: The method of the present invention uses an optimization method based on a multi-objective particle swarm to obtain an optimized deployment scheme for airborne distributed MIMO radar nodes in the context of mission reinforcement. First, according to whether the radar is in a mission support or mission execution state, the radar is assigned to the fleet F and W; then the flight cost of the initial and final positions is calculated for the fleet W and F; then the arrival boundary cost of the fleet F is calculated for the fleet F; secondly, the total flight cost is calculated by combining the initial and final position costs and the arrival boundary with the weighting factor; then, the detection probability of each target point in the radar mission area is calculated using the Malkum function; then, a multi-objective optimization model for radar position deployment is established using the total flight cost and the detection probability; finally, the optimization model is solved using an optimization method based on a multi-objective particle swarm, and the Pareto frontier is output as the optimization result. The advantage of the present invention is that the node position deployment of airborne distributed MIMO radars in the context of mission reinforcement is realized, the solution process is simple, and the computational complexity is low. The present invention can be applied to the fields of large-scale airborne MIMO radar collaborative detection, military applications, etc. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 Provide a flowchart of the method of the present invention;

[0015] Figure 2 A task scenario diagram for providing a method of the present invention;

[0016] Figure 3 This is a simulation result diagram of the optimization problem established by solving the multi-objective particle swarm algorithm in the present invention;

[0017] Figure 4 For the optimization results of the present invention Figure 3 The deployment results corresponding to the two selected results;

[0018] Among them, (a) is the first deployment result on the left side of the optimized Pareto front, and (b) is the second deployment result on the right side of the optimized Pareto front.

[0019] Figure 5 For the present invention Figure 3 The matching relationship between the deployment positions corresponding to the two selected results and the initial positions;

[0020] Among them, (a) is the matching relationship between the first deployment position on the left side of the optimized Pareto front and the initial position, and (b) is the matching relationship between the second deployment position on the right side of the optimized Pareto front and the initial position. DETAILED DESCRIPTION

[0021] The present invention is verified by using a Matlab simulation experiment method, and the correctness and effectiveness of the present invention are verified on the scientific computing software Matlab R2022a. The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0022] like Figure 1 As shown, the present invention proposes a method for optimizing the position deployment of airborne distributed MIMO radar nodes in the context of mission reinforcement, which is specifically implemented through the following process:

[0023] S1. Assign radars to fleets F and W based on whether they are in mission support or mission execution status;

[0024] S2. Calculate the flight cost of the start and end positions for the fleets W and F;

[0025] S3. For cluster F, the cost of reaching the boundary of cluster F;

[0026] S4. Calculate the total cost of the flight using the cost of the initial and final positions and the arrival boundary, combined with a weighting factor;

[0027] S5. Calculate the detection probability of each target point in the radar mission area using the Malkum function;

[0028] S6. Using the total flight cost and detection probability, a multi-objective optimization model for radar position deployment is established;

[0029] S7. Solve the optimization model using a multi-objective particle swarm optimization method;

[0030] S8. Output the Pareto front as the optimization result.

[0031] The implementation process of the present invention is as follows:

[0032] Step 1: In the context of mission reinforcement, radars have two mission states: mission execution state and mission reinforcement state. According to the current mission situation of the radar, radars in the mission execution state are assigned to fleet W, and radars in the mission support state are assigned to fleet F.

[0033] Step 2: Calculate the initial and final position flight cost for the fleets W and F. The initial and final position flight cost represents the flight cost of the radar from the initial position to the station location. The fleet F includes R 1 nodes, the cluster W contains R 2 nodes.

[0034] The flight cost of the initial and final positions is composed of the flight cost from the initial position of the group F and the group W to the station position, which can be expressed as:

[0035]

[0036] in and They represent the flight cost of radar nodes from the initial position to the station location in groups F and W respectively, and They represent the locations of radar nodes in group F and group W respectively.

[0037] Before calculating each part of the cost, it is necessary to first use the matching criterion to associate the initial position of the radar node with the station location. Here we use the shortest total distance criterion for matching, which can be expressed as

[0038]

[0039] in and and Respectively represent the Euclidean distance of each node from the initial position to the station location in groups F and W, which can be expressed as:

[0040]

[0041] in and Respectively represent the initial position coordinates of each node of groups F and W, and Respectively represent the coordinates of the radar node locations of groups F and W.

