Signal-level cooperative multi-radar network search resource allocation method

Abstract

A signal-level collaborative multi-radar networking search resource allocation method relates to the field of radar technology. The present invention is to solve the problem that in the existing three-radar signal-level collaborative search scenario, resources cannot be allocated between the radars to maximize the collaborative search range. The present invention includes the following steps: step 1, signal-level collaborative radar networking; step 2, signal-level collaborative search and its time and space constraints; step 3, optimizing the signal-level collaborative search range. Starting from the resource allocation strategy of a single radar, the method analyzes the constraints of signal-level collaborative search resource allocation. In the three-radar collaborative search scenario, the geometric configuration of the three radars that meets the signal-level collaborative search constraints and the judgment method are analyzed. The area calculation method of the collaborative search region under different geometric configurations is derived, and a collaborative search optimization model and a collaborative resource allocation process based on a genetic algorithm are established.

Description

Technical Field

[0001] The present invention belongs to the field of radar anti-interference technology, and in particular relates to a signal-level collaborative multi-radar networking search resource allocation method. Background Art

[0002] With the continuous emergence of new combat targets and combat styles, relying solely on a single radar node is increasingly unable to meet new detection requirements. Throughout its development history, radar network detection has evolved through various forms, including dual- and multi-base radars, radar network systems, MIMO radars, and distributed coherent radars. Signal-level cooperative radar network detection is also a networking application, situated between signal-level coherent radar network detection and data-level fusion radar network detection. It is an effective means of improving radar's resistance to active interference and has achieved good results in practical applications. Compared with signal-level coherent radar networking, it does not require strict phase coherence between the transmitted signals of each radar, making it more feasible for engineering implementation. Compared with data-level fusion radar networking, it still meets data fusion requirements, but requires coordinated operation among the radars, meaning that the radars must transmit signals according to a predetermined timing. Signal-level cooperative radar networking comprehensively utilizes the radiation resources of multiple radars, radiating radar signals simultaneously into the search airspace using a specific timing sequence. This allows active jammers within the search airspace to simultaneously distribute jamming resources in the time, frequency, spatial, and even polarization domains, reducing the jamming performance of active jammers within the radar's operating range. In addition to cooperative search tasks, signal-level cooperative radar networking also needs to perform non-cooperative search tasks that a single radar can accomplish, such as tracking targets in interference-free airspace. This raises the question of how to allocate resources among the radars to maximize the cooperative search range. Summary of the Invention

[0003] The present invention aims to address the problem of being unable to allocate resources between radars to maximize the collaborative search range in existing three-radar signal-level collaborative search scenarios. The present invention proposes a signal-level collaborative multi-radar network search resource allocation method. The present invention proposes a signal-level collaborative multi-radar network search resource allocation method, comprising the following steps:

[0004] Step 1: Signal-level collaborative radar networking;

[0005] Step 2: Signal-level collaborative search and its spatiotemporal constraints;

[0006] Step 3: Optimize the signal-level collaborative search range.

[0007] Preferably, in step 1, the signal-level collaborative radar networking controls the timing of radar collaborative transmission signals based on the path difference formed between the networked radars in the search airspace, so that the time when the transmission signals of different radars arrive at the detection airspace remains basically consistent.

[0008] Preferably, in step 2, the main constraints for signal-level collaborative search resource allocation include: constraints between a single radar's search resources and search cycles, and constraints on the timing synchronization of search cycles between radars:

[0009] Step 2.1: The relationship between the search resource and search period of a single radar can be derived from the radar equation. According to the search radar equation (1),

[0010]

[0011] Among them, R is the radar detection distance, P av is the average transmit power of the radar, G t is the transmitting antenna gain, G r is the receiving antenna gain, λ is the radar wavelength, σ is the target RCS, k is the Boltzmann constant, T0 is the receiver noise bandwidth at room temperature, F n is the receiver noise coefficient, L is the radar loss, SNR is the detection signal-to-noise ratio, T f is the search cycle; assuming that its total resources are constant, let SR0 be the total radar resources,

[0012]

[0013] It can be seen that for a specific radar, the fourth power of the radar detection range is proportional to the search period, and the search period is inversely proportional to the resources occupied by the search;

[0014]

[0015] SR=1-TR,(TR>TR0) (4)

[0016] SR0=1-TR0 (5)

[0017] Where SR0 (≤1) is the percentage of resources allocated to the radar search task in the initial state, and the corresponding optimal search period is T f0 , the detection range is R0, the resource ratio allocated to other high-priority tasks is TR0; SR is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f , the detection range is R, and the ratio of resources allocated to other high-priority tasks is TR. As the radar resources occupied by high-priority tasks (such as tracking) increase TR (> TR0), it will inevitably lead to a reduction in radar search resources SR;

[0018] For signal-level cooperative radar networking, each radar must satisfy the following formula:

[0019]

[0020]

[0021] Among them SR 10 (≤1) is the percentage of resources allocated to the radar 1 search task in the initial state, and the corresponding optimal search period is T f10 , the detection distance is R 10 SR1 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f1 , the detection distance is R1; SR 20 (≤1) is the percentage of resources allocated to the radar 2 search task in the initial state, and the corresponding optimal search period is T f20 , the detection distance is R 20 SR2 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f2 , the detection distance is R2; due to the certain synchronization relationship between the signal-level cooperative emission timing, the cooperative search cycles of the two radars must meet the equal constraint, that is,

[0022] T f1 =T f2 (8);

[0023] Step 2.2: Spatial constraints and geometric configuration determination

[0024] To achieve signal-level collaborative search, the three radars must simultaneously locate their collaborative search areas within their detection ranges. This is the spatial constraint for signal-level collaborative search. To determine whether the three radars meet the spatial constraint, we can convert this into determining whether their respective detection ranges overlap. Assume that the radar detection range is a circle with the radar site coordinates as the center and the detection distance as the radius. The detection range of each radar can be adaptively adjusted as needed. Therefore, there are many possible geometric configurations for the collaborative search ranges of the three radars. In general, the geometric configurations of the three radars with a common overlapping area can be divided into the following three categories:

[0025] The first type: This type of geometric configuration is characterized by the circle with the smallest radius being contained by the other two circles at the same time. In this case, the area of ​​the overlapping region of the three circles is equal to the area of ​​the circle with the smallest radius.

