Fully connected network structure selection method for distributed MIMO radar target positioning

Abstract

This application discloses a method for selecting a fully connected network structure for distributed MIMO radar target positioning, relating to the field of signal processing technology. This application includes collecting the target's echo signal and arranging it into a column of received signals in the order of signal sampling values; processing the received signals and calculating the maximum likelihood estimate of the time delay of each signal path; integrating the time delay estimates of all paths into an estimation vector, and using the FCN as an estimator based on the estimation vector to obtain the final target object position estimate; deriving a mean square error bound for a given FCN, training set, and training method, and constructing an optimization problem for network structure design based on the mean square error bound; and using a genetic algorithm to solve the optimization problem for network structure design and obtain the optimal FCN structure. The FCN structure selected in this application achieves better estimation performance.

Description

Technical Field

[0001] The present application relates to the field of signal processing technology, and in particular to a method for selecting a fully connected network structure for distributed MIMO radar target positioning. Background Art

[0002] Target localization is a crucial issue in distributed Multiple Input Multiple Output (MIMO) radars. In this type of problem, intermediate observations, such as time of arrival, time difference of arrival, or angle of arrival, are first estimated through local processing. These intermediate observations are then sent to a fusion center to estimate the target's position. While intermediate observations are generated through local signal processing, the mapping between them and the target's position remains complex.

[0003] Learning-based methods can better fit complex mappings within a controllable complexity, but the performance of learning-based methods is closely related to the structure of the neural network.

[0004] Therefore, it is necessary to study the FCN structure design method for distributed MIMO radar target positioning. Summary of the Invention

[0005] To address the shortcomings of the prior art, this application provides a method for selecting a fully connected network structure for distributed MIMO radar target localization, addressing the aforementioned issues. Because the performance of MIMO radar target localization is strongly related to the fully connected network (FCN) structure, and the performance of learning methods is largely related to the structure of the neural network, this application utilizes FCNs from machine learning to achieve target localization.

[0006] This application is implemented through the following technical solutions:

[0007] In a first aspect, the present application provides a method for selecting a fully connected network structure for distributed MIMO radar target positioning, comprising:

[0008] Collect the target's echo signal and arrange it into a column of received signals in the order of signal sampling values;

[0009] Process the received signal and calculate the maximum likelihood estimate of the delay of each signal path;

[0010] Integrate the delay estimates of all paths into an estimation vector, and use FCN as an estimator based on the estimation vector to obtain the final target object position estimate;

[0011] Derive the mean squared error bound for a given FCN, training set, and training method and formulate an optimization problem for network structure design based on the mean squared error bound.

[0012] Genetic algorithm is used to solve the optimization problem of network structure design and obtain the optimal FCN structure.

[0013] Optionally, collecting the echo signal transmitted by the MIMO radar to the target and arranging it into a column of received signals in the order of sampling values ​​includes:

[0014] The transmission signals transmitted by multiple transmitters of the distributed MIMO radar system to the target are received by multiple receivers after passing through the target and are arranged in sequence into a column of received signals based on the signal sampling values ​​of the received signals. The transmission signals are orthogonal and remain orthogonal over time. The column of received signals includes the reflection coefficient of the target object under the path, Gaussian noise with time white and space white, the transmission signal power and the sampling time interval.

[0015] Optionally, the training set is generated based on the relationship between time delay and position, and the process of collecting the training set, that is, the process of constructing the training set, includes:

[0016] An area is selected, and two dimensions of the two-dimensional coordinate system are sampled at intervals. The sampled data are processed, including processing the time delay until each element of the time delay is within the range [0, 1], and normalizing the target object position until each element of the target object position is within the range [0, 1].

[0017] Optionally, deriving a mean square error bound for a given FCN, a training set, and a training method and constructing an optimization problem for network structure design based on the mean square error bound includes:

[0018] The input of FCN is the normalized time delay, and the output is linearly transformed to obtain the final target object position estimate. MSE is used as the loss function in the training stage. When the number of training iterations reaches the set value, the iteration stops and the optimized FCN network parameters are obtained.

[0019] Optionally, for FCN, the workflow under a given training set includes:

[0020] Training phase: obtaining the optimized FCN network parameters;

[0021] Testing phase: Calculate the distribution of the delay estimates. The forward propagation of each FCN layer includes a linear transformation and an activation function. The output layer undergoes a backward linear transformation to obtain the target object's position estimate. Obtain the MSEB at a given location, and then use the MSEB to design the optimal FCN structure. Under the condition of restricting the depth and size of the FCN network, design the optimal network configuration and depth (the depth refers to the number of hidden layers in the FCN). Develop an optimization problem for constructing the network structure design, namely an integer programming problem, and then design a genetic algorithm to solve the integer programming problem.

