Node selection and power-time collaborative optimization method for networked radar under multi-target search and tracking

Abstract

The present invention discloses a method for collaborative optimization of networked radar node selection and power time under multi-target search and tracking, including: constructing a motion model of radar carrier and target; constructing a radar search performance measurement index with airborne radar radiation power and dwell time as optimization variables; constructing a radar tracking performance measurement index with airborne radar radiation power and dwell time as optimization variables; taking a given upper limit of airborne radar total radiation power and dwell time limit as constraints, taking maximization of radar search performance index and tracking performance index as optimization goals, establishing a collaborative optimization model of networked radar node selection and power time under multi-target search and tracking; solving the optimization model by combining interior point method and particle swarm algorithm; realizing collaborative optimization of networked radar node selection and power time. The present invention realizes the optimal airborne radar node selection and power time allocation, and effectively improves the multi-target search and tracking performance of airborne radar.

Description

Technical Field

[0001] The present invention relates to a radar signal processing technology, and specifically to a method for selecting networked radar nodes and coordinating power and time under multi-target search and tracking. Background Art

[0002] In recent years, airborne networked radars have gradually attracted the attention of many scholars and research institutions. Compared with traditional base station radars, airborne networked radars make up for the lack of detection capabilities. They can adjust the working status of each radar node in real time according to the actual battlefield situation. At the same time, they can effectively complete tasks such as target search, tracking and attack through collaborative work. Therefore, it has a wide range of application scenarios in long-range reconnaissance and monitoring, rapid battlefield response, border defense against enemies, and battlefield covert penetration, providing important support for information acquisition and security assurance.

[0003] For actual radar detection scenarios, by optimizing the allocation of resources such as power and time, the radar system performance and work efficiency can be significantly improved, and more accurate target detection results can be obtained, which is an important means of battlefield situation awareness. Therefore, in order to further tap the working potential of airborne radar networks, more effective resource allocation methods need to be studied. In addition, since the performance of each radar detection in the multi-target search and tracking scenario is different, node selection for airborne networked radars is of great significance to improving system performance.

[0004] At present, the allocation of networked radar resources for multi-platform multi-target search or tracking has become a hot topic of research, and many scholars at home and abroad have achieved remarkable results in this regard. However, existing studies have mainly focused on improving the multi-target tracking accuracy or regional search performance by optimizing radiation parameters, and have not comprehensively considered the resource allocation problem of target search and tracking, which has certain limitations. Summary of the invention

[0005] Purpose of the invention: The purpose of the present invention is to provide a method for collaborative optimization of networked radar node selection and power time under multi-target search and tracking, so as to improve the multi-target search and tracking performance of airborne radar.

[0006] Technical solution: A method for selecting networked radar nodes and coordinating power and time optimization under multi-target search and tracking of the present invention comprises the following steps:

[0007] Firstly, the motion model of radar carrier and target is constructed; based on signal detection theory, radar search performance measurement index with airborne radar radiation power and dwell time as optimization variables is constructed; based on Cramer-Rao lower bound, radar tracking performance measurement index with airborne radar radiation power and dwell time as optimization variables is constructed; with the given upper limit of airborne radar total radiation power and dwell time limit as constraints, and maximizing radar search performance index and tracking performance index as optimization objectives, a networked radar node selection and power-time collaborative optimization model under multi-target search and tracking is established; the optimization model is solved by combining interior point method and particle swarm algorithm, including: firstly, the optimization model is decomposed into networked radar node selection optimization model under multi-target search and tracking and networked radar power-time collaborative optimization optimization model under multi-target search and tracking; secondly, the networked radar node selection optimization model under multi-target search and tracking is solved by combining interior point method; finally, the networked radar power-time collaborative optimization optimization model under multi-target search and tracking is solved by combining particle swarm algorithm; the networked radar node selection and power-time collaborative optimization under multi-target search and tracking are realized.

[0008] Furthermore, the motion model of the radar carrier and the target is constructed as follows:

[0009]

[0010]

[0011] in, represents the state vector of aircraft i, represents the state vector of target m, and represents the position coordinates of aircraft i, and represents the flight speed of aircraft i, and represents the position coordinates of the target m, and represents the flight speed of target m, {·} T Represents the transpose operation of a matrix.

