A small sample HRRP identification method based on deep probabilistic dynamic modeling

Abstract

The present invention provides a small sample HRRP recognition method based on deep probability dynamic modeling, which relates to the field of radar target recognition technology. It includes: pre-processing and converting HRRP sample data into sequence form in sequence to obtain sequence data; constructing a tensor probability dynamic network model corresponding to the sequence data, the tensor probability dynamic network model includes a tensor probability dynamic network generation model and a tensor recursive inference network module; inputting the sequence data to be identified into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category of the sequence data to be identified, and the trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using a target loss function. Under the condition of a small sample, the trained tensor probability dynamic network model can better classify and identify the sequence data to be identified, so that the accuracy of HRRP target recognition is higher.

Description

Technical Field

[0001] The present invention relates to the field of radar target recognition technology, and in particular to a small sample high resolution range profile (HRRP) recognition method based on deep probability dynamic modeling. Background Art

[0002] Radar Automatic Target Recognition (RATR) is an important direction of radar application. It can extract target features from radar echo signals and make classification decisions. Therefore, RATR has been widely studied in academia. From the perspective of using echo signals, RATR can be roughly divided into two categories: one is target recognition based on two-dimensional imaging radar, that is, target recognition using synthetic aperture radar (SAR) imaging or inverse synthetic aperture radar (ISAR) imaging; the other is target recognition based on HRRP. HRRP contains rich target physical structure information, which can be used for target recognition. Compared with SAR images, HRRP has the advantages of small data volume, easy processing and fast computing speed. Therefore, target recognition based on HRRP has attracted more and more attention from researchers. Among them, HRRP feature extraction is the key to HRRP target recognition.

[0003] At present, the target recognition of HRRP is usually achieved by using the deep dynamic Poisson factor method, which combines recursive neural networks with Poisson factor analysis to capture the long-term time dependence of potential factors through recursive neural networks. However, recursive neural network representations are usually difficult to access and interpret, and the training of recursive neural networks requires a high number of samples. HRRP is generally difficult to obtain as a non-cooperative target, and the distribution of sample posture angles is not comprehensive, resulting in insufficient sample diversity. Especially when the number of samples is limited, the distribution of samples to be identified may be significantly different from the distribution of training samples, which affects the test performance of HRRP target recognition and leads to low accuracy of HRRP target recognition. Summary of the invention

[0004] The purpose of the embodiment of the present invention is to provide a small sample HRRP recognition method based on deep probabilistic dynamic modeling to solve the problem of low accuracy in HRRP target recognition.

[0005] To solve the above technical problems, the embodiments of the present invention provide the following technical solutions:

[0006] The present invention provides a small sample HRRP identification method based on deep probability dynamic modeling, comprising:

[0007] The HRRP sample data is preprocessed and converted into sequence form in turn to obtain sequence data;

[0008] Constructing a tensor probability dynamic network model corresponding to the sequence data, the tensor probability dynamic network model includes a tensor probability dynamic network generation model and a tensor recursive inference network module, the tensor probability dynamic network generation model is used to generate target sequence data, and the tensor recursive inference network module is used to infer the hidden variables after distribution corresponding to the sequence data;

[0009] The sequence data to be identified is input into the trained tensor probability dynamic network model so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified. The trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using the target loss function. The target loss function is a loss function determined based on the target sequence data, the distributed hidden variables and the cross entropy function.

[0010] Compared with the prior art, the present invention provides a small sample HRRP recognition method based on deep probability dynamic modeling, which pre-processes and converts the HRRP sample data into a sequence form in sequence to obtain sequence data; constructs a tensor probability dynamic network model corresponding to the sequence data, and the tensor probability dynamic network model includes a tensor probability dynamic network generation model and a tensor recursive inference network module; inputs the sequence data to be identified into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified, and the trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using the target loss function. In this way, the tensor probability dynamic network model can assign the distributed hidden variables to the mixture of gamma distribution parameters to simulate complex sequences and describe nonlinear dynamics, while capturing various time dependencies. Under small sample conditions, the trained tensor probability dynamic network model can better classify and identify the sequence data to be identified, so that the accuracy of HRRP target recognition is higher. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] By reading the detailed description below with reference to the accompanying drawings, the above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:

[0012] Figure 1The flowchart of the small sample HRRP identification method based on deep probabilistic dynamic modeling is schematically shown;

[0013] Figure 2 Schematically shows the architecture of the tensor probabilistic dynamic network generation model;

[0014] Figure 3 The architecture of the tensor probabilistic dynamic network model is schematically shown. DETAILED DESCRIPTION

[0015] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.

[0016] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present invention should have the common meanings understood by those skilled in the art to which the present invention belongs.

[0017] The method in the embodiment of the present invention is described in detail below.

[0018] Figure 1 The flowchart of the small sample HRRP identification method based on deep probability dynamic modeling in the embodiment of the present invention is schematically shown. Figure 1 As shown, the small sample HRRP identification method based on deep probability dynamic modeling may include:

[0019] S101. Preprocess and convert HRRP sample data into sequence form in sequence to obtain sequence data.

