Array information source number estimation method based on variable granularity interval information granulation

Abstract

An array information source number estimation method based on variable granularity interval information granulation comprises the steps that a uniform linear model is established, and a received signal column vector is acquired; calculating a data covariance matrix of a received signal column vector to obtain characteristic values and a characteristic value sequence formed by the characteristic values; selecting a division reference point, and dividing the characteristic value sequence into two subsequences; calculating variable granularity interval information particles corresponding to the two subsequences and the volume sum of the variable granularity interval information particles; judging whether the variable granularity interval information particle volume sum with the characteristic value number minus 1 is obtained or not; if not, returning to the third step; if yes, comparing the size of the total volume of the information particles in the variable granularity interval with the number of the characteristic values minus 1, and recording the minimum value; extracting a corresponding division mode serial number; dividing a characteristic value sequence to obtain a sub-sequence I and a sub-sequence II; counting the number of characteristic values in the first sub-sequence, namely the number of information sources; according to the method, the adaptability to small snapshot number and low signal-to-noise ratio scenes is enhanced, and the success rate of array signal source number estimation is improved.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing technology, specifically relating to array parameter estimation techniques. More specifically, it is a method for estimating the number of array sources based on variable granularity interval information granulation, applicable to sensor arrays to estimate the number of sources for space targets. This invention aims to solve the technical problem of accurately estimating the number of sources for space targets using sensor arrays under conditions of small snapshot counts and low signal-to-noise ratio signals. Background Technology

[0002] Information granulation is a cognitive and computational method that decomposes complex problems into multiple "information granules" with specific relationships. The core of information granulation is to abstract and generalize complex problems through similarity, functional proximity, or indistinguishability criteria to form operable semantic units, i.e., information granules.

[0003] Each information particle can be viewed as a relatively independent unit of information with a specific meaning and purpose. An information particle can be a subset of data, a concept, a category, a feature vector, or other information structure with specific semantics. One characteristic of information particles is internal similarity: the elements or data within an information particle have high similarity. A second characteristic is external difference: different information particles have obvious differences to facilitate differentiation and identification. A third characteristic is semantic clarity: each information particle has a certain meaning and can represent a specific concept or feature. Information particles mainly have four forms of representation: data intervals, category labels, propositions, and feature vectors. A data interval refers to an information particle consisting of a data interval in numerical data. A category label refers to the fact that for categorical data, information particles are usually represented as category labels, grouping data with similar characteristics into the same information particle. A proposition refers to the fact that in knowledge representation and processing, an information particle can be a concept or proposition to convey specific knowledge. A feature vector refers to the fact that in machine learning and pattern recognition, an information particle can be a feature vector, composed of a set of related feature values ​​used to describe the characteristics of an object or phenomenon. The role of information granules is to reduce the complexity of data processing, highlight the key features of data, facilitate the representation and transmission of data, and enhance data stability and noise resistance.

[0004] Interval information granulation is a specific method of information granulation, which refers to dividing complex data into specific numerical intervals to form information granules with clear boundaries or semantic interpretations, thereby achieving structured abstraction and efficient processing of complex data. The main methods of interval information granulation include equal-interval partitioning, equal-frequency partitioning, cluster-based partitioning, and entropy-based partitioning. Equal-interval partitioning divides the data range into equal intervals, with each interval having a fixed length. Its advantages are simplicity, intuitiveness, ease of understanding and implementation, and suitability for relatively uniform data distribution. Equal-frequency partitioning, also called quantile partitioning, ensures that the number of data points within each interval is approximately equal. This method guarantees a relatively balanced amount of data within each interval and can be used to handle unevenly distributed data. Cluster-based partitioning uses clustering algorithms to divide data points into different clusters, with each cluster corresponding to an interval. This method can partition based on the inherent structure and similarity of the data, discovering natural groupings within the data. Entropy-based partitioning determines the interval division points based on the concept of information entropy, minimizing the information entropy of the data within each interval. Information entropy measures the degree of uncertainty or disorder in data. By minimizing entropy, data within each interval can be made more homogeneous. This method requires calculating the entropy value of the data and finding the optimal partition point through iteration. It performs well when dealing with data with complex distributions and uncertainties, and can more accurately reflect the inherent characteristics of the data. Interval information granularization has wide applications in data preprocessing, knowledge representation and visualization, decision support, and other fields.

[0005] Variable granularity refers to flexibly changing the coarseness of information granulation based on data characteristics or task requirements, enabling multi-level, adaptive data abstraction and processing. Variable granularity facilitates the representation, processing, and analysis of data at different levels, better uncovering patterns, rules, and knowledge within the data, reducing the difficulty of handling complex problems, and improving the efficiency and accuracy of problem-solving.

[0006] Source number estimation is a technique used by array sensors to estimate the number of independent sources contained in a mixed signal observed from the signal. It can be applied in communication systems to determine the number of users transmitting simultaneously for resource allocation and signal detection; it can also be used in array signal processing to determine the number of targets; in speech separation and recognition problems, source number estimation helps determine the number of speakers in mixed speech, which is of great significance for improving the performance of speech recognition systems and implementing speech separation algorithms.

[0007] The existing technical solutions mainly include:

[0008] Reference 1 (Zhang Na. An Improved Source Number Estimation Algorithm [J]. Information and Communication, 2017(02):44-45) proposes an improved method based on the minimum description length criterion of information theory to achieve source number estimation. Specifically, based on the distribution theory of the covariance eigenvalues ​​of array signal samples, the method amplifies the sample eigenvalues ​​corresponding to the signal, increases the difference between the signal and noise, and achieves accurate estimation of the number of array sources. However, this method suffers from a decrease in the success rate of source number estimation when the number of snapshots is small and the signal-to-noise ratio is low.