[0012] Furthermore, the radar search performance measurement index expression is:

[0013]

[0014] in, represents the search performance measurement index of radar i for search unit q, represents the radiation power allocated by radar i to search unit q, t iq represents the dwell time assigned by radar i to search unit q, n iq Represents time period t iqThe number of radar detections within a period of time, the farthest detectable position of each search unit by the radar is defined as a false search target, SNR iq represents the expected signal-to-noise ratio of radar i to the false search target echo signal in search unit q, a iq (γ) represents the degree of correspondence between radar i and the false search target in search unit q, represents the distance between radar i and the false search target in search unit q, w0 represents the number of wave bits required to detect each search unit, η represents the maximum number of effective detections achieved by the radar within the time period T0; R1 represents the distance between the radar and the reference target, P t1 It represents the radar radiation power to the reference target. SNR1 represents the signal-to-noise ratio of the reference target echo received by the radar when the distance between the radar and the reference target is R1 and the angle between the azimuth and the radar antenna is 0°.

[0015] Furthermore, the radar tracking performance measurement index expression is:

[0016]

[0017] in, represents the tracking performance measurement index of radar i for target m, represents the radiation power allocated by radar i to target m, t im represents the dwell time assigned by radar i to target m, n im Represents time period t im The number of radar detections within represents the mean square error of the estimated parameter of target m by radar i, η represents the maximum number of effective detections achieved by the radar within time period T0, P d Represents the probability of radar detecting the target, N exp is the number of measurements expected by the radar beam, P n represents the noise power, f1 represents the pulse repetition frequency, represents the distance between radar i and target m, represents the radar cross-sectional area of ​​target m; R1 represents the distance between the radar and the reference target, P t1 It represents the radar radiation power to the reference target, RCS1 represents the radar scattering cross-section of the reference target, and SNR1 represents the signal-to-noise ratio of the reference target echo received when the target radar scattering cross-section is RCS1.

[0018] Furthermore, the network radar node selection and power-time collaborative optimization model under multi-target search and tracking is:

[0019]

[0020] in, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m; I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1 and ω2 represent the proportion of tracking performance and search performance considered in the model respectively; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned to target m by radar i; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Indicates the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; Indicates the maximum dwell time assigned to a single target.

[0021] Furthermore, the optimization model is decomposed into a radar node selection optimization model for networked radars under multi-target search and tracking and a power-time collaborative optimization optimization model for networked radars under multi-target search and tracking, specifically:

[0022] The expression of the optimization model for selecting networked radar nodes under multi-target search and tracking is:

[0023]

[0024] in, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m, I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1 and ω2 represent the proportion of tracking performance and search performance considered in the model respectively; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar;

[0025] The expression of the power-time collaborative optimization model of networked radar under multi-target search and tracking is:

[0026]

[0027] in, represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned by radar i to target m; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Indicates the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; Indicates the maximum dwell time assigned to a single target.

[0028] Furthermore, the optimization model of radar node selection for multi-target search and tracking is solved by combining the interior point method, including the following steps:

[0029] i) Input the parameters of the optimization model: the radiation power and dwell time allocated to all nodes are the same constant value, and the search performance matrix of radar i for search unit q is calculated And the tracking performance matrix of radar i for target m q=1,2,…,Q,m=1,2,…,M;initialize the interior point matrix U S and U T , set the interior point feasible region:

[0030] Objective function: and Set the iteration index Set the algorithm termination indicator ε>0;

[0031] ii) Take is the initial point;

[0032] iii) Solve the following problem:

[0033] iv) Let the maximum point of the above problem be

[0034] v) Check the termination condition and calculate the objective function value corresponding to the current maximum point and If the objective function value converges, the algorithm terminates; otherwise, the next iteration is executed: Update Update the initial point: use the current maximum point as the initial point for the next iteration;

[0035] vi) Output the node selection results of radar search task and tracking task and

[0036] Furthermore, the particle swarm algorithm is combined to solve the power-time collaborative optimization model of networked radar under multi-target search and tracking, including the following steps:

[0037] i) Initialize the particle swarm, given the swarm size P', inertia factor ρ1 and learning factor ρ2, and use the particle position x to represent the radar radiation power and residence time allocated to the node, that is, the particle position matrix Set the particle flight speed v and the particle feasible domain:

[0038]

[0039] , set the objective function: Set the iteration index φ = 1, and set the number of algorithm iterations N;

[0040] ii) Randomly generate the position X and velocity v of particle p' (p'=1,2,…,P');

[0041] iii) Solve the following problem:

[0042] iv) Calculate the fitness of each particle through the objective function

[0043] v) Update the individual optimal particle position x φ and the global optimal group position X φ , update the velocity of all particles and location

[0044] vi) Check the number of iterations. If the termination condition is met, exit; otherwise, execute the next iteration: update φ=φ+1, update the initial point: use the current maximum point as the initial point of the next iteration;

[0045] vii) Output radar radiation power and task time allocation results P tiq ,t iq ,P tim ,t im .

