An optimized deployment method, system, and storage medium based on meter-wave multi-base radar.

Abstract

This invention discloses an optimized deployment method, system, and storage medium based on meter-wave multi-base radar, comprising: S1, constructing a target localization model for meter-wave multi-base radar; S2, obtaining the Fisher information matrix for target position estimation by meter-wave multi-base radar, and using the Cramer-Rao lower bound to measure the localization performance of meter-wave multi-base radar for target position based on the Fisher information matrix; S3, obtaining the potential of the set of feasible deployment positions in the feasible deployment area based on the minimum three-dimensional interval of the transmitting and receiving stations and the size of the feasible deployment area; S4, dynamically playing a game with the transmitting and receiving stations of the meter-wave multi-base radar as participants, each participant choosing the strategy that maximizes its contribution to the effective monitoring area volume, and obtaining the Pareto optimal deployment of the meter-wave multi-base radar. This invention can effectively improve the localization accuracy of radar targets, thereby making more efficient use of limited radar resources and improving the resource utilization efficiency of the entire radar system.

Description

Technical Field

[0001] This invention relates to the field of radar deployment technology, and more specifically to an optimized deployment method, system, and storage medium based on meter-wave multi-base radar. Background Technology

[0002] Meter-wave multi-station radar is an important type of hybrid network system for meter-wave radar. It utilizes multiple spatially distributed transceiver stations to detect targets, offering numerous advantages over monostatic radar.

[0003] Compared to monostatic meter-wave radar arrays, meter-wave multistatic radars possess the ability to achieve effective detection coverage over a target airspace by altering the positions of transceiver stations. Assuming cooperative signal reception—meaning each receiving station can receive and process all transmitted signals—meter-wave multistatic radars achieve a significant power advantage. Monostatic radars typically have much lower lateral range accuracy than radial range accuracy in target localization, while meter-wave multistatic radars, through information fusion processing with separate transceiver stations, can achieve higher accuracy in target localization. Furthermore, when the receiving station of a meter-wave multistatic radar receives spatially correlated signals, it achieves higher spatial resolution than meter-wave monostatic radars.

[0004] Radars can typically effectively cancel interference entering from the sidelobes of the receiver, but interference entering from the main lobe is difficult to eliminate. The separate transmit and receive system architecture of meter-wave multi-base radar makes it difficult for interference to be directed at high power into the main lobe of each receiving station's antenna. To achieve interference on the main lobe of each receiving station's antenna, the interference power density cannot be very high. Spatially coherent meter-wave multi-base radar can effectively cancel noise-like interference on the main lobe of the receiving antenna without suppressing the target echo.

[0005] Stealth aircraft primarily achieve stealth by altering the scattering direction of electromagnetic waves, reducing the target's radar cross-section (RCS) within a 45-degree range to the left and right of the nose cone. However, the reduction in RCS is limited or nonexistent in other angular ranges. Since meter-wave multi-static radar transmits and receives signals in multiple directions, the target's bistatic RCS varies significantly between different transceiver stations, making it difficult for stealth aircraft to reduce the bistatic RCS of all transceiver stations. Furthermore, meter-wave multi-static radar operates in the meter-wave band, and the stealth materials used in existing stealth aircraft have limited absorption capabilities for meter-wave electromagnetic waves, making it difficult to guarantee effective low-observable characteristics. Therefore, meter-wave multi-static radar possesses extremely strong anti-stealth capabilities.

[0006] Because the transceiver stations of meter-wave multi-base radar are spatially distributed, even if one or more stations of a meter-wave multi-base radar with redundant stations are destroyed, the positioning information is not completely lost; only the positioning performance will be reduced. Similarly, if one station fails, the information from other stations can still ensure the radar's target positioning function. In addition, the receiving stations of the meter-wave multi-base radar system with separate transceiver stations do not radiate signals outward, and the antenna size required for anti-radiation missiles to effectively measure the angle of a transmitting station operating in the meter-wave band is difficult to accommodate by the diameter of existing anti-radiation missiles. In other words, meter-wave multi-base radar has extremely strong battlefield survivability.

[0007] In summary, meter-wave multi-base radar has significant advantages in power, positioning accuracy, spatial resolution, anti-jamming capability, anti-stealth capability, battlefield survivability, and reliability. The rational deployment of transceiver stations is crucial to maximizing the advantages of meter-wave multi-base radar; therefore, optimizing the deployment of meter-wave multi-base radar transceiver stations is an important research topic in this field. Summary of the Invention

[0008] The purpose of this invention is to provide an optimized deployment method, system, and storage medium based on meter-wave multi-base radar. A meter-wave multi-base radar deployment model is established, and the optimized deployment problem of meter-wave multi-base radar is analyzed. The Pareto optimal deployment scheme of meter-wave multi-base radar can be obtained quickly, giving full play to the advantages of meter-wave multi-base radar and achieving high-precision target detection in specific airspace.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] An optimized deployment method based on meter-wave multi-base radar includes the following steps:

[0011] S1. Based on the bistatic distances between the receiving station, transmitting station and target position of the meter-wave multi-base radar, the azimuth angle of the receiving station relative to the target position, and the elevation angle of the receiving station relative to the target position, construct the target localization model of the meter-wave multi-base radar.

[0012] S2. Based on the target localization model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix for target position estimation by the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the localization performance of the meter-wave multi-base radar for target position.

[0013] S3. Determine the feasible deployment area of ​​the transmitter and receiver of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver and the size of the feasible deployment area, obtain the potential of the set of feasible deployment locations in the feasible deployment area.

[0014] S4. The transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, and their feasible space is the feasible deployment location. Each participant chooses the strategy that contributes the most to the volume of the effective monitoring area. Through the method of finitely repeated dynamic game, the Pareto optimal deployment of the meter-wave multi-base radar is obtained.

[0015] Furthermore, in step S1, a target localization model for the meter-wave multi-base radar is constructed based on the bistatic distances between the receiving station, the transmitting station, and the target location, the azimuth angle of the receiving station relative to the target location, and the elevation angle of the receiving station relative to the target location. Specifically:

[0016] Suppose that a meter-wave multi-base radar uses range, azimuth, and elevation information to locate the target position. The estimated target position is defined as follows:

[0017] Θ = [x, y, z]

[0018] Let the Kth wave of the meter-wave multi-base radar be... t The launch station locations are k t =1,2,L,K t , Kth r The location of each receiving station is k r =1,2,L,K r ;

[0019] set up For receiving station k r Launch station k t Bibase distance from the target location, For receiving station k r Azimuth estimation of the target location. For receiving station k r Based on the elevation angle estimation of the target, the mathematical model for target localization using meter-wave multi-base radar is as follows:

[0020]

[0021]

[0022] Further, in step S2, based on the target localization model of the meter-wave multi-base radar and the operating parameters of the meter-wave multi-base radar, the Fisher information matrix for the target position estimation by the meter-wave multi-base radar is obtained, specifically as follows:

[0023] set up For radar transmission power, For antenna transmit gain, For antenna receiving gain, Let T be the target's radar cross-section, λ be the wavelength of the transmitted signal, and T be the target's radar cross-section. intT is the radar synthesis time, K is the Boltzmann constant, and T is the radar synthesis time. s For temperature, N F The equivalent noise figure;

[0024] Let the kth t The distance between each launch station and the target is:

[0025]

[0026] Let the kth r The distance between each receiving station and the target is

[0027]

[0028] The signal-to-noise ratio of the received signal It can be represented as:

[0029]

[0030] Let the standard root mean square error of the azimuth angle estimation be... The standard root mean square error of pitch angle estimation is The standard root mean square error of the distance estimation is

[0031] Let the standard root mean square error of the azimuth angle estimation be... The standard root mean square error of pitch angle estimation is The standard root mean square error of the distance estimation is

[0032] Let ρ(*) be the probability density distribution function; Θ j and Θ h Let be the j-th and h-th terms of the target location estimate; m and n are the indices of different transceiver station combinations, m = 1, 2, ..., K. r K t n = 1, 2, ..., K r K t ; This is used to indicate whether meter-wave multi-base radar positioning utilizes azimuth information. This indicates that azimuth information was used. This indicates that azimuth information was not used; μ θ μ is used to indicate whether meter-wave multi-base radar positioning utilizes elevation angle information. θ =1 indicates that pitch angle information was used, μ θ =0 indicates that pitch angle information was not used; μ R μ is used to indicate whether meter-wave multi-base radar positioning utilizes range information. R =1 indicates that distance information was used, μ R=0 indicates that range information was not used; therefore, the element in the j-th row and h-th column of the Fisher information matrix for target position estimation by meter-wave multi-base radar can be represented as:

[0033]

[0034] Furthermore, in step S2, the Cramer-Rao lower bound is used to measure the target localization performance of the meter-wave multi-base radar, specifically as follows:

[0035]

[0036] Further, in step S3, the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar are determined. Based on the minimum three-dimensional interval of the transmitter and receiver stations and the size of the feasible deployment area, the potential of the set of feasible deployment locations within the feasible deployment area is obtained, specifically:

[0037] Let the length, width, and height of the feasible deployment area be Le, We, and He, respectively;

[0038] set up If we denote rounding down, then the cardinality Nu of the set of feasible deployment locations in the feasible deployment zone can be expressed as:

[0039]

[0040] Furthermore, in step S4, the transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, with their feasible space representing feasible deployment locations. Each participant selects the strategy that maximizes its contribution to the effective monitoring area volume. Through a finitely repeated dynamic game method, the Pareto optimal deployment of the meter-wave multi-base radar is obtained, specifically as follows:

[0041] If we consider the transmitting and receiving stations of the meter-wave multi-base radar as the participants in the game, then the feasible space is the feasible deployment location of the transmitting and receiving stations.

[0042] Let the positions chosen by all participants in phase q be...

[0043]

[0044] Let the positions chosen by the participants other than the k-th participant in the q-th stage be...

[0045]

[0046] Let s = (x, y, z) be the discrete point location in the effective monitoring area, σ[s, P(q)] represent the positioning performance at point s when using P(q), V[P(q)] represent the volume of the effective monitoring area when using P(q), σ[s, K(q)] represent the positioning performance at point s when using K(q), and V[K(q)] represent the volume of the effective monitoring area when using P(q).

[0047] V[P(q)]=χ{s|σ[s,P(q)]≤σ a ,s∈S a}×v

[0048] V[K(q)]=χ{s|σ[s,K(q)]≤σ a ,s∈S a}×v

[0049] Let V be the contribution of the k-th participant to the effective monitoring area volume in stage q. k (q) is

[0050] V k (q)=V[P(q)]-V[K(q)]

[0051] Each participant chooses the strategy that maximizes their contribution to the effective monitoring area volume, i.e., Max V k (q);

[0052] In a dynamic game, when the k-th player considers its strategy, the strategies of the other players remain unchanged. At this time, V[K(q)] remains unchanged, making V k (q) is equivalent to maximizing V[P(q)], and maximizing V[P(q)] is precisely the optimization objective of the optimal deployment of meter-wave multi-base radar; the reward of the k-th participant is set as the volume of the effective monitoring area corresponding to all participants, i.e., u k (q) = V[P(q)].

[0053] This invention also provides a system for optimized deployment based on meter-wave multi-base radar, comprising:

[0054] Target localization model construction module: Based on the bistatic distance between the receiving station, transmitting station and the target position of the meter-wave multi-base radar, the azimuth angle of the receiving station to the target position, and the elevation angle of the receiving station to the target position, a target localization model of the meter-wave multi-base radar is constructed.

[0055] Positioning performance measurement module: Based on the target positioning model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix of the target position estimation of the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the positioning performance of the meter-wave multi-base radar for the target position.

[0056] Deployment module: Determines the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver stations and the size of the feasible deployment area, it obtains the potential of the set of feasible deployment locations in the feasible deployment area.

[0057] Dynamic game module: The transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, and their feasible space is the feasible deployment location. Each participant chooses the strategy that contributes the most to the volume of the effective monitoring area. Through a finitely repeated dynamic game method, the Pareto optimal deployment of the meter-wave multi-base radar is obtained.

[0058] The present invention also provides a computer-readable storage medium storing computer program instructions that, when executed on a processor, perform an optimized deployment method for a meter-wave multi-base radar.

[0059] According to specific embodiments provided by the present invention, the following technical effects are disclosed: By establishing an accurate mathematical model and using the Cramer-Rao lower bound to measure positioning performance, the positioning accuracy of radar targets can be effectively improved; by treating the deployment of transmitting and receiving stations as a game process, the optimal deployment position can be found for each participant, thereby maximizing coverage of the effective monitoring area and improving the positioning performance of meter-wave multi-base radar; by rationally configuring the positions of transmitting and receiving stations of meter-wave multi-base radar within the feasible deployment area, the monitoring capability of specific areas can be effectively enhanced; by calculating the contribution of each transmitting and receiving station to the volume of the effective monitoring area, limited radar resources can be utilized more efficiently, thereby improving the resource utilization efficiency of the entire radar system; through accurate mathematical model prediction and game strategy selection, the overall cost can be reduced while meeting monitoring requirements. Attached Figure Description

[0060] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0061] The following description, in conjunction with the accompanying drawings, further illustrates the optimized deployment method, system, and storage medium of the present invention based on meter-wave multi-base radar.

[0062] Figure 1 This is the overall flowchart of the optimized deployment method based on meter-wave multi-base radar provided by the present invention;

[0063] Figure 2This is a flowchart of obtaining the Pareto optimal deployment of meter-wave multi-base radar in the optimized deployment method based on meter-wave multi-base radar provided by the present invention;

[0064] Figure 3 This is a volume diagram of the effective monitoring area in the meter-wave multi-base radar based on distance information positioning, provided by the present invention in the optimized deployment method based on meter-wave multi-base radar;

[0065] Figure 4 This invention provides an optimized deployment method based on meter-wave multi-base radar, which is a volume diagram of the effective monitoring area for high-altitude targets in a meter-wave multi-base radar based on angle information positioning.