[0042] Step 3: For cluster F, the cost of reaching the boundary of cluster F

[0043] First, define the boundary intersection point: The boundary intersection point is the intersection point of the flight track and the effective detection boundary when the initial and final positions of the radar nodes in the group F are determined and a straight line flight path is adopted, which can be expressed as

[0044]

[0045] Using the initial position of each radar in the group F and the position of its corresponding boundary intersection, the effective detection boundary refers to the boundary where the radar can effectively detect the mission area after reaching the boundary, such as Figure 2 As shown. The rth 1 The out-of-bounds flight distance of a radar node is:

[0046]

[0047] · represents the 1-norm.

[0048] Using the out-of-bounds flight distance of each node in group F, we can calculate the cost of reaching the boundary as:

[0049]

[0050] Step 4: Calculate the total cost of the flight using the cost of the start and end positions and the arrival boundary, combined with the weighting factor

[0051] The total flight cost of the radar node includes the flight cost between the initial position and the deployment position of the F group and the W group, as well as the cost of reaching the boundary of the F group. The calculation method of the total flight cost is as follows

[0052] L R (ψ node ,ψ end ,P AF ,P AW )=h 1 L R1 (P,ψ end )+h 2 L R2 (P AF ,ψ node ),

[0053] where h 1 and h 2 Indicates the weight of the total flight cost. The value of the weight coefficient can be determined according to the requirements of the current mission on detection performance and flight cost.

[0054] Step 5: Use the Malkum function to calculate the detection probability of each target point in the radar mission area

[0055] When calculating the detection probability of each target point in the radar mission area, the mission area needs to be rasterized first, and the corresponding grid is represented by the center coordinates of each grid after rasterization. For a two-dimensional radar mission area, find the maximum and minimum coordinate values ​​on the x and y axes respectively, and calculate the length of the mission area on the x and y axes based on the maximum and minimum coordinates. Then divide this length into n distances of the same length along the x and y directions, and get the coordinates of each point after division, and then use the points obtained by division on x and y to form a grid.

[0056] After rasterizing the radar mission area, the coordinate vector formed by the coordinates of each grid center point can be expressed as:

[0057]

[0058] Where J represents the number of grids in the monitoring area after rasterization. Represents the coordinate position of the jth grid.

[0059] Then, using the Malkum function, the detection probability and false alarm probability of the jth grid can be expressed as

[0060]

[0061] Among them, P fa The simulation value is 1×10 -6 , through the known P fa Calculate the detection threshold γ T , thereby calculating the detection probability of the current cell Q(.) represents the Malkum function, R represents the total number of radar nodes, It represents the output signal-to-noise ratio after the echo signals of all transceiver channels are accumulated after being reflected by the detection target, which can be calculated as:

[0062]

[0063] in represents the single channel signal-to-noise ratio, can be calculated as:

[0064]

[0065] Where D 0 represents the detection factor, R max , and They represent the bistatic radar for The RCS of the target at The RCS of the target, the maximum detection distance, the distance from the jth grid to the mth transmitting node and the distance from the jth grid to the nth receiving node.

[0066] Step 6: Use the total flight cost and detection probability to establish a multi-objective optimization model for radar location deployment

[0067] Among them, the specific steps of S6 are as follows:

[0068] S61, calculation of effective coverage;

[0069] The radar mission is to effectively detect the radar mission area. The effective coverage rate is selected as the evaluation index. The following method is used to calculate the effective coverage rate:

[0070]

[0071] Where P dt represents the detection probability threshold, Represents the grid coordinates within the jth radar mission area. Φ e A matrix representing the coordinates of all grid points within the radar mission area.

[0072] S62, establishment of multi-objective optimization model;

[0073] Using the above calculations of effective coverage and total flight cost, combined with system constraints, a multi-objective optimization model for radar station locations is constructed;

[0074]

[0075] stψ end ∈Φ e ,

[0076] △x r >d x ,r=1,2,...,R

[0077] △y r >d y ,r=1,2,...,R,

[0078] where △x r and △y r represents the distance between the rth radar node and the surrounding radar nodes in the x-axis direction and the y-axis direction, respectively, d x and d y They represent the safety distances between radar nodes in the x-axis direction and the y-axis direction respectively.

[0079] Step 7: Model solution based on multi-objective particle swarm optimization method

[0080] For this multi-objective optimization problem, the following three steps are adopted: initialization and input; particle update; output.

[0081] Step 7.1: Initialization and input;

[0082] In the optimization problem, each element of each particle represents a dimension of the corresponding radar coordinates, and each column of the particle position represents the coordinates of a certain radar. We assume that there are S particles. In the tth iteration, the sth particle knows its position Θ s (t) and speed V s (t), s=1,...S, its own best historical position is The optimal position of all particles is Θ g .