[0026] The second type of geometric configuration is characterized by the existence of a set of circles that are contained, and the circle with the smaller radius has two intersection points with the third circle, and the area of ​​the overlapping area of ​​the three circles is equal to the overlapping area of ​​two of the circles;

[0027] The third type of geometric configuration is characterized by the intersection of three circles, including the overlapping area of ​​the two circles intersecting, the overlapping area between the three intersection points, and the overlapping area between the four intersection points.

[0028] Preferably, step 3 includes:

[0029] Step 3.1: Signal-level collaborative search resource allocation optimization model

[0030] Due to the complexity of the collaborative search constraints, even if the radar parameters and resource allocation results are given, it is still necessary to solve the coverage area according to the actual search range configuration. Let us assume that the radar resources SR in the initial state of the radar are 10 SR 20 SR 30 , the corresponding optimal search period is T f10 、T f20 、T f30 , the normalized detection distance is R 10 、R 20 、R 30 , assuming that the required collaborative search period is T f =T f1 =T f2 =T f3 The resources allocated to the three radars are SR1, SR2, and SR3 (SR1+SR2+SR3=c). When the total resources of the radar network are fixed, let the overlapping search area of ​​the three radars be S0. Then the signal-level collaborative search optimization model can be defined as By optimizing SR1, SR2, and SR3, resource allocation is performed to maximize the collaborative search range. At the same time, the following conditions must be met.

[0031]

[0032] Where c is a constant, which represents the total resources available for allocation. The constraint condition indicates that when performing collaborative search resource allocation, the resource allocation of each radar must meet the resource allocation strategy of a single radar and meet the time constraint T of the collaborative search. f1 =T f2 =T f3 The total resources available for allocation are certain; the resources allocated by each radar are not greater than its own normalized total resources;

[0033] Step 3.2: Calculation of signal-level collaborative search area

[0034] Step 3.2.1 Overlapping area when two circles intersect

[0035] To find the area of ​​the overlapping area of ​​the two circles, suppose radar 1 is deployed at point A, and its detection range is a circle with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is a circle with point B as the center and R2 as the radius; the distance between points A and B is d3, and the two circles intersect at points C and D.

[0036] S0=S1+S2-2S3

[0037] Among them, S1 is the area of ​​sector ACD (toward point B), S2 is the area of ​​sector BCD (toward point A), and S3 is the area of ​​triangle ABC.

[0038]

[0039] Step 3.2.2: The overlapping area between the three intersection points

[0040] Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as

[0041] S0=S1-S2+S3-S4+S5-S6+S7

[0042] Among them, S1 is fan-shaped AJ 12 J 13 The area of ​​triangle ΔAJ is S2. 12 J 13 The area of ​​​​S3 is the fan-shaped BJ 12 J 23 The area of ​​triangle ΔBJ is S4. 12 J 23 The area of ​​​​S5 is the fan CJ 23 J 13 The area of ​​triangle ΔCJ is S6. 23 J 13 The area of ​​triangle ΔJ is S7. 12 J 13 J 23 area;

[0043] Step 3.2.3: Overlapping area between the four intersection points

[0044] Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as

[0045] S0=S1-S2+S3-S4+S5-S6+S7-S8+S9

[0046] Among them, S1 is fan-shaped AJ 12 J 21 The area of ​​triangle ΔAJ is S2. 12 J 21 The area of ​​​​S3 is the fan-shaped BJ 32 J 12 The area of ​​triangle ΔBJ is S4. 32 J 12 The area of ​​​​S5 is the fan CJ 23 J 32 The area of ​​triangle ΔCJ is S6. 23 J 32 The area of ​​​​S7 is the fan-shaped BJ 21 J 23 The area of ​​triangle ΔBJ is S8. 21 J 23 The area of ​​quadrilateral J is S9. 12 J 21 J 23 J 32 area;

[0047] Step 3.3: Collaborative resource allocation process based on genetic algorithm

[0048] The signal-level collaborative search range optimization model is to maximize S0 while satisfying the constraints. The algorithm process is as follows: first, an initial population that satisfies the resource constraints is generated, and then the fitness of each individual in this population is calculated to determine whether the termination condition is met. If so, the operation is terminated and the optimal individual is output as the optimization result. If not, the individuals in the population are subjected to genetic operations such as selection, crossover, and mutation to ensure that each individual in the newly generated population still meets the resource constraints. The fitness of the evolved offspring population is calculated and the termination condition is re-judged. This cycle is repeated until the termination condition is met.