[0046] Based on the same inventive concept, the networked radar node selection and power-time coordinated optimization system under multi-target search and tracking of the present invention includes:

[0047] A motion model building unit, used to build motion models of radar carriers and targets;

[0048] An index construction unit, used for constructing a radar search performance measurement index with airborne radar radiation power and dwell time as optimization variables based on signal detection theory, and for constructing a radar tracking performance measurement index with airborne radar radiation power and dwell time as optimization variables based on Cramer-Rao lower bound;

[0049] The optimization model building unit is used to establish a collaborative optimization model of network radar node selection and power time under multi-target search and tracking, taking the given upper limit of the total radiation power and the dwell time limit of the airborne radar as constraints and maximizing the radar search performance index and tracking performance index as the optimization goal;

[0050] The optimization model solving unit is used to solve the optimization model by combining the interior point method and the particle swarm algorithm, including: firstly, decomposing the optimization model into a node selection optimization model for networked radar under multi-target search and tracking and a power-time coordinated optimization model for networked radar under multi-target search and tracking; secondly, solving the node selection optimization model for networked radar under multi-target search and tracking by combining the interior point method; finally, solving the power-time coordinated optimization model for networked radar under multi-target search and tracking by combining the particle swarm algorithm; realizing the node selection and power-time coordinated optimization of networked radar under multi-target search and tracking.

[0051] Based on the same inventive concept, an electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the method for selecting networked radar nodes and co-optimizing power and time under multi-target search and tracking are implemented.

[0052] Beneficial effects: Compared with the prior art, the advantages of the present invention are:

[0053] The method of the present invention constructs an evaluation index that characterizes the radar search performance and tracking performance. At the same time, the node selection, radiation power and residence time allocation results of the airborne radar will also affect the quality of the corresponding echo, and then affect the index; on this basis, taking the upper limit of the total radiation power of the airborne radar system and the residence time limit as constraints, taking maximizing the radar search performance index and tracking performance index as the optimization goal, a networked radar node selection and power time collaborative optimization model under multi-target search and tracking is established, the node selection of the airborne radar is adaptively performed, and the corresponding radiation power and residence time resource allocation is performed, so as to realize the coordinated optimization of parameters such as airborne radar node selection, radiation power and residence time in the process of multi-target search and tracking, so as to achieve the purpose of improving the multi-target search and tracking performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Flow chart of the method for collaborative optimization of networked radar node selection and power time under multi-target search and tracking;

[0055] Figure 2 It is a schematic diagram of the motion trajectory of multiple targets and the motion trajectory of airborne radar;

[0056] Figure 3 Schematic diagram of the results of the airborne radar search task node selection;

[0057] Figure 4 Schematic diagram of the result of selecting nodes for the airborne radar tracking task;

[0058] Figure 5 This is a schematic diagram of the results of radiated power resource allocation for airborne radar search missions;

[0059] Figure 6 This is a schematic diagram of the results of radiated power resource allocation for airborne radar search missions;

[0060] Figure 7 This is a schematic diagram of the results of the dwell time resource allocation for the airborne radar search mission;

[0061] Figure 8 This is a schematic diagram of the results of the dwell time resource allocation for the airborne radar search mission;

[0062] Fig. 9 Schematic diagram of the comparison results of different algorithms. DETAILED DESCRIPTION

[0063] The structure and working process of the present invention are further described below in conjunction with the accompanying drawings and specific embodiments.

[0064] like Figure 1 As shown, the present invention provides a method for selecting networked radar nodes and coordinating power and time optimization under multi-target search and tracking, comprising the following steps:

[0065] S1. Construct the motion model of radar aircraft i and target m at time k, as shown in equations (1) and (2):

[0066]

[0067]

[0068] In the formula, represents the state vector of aircraft i, represents the state vector of target m, and represents the position coordinates of aircraft i, and represents the flight speed of aircraft i, and represents the position coordinates of the target m, and represents the flight speed of target m, {·} T Represents the transpose operation of a matrix.

