Distributed radar deployment strategy optimization method for TDOA positioning

Abstract

The invention belongs to the technical field of radar resource scheduling, and particularly relates to a distributed radar deployment strategy optimization method for TDOA positioning, and the method comprises the specific steps: 1, carrying out the modeling of a distributed radar positioning scene for TDOA positioning; 2, constructing system performance evaluation indexes and an optimization problem, wherein the evaluation indexes comprise a key subarea KS positioning performance evaluation index and a radar reconnaissance area RSA monitoring performance evaluation index; the optimization problem comprises a positioning task-oriented single-target optimization problem and a positioning and monitoring task-considered multi-target optimization problem; and step 3, solving the optimization problem to obtain a distributed radar optimization deployment strategy.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar resource scheduling, and in particular relates to a distributed radar deployment strategy optimization method for TDOA positioning. Background Art

[0002] The positioning of radiation sources is of key significance in electronic countermeasures. By accurately positioning enemy radars, communication equipment, jammers and other targets, it can significantly improve battlefield surveillance and strike capabilities and provide real-time prior information for countermeasure strategies. Distributed radars can obtain multi-perspective and multi-dimensional observation information, such as arrival time, time difference of arrival (TDOA) and arrival angle, by virtue of the advantages of flexible node deployment and signal-level collaborative processing. They have been widely used in the field of radiation source positioning. Among them, the positioning method based on TDOA has shown significant application potential because it does not need to rely on waveform prior information, has high positioning accuracy, and is robust to multipath effects. However, when deploying radars, the existing TDOA positioning methods usually only consider fixed point layouts in two-dimensional planes or three-dimensional spaces, ignoring the impact of the rationality of node deployment strategies on system performance. Reasonable node layout is directly related to multiple performance indicators such as positioning accuracy and coverage. By carefully designing and optimizing node deployment, the optimal system positioning performance can be achieved under limited resource conditions.

[0003] At present, many scholars at home and abroad have conducted extensive research in the field of distributed radar node deployment strategy optimization methods. For the TDOA positioning task in a single task area, the optimal node configuration is usually determined by minimizing the Cramer-Rao Lower Bound (CRLB). When the radiation source is located inside the sensor area, the optimal configuration is that the sensors are arranged symmetrically around the radiation source; when the radiation source is located outside the sensor area, the optimal configuration is located at the tangent point from the radiation source to the area boundary. For multi-task area positioning tasks with different importance, considering the system monitoring performance indicators, existing studies mostly model them as multi-objective optimization problems and use heuristic algorithms such as Multi-Objective Particle Swarm Optimization (MOPSO) to solve them. Although these studies have made some progress in improving the positioning and monitoring performance of distributed radars, most of them are still limited to the optimization of node positions and fail to fully consider the coupling relationship between the node normal direction and the system monitoring performance. Ignoring this key factor may cause the system to fail to achieve the expected monitoring effect in practical applications. Summary of the invention

[0004] In view of this, the present invention comprehensively considers the joint optimization of node position and normal pointing, constructs a single-objective optimization problem for positioning tasks and a multi-objective optimization problem that takes into account both positioning and monitoring tasks, and proposes a distributed radar deployment strategy optimization method for TDOA positioning.

[0005] The technical solution for implementing the present invention is as follows:

[0006] A distributed radar deployment strategy optimization method for TDOA positioning, the specific process is as follows:

[0007] Step 1: Distributed radar positioning scenario modeling for TDOA positioning;

[0008] Step 2, construct system performance evaluation indicators and optimization problems, the evaluation indicators include key sub-area KS positioning performance evaluation indicators and radar reconnaissance area RSA monitoring performance evaluation indicators; the KS positioning performance evaluation indicator is: in each KS, take the maximum root mean square positioning error RMSPE of all grid points, and use it to measure the system positioning performance under the node deployment scheme Φ, the RSA monitoring performance evaluation indicator is: calculate the proportion of effective monitoring points to all RSA grid points, called the effective monitoring area coverage, as an evaluation indicator for measuring system monitoring performance; the optimization problem includes a single-objective optimization problem for positioning tasks and a multi-objective optimization problem that takes into account both positioning and monitoring tasks;

[0009] Step 3: Solve the optimization problem constructed in step 2 to obtain the distributed radar optimization deployment strategy.