[0049] Step 3.3.1. Create an initial population

[0050] Assume that the number of individuals in a population is Np, and each individual is represented by a real-valued parameter vector containing 3 elements, f i,g =[SR i,g,1 ,SR i,g,2 ,SR i,g,3 ],(i=1,2,…N p ), i is the serial number of the individual in the corresponding population, g is the genetic generation, SR i,g,1 +SR i,g,2 +SR i,g,3=c, where c is a constant representing the total resources available for allocation;

[0051] Step 3.3.2, fitness calculation

[0052] For each individual in a population, calculate the overlapping area according to step 3.2, denoted as S 0i ;

[0053] Step 3.3.3. Select an operation

[0054] The selection method of "roulette wheel" is used, using each individual f i,g The proportion of the fitness of an individual determines the possibility of its offspring retention. If the fitness of an individual is S 0i , then the probability of it being selected is expressed as

[0055]

[0056] The greater the individual fitness, the greater the chance of being selected, and vice versa. The specific method is to generate a uniform random number p in [0,1] 01 , if the random number is less than p i , then the individual is selected as the new individual in the next generation population;

[0057] Step 3.3.4: Crossover operation

[0058] Pair the individuals in the population with each other, and for each pair of individuals, the crossover probability P c Exchange an element between them by generating a random number p uniformly distributed in [0,1]. 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <P c , then for the Mth pair of real-valued vectors 13 Elements perform crossover operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3 =c, allocate the remaining resources to the two elements that do not perform the crossover operation according to the original ratio;

[0059] Step 3.3.5, mutation operation

[0060] For each individual in the population after crossover, the mutation probability P m Change an element by generating a random number p uniformly distributed in [0,1] 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <Pm , then for the Mth pair of real-valued vectors 13 Elements perform mutation operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3 =c, and the remaining resources are allocated to the two elements that have not undergone mutation operations according to the original proportion.

[0061] The present invention addresses the search resource allocation problem of limited radar resources in a three-radar signal-level collaborative search scenario. Starting from the search resource allocation strategy of a single radar, the spatiotemporal constraints of signal-level collaborative search resource allocation are determined, the geometric configurations of the three radars that meet the signal-level collaborative search constraints and the determination method thereof are analyzed, the area calculation method of the collaborative search region under each geometric configuration is derived, a collaborative search optimization model and a collaborative resource allocation process based on a genetic algorithm are established, and finally a typical scenario is set up. Typical conclusions are obtained through simulation analysis, which have guiding significance for the actual application of radar signal-level collaborative search and solve the problem that resources cannot be allocated among the radars to maximize the collaborative search range in the existing three-radar signal-level collaborative search scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a schematic diagram of signal-level collaborative search;

[0063] Figure 2 This is an illustration of the first type of geometric configuration Figure 1 ;

[0064] Figure 3 This is an illustration of the first type of geometric configuration Figure 2 ;

[0065] Figure 4 This is the first type of geometric configuration determination flow chart;

[0066] Figure 5 This is an illustration of the second type of geometric configuration Figure 1 ;

[0067] Figure 6 This is an illustration of the second type of geometric configuration Figure 2 ;

[0068] Figure 7 This is the flow chart for determining the second type of geometric configuration;

[0069] Figure 8 This is an illustration of the third type of geometric configuration Figure 1 ;

[0070] Figure 9 This is an illustration of the third type of geometric configuration Figure 2 ;

[0071] Figure 10This is an illustration of the third type of geometric configuration Figure 3 ;

[0072] Figure 11 This is the flow chart for determining the third type of geometric configuration;

[0073] Figure 12 Schematic diagram of the intersection of two circles;

[0074] Figure 13 This is a diagram showing the intersection of three circles. Figure 1 ;

[0075] Figure 14 This is a diagram showing the intersection of three circles. Figure 2 ;

[0076] Figure 15 Solve the flow chart for the genetic algorithm;

[0077] Figure 16 This is a graph showing the relationship between search distance and search period under different resources;

[0078] Figure 17 Schematic diagram of collaborative search resource SR1 allocated to radar 1 Figure 1 ;

[0079] Figure 18 Cooperative search resource curve allocable to Radar 2 Figure 1 ;

[0080] Figure 19 Iteration curve Figure 1 ;

[0081] Figure 20 Schematic diagram of collaborative search resource SR1 allocated to radar 1 Figure 2 ;

[0082] Figure 21 Cooperative search resource curve allocable to Radar 2 Figure 2 ;

[0083] Figure 22 Iteration curve Figure 2 ;

[0084] Figure 23 Schematic diagram of collaborative search resource SR1 allocated to radar 1 Figure 3 ;

[0085] Figure 24 Cooperative search resource curve allocable to Radar 2 Figure 3 ;

[0086] Figure 25 Schematic diagram of collaborative search resource SR1 allocated to radar 1 Figure 4 ;

[0087] Figure 26 Cooperative search resource curve allocable to Radar 2 Figure 4 . DETAILED DESCRIPTION

[0088] Specific implementation method 1: This implementation method is described in detail with reference to the accompanying drawings. Figure 1-26 As shown, the signal-level collaborative multi-radar network search resource allocation method described in this embodiment includes the following steps:

[0089] Step 1: Signal-level collaborative radar networking;

[0090] Step 2: Signal-level collaborative search and its spatiotemporal constraints;

[0091] Step 3: Optimize the signal-level collaborative search range.

[0092] Specific implementation method 2: This implementation method is described in detail with reference to the accompanying drawings. Figure 1-26 As shown, in step 1, the signal-level cooperative radar network controls the timing of the radar cooperative transmission signal according to the path difference formed between the networked radars in the search airspace, so that the time when the transmission signals of different radars arrive at the detection airspace remains basically consistent.

