Robust multi-intermittent radiation source direct positioning method without signal source number estimation

Abstract

The invention discloses a robust multi-intermittent radiation source direct positioning method without signal source number estimation. The method comprises the following steps: firstly, constructing a received signal model of an observation station in a multi-intermittent radiation source scene; secondly, on the basis of a received signal model, constructing a multi-radiation-source direct positioning spatial spectrum by using space-time correlation matrixes of received signals at different lag moments; finally, constructing an initial direct positioning spatial spectrum by using the radiation time slot number; sorting the states of the radiation sources by taking the spatial positions of the radiation sources as correlation basis, and distinguishing the types of the radiation sources through spectral value binary clustering under all observation time slots; aiming at an intermittent radiation source, changing the radiation time slot number in the initial direct positioning spatial spectrum according to a clustering result, and then estimating the position of the radiation source; and for a non-intermittent radiation source, the multi-radiation-source direct positioning spatial spectrum is used for estimating the radiation source position, so that a high-precision and super-resolution positioning result is obtained.

Description

Technical Field

[0001] This invention relates to the field of passive positioning technology, specifically to a robust direct positioning method for multiple intermittent radiation sources that does not require source number estimation, which can be used for direct satellite positioning of ground radiation sources. Background Technology

[0002] In real-world scenarios, due to the complex spatial scanning, frequency agility, and time-division multiple access (TDMA) operating modes of radiation sources, reconnaissance systems can only receive signals intermittently, resulting in a inconsistent number of radiation sources per observation time slot. Common examples of intermittent radiation sources include fire control intermittent radiation radars and terminals and base stations using TDMA communication. To counter anti-radiation radar attacks, fire control radars use intermittent radiation to reduce the probability of detection by anti-radiation missiles and improve their survivability. For terminals and base stations using TDMA communication, because they divide time into several time slots within a communication frame, with each time slot allocated to a specific base station for radiation, they also exhibit intermittent radiation characteristics at the reconnaissance receiving end. Simultaneously, a large number of mechanically scanned radar radiation sources exist in real-world scenarios. These sources achieve active detection of targets within a 360° search area through the periodic movement of their transmitting antennas, and most possess characteristics such as high main lobe signal-to-noise ratio, narrow beam, and stable scanning period. When locating the radiation source of a mechanically scanned radar, the narrow beam characteristics of its main lobe signal limit the area covered by the main lobe signal, resulting in intermittent interception of the radiation source signal during reconnaissance, and the intermittent radiation characteristics also appear at the receiving end.

[0003] Currently, the most in-depth research on direct localization methods for intermittent radiation sources is by Oispuu et al., who first proposed the target localization problem for intermittent radiation sources and put forward the Capon Direct Localization (CDPD) and ML direct localization methods. The former uses multidimensional search to estimate the position of each target, while the latter uses Alternation Projection (AP) to reduce the search dimensionality when localizing multiple targets. The AP algorithm reduces the computational complexity of direct localization of multiple targets. Building on this, Hao et al. proposed intermittent radiation source localization based on improved MVDR, which achieves localization by alternately estimating the radiation time slot and the radiation source position. Compared with the AP algorithm, it has higher localization accuracy; however, this method is poor at localizing nearby radiation sources.

[0004] Most existing direct positioning methods are suitable for continuous radiation source targets, but suffer from weak signal inundation for intermittent radiation sources. Therefore, how to further improve positioning accuracy and resolution to locate nearby intermittent radiation sources is a pressing technical problem to be solved in this field. Summary of the Invention

[0005] The purpose of this invention is to provide a robust direct localization method for multiple intermittent radiation sources without the need for source number estimation, thereby further improving the localization accuracy and resolution for nearby intermittent radiation sources.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A robust method for direct localization of multiple intermittent radiation sources without requiring source number estimation includes: First, a received signal model of the observation station under multiple intermittent radiation source scenarios is constructed. Second, based on the received signal model, a multi-radiation source direct location spatial spectrum is constructed using the spatiotemporal correlation matrix of the received signal at different lag times. Finally, an initial direct location spatial spectrum is constructed using the number of radiation time slots. The radiation source states are sorted based on the spatial location of the radiation source, and the radiation source type is determined by binary clustering of spectral values ​​under all observation time slots. For intermittent radiation sources, the radiation source location is estimated by updating the number of radiation time slots in the initial direct location spatial spectrum based on the clustering results. For non-intermittent radiation sources, the radiation source location is estimated using the multi-radiation source direct location spatial spectrum.