[0010] Furthermore, the KS positioning performance evaluation index of the present invention is:

[0011]

[0012] in, represents any grid point in the KS region under the radar deployment scheme Φ RMSPE, Φ = [s, α], s represents the distributed radar node position vector, α is the azimuth normal pointing vector of the distributed radar.

[0013] Furthermore, the RSA monitoring performance evaluation index of the present invention is:

[0014]

[0015] Where b(·) represents a Boolean function, A i represents the effective reconnaissance interval of the i-th radar node under the node deployment scheme Φ, Represents a grid point in RSA.

[0016] Furthermore, the present invention is based on the KS positioning performance evaluation index The objective function is established as:

[0017]

[0018] in: represents the effect function of KS positioning performance, To set the positioning weight;

[0019]

[0020] Among them: β1 and β2 are penalty coefficients, satisfying β1>β2>0, and β1+β2=1, For the expected positioning accuracy,

[0021] Based on the objective function and the RSA monitoring performance evaluation index, a single-objective positioning performance optimization problem and a multi-objective optimization problem that takes both positioning and monitoring performance into consideration are constructed.

[0022] Furthermore, the single target positioning performance optimization problem described in the present invention is:

[0023]

[0024] The multi-objective optimization problem taking into account both positioning and monitoring performance is:

[0025]

[0026] in, Indicates that the distributed radar is located in the radar deployment area. represents the kth KS Each boundary point is covered by the beams of more than four radar nodes.

[0027] Furthermore, in step 1 of the present invention, when modeling distributed scenes, the measurement error n r The noise considered includes constant noise SNR Correlated Noise Its covariance matrix Q r for:

[0028]

[0029] Furthermore, the signal-to-noise ratio-related noise of the present invention for:

[0030]

[0031] Among them: B j and B n They represent the signal bandwidth of the radiation source and the noise bandwidth of the receiver respectively; T represents the observation time; SNRi It represents the SNR of the signal transmitted by the radiation source received by the i-th radar node, i=0,1,…,N-1.

[0032] Furthermore, the root mean square positioning error RMSPE of the present invention is: based on the covariance matrix Q r Obtained by calculation.

[0033] Furthermore, step three of the present invention is based on the RC-MOPSO algorithm. By introducing regional constraints in the particle initialization and update process, it is ensured that the particles always meet the complex constraints of the optimization problem during the iteration process, thereby obtaining the optimal deployment strategy and achieving the optimal balance between the system positioning performance and the monitoring performance.

[0034] Furthermore, the specific process of step three of the present invention is:

[0035] (1) Node position information of particles in the population and the node normal points to Initialize and set constraints including: particle deployment position cannot exceed RDA and node normal pointing vector is within the lower and upper bounds of normal pointing;

[0036] (2) Setting the updating rules and constraints for the speed and position of particles in the population. The constraints are: the particle speed cannot exceed the preset boundary [v min ,v max ].

[0037] (3) Set the individual optimal particle update rule: At the tth iteration, if the current position x of particle m is m (t) dominates p m (t-1), it is updated to the new individual optimal position; if x m (t) is p m (t-1) dominates, the individual optimal position is not updated; if x m (t) and p m (t-1) do not dominate each other, then the optimal position of the individual is x with a set probability m (t) or p m (t-1);

[0038] (4) The global particle update rule is set as follows: the sparsest particles in the external archive are selected as the global optimal particles, and the external archive is updated in real time according to the dominance relationship between the individual optimal particles.

[0039] Beneficial effects:

[0040] First, the present invention comprehensively considers the joint optimization of node position and normal orientation, constructs a single-objective optimization problem for positioning tasks and a multi-objective optimization problem that takes into account both positioning and monitoring tasks; the present invention can optimize the deployment strategy of distributed radars and achieve the optimal balance between system positioning performance and monitoring performance. Compared with random deployment schemes, the present invention shows significant advantages in improving system positioning and monitoring performance.