[0069] S2. Based on the signal detection theory, a radar search performance measurement index is constructed with the airborne radar radiation power and dwell time as optimization variables, as shown in formula (3):

[0070]

[0071] In the formula, represents the search performance measurement index of radar i for search unit q, represents the radiation power allocated by radar i to search unit q, t iq represents the dwell time assigned by radar i to search unit q, n iq Represents time period t iq The number of radar detections within a period of time, the farthest detectable position of each search unit by the radar is defined as a false search target, SNR iq represents the expected signal-to-noise ratio of radar i to the false search target echo signal in search unit q, a iq (γ) represents the degree of correspondence between radar i and the false search target in search unit q, represents the distance between radar i and the false search target in search unit q, w0 represents the number of wave bits required to detect each search unit, and η represents the maximum number of effective detections achieved by the radar within the time period T0. The radar search performance measurement index selects a reference target. It is known that the distance between the reference target and the radar is R1 and the angle between the azimuth and the radar antenna is 0°. When the radar radiation power is P t1 When , the reference target echo signal-to-noise ratio is SNR1.

[0072] The specific explanations of the parameters in the radar search performance measurement index are as follows:

[0073] The main method of target search is to divide the given airspace into Q search units, and the radar scans each search unit in turn to find the target. The method of the present invention selects the farthest detection position of the radar to the search unit q as the q'th (q'=1,2,…,Q) false search target, and the distance between the false search target q' and the radar i is The degree of opposition is a iq (γ), the expected signal-to-noise ratio (SNR) of the generated echo iq It can be defined as:

[0074]

[0075] In the formula, time period t iq The number of searches that can be performed within niq It can be expressed as:

[0076]

[0077] In the formula, η represents the number of detections that the radar can perform within a known time period T0, and τ0 represents the time taken for each detection, that is, the number of detections η = T0 / τ0. This formula indicates that the radar uses coherent accumulation technology to continuously transmit multiple pulses to detect targets.

[0078] In formula (4), a iq The expression of (γ) is defined as:

[0079]

[0080] In the formula, the radar position is taken as the origin of the reference system, α represents the azimuth of the false search target, β represents the radar antenna orientation angle, and γ represents the angle between the false search target and the radar antenna orientation angle. The expressions of α and β can be obtained by combining the carrier and target motion models:

[0081]

[0082]

[0083] S3. Based on the Cramer-Rao lower bound, a radar tracking performance measurement index is constructed with the airborne radar radiation power and dwell time as optimization variables, as shown in formula (9):

[0084]

[0085] In the formula, represents the tracking performance measurement index of radar i for target m, represents the radiation power allocated by radar i to target m, t im represents the dwell time assigned by radar i to target m, n im Represents time period t im The number of radar detections within represents the mean square error of the estimated parameter of target m by radar i, η represents the maximum number of effective detections achieved by the radar within time period T0, P d Represents the probability of radar detecting the target, N exp is the number of measurements expected by the radar beam, P n represents the noise power, f1 represents the pulse repetition frequency, represents the distance between radar i and target m, Represents the radar cross-section of target m. The radar tracking performance measurement index requires the selection of a reference target. It is known that the radar cross-section of the reference target is RCS1 and the distance from the radar is R1. When the radar transmitter transmits power P t1When the power of a single echo is received, P r1 .

[0086] The specific explanations of the parameters in the radar tracking performance measurement indicators are as follows:

[0087] Similar to the above search process, time period t im The number of searches that can be performed within n im It can be expressed as:

[0088]

[0089] In the formula, η represents the maximum number of effective detections achieved by the radar within the time period T0, and τ0 represents the time taken for each detection, that is, the number of detections η = T0 / τ0. This formula indicates that the radar uses coherent accumulation technology to continuously transmit multiple pulses to detect targets.

[0090] Mean squared error of parameter estimates It is related to the signal-to-noise ratio of the target signal and can be expressed as:

[0091]

[0092] In the formula, SNR im represents the echo signal-to-noise ratio generated by radar i tracking target m, represents the echo signal power generated by radar i tracking target m, It can be expressed as:

[0093]

[0094] In the formula, It represents the echo power of a single pulse emitted by radar i and can be expressed as:

[0095]

[0096] N im It represents the number of echo pulses received by radar i per unit time, which can be expressed as:

[0097]

[0098] S4. Establish a network radar node selection and power-time collaborative optimization model under multi-target search and tracking:

[0099] Taking the given upper limit of the total radiation power and the dwell time limit of the airborne radar as the constraints, and maximizing the radar search performance index and tracking performance index as the optimization goal, a collaborative optimization model of networked radar node selection and power time under multi-target search and tracking is established, as shown in formula (15):

[0100]

[0101] In the formula, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m; I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1, ω2 are weighting factors (ω1+ω2=1), indicating the proportion of tracking performance and search performance considered in the model; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned to target m by radar i; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Indicates the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; Indicates the maximum dwell time assigned to a single target.