[0009] Reference 2 (Luo Haikun, Zhou Lin, Zhang Zhenghong. A new algorithm for estimating the number of information sources based on the improved Gaisel disk method [J]. Electronic Information Countermeasures Technology, 2016, 31(06):24-28) proposes a method for estimating the number of information sources in an array based on a unitary transformation matrix and an eigenvalue weighted matrix combined with a robustness criterion. Specifically, it constructs an upgraded autocorrelation matrix and introduces a new unitary transformation matrix and an eigenvalue weighted matrix to increase the difference in Gaisel circle radius grouping. Combined with the information source number determination criterion, it achieves accurate estimation of the number of information sources in an array under colored noise background. However, this method loses the degree of freedom of the sensor array aperture, resulting in a reduction in the upper limit of the estimable number of information sources in the sensor array. Summary of the Invention

[0010] To overcome the shortcomings of existing technologies, such as reduced source number estimation success rate under small snapshot counts and low signal-to-noise ratios, and the loss of sensor array aperture degrees of freedom due to dimensionality increase processing, which leads to a reduction in the upper limit of the estimable source number of the sensor array, the present invention aims to provide an array source number estimation method based on variable granularity interval information granulation. On the one hand, this method overcomes the problem of reduced sensor array aperture degrees of freedom due to dimensionality increase processing by directly performing non-dimensional interval information granulation processing on the feature value sequence, ensuring that the upper limit of the estimable source number detection capability of the sensor array is not lost. On the other hand, by using interval information granulation operations with variable granularity, this method significantly improves the distinguishability between signal feature values ​​and noise feature values ​​under small snapshot counts and low signal-to-noise ratios, thus significantly improving the source number estimation success rate in scenarios with small snapshot counts and low signal-to-noise ratios.

[0011] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0012] A method for estimating the number of array sources based on variable granularity interval information granulation includes: establishing a uniform linear model to obtain the received signal column vector; calculating the data covariance matrix of the received signal column vector to obtain eigenvalues ​​and their constituent eigenvalue sequences; selecting a partitioning reference point to divide the eigenvalue sequence into two subsequences; calculating the variable granularity interval information particles corresponding to the two subsequences; calculating the total volume of the variable granularity interval information particles of the two subsequences; determining whether the number of eigenvalues ​​minus the total volume of one variable granularity interval information particle has been obtained; if not, selecting another partitioning reference point to divide the eigenvalue sequence into two subsequences, calculating the variable granularity interval information particles and their total volume corresponding to the two subsequences; if yes, comparing the number of eigenvalues ​​minus the total volume of one variable granularity interval information particle and recording the minimum value; extracting the partitioning method number corresponding to the minimum total volume of the variable granularity interval information particle; partitioning the eigenvalue sequence according to the partitioning method number to obtain subsequence one and subsequence two; counting the number of eigenvalues ​​in subsequence one, which is the number of sources.

[0013] Specifically, the following steps are included:

[0014] Step 1: Establish a uniform linear model and obtain the column vector x(t) of the received signal;

[0015] Step 2: Based on the expression for the received signal column vector x(t) obtained in Step 1, calculate the data covariance matrix of the received signal column vector x(t), and perform eigenvalue decomposition on the data covariance matrix to obtain the eigenvalues ​​and the eigenvalue sequence K = {κ1,κ2,...,κ}. M};

[0016] Step 3, for the feature value sequence K = {κ1,κ2,…,κ2} obtained in Step 2 M}, select an eigenvalue κ m As the reference point for the division, where the value of m takes the positive integer from 1 to M, the eigenvalue sequence K = {κ1,κ2,…,κ} is used. M The sequence is divided into two subsequences, namely subsequence one. and subsequence two After selecting the reference point κ m And the eigenvalue sequence K = {κ1,κ2,...,κ} M The operation of dividing the sequence into subsequences results in M-1 groups of subsequences, namely: the first group of subsequences contains and The second subsequence contains and ..., No. Subsequences contain and ..., the (M-1)th subsequence contains and

[0017] Step 4: For the M-1 subsequences obtained in step 3, calculate the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two

[0018] Step 5, based on the result obtained in Step 4, in the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two Calculate the sum of the information particle volumes of the variable granularity intervals of the two subsequences;

[0019] Step 6: Use the symbol num to represent the total number of variable granularity interval information particles calculated in Step 5. Each time Step 5 is executed, the value of num is incremented by 1. The initial value of num is set to 0.

[0020] Step 7: Based on the result of step 6, determine whether num equals M-1. If so, the total volume of M-1 variable granularity interval information particles is obtained. If not, proceed to step 8; otherwise, return to step 3 and execute sequentially starting from step 3.

[0021] Step 8: Based on the sum of the particle volumes of the M-1 variable particle size intervals obtained in Step 7, compare the magnitudes of the sums of the particle volumes of the M-1 variable particle size intervals and record the minimum value.

[0022] Step 9, based on the minimum value obtained in Step 8 Record the partitioning method number t corresponding to the minimum total particle size of the variable particle size range. opt ;

[0023] Step 10, based on the partitioning method number t recorded in Step 9. opt Divide the feature value sequence to obtain subsequence one and subsequence two;

[0024] Step 11, Statistically analyze the subsequence obtained in Step 10. The number of eigenvalues ​​P′ is the number of information sources; according to step 2.3, the second subsequence... The eigenvalues ​​are small and therefore considered noise eigenvalues.

[0025] The specific method of step 1 includes:

[0026] Step 1.1: Suppose P far-field narrowband spatial signals are incident on a uniform linear array with M antennas, which are arranged linearly in sequence, M > P; taking the first antenna as the reference antenna, the spacing between adjacent antennas is... λ represents the wavelength, and the incident angles of the P far-field narrowband spatial signals are θ1, θ2, ..., θ P ;

[0027] Step 1.2: At time t, the signals received by the 1st antenna, the 2nd antenna, ..., the Mth antenna are x1(t), x2(t), ..., xm respectively. M (t), the specific expression is:

[0028] x1(t)=1·s1(t)+1·s2(t)+…+1·s P (t)+n1(t) (1)

[0029]

[0030] Where s1(t), s2(t), ..., s P (t) represent the envelopes of the 1st source, the 2nd source, ..., the Pth source, respectively; 1, Let n1(t), n2(t), ..., nm represent the phase difference of the first antenna, the phase difference of the second antenna, ..., the phase difference of the Mth antenna, respectively. M (t) represent the additive white Gaussian noise on the first antenna, the additive white Gaussian noise on the second antenna, ..., the additive white Gaussian noise on the Mth antenna, respectively;