[0020] The HRRP sample data used in the present invention comes from inverse synthetic aperture radar measurements of three real aircraft conducted by a Chinese research institute. There are a total of 7800 HRRP sample data for each target to be identified.

[0021] Specifically, the HRRP sample data is preprocessed and converted into a sequence form in sequence, and the sequence data obtained includes:

[0022] Step A1: Use the modulo-2 norm normalization method to process the HRRP sample data to obtain normalized sample data.

[0023] The HRRP sample data can be defined as , arrive They correspond to the amplitudes of each distance unit in the HRRP sample data, where: is the amplitude in the first distance unit in the HRRP sample data, is the first The amplitude within a distance unit, is the total number of amplitudes in the distance unit in the HRRP sample data. After the modulo-2 norm normalization method, the normalized sample data is obtained. :

[0024] ;

[0025] in, is the normalized sample data, is the HRRP sample data, is the first The amplitude within a distance unit.

[0026] Step A2: Referring to the centroid of the normalized sample data, the normalized sample data is aligned using an absolute alignment method to obtain aligned sample data.

[0027] The absolute alignment method takes the centroid of each normalized sample data as the criterion, and translates the normalized sample data respectively to align the center position of the normalized sample data with the centroid position to obtain the aligned sample data. .

[0028] The centroid of the normalized sample data is:

[0029] ;

[0030] in, is the centroid of the normalized sample data, is the normalized sample data distance units, is the total number of distance units in the normalized sample data.

[0031] For HRRP sample data, modulo-2 norm normalization method and absolute alignment method are used to eliminate the influence of amplitude sensitivity and translation sensitivity on HRRP sample data.

[0032] Step A3: Use a sliding window method to convert the aligned sample data into sequence data.

[0033] The expression for the sequence data is:

[0034] ;

[0035] in, For the The sequence data input at each moment, is the aligned sample data, is the window length, The number of overlapping distance units between adjacent input sequence data.

[0036] S102. Construct a tensor probability dynamic network model corresponding to the sequence data.

[0037] Among them, the tensor probability dynamic network model includes a tensor probability dynamic network generation model and a tensor recursive inference network module. The tensor probability dynamic network generation model is used to generate target sequence data, and the tensor recursive inference network module is used to infer the distributed hidden variables corresponding to the sequence data.

[0038] The sequence data includes the sequence data at the current moment and the sequence data at the previous moment.

[0039] Specifically, the tensor probability dynamic network model corresponding to the sequence data is constructed, including:

[0040] Step B1: According to the category distribution parameters corresponding to the sequence data at the current moment, the latent variables and the load matrix corresponding to the sequence data at the previous moment, a tensor probability dynamic network generation model is constructed using the gamma distribution, Poisson distribution and category distribution.

[0041] Specifically, the expression of the tensor probability dynamic network generation model is:

[0042] ;

[0043] in, For the Moment The category distribution parameter corresponding to the sequence data is , For the Moment The probability value of the first category in the category distribution parameter corresponding to the sequence data, is the category distribution, For the Moment The categorical variables corresponding to the sequence data are , For the Moment The first element of the categorical variable corresponding to the sequence data, The value is 0 or 1. is the cumulative multiplication operation, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, To control the scaling parameter of the gamma distribution, For the The implicit transfer matrix under categories, is a positive number, For the Moment Hidden variables of sequence data, For the Scaling parameter that controls the diversity of temporal amplitude variation of hidden states under categories, is a positive number, For the Moment The categorical variables corresponding to the sequence data are is a gamma distribution, For the Moment Hidden variables of sequence data, , for The set of positive real numbers of dimension , is the scaling parameter, , is the set of positive real numbers, is the load matrix, , for The set of positive real numbers of dimension , is the number of rows in the loading matrix, is the number of columns of the loading matrix, is a Poisson distribution, For the Moment observed target sequence data.

[0044] right Marginalization yields:

[0045] ;

[0046] in, For a given Under the conditions of parameters Probability, For the Moment Hidden variables of sequence data, For the Moment Hidden variables of sequence data, For the 1st to The implicit transfer matrix under the category and the first to the Scaling parameter that controls the diversity of temporal amplitude variation of hidden states under categories, For the The implicit transfer matrix under categories, , for The set of positive real numbers of dimension , For the Scaling parameter that controls the diversity of temporal amplitude variation of hidden states under categories, To control the scaling parameter of the gamma distribution, For the Moment The first of the category distribution parameters corresponding to the sequence data The probability value under each category, for The gamma distribution of The first parameter of the gamma distribution is , , , the product of The second parameter of the gamma distribution is , is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, is a gamma distribution.

[0047] The above The formula obtained by marginalization is a mixture of gamma distributions, which can more accurately characterize the complex and diverse sequential relationships between time steps than existing probabilistic dynamic network models. The implicit transfer matrix under the category The number of categories that can capture the gamma distribution is Various temporal dependencies between classification modules. Moment Hidden variables of sequence data The expected value of , for and Under known conditions The conditional expectation of For the 1st to The implicit transfer matrix under categories, For the Moment The category distribution parameters corresponding to the sequence data can be seen The latent representation is transferred in time and is represented by control, and thus can concisely and accurately capture the original pattern of sequence data.