[0007] Furthermore, the scenario of the method includes a moving observation station and multiple fixed radiation sources, with the observation station performing multiple array snapshots in each observation time slot; The received signal model is characterized using the array steering vector, the radiation state of the radiation source, the radiation signal, and noise.

[0008] Furthermore, based on the received signal model, the received signal is defined. Lag The spatiotemporal correlation matrix at time t is Assuming the noise is zero-mean complex Gaussian white noise, the following holds true: ; in, Let be the array manifold matrix; since the radiation sources are uncorrelated, the spatiotemporal correlation matrix of the radiation sources is written as: ; in, For the first Each radiation source has a time delay The autocorrelation function under the given conditions; construction Different delays Different time delays Substitution The spatiotemporal correlation matrix of this delay is obtained. ; It has a joint diagonalization structure and is associated with the array manifold matrix. Zhang Cheng shares the same space; then utilize this The joint diagonalization structure of the spatiotemporal correlation matrices can determine the array manifold matrix. The value space is used to locate and estimate the radiation source.

[0009] Furthermore, for the first For every radiation source, there always exists a vector. With except the first Within the first observation time slot Array steering vector of each radiation source Other The value spaces spanned by the array guide vectors are orthogonal; therefore, we can obtain: ; in, Indicates the first The location of the radiation source ;So: ; In the formula, It is a scalar; the above formula shows that if the variable It is the actual location of the radiation source. Then there always exists a scalar. Make and They are collinear, that is: ; The above formula applies to all delays All of these conditions hold true, and different observation time slots are independent. Therefore, the positioning problem can be transformed into the following optimization problem:

[0010] Among them, variables The location of the radiation source to be estimated. For variables The corresponding array steering vector; where It is a vector The vector formed by calculation, It is a scalar The vector formed; , yes and A set of.

[0011] Furthermore, the optimization problem is expanded, and the equality constraints and objective function are combined into a single Lagrange function using the Lagrange multiplier method; by applying vectors... Solve the problem to simplify the optimization process; the final constructed spatial spectrum of direct localization of multiple radiation sources is as follows: ; in, , Parameter superscript , Represent the conjugate transpose and the pseudo-inverse, respectively. This indicates finding the largest eigenvalue of a matrix.

[0012] Furthermore, the initial direct location spatial spectrum is constructed as follows: ; in, The initial number of radiation time slots for the radiation source;

[0013] in, Indicates descending order. express Take the first one after sorting in descending order The first item Term; Position spectral function Represented as:

[0014] for Set an initial value, divide the region of interest into grids, and calculate the initial direct localization spatial spectrum of each grid point. Then, by using the CFAR detection criterion, detection and estimation are performed on the initial positioning spatial spectrum to obtain the number of radiation sources and the initial location information of each radiation source in the scenario.

[0015] Furthermore, for the first The initial location information of each radiation source was obtained using the K-means clustering method. place spectral values ​​at each location They are clustered into two categories, with the larger value corresponding to the radiation receiving time slot and the smaller value corresponding to the idle receiving time slot:

[0016] in, and These are the center values ​​of the radiation receiving time slot and the idle receiving time slot, respectively. and This represents the number of radiation time slots for the corresponding category; based on the cluster center distance, non-intermittent radiation sources are identified according to the following criteria:

[0017] in, It is a pre-set discrimination threshold; if the discrimination condition is met, the current radiation source is an intermittent radiation source, otherwise it is a continuous radiation source.

[0018] Furthermore, when the radiation source type is determined to be an intermittent radiation source, it is necessary to prevent non-radiative time slots from entering the positioning spatial spectrum calculation. Therefore, the number of radiation time slots in the initial direct positioning spatial spectrum is updated to... The location of the radiation source is estimated based on the new spatial spectrum function; when the radiation source type is identified as a non-intermittent radiation source, the location of the radiation source is estimated directly by using the multi-radiation source direct positioning spatial spectrum.

[0019] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the robust multi-intermittent radiation source direct localization method that does not require source number estimation.

[0020] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the robust multi-intermittent radiation source direct localization method without source number estimation.