[0041] Second, the present invention proposes the RC-MOPSO method to solve the above optimization problem. By introducing regional constraints in the particle initialization and update process, it ensures that the particles always meet the complex constraints of the optimization problem during the iteration process, thereby obtaining the optimal deployment strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0043] Figure 1 A flow chart of the method for optimizing the deployment strategy of distributed radar;

[0044] Figure 2 It is a distributed radar emitter location scenario based on TDOA measurement information;

[0045] Figure 3 To compare the performance of different deployment schemes in the simulation instance;

[0046] Figure 4 is the optimal random deployment scheme in the simulation instance;

[0047] Figure 5 Optimize deployment plans for single objectives in simulation instances;

[0048] Figure 6 Deployment scheme for multi-objective optimization in simulation instances. DETAILED DESCRIPTION

[0049] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0050] It should be noted that the following embodiments and features in the embodiments may be combined with each other in the absence of conflict; and, based on the embodiments in the present disclosure, all other embodiments obtained by ordinary technicians in the field without making any creative work are within the scope of protection of the present disclosure.

[0051] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein may be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present disclosure, it should be understood by those skilled in the art that an aspect described herein may be implemented independently of any other aspect, and two or more of these aspects may be combined in various ways. For example, any number of aspects described herein may be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein may be used to implement this device and / or practice this method.

[0052] The present application embodiment provides a distributed radar deployment strategy optimization method for TDOA positioning, such as Figure 1 As shown, the specific steps include:

[0053] Step 1: Distributed radar positioning scenario modeling.

[0054] Distributed radar emitter location scenarios based on TDOA measurement information Figure 2 The scene consists of two parts: the radar reconnaissance area (RSA) and the radar deployment area (RDA), which are denoted as and In RSA, the areas where the radiation source has a high probability of appearing are defined as key subareas (KS). These areas need to be focused on and are expressed as

[0055] Distributed radar consists of N radars located at known coordinates i=0,1,…,N-1 directional radars, the azimuth normal pointing direction and the maximum beam scanning angle of each radar are α i and in(·) T Represents a transposition operation. Each node can receive The radiation source transmits a signal, and the radiation source is located by calculating its time difference of arrival (TDOA). Since TDOA and range difference of arrival (RDOA) can be converted to each other, in order to facilitate subsequent derivation, the present invention chooses to use RDOA to replace TDOA.

[0056] Without loss of generality, let s0 be the reference radar. The distributed radar can obtain N-1 RDOA measurements, which can be expressed as the following vector form:

[0057]

[0058] Where: r represents the measurement vector of the real RDOA of the radiation source, r = [r 1,0 ,r 2,0 ,…,r N-1,0 ] T , r i,0 =d i -d0,i=1,2,…,N-1, i=0,1,…,N-1 represents the radiation source u and the radar node s i The true distance. The measurement error vector n r =[n r,1 ,n r,2 ,…,n r,N-1 ] T It obeys a zero-mean Gaussian independent distribution, and its covariance matrix Q r for

[0059]

[0060] in: represents the mathematical expectation, i=1,2,…,N-1 consists of two parts: a constant noise term and a signal-to-noise ratio (SNR) related noise term, expressed as

[0061]

[0062] Where: Constant noise term Mainly due to instrument errors, such as clock synchronization errors or calibration errors. SNR-related noise terms It can be expressed as

[0063]

[0064] Among them: B j and B n They represent the radiation source signal bandwidth and the receiver noise bandwidth respectively. Usually, B j ≈B n ; T represents the observation time; SNR i represents the SNR of the signal transmitted by the radiation source received by the i-th radar node, i=0,1,…,N-1

[0065]

[0066] Where: P j Represents the average emission power of the radiation source; G r,i represents the antenna receiving gain of the i-th radar node; Fr Indicates the receiving pattern response; k, F n , T0, B, L s They represent the Boltzmann constant, receiver noise figure, standard temperature, receiver bandwidth and loss factor respectively.