[0048] In order to improve the diverse tensor probability dynamic network generation model, the present invention introduces factor weights, The implicit transfer matrix under the category The specific expression is:

[0049] ;

[0050] in, It is The implicit transfer matrix under the category No. List, , For the The implicit transfer matrix under the category No. The first elements, is the Dirichlet function, For the Category 1 to The folding stick ratio parameter, , For the Category Folding stick ratio parameters The scale parameter of the gamma distribution follows, is the first parameter of the gamma distribution, is the second parameter of the gamma distribution.

[0051] Figure 2 The schematic diagram shows the architecture of the tensor probability dynamic network generation model, which shows the Moment Observed target sequence data The generation of the load matrix and Moment Hidden variables of sequence data decision; Moment Hidden variables of sequence data By Moment Hidden variables of sequence data and Moment The implicit transfer matrix under the category Decision. The implicit transfer matrix under the category The choice depends on Moment Categorical variables corresponding to sequence data ;No. Moment Categorical variables corresponding to sequence data By Moment The category distribution parameter corresponding to the sequence data Decide.

[0052] Step B2: According to the sequence data at the previous moment, the category distribution parameters corresponding to the sequence data at the previous moment, the variables obeying the standard Gaussian distribution under the category corresponding to the sequence data, and the hidden units at the previous moment, a tensor recursive inference network module is constructed using the Gumbel-normalized exponential function distribution and the Kumaraswamy distribution.

[0053] The tensor recursive inference network module can convert the first The sequence data input at each moment is directly mapped to latent variables, and the Gumbel-softmax function is used to approximate the categorical variables of the categorical distribution. The Weibull distribution is used to approximate the conditional latent representation of the gamma distribution, and the stick-breaking variational inference network, namely the Kumaraswamy distribution and the Beta distribution, is used to achieve non-parametric inference of categorical variables.

[0054] Specifically, according to the sequence data at the previous moment, the category distribution parameters corresponding to the sequence data at the previous moment, the variables under the category corresponding to the sequence data that obey the standard Gaussian distribution, and the hidden units at the previous moment, the Gumbel-normalized exponential function distribution and the Kumaraswamy distribution are used to construct a tensor recursive inference network module, including:

[0055] Step B21: According to the category distribution parameters corresponding to the sequence data at the previous moment, the sequence data at the previous moment is converted into the category distribution parameters corresponding to the sequence data at the current moment by using a normalized exponential function network.

[0056] In the The sequence data input at each moment is expressed as , then in Moment, 1st to 2nd The sequence data are , For the Moment A sequence data.

[0057] No. Moment Categorical variables corresponding to sequence data Control Moment Hidden variables of sequence data From time arrive In general, the Moment The dynamic changes of the sequence data depend on the historical sequence data of the tensor probability dynamic network generation model and are determined by the input of the tensor probability dynamic network generation model. Moment The range of sequence data is from 0 to Here, the present invention allows Moment Categorical variables corresponding to sequence data Depend on is determined by the learnable function and modulated by the tensor recursive inference network module, where From the first moment to the The moment observed target sequence data.

[0058] Specifically, the expression of the category distribution parameter corresponding to the sequence data at the current moment is:

[0059] ;

[0060] in, For the Moment The category distribution parameter corresponding to the sequence data is is the normalized exponential function network, For the Moment Sequence data, For the Moment The conversion matrix between sequence data and the category parameters of the normalized exponential function network, is the conversion matrix between the category parameters of the normalized exponential function network and the category parameters of the normalized exponential function network, For the Moment The category distribution parameter corresponding to the sequence data is is the bias of the normalized exponential function network.

[0061] Step B22: According to the category distribution parameters corresponding to the sequence data at the current moment, using the Kumaraswamy distribution, determine the elements in the implicit transfer matrix corresponding to the sequence data at the current moment.

[0062] Among them, the elements in the implicit transfer matrix corresponding to the sequence data at the current moment include The elements in the implicit transfer matrix corresponding to the sequence data at the current moment under each category.

[0063] In order to select the number of categories in the mixture of multiple gamma distributions, the stick-breaking variational inference network procedure is used as the Moment Categorical variables corresponding to sequence data In order to achieve the Moment The elements in the implicit transfer matrix corresponding to the sequence data The stick-breaking variational inference network is introduced here. Specifically, the stick-breaking variational inference network, namely the Kumaraswamy distribution and the Beta distribution, is used to implement the first Moment The elements in the implicit transfer matrix corresponding to the sequence data Nonparametric inference.

[0064] Specifically, according to the category distribution parameters corresponding to the sequence data at the current moment, the elements in the implicit transfer matrix corresponding to the sequence data at the current moment are determined using the Kumaraswamy distribution, including:

[0065] Step B221: Determine the first shape parameter and the second shape parameter of the Kumaraswamy distribution according to the category distribution parameter corresponding to the sequence data at the current moment, the first learnable parameter of the stick-breaking variational inference network, the second learnable parameter of the stick-breaking variational inference network, the third learnable parameter of the stick-breaking variational inference network, and the fourth learnable parameter of the stick-breaking variational inference network.