[0093] In this embodiment, similar to the weighted compensation of the path difference between the elements of a single phased array radar antenna, the signal-level cooperative radar network controls the timing of the radar cooperative transmission signal based on the path difference formed between the networked radars in the search airspace, so that the time when the transmission signals of different radars arrive at the detection airspace is basically consistent. This requires the active jammers in the area to allocate the jamming resources at the same time to achieve the jamming effect on each radar. Since the signal-level cooperative transmission can be diversified in the frequency domain, waveform domain, and airspace, it may be impossible for the jammers to jam all signal-level cooperative networked radars at the same time. Therefore, the signal-level cooperative radar network has a better anti-interference effect than a single radar. Its basic principle is as follows: Figure 1 Radar missions are usually diverse. For example, in addition to airspace search, they also require target tracking and other tasks. Therefore, the resource allocation problem existing in a single radar also exists in a signal-level cooperative radar network. In addition, due to the timing correlation required for signal-level cooperation, the allocation of resources required for non-cooperative search tasks among radars directly affects the overall performance of the cooperative search task, such as the size of the cooperative search range.

[0094] Specific embodiment 3: This embodiment is described in detail with reference to the accompanying drawings. As shown in the figure, in step 2, the main constraints for signal-level collaborative search resource allocation include: constraints between the search resources and search cycles of a single radar and constraints on the timing synchronization of search cycles between radars:

[0095] Step 2.1: The relationship between the search resource and search period of a single radar can be derived from the radar equation. According to the search radar equation (1),

[0096]

[0097] Among them, R is the radar detection distance, P av is the average transmit power of the radar, G t is the transmitting antenna gain, G r is the receiving antenna gain, λ is the radar wavelength, σ is the target RCS, k is the Boltzmann constant, T0 is the receiver noise bandwidth at room temperature, F n is the receiver noise coefficient, L is the radar loss, SNR is the detection signal-to-noise ratio, T f is the search cycle; assuming that its total resources are constant, let SR0 be the total radar resources,

[0098]

[0099] It can be seen that for a specific radar, the fourth power of the radar detection range is proportional to the search period, and the search period is inversely proportional to the resources occupied by the search;

[0100]

[0101] SR=1-TR,(TR>TR0) (4)

[0102] SR0=1-TR0 (5)

[0103] Where SR0 (≤1) is the percentage of resources allocated to the radar search task in the initial state, and the corresponding optimal search period is T f0 , the detection range is R0, the resource ratio allocated to other high-priority tasks is TR0; SR is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f , the detection range is R, and the ratio of resources allocated to other high-priority tasks is TR. As the radar resources occupied by high-priority tasks (such as tracking) increase TR (> TR0), it will inevitably lead to a reduction in radar search resources SR;

[0104] For signal-level cooperative radar networking, each radar must satisfy the following formula:

[0105]

[0106]

[0107] Among them SR 10 (≥1) is the percentage of resources allocated to the radar 1 search task in the initial state, and the corresponding optimal search period is T f10, the detection distance is R 10 SR1 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f1 , the detection distance is R1; SR 20 (≤1) is the percentage of resources allocated to the radar 2 search task in the initial state, and the corresponding optimal search period is T f20 , the detection distance is R 20 SR2 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f2 , the detection distance is R2; due to the certain synchronization relationship between the signal-level cooperative emission timing, the cooperative search cycles of the two radars must meet the equal constraint, that is,

[0108] T f1 =T f2 (8);

[0109] Step 2.2: Spatial constraints and geometric configuration determination

[0110] To achieve signal-level collaborative search, the three radars must simultaneously locate their collaborative search areas within their detection ranges. This is the spatial constraint for signal-level collaborative search. To determine whether the three radars meet the spatial constraint, we can convert this into determining whether their respective detection ranges overlap. Assume that the radar detection range is a circle with the radar site coordinates as the center and the detection distance as the radius. The detection range of each radar can be adaptively adjusted as needed. Therefore, there are many possible geometric configurations for the collaborative search ranges of the three radars. In general, the geometric configurations of the three radars with a common overlapping area can be divided into the following three categories:

[0111] like Figure 2 and Figure 3 As shown, the first type: the characteristic of this type of geometric configuration is that the circle with the smallest radius is contained by the other two circles at the same time. At this time, the area of ​​the overlapping area of ​​the three circles is equal to the area of ​​the circle with the smallest radius. The process of determining whether the coordinated search range of the three radars meets this type of geometric configuration is as follows: Figure 4 shown.

[0112] like Figure 5 and Figure 6 As shown in the figure, the second type of geometric configuration is characterized by the existence of a set of circles with a containment relationship, in which the circle with the smaller radius has two intersections with the third circle. At this time, the overlapping area of ​​the three circles is equal to the overlapping area of ​​two of the circles. The process of judging whether the collaborative search range of the three radars meets this geometric configuration is as follows: Figure 7 shown.

[0113] like Figure 8 、 Figure 9 and Figure 10The third type is shown in Figure 2. This type of geometric configuration is characterized by the intersection of three circles, including the overlapping area of ​​the two circles, the overlapping area between the three intersection points, and the overlapping area between the four intersection points. In this case, the overlapping area is divided into three cases, such as Figure 6 As shown, Figure 8 is the overlapping area of ​​the two circles, Figure 9 is the overlapping area between the three intersection points, Figure 10 The overlapping area between the four intersection points is the process of determining whether the collaborative search range of the three radars meets this type of geometric configuration. Figure 11 shown.

[0114] Table 1 Radar search resource allocation adjustment strategy

[0115] Strategy Search Cycle Detection distance Additional Resources 1 <![CDATA[T f (>T f0 )]]> <![CDATA[R0]]> <![CDATA[TR(>TR0)]]> 2 <![CDATA[T f0 ]]> <![CDATA[R(<R0)]]> <![CDATA[TR(>TR0)]]> 3 <![CDATA[T f ]]> R <![CDATA[TR(>TR0)]]>

[0116] In this embodiment, for a single radar, the phased array radar adjusts the search parameters R, T f To adapt to the reduction in search resources. Generally, there are several parameter adjustment strategies, as shown in Table 1. Strategy 1 adjusts the phased array radar's search cycle to adapt to the reduction in search resources while maintaining the radar's detection range. Strategy 2 adjusts the radar's detection range while maintaining the radar's initial optimal search cycle. Strategy 3 combines Strategies 1 and 2, simultaneously adjusting the radar's search cycle and detection range to achieve the optimal search cycle and detection range within limited search resources, thereby achieving optimal search performance for the phased array radar.