[0066] Figure 5 This is a volume diagram of the effective monitoring area for low-altitude targets in the meter-wave multi-base radar based on angle information positioning in the optimized deployment method based on meter-wave multi-base radar provided by the present invention.

[0067] Figure 6 This invention provides an optimized deployment method for meter-wave multi-base radar, which uses joint range and angle information for positioning the effective monitoring area of ​​high-altitude targets in a meter-wave multi-base radar.

[0068] Figure 7 This invention provides an optimized deployment method for meter-wave multi-base radar, which uses joint range and angle information for localization, to effectively monitor low-altitude targets. The volume of the effective monitoring area for low-altitude targets in the meter-wave multi-base radar is shown in the effective deployment method for meter-wave multi-base radar.

[0069] Figure 8 This invention provides an effective monitoring area volume map based on distance information positioning in the optimized deployment method based on meter-wave multi-base radar.

[0070] Figure 9 This invention provides an effective monitoring area volume diagram for high-altitude target positioning based on angle information in Pareto optimal deployment and global optimal deployment.

[0071] Figure 10 This is an effective monitoring area volume diagram for low-altitude target positioning based on angle information in Pareto optimal deployment and global optimal deployment provided by the present invention;

[0072] Figure 11 This invention provides an effective monitoring area volume diagram for high-altitude target positioning based on joint distance and angle information in Pareto optimal deployment and global optimal deployment.

[0073] Figure 12 This invention provides an effective monitoring area volume diagram for low-altitude target localization based on joint distance and angle information in Pareto optimal deployment and global optimal deployment.

[0074] Figure 13This invention provides an effective monitoring area volume diagram based on distance information positioning in Pareto optimal deployment and global optimal deployment.

[0075] Figure 14 This invention provides an effective monitoring area volume diagram for high-altitude target positioning based on angle information, which is part of the impact of feasible deployment intervals on deployment performance.

[0076] Figure 15 This invention provides an effective monitoring area volume diagram for low-altitude target positioning based on angle information, which is part of the impact of feasible deployment intervals on deployment performance.

[0077] Figure 16 This invention provides an effective monitoring area volume diagram for high-altitude target positioning based on joint distance and angle information, which is part of the impact of feasible deployment intervals on deployment performance.

[0078] Figure 17 This invention provides an effective monitoring area volume diagram for low-altitude target positioning based on joint distance and angle information, which is part of the impact of feasible deployment intervals on deployment performance. Detailed Implementation

[0079] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0080] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0081] This invention provides an optimized deployment method based on meter-wave multi-base radar, comprising the following steps:

[0082] S1. Based on the bistatic distances between the receiving station, transmitting station and target position of the meter-wave multi-base radar, the azimuth angle of the receiving station relative to the target position, and the elevation angle of the receiving station relative to the target position, construct the target localization model of the meter-wave multi-base radar.

[0083] S2. Based on the target localization model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix for target position estimation by the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the localization performance of the meter-wave multi-base radar for target position.

[0084] S3. Determine the feasible deployment area of ​​the transmitter and receiver of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver and the size of the feasible deployment area, obtain the potential of the set of feasible deployment locations in the feasible deployment area.

[0085] S4. The transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, and their feasible space is the feasible deployment location. Each participant chooses the strategy that contributes the most to the volume of the effective monitoring area. Through the method of finitely repeated dynamic game, the Pareto optimal deployment of the meter-wave multi-base radar is obtained.

[0086] In step S1, a target localization model for the meter-wave multi-base radar is constructed based on the bistatic distances between the receiving station, transmitting station, and target position of the meter-wave multi-base radar, the azimuth angle of the receiving station relative to the target position, and the elevation angle of the receiving station relative to the target position. Specifically:

[0087] Suppose that a meter-wave multi-base radar uses range, azimuth, and elevation information to locate the target position. The estimated target position is defined as follows:

[0088] Θ = [x, y, z]

[0089] Let the Kth wave of the meter-wave multi-base radar be... t The launch station locations are k t =1,2,L,K t , Kth r The location of each receiving station is k r =1,2,L,K r ;

[0090] set up For receiving station k r Launch station k t Bibase distance from the target location, For receiving station k r Azimuth estimation of the target location. For receiving station k r Based on the elevation angle estimation of the target, the mathematical model for target localization using meter-wave multi-base radar is as follows:

[0091]

[0092] In step S2, based on the target localization model of the meter-wave multi-base radar and the operating parameters of the meter-wave multi-base radar, the Fisher information matrix for target position estimation by the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, specifically:

[0093] set up For radar transmission power, For antenna transmit gain, For antenna receiving gain, Let T be the target's radar cross-section, λ be the wavelength of the transmitted signal, and T be the target's radar cross-section. int T is the radar synthesis time, K is the Boltzmann constant, and T is the radar synthesis time. sFor temperature, N F The equivalent noise figure;

[0094] Let the kth t The distance between each launch station and the target is:

[0095]

[0096] Let the kth r The distance between each receiving station and the target is

[0097]

[0098] The signal-to-noise ratio of the received signal It can be represented as:

[0099]

[0100] Let the standard root mean square error of the azimuth angle estimation be... The standard root mean square error of pitch angle estimation is The standard root mean square error of the distance estimation is

[0101] Let the standard root mean square error of the azimuth angle estimation be... The standard root mean square error of pitch angle estimation is The standard root mean square error of the distance estimation is

[0102] Let ρ(*) be the probability density distribution function; Θ j and Θ h Let be the j-th and h-th terms of the target location estimate; m and n are the indices of different transceiver station combinations, m = 1, 2, ..., K. r K t n = 1, 2, ..., K r K t ; This is used to indicate whether meter-wave multi-base radar positioning utilizes azimuth information. This indicates that azimuth information was used. This indicates that azimuth information was not used; μ θ μ is used to indicate whether meter-wave multi-base radar positioning utilizes elevation angle information. θ =1 indicates that pitch angle information was used, μ θ =0 indicates that pitch angle information was not used; μ R μ is used to indicate whether meter-wave multi-base radar positioning utilizes range information. R =1 indicates that distance information was used, μ R =0 indicates that range information was not used; therefore, the element in the j-th row and h-th column of the Fisher information matrix for target position estimation by meter-wave multi-base radar can be represented as:

[0103]

[0104] In step S2, the Cramer-Rao lower bound is used to measure the target localization performance of the meter-wave multi-base radar, specifically as follows:

[0105]

[0106] In step S3, the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar are determined. Based on the minimum three-dimensional interval of the transmitter and receiver stations and the size of the feasible deployment areas, the potential of the set of feasible deployment locations within the feasible deployment areas is obtained, specifically:

[0107] Let the length, width, and height of the feasible deployment area be Le, We, and He, respectively;

[0108] set up If we denote rounding down, then the cardinality Nu of the set of feasible deployment locations in the feasible deployment zone can be expressed as:

[0109]

[0110] In step S4, the transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, with their feasible space representing feasible deployment locations. Each participant selects the strategy that maximizes its contribution to the effective monitoring area volume. Through a finitely repeated dynamic game method, the Pareto optimal deployment of the meter-wave multi-base radar is obtained, specifically as follows:

[0111] If we consider the transmitting and receiving stations of the meter-wave multi-base radar as the participants in the game, then the feasible space is the feasible deployment location of the transmitting and receiving stations.