[0066] The expressions for the first shape parameter of the Kumaraswamy distribution and the second shape parameter of the Kumaraswamy distribution are:

[0067] ;

[0068] in, is the first shape parameter of the Kumaraswamy distribution, is the first learnable parameter of the stick-breaking variational inference network, For the Moment The category distribution parameter corresponding to the sequence data is is the second learnable parameter of the stick-breaking variational inference network, is the second shape parameter of the Kumaraswamy distribution, is the third learnable parameter of the stick-breaking variational inference network, The fourth learnable parameter of the stick-breaking variational inference network.

[0069] Step B222: The Kumaraswamy distribution corresponding to the first shape parameter of the Kumaraswamy distribution and the second shape parameter of the Kumaraswamy distribution is used as the variational distribution of the broken stick scale parameter matrix.

[0070] The expression of the variational distribution of the stick ratio parameter matrix is:

[0071] ;

[0072] in, For the Moment The variational distribution of the stick ratio parameter matrix of the sequence data, For Kumaraswamy distribution, is the first shape parameter of the Kumaraswamy distribution, is the second shape parameter of the Kumaraswamy distribution.

[0073] By specifying To approximate the first Moment The stick ratio parameter matrix of the sequence data , where the first shape parameter of the Kumaraswamy distribution is and the second shape parameter of the Kumaraswamy distribution It is nonlinear from Moment The category distribution parameter corresponding to the sequence data Converted.

[0074] Step B223: Determine the elements in the implicit transfer matrix corresponding to the sequence data at the current moment according to the folded-stick ratio parameter matrix corresponding to the variational distribution of the folded-stick ratio parameter matrix.

[0075] The expression of the elements in the implicit transfer matrix corresponding to the sequence data at the current moment is:

[0076] ;

[0077] in, For the Moment The elements in the implicit transfer matrix corresponding to the sequence data are For the Category Moment The elements in the implicit transfer matrix corresponding to the sequence data are For the first category Moment The stick ratio parameter matrix of the sequence data, For the Category Moment The stick ratio parameter matrix of the sequence data, , is the number of categories in a mixture of gamma distributions. Moment The stick ratio parameter matrix of the sequence data Contains Category Moment The stick ratio parameter matrix of the sequence data .

[0078] Step B23: According to The elements in the implicit transfer matrix corresponding to the sequence data at the current moment under the categories and the variables under the categories corresponding to the sequence data obey the standard Gaussian distribution are used to determine the distributed categorical variables corresponding to the sequence data at the current moment using the Gumbel-normalized exponential function distribution.

[0079] In order to Moment Variational distribution of categorical variables corresponding to sequence data The HRRP sample data was obtained and Moment Categorical variables corresponding to sequence data For back propagation, the present invention uses To approximate ,in, For the Moment Category The variational distribution of the categorical variable after the distribution corresponding to the sequence data, For the Moment Category The categorical variables corresponding to the distribution of sequence data are For the Moment The elements in the implicit transfer matrix corresponding to the sequence data are is the Gumbel-normalized exponential function distribution.

[0080] Specifically, the expression of the distributed categorical variable corresponding to the sequence data at the current moment is:

[0081] ;

[0082] in, For the Moment Category The categorical variables corresponding to the distribution of sequence data are For the Category Moment The elements in the implicit transfer matrix corresponding to the sequence data are For the Moment The sequence data corresponds to The variables with standard Gumbel distribution under categories, is the parameter of the normalized exponential function, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, is the gamma distribution, For the Moment The sequence data corresponds to The variables with standard Gaussian distribution under categories, For real numbers An exponential function with base .

[0083] When the parameter of the normalized exponential function When it is close to 0, from The samples of the distribution become one-hot vectors, and The distribution of Moment Category Variational distribution of categorical variables after the distribution corresponding to the sequence data With Moment Variational distribution of categorical variables corresponding to sequence data same.

[0084] Step B24: According to the distributed categorical variables corresponding to the sequence data at the current moment and the hidden units at the previous moment, the distributed hidden variables corresponding to the sequence data are determined to construct a tensor recursive inference network module.

[0085] By To approximate the gamma distribution, random HRRP sample data can be obtained by transforming Moment The variables corresponding to the sequence data follow the standard Gaussian distribution Obtain, among which, For Under known conditions, The distribution of For the Moment Hidden variables of sequence data, For the Moment The categorical variables corresponding to the sequence data are is the Weibull distribution, is the first parameter of the Weibull distribution, is the second parameter of the Weibull distribution.