[0022] Optionally, the use of a genetic algorithm to solve the optimization problem of network structure design to obtain the optimal FCN structure includes:

[0023] Construct an initialization population, where the population represents a bunch of FCN structures, and any FCN in it is called an individual;

[0024] Calculate the fitness value of each individual in the initial population;

[0025] The optimal FCN structure is obtained after multiple evolution iterations of the initial population, where each iteration includes selection, crossover and mutation operations.

[0026] In a second aspect, the present application further provides a fully connected network structure selection device for distributed MIMO radar target positioning, comprising:

[0027] The acquisition module is used to collect the echo signal of the target and arrange it into a column of received signals in the order of signal sampling values;

[0028] A calculation module, configured to process received signals and calculate a maximum likelihood estimate of the time delay of each signal path;

[0029] A fusion center is used to integrate the delay estimates of all paths into an estimation vector, and use FCN as an estimator based on the estimation vector to obtain the final target object position estimate;

[0030] An optimization problem construction module is used to derive the mean square error bound under a given FCN, training set, and training method and construct an optimization problem for network structure design based on the mean square error bound;

[0031] The processing module is used to use genetic algorithms to solve the optimization problem of network structure design and obtain the optimal FCN structure.

[0032] In a third aspect, the present application provides an electronic device comprising: a processor and a memory communicatively connected to the processor.

[0033] Memory stores computer-executable instructions;

[0034] The processor executes the computer-executable instructions stored in the memory, and the processor implements the method described in any one of the first aspects of the present application.

[0035] In a fourth aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores computer-executable instructions, and when the computer-executable instructions are executed by a processor, they are used to implement the method as described in any one of the first aspects.

[0036] In a fifth aspect, the present application provides a computer program product, comprising a computer program, which, when executed by a processor or a chip, implements the method as described in any one of the first aspects.

[0037] This application has the following advantages and beneficial effects:

[0038] This application can obtain the MSEB of the network for target localization tasks when the FCN, training set, and training method are fixed. Based on the MSEB, a GA algorithm is designed to select the most suitable FCN structure from a theoretical perspective. The FCN structure selected in this application achieves better estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the embodiments of the present application, constitute a part of the present application, and do not constitute a limitation of the embodiments of the present application. In the drawings:

[0040] Figure 1 This is a schematic diagram of the FCN provided in an embodiment of the present application.

[0041] Figure 2 This is a coding diagram of the GA algorithm provided in the embodiment of the present application.

[0042] Figure 3 1 is an estimated performance diagram of FCNs with different structures designed based on GA provided in an embodiment of the present application.

[0043] Figure 4 This is a flow chart of the method provided in the embodiment of the present application. DETAILED DESCRIPTION

[0044] Before describing any embodiment of the present application in detail, it should be understood that the application of the present application is not limited to the details of the structure shown in the following description or the drawings. The present application may adopt other embodiments and may be implemented or executed in various ways. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative improvements are within the scope of protection of this application.

[0045] For the convenience of description, we first make the following definitions:

[0046] () Tis transposed, () H is the conjugate transpose, Re{·} is the real part, ⊙ is the Hadamard product, ε{·} is the expectation, I represents the identity matrix, [·] i represents the i-th element of a vector, [·] i,j represents the (i, j)th element of the matrix, ||·||2 represents the L2 norm, and ||·||0 represents the L0 norm.

[0047] This application provides a method for selecting a fully connected network structure for distributed MIMO radar target positioning, such as Figure 4 As shown, the following steps are included:

[0048] Step 1: Arrange the signal sampling values ​​contributed by the mth transmitter received by the nth receiver of the distributed MIMO radar system into a column in order to form the received signal r nm ;

[0049] r nm =[r nm [1],...,r nm [K]] T

[0050] =u nm +w nm ,

[0051] in,

[0052]

[0053] u nm =[u nm [1],...,u nm [K]] T

[0054] w nm =[w nm [1],...,w nm [K]] T

[0055]