[0083] Before initializing the population, we should clarify the parameters of the radar system, including the number of airborne radars and the radar mission area, to determine the range of particle positions. Then start population initialization. Starting from time t = 1, we randomly initialize the particle velocity V in the given solution space. 1 (1),...,V S (t) and position Θ 1 (t),...,Θ S (t). Then, we obtain the objective function value of each particle and store the particles that are not mutually dominant in objective function value in the external storage space.

[0084] Explanation of the meaning of "non-dominant": For example, there are two sets of station layout plans A and B. The coverage calculated by plan A is larger than that of plan B, but the flight cost of plan A is greater than that of plan B; therefore, A and B are particles that are non-dominant.

[0085] Step 7.2: Particle update;

[0086] Particle updating is divided into two parts: 1) updating the optimal particles (including individual optimal particles and global optimal particles); 2) updating particle speed and position.

[0087] Step 7.2.1: Update the optimal particle;

[0088] In each iteration, particles that are not mutually dominant in the objective function vector in the external storage will be selected as the best individual particles, which can be expressed as in represents the selected particles, and the objective function vectors of these particles form a Pareto frontier. D represents the number of selected particles. After iteration T, the algorithm ends up with the optimal result Θ e (T) Stop. We can choose the solution as needed. Individual best value Updated to

[0089]

[0090] Among them, < indicates positive definite, Indicates the station layout plan Θ s (t) The corresponding coverage and flight cost are better than the station layout solution The corresponding coverage and flight cost. After obtaining the Pareto front, the optimal particle in this iteration will be selected. In order to make the solution distribution of the Pareto front more uniform, the relative crowding distance (RCD, Relativedistance Closeness Degree) is used to update the global optimal particle. Since the density of the objective function calculated by the particle during the iteration may be higher in a certain direction, the effectiveness of the optimization information provided in this direction (RCD in this direction) may be lower than that in other directions. Therefore, it is necessary to weaken the contribution of the RCD in this direction to the calculation of the total RCD of the particle by adjusting the weight assigned to this direction. The entire update process of the dth solution on the Pareto front is as follows.

[0091]

[0092] where κ o (t) represents the dynamic weight on the oth objective function RCD. The calculation steps of the dynamic weight are as follows:

[0093] First, in each target direction of the Pareto front, find the minimum RCD of all particles on the Pareto front in that direction. Second, find Record the sequence number of the minimum objective function and denote it as o′. Third, set the activation threshold ε thre .if Then in this iteration, the weights of all objective functions are set to κ c .when When , the solution in the direction of the o′th objective function is too crowded, which indicates that we need to calculate the following dynamic weights for each objective function

[0094] κ o =κ c +η o o=1,2

[0095] Among them, κ c ∈[0,1] represents the initial dynamic weight of the oth objective function, η o is the weight change coefficient, defined as

[0096]

[0097] Where λ∈[0,1] represents the step size change coefficient. The dynamic weight is initialized to κ c.

[0098] Step 7.2.2: Particle velocity and position update;

[0099] The position and velocity of the sth particle are updated as follows:

[0100]

[0101] Θ s (t+1)=θ s (t)+V s (t+1),

[0102] Among them, c 1 and c 2 is the learning factor, ω(t) is the inertia weight, set to 0.9-0.5×(t / T), where T is the maximum number of iterations.

[0103] Step 8: Output the Pareto front as the optimization result;

[0104] The iteration will stop at t = T, and the external archive contains the Pareto optimal solution set Θ e (T). We choose e The deployment method corresponding to the solution in (T) is taken as the output result. Since there are many possible deployment solutions, the choice depends on the actual application requirements.

[0105] Figure 3 The Pareto front solution of the established optimization model is given by using the multi-objective particle swarm optimization algorithm. It can be seen that the performance of the solution of the optimization problem solved by the algorithm in the proposed method is improved compared with other algorithms (the solution on the Pareto front dominates the Pareto front solution obtained by other algorithms).

[0106] Figure 4 For the optimization results of the present invention Figure 3 The deployment results corresponding to the two selected results. Select the first result on the left and the second result on the right on the Pareto front obtained by optimization, and draw the station layout results corresponding to the results. Figure 5 For the present invention Figure 3 The matching relationship between the deployment position corresponding to the leftmost and the second right result on the Pareto front and the initial position. Figure 4 ,5, we know that when the decision-making end tends to choose better area coverage performance, choosing the point on the left can get a larger area coverage, but the flight cost will increase at this time; on the contrary, when the decision-making end tends to adopt a smaller flight cost strategy, we choose the point on the right, which can get a smaller flight cost, but at this time a certain area coverage is sacrificed.