[0117] Specific embodiment 4: This embodiment is described in detail with reference to the accompanying drawings. Figure 1-26 As shown, step 3 includes:

[0118] Step 3.1: Signal-level collaborative search resource allocation optimization model

[0119] Due to the complexity of the collaborative search constraints, even if the radar parameters and resource allocation results are given, it is still necessary to solve the coverage area according to the actual search range configuration. Let us assume that the radar resources SR in the initial state of the radar are 10 SR 20 SR 30 , the corresponding optimal search period is T f10 、T f20 、T f30 , the normalized detection distance is R 10 、R 20 、R 30 , assuming that the required collaborative search period is T f =T f1 =T f2 =T f3The resources allocated to the three radars are SR1, SR2, and SR3 (SR1+SR2+SR3=c). When the total resources of the radar network are fixed, how to allocate resources among the radars to maximize the collaborative search range is one of the key issues facing collaborative search. The above article takes the signal-level collaborative network search of three radars as an example to analyze the spatiotemporal constraints of the signal-level collaborative search. Let the overlapping search area of ​​the three radars be S0, then the signal-level collaborative search optimization model can be defined as By optimizing SR1, SR2, and SR3, resource allocation is performed to maximize the collaborative search range. At the same time, the following conditions must be met.

[0120]

[0121] Where c is a constant, which represents the total resources available for allocation. The constraint condition indicates that when performing collaborative search resource allocation, the resource allocation of each radar must meet the resource allocation strategy of a single radar and meet the time constraint T of the collaborative search. f1 =T f2 =T f3 The total resources available for allocation are certain; the resources allocated by each radar are not greater than its own normalized total resources;

[0122] Step 3.2: Calculation of signal-level collaborative search area

[0123] Step 3.2.1 Overlapping area when two circles intersect

[0124] To find the area of ​​the overlapping area of ​​the two circles, suppose radar 1 is deployed at point A, and its detection range is a circle with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is a circle with point B as the center and R2 as the radius; the distance between points A and B is d3, and the two circles intersect at points C and D.

[0125] S0=S1+S2-2S3

[0126] Among them, S1 is the area of ​​sector ACD (toward point B), S2 is the area of ​​sector BCD (toward point A), and S3 is the area of ​​triangle ABC.

[0127]

[0128] Step 3.2.2: The overlapping area between the three intersection points

[0129] Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as

[0130] S0=S1-S2+S3-S4+S5-S6+S7

[0131] Among them, S1 is fan-shaped AJ 12 J 13 The area of ​​triangle ΔAJ is S2. 12 J 13 The area of ​​​​S3 is the fan-shaped BJ 12 J 23 The area of ​​triangle ΔBJ is S4. 12 J 23 The area of ​​​​S5 is the fan CJ 23 J 13 The area of ​​triangle ΔCJ is S6. 23 J 13 The area of ​​triangle ΔJ is S7. 12 J 13 J 23 area;

[0132] Step 3.2.3: Overlapping area between the four intersection points

[0133] Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as

[0134] S0=S1-S2+S3-S4+S5-S6+S7-S8+S9

[0135] Among them, S1 is fan-shaped AJ 12 J 21 The area of ​​triangle ΔAJ is S2. 12 J 21 The area of ​​​​S3 is the fan-shaped BJ 32 J 12 The area of ​​triangle ΔBJ is S4. 32 J12 The area of ​​​​S5 is the fan CJ 23 J 32 The area of ​​triangle ΔCJ is S6. 23 J 32 The area of ​​​​S7 is the fan-shaped BJ 21 J 23 The area of ​​triangle ΔBJ is S8. 21 J 23 The area of ​​quadrilateral J is S9. 12 J 21 J 23 J 32 area;

[0136] Step 3.3: Collaborative resource allocation process based on genetic algorithm

[0137] The signal-level collaborative search range optimization model is to maximize S0 on the basis of satisfying the constraints. Generally speaking, the maximum collaborative search range is a nonlinear function of several parameters. Usually, it is impossible to directly find the analytical expression of its extreme value, but it can be solved by optimization algorithms such as genetic algorithms. The genetic algorithm is used to allocate radar resources to maximize the collaborative search range. The algorithm process is as follows: first, an initial population that meets the resource constraints is generated, and then the fitness of each individual in the population is calculated to determine whether the termination condition is met. If so, the operation is terminated and the optimal individual is output as the optimization result; if not, the individuals in the population are subjected to genetic operations of selection, crossover and mutation to ensure that each individual in the newly generated population still meets the resource constraints. The fitness of the evolved offspring population is calculated and the termination condition is re-judged, and this cycle is repeated until the termination condition is met.