[0067] Similarly, the location of distributed radar stations will also be subject to error disturbances, expressed as

[0068]

[0069] in: Represents the real site vector of the distributed radar, the site error vector It obeys a zero-mean Gaussian independent distribution, and its covariance matrix is

[0070]

[0071] in: Indicates the standard deviation of the radar node's position error in the x, y, and z coordinate directions.

[0072] The goal of this application is to use RDOA to measure vector and the location of distributed radar sites To realize the positioning solution of the radiation source.

[0073] Step 2: Construct system performance evaluation indicators and optimization problems.

[0074] To facilitate derivation, RSA is first discretized and and represents the set of grid points in RSA and each KS. The set of all KS is defined as therefore, and It can be expressed as

[0075]

[0076] Where: n =[x n ,y n ,z n ] T Represents the coordinates of the nth grid point in the RSA region, N rsa and are the number of grid points in RSA and each KS, respectively.

[0077] (1) KS positioning performance evaluation indicators

[0078] In passive positioning tasks, the root mean square position error (RMSPE) is usually used to measure the positioning performance of the system, and its expression is:

[0079]

[0080] Where: tr(·) represents the trace of the matrix, P du is the covariance matrix of the positioning error, which can be expressed as

[0081]

[0082] Where: B = (F T F) -1 F T , F and M are represented as follows

[0083]

[0084] in

[0085]

[0086] Define the distributed radar azimuth normal pointing vector as α = [α0, α1, …, α N-1 ] T , the maximum scanning angle vector in azimuth is Let the distributed radar deployment scheme be Φ = [s, α]. According to equation (11), in the KS area under the radar deployment scheme Φ, any grid point The RMSPE can be expressed as

[0087]

[0088] In each KS, the maximum RMSPE of all grid points is taken to measure the system positioning performance under the node deployment scheme Φ, which is expressed as

[0089]

[0090] (2) RSA monitoring performance evaluation indicators

[0091] When the grid point in RSA When covered by beams of 4 or more radar nodes, is the effective monitoring point. By calculating the ratio of effective monitoring points to all grid points of RSA, it is called the effective monitoring area coverage rate, which is used as an evaluation index to measure the monitoring performance of the system, and is expressed as follows

[0092]

[0093] in

[0094]

[0095] Used to determine Is it a valid monitoring point? i represents the effective reconnaissance interval of the i-th radar node under the node deployment scheme Φ, that is, the intersection of the beam scanning range and the RSA; b(·) represents a Boolean function, which is used to determine whether the specific conditions in the brackets are met.

[0096] (3) Optimization problem construction

[0097] Considering the different occurrence probabilities of radiation sources in different KS and their different effects on radar detection performance, in the specific deployment strategy, a set of positioning weights w is preset for all KS loc and the expected positioning accuracy δ ex , defined as the following vector form:

[0098]

[0099] in: and They represent the positioning weight and expected positioning accuracy of the kth KS, which are related to the importance of KS. Combining equations (17) and (21), the objective function is defined as:

[0100]

[0101] in: The effect function representing the KS positioning performance.

[0102]

[0103] Wherein: β1 and β2 are penalty coefficients, satisfying β1>β2>0, and β1+β2=1.

[0104] In addition, to achieve 3D TDOA positioning, each KS needs to be covered by at least 4 nodes at the same time. Given the limited coverage of the radar node beam, the node deployment scheme Φ needs to be constrained. Since KS is usually a closed area, the radar node beam only needs to cover the boundary points of each KS to meet the requirements. Define the boundary point set of the kth KS as in represents the number of boundary points. Then the node deployment plan Φ needs to satisfy the following constraints:

[0105]

[0106] In summary, the distributed radar deployment strategy optimization problem for TDOA positioning can be described as the following single-objective optimization problem with complex constraints:

[0107]

[0108] If we want to take into account both the distributed positioning performance in the KS area and the monitoring performance in the RSA area, we can combine the objective function of formula (22) and the monitoring performance evaluation index in formula (18) to form a multi-objective optimization problem. The corresponding optimization problem can be described as

[0109]

[0110] in: represents the objective function vector, N obj is the number of objective functions. In this embodiment, the number of objective functions is 2, that is, N obj =2, f(f1,f2), in formula (26),

[0111] Step 3: Distributed radar deployment strategy optimization based on RC-MOPSO algorithm.