[0031] Step 1.3 involves merging the envelopes of the first source, the second source, ..., the Pth source at time t into a single source envelope column vector s(t), specifically expressed as:

[0032]

[0033] Step 1.4: Combine the phase differences of the first antenna, the second antenna, ..., the Mth antenna into a phase difference matrix A(θ), the specific expression of which is:

[0034]

[0035] Step 1.5: The expressions for the additive white Gaussian noise on the first antenna, the second antenna, ..., the Mth antenna at time t are combined and written as a noise column vector n(t), specifically:

[0036]

[0037] Step 1.6 involves receiving signals x1(t), x2(t), ..., xm at time t for the 1st array element, the 2nd array element, ..., the Mth array element. M The expressions for (t) are combined into the received signal column vector x(t), and the specific expression is as follows:

[0038]

[0039] Step 1.7, according to formula (4) from Step 1.3 to formula (7) from Step 1.6, the received signal column vector x(t) is written in the form of source envelope column vector s(t), phase difference matrix A(θ), and noise column vector n(t):

[0040] x(t)=A(θ)s(t)+n(t) (8).

[0041] The specific method for step 2 includes:

[0042] Step 2.1: Based on the expression for the received signal column vector x(t) of the M receiving antennas obtained in Step 1.7, calculate the data covariance matrix R. x :

[0043]

[0044] Where E{·} represents the expectation operator, (·) H R represents the conjugate transpose operator. S σ represents the signal covariance moment. 2 The power of additive white Gaussian noise is represented by I, which represents the identity matrix.

[0045] Step 2.2, the data covariance matrix R calculated in step 2.1 is... x Perform eigenvalue decomposition to obtain R. x M eigenvalues ​​κ1',κ'2,…,κ' M The specific expression is:

[0046]

[0047] Among them, κ' m R represents x The m-th eigenvalue, 1≤m≤M, There are M eigenvalues ​​in total; u m Represents the m-th eigenvalue κ' m The corresponding feature vectors, there are M feature vectors in total;

[0048] Step 2.3, take the R obtained in step 2.2 x M eigenvalues ​​κ1',κ'2,…,κ' MA new sequence of eigenvalues ​​K = {κ1, κ2, ..., κ} is formed in descending order. M}

[0049] The specific method for step 3 includes:

[0050] Select the new feature value sequence K = {κ1,κ2,…,κ} from step 2.3. M Any eigenvalue in} Using this as a reference point, the eigenvalue sequence is divided into two subsequences, namely subsequence one. and subsequence two Since the eigenvalue sequence K has M eigenvalues, there are M-1 ways to partition the eigenvalue sequence K into two non-empty subsequences; the M-1 subsequences generated under the M-1 partitioning methods are denoted as follows: The result of the first partitioning method is represented by subsequence one. and subsequence two The result of the second partitioning method is composed of subsequence one. and subsequence two Composition, ..., the first The result of this partitioning method is derived from subsequence one and subsequence two Composition, ..., the result of the (M-1)th partitioning method is derived from subsequence one and subsequence two composition.

[0051] The specific method for step 4 includes:

[0052] Step 4.1, regarding the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α n ,…,α N At that time, N variable granularity interval information granules lower bound Where α1=0, α N =1, 0<α n <1, 1<n<N,

[0053] When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0054]

[0055] Where max[·] represents taking the maximum value of the function within the square brackets, and arg{max[·]} represents the condition that makes the function within the square brackets reach its maximum value. The value of the function The specific form is The function card[·] returns the number of elements within square brackets, and the function med(·) returns the median within parentheses.

[0056] When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0057]

[0058] Among them, the function The specific form is

[0059] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0060]

[0061] Among them, the function The specific form is

[0062] Step 4.2, for the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm

[0063] When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0064]

[0065] Among them, the function The specific form is

[0066] When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0067]

[0068] Among them, the function The specific form is

[0069] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0070]

[0071] Among them, the function The specific form is

[0072] Step 4.3, based on the lower bound calculated in Step 4.1 and the upper bound calculated in step 4.2 Get in the first In the group subsequence, subsequence one N variable granularity interval information granules The specific expression:

[0073]

[0074] Step 4.4, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules lower bound

[0075] When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0076]

[0077] Among them, the function The specific form is

[0078] When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0079]

[0080] Among them, the function The specific form is

[0081] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0082]

[0083] Among them, the function The specific form is

[0084] Step 4.5, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm

[0085] When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0086]

[0087] Among them, the function The specific form is

[0088] When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0089]

[0090] Among them, the function The specific form is

[0091] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0092]

[0093] Among them, the function The specific form is

[0094] Step 4.6, based on the lower bound calculated in Step 4.4 and the upper bound calculated in step 4.5 Get in the first In the group subsequence, subsequence two N variable granularity interval information granules The specific expression:

[0095]

[0096] The specific method for step 5 includes:

[0097] Step 5.1, calculate the subsequence obtained in step 4.3. Variable granularity range information The sum of volumes, the result is calculated using express:

[0098]

[0099] Step 5.2, calculate the subsequence two obtained in step 4.6. Variable granularity range information The sum of volumes, the result is calculated using express;

[0100]

[0101] Step 5.3, take the subsequence obtained in step 5.1... Variable granularity range information The sum of volumes Subsequence 2 obtained in step 5.2 Variable interval information granules The sum of volumes Perform the addition operation to obtain the result at the th... The eigenvalue sequence K = {κ1,κ2,...,κ} under the following partitioning methods M The sum of the variable granularity interval information of the two subsequences of} The calculation expression is:

[0102]

[0103] The specific method for step 8 includes:

[0104] Minimum sum of particle volume for M-1 variable particle size intervals The specific calculation expression is as follows:

[0105]

[0106] Where min[·] represents the minimum value of all elements within the square brackets, 1≤t opt ≤M-1,

[0107] The specific method of step 10 includes:

[0108] According to the partitioning method number t recorded in step 9 opt Divide the eigenvalue sequence K = {κ1,κ2,...,κ} M}, thus obtaining the corresponding subsequence one and subsequence two The specific expression is:

[0109]

[0110] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0111] 1. This invention solves the problem of reduced source number estimation success rate in existing technologies under conditions of low snapshot number and low signal-to-noise ratio due to low signal-to-noise differentiation by constructing multiple information particles with variable granularity and dynamically adjusting the value of the variable granularity according to the feature value sequence, as shown in steps 4.1, 4.2, 4.4, and 4.5. It significantly improves the signal-to-noise differentiation under conditions of low snapshot number and low signal-to-noise ratio, and significantly improves the array source number estimation success rate in scenarios of low snapshot number and low signal-to-noise ratio.