[0056] The number of transmitting antennas in a distributed MIMO radar system is M, the number of receiving antennas is N, and the distance between each antenna is very far; the coordinates of the mth transmitting antenna are (x tm ,y tm ), the coordinates of the nth receiving antenna are (x rn ,y rn ); a stationary target object is located at (x, y), the position of which is unknown; the transmission signal of the mth transmitting antenna is at kT s The sampling value at the moment is Where E is the total transmitted signal power, T s is the sampling time interval, k is the sampling number, s m Represents the transmitted signal; the distance between the mth transmitting antenna and the target object is d tm , the distance between the nth receiving antenna and the target object is d rn ; τ nm represents the delay of the (n,m)th path, ζ nm represents the reflection coefficient of the target object in the path, assuming it is known; w nm [k] represents temporal and spatial white Gaussian noise, and its variance Known; define unknown parameter vector θ=[x,y] T ;

[0057] Step 2: Obtain the maximum likelihood estimate of each path delay locally

[0058] Step 3: The fusion center integrates the delay estimates of all paths into a vector And based on the estimated vector, the final target object position estimation is obtained Use FCN as the fusion center estimator to complete the target object position estimation;

[0059] Step 4: Derive the mean square error bound (MSEB) for a given FCN, training set, and training method.

[0060] Step 5: Based on MSEB, construct the optimization problem of network structure design;

[0061] Step 6: Use Genetic Algorithm (GA) to solve the optimization problem of network structure design; first, construct an initial population;

[0062] Step 7: Calculate the fitness value of each individual in the initial population;

[0063] Step 8: The optimal FCN structure is obtained after multiple evolution iterations of the initial population, where each iteration includes selection, crossover, and mutation operations.

[0064] Example 1:

[0065] Consider a distributed MIMO radar system with M transmitting antennas and N receiving antennas, where the mth (m=1,...,M) radar transmitting antenna is located at (x tm ,y tm ), the nth (n=1,...,N) radar receiving antenna is located at (x rn ,yrn ). The transmission signal of the mth radar transmitting antenna is in kT s The sampling value at the moment is in, E is the total transmitted signal energy, T s is the sampling interval. Assume that a stationary target object is located at (x, y). To simplify the analysis, assume that the transmitted signals are orthogonal and remain orthogonal after the delay. Then, at kT s The signal contributed by the mth transmitter received by the nth receiving antenna at time is

[0066]

[0067] And the received signal vector is

[0068]

[0069] in

[0070] u nm =[u nm [1],...,u nm [K]] T (3)

[0071] w nm =[w nm [1],...,w nm [K]] T (4)

[0072]

[0073] Assume that the clutter plus noise w nm [k] is a zero-mean complex Gaussian distribution of temporal and spatial whitening with a known variance of Right now therefore, τ nm represents the time delay of the (n,m)th path. For simplicity, it is assumed that the reflection coefficient of the target object ζ nm is known. Define the position parameter vector

[0074] θ=[x,y] T (6)

[0075] Through local signal processing, the maximum likelihood estimate of each path delay can be obtained The fusion center fuses the delay estimates of all paths into a vector

[0076]

[0077] The position of the target object is estimated based on this vector. The most basic FCN in the neural network is used as the estimator of the fusion center to obtain the position estimation of the target object.

[0078] The good performance of a neural network benefits from the data collected during the training phase. Therefore, a training set is necessary. To simplify the derivation of the MSEB, a noise-free training set is constructed. The training data is directly generated based on the following relationship between time delay and position:

[0079]

[0080] The training data collection process is as follows: for a region of interest G = {(x,y)|x∈[x min ,x max ],y∈[y min ,y max ]}, the x-axis and y-axis are Δ x and Δ y For the i-th position The corresponding delay is S tr is the number of training data. Considering that the order of magnitude difference between the time delay and the position of the target object is too large, it is not ideal to use it directly as training data. Therefore, the collected data is processed as follows: Multiply it by a constant cT s T L Make each of its elements within the range [0,1], that is

[0081]

[0082] T L is the pulse width of the transmitted signal. Use normalization in machine learning to make each element within the range [0,1], that is,

[0083]

[0084] in

[0085]

[0086] α=[x min ,y min ] T (12)

[0087] Therefore, the training set can be written as in is the i-th training data, is its corresponding label.

