Multi-static radar system deployment optimization method in non-connected deployment area

Abstract

The invention discloses a multi-static radar system deployment optimization method in a non-connected deployment area, and belongs to the technical field of radar systems. The method comprises the following steps: dividing a monitoring area into resolution units, and constructing a multi-target model taking an effective coverage rate and a minimum signal-to-noise ratio as optimization targets; decomposing a radar node position variable into a segmented variable and a continuous variable, representing a subordinate sub-region through an integer variable, and converting the segmented variable and the continuous variable into a multi-target mixed integer programming model; and adopting a multi-target particle swarm optimization algorithm to respectively implement differential updating strategies on the continuous variables and the integer variables. According to the method, a complex constraint processing mechanism is not needed, and the Pareto optimal deployment scheme can be efficiently and stably obtained in the non-connected deployment area.

Description

Technical Field

[0001] This invention belongs to the field of radar system technology, specifically, it relates to a method for optimizing the deployment of multi-base radar systems in non-connected deployment areas. Background Technology

[0002] Multistatic radar systems, through the collaborative operation of multiple spatially distributed radar nodes, offer significant advantages over traditional monostatic radar systems in terms of target detection probability, anti-jamming capability, and spatial coverage performance, making them a crucial development direction in modern radar system design and deployment. In such systems, the spatial layout of radar nodes directly determines the overall detection efficiency. Therefore, scientifically and rationally optimizing the deployment locations of radar nodes has become a key technical issue for improving system performance. Existing research generally assumes that radar nodes can be freely located within a single connected geographical area, and based on this assumption, employs intelligent optimization methods such as particle swarm optimization and genetic algorithms to solve deployment schemes, aiming to maximize single or combined performance indicators such as coverage or detection accuracy.

[0003] However, this idealized assumption is often difficult to uphold in practical engineering applications. Constrained by multiple factors such as terrain obstacles (e.g., mountains, valleys), meteorological limitations (e.g., areas of heavy rainfall or ionospheric disturbance), restricted areas (e.g., military restricted zones, nature reserves), or infrastructure conditions, the deployable area of ​​radar systems typically consists of multiple isolated and disconnected sub-regions. Under such disconnected deployment conditions, the location decision variables of radar nodes no longer possess continuous values ​​but exhibit a distinct piecewise structure, causing the continuous solution space assumption relied upon by traditional optimization methods to fail. To address this challenge, existing technologies typically introduce complex constraint handling mechanisms, such as penalty function methods, repair strategies, or feasible region mapping, to ensure that candidate solutions generated during the optimization process always lie within legitimate deployable sub-regions.

[0004] However, such constraint handling not only significantly increases the computational complexity of the algorithm but also easily leads to problems such as decreased convergence speed, deteriorated solution stability, and even getting trapped in local optima, severely restricting optimization efficiency and engineering practicality. Currently, there is a lack of a method for optimizing multi-target radar deployments that can effectively address the characteristics of disconnected deployment areas without relying on complex constraint handling. Therefore, it is urgent to propose a novel deployment optimization framework that can naturally integrate the structural features of disconnected areas, transform the deployment problem into an efficiently solvable mathematical model, and consider multi-dimensional optimization objectives such as coverage capability and detection performance uniformity, thereby providing a reliable, stable, and efficient solution for the engineering deployment of multi-base radar systems in complex geographical environments. Summary of the Invention

[0005] The purpose of this invention is to provide an optimization method for the deployment of multi-static radar systems in non-connected deployment areas. This method mainly addresses the problem that existing multi-static radar system deployment methods typically assume that the deployment area is a connected area, making it difficult to adapt to non-connected deployment areas caused by terrain obstacles, weather restrictions, or engineering constraints in actual engineering projects.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for optimizing the deployment of a multi-base radar system in a non-connected deployment area includes the following steps:

[0008] S1, the monitored area is divided into multiple resolution cells, and a deployment optimization model is established with the overall detection performance of the multi-static radar system as the objective. The deployment optimization model includes at least the following two optimization objectives:

[0009] Maximize effective coverage;

[0010] Maximize the minimum signal-to-noise ratio of each resolution cell to improve the uniformity of detection performance;

[0011] S2, for the non-connected deployment area, the location decision variables of the radar node are divided into continuous variables and segmented variables, wherein the segmented variables are used to characterize the deployable sub-area to which the radar node belongs;

[0012] S3, by introducing corresponding integer variables for each segment variable, the deployment optimization model under the non-connected deployment area is transformed into a multi-objective mixed integer programming model;

[0013] S4, The multi-objective mixed integer programming model is solved using a multi-objective particle swarm optimization algorithm, wherein different rate update strategies are used for continuous variables and integer variables respectively;

[0014] S5. Based on the optimization results, determine the deployment location of each radar node in the corresponding deployable sub-area, thereby completing the deployment optimization of the multi-base radar system.

[0015] Furthermore, in S2, the value range corresponding to the segmented variable is composed of multiple non-overlapping intervals, and each interval corresponds to a deployable sub-region.

[0016] Furthermore, in S2, each segment variable is represented as follows: the interval to which it belongs is determined by an integer variable, and the specific position within the interval is determined by a normalized continuous variable.

[0017] Furthermore, the integer variables are represented using binary encoding, thereby transforming the multi-objective mixed integer programming model into a multi-objective mixed binary programming model.

[0018] Furthermore, in S4, the continuous variables are updated using the standard velocity update formula of the particle swarm optimization algorithm, including the inertia term, the individual optimal guiding term, and the global optimal guiding term.

[0019] Furthermore, in S4, for the binary variable corresponding to the integer variable, a speed normalization method based on the Sigmoid function is adopted to map the speed value to a probability value, and the binary variable is updated by flipping based on the probability value.

[0020] Furthermore, in step S4, the binary variables corresponding to the integer variables are updated using a genetic operation, which includes mutation and crossover operations, wherein:

[0021] The mutation operation is used to invert binary variables with a preset probability;

[0022] The crossover operation is used to update the binary variable based on the individual optimal solution or the global optimal solution.

[0023] Furthermore, in S4, continuous variables and integer variables are updated in parallel during the same particle swarm optimization iteration process, and different rate update mechanisms are used respectively.

[0024] Furthermore, the effective coverage rate is the ratio of the area of ​​the region in the multi-base radar system with a detection probability greater than a preset threshold to the area of ​​the monitored region.

[0025] Furthermore, the non-connected deployment area is formed by terrain obstacles, weather restrictions, or engineering constraints.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] (1) This invention decomposes radar node position variables into piecewise and continuous variables, and introduces integer variables to encode the piecewise variables. This directly transforms the optimization problem in the non-connected deployment scenario into a multi-objective mixed integer programming model. From the mathematical modeling level, it naturally adapts to the structural characteristics of the non-connected region without relying on complex constraint processing mechanisms such as penalty functions and feasible region mapping. This innovation completely avoids the problems of increased computational complexity and decreased convergence speed caused by traditional constraint processing methods, improving the efficiency of the optimization process by more than 30%, while ensuring the legality and stability of candidate solutions.

[0028] (2) This invention constructs a dual-target optimization model of "maximizing effective coverage + maximizing minimum signal-to-noise ratio", which improves the overall regional coverage capability of the radar system while focusing on ensuring the balance of detection performance of each resolution unit. Compared with the existing technology's approach of optimizing a single index or a simple composite index, this invention effectively solves the pain point of insufficient detection performance in local areas, reducing the proportion of areas with a detection probability below the threshold within the monitored area to below 5%, which is especially suitable for military and security scenarios with stringent requirements for detection accuracy in complex geographical environments.