[0112] The Region-Constrained Multi-Objective Particle Swarm Optimization (RC-MOPSO) algorithm is used to solve the optimization problem in step 2 to obtain the optimal deployment strategy. The specific steps of the algorithm are as follows:

[0113] (1) Constrained random initialization

[0114] Assume that the population size is M, that is, the number of particles is M. In the tth iteration, the positions and velocities of the mth, m=1, 2, ..., Mth particles in the population are x m (t) and v i (t). The position x of each particle m (t) represents a radar node deployment scheme

[0115] First, the node position information of particles in the population Initialize.

[0116] In actual distributed radar systems, due to limited resources, it is impossible to allocate 4 nodes to each KS for TDOA positioning. Therefore, the beams of some radar nodes need to cover at least 2 or more KSs. Assume that before initialization, the strategy has given the corresponding coverage relationship between the nodes and each KS, and define the set of KS boundary points that need to be covered by node i, i = 0, 1, ..., N-1 as

[0117]

[0118] in: Indicates the number of boundary points of KS that need to be covered. To meet the beam coverage requirements, node i and The angle between any two points in the image should be smaller than the maximum scanning angle in the azimuth direction. Considering that the node deployment location cannot exceed RDA, s should satisfy

[0119]

[0120] in:

[0121]

[0122] At initialization, the node position of the particle Randomly distributed in the area middle.

[0123] Secondly, the node normal points to Initialize.

[0124] In the node beam coverage area and Under the initial condition of no intersection, the node normal direction will be scanned clockwise and counterclockwise, and the node beam coverage will be recorded for the first time. The normal direction of all grid points in is α min,i (t) and α max,i (t), where α min,i (t)<α max,i (t), α min,i (t),α max,i (t)∈[0,2π].

[0125] The node normal direction should satisfy

[0126]

[0127] Where: α min (t) = [α min,0 (t),…,α min,N-1 (t)] T , α max (t) = [α max,0 (t),…,α max,N-1 (t)] T The initial direction that the node normal points to Randomly distributed in [α min (0),α max (0)] area. Formula (30) means that the node normal pointing vector is within the lower and upper bounds of the normal pointing, so as to ensure that the node beam can always cover the corresponding key sub-area.

[0128] (2) Particle velocity and position update rules

[0129] The update rules for the velocity and position of the mth particle in the population are as follows:

[0130] v m (t+1)=w(t)v m (t)+c1r1(t)(p m (t)-x m (t))+c2r2(t)(g(t)-x m (t)) (31)

[0131] x m (t+1)=x m (t)+v m (t+1) (32)

[0132] Where: x m (t), v m (t), x m (t+1) and v m (t+1) represents the current position and velocity of the t-th and t+1-th generation particles respectively; w(t) = 0.9-0.5×(t / T max ) is the inertia weight, T max represents the maximum number of iterations; c1 and c2 are the individual learning factor and the population learning factor respectively; p m (t) and g(t) represent the individual optimal position of the particle and the global optimal position of the population, respectively, which are continuously updated during the iteration process; the random numbers r1(t), r2(t) obey the uniform distribution in the interval [0,1].

[0133] In the iterative update process of the particle swarm algorithm, the particle position x m (t) must satisfy the constraints defined in equations (28) and (30). In addition, this step sets a boundary for the particle velocity, i.e. [v min ,v max Specifically, if the velocity or position of a particle exceeds the constraint interval, it is constrained to return to the nearest boundary.

[0134] (3) Individual optimal particle update rule

[0135] At the tth iteration, if the current position x of particle m is m (t) dominates p m (t-1), it is updated to the new individual optimal position; if x m (t) is p m (t-1) dominates, the individual optimal position is not updated; if x m (t) and pm (t-1) do not dominate each other, then the optimal position of the individual is x with a probability of 50%. m (t) or p m (t-1); the domination means that the target fitness function value is better than the previous individual optimal particle position.