[0112] Let the positions chosen by all participants in phase q be...

[0113]

[0114] Let the positions chosen by the participants other than the k-th participant in the q-th stage be...

[0115]

[0116] Let s = (x, y, z) be the discrete point location in the effective monitoring area, σ[s, P(q)] represent the positioning performance at point s when using P(q), V[P(q)] represent the volume of the effective monitoring area when using P(q), σ[s, K(q)] represent the positioning performance at point s when using K(q), and V[K(q)] represent the volume of the effective monitoring area when using P(q).

[0117] V[P(q)]=χ{s|σ[s,P(q)]≤σ a ,s∈S a}×v

[0118] V[K(q)]=χ{s|σ[s,K(q)]≤σ a ,s∈S a}×v

[0119] Let V be the contribution of the k-th participant to the effective monitoring area volume in stage q. k (q) is

[0120] V k (q)=V[P(q)]-V[K(q)]

[0121] Each participant chooses the strategy that maximizes their contribution to the effective monitoring area volume, i.e., Max V k (q);

[0122] In a dynamic game, when the k-th player considers its strategy, the strategies of the other players remain unchanged. At this time, V[K(q)] remains unchanged, making V k (q) is equivalent to maximizing V[P(q)], and maximizing V[P(q)] is precisely the optimization objective of the optimal deployment of meter-wave multi-base radar; the reward of the k-th participant is set as the volume of the effective monitoring area corresponding to all participants, i.e., u k (q) = V[P(q)].

[0123] This invention provides a system for optimized deployment based on meter-wave multi-base radar, comprising:

[0124] Target localization model construction module: Based on the bistatic distance between the receiving station, transmitting station and the target position of the meter-wave multi-base radar, the azimuth angle of the receiving station to the target position, and the elevation angle of the receiving station to the target position, a target localization model of the meter-wave multi-base radar is constructed.

[0125] Positioning performance measurement module: Based on the target positioning model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix of the target position estimation of the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the positioning performance of the meter-wave multi-base radar for the target position.

[0126] Deployment module: Determines the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver stations and the size of the feasible deployment area, it obtains the potential of the set of feasible deployment locations in the feasible deployment area.

[0127] Dynamic game module: The transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, and their feasible space is the feasible deployment location. Each participant chooses the strategy that contributes the most to the volume of the effective monitoring area. Through a finitely repeated dynamic game method, the Pareto optimal deployment of the meter-wave multi-base radar is obtained.

[0128] The present invention also provides a computer-readable storage medium storing computer program instructions that, when executed on a processor, perform an optimized deployment method for a meter-wave multi-base radar.

[0129] This application further provides a simulation analysis process for optimal Pareto deployment of meter-wave multi-base radar within a feasible deployment area.

[0130] As shown in Tables 1-3, three sets of position coordinates were randomly selected as three sets of initial values ​​for the Pareto optimal method.

[0131] Equivalent transmit power of meter-wave radar array The receiving gain of the meter-wave radar array antenna is 100 dBW. The value is 12dB, and the target's radar cross-section is... 7m 2 The transmitted signal wavelength λ is 1m, and the radar integration time T int For 2 seconds, at temperature T s The value is 290K, and the equivalent noise figure is N. F The value is 35dB. The array antenna of the meter-wave radar is a nested array with 14 array elements.

[0132] Table 1 Initial Values ​​for Example 1

[0133]

[0134] Table 2 Initial Values ​​for Example 2

[0135]

[0136] Table 3 Initial Values ​​for Example 3

[0137]

[0138]

[0139] A 3-transmit, 3-receive meter-wave multi-base radar needs to be deployed in a square area with sides of 60 km, and the antenna height of the transceiver station is set at 10 m. Assume an acceptable error limit σ. a It is 300m.

[0140] like Figure 3 As shown, the Fisher information matrix [FIM] for target position estimation using meter-wave multi-base radar based on range information localization.j,h medium μ R =1, μ θ =0, let the standard root mean square error of the distance estimation be...

[0141]

[0142] Simulation conditions: The monitoring area is a cuboid region with sides of 200km long, 200km wide, and 30km high. The long side of the monitoring area is between -100km and 100km, the wide side is between -100km and 100km, and the high side is between 100m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area. The feasible deployment area has sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 2km long and 2km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 961 discrete points in the feasible space.

[0143] With both the feasible space and the monitoring area being large, and both the feasible space interval and the monitoring area interval being small, the computational cost of the global optimal solution is 916. 6 ×1323κ R =7.8151×10 20 κ R The time cost of such a method is extremely high, while the Pareto optimal deployment proposed in this application requires less computation.

[0144] like Figure 3 As shown, Examples 1 to 3 obtain Pareto optimal deployment results after 2 to 4 repeated dynamic games. While the results of the three examples are not identical, their performance is very similar. Even when the discrete intervals of feasible deployment areas are small and there are many corresponding feasible deployment locations, the Pareto optimal method can still achieve excellent performance after a few stages of repeated dynamic games. The computational cost of obtaining the Pareto optimal solution is less than or equal to 4 × 6 × 916 × 1323κ. R =2.9084832×10 7 κ R The computational cost to obtain the global optimal solution is 7.8151 × 10⁻⁶. 20 κ R The Pareto optimality method has a significant advantage in terms of computational cost.

[0145] like Figure 3 The simulation results of meter-wave multi-base radar for high-altitude target localization based on angle information are shown.

[0146] Fisher Information Matrix [FIM] for Target Position Estimation using Meter-Wave Multi-Station Radar Based on Angle Information Localization j,h middle μθ =1,μ R =0.

[0147] Simulation conditions: The monitoring area is a cuboid region with sides of 200km long, 200km wide, and 30km high. The long side of the monitoring area is between -100km and 100km, the wide side is between -100km and 100km, and the high side is between 2000m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 2km long and 2km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 961 discrete points in the feasible space.

[0148] Let the standard root mean square error for estimating the azimuth angle of a high-altitude target be...

[0149]

[0150] The standard root mean square error of pitch angle estimation is

[0151]

[0152] like Figure 4 As shown, Pareto optimal deployment results are obtained after 3 to 5 repeated dynamic games. The results of the three examples are not exactly the same, but the performance is very close. Even when the discrete interval of feasible deployment areas is small and there are many corresponding feasible deployment locations, the Pareto optimal method can still achieve excellent performance results after a few stages of repeated dynamic games.

[0153] like Figure 5 The simulation results shown are for low-altitude targets using meter-wave multi-base radar based on angle information localization.