[0112] 2. This invention constructs interval information granules about the feature value sequence without involving dimensionality processing, as shown in steps 4.3 and 4.6. This effectively avoids the problem of sensor array aperture degree of freedom loss caused by dimensionality increase processing in existing technologies, ensuring that the upper limit of the number of array sources that can be estimated under conditions of small snapshot number and low signal-to-noise ratio is not affected. This breaks through the bottleneck of the upper limit of array source number estimation due to array degree of freedom loss in existing technologies.

[0113] 3. This invention achieves source number estimation by directly manipulating the feature value sequence, i.e., step 3. This avoids complex mathematical operations such as constructing and decomposing the received signal subspace, reduces the accumulation of source number estimation errors caused by calculations on the received signal subspace, and improves the success rate of array source number estimation under conditions of small snapshot number and low signal-to-noise ratio.

[0114] 4. This invention calculates the total volume of information particles in variable granularity intervals under various partitioning methods, and uses the minimum value of the total volume as the criterion to achieve the optimal partitioning of the feature value sequence, thereby obtaining the source number estimate under the conditions of small snapshot number and low signal-to-noise ratio, as shown in steps 5, 8, 9 and 10. This breaks the limitation of relying on manually set judgment thresholds and realizes adaptive decision-making for array source number estimation.

[0115] 5. This invention combines the problem of estimating the number of array sources with the information granulation theory. By directly transforming the feature value sequence into multiple interval information particles with variable granularity through the information granulation theory, the optimal partitioning of the feature value sequence is achieved by using the minimum sum of the interval information particle volumes as the criterion. Finally, the source number estimate under the conditions of small snapshot number and low signal-to-noise ratio is obtained from the result of the optimal partitioning of the feature value sequence, which enhances the adaptability to small snapshot number and low signal-to-noise ratio scenarios and improves the success rate of array source number estimation.

[0116] In summary, this invention combines the array source number estimation problem with information granulation theory, directly operates on the eigenvalue sequence, constructs interval information granules with variable granularity that do not involve dimensionality processing, and obtains the optimal partitioning result of the eigenvalue sequence by using the minimum sum of the interval information granule volumes as the criterion. This effectively solves the problem of low success rate in array source number estimation under small snapshot numbers and low signal-to-noise ratio conditions in existing technologies from multiple aspects, including improving signal-to-noise differentiation, avoiding array degree-of-freedom loss, achieving adaptive decision-making in array source number estimation, and enhancing adaptability to scenarios with small snapshot numbers and low signal-to-noise ratio. It also breaks through the bottleneck of reduced upper limit of array source number estimation due to array degree-of-freedom loss in existing technologies, and has significant advantages such as high success rate of array source number estimation and no loss of upper limit of array source number estimation. Attached Figure Description

[0117] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0118] Figure 2 This is a simulation result diagram showing the change in the success rate of source number estimation as a function of the signal-to-noise ratio when using this invention to estimate the number of sources.

[0119] Figure 3 This is a simulation result graph showing the change in the success rate of source number estimation as a function of the number of snapshots when using this invention to estimate the number of sources. Detailed Implementation

[0120] The technical solutions adopted by the present invention will be further described below with reference to the accompanying drawings and specific embodiments. However, those skilled in the art will understand that the following embodiments are only used to illustrate the present invention and should not be regarded as limiting the scope of the present invention.

[0121] refer to Figure 1 The present invention provides a method for estimating the number of array sources based on variable granularity interval information granulation, comprising the following steps:

[0122] Step 1: Establish a uniform linear model and obtain the column vector x(t) of the received signal;

[0123] The specific method of step 1 includes:

[0124] Step 1.1: Suppose P far-field narrowband spatial signals are incident on a uniform linear array with M antennas, which are arranged linearly in sequence, M > P; taking the first antenna as the reference antenna, the spacing between adjacent antennas is... λ represents the wavelength, and the incident angles of the P far-field narrowband spatial signals are θ1, θ2, ..., θ P ;

[0125] Step 1.2: At time t, the signals received by the 1st antenna, the 2nd antenna, ..., the Mth antenna are x1(t), x2(t), ..., xm respectively. M (t), the specific expression is:

[0126] x1(t)=1·s1(t)+1·s2(t)+…+1·s P (t)+n1(t) (1)

[0127]

[0128] Where s1(t), s2(t), ..., s P (t) represent the envelopes of the 1st source, the 2nd source, ..., the Pth source, respectively; 1, Let n1(t), n2(t), ..., nm represent the phase difference of the first antenna, the phase difference of the second antenna, ..., the phase difference of the Mth antenna, respectively. M (t) represent the additive white Gaussian noise on the first antenna, the additive white Gaussian noise on the second antenna, ..., the additive white Gaussian noise on the Mth antenna, respectively;

[0129] Step 1.3 involves merging the envelopes of the first source, the second source, ..., the Pth source at time t into a single source envelope column vector s(t), specifically expressed as:

[0130]

[0131] Step 1.4: Combine the phase differences of the first antenna, the second antenna, ..., the Mth antenna into a phase difference matrix A(θ), the specific expression of which is:

[0132]

[0133] Step 1.5: The expressions for the additive white Gaussian noise on the first antenna, the second antenna, ..., the Mth antenna at time t are combined and written as a noise column vector n(t), specifically:

[0134]

[0135] Step 1.6 involves receiving signals x1(t), x2(t), ..., xm at time t for the 1st array element, the 2nd array element, ..., the Mth array element. M The expressions for (t) are combined into the received signal column vector x(t), and the specific expression is as follows:

[0136]

[0137] Step 1.7, according to formula (4) from Step 1.3 to formula (7) from Step 1.6, the received signal column vector x(t) is written in the form of source envelope column vector s(t), phase difference matrix A(θ), and noise column vector n(t):

[0138] x(t)=A(θ)s(t)+n(t) (8).