[0102] In equation (15), the first constraint indicates that in the radar search task, each search unit is scanned by only one radar and a single radar scans at most search units; the second constraint indicates that in the radar tracking task, each target is tracked by only one radar and a single radar can track at most The third constraint indicates that the node selection parameter is a binary variable. The fourth constraint indicates the limit of the total radiated power allocated to all search units and tracked targets by the radar network. The fifth constraint indicates the limit of the total dwell time of a single radar. The last two constraints indicate the limits of the radiated power and dwell time allocated to each node.

[0103] S5. Combining the interior point method and particle swarm algorithm, the optimization model (15) is solved in three steps:

[0104] Step 1: Decompose the optimization model (15) into the optimization model for selecting networked radar nodes under multi-target search and tracking and the optimization model for coordinated power and time optimization of networked radars under multi-target search and tracking:

[0105]

[0106]

[0107] Step 2: Solve the optimization model (16) using the interior point method:

[0108] i) Input parameters of the optimization model: Assuming that the radiation power and dwell time allocated to all nodes are the same, calculate the search performance matrix of radar i for search unit q (q = 1, 2, ..., Q) And the tracking performance matrix of radar i for target m (m=1,2,…,M) Initialize the interior point matrix U S and U T , set the interior point feasible region:

[0109] Objective function: and Set the iteration index Set the algorithm termination indicator ε>0;

[0110] ii) Take is the initial point;

[0111] iii) Solve the following problem:

[0112] iv) Let the maximum point of the above problem be

[0113] v) Check the termination condition and calculate the objective function value corresponding to the current maximum point and If the objective function value converges, the algorithm terminates; otherwise, the next iteration is executed: Update Update the initial point: use the current maximum point as the initial point for the next iteration;

[0114] vi) Output the node selection results of radar search task and tracking task and

[0115] Step 3: Solve the optimization model (17) by combining the particle swarm algorithm:

[0116] i) Initialize the particle swarm, given the swarm size P', inertia factor ρ1 and learning factor ρ2, and use the particle position x to represent the radar radiation power and residence time allocated to the node, that is, the particle position matrix Set the particle flight speed v and the particle feasible domain:

[0117]

[0118] , set the objective function: Set the iteration index φ = 1, and set the number of algorithm iterations N;

[0119] ii) Randomly generate the position X and velocity v of particle p' (p'=1,2,…,P');

[0120] iii) Solve the following problem:

[0121] iv) Calculate the fitness of each particle through the objective function

[0122] v) Update the individual optimal particle position x φ and the global optimal group position X φ , update the velocity of all particles and location

[0123] vi) Check the number of iterations. If the termination condition is met, exit; otherwise, execute the next iteration: update φ=φ+1, update the initial point: use the current maximum point as the initial point of the next iteration;

[0124] vii) Output radar radiation power and mission time allocation results

[0125] Simulation results:

[0126] The operating parameters of the airborne radar are set as shown in Table 1:

[0127] Table 1 Simulation parameter settings

[0128]

[0129] Assume that there are I = 3 airborne phased array radars and M = 9 targets in the current two-dimensional airspace, and the target RCS is 10m 2 The carrier and the target both fly in a straight line at a constant speed in a certain direction and are independent of each other. The flight trajectory parameters of the target and the carrier are set as shown in Table 2 and Table 3 respectively. The current airspace can be divided into Q = 8 search units. The midpoint of the farthest position of each unit is used as the radar limit search distance and as an indicator to measure the radar search performance, as shown in Table 4. Maximum number of search nodes for a single radar and the maximum number of tracked nodes The total radiated power of the airborne radar network is capped at P w =10kW, the total dwell time for the search and tracking missions is T w = 30s, the maximum radiation power allocated to each search node and the maximum radiated power allocated to each tracking node The maximum dwell time allocated to each search node is 4kW. The maximum dwell time allocated for each tracking node Both are 20 seconds.