[0154] Simulation conditions: The monitoring area is a cuboid region with sides of 200km long, 200km wide, and 2km high. The long side of the monitoring area is between -100km and 100km, the wide side is between -100km and 100km, and the high side is between 100m and 2000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 0.2km high, containing 3969 discrete points. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 2km long and 2km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, containing 961 discrete points.

[0155] Let the standard root mean square error for estimating the azimuth angle of a low-altitude target be...

[0156]

[0157] The standard root mean square error of pitch angle estimation is

[0158]

[0159] like Figure 5 As shown, Pareto optimal deployment results are obtained after 3 to 4 repeated dynamic games. The results of the three examples are not exactly the same, but the performance is very close. Even when the discrete interval of feasible deployment areas is small and there are many corresponding feasible deployment locations, the Pareto optimal method can still achieve excellent performance results after a few stages of repeated dynamic games.

[0160] Suppose that the computational complexity of CRLB for locating a target position in a deployment scenario of a meter-wave multi-base radar based on angle information is κ. θ The meter-wave multi-base radar, based on angle information positioning, locates high-altitude targets, and the computational complexity for obtaining the global optimal solution is 916. 6 ×1323κ θ =7.8151×10 20 κ θ In other words, the computational cost of obtaining the global optimal solution is too high, while the computational cost of obtaining the Pareto optimal solution is less than or equal to 5×6×916×1323κ. θ =3.6356040×10 7 κ θ The computational complexity for obtaining the global optimal solution using meter-wave multi-base radar based on angle information to locate low-altitude targets is 916. 6 ×3969κ θ =2.3445×10 21 κ θ In other words, the computational cost of obtaining the global optimal solution is too high, while the computational cost of the Pareto optimal solution is less than or equal to 4 × 6 × 916 × 3969κ. θ =8.7254496×10 7 κ θ Therefore, the Pareto optimality method has a significant advantage in terms of computational cost.

[0161] like Figure 6 As shown, the simulation results of meter-wave multi-base radar for high-altitude target localization based on joint range and angle information are presented.

[0162] Fisher Information Matrix [FIM] for Target Position Estimation using Meter-Wave Multi-Station Radar Based on Joint Range and Angle Information j,h middle μ θ =1,μ R =1.

[0163] Simulation conditions: The monitoring area is a cuboid region with sides of 200km long, 200km wide, and 30km high. The long side of the monitoring area is between -100km and 100km, the wide side is between -100km and 100km, and the high side is between 2000m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 2km long and 2km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 961 discrete points in the feasible space.

[0164] Let the standard root mean square error of the distance estimation be...

[0165]

[0166] Let the standard root mean square error for estimating the azimuth angle of a high-altitude target be...

[0167]

[0168] The standard root mean square error of pitch angle estimation is

[0169]

[0170] like Figure 6 As shown, Pareto optimal deployment results are obtained after 3 to 4 repeated dynamic games. The results of the three examples are not exactly the same, but the performance is very close. Even when the discrete interval of feasible deployment areas is small and there are many corresponding feasible deployment locations, the Pareto optimal method can still achieve excellent performance results after a few stages of repeated dynamic games.

[0171] like Figure 7 As shown, the simulation results of meter-wave multi-base radar for low-altitude target localization based on joint range and angle information are presented.

[0172] Simulation conditions: The monitoring area is a cuboid region with sides of 200km long, 200km wide, and 2km high. The long side of the monitoring area is between -100km and 100km, the wide side is between -100km and 100km, and the high side is between 100m and 2000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 0.2km high, containing 3969 discrete points. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 2km long and 2km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, containing 961 discrete points.

[0173] Let the standard root mean square error of the distance estimation be...

[0174]

[0175] Let the standard root mean square error for estimating the azimuth angle of a low-altitude target be...

[0176]

[0177] The standard root mean square error of pitch angle estimation is

[0178]

[0179] like Figure 7 As shown, Pareto optimal deployment results are obtained after 3 to 6 repeated dynamic games. The results of the three examples are not exactly the same, but the performance is very close. Even when the discrete interval of feasible deployment areas is small and there are many corresponding feasible deployment locations, the Pareto optimal method can still achieve excellent performance results after a few stages of repeated dynamic games.

[0180] Suppose that the computational complexity of CRLB for locating a target using a meter-wave multi-base radar based on joint range and angle information in one deployment scenario is κ. U The meter-wave multi-base radar, based on joint range and angle information, locates high-altitude targets, and the computational complexity for obtaining the global optimal solution is 916. 6 ×1323κ U =7.8151×10 20 κ U In other words, the computational cost of obtaining the global optimal solution is too high, while the computational cost of obtaining the Pareto optimal solution is less than or equal to 4 × 6 × 916 × 1323κ. U =2.9084832×10 7 κ U The meter-wave multi-base radar, based on joint range and angle information, locates low-altitude targets, and the computational complexity for obtaining the global optimal solution is 916. 6 ×3969κ U =2.3445×10 21 κ U In other words, the computational cost of obtaining the global optimal solution is too high, while the computational cost of the Pareto optimal solution is less than or equal to 6 × 6 × 916 × 3969κ. U =1.30881744×10 8 κ U Therefore, the Pareto optimality method has a significant advantage in terms of computational cost.

[0181] like Figure 8 The simulation results of Pareto optimal deployment and global optimal deployment for distance information localization are shown.

[0182] The global optimal solution is obtained through a traversal approach, which involves enumerating all possible deployment scenarios and selecting the optimal one. Therefore, the computational cost is very high, and obtaining the global optimal solution takes a long time. The time cost of obtaining the global optimal solution is only acceptable when the monitoring area is small and the discrete interval between the monitoring area and the feasible deployment area is large. To compare and analyze Pareto optimal deployment with the global optimal deployment, simulations were conducted using a small monitoring area, a large monitoring area, and a discrete interval between the feasible deployment areas.

[0183] Simulation conditions: The monitoring area is a cuboid region with sides of 40km long, 40km wide, and 20km high. The long side of the monitoring area is between -20km and 20km, the wide side is between -20km and 20km, and the high side is between 2000m and 22000m. The discrete interval of the monitoring area is 20km long, 20km wide, and 20km high, and there are 18 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 20km long and 20km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 16 discrete points in the feasible space.

[0184] like Figure 8 As shown, Pareto optimal deployment results are obtained after 3 to 6 repeated dynamic games. The results of the three examples are not the same, indicating that the Pareto optimal solution is not unique. The Pareto optimal results of the three examples are not as large as the effective monitoring area of ​​the global optimal solution, but they are closer to the performance of the global optimal solution than the three randomly selected initial deployment positions.

[0185] Suppose that the computational complexity of CRLB for locating a target position in a deployment of a meter-wave multi-base radar based on range information is κ. R In Simulation 1, when both the feasible space and the effective monitoring area are small, and both the feasible space interval and the effective monitoring area interval are large, the computational cost of the global optimal solution is 16. 6 ×18κ R =8.39808×10 5 κ R The computational cost of the Pareto optimal solution is less than or equal to 6 × 6 × 16 × 18κ. R =1.0368×10 4 κ R .