[0139] Step 2: Based on the expression for the received signal column vector x(t) obtained in Step 1, calculate the data covariance matrix of the received signal column vector x(t), and perform eigenvalue decomposition on the data covariance matrix to obtain the eigenvalues ​​and the eigenvalue sequence K = {κ1,κ2,…,κ}. M};

[0140] The specific method for step 2 includes:

[0141] Step 2.1: Based on the expression for the received signal column vector x(t) of the M receiving antennas obtained in Step 1.7, calculate the data covariance matrix R. x :

[0142]

[0143] Where E{·} represents the expectation operator, (·) H R represents the conjugate transpose operator. S σ represents the signal covariance moment. 2 The power of additive white Gaussian noise is represented by I, which represents the identity matrix.

[0144] Step 2.2, the data covariance matrix R calculated in step 2.1 is... x Perform eigenvalue decomposition to obtain R. x M eigenvalues ​​κ1',κ'2,…,κ' M The specific expression is:

[0145]

[0146] Among them, κ' m R represents x The m-th eigenvalue, 1≤m≤M, There are M eigenvalues ​​in total; um Represents the m-th eigenvalue κ' m The corresponding feature vectors, there are M feature vectors in total;

[0147] Step 2.3, take the R obtained in step 2.2 x M eigenvalues ​​κ1',κ'2,...,κ' M A new sequence of eigenvalues ​​K = {κ1, κ2, ..., κ} is formed in descending order. M}

[0148] Step 3, for the feature value sequence K = {κ1,κ2,…,κ2} obtained in Step 2 M}, select an eigenvalue κ m As the reference point for the division, where the value of m takes the positive integer from 1 to M, the eigenvalue sequence K = {κ1,κ2,…,κ} is used. M The sequence is divided into two subsequences, namely subsequence one. and subsequence two After selecting the reference point κ m And the eigenvalue sequence K = {κ1,κ2,...,κ} M The operation of dividing the sequence into subsequences results in M-1 groups of subsequences, namely: the first group of subsequences contains and The second subsequence contains and ..., No. Subsequences contain and ..., the (M-1)th subsequence contains and

[0149] The specific method for step 3 includes:

[0150] Select the new feature value sequence K = {κ1,κ2,...,κ} from step 2.3. M Any eigenvalue in} Using this as a reference point, the eigenvalue sequence is divided into two subsequences, namely subsequence one. and subsequence two Since the eigenvalue sequence K has M eigenvalues, there are M-1 ways to partition the eigenvalue sequence K into two non-empty subsequences; the M-1 subsequences generated under the M-1 partitioning methods are denoted as follows: The result of the first partitioning method is represented by subsequence one. and subsequence two The result of the second partitioning method is composed of subsequence one. and subsequence two Composition, ..., the first The result of this partitioning method is derived from subsequence one and subsequence two Composition, ..., the result of the (M-1)th partitioning method is derived from subsequence one and subsequence two composition.

[0151] This step divides the feature value sequence K = {κ1,κ2,…,κ} using different partitioning methods. M The problem of estimating the number of array sources under conditions of small snapshot number and low signal-to-noise ratio is divided into two different subsequences. This is transformed into calculating the eigenvalue sequence K = {κ1,κ2,…,κ}. M The problem of partitioning the array simplifies the problem of estimating the number of array sources and reduces computational complexity.

[0152] Step 4: For the M-1 subsequences obtained in step 3, calculate the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two

[0153] The specific method for step 4 includes:

[0154] Step 4.1, regarding the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α n ,…,α N At that time, N variable granularity interval information granules lower bound Where α1=0, α N =1, 0<α n <1, 1<n<N,

[0155] In this step, by dynamically adjusting the value of the variable granularity α, the array source number estimation method of the present invention can dynamically adapt to signal environments with small snapshot numbers and low signal-to-noise ratios. This breaks the limitation that the array source number estimation method with fixed granularity only performs well under specific signal environments, and improves the adaptability of the array source number estimation method of the present invention to scenarios with small snapshot numbers and low signal-to-noise ratios.

[0156] When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0157]

[0158] Where max[·] represents taking the maximum value of the function within the square brackets, and arg{max[·]} represents the condition that makes the function within the square brackets reach its maximum value. The value of the function The specific form is The function card[·] returns the number of elements within square brackets, and the function med(·) returns the median within parentheses.

[0159] When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0160]

[0161] Among them, the function The specific form is

[0162] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0163]

[0164] Among them, the function The specific form is

[0165] Step 4.2, for the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm

[0166] In this step, by dynamically adjusting the value of the variable granularity α, the array source number estimation method of the present invention can dynamically adapt to signal environments with small snapshot numbers and low signal-to-noise ratios. This breaks the limitation that the array source number estimation method with fixed granularity only performs well under specific signal environments, and improves the adaptability of the array source number estimation method of the present invention to scenarios with small snapshot numbers and low signal-to-noise ratios.

[0167] When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0168]

[0169] Among them, the function The specific form is

[0170] When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0171]

[0172] Among them, the function The specific form is

[0173] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0174]

[0175] Among them, the function The specific form is

[0176] Step 4.3, based on the lower bound calculated in Step 4.1 and the upper bound calculated in step 4.2 It can be obtained in the first place In the group subsequence, subsequence one N variable granularity interval information granules The specific expression:

[0177]

[0178] Step 4.4, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules lower bound

[0179] In this step, by dynamically adjusting the value of the variable granularity α, the array source number estimation method of the present invention can dynamically adapt to signal environments with small snapshot numbers and low signal-to-noise ratios. This breaks the limitation that the array source number estimation method with fixed granularity only performs well under specific signal environments, and improves the adaptability of the array source number estimation method of the present invention to scenarios with small snapshot numbers and low signal-to-noise ratios.