[0088] FCN can be viewed as a parametric equation f φ :h0→h L+1 , where φ represents the set of all trainable parameters, is a real input vector of Y0×1, It's Y L+1 ×1 real output vector, L is the number of hidden layers. The input of the neural network is The forward propagation of the lth layer of the neural network can be written as follows

[0089] z l =W l h l-1 +b l ,h l =ρ l (z l ) (13)

[0090] where ρ l (·) is the activation function. The hidden layer uses a nonlinear activation function, and the output layer uses a linear activation function. l and b l is the weight matrix and bias vector of the lth layer, and the parameters to be trained for the entire FCN can be written as

[0091]

[0092] vec{·} represents vectorized operation,

[0093]

[0094] is the total number of FCN parameters to be trained. The output of the neural network is Based on this output, the final target object position estimate can be obtained through the following linear transformation

[0095]

[0096] During the training phase, MSE is used as the loss function

[0097]

[0098] in, is the output of the FCN corresponding to the i-th training data sample, is its corresponding label. The dth iteration of the network trainable parameters is

[0099]

[0100] where Ω{·} represents the optimizer function, is the training loss The gradient of φ is in φ=φ( d-1 ) is the value at which η is the internal parameter of the optimizer; when the number of training iterations reaches the set value D, the iteration stops. At this time, the loss function should be less than a preset value δ, and the optimized FCN network parameters are obtained.

[0101]

[0102] Next, we will give the derivation process of MSEB under a given neural network, training set, and training method. The workflow of the neural network includes two stages: training and testing. In the training stage, since noise-free training data is used, the optimized parameter φ after training can be directly obtained. * .

[0103] In the testing phase, we first need to obtain the input distribution. Under the high signal-to-clutter-plus-noise ratio (SCNR) assumption, it is an asymptotically unbiased estimator that follows a Gaussian distribution, and its variance is asymptotically close to the following Cramer-Rao bound (CRB):

[0104]

[0105] Among them, Re{·} represents the real part operation. Therefore, we can get Distribution in,

[0106] yes The CRB matrix, its (i,j)th element is

[0107]

[0108] The test phase only includes forward propagation, and the forward propagation of each layer includes a linear transformation and an activation function. l The mean and variance of and Put h l The mean and variance of and In particular, the mean and variance of the input layer are

[0109]

[0110]

[0111] For the hidden layer, z l The mean and variance of

[0112]

[0113]

[0114] h l The mean and variance of

[0115]

[0116]

[0117] Where ⊙ represents the Hadamard product. Since the output layer uses a linear activation function, its mean and variance are

[0118]

[0119]

[0120] The output is linearly transformed to obtain the position estimate of the target object, so we can get The mean and variance of

[0121]

[0122]

[0123] Therefore, the MSEB at a given position can be obtained as

[0124]

[0125] Considering that the initialization method is random and the target object position will appear in the range of interest,

[0126] By integrating the initialization method and the target object position, we can get the following MSEB expression:

[0127]

[0128] Among them, p(φ (0) ) represents the probability density function of the initialization method, and p(θ) is the uniform distribution in the region G.

[0129] Next, consider using the MSEB in (33) to design the optimal FCN structure. For convenience, we first define some quantities related to the FCN structure, define the number of hidden layers L of the FCN as the depth of the network, and define

[0130]

[0131] Defined as the size of the network,

[0132]

[0133] is defined as the configuration of the network. Considering that MSEB is a function of various network parameters, and the main concern is the structural design of the network, the MSEB in (33) is written as MSEB(y,L) to highlight the variables that need to be optimized. Considering that the input and output dimensions of FCN are fixed, only the structure design of the hidden layer is performed, that is, the task of designing the number of hidden layers and the number of nodes in each layer of FCN is to design the optimal network configuration y under the condition of limiting the depth and size of the network. opt and depth L opt , which can be organized into the following optimization problem

[0134]

[0135] Among them, Y max is the upper bound of the size, L max is the upper bound of the depth.

[0136] Considering that the optimization problem in formula (36) is an integer programming problem, GA is designed to solve the problem. GA obtains the optimal solution through multiple iterative evolution of the population. In this problem, the population represents a bunch of FCN structures, and any FCN in it is called an individual. First, a fixed-length encoding method is used to encode each individual. Figure 2 As shown, for an FCN that satisfies the conditions in (36), it can be represented by an L max ×1 real-valued vector Encode, where the first L elements of p are the number of nodes in the FCN hidden layer, and the remaining elements are 0, that is,

[0137]

[0138] After encoding, the optimization problem P1 in (36) is rearranged into the following form:

[0139]

[0140] Each individual has a corresponding fitness value. The higher the fitness value of an individual, the better the individual's performance and the greater the probability of survival. Therefore, the negative MSEB is set as the fitness function for this problem.