[0186] like Figure 9 As shown, the simulation results for high-altitude target localization based on angle information are presented.

[0187] Simulation conditions: The monitoring area is a cuboid region with sides of 40km long, 40km wide, and 20km high. The long side of the monitoring area is between -20km and 20km, the wide side is between -20km and 20km, and the high side is between 2000m and 22000m. The discrete interval of the monitoring area is 20km long, 20km wide, and 20km high, and there are 18 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 20km long and 20km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 16 discrete points in the feasible space.

[0188] After three to four repeated dynamic games, Pareto optimal deployment results were obtained. The results of the three examples were different, indicating that the Pareto optimal solution is not unique. None of the three Pareto optimal results had a larger effective monitoring area than the global optimal solution, but compared with the three randomly selected initial deployment locations, they were very close to the performance of the global optimal solution.

[0189] A meter-wave multi-base radar based on angle information is used to locate high-altitude targets. In Simulation 2, both the feasible space and the effective monitoring area are small, while the feasible space interval and the effective monitoring area interval are large. In this case, the computational cost of the global optimal solution is 16. 6 ×18κ θ =8.39808×10 5 κ θ The computational cost of the Pareto optimal solution is less than or equal to 4 × 6 × 16 × 18κ. θ =6.912×10 3 κ θ .

[0190] like Figure 10 As shown, low-altitude target localization is based on angle information.

[0191] Simulation conditions: The monitoring area is a cuboid region with sides of 40km long, 40km wide, and 1km high. The long side of the monitoring area is between -20km and 20km, the wide side is between -20km and 20km, and the high side is between 500m and 1500m. The discrete interval of the monitoring area is 20km long, 20km wide, and 0.5km high, and there are 27 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 20km long and 20km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 16 discrete points in the feasible space.

[0192] like Figure 10As shown, Pareto optimal deployment results are obtained after 3 to 5 repeated dynamic games. The results of the three examples are different, indicating that the Pareto optimal solution is not unique. The Pareto optimal results of the three examples are not as large as the effective monitoring area of ​​the global optimal solution, but they are very close to the performance of the global optimal solution compared with the three randomly selected initial deployment positions.

[0193] A meter-wave multi-base radar based on angle information is used to locate low-altitude targets. In simulation 3, both the feasible space and the effective monitoring area are small, while the feasible space interval and the effective monitoring area interval are large. In this case, the computational cost of the global optimal solution is 16. 6 ×27κ θ =1259712×10 6 κ θ The computational cost of the Pareto optimal solution is less than or equal to 5 × 6 × 16 × 27κ. θ =1.296×10 4 κ θ .

[0194] like Figure 11 As shown, a simulation analysis of high-altitude target localization based on joint distance and angle information is presented.

[0195] Simulation conditions: The monitoring area is a cuboid region with sides of 40km long, 40km wide, and 20km high. The long side of the monitoring area is between -20km and 20km, the wide side is between -20km and 20km, and the high side is between 2000m and 22000m. The discrete interval of the monitoring area is 20km long, 20km wide, and 20km high, and there are 18 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 20km long and 20km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 16 discrete points in the feasible space.

[0196] like Figure 11 As shown, Examples 1 to 3 obtained Pareto optimal deployment results after 2 to 3 repeated dynamic games. The results of the three examples are not the same, indicating that the Pareto optimal solution is not unique. The Pareto optimal results of the three examples are not as large as the effective monitoring area of ​​the global optimal solution, but compared with the three randomly selected initial deployment positions, they are very close to the performance of the global optimal solution.

[0197] A meter-wave multi-base radar based on joint range and angle information is used to locate high-altitude targets. In Simulation 4, both the feasible space and effective monitoring area are small, while the feasible space interval and effective monitoring area interval are large. In this case, the computational cost of the global optimal solution is 16. 6 ×18κ U =8.39808×10 5 κ UThe computational cost of the Pareto optimal solution is less than or equal to 3 × 6 × 16 × 18κ. U =5.184×10 3 κ U .

[0198] like Figure 12 As shown, a simulation analysis of low-altitude target localization based on joint distance and angle information is presented.

[0199] Simulation conditions: The monitoring area is a cuboid region with sides of 40km long, 40km wide, and 1km high. The long side of the monitoring area is between -20km and 20km, the wide side is between -20km and 20km, and the high side is between 500m and 1500m. The discrete interval of the monitoring area is 20km long, 20km wide, and 0.5km high, and there are 27 discrete points in the monitoring area. The feasible deployment area is a cuboid region with sides of 60km long and 60km wide. The discrete interval of the feasible deployment area is 20km long and 20km wide. The long side of the feasible deployment area is between -30km and 30km, and the wide side is between -30km and 30km, and there are 16 discrete points in the feasible space.

[0200] like Figure 12 As shown, Examples 1 to 3 obtained Pareto optimal deployment results after 3 to 4 repeated dynamic games. The results of the three examples are different, indicating that the Pareto optimal solution is not unique. Only the Pareto optimal result of Example 3 is the same as the global optimal solution. The Pareto optimal results of the other two examples are not as large as the effective monitoring area of ​​the global optimal solution, but compared with the randomly selected initial deployment position, they are very close to the performance of the global optimal solution.

[0201] A meter-wave multi-base radar based on joint range and angle information is used to locate low-altitude targets. In simulation 5, both the feasible space and effective monitoring area are small, while the feasible space interval and effective monitoring area interval are large. In this case, the computational cost of the global optimal solution is 16. 6 ×27κ U =1259712×10 6 κ U The computational cost of the Pareto optimal solution is less than or equal to 4 × 6 × 16 × 27κ. U =1.0368×10 4 κ U .

[0202] It should be explained that Pareto optimal deployment is a type of deployment with superior performance. Compared with the global optimal solution, the Pareto optimal method has a much lower computational cost.

[0203] Simulation results and analysis of the impact of feasible deployment interval on deployment performance

[0204] Using the initial values ​​from Example 1 as the initial values ​​for the simulation in this section, the feasible deployment area is 60km long and 60km wide. Let the discrete interval of the feasible deployment area be F for both length and width. The long side of the feasible deployment area lies between -30km and 30km, and the wide side lies between -30km and 30km. The feasible space contains a total of... There are discrete points. F is taken as 0.5km, 1km, 2km, 4km, 8km and 16km respectively.

[0205] like Figure 13 As shown, simulation analysis of positioning based on distance information.

[0206] Simulation conditions: The monitoring area is a cuboid region with a side length of 200km, a width of 200km, and a height of 30km. The long side of the monitoring area is located between -100km and 100km, the wide side is located between -100km and 100km, and the height side is located between 100m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area.