[0107] Figure 3 Here, MOPSO-DWRCD, MOPSO-CD and Random respectively represent dynamic relative crowding distance-multi-objective particle swarm algorithm (the algorithm adopted by the present invention), crowding distance-multi-objective particle swarm algorithm (comparison algorithm) and random method (comparison algorithm).

[0108] Figure 5 In it, Initial positions, Deployment positions and effective detection boundary respectively represent: initial positions, deployment positions and effective detection boundary.

[0109] Table 1 Figure 3 , Figure 4 , Figure 5 Corresponding parameters

[0110] parameter symbol Numeric Radar mission area \ 380km×380km Grid size \ 10km×10km Effective detection of boundaries \ 400km×400km False alarm probability <![CDATA[P fa ]]> <![CDATA[1×10 -6 ]]> Detection Factor <![CDATA[D 0 ]]> 12.5dB Weighting coefficient <![CDATA[h 1 ,h 2 ]]> 0.5 Initial position of group F <![CDATA[P AF ]]> [(-100,0),(0,100)]km Initial position of group W <![CDATA[P AW ]]> [(200,0),(0,200)]km Number of particles S 500 Detection probability threshold <![CDATA[P dt ]]> 0.8 Dynamic weight initial value <![CDATA[κ c ]]> 0.5 Safe distance <![CDATA[d x ,d y ]]> 1km

[0111] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the principles of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. For those skilled in the art, the present invention may have various changes and variations. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context, characterized in that: include: S1. The radars in the mission execution state are assigned to the fleet W, and the radars in the mission support state are assigned to the fleet F; S2. Calculate the flight cost of the start and end positions for the fleets W and F; S3. For cluster F, the cost of reaching the boundary of cluster F; S4. Calculate the total cost of the flight using the cost of the start and end positions and the cost of reaching the boundary, combined with a weighting factor; S5. Calculate the detection probability of each target point in the radar mission area using the Malkum function; S6. Establish a multi-objective optimization model for radar position deployment with maximizing coverage and minimizing total flight cost as the optimization objectives; S7. Using the optimization method based on multi-objective particle swarm, solve the multi-objective optimization model established in step S6; and obtain the optimal deployment plan.

2. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 1, characterized in that: The flight cost of the initial and final positions in step S2 includes the flight cost from the initial position of the fleet F and the fleet W to the station location, expressed as: Among them, L R1 represents the flight cost of the initial and final positions, P represents the initial position of the radar nodes in the fleet F and the fleet W, ψ end Indicates the location of the radar nodes in fleet F or fleet W. represents the flight cost of the radar node in the fleet F from the initial position to the station location, represents the flight cost of the radar node in the fleet W from the initial position to the station location, and Respectively represent the locations of radar nodes in fleet F and fleet W, P AF represents the initial position of the radar node in the swarm F, P AW represents the initial position of the radar node in the swarm W.

3. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 2, characterized in that: Before calculating the flight cost of the initial and final positions, the initial position of the radar node and the station position are associated with each other using a matching criterion.

4. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 3, characterized in that: The matching criterion adopts the shortest total distance criterion.

5. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 3, characterized in that: The arrival boundary cost of the group F in step S3 is specifically: the cost from the initial position of the radar node in the group F to its corresponding boundary intersection point, and the boundary intersection point is the intersection of the flight track and the effective detection boundary when a straight line flight path is adopted after the initial position and final position of the radar node in the group F are determined.

6. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 5, characterized in that: The multi-objective optimization model in step S6 is expressed as: stψ end ∈Φ e , △x r >d x ,r=1,2,...,R △y r >d y ,r=1,2,...,R, Among them, C R (ψ end ,Φ e ) represents the effective coverage, L R (ψnode,ψend,P AF ,P AW ) represents the total flight cost, ψ node represents the intersection of the flight track and the effective detection boundary; Φ e It represents the coordinate vector formed by the coordinates of each grid center point after the radar mission area is rasterized; R represents the total number of radar nodes, △x r and △y r represents the distance between the rth radar node and the surrounding radar nodes in the x-axis direction and the y-axis direction, respectively, d x and d y They represent the safety distances between radar nodes in the x-axis direction and the y-axis direction respectively.

7. The method for deploying airborne distributed MIMO radar nodes in a mission reinforcement context according to claim 6, characterized in that: Step S7 is specifically as follows: Calculate the objective function value of each particle, and store the particles that are not mutually dominant in objective function value in the external storage space; In each iteration, the Pareto front is updated using the individual particle optimality; in each target direction of the Pareto front, the minimum relative crowding distance of all particles on the Pareto front in that direction is calculated, and the global optimal particle is updated using the relative crowding distance; When the iteration stops, the Pareto front is output as the optimization result.

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