[0136] The update formula is as follows:

[0137]

[0138] Among them: the random number r3(t) obeys the uniform distribution in the interval [0,1].

[0139] (4) Global particle update rules

[0140] MOPSO uses an external archive mechanism to store the optimal solution set during the iteration process, and updates the external archive in real time according to the dominance relationship between individual optimal particles. The global optimal particle will be selected from the external archive. In order to ensure the diversity of the solution set, the particle in the most "sparse" part of the external archive is selected as the global optimal particle. Let the size of the external archive be L, and let the particle l in the external archive at the tth iteration be y l (t), l=1,2,...,L, define the relative distance between the q,q=2,...,L-1th particle and the surrounding particles as:

[0141]

[0142] Among them: |·| means taking the absolute value. The particle with the largest relative distance to the surrounding is selected as the global optimal particle:

[0143]

[0144] The particle with the best comprehensive performance is selected from the optimized solution or solution set as the final deployment strategy output.

[0145] The embodiment of the present application comprehensively considers the joint optimization of node position and normal orientation, constructs a single-objective optimization problem for positioning tasks and a multi-objective optimization problem that takes into account both positioning and monitoring tasks, and proposes a regional constrained multi-objective particle swarm optimization algorithm RC-MOPSO to obtain the optimal deployment solution. Compared with the random deployment solution, the present invention shows significant advantages in improving the system positioning and monitoring performance.

[0146] Examples:

[0147] Step 1: Distributed radar positioning scenario modeling.

[0148] The simulation example considers a non-overlapping positioning scenario of RSA and RDA, where the horizontal and vertical coordinates of RSA are distributed in the range of -200km to 200km and 0km to 380km, respectively, and the horizontal and vertical coordinates of RDA are distributed in the range of -40km to 40km and 0km to 80km, respectively, and the grid size is 2km×2km. Two non-overlapping KS areas are set in the RSA area, and the main parameters are set as follows

[0149]

[0150] The transmitting power of the radiation source is 1500W. The distributed radar system used to perform the radiation source positioning task consists of 5 nodes, and its performance parameters are set as follows:

[0151]

[0152]

[0153] Step 2: Construct system performance evaluation indicators and optimization problems.

[0154] Considering the importance of different KS, the expected positioning accuracy of KS1 and KS2 is set to 330m, and the positioning weights are 0.4 and 0.6 respectively. Based on the above conditions, the single-target positioning performance optimization problem and the multi-objective optimization problem taking into account both positioning and monitoring performance are constructed according to equations (25) and (26).

[0155] Step 3: Distributed radar deployment strategy optimization based on RC-MOPSO algorithm.

[0156] The population size of the RC-MOPSO algorithm is set to 100, the maximum number of iterations is 150, and the individual learning factor and population learning factor are both 1.4.

[0157] Figure 3 The performance comparison of 1000 random deployment schemes and the deployment scheme optimized by the present invention is shown. It can be seen that the single-objective optimization scheme has the best positioning performance, but is inferior to the random deployment scheme in monitoring performance. The multi-objective optimization scheme has achieved a good balance in taking into account positioning and monitoring performance, and its overall performance is better than random deployment and single-objective optimization deployment.

[0158] Figure 4 , Figure 5 and Figure 6The deployment schemes with the best comprehensive performance selected from random deployment, single-objective optimization and multi-objective optimization solutions are shown respectively. Specifically, the worst RMSPE of the random deployment scheme in the two KSs is 533.8m and 283.7m, and the effective monitoring area coverage is 62.6%. In contrast, the single-objective optimization deployment scheme meets the expected positioning accuracy, but brings a 2.6% monitoring performance loss. The multi-objective optimization scheme has positioning errors of 311.1m and 260.1m in the two KSs, respectively, and at the same time increases the monitoring coverage to 65.8%, achieving a good balance effect.