[0207] like Figure 13 As shown, when the feasible deployment area interval is large, such as 8km and 16km, the Pareto optimal performance is poor; when the feasible deployment area interval is small, such as 0.5km and 4km, the Pareto optimal performance is good. For meter-wave multi-base radar based on range information positioning, the smaller the interval, the better the performance. However, when the interval is even smaller (e.g., 0.5km), the performance improvement of the Pareto optimal solution is also small. It should be noted that the smaller the interval, the greater the computational cost of the game at each stage. Therefore, for meter-wave multi-base radar based on range information positioning, 1km is the optimal feasible deployment area discrete interval.

[0208] like Figure 14 As shown, the simulation analysis of high-altitude target localization based on angle information is presented.

[0209] Simulation conditions: The monitoring area is a cuboid region with a side length of 200km, a width of 200km, and a height of 30km. The long side of the monitoring area is located between -100km and 100km, the wide side is located between -100km and 100km, and the height side is located between 2000m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area.

[0210] like Figure 14As shown, in general, for meter-wave multi-base radar based on angle information positioning to locate high-altitude targets, the smaller the interval, the better the performance. However, when the interval becomes even smaller (e.g., 0.5 km), the performance of the Pareto optimal solution no longer improves, and the number of stages required to obtain the Pareto optimal solution is still relatively large. It should be noted that the smaller the interval, the greater the computational cost of each stage of the game. Therefore, appropriately selecting the discrete interval of the feasible deployment area can fully leverage the advantages of the Pareto optimal method, obtaining a high-performance meter-wave multi-base radar deployment with minimal computational cost. Therefore, when meter-wave multi-base radar based on angle information positioning is used to locate high-altitude targets, 1 km is the optimal discrete interval for the feasible deployment area.

[0211] like Figure 15 As shown, the simulation analysis of low-altitude target localization based on angle information is presented.

[0212] Simulation conditions: The monitoring area is a cuboid region with a side length of 200km, a width of 200km, and a height of 2km. The long side of the monitoring area is located between -100km and 100km, the wide side is located between -100km and 100km, and the height side is located between 100m and 2000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 0.2km high. There are 3969 discrete points in the monitoring area.

[0213] like Figure 15 As shown, generally speaking, for meter-wave multi-base radar based on angle information positioning to locate low-altitude targets, the smaller the interval, the better the performance. However, it should be noted that the smaller the interval, the greater the computational burden of each stage of the game. When the interval is further reduced (e.g., less than 2 km), the performance improvement of the Pareto optimal solution is minimal. Therefore, for meter-wave multi-base radar based on angle information positioning to locate low-altitude targets, 2 km is the optimal discrete interval for the feasible deployment area.

[0214] like Figure 16 As shown, a simulation analysis of high-altitude target localization based on joint distance and angle information is presented.

[0215] Simulation conditions: The monitoring area is a cuboid region with a side length of 200km, a width of 200km, and a height of 30km. The long side of the monitoring area is located between -100km and 100km, the wide side is located between -100km and 100km, and the height side is located between 2000m and 30000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 10km high, and there are 1323 discrete points in the monitoring area.

[0216] As shown in Figure 16, generally speaking, for meter-wave multi-base radar based on joint range and angle information to locate high-altitude targets, the smaller the interval, the better the performance. However, it should be noted that the smaller the interval, the greater the computational cost of each stage of the game. When the interval is even smaller (e.g., less than 4 km), the performance improvement of the Pareto optimal solution is minimal. Therefore, when meter-wave multi-base radar based on joint range and angle information is used to locate high-altitude targets, 4 km is the optimal discrete interval for the feasible deployment area.

[0217] like Figure 17 As shown, a simulation analysis of low-altitude target localization based on joint distance and angle information is presented.

[0218] Simulation conditions: The monitoring area is a cuboid region with a side length of 200km, a width of 200km, and a height of 2km. The long side of the monitoring area is located between -100km and 100km, the wide side is located between -100km and 100km, and the height side is located between 100m and 2000m. The discrete interval of the monitoring area is 10km long, 10km wide, and 0.2km high. There are 3969 discrete points in the monitoring area.

[0219] like Figure 17 As shown, generally speaking, for meter-wave multi-base radar based on joint range and angle information to locate low-altitude targets, the smaller the interval, the better the performance. However, it should be noted that the smaller the interval, the greater the computational cost of each stage of the game. When the interval is even smaller (e.g., less than 1 km), the performance improvement of the Pareto optimal solution is minimal. Therefore, when meter-wave multi-base radar based on joint range and angle information is used to locate low-altitude targets, 1 km is the optimal discrete interval for the feasible deployment area.

[0220] It should be explained that the smaller the feasible deployment interval, the better the performance of the Pareto optimal solution. However, when the feasible deployment interval is small, a smaller feasible deployment interval can no longer effectively improve the performance of the Pareto optimal solution. On the other hand, a smaller feasible deployment interval will lead to a larger amount of computation. Therefore, choosing an appropriate feasible deployment interval is an important prerequisite for quickly obtaining a high-performance Pareto optimal deployment.

[0221] It should be explained that the method in this invention has low computational complexity and can quickly obtain the Pareto optimal deployment of meter-wave multi-base radar, thereby achieving high-precision target detection in a specific airspace. The following conclusions are drawn:

[0222] (1) The optimization deployment of meter-wave multi-base radar was analyzed from two aspects: the evaluation criteria for the deployment quality of meter-wave multi-base radar and the possible deployment locations of meter-wave multi-base radar.

[0223] (2) The Pareto optimality theory is summarized, and a Pareto optimal deployment method for meter-wave multi-base radar is proposed. The method in this invention has low computational complexity and can quickly obtain the Pareto optimal deployment of meter-wave multi-base radar. Pareto optimal deployment is a deployment situation in which the detection performance of meter-wave multi-base radar cannot be improved by changing the deployment of a single station, and it is a deployment situation in which high-precision detection of targets in a specific airspace can be achieved.

[0224] (3) In the simulation results and analysis, the Pareto optimal deployment method of meter-wave multi-base radar was first simulated under three different conditions based on different positioning information: the first is positioning based on range information; the second is positioning based on angle information; and the third is positioning based on a combination of range and angle information. Secondly, the Pareto optimal deployment results under these three conditions were compared and analyzed with the global optimal deployment results. Finally, the impact of feasible deployment intervals was simulated and analyzed. The simulation results show that: firstly, the Pareto optimal deployment algorithm has low computational cost and can quickly obtain deployment results; secondly, Pareto optimal deployment is a type of deployment with excellent performance; and thirdly, reasonably selecting feasible deployment intervals is an important condition for reducing computational cost and obtaining high-performance Pareto optimal deployments.