[0180] When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0181]

[0182] Among them, the function The specific form is

[0183] When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0184]

[0185] Among them, the function The specific form is

[0186] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows:

[0187]

[0188] Among them, the function The specific form is

[0189] Step 4.5, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm

[0190] In this step, by dynamically adjusting the value of the variable granularity α, the array source number estimation method of the present invention can dynamically adapt to signal environments with small snapshot numbers and low signal-to-noise ratios. This breaks the limitation that the array source number estimation method with fixed granularity only performs well under specific signal environments, and improves the adaptability of the array source number estimation method of the present invention to scenarios with small snapshot numbers and low signal-to-noise ratios.

[0191] When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0192]

[0193] Among them, the function The specific form is

[0194] When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0195]

[0196] Among them, the function The specific form is

[0197] When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows:

[0198]

[0199] Among them, the function The specific form is

[0200] Step 4.6, based on the lower bound calculated in Step 4.4 and the upper bound calculated in step 4.5 It can be obtained in the first place In the group subsequence, subsequence two N variable granularity interval information granules The specific expression:

[0201]

[0202] Step 5, based on the result obtained in Step 4, in the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two Calculate the sum of the information particle volumes of the variable granularity intervals of the two subsequences;

[0203] Step 5.1, calculate the subsequence obtained in step 4.3. Variable granularity range information The sum of volumes, the result is calculated using express:

[0204]

[0205] Step 5.2, calculate the subsequence two obtained in step 4.6. Variable granularity range information The sum of volumes, the result is calculated using express;

[0206]

[0207] Step 5.3, take the subsequence obtained in step 5.1... Variable granularity range information The sum of volumes Subsequence 2 obtained in step 5.2 Variable interval information granules The sum of volumes Perform the addition operation to obtain the result at the th... The eigenvalue sequence K = {κ1,κ2,...,κ} under the following partitioning methods M The sum of the variable granularity interval information of the two subsequences of} The calculation expression is:

[0208]

[0209] Step 6: Use the symbol num to represent the total number of variable granularity interval information particles calculated in Step 5. Each time Step 5 is executed, the value of num is incremented by 1. The initial value of num is set to 0.

[0210] Step 7: Based on the result of step 6, determine whether num equals M-1. If so, the total volume of M-1 variable granularity interval information particles is obtained. If not, proceed to step 8; otherwise, return to step 3 and execute sequentially starting from step 3.

[0211] Step 8: Based on the sum of the particle volumes of the M-1 variable particle size intervals obtained in Step 7, compare the magnitudes of the sums of the particle volumes of the M-1 variable particle size intervals and record the minimum value.

[0212] The specific method for step 8 includes:

[0213] Minimum sum of particle volume for M-1 variable particle size intervals The specific calculation expression is as follows:

[0214]

[0215] Where min[·] represents the minimum value of all elements within the square brackets, 1≤t opt ≤M-1,

[0216] Step 9, based on the minimum value obtained in Step 8 Record the partitioning method number t corresponding to the minimum total particle size of the variable particle size range. opt ;

[0217] Step 10, based on the partitioning method number t recorded in Step 9. opt Divide the feature value sequence to obtain subsequence one and subsequence two;

[0218] The specific method of step 10 includes:

[0219] According to the partitioning method number t recorded in step 9 opt Divide the eigenvalue sequence K = {κ1,κ2,...,κ} M}, thus obtaining the corresponding subsequence one and subsequence two The specific expression is:

[0220]

[0221] Step 11, Statistically analyze the subsequence obtained in Step 10. The number of eigenvalues ​​P′ is the number of information sources; according to step 2.3, the second subsequence... The eigenvalues ​​are small and represent noise characteristics, which are unrelated to the signal and do not affect the final result of the array source number estimation. Therefore, no further processing is required.

[0222] Experimental Analysis

[0223] Experimental conditions

[0224] 1. Simulation Environment

[0225] The simulation software used is MATLAB R2023a, and the operating environment is an Intel Core i9-13900K processor (3.0GHz), 32GB of memory, and a Windows 11 64-bit operating system.

[0226] 2. Array signal model parameter settings

[0227] Array structure: A uniform linear array with M=8 antennas is used, the signal wavelength λ=1m, and the element spacing d=0.5m;

[0228] Source settings: The number of far-field narrowband spatial signals is set to P=7, and the incident angles are set to θ1=-45°, θ2=-30°, θ3=-20°, θ4=0°, θ5=5°, θ6=15°, and θ7=30° respectively;

[0229] Noise characteristics: Additive white Gaussian noise.

[0230] 3. Key parameter configuration

[0231] Signal-to-noise ratio: -25dB to -15dB, with a variation interval of 5dB;

[0232] Number of quick shots: 16 to 32, with an interval of 2 shots;

[0233] Variable particle size α: Number N = 9, with values ​​set to 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9;

[0234] Number of independent experiments: 2000.

[0235] 4. Performance Evaluation Indicators

[0236] Success rate of array source number estimation = number of correct estimations / total number of simulations.

[0237] Experimental content

[0238] Based on the above experimental conditions, simulations were performed using this invention:

[0239] 1. Estimate the success rate as a function of signal-to-noise ratio;

[0240] 2. Estimate how the success rate changes with the number of snapshots.

[0241] Experimental results

[0242] like Figure 2 As shown, the performance curve of the source number estimation success rate as a function of the signal-to-noise ratio (SNR) is illustrated. The horizontal axis represents the SNR in dB, reflecting the power difference between the signal and noise. The vertical axis represents the estimation success rate, indicating the percentage of experiments that correctly estimated the number of array sources. A higher value indicates better method performance. The curve shows an increasing trend, indicating that a higher SNR results in a higher source number estimation success rate. As the SNR increases from -25 dB to -15 dB, the accuracy of this invention in estimating the number of array sources gradually improves. At an SNR of -19 dB, the estimation success rate reaches 0.94. Subsequently, as the SNR increases, the estimation success rate continues to approach 1, verifying that this invention can improve the success rate of array source number estimation in low SNR scenarios.