[0086] Specifically, the expression of the hidden variable after the distribution corresponding to the sequence data is:

[0087] ;

[0088] ;

[0089] ;

[0090] in, For the Moment The hidden variables corresponding to the distribution of sequence data are is the first parameter of the Weibull distribution, For the Moment The variables corresponding to the sequence data obey the standard Gaussian distribution, is the second parameter of the Weibull distribution, is the first learnable parameter of the tensor recursive inference network module, , for dimensional set of real numbers, For the Moment The hidden units corresponding to the sequence data are The second learnable parameter of the tensor recursive inference network module, , for dimensional set of real numbers, The third learnable parameter of the tensor recursive inference network module, , The fourth learnable parameter of the tensor recursive inference network module, , is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, is the input-hidden weight matrix, , for dimensional set of real numbers, For the Moment Sequence data, , For the The hidden state connection matrix under each category is For the Moment The hidden units corresponding to the sequence data are are the learnable parameters of the hidden state network, For the Moment Category The categorical variable corresponding to the distribution of the sequence data.

[0091] Second parameter of the Weibull distribution , the first parameter of the Weibull distribution It is nonlinear from Moment Hidden units corresponding to sequence data Converted, Moment Hidden units corresponding to sequence data It is from Moment Sequence data and Moment Hidden units corresponding to sequence data Converted from.

[0092] The tensor recursive inference network module takes into account the diverse temporal dependencies between different time steps.

[0093] S103, inputting the sequence data to be identified into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified.

[0094] The trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using the target loss function. The target loss function is a loss function determined based on the target sequence data, the distributed latent variables and the cross entropy function.

[0095] Specifically, the sequence data to be identified is input into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified, including:

[0096] Step C1: According to Moment The hidden variables and self-attention mechanism of the sequence data are used to determine the target feature information of the sequence data to be identified.

[0097] In order to process the classification task of sequence data, the present invention introduces label supervision at the final time step of the tensor probability dynamic network model, so that the tensor probability dynamic network model is extended with supervision capability. In order to further improve the classification performance of the tensor probability dynamic network model, a self-attention mechanism is introduced into the tensor probability dynamic network model. Figure 3 The architecture of the tensor probability dynamic network model is schematically shown. Specifically, after obtaining the first Moment Hidden variables of sequence data Afterwards, in order to reward the time step of the sequence data that provides important clues for correct classification, the present invention applies the attention mechanism to measure the importance of different time steps; Moment Observed target sequence data The generation of the load matrix and Moment Hidden variables of sequence data decision; Moment Hidden variables of sequence data By Moment Hidden variables of sequence data and Moment The implicit transfer matrix under the category Decision. Moment The implicit transfer matrix under the category The choice depends on Moment Categorical variables corresponding to sequence data ; The tensor probability dynamic network model can utilize the The hidden variables at each moment of the sequence data , that is, The sequence data from the first moment to the Hidden variables at time , restore the Observed target sequence data ,in, is the total number of moments; Observed target sequence data Including Moment Observed target sequence data , No. Moment Observed target sequence data , No. Moment Observed target sequence data , then The hidden variables at each moment of the sequence data The characteristic information of HRRP sample data is contained in The hidden variables at each moment of the sequence data Combining self-attention mechanism with global contrast feature vector in tensor probabilistic dynamic network model , and the The weights of the latent variables at each moment of the sequence data , the corresponding time and Multiply and accumulate to obtain the target feature information of the sequence data to be identified , we can finally predict The category to which the HRRP sample data corresponding to the sequence data belongs .

[0098] The expression of the target feature information of the sequence data to be identified is:

[0099] ;

[0100] in, is the target feature information of the sequence data to be identified, For the Moment The proportion of latent variables in sequence data, For the Moment Hidden variables of sequence data, For the Moment Hidden variables of sequence data The feature map after the neural network, For the Moment Hidden variables of sequence data Feature map after neural network The transposed matrix of is the global contrast feature vector in the tensor probability dynamic network model, is the first learnable parameter in the tensor probability dynamic network model, is the second learnable parameter in the tensor probability dynamic network model. The target feature information of the sequence data to be identified Summarizes the characteristic information of all moments of the sequence data. For real numbers An exponential function with base .

[0101] Step C2: Input the target feature information into the fully connected network to map the target feature information into a column vector, and input the column vector into a normalized exponential (softmax) function so that the normalized exponential function outputs the probability value of each category corresponding to the sequence data to be identified.

[0102] A fully connected network and a softmax function can be used to predict the category of the target feature information of the sequence data to be identified.

[0103] Assume that the category in the experiment is The sequence data to be identified is First, the target feature information of the sequence data to be identified Input fully connected network, mapped to column vector , column vector yes dimensional, and then the column vector After passing through the softmax function, the softmax function outputs the probability distribution value of the sequence data to be identified belonging to each category :

[0104] ;

[0105] in, is the probability value of each category corresponding to the sequence data to be identified, The sequence data to be identified belongs to The probability value of each category, is a column vector, is the normalized exponential function, is a column vector The The element value corresponding to each category, The base of the natural logarithm Base is the value of the index.

[0106] Step C3: Select the maximum probability value from the probability values ​​of each category, determine the category index corresponding to the maximum probability value, and use the category corresponding to the category index as the category of the sequence data to be identified.