[0130] Table 2 Target flight trajectory parameters

[0131]

[0132] Table 3 Aircraft flight trajectory parameters

[0133]

[0134] Table 4 Search area division

[0135]

[0136] The flow chart of the joint optimization method of airborne radar flight path and power for multi-target tracking is as follows: Figure 1 As shown; the motion trajectory of multiple targets and the motion trajectory of airborne radar are shown in Figure 2 As shown in the figure, the motion trajectories of multiple targets and airborne radars within 60 seconds; the airborne radar node selection results in the search task and tracking task are shown in Figure 3 and Figure 4 As shown in the figure, the black area indicates that the current node is assigned to the corresponding radar, and the red area indicates that the current node is not assigned to the corresponding radar; the distribution of airborne radar radiation power in the search task and tracking task are shown in Figure 5 and Figure 6 As shown in the figure, the numbers marked in the figure represent the node numbers assigned to the radar; the distribution of the airborne radar dwell time in the search mission and the tracking mission are shown in Figure 7 and Figure 8 As shown in the figure, the numbers marked in the figure represent the node numbers assigned to the radar. Figure 3 and Figure 4 It can be seen that the distance parameter has a greater impact on the performance index, and the airborne radar gives priority to searching nodes or tracking nodes with larger performance indexes. Figures 5 to 8 It can be seen that the airborne radar allocates more resources to targets with greater performance indicators, thereby improving the overall performance indicators of the system.

[0137] In order to verify the effectiveness of the algorithm proposed in this paper, the radar working performance under average time allocation, average power allocation and random power time allocation is also compared. Fig. 9 As shown in the figure, it can be seen that after the airborne radar network node selection, radiation power and dwell time are adaptively planned, the multi-target search and tracking performance is further improved, which shows the effectiveness of the algorithm proposed in this paper.

[0138] In summary, based on actual combat scenarios, the present invention proposes a method for collaborative optimization of networked radar node selection and power time under multi-target search and tracking. Under the constraints of a given upper limit of the total radiation power of the airborne radar and a limit on the dwell time, the optimization goal is to maximize the radar search performance index and the tracking performance index. The parameters such as the node selection, radiation power and dwell time of the airborne radar in the multi-target search and tracking process are adaptively optimized, thereby improving the multi-target search and tracking performance of the airborne radar. Firstly, a networked radar system consisting of multiple airborne phased array radars with multi-beam working capability in two-dimensional space is considered, and multiple moving targets dispersed in space are searched and tracked at the same time. Secondly, for the scenario of airborne radar searching and tracking multiple targets, the radiation power and dwell time of the airborne radar are taken as optimization variables, and evaluation indicators characterizing the radar search performance and tracking performance are constructed based on signal detection theory and Cramer-Rao lower bound respectively. On this basis, with the given upper limit of the total radiation power resource of the airborne networked radar system and the dwell time limit as constraints, and with maximizing the radar search performance index and tracking performance index as the optimization goal, a collaborative optimization model of networked radar node selection and power time under multi-target search and tracking is established. Finally, the interior point method and particle swarm algorithm are used to solve the optimization model. By solving the optimization model, the node selection parameter u that maximizes the radar multi-target search and tracking performance under the given upper limit of the total radiation power resource of the airborne radar system and the dwell time limit is obtained. Siq and u Tim , radiated power P tiq and P tim and the residence time t iq and t im The optimal solution of the model is achieved by adaptively and dynamically optimizing node selection, radiation power and dwell time in radar search and tracking tasks to improve multi-target search and tracking performance.

[0139] Based on the same inventive concept, the networked radar node selection and power-time coordinated optimization system under multi-target search and tracking of the present invention includes:

[0140] A motion model building unit, used to build motion models of radar carriers and targets;

[0141] An index construction unit, used for constructing a radar search performance measurement index with airborne radar radiation power and dwell time as optimization variables based on signal detection theory, and for constructing a radar tracking performance measurement index with airborne radar radiation power and dwell time as optimization variables based on Cramer-Rao lower bound;

[0142] The optimization model building unit is used to establish a collaborative optimization model of network radar node selection and power time under multi-target search and tracking, taking the given upper limit of the total radiation power and the dwell time limit of the airborne radar as constraints and maximizing the radar search performance index and tracking performance index as the optimization goal;

[0143] The optimization model solving unit is used to solve the optimization model by combining the interior point method and the particle swarm algorithm, including: firstly, decomposing the optimization model into a node selection optimization model for networked radar under multi-target search and tracking and a power-time coordinated optimization model for networked radar under multi-target search and tracking; secondly, solving the node selection optimization model for networked radar under multi-target search and tracking by combining the interior point method; finally, solving the power-time coordinated optimization model for networked radar under multi-target search and tracking by combining the particle swarm algorithm; realizing the node selection and power-time coordinated optimization of networked radar under multi-target search and tracking.