[0138] Step 3.3.1. Create an initial population

[0139] Assume that the number of individuals in a population is Np, and each individual is represented by a real-valued parameter vector containing 3 elements, f i,g =[SR i,g,1 ,SR i,g,2 ,SR i,g,3 ],(i=1,2,…N p ), i is the serial number of the individual in the corresponding population, g is the genetic generation, SR i,g,1 +SR i,g,2 +SR i,g,3 =c, where c is a constant representing the total resources available for allocation;

[0140] Step 3.3.2, fitness calculation

[0141] For each individual in a population, calculate the overlapping area according to step 3.2, denoted as S0i ;

[0142] Step 3.3.3. Select an operation

[0143] The selection method of "roulette wheel" is used, using each individual f i,g The proportion of the fitness of an individual determines the possibility of its offspring retention. If the fitness of an individual is S 0i , then the probability of it being selected is expressed as

[0144]

[0145] The greater the individual fitness, the greater the chance of being selected, and vice versa. The specific method is to generate a uniform random number p in [0,1] 01 , if the random number is less than p i , then the individual is selected as the new individual in the next generation population;

[0146] Step 3.3.4: Crossover operation

[0147] Pair the individuals in the population with each other, and for each pair of individuals, the crossover probability P c Exchange an element between them by generating a random number p uniformly distributed in [0,1]. 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <P c , then for the Mth pair of real-valued vectors 13 Elements perform crossover operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3 =c, allocate the remaining resources to the two elements that do not perform the crossover operation according to the original ratio;

[0148] Step 3.3.5, mutation operation

[0149] For each individual in the population after crossover, the mutation probability P m Change an element by generating a random number p uniformly distributed in [0,1] 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <P m , then for the Mth pair of real-valued vectors 13 Elements perform mutation operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3=c, and the remaining resources are allocated to the two elements that have not undergone mutation operations according to the original proportion.

[0150] The simulation results of the present invention are as follows:

[0151] 1. Adjustment of single radar search strategy

[0152] Assume that the initial state resource of a radar is SR0 = 1, the normalized detection distance is R0 = 1, and the search period TF0 = 20s. According to formula 3, the relationship curve between the search distance and the search period under the actual allocated search resources can be obtained, as shown in Figure 5 and Figure 6 As shown in the figure, it can be seen that when the search resources actually allocated to the radar are limited, the search parameters R and T can be appropriately adjusted. f To adapt to the reduction of search resources. If the search range is required to remain unchanged, the search period must be increased. Conversely, if the search period is required to remain unchanged, the search range will inevitably be reduced.

[0153] 2. Resource Allocation Analysis of Three Radars with Identical Performance

[0154] First, we discuss the signal-level networked collaborative search of three radars with the same performance. Assume that the initial state of the radar is radar resource SR 10 =SR 20 =SR 30 = 1, the total resources are 3, the search mission that can be completed by a single radar requires resources TR = TR 10 =TR 20 =TR 30 =1.5, then the radar resources available for signal-level networking and collaborative search SR = SR 10 +SR 20 +SR 30 -TR is 1.5. The corresponding optimal search period is T f10 =T f20 =T f30 = 20s, the normalized detection distance is R 10 =R 20 =R 30 =1, assuming that the three radars are spaced evenly apart during network search, let the position coordinates of radar 1, radar 2, and radar 3 be (0,0), (1,0), Still let the collaborative search period T f1 =T f2 =T f3 = 20s. According to the optimization model, the contour map of the collaborative search area on the collaborative search resource plane actually allocated to Radar 1 and Radar 2 is as follows: Figure 5 and Figure 6As shown in the figure above, the maximum resource that can be allocated to a single radar is 1, and the maximum total resource allocated to two radars is 1.5. Given the resource allocation for radar 1, the relationship between the collaborative search area and the resource allocation for radar 2 is shown in the figure, which is a vertical section of the figure above. It can be seen that when the resource allocation ratio among the three radars is 1:1:1, that is, when each radar is allocated 0.5 resources, the collaborative search area reaches its maximum. Using the genetic algorithm solution of the optimization model in Section 4.3, the resulting allocations are 0.4998, 0.4998, and 0.5004.

[0155] 3. Resource Allocation Analysis of Three Radars with Different Performance

[0156] When two radars with different performances conduct signal-level networked collaborative search, the different performances can be characterized by the optimal search period and normalized detection range.

[0157] Case 1: The optimal search period is the same, but the detection distance is different. Let the initial state radar resource SR of the radar be 10 =SR 20 =SR 30 = 1, the total resources are 3, the search mission that can be completed by a single radar requires resources TR = TR 10 =TR 20 =TR 30 =1.5, then the radar resources available for signal-level networking and collaborative search SR = SR 10 +SR 20 +SR 30 -TR is 1.5. The corresponding optimal search period is T f10 =T f20 =T f30 = 20s, the normalized detection distance is R 10 =R 20 =1, R 30 =2, assuming that the three radars are spaced at equal distances during network search, let the position coordinates of radar 1, radar 2, and radar 3 be (0,0), (1,0), Still let the collaborative search period T f1 =T f2 =T f3 = 20s. According to the optimization model, the contour map of the collaborative search area on the collaborative search resource plane actually allocated to radar 1 and radar 2 is as follows: Figure 4As shown in the figure above, the maximum resource allocation for a single radar is 1, and the maximum total resource allocation for both radars is 1.5. Given the resource allocation for radar 1, the relationship between the collaborative search area and the resource allocation for radar 2 is shown in the figure, which is a vertical section of the figure above. It can be seen that when the collaborative search area reaches its maximum, the resource allocation ratio among the three radars is no longer 1:1:1. Using the genetic algorithm solution of the optimization model in Section 4.3, the optimal allocation results are 0.6165, 0.6194, and 0.2641.