[0225] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An optimized deployment method based on meter-wave multi-base radar, characterized in that, Includes the following steps: S1. Based on the bistatic distances between the receiving station, transmitting station and target position of the meter-wave multi-base radar, the azimuth angle of the receiving station relative to the target position, and the elevation angle of the receiving station relative to the target position, construct the target localization model of the meter-wave multi-base radar. S2. Based on the target localization model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix for target position estimation by the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the localization performance of the meter-wave multi-base radar for target position. S3. Determine the feasible deployment area of ​​the transmitter and receiver of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver and the size of the feasible deployment area, obtain the potential of the set of feasible deployment locations in the feasible deployment area. S4. A dynamic game is played, with the transmitting and receiving stations of the meter-wave multi-base radar as participants. Their feasible space represents feasible deployment locations. Each participant chooses the strategy that maximizes their contribution to the effective monitoring area volume. The Pareto optimal deployment of the meter-wave multi-base radar is obtained through a finitely repeated dynamic game method. Specifically: If we consider the transmitting and receiving stations of the meter-wave multi-base radar as the participants in the game, then the feasible space is the feasible deployment location of the transmitting and receiving stations. Let the positions chosen by all participants in phase q be: Among them, K t K represents the number of launch stations. r The number of receiving stations; Let the positions chosen by the participants other than the k-th participant in the q-th stage be: Let s = (x, y, z) be the discrete point location in the effective monitoring area, σ[s, P(q)] represent the positioning performance at point s when using P(q), V[P(q)] represent the volume of the effective monitoring area when using P(q), σ[s, K(q)] represent the positioning performance at point s when using K(q), and V[K(q)] represent the volume of the effective monitoring area when using P(q). Then: V[P(q)]=χ{s|σ[s,P(q)]≤σ a ,s∈S a }×v V[K(q)]=χ{s|σ[s,K(q)]≤σ a ,s∈S a }×v Let V be the contribution of the k-th participant to the effective monitoring area volume in stage q. k (q) is: V k (q)=V[P(q)]-V[K(q)] Each participant chooses the strategy that maximizes their contribution to the effective monitoring area volume, i.e., Max V k (q); In a dynamic game, when the k-th player considers its strategy, the strategies of the other players remain unchanged. At this time, V[K(q)] remains unchanged, making V k (q) is equivalent to maximizing V[P(q)], and maximizing V[P(q)] is precisely the optimization objective of the optimal deployment of meter-wave multi-base radar; the reward of the k-th participant is set as the volume of the effective monitoring area corresponding to all participants, i.e., u k (q) = V[P(q)].

2. The optimized deployment method based on meter-wave multi-base radar according to claim 1, characterized in that, In step S1, a target localization model for the meter-wave multi-base radar is constructed based on the bistatic distances between the receiving station, transmitting station, and target position of the meter-wave multi-base radar, the azimuth angle of the receiving station relative to the target position, and the elevation angle of the receiving station relative to the target position. Specifically: Suppose that a meter-wave multi-base radar uses range, azimuth, and elevation information to locate the target position. The estimated target position is defined as follows: Θ = [x, y, z] Let K be the K of the meter-wave multi-base radar. t The launch station locations are k t =1,2,…,K t K r The location of each receiving station is set up For receiving station k r Launch station k t Bibase distance from the target location, For receiving station k r Azimuth estimation of the target location. For receiving station k r Based on the elevation angle estimation of the target, the mathematical model for target localization using meter-wave multi-base radar is as follows:

3. The optimization method based on meter-wave multi-base radar according to claim 2, characterized in that, In step S2, based on the target localization model of the meter-wave multi-base radar and the operating parameters of the meter-wave multi-base radar, the Fisher information matrix for target position estimation by the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, specifically: set up For radar transmission power, For antenna transmit gain, For antenna receiving gain, Let T be the target's radar cross-section, λ be the wavelength of the transmitted signal, and T be the target's radar cross-section. int T is the radar synthesis time, K is the Boltzmann constant, and T is the radar synthesis time. s For temperature, N F The equivalent noise figure; Let the kth t The distance between each launch station and the target is: Let the kth r The distance between each receiving station and the target is: The signal-to-noise ratio of the received signal Represented as: Let the standard root mean square error of the azimuth angle estimation be... The standard root mean square error of pitch angle estimation is The standard root mean square error of the distance estimation is Let ρ(*) be the probability density distribution function; Θ j and Θ h Let be the j-th and h-th terms of the target location estimate; m and n are the indices of different transceiver station combinations, m = 1, 2, ..., K. r K t n = 1, 2, ..., K r K t ; This is used to indicate whether meter-wave multi-base radar positioning utilizes azimuth information. This indicates that azimuth information was used. This indicates that azimuth information was not used; μ θ μ is used to indicate whether meter-wave multi-base radar positioning utilizes elevation angle information. θ =1 indicates that pitch angle information was used, μ θ =0 indicates that pitch angle information was not used; μ R μ is used to indicate whether meter-wave multi-base radar positioning utilizes range information. R =1 indicates that distance information was used, μ R =0 indicates that range information was not used; therefore, the element in the j-th row and h-th column of the Fisher information matrix for target position estimation by meter-wave multi-base radar is represented as:

4. The method for optimizing the deployment of meter-wave multi-base radar according to claim 3, characterized in that, In step S2, the Cramer-Rao lower bound is used to measure the target localization performance of the meter-wave multi-base radar, specifically as follows:

5. The method for optimizing the deployment of meter-wave multi-base radar according to claim 1, characterized in that, In step S3, the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar are determined. Based on the minimum three-dimensional interval of the transmitter and receiver stations and the size of the feasible deployment areas, the potential of the set of feasible deployment locations within the feasible deployment areas is obtained, specifically: Let the length, width, and height of the feasible deployment area be Le, We, and He, respectively; set up If we denote rounding down, then the potential of the set of feasible deployment locations in the feasible deployment zone, Nu, is expressed as:

6. An optimized deployment system based on meter-wave multi-base radar, used to execute the optimized deployment method based on meter-wave multi-base radar as described in any one of claims 1-5, characterized in that it comprises: Target localization model construction module: Based on the bistatic distance between the receiving station, transmitting station and the target position of the meter-wave multi-base radar, the azimuth angle of the receiving station to the target position, and the elevation angle of the receiving station to the target position, a target localization model of the meter-wave multi-base radar is constructed. Positioning performance measurement module: Based on the target positioning model of the meter-wave multi-base radar and the working parameters of the meter-wave multi-base radar, the Fisher information matrix of the target position estimation of the meter-wave multi-base radar is obtained, and based on the Fisher information matrix, the Cramer-Rao lower bound is used to measure the positioning performance of the meter-wave multi-base radar for the target position. Deployment module: Determines the feasible deployment areas of the transmitter and receiver stations of the meter-wave multi-base radar. Based on the three-dimensional interval of the minimum deployment of the transmitter and receiver stations and the size of the feasible deployment area, it obtains the potential of the set of feasible deployment locations in the feasible deployment area. Dynamic game module: The transmitting and receiving stations of the meter-wave multi-base radar are treated as participants in a dynamic game, and their feasible space is the feasible deployment location. Each participant chooses the strategy that contributes the most to the volume of the effective monitoring area. Through a finitely repeated dynamic game method, the Pareto optimal deployment of the meter-wave multi-base radar is obtained.

7. A computer-readable storage medium, characterized in that, The system stores computer program instructions that, when executed on a processor, perform the optimized deployment method for meter-wave multi-base radar as described in any one of claims 1 to 5.

Images