[0144] Based on the same inventive concept, an electronic device of the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the steps of the method for selecting networked radar nodes and co-optimizing power and time under multi-target search and tracking are implemented.

Claims

1. A method for collaborative optimization of networked radar node selection and power time under multi-target search and tracking, characterized in that: The following steps are involved: First, the motion model of the radar carrier and the target is constructed; based on the signal detection theory, the radar search performance measurement index with the airborne radar radiation power and dwell time as the optimization variables is constructed; based on the Cramer-Rao lower bound, the radar tracking performance measurement index with the airborne radar radiation power and dwell time as the optimization variables is constructed; with the given airborne radar total radiation power upper limit and dwell time limit as constraints, and with maximizing the radar search performance index and tracking performance index as the optimization goal, a network radar node selection and power-time collaborative optimization model under multi-target search and tracking is established; The optimization model is solved by combining the interior point method and the particle swarm algorithm, including: firstly, decomposing the optimization model into the optimization model of networked radar node selection under multi-target search and tracking and the optimization model of networked radar power time collaborative optimization under multi-target search and tracking; secondly, solving the optimization model of networked radar node selection under multi-target search and tracking by combining the interior point method; finally, solving the optimization model of networked radar power time collaborative optimization under multi-target search and tracking by combining the particle swarm algorithm; realizing the coordinated optimization of networked radar node selection and power time under multi-target search and tracking; The network radar node selection and power-time collaborative optimization model under multi-target search and tracking is: in, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m; I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1 and ω2 represent the proportion of tracking performance and search performance considered in the model respectively; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned to target m by radar i; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Represents the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; Indicates the maximum dwell time assigned to a single target.

2. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 1, characterized in that: The motion model of the radar carrier and the target is constructed as follows: in, represents the state vector of aircraft i, represents the state vector of target m, and represents the position coordinates of aircraft i, and represents the flight speed of aircraft i, and represents the position coordinates of the target m, and represents the flight speed of target m, {·} T Represents the transpose operation of a matrix.

3. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 1, characterized in that: The radar search performance measurement index expression is: in, represents the search performance measurement index of radar i for search unit q, represents the radiation power allocated by radar i to search unit q, t iq represents the dwell time assigned by radar i to search unit q, n iq Represents time period t iq The number of radar detections within a period of time, the farthest detectable position of each search unit by the radar is defined as a false search target, SNR iq represents the expected signal-to-noise ratio of radar i to the false search target echo signal in search unit q, a iq (γ) represents the degree of correspondence between radar i and the false search target in search unit q, represents the distance between radar i and the false search target in search unit q, w0 represents the number of wave bits required to detect each search unit, η represents the maximum number of effective detections achieved by the radar within the time period T0; R1 represents the distance between the radar and the reference target, P t1 It represents the radar radiation power to the reference target. SNR1 represents the signal-to-noise ratio of the reference target echo received by the radar when the distance between the radar and the reference target is R1 and the angle between the azimuth and the radar antenna is 0°.

4. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 1, characterized in that: The radar tracking performance measurement index expression is: in, represents the tracking performance measurement index of radar i for target m, represents the radiation power allocated by radar i to target m, t im represents the dwell time assigned by radar i to target m, n im Represents time period t im The number of radar detections within represents the mean square error of the estimated parameter of target m by radar i, η represents the maximum number of effective detections achieved by the radar within time period T0, P d Represents the probability of radar detecting the target, N exp is the number of measurements expected by the radar beam, P n represents the noise power, f1 represents the pulse repetition frequency, represents the distance between radar i and target m, represents the radar cross-sectional area of ​​target m; R1 represents the distance between the radar and the reference target, P t1 represents the radar radiation power to the reference target, RCS1 represents the reference target radar scattering cross-sectional area, P r1 is the reference target signal echo power.

5. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 1, characterized in that: The optimization model is decomposed into the optimization model of networked radar node selection under multi-target search and tracking and the optimization model of networked radar power-time collaborative optimization under multi-target search and tracking, specifically: The expression of the optimization model for selecting networked radar nodes under multi-target search and tracking is: in, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m, I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1 and ω2 represent the proportion of tracking performance and search performance considered in the model respectively; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar; The expression of the power-time collaborative optimization model of networked radar under multi-target search and tracking is: in, represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned by radar i to target m; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Indicates the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; Indicates the maximum dwell time assigned to a single target.

6. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 5, characterized in that: Combined with the interior point method, the optimization model of networked radar node selection under multi-target search and tracking is solved, including the following steps: i) Input the parameters of the optimization model: the radiation power and dwell time allocated to all nodes are the same constant value, and the search performance matrix of radar i for search unit q is calculated And the tracking performance matrix of radar i for target m q=1,2,…,Q,m=1,2,…,M;initialize the interior point matrix U S and U T , set the interior point feasible region: Objective function: and Set the iteration index Set the algorithm termination indicator ε>0; ii) Take is the initial point; iii) Solve the following problem: iv) Let the maximum point of the above problem be v) Check the termination condition and calculate the objective function value corresponding to the current maximum point and If the objective function value converges, the algorithm terminates; otherwise, the next iteration is executed: Update Update the initial point: use the current maximum point as the initial point for the next iteration; vi) Output the node selection results of radar search task and tracking task and 7. The method for selecting networked radar nodes and coordinating power and time for optimizing multi-target search and tracking according to claim 5, characterized in that: The particle swarm algorithm is combined to solve the power-time collaborative optimization model of networked radar under multi-target search and tracking, including the following steps: i) Initialize the particle swarm, given the swarm size P', inertia factor ρ1 and learning factor ρ2, and use the particle position x to represent the radar radiation power and residence time allocated to the node, that is, the particle position matrix X = [P tiq ,t iq ,P tim ,t im ], set the particle flight speed v, and set the particle feasible region: Set the objective function: Set the iteration index φ = 1, and set the number of algorithm iterations N; ii) Randomly generate the position X and velocity v of particle p', p' = 1, 2, ..., P'; iii) Solve the following problem: Where D is the interior point feasible region; iv) Calculate the fitness of each particle through the objective function v) Update the individual optimal particle position x φ and the global optimal group position X φ , update the velocity of all particles and location vi) Check the number of iterations. If the termination condition is met, exit; otherwise, execute the next iteration: update φ=φ+1, update the initial point: use the current maximum point as the initial point of the next iteration; vii) Output radar radiation power and mission time allocation results t iq , t im .

8. The networked radar node selection and power-time coordinated optimization system under multi-target search and tracking is characterized by: include: A motion model building unit, used to build motion models of radar carriers and targets; An index construction unit, used for constructing a radar search performance measurement index with airborne radar radiation power and dwell time as optimization variables based on signal detection theory, and for constructing a radar tracking performance measurement index with airborne radar radiation power and dwell time as optimization variables based on Cramer-Rao lower bound; The optimization model building unit is used to establish a collaborative optimization model of networked radar node selection and power time under multi-target search and tracking, taking the given upper limit of the total radiation power and the dwell time limit of the airborne radar as constraints, and maximizing the radar search performance index and tracking performance index as the optimization goal; the model expression is: in, represents the search performance measurement index of radar i for search unit q, represents the tracking performance measurement index of radar i for target m; I represents the total number of radars, Q represents the total number of search units obtained by dividing a given airspace, and M represents the total number of targets; ω1 and ω2 represent the proportion of tracking performance and search performance considered in the model respectively; Indicates the airborne radar search node selection parameters; Indicates the airborne radar tracking node selection parameters; represents the radiated power of radar i allocated to the search mission in area q; represents the radiated power of radar i assigned to the tracking task of target m; t iq represents the dwell time of the search mission assigned to area q by radar i; t im represents the dwell time of the tracking task assigned to target m by radar i; Indicates the maximum number of search nodes for a single radar; Indicates the maximum number of tracking nodes for a single radar; P w Represents the total radiated power of a single radar transmitter; T w Indicates the total working time of a single radar; Indicates the maximum power allocated to a single search unit; Indicates the maximum power allocated to a single target; Indicates the maximum dwell time assigned to a single search unit; represents the maximum dwell time assigned to a single target; The optimization model solving unit is used to solve the optimization model by combining the interior point method and the particle swarm algorithm, including: firstly, decomposing the optimization model into a node selection optimization model for networked radar under multi-target search and tracking and a power-time coordinated optimization model for networked radar under multi-target search and tracking; secondly, solving the node selection optimization model for networked radar under multi-target search and tracking by combining the interior point method; finally, solving the power-time coordinated optimization model for networked radar under multi-target search and tracking by combining the particle swarm algorithm; realizing the node selection and power-time coordinated optimization of networked radar under multi-target search and tracking.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into the processor, the steps of the method for selecting networked radar nodes and co-optimizing power and time under multi-target search and tracking according to any one of claims 1 to 7 are implemented.

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