[0243] like Figure 3 As shown, the performance curve of the success rate of source number estimation varies with the number of snapshots. The horizontal axis represents the number of snapshots, indicating the number of snapshots of the received signal. The vertical axis represents the estimation success rate, indicating the proportion of experiments that correctly estimated the number of array sources. A higher value indicates better method performance. The curve shows an increasing trend, indicating that the more snapshots, the higher the success rate of array source number estimation. When the number of snapshots increases from 16 to 32, the success rate of the present invention for estimating the number of array sources gradually improves. At 24 snapshots, the success rate reaches 0.9. Subsequently, as the number of snapshots increases, the estimation success rate continues to approach 1, verifying that the present invention can improve the success rate of array source number estimation in scenarios with a small number of snapshots.

[0244] The key points and protection points of this invention are as follows:

[0245] 1. This invention transforms the problem of estimating the number of signal sources in a sensor array into a reasonable binary classification problem of the eigenvalue sequence of the covariance matrix of the received data from the sensor array. The entire eigenvalue sequence is reasonably divided into two subsequences, namely subsequence one and subsequence two. The number of signal sources in the array is estimated by counting the number of eigenvalues ​​in subsequence one. This invention refines and simplifies the problem of estimating the number of signal sources in an array under conditions of small snapshot number and low signal-to-noise ratio, reducing the difficulty of handling complex problems and improving the efficiency of problem-solving.

[0246] 2. This invention utilizes the information granulation method in granular computing theory, while also considering the numerical characteristics of each eigenvalue within the eigenvalue sequence, and employs an interval information granulation method to perform binary classification of the eigenvalue sequence. This invention combines the information granulation method with the array source number estimation problem, representing a novel solution to the array source number estimation problem under conditions of small snapshot number and low signal-to-noise ratio.

[0247] 3. This invention utilizes a variable granularity approach, which flexibly changes the size of the interval information granules based on the data characteristics of the feature value sequence, and analyzes and processes the feature value sequence at multiple levels, thereby improving the accuracy of array source number estimation results under conditions of small snapshot number and low signal-to-noise ratio.

Claims

1. A method for estimating the number of array sources based on variable granularity interval information granulation, characterized in that, include: Establish a uniform linear model to obtain the column vector of the received signal; Calculate the data covariance matrix of the received signal column vectors to obtain the eigenvalues ​​and the eigenvalue sequence they form. Select a reference point for partitioning and divide the feature value sequence into two subsequences; calculate the variable granularity interval information particles corresponding to the two subsequences; calculate the total volume of the variable granularity interval information particles of the two subsequences; determine whether the sum of the volume of variable granularity interval information particles equal to the number of feature values ​​minus 1 is obtained; if not, continue to select a reference point for partitioning and divide the feature value sequence into two subsequences, calculate the variable granularity interval information particles corresponding to the two subsequences and the total volume of the variable granularity interval information particles; if yes, compare the size of the sum of the volume of variable granularity interval information particles equal to the number of feature values ​​minus 1 and record the minimum value; extract the partitioning method number corresponding to the minimum value of the total volume of variable granularity interval information particles; partition the feature value sequence according to the partitioning method number to obtain subsequence one and subsequence two; count the number of feature values ​​in subsequence one, which is the number of information sources.

2. The array source number estimation method based on variable granularity interval information granulation according to claim 1, characterized in that, Specifically, the following steps are included: Step 1: Establish a uniform linear model and obtain the column vector x(t) of the received signal; Step 2: Based on the expression for the received signal column vector x(t) obtained in Step 1, calculate the data covariance matrix of the received signal column vector x(t), and perform eigenvalue decomposition on the data covariance matrix to obtain the eigenvalues ​​and the eigenvalue sequence K = {κ1,κ2,…,κ}. M }; Step 3, for the feature value sequence K = {κ1,κ2,…,κ2} obtained in Step 2 M }, select an eigenvalue κ m As the reference point for the division, where the value of m takes the positive integer from 1 to M, the eigenvalue sequence K = {κ1,κ2,…,κ} is used. M The sequence is divided into two subsequences, namely subsequence one. and subsequence two After selecting the reference point κ m And the eigenvalue sequence K = {κ1,κ2,...,κ} M The operation of dividing the sequence into subsequences results in M-1 groups of subsequences, namely: the first group of subsequences contains and The second subsequence contains No. Subsequences contain and The M-1th subsequence contains and Step 4: For the M-1 subsequences obtained in step 3, calculate the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two Step 5, based on the result obtained in Step 4, in the... The variable granularity interval information corresponding to the subsequence generated under this partitioning method The variable granularity interval information corresponding to subsequence two Calculate the sum of the information particle volumes of the variable granularity intervals of the two subsequences; Step 6: Use the symbol num to represent the total number of variable granularity interval information particles calculated in Step 5. Each time Step 5 is executed, the value of num is incremented by 1. The initial value of num is set to 0. Step 7: Based on the result of step 6, determine whether num equals M-1. If so, the total volume of M-1 variable granularity interval information particles is obtained. If not, proceed to step 8; otherwise, return to step 3 and execute sequentially starting from step 3. Step 8: Based on the sum of the particle volumes of the M-1 variable particle size intervals obtained in Step 7, compare the magnitudes of the sums of the particle volumes of the M-1 variable particle size intervals and record the minimum value. Step 9, based on the minimum value obtained in Step 8 Record the partitioning method number t corresponding to the minimum total particle size of the variable particle size range. opt ; Step 10, based on the partitioning method number t recorded in Step 9. opt Divide the feature value sequence to obtain subsequence one and subsequence two; Step 11, Statistically analyze the subsequence obtained in Step 10. The number of eigenvalues ​​P′ is the number of information sources; according to step 2.3, the second subsequence... The eigenvalues ​​are small and therefore considered noise eigenvalues.

3. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method of step 1 includes: Step 1.1: Suppose P far-field narrowband spatial signals are incident on a uniform linear array with M antennas, which are arranged linearly in sequence, M > P; taking the first antenna as the reference antenna, the spacing between adjacent antennas is... λ represents the wavelength, and the incident angles of the P far-field narrowband spatial signals are θ1, θ2, ..., θ P ; Step 1.2: At time t, the signals received by the 1st antenna, the 2nd antenna, ..., the Mth antenna are x1(t), x2(t), ..., xm respectively. M (t), the specific expression is: x1(t)=1·s1(t)+1·s2(t)+…+1·s P (t)+n1(t) (1) Where s1(t), s2(t), ..., s P (t) represent the envelopes of the first source, the second source, ..., the Pth source, respectively; Let n1(t), n2(t), ..., nm represent the phase difference of the first antenna, the phase difference of the second antenna, ..., the phase difference of the Mth antenna, respectively. M (t) represent the additive white Gaussian noise on the first antenna, the additive white Gaussian noise on the second antenna, ..., the additive white Gaussian noise on the Mth antenna, respectively; Step 1.3 involves merging the envelopes of the first source, the second source, ..., the Pth source at time t into a single source envelope column vector s(t), specifically expressed as: Step 1.4: Combine the phase differences of the first antenna, the second antenna, ..., the Mth antenna into a phase difference matrix A(θ), the specific expression of which is: Step 1.5: The expressions for the additive white Gaussian noise on the first antenna, the second antenna, ..., the Mth antenna at time t are combined and written as a noise column vector n(t), specifically: Step 1.6 involves receiving signals x1(t), x2(t), ..., xm at time t for the 1st array element, the 2nd array element, ..., the Mth array element. M The expressions for (t) are combined into the received signal column vector x(t), and the specific expression is as follows: Step 1.7, according to formula (4) from Step 1.3 to formula (7) from Step 1.6, the received signal column vector x(t) is written in the form of source envelope column vector s(t), phase difference matrix A(θ), and noise column vector n(t): x(t)=A(θ)s(t)+n(t) (8).

4. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method for step 2 includes: Step 2.1: Based on the expression for the received signal column vector x(t) of the M receiving antennas obtained in Step 1.7, calculate the data covariance matrix R. x : Where E{·} represents the expectation operator, (·) H R represents the conjugate transpose operator. S σ represents the signal covariance moment. 2 The power of additive white Gaussian noise is represented by I, which represents the identity matrix. Step 2.2, the data covariance matrix R calculated in step 2.1 is... x Perform eigenvalue decomposition to obtain R. x M eigenvalues ​​κ'1,κ'2,…,κ' M The specific expression is: Among them, κ' m R represents x The m-th eigenvalue, 1≤m≤M, There are M eigenvalues ​​in total; u m Represents the m-th eigenvalue κ' m The corresponding feature vectors, there are M feature vectors in total; Step 2.3, take the R obtained in step 2.2 x M eigenvalues ​​κ'1,κ'2,…,κ' M A new sequence of eigenvalues ​​K = {κ1, κ2, ..., κ} is formed in descending order. M } 5. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method for step 3 includes: Select the new feature value sequence K = {κ1,κ2,…,κ} from step 2.

3. M Any eigenvalue in} Using this as a reference point, the eigenvalue sequence is divided into two subsequences, namely subsequence one. and subsequence two Since the eigenvalue sequence K has M eigenvalues, there are M-1 ways to partition the eigenvalue sequence K into two non-empty subsequences; the M-1 subsequences generated under the M-1 partitioning methods are denoted as follows: The result of the first partitioning method is represented by subsequence one. and subsequence two The result of the second partitioning method is composed of subsequence one. and subsequence two Composition, ..., the first The result of this partitioning method is derived from subsequence one and subsequence two Composition, ..., the result of the (M-1)th partitioning method is derived from subsequence one and subsequence two composition.

6. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method for step 4 includes: Step 4.1, regarding the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α n ,…,α N At that time, N variable granularity interval information granules lower bound Where α1=0, α N =1, 0<α n <1, 1<n<N, When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Where max[·] represents taking the maximum value of the function within the square brackets, and arg{max[·]} represents the condition that makes the function within the square brackets reach its maximum value. The value of the function The specific form is i = 1, 2, ..., t, the function card[·] represents the number of elements in the square brackets, and the function med(·) represents the median in the parentheses; When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Among them, the function The specific form is When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Among them, the function The specific form is Step 4.2, for the first Subsequence one in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is Step 4.3, based on the lower bound calculated in Step 4.1 and the upper bound calculated in step 4.2 Get in the first In the group subsequence, subsequence one N variable granularity interval information granules The specific expression: Step 4.4, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules lower bound When the variable granularity α = α1, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Among them, the function The specific form is When the variable granularity α = α2, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Among them, the function The specific form is When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. lower bound The specific calculation expression is as follows: Among them, the function The specific form is Step 4.5, for the first subsequence two in group subsequence Calculate the values ​​of the variable particle size α as α1, α2, ..., α N At that time, N variable granularity interval information granules The upper realm When the variable granularity α = α1, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is When the variable granularity α = α2, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is When the variable particle size α = α N At that time, calculate the variable granularity interval information granules. The upper realm The specific calculation expression is as follows: Among them, the function The specific form is Step 4.6, based on the lower bound calculated in Step 4.4 and the upper bound calculated in step 4.5 Get in the first In the group subsequence, subsequence two N variable granularity interval information granules The specific expression:

7. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method for step 5 includes: Step 5.1, calculate the subsequence obtained in step 4.

3. Variable granularity range information The sum of volumes, the result is calculated using express: Step 5.2, calculate the subsequence two obtained in step 4.

6. Variable granularity range information The sum of volumes, the result is calculated using express; Step 5.3, take the subsequence obtained in step 5.1... Variable granularity range information The sum of volumes Subsequence 2 obtained in step 5.2 Variable interval information granules The sum of volumes Perform the addition operation to obtain the result at the th... The eigenvalue sequence K = {κ1,κ2,...,κ} under the following partitioning methods M The sum of the variable granularity interval information of the two subsequences of} The calculation expression is:

8. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method for step 8 includes: Minimum sum of particle volume for M-1 variable particle size intervals The specific calculation expression is as follows: Where min[·] represents the minimum value of all elements within the square brackets, 1≤t opt ≤M-1, 9. The array source number estimation method based on variable granularity interval information granulation according to claim 2, characterized in that, The specific method of step 10 includes: According to the partitioning method number t recorded in step 9 opt Divide the eigenvalue sequence K = {κ1,κ2,...,κ} M }, thus obtaining the corresponding subsequence one and subsequence two The specific expression is:

Images