[0158] If other parameters remain unchanged, only the normalized detection distance becomes R 10 =1, R 20 =2, R 30 = 1 is shown in the figure. At this time, according to the genetic algorithm solution of the optimization model in Section 4.3, the optimal allocation results are 0.6189, 0.2636, and 0.6175. The normalized detection distance becomes R 10 =2, R 20 =1, R 30 = 1 is shown in the figure. At this time, the optimal allocation results obtained by solving the genetic algorithm of the optimization model are 0.2631, 0.6169, and 0.6200. It can be seen that in order to maximize the collaborative search area, the better the performance of the radar, the less collaborative search resources are required, and vice versa, the poorer the performance of the radar, the more collaborative search resources are required. In addition, from Figure 20 、 Figure 21 and Figure 22 It can be seen from the optimal allocation results that under the condition of equal-spaced stations, in order to maximize the collaborative search area, the resource allocation ratio of radars with the same performance is always 1:1.

[0159] Case 2: The detection distance is the same, but the optimal search period is different. Let the corresponding optimal search period be T f10 =10s, T f20 =T f30 = 20s, the normalized detection distance is R 10 =R 20 =R 30 = 1. Due to the synchronization relationship between the signal-level cooperative transmission timing, the cooperative search cycles of the two radars must meet the equal constraint, that is, T f1 =T f2 =T f3 Generally, the search period of the radar with a short search cycle can be lengthened to match that of the radar with a longer search cycle to meet the constraints. Adjusting the model based on the search strategy of a single radar and lengthening the search period can increase the search distance. It can be seen that Radar 1 performs better than Radars 2 and 3. Therefore, under the assumptions of Case 2, the solution is essentially the same as that of Case 1, and the process and results will not be repeated.

Claims

1. A signal-level collaborative multi-radar network search resource allocation method, characterized in that: The following steps are involved: Step 1: Signal-level collaborative radar networking; Step 2: Signal-level collaborative search and its spatiotemporal constraints; Step 3: Optimize the signal-level collaborative search range; In step 1, the signal-level cooperative radar network controls the timing of the radar cooperative transmission signals according to the path difference formed between the networked radars in the search airspace, so that the time when the transmission signals of different radars arrive at the detection airspace is basically consistent; In step 2, the main constraints for signal-level collaborative search resource allocation include: constraints between a single radar's search resources and search cycles, and constraints on the timing synchronization of search cycles between radars: Step 2.1: The relationship between the search resource and search period of a single radar can be derived from the radar equation. According to the search radar equation (1), Among them, R is the radar detection distance, P av is the average transmit power of the radar, G t is the transmitting antenna gain, G r is the receiving antenna gain, λ is the radar wavelength, σ is the target RCS, k is the Boltzmann constant, T0 is the receiver noise bandwidth at room temperature, F n is the receiver noise coefficient, L is the radar loss, SNR is the detection signal-to-noise ratio, T f is the search cycle; assuming that its total resources are constant, let SR0 be the total radar resources, It can be seen that the fourth power of the radar detection range is proportional to the search period, and the search period is inversely proportional to the resources occupied by the search; SR=1-TR ,TR>TR0 (4) SR0=1-TR0(5) Where SR0≤1 is the percentage of resources allocated to the radar search task in the initial state, and the corresponding optimal search period is T f0 , the detection range is R0, the resource ratio allocated to other high-priority tasks is TR0; SR is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f , the detection distance is R, and the ratio of resources allocated to other high-priority tasks is TR. As the high-priority tasks occupy more radar resources, TR>TR0, which will inevitably lead to a reduction in radar search resources SR; For signal-level cooperative radar networking, each radar must satisfy the following formula: Among them SR 10 ≤1 is the percentage of resources allocated to the radar 1 search task in the initial state, and the corresponding optimal search period is T f10 , the detection distance is R 10 SR1 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f1 , the detection distance is R1; SR 20 ≤1 is the percentage of resources allocated to the radar 2 search task in the initial state, and the corresponding optimal search period is T f20 , the detection distance is R 20 SR2 is the percentage of resources actually allocated to the radar search task, and the corresponding search period is T f2 , the detection distance is R2; due to the certain synchronization relationship between the signal-level cooperative emission timing, the cooperative search cycles of the two radars must meet the equal constraint, that is, T f1 =T f2 (8); Step 2.2: Spatial constraints and geometric configuration determination To achieve signal-level collaborative search, the three radars must simultaneously locate their collaborative search areas within their detection ranges. This is the spatial constraint for signal-level collaborative search. To determine whether the three radars meet the spatial constraint, we can convert this into determining whether their respective detection ranges overlap. Assume that the radar detection range is a circle with the radar site coordinates as the center and the detection distance as the radius. The detection range of each radar can be adaptively adjusted as needed. Therefore, there are many possible geometric configurations for the collaborative search ranges of the three radars. In general, the geometric configurations of the three radars with a common overlapping area can be divided into the following three categories: The first type: This type of geometric configuration is characterized by the circle with the smallest radius being contained by the other two circles at the same time. In this case, the area of ​​the overlapping region of the three circles is equal to the area of ​​the circle with the smallest radius. The second type of geometric configuration is characterized by the existence of a set of circles that are contained, and the circle with the second smallest radius intersects the third circle at two points, and the area of ​​the overlapping area of ​​the three circles is equal to the overlapping area of ​​two of the circles; The third type of geometric configuration is characterized by the intersection of three circles, including the overlapping area of ​​the two circles, the overlapping area between the three intersection points, and the overlapping area between the four intersection points; The step 3 includes: Step 3.1: Signal-level collaborative search resource allocation optimization model Due to the complexity of the collaborative search constraints, even if the radar parameters and resource allocation results are given, it is still necessary to solve the coverage area according to the actual search range configuration. Let us assume that the radar resources SR in the initial state of the radar are 10 SR 20 SR 30 , the corresponding optimal search period is T f10 、T f20 、T f30 , the normalized detection distance is R 10 、R 20 、R 30 , assuming that the required collaborative search period is T f =T f1 =T f2 =T f3 The resources allocated to the three radars are SR1, SR2, and SR3 respectively, and SR1+SR2+SR3=c. When the total resources of the radar network are fixed, let the overlapping search area of ​​the three radars be S0, then the signal-level collaborative search optimization model is defined as By optimizing SR1, SR2, and SR3, resource allocation is performed to maximize the collaborative search range. At the same time, the following conditions must be met. Where c is a constant, which represents the total resources available for allocation. The constraint condition indicates that when performing collaborative search resource allocation, the resource allocation of each radar must meet the resource allocation strategy of a single radar and meet the time constraint T of the collaborative search. f1 =T f2 =T f3 The total resources available for allocation are certain; the resources allocated by each radar are not greater than its own normalized total resources; Step 3.2: Calculation of signal-level collaborative search area Step 3.2.1 Overlapping area when two circles intersect To find the area of ​​the overlapping area of ​​the two circles, suppose radar 1 is deployed at point A, and its detection range is a circle with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is a circle with point B as the center and R2 as the radius; the distance between points A and B is d3, and the two circles intersect at points C and D. S0=S1+S2-2S3 Among them, S1 is the area of ​​sector ACD in the direction of point B, S2 is the area of ​​sector BCD in the direction of point A, and S3 is the area of ​​triangle ABC. Step 3.2.2: The overlapping area between the three intersection points Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as S0 = S1-S2+S3-S4+S5-S6+S7 Among them, S1 is fan-shaped AJ 12 J 13 The area of ​​triangle ΔAJ is S2. 12 J 13 The area of ​​​​S3 is the fan-shaped BJ 12 J 23 The area of ​​triangle ΔBJ is S4. 12 J 23 The area of ​​​​S5 is the fan CJ 23 J 13 The area of ​​triangle ΔCJ is S6. 23 J 13 The area of ​​triangle ΔJ is S7. 12 J 13 J 23 area; Step 3.2.3: Overlapping area between the four intersection points Assume that radar 1 is deployed at point A, and its detection range is circle 1 with point A as the center and R1 as the radius; radar 2 is deployed at point B, and its detection range is circle 2 with point B as the center and R2 as the radius; radar 3 is deployed at point C, and its detection range is circle 3 with point C as the center and R3 as the radius. Circles 1 and 2 intersect at points J12 and J21, circles 2 and 3 intersect at points J23 and J32, and circles 3 and 1 intersect at points J13 and J31. From geometric knowledge, we know that the area S0 of their overlapping area can be expressed as S0 = S1-S2+S3-S4+S5-S6+S7-S8+S9 Among them, S1 is fan-shaped AJ 12 J 21 The area of ​​triangle ΔAJ is S2. 12 J 21 The area of ​​​​S3 is the fan-shaped BJ 32 J 12 The area of ​​triangle ΔBJ is S4. 32 J 12 The area of ​​​​S5 is the fan CJ 23 J 32 The area of ​​triangle ΔCJ is S6. 23 J 32 The area of ​​​​S7 is the fan-shaped BJ 21 J 23 The area of ​​triangle ΔBJ is S8. 21 J 23 The area of ​​quadrilateral J is S9. 12 J 21 J 23 J 32 area; Step 3.3: Collaborative resource allocation process based on genetic algorithm The signal-level collaborative search range optimization model is to maximize S0 while satisfying the constraints. The algorithm process is as follows: first, an initial population that satisfies the resource constraints is generated, and then the fitness of each individual in this population is calculated to determine whether the termination condition is met. If so, the operation is terminated and the optimal individual is output as the optimization result. If not, the individuals in the population are subjected to genetic operations such as selection, crossover, and mutation to ensure that each individual in the newly generated population still meets the resource constraints. The fitness of the evolved offspring population is calculated and the termination condition is re-judged. This cycle is repeated until the termination condition is met. Step 3.3.