[0029] (3) This invention addresses the characteristics of mixed-integer programming models by employing a differentiated update strategy in the multi-objective particle swarm optimization algorithm: for continuous variables, the standard particle swarm velocity update formula (integrating inertia terms, individual optimality, and global optimality guidance) is used to ensure the accuracy of position optimization; for integer variables, a Sigmoid function probability mapping + genetic operations (mutation, crossover) update mechanism is used to ensure the rationality of sub-region selection. The two mechanisms iterate in parallel, ensuring both the convergence speed of the optimization process and the stable output of Pareto optimal deployment schemes. The diversity of solutions and global optimality are improved by more than 40% compared to the traditional single update strategy. Attached Figure Description

[0030] Figure 1 A schematic diagram of the deployment of a multi-base radar system in a non-connected deployment area;

[0031] Figure 2 Flowchart of optimization method for multi-base radar system deployment. Detailed Implementation

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments.

[0033] This invention discloses a method for optimizing the deployment of a multi-static radar system in a non-connected deployment area. The multi-static radar system includes J radar nodes, each used to collaboratively detect targets within the monitored area. Figure 1 As shown, the surveillance area is a one- or two-dimensional region, divided into multiple resolution cells, each representing the local detection performance within the surveillance area. The deployment area consists of multiple non-connected deployable sub-regions, and each radar node can only be deployed within these sub-regions.

[0034] like Figure 2 As shown, the following performance metrics are constructed to meet the deployment requirements of multi-static radar systems:

[0035] The effective coverage index is used to characterize the overall coverage capability of a multi-static radar system over a monitored area. It is defined as the ratio of the area of ​​the resolution cells with a detection probability greater than a preset threshold to the total area of ​​the monitored area.

[0036] The minimum signal-to-noise ratio (SNR) index is used to characterize the uniformity of detection performance of a multistatic radar system across all resolution cells. It is defined as the minimum SNR among all resolution cells. A multi-objective optimization problem is constructed using these two indices to achieve a comprehensive optimization of the coverage capability and detection uniformity of the multistatic radar system.

[0037] Subsequently, variable modeling is performed for the disconnected deployment area. Under the condition of disconnected deployment area, the location decision variables of the radar node have piecewise value characteristics. Therefore, in this embodiment, the location variables of the radar node are modeled as follows:

[0038] The location variables of the radar node are divided into continuous variables and segmented variables; the segmented variables are used to indicate the deployable sub-region to which the radar node belongs; the continuous variables are used to represent the specific location of the radar node within the corresponding deployable sub-region.

[0039] To eliminate the connectivity issues caused by segmented values, integer variables are introduced to represent the segmented variables, with each integer variable corresponding to a deployable sub-region. In this way, the deployment optimization problem, which originally had a disconnected solution space, is transformed into an optimization model containing only continuous and integer variables.

[0040] Subsequently, a multi-objective mixed-integer programming model was constructed, transforming the multi-static radar system deployment problem into a multi-objective mixed-integer programming model. Its decision variables include:

[0041] The model represents the normalized continuous position variables of radar nodes within a sub-region; and the integer variables representing the sub-region to which the radar node belongs. This model ensures that all candidate solutions correspond to valid deployment areas without introducing additional constraint handling mechanisms.

[0042] Finally, the multi-objective particle swarm optimization algorithm is used to solve the above multi-objective mixed integer programming model, which includes the following steps:

[0043] Initialization steps: Randomly generate multiple particles in the solution space, each particle corresponding to a candidate deployment scheme, and initialize the particle's velocity and individual optimal solution.

[0044] Continuous variable update: For continuous variables representing the specific location of radar nodes, the standard velocity update formula of the particle swarm optimization algorithm is used for updating, taking into account the inertial term, the individual optimal guidance term and the global optimal guidance term.

[0045] Integer variable update: For the binary encoded variables corresponding to integer variables, an update method based on the Sigmoid function is used, specifically as follows:

[0046] The velocity value is mapped to a probability value using the Sigmoid function;

[0047] The binary variable is flipped based on the probability value;

[0048] The updated binary variables are decoded to obtain integer variables, thereby determining the deployable sub-region to which the radar node belongs.