[0141] Algorithm 1 presents a GA algorithm based on MSEB for solving network structure design problems. First, the algorithm randomly generates Z individuals as the initial population (line 1). Then, the fitness of each individual in the initial population is calculated (line 2). The initial population then evolves over T generations (lines 3-15), ultimately returning the optimal individual.

[0142] During the evolution process, an empty set D is first initialized. t It is used to encapsulate the offspring (line 5), which are generated by the selected parents through crossover and mutation operations (lines 6-10). t Individuals that do not meet the size constraints are removed (line 11). t After the fitness of each individual in P is obtained (line 12), the environment selection operation is performed from P t ∪D t Select individuals as the new generation of population P t+1 (Line 13). The |·| in line 6 represents the cardinality of the set.

[0143]

[0144] How this application works

[0145] 1. How to generate the initial population P0 in Algorithm 1

[0146]

[0147]

[0148] 2. Selection, crossover, and mutation operations in Algorithm 1

[0149] 1) Selection: Use the commonly used binary tournament method to perform the selection operation, that is, randomly select two individuals from the population and retain the one with the higher fitness value as the parent individual. Repeat the above process to obtain another parent individual.

[0150] 2) Crossover Operation

[0151]

[0152]

[0153] 3) Mutation Operation

[0154]

[0155]

[0156] Among them, {·} / a represents removing element a from the set {·}.

[0157] 3. Environment selection operation in Algorithm 1

[0158]

[0159]

[0160] 4. The effectiveness of the proposed network structure design method is verified through simulation. The simulation parameters are set as follows:

[0161] The transmitting antenna and receiving antenna of the distributed MIMO radar are both 70km away from the origin. The transmitted signal is as follows

[0162]

[0163] Among them, f Δ Is the frequency compensation between adjacent transmitted signals. Set f Δ =500Hz and T L = 0.01s. SCNR is defined as follows: In the simulation, Set to 0.01.

[0164] The sampling area of ​​the training data is G = {(x,y)|x∈[2.5,12.75]km,y∈[1.2,11.2]km}. In this area, Δ x =250m is used to sample the x-axis, and Δ y =200m is the interval for sampling the y-axis. Therefore, the training set contains S tr =50 2 = 2500 training data points. For the test set, the signal-to-noise ratio range was considered from -5dB to 30dB. At each signal-to-noise ratio, 10 objects were considered within region G. The activation function used in the hidden layer was the hyperbolic tangent activation function (Tanh). The optimizer used during training was the ADAM optimizer, and the number of training iterations was 100.

[0165] exist Figure 3 In this paper, the effect of structure on FCN estimation performance is studied, where the upper bound of FCN depth is set to L max =3, the upper limit of the network size is set to Y max = 16. The best and worst structures of FCN are obtained by GA, where the population size is Z = 30, the maximum number of generations is T = 30, and the crossover probability is p c =0.9, mutation probability p m= 0.2. The performance of the optimal structure (MSEB) selected by the GA algorithm is found to be close to the optimal performance (SMSE: MLE). Furthermore, the performance of the worst structure (MSEB: worst GA) is also presented. Two FCNs with size Y = 16 and depth L = 3 are used as specific examples to illustrate the impact of structure on performance. One FCN has the configuration y = [8, 4, 4], denoted as FCN1, and the other has the configuration y = [8, 1, 7], denoted as FCN2. The figure shows that the performance of FCN1 (SMSE: FCN1) is close to that of the optimal structure, and its corresponding MSEB (MSEB: FCN1) is a tight lower bound at high SCNR. In contrast, the estimated performance of FCN2 (SMSE: FCN2) is far less than ideal, approaching that of the worst structure. Similarly, its MSEB (MSEB: FCN2) is a tight lower bound at high SCNR.

[0166] This example provides several conclusions: MSEB is a tight lower bound at high SCNR, so it can be used to guide network structure design. Furthermore, FCN performance is affected by its structure, and the designed GA algorithm can effectively select a network structure that is close to optimal.

[0167] The specific implementation methods described above further illustrate the purpose, technical solutions and beneficial effects of this application. It should be understood that the above description is only the specific implementation methods of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of this application should be included in the scope of protection of this application.