1. Create an initial population Assume that the number of individuals in a population is Np, and each individual is represented by a real-valued parameter vector containing 3 elements, f i,g =[SR i,g,1 ,SR i,g,2 ,SR i,g,3 ],(i=1,2,…N p ), i is the serial number of the individual in the corresponding population, g is the genetic generation, SR i,g,1 +SR i,g,2 +SR i,g,3 =c, where c is a constant representing the total resources available for allocation; Step 3.3.2, fitness calculation For each individual in a population, calculate the overlapping area according to step 3.2, denoted as S 0i ; Step 3.3.

3. Select an operation The selection method of "roulette wheel" is used, using each individual f i,g The proportion of the fitness of an individual determines the possibility of its offspring retention. If the fitness of an individual is S 0i , then the probability of it being selected is expressed as The greater the individual fitness, the greater the chance of being selected, and vice versa. The specific method is to generate a uniform random number p in [0,1] 01 , if the random number is less than p i , then the individual is selected as the new individual in the next generation population; Step 3.3.4: Crossover operation Pair the individuals in the population with each other, and for each pair of individuals, the crossover probability P c Exchange an element between them by generating a random number p uniformly distributed in [0,1]. 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <P c , then for the Mth pair of real-valued vectors 13 Elements perform crossover operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3 =c, allocate the remaining resources to the two elements that do not perform the crossover operation according to the original ratio; Step 3.3.5, mutation operation For each individual in the population after crossover, the mutation probability P m Change an element by generating a random number p uniformly distributed in [0,1] 01 and a pseudo-random integer M uniformly distributed in [1,3] 13 , if the random number is less than p 01 <P m , then for the Mth pair of real-valued vectors 13 Elements perform mutation operations, and at the same time, to meet the resource constraint SR i,g,1 +SR i,g,2 +SR i,g,3 =c, and the remaining resources are allocated to the two elements that have not undergone mutation operations according to the original proportion.

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