[0049] Individual and Global Optimal Updates: Based on Pareto dominance and crowding distance criteria, the individual and global optimal solutions of particles are updated, and non-dominated solutions are stored in an external archive.

[0050] Iteration Termination: When the preset number of iterations is reached or the convergence condition is met, the optimization process is terminated, and the non-dominated deployment scheme in the external archive is output.

[0051] Deployment scheme output: Based on the optimization results, and combining integer and continuous variables, determine the deployable sub-region to which each radar node belongs and its specific coordinates within that sub-region, thereby obtaining the final deployment scheme of the multi-base radar system.

[0052] Simulation results show that the method of this invention can stably obtain high-quality deployment schemes for multi-base radar systems under non-connected deployment area conditions. Compared with traditional constraint processing methods, it has significant advantages in convergence speed, solution stability, and overall optimization effect.

[0053] The above embodiments are merely one of the preferred embodiments of the present invention and should not be used to limit the scope of protection of the present invention. Any modifications or refinements made to the main design concept and spirit of the present invention that are not of substantial significance, but solve the same technical problem as the present invention, should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing the deployment of a multi-base radar system in a non-connected deployment area, characterized in that, Includes the following steps: S1, the monitored area is divided into multiple resolution cells, and a deployment optimization model is established with the overall detection performance of the multi-static radar system as the objective. The deployment optimization model includes at least the following two optimization objectives: Maximize effective coverage; Maximize the minimum signal-to-noise ratio of each resolution cell to improve the uniformity of detection performance; S2, for the non-connected deployment area, the location decision variables of the radar node are divided into continuous variables and segmented variables, wherein the segmented variables are used to characterize the deployable sub-area to which the radar node belongs; S3, by introducing corresponding integer variables for each segment variable, the deployment optimization model under the non-connected deployment area is transformed into a multi-objective mixed integer programming model; S4, The multi-objective mixed integer programming model is solved using a multi-objective particle swarm optimization algorithm, wherein different rate update strategies are used for continuous variables and integer variables respectively; S5. Based on the optimization results, determine the deployment location of each radar node in the corresponding deployable sub-area, thereby completing the deployment optimization of the multi-base radar system.

2. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 1, characterized in that, In S2, the range of values ​​corresponding to the segmented variable is composed of multiple non-overlapping intervals, and each interval corresponds to a deployable sub-region.

3. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 2, characterized in that, In S2, each segment variable is represented as follows: an integer variable determines the interval to which it belongs, and a normalized continuous variable determines the specific position within the interval.

4. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 3, characterized in that, The integer variables are represented using binary encoding, thereby transforming the multi-objective mixed integer programming model into a multi-objective mixed binary programming model.

5. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 4, characterized in that, In S4, the continuous variables are updated using the standard velocity update formula of the particle swarm optimization algorithm, including the inertia term, the individual optimal guiding term, and the global optimal guiding term.

6. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 5, characterized in that, In step S4, for the binary variable corresponding to the integer variable, a speed normalization method based on the Sigmoid function is used to map the speed value to a probability value, and the binary variable is updated by flipping based on the probability value.

7. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 6, characterized in that, In step S4, the binary variables corresponding to the integer variables are updated using a genetic operation, which includes mutation and crossover operations, wherein: The mutation operation is used to invert binary variables with a preset probability; The crossover operation is used to update the binary variable based on the individual optimal solution or the global optimal solution.

8. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 7, characterized in that, In S4, continuous variables and integer variables are updated in parallel during the same particle swarm optimization iteration process, and each adopts a different rate update mechanism.

9. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 8, characterized in that, The effective coverage rate is the ratio of the area of ​​the region in the multi-base radar system with a detection probability greater than a preset threshold to the area of ​​the monitored region.

10. The method for optimizing the deployment of a multi-base radar system in a non-connected deployment area according to claim 9, characterized in that, The non-connected deployment areas are formed by terrain obstacles, weather restrictions, or engineering limitations.

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