Claims

1. A method for selecting a fully connected network structure for distributed MIMO radar target positioning, characterized in that: include: Collect the target's echo signal and arrange it into a column of received signals in the order of signal sampling values; Process the received signal and calculate the maximum likelihood estimate of the delay of each signal path; Integrate the delay estimates of all paths into an estimation vector, and use FCN as an estimator based on the estimation vector to obtain the final target object position estimate; Derive the mean squared error bound for a given FCN, training set, and training method and, based on the mean squared error bound, construct an optimization problem for network structure design: ； in, is the upper bound of the size, is the upper bound of the depth, MSEB is the mean square error bound, For the neural network Layer, optimal network configuration and depth ; Genetic algorithm is used to solve the optimization problem of network structure design and obtain the optimal FCN structure.

2. The method according to claim 1, characterized in that The step of collecting the target's echo signals and arranging them into a column of received signals in the order of signal sampling values ​​includes: The transmission signals transmitted by multiple transmitters of the distributed MIMO radar system to the target are received by multiple receivers after passing through the target and are arranged in sequence into a column of received signals based on the signal sampling values ​​of the received signals. The transmission signals are orthogonal and remain orthogonal over time. The column of received signals includes the reflection coefficient of the target object under the path, Gaussian noise with time white and space white, the transmission signal power and the sampling time interval.

3. The method according to claim 1, characterized in that The training set is generated based on the relationship between the time delay and the position. The process of collecting the training set, that is, the process of constructing the training set, includes: An area is selected, and two dimensions of the two-dimensional coordinate system are sampled at intervals. The sampled data are processed, including processing the time delay until each element of the time delay is within the range [0, 1], and normalizing the target object position until each element of the target object position is within the range [0, 1].

4. The method according to claim 3, characterized in that The method of deriving a mean square error bound for a given FCN, a training set, and a training method and constructing an optimization problem for network structure design based on the mean square error bound includes: The input of FCN is the normalized time delay, and the output is linearly transformed to obtain the final target object position estimate. MSE is used as the loss function in the training stage. When the number of training iterations reaches the set value, the iteration stops and the optimized FCN network parameters are obtained.

5. The method according to claim 4, characterized in that For FCN, the workflow under a given training set includes: Training phase: obtaining the optimized FCN network parameters; Testing phase: Calculate the distribution of the delay estimates. The forward propagation of each FCN layer includes a linear transformation and an activation function. The output layer undergoes a backward linear transformation to obtain the target object's position estimate. Obtain the MSEB at a given location, and then use the MSEB to design the optimal FCN structure. Under the condition of restricting the depth and size of the FCN network, design the optimal network configuration and depth (the depth refers to the number of hidden layers in the FCN). Develop an optimization problem for constructing the network structure design, namely an integer programming problem, and then design a genetic algorithm to solve the integer programming problem.

6. The method according to claim 5, characterized in that The genetic algorithm is used to solve the optimization problem of network structure design to obtain the optimal FCN structure, including: Construct an initialization population, where the population represents a bunch of FCN structures, and any FCN in it is called an individual; Calculate the fitness value of each individual in the initial population; The optimal FCN structure is obtained after multiple evolution iterations of the initial population, where each iteration includes selection, crossover and mutation operations.

7. A fully connected network structure selection device for distributed MIMO radar target positioning, characterized in that: include: The acquisition module is used to collect the echo signal of the target and arrange it into a column of received signals in the order of signal sampling values; A calculation module, configured to process received signals and calculate a maximum likelihood estimate of the time delay of each signal path; A fusion center is used to integrate the delay estimates of all paths into an estimation vector, and use FCN as an estimator based on the estimation vector to obtain the final target object position estimate; The optimization problem construction module is used to derive the mean square error bound under a given FCN, training set, and training method, and based on the mean square error bound, construct the optimization problem of network structure design: ； in, is the upper bound of the size, is the upper bound of the depth, MSEB is the mean square error bound, For the neural network Layer, optimal network configuration and depth ; The processing module is used to use genetic algorithms to solve the optimization problem of network structure design and obtain the optimal FCN structure.

8. An electronic device, characterized in that: include: a processor, and a memory communicatively connected to the processor; The memory stores computer-executable instructions; The processor executes the computer-executable instructions stored in the memory to implement the method according to any one of claims 1 to 6.

9. A computer program product, characterized in that The invention comprises a computer program, which implements the method according to any one of claims 1 to 6 when being executed by a processor or a chip.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer-executable instructions, which are used to implement the method according to any one of claims 1 to 6 when executed by a processor.

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