[0107] The category corresponding to the category index is used as the category of the sequence data to be identified:

[0108] ;

[0109] in, The probability value of each category corresponding to the sequence data to be identified The category index corresponding to the maximum probability value in is the category to be identified. kind, is the probability value of each category corresponding to the sequence data to be identified, The probability value of each category corresponding to the sequence data to be identified The category index of .

[0110] Before step S103, it is necessary to determine the lower bound of evidence based on the target sequence data and the distributed latent variables, construct a target loss function based on the lower bound of evidence and the cross entropy function, and use the target loss function to train the tensor probability dynamic network model to obtain a trained tensor probability dynamic network model.

[0111] The expression of the objective loss function is:

[0112] ;

[0113] ;

[0114] in, is the target loss function, is the objective function of the tensor probability dynamic network model, is the regularization hyperparameter, is the cross entropy function, To provide evidence for the lower bound, is the number of sequence data to be identified, For the The true labels of the sequence data to be identified, For the The sequence data to be identified corresponds to the The probability value of each category, is the number of moments, is the load matrix, For the Moment Hidden variables of sequence data, For the Moment Observed target sequence data, For The logarithmic operation with base , For a given The variational distribution of , Under known conditions The expected value of for , and known The conditional prior distribution of for The variational distribution of Under known conditions, The prior distribution between Divergence, For the Moment The hidden variables of the sequence data, to Moment The implicit transfer matrix of information transmission corresponding to the hidden variables of sequence data, For the Moment The variational distribution of the latent variable corresponding to the distribution of sequence data, For Under known conditions The prior distribution of For the Moment Hidden variables of sequence data, For the Moment The categorical variables corresponding to the sequence data are for The variational distribution of The prior distribution between Divergence, For the Moment The categorical variables corresponding to the distribution of sequence data The variational distribution of For the Moment The prior distribution of the categorical variable corresponding to the sequence data, for The variational distribution of The prior distribution between Divergence, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, For the Moment The stick ratio parameter matrix of the sequence data The variational distribution of The tensor probability dynamic network generation model Moment The stick ratio parameter matrix of the sequence data The prior distribution of .

[0115] The first term in the expression of the evidence lower bound is is the log-likelihood expectation that guarantees the reconstruction capability of the tensor probability dynamic network generative model. The second term middle, The smaller the divergence, the The variational distribution and The closer the variational distribution of .

[0116] is a regularization hyperparameter that balances the generation of sequence data to be identified and the classification task. It is set in the experiment .

[0117] The tensor probability dynamic network model distributes hidden variables to a mixture of gamma distribution parameters to simulate complex sequences and describe nonlinear dynamics, while capturing various time dependencies, enabling the tensor probability dynamic network model to represent and model sequence data with complex sequences and dynamic characteristics. Combining the representation ability of the tensor probability dynamic network model, the discrimination ability of deep neural networks, and the selection ability of the self-attention mechanism under the principled probability framework, the tensor probability dynamic network model can achieve superior performance even under small sample conditions.

[0118] The present invention applies the tensor probability dynamic network model to the field of HRRP target recognition. The tensor probability dynamic network model performs better in fitting modeling of complex dynamic sequences, especially under small sample conditions, and can also construct more recognizable feature vectors for classification and recognition.

[0119] The simulation experiment and simulation results of the present invention are as follows:

[0120] Simulation experiment: The HRRP sample data used in the present invention comes from the Inverse Synthetic Aperture Radar (ISAR) measurements of three real aircraft conducted by a Chinese research institute. The three real aircraft are: a medium-sized propeller aircraft, a small jet aircraft, and a large jet aircraft. The HRRP sample data comes from the institute's inverse synthetic aperture C-band experimental radar. The pulse repetition frequency of the radar is 400 Hz and the signal bandwidth is 400 MHz. Specifically, under 7800 HRRP sample data, 2600 sample data of each of the three categories are used for training, and 5200 HRRP sample data are used for testing. Each HRRP sample data is a vector of length 256.

[0121] Simulation results: The simulation experiment of the present invention tests the recognition performance of various methods under different HPPR sample data sizes. The tensor probability dynamic network model in the small sample HRRP recognition method based on deep probability dynamic modeling of the present invention is compared with the existing recurrent neural network, target-sensitive recurrent attention network, probability dynamic network, tensor probability network, and supervised tensor probability dynamic network methods. The comparison results are shown in Table 1 below, which shows the comparison results of the recognition accuracy of various methods under different HRRP sample data sizes.

[0122] Table 1 Comparison of recognition accuracy of various methods under different HRRP sample data sizes

[0123]

[0124] From the comparison results in Table 1, it can be seen that the robustness of the tensor probability dynamic network model in the small sample HRRP recognition method based on deep probability dynamic modeling of the present invention is much better than that of the existing recurrent neural network, target-sensitive recurrent attention network, probability dynamic network, tensor probability network, and supervised tensor probability dynamic network model; the tensor probability dynamic network model in the small sample HRRP recognition method based on deep probability dynamic modeling of the present invention can maintain acceptable performance even when the scale of the HPPR sample data used in training is very small, because the tensor probability dynamic network model of the present invention utilizes the uncertainty of the weights in the hidden variables after the distribution corresponding to the sequence data. Under the condition of 10% training sample data, the test accuracy of the tensor probability dynamic network model of the present invention also reached about 91%, achieving the best accuracy among all models in Table 1. The tensor probability dynamic network model of the present invention is used to construct a diversified sequence relationship with a tensor mechanism and an attention mechanism. Through the above simulation experimental analysis, it is shown that the small sample HRRP recognition method based on deep probability dynamic modeling of the present invention significantly improves the accuracy of HRRP target recognition.