[0159] In summary, the above are only implementation cases of the present invention and are not intended to limit the protection scope of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A distributed radar deployment strategy optimization method for TDOA positioning, characterized in that: The specific process is: Step 1: Distributed radar positioning scenario modeling for TDOA positioning; Step 2, construct system performance evaluation indicators and optimization problems, the evaluation indicators include key sub-area KS positioning performance evaluation indicators and radar reconnaissance area RSA monitoring performance evaluation indicators; the KS positioning performance evaluation indicator is: in each KS, take the maximum root mean square positioning error RMSPE of all grid points, and use it to measure the system positioning performance under the node deployment scheme Φ, the RSA monitoring performance evaluation indicator is: calculate the proportion of effective monitoring points to all RSA grid points, called the effective monitoring area coverage, as an evaluation indicator for measuring system monitoring performance; the optimization problem includes a single-objective optimization problem for positioning tasks and a multi-objective optimization problem that takes into account both positioning and monitoring tasks; Step 3: Solve the optimization problem constructed in step 2 to obtain the distributed radar optimization deployment strategy.

2. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 1 is characterized in that: The KS positioning performance evaluation index is: in, represents any grid point in the KS region under the radar deployment scheme Φ RMSPE, Φ = [s, α], s represents the distributed radar node position vector, α is the azimuth normal pointing vector of the distributed radar.

3. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 1 is characterized in that: The RSA monitoring performance evaluation index is: Where b(·) represents a Boolean function, A i represents the effective reconnaissance interval of the i-th radar node under the node deployment scheme Φ, Represents a grid point in RSA.

4. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 2 is characterized in that: Based on the KS positioning performance evaluation index The objective function is established as: in: represents the effect function of KS positioning performance, To set the positioning weight; Among them: β1 and β2 are penalty coefficients, satisfying β1>β2>0, and β1+β2=1, For the expected positioning accuracy, Based on the objective function and the RSA monitoring performance evaluation index, a single-objective positioning performance optimization problem and a multi-objective optimization problem that takes both positioning and monitoring performance into consideration are constructed.

5. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 4 is characterized in that: The single target positioning performance optimization problem is: The multi-objective optimization problem taking into account both positioning and monitoring performance is: in, Indicates that the distributed radar is located in the radar deployment area. represents the kth KS Each boundary point is covered by the beams of more than four radar nodes.

6. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 1 is characterized in that: Step 1: When modeling distributed scenarios, measure the error n r The noise considered includes constant noise SNR Correlated Noise Its covariance matrix Q r for:

7. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 6 is characterized in that: The signal-to-noise ratio is related to the noise for: Among them: B j and B n They represent the signal bandwidth of the radiation source and the noise bandwidth of the receiver respectively; T represents the observation time; SNR i It represents the SNR of the signal transmitted by the radiation source received by the i-th radar node, i=0,1,…,N-1.

8. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 7 is characterized in that: The root mean square positioning error RMSPE is: based on the covariance matrix Q r Obtained by calculation.

9. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 1, characterized in that: Step three is based on the RC-MOPSO algorithm. By introducing regional constraints in the particle initialization and update process, it is ensured that particles always meet the complex constraints of the optimization problem during the iteration process, and then the optimal deployment strategy is obtained to achieve the optimal balance between the system positioning performance and monitoring performance.

10. The distributed radar deployment strategy optimization method for TDOA positioning according to claim 1, characterized in that: The specific process of step three is: (1) Node position information of particles in the population and the node normal points to Initialize and set constraints including: particle deployment position cannot exceed RDA and node normal pointing vector is within the lower and upper bounds of normal pointing; (2) Setting the updating rules and constraints for the speed and position of particles in the population. The constraints are: the particle speed cannot exceed the preset boundary [v min ,v max ]; (3) Set the individual optimal particle update rule: At the tth iteration, if the current position x of particle m is m (t) dominates p m (t-1), it is updated to the new individual optimal position; if x m (t) is p m (t-1) dominates, the individual optimal position is not updated; if x m (t) and p m (t-1) do not dominate each other, then the optimal position of the individual is x with a set probability m (t) or p m (t-1); (4) The global particle update rule is set as follows: the sparsest particles in the external archive are selected as the global optimal particles, and the external archive is updated in real time according to the dominance relationship between the individual optimal particles.

Images