[0125] Based on the above Figure 1It can be seen from the implementation method that the embodiment of the present invention sequentially preprocesses and converts the HRRP sample data into a sequence form to obtain sequence data; constructs a tensor probability dynamic network model corresponding to the sequence data, and the tensor probability dynamic network model includes a tensor probability dynamic network generation model and a tensor recursive inference network module; inputs the sequence data to be identified into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified, and the trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using the target loss function. In this way, the tensor probability dynamic network model can assign the distributed latent variables to a mixture of gamma distribution parameters to simulate complex sequences and describe nonlinear dynamics, while capturing various time dependencies. Under small sample conditions, the trained tensor probability dynamic network model can better classify and identify the sequence data to be identified, so that the accuracy of HRRP target recognition is higher.

[0126] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A small sample HRRP identification method based on deep probabilistic dynamic modeling, characterized in that: include: Preprocessing and converting the HRRP sample data into a sequence form in sequence to obtain sequence data, wherein the sequence data includes sequence data at a current moment and sequence data at a previous moment; Constructing a tensor probability dynamic network model corresponding to the sequence data, the tensor probability dynamic network model comprising a tensor probability dynamic network generation model and a tensor recursive inference network module, the tensor probability dynamic network generation model is used to generate target sequence data, and the tensor recursive inference network module is used to infer the distributed hidden variables corresponding to the sequence data; Inputting the sequence data to be identified into the trained tensor probability dynamic network model, so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified, wherein the trained tensor probability dynamic network model is a network model obtained by training the tensor probability dynamic network model according to the sequence data using a target loss function, wherein the target loss function is a loss function determined based on the target sequence data, the distributed hidden variables and a cross entropy function; The constructing of a tensor probability dynamic network model corresponding to the sequence data includes: According to the category distribution parameters corresponding to the sequence data at the current moment, the latent variables and the load matrix corresponding to the sequence data at the previous moment, the tensor probability dynamic network generation model is constructed using the gamma distribution, the Poisson distribution and the category distribution; According to the sequence data at the previous moment, the category distribution parameters corresponding to the sequence data at the previous moment, the variables obeying the standard Gaussian distribution under the category corresponding to the sequence data, and the hidden units at the previous moment, the tensor recursive inference network module is constructed using the Gumbel-normalized exponential function distribution and the Kumaraswamy distribution.

2. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 1 is characterized in that: The HRRP sample data is preprocessed and converted into a sequence form in sequence to obtain sequence data including: Using a modulo-2 norm normalization method to process the HRRP sample data to obtain normalized sample data; Referring to the centroid of the normalized sample data, the normalized sample data are aligned using an absolute alignment method to obtain aligned sample data; The aligned sample data is converted into the sequence data by using a sliding window method.

3. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 1 is characterized in that: The expression of the tensor probability dynamic network generation model is: ； in, For the Moment The category distribution parameter corresponding to the sequence data is , For the said Moment The probability value of the first category in the category distribution parameter corresponding to the sequence data, is the category distribution, For the Moment The categorical variables corresponding to the sequence data are , For the said Moment The first element of the categorical variable corresponding to the sequence data, is the cumulative multiplication operation, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, To control the scaling parameter of the gamma distribution, is the first The implicit transfer matrix under categories is For the Moment Hidden variables of sequence data, For the Scaling parameter that controls the diversity of temporal amplitude variation of hidden states under categories, For the Moment The categorical variables corresponding to the sequence data are is the gamma distribution, For the Moment Hidden variables of sequence data, , for The set of positive real numbers of dimension , is the scaling parameter, , is the set of positive real numbers, is the loading matrix, , for The set of positive real numbers of dimension , is the number of rows of the loading matrix, is the number of columns of the loading matrix, is the Poisson distribution, For the Moment observed target sequence data.

4. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 1 is characterized in that: The tensor recursive inference network module is constructed according to the sequence data at the previous moment, the category distribution parameter corresponding to the sequence data at the previous moment, the variable obeying the standard Gaussian distribution under the category corresponding to the sequence data, and the hidden unit at the previous moment, using the Gumbel-normalized exponential function distribution and the Kumaraswamy distribution, including: According to the category distribution parameters corresponding to the sequence data at the previous moment, using a normalized exponential function network, the sequence data at the previous moment is converted into the category distribution parameters corresponding to the sequence data at the current moment; According to the category distribution parameter corresponding to the sequence data at the current moment, the elements in the implicit transfer matrix corresponding to the sequence data at the current moment are determined by using the Kumaraswamy distribution, and the elements in the implicit transfer matrix corresponding to the sequence data at the current moment include the first The elements in the implicit transfer matrix corresponding to the sequence data at the current moment under each category; According to the said The elements in the implicit transfer matrix corresponding to the sequence data at the current moment under the category, and the variables under the category corresponding to the sequence data that obey the standard Gaussian distribution, use the Gumbel-normalized exponential function distribution to determine the distributed classification variables corresponding to the sequence data at the current moment; According to the distributed categorical variables corresponding to the sequence data at the current moment and the hidden units at the previous moment, the distributed hidden variables corresponding to the sequence data are determined to construct the tensor recursive inference network module.

5. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 4 is characterized in that: The expression of the category distribution parameter corresponding to the sequence data at the current moment is: ； in, For the Moment The category distribution parameter corresponding to the sequence data is is the normalized exponential function network, For the Moment Sequence data, For the said Moment The conversion matrix between the sequence data and the category parameters of the normalized exponential function network, is a conversion matrix from the category parameters of the normalized exponential function network to the category parameters of the normalized exponential function network, For the Moment The category distribution parameter corresponding to the sequence data is is the bias of the normalized exponential function network.

6. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 4 is characterized in that: The expression of the distributed categorical variable corresponding to the sequence data at the current moment is: ； in, For the Moment Category The categorical variables corresponding to the distribution of sequence data are For the Category Moment The elements in the implicit transfer matrix corresponding to the sequence data are For the Moment The sequence data corresponds to The variables with standard Gumbel distribution under categories, is the parameter of the normalized exponential function, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, is the gamma distribution, For the Moment The sequence data corresponds to The variables with standard Gaussian distribution under categories, For real numbers An exponential function with base .

7. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 4 is characterized in that: The expression of the distributed hidden variable corresponding to the sequence data is: ； ； ； in, For the Moment The hidden variables corresponding to the distribution of sequence data are is the first parameter of the Weibull distribution, For the Moment The variables corresponding to the sequence data obey the standard Gaussian distribution, is the second parameter of the Weibull distribution, a first learnable parameter for the tensor recursive inference network module, , for dimensional set of real numbers, For the Moment The hidden units corresponding to the sequence data are a second learnable parameter for the tensor recursive inference network module, , for dimensional set of real numbers, is the third learnable parameter of the tensor recursive inference network module, , is the fourth learnable parameter of the tensor recursive inference network module, , is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, is the input-hidden weight matrix, , for dimensional set of real numbers, For the Moment Sequence data, , For the The hidden state connection matrix under each category is For the Moment The hidden units corresponding to the sequence data are are the learnable parameters of the hidden state network, For the Moment Category The categorical variable corresponding to the distribution of the sequence data.

8. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 3 is characterized in that: The step of inputting the sequence data to be identified into the trained tensor probability dynamic network model so that the tensor probability dynamic network model outputs the category corresponding to the sequence data to be identified includes: According to the said Moment The hidden variables of the sequence data and the self-attention mechanism are used to determine the target feature information of the sequence data to be identified; Inputting the target feature information into a fully connected network to map the target feature information into a column vector, and inputting the column vector into a normalized exponential function so that the normalized exponential function outputs probability values ​​of each category corresponding to the sequence data to be identified; A maximum probability value is selected from the probability values ​​of the various categories, a category index corresponding to the maximum probability value is determined, and the category corresponding to the category index is used as the category of the sequence data to be identified.

9. The small sample HRRP identification method based on deep probabilistic dynamic modeling according to claim 7 is characterized in that: The expression of the objective loss function is: ； ； in, is the objective loss function, is the objective function of the tensor probability dynamic network model, is the regularization hyperparameter, is the cross entropy function, To provide evidence for the lower bound, is the number of sequence data to be identified, For the The true labels of the sequence data to be identified, For the The sequence data to be identified corresponds to the The probability value of each category, is the number of moments, is the loading matrix, For the said Moment Hidden variables of sequence data, For the said Moment Observed target sequence data, For The logarithmic operation with base , For a given The variational distribution of , Under known conditions The expected value of for , and known The conditional prior distribution of for The variational distribution of Under known conditions, The prior distribution between Divergence, For the said Moment hidden variables of sequence data, to the Moment The implicit transfer matrix of information transmission corresponding to the hidden variables of sequence data, For the Moment The variational distribution of the latent variable corresponding to the distribution of sequence data, For Under known conditions The prior distribution of For the said Moment Hidden variables of sequence data, For the said Moment The categorical variables corresponding to the sequence data are for The variational distribution of The prior distribution between Divergence, For the Moment The categorical variables corresponding to the distribution of sequence data The variational distribution of For the said Moment The prior distribution of the categorical variable corresponding to the sequence data, for The variational distribution of The prior distribution between Divergence, is the number of categories in the mixed gamma distribution composed of multiple gamma distributions, For the Moment The stick ratio parameter matrix of the sequence data The variational distribution of is the tensor probability dynamic network generation model Moment The stick ratio parameter matrix of the sequence data The prior distribution of .

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