[0021] Compared with the prior art, the present invention has the following technical features: This invention utilizes a spatiotemporal correlation matrix to construct a super-resolution spatial spectrum that does not require prior source number estimation. Based on this, it sorts the states of intermittent radiation sources using their spatial locations as the correlation criterion, thus distinguishing between radiation receiving time slots and idle receiving time slots. Super-resolution direct localization is performed using observation data from all radiation receiving time slots, yielding high-precision, super-resolution localization results. Compared to existing technologies, this invention fully utilizes radiation receiving time slot data for direct localization, improving the localization accuracy of intermittent radiation sources. It also designs a super-resolution direct localization spatial spectrum cost function, which, compared to subspace-based methods, eliminates the need for source number estimation and improves the localization resolution of intermittent radiation sources. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of a motion observation station detecting signals from intermittent radiation sources; Figure 2 This is a flowchart illustrating the method of the present invention; Figure 3 These are the initial position spectra of a single intermittent radiation source and a single continuous radiation source in embodiments of the present invention; Figure 4 This is a diagram showing the location results of a continuous radiation source in an embodiment of the present invention; where (a) is a two-dimensional spatial spectrum and (b) is a three-dimensional spatial spectrum. Figure 5 This is a diagram showing the location results of intermittent radiation sources in an embodiment of the present invention; where (a) is a two-dimensional spatial spectrum and (b) is a three-dimensional spatial spectrum. Figure 6 This is a schematic diagram illustrating the relationship between the root mean square error (RMSE) of the location of a single intermittent radiation source and a single continuous radiation source and the signal-to-noise ratio in an embodiment of the present invention. Detailed Implementation

[0023] This invention provides a robust direct localization method for multiple intermittent radiation sources without requiring source number estimation. The method first constructs a received signal model of an observation station in a scenario with multiple intermittent radiation sources. Second, it utilizes the spatiotemporal correlation matrix of the received signals at different lag times to construct a direct localization spatial spectrum for multiple radiation sources. Finally, it constructs an initial direct localization spatial spectrum using the number of radiation time slots. Based on the spatial location of the radiation sources, the radiation source states are sorted, and the radiation source type is determined through binary clustering of spectral values ​​across all observation time slots. For intermittent radiation sources, the radiation source location is estimated by updating the number of radiation time slots in the initial direct localization spatial spectrum based on the clustering results. For non-intermittent radiation sources, the location is estimated using the multi-radiation-source direct localization spatial spectrum, thereby obtaining high-precision, super-resolution localization results.

[0024] In the scenario of this invention, there exists a moving observation station, and the observation station is equipped with... An antenna array with individual elements; the observation station moves along a predetermined orbit, respectively at... Observations were conducted at the location and in each observation time slot. Each array of snapshots is sampled. This refers to the number of observation locations (observation time slots); there are a total of [number] observation locations (time slots) in the scene. A fixed radiation source intermittently radiates a carrier wavelength of [wavelength value] within the observation time slot. Narrowband signals. Using a point on the Earth's surface in the scene as the origin, a station-centered local coordinate system is constructed with the east direction as the x-axis, the north direction as the y-axis, and the direction perpendicular to the surface upwards as the z-axis. Where the... The location of each radiation source is , The number of radiation sources, The coordinates are in the local coordinate system of the station center. The observation station constructs a received signal model by detecting the signals emitted by the radiation source, and designs a super-resolution direct positioning spatial spectrum; based on the binary nature of the radiation source state, it performs binary clustering of the received state, and finally achieves high-precision, super-resolution positioning of intermittent radiation sources.

[0025] In this scheme, parameters or superscripts within parentheses , , , and These represent matrix transpose, matrix conjugate transpose, matrix inversion, matrix pseudo-inversion, and matrix (or vector) conjugate, respectively. This represents the complex space, and its superscript indicates the spatial dimension. This indicates a demand for expectation; Represents the trace of a matrix; Represents the 2-norm; This indicates the construction of a diagonal matrix; This represents the calculation of the determinant of a square matrix; To express summation, the detailed steps are as follows: Step 1: Construct the received signal model of the observation station.

[0026] In this scheme, the number of array sampling snapshots per observation time slot at each observation station is: Then the first The first observation time slot The received signal of the next snapshot can be represented as: (1) Among them, the received signal , Indicates the first The radiation source was at the first The binary variable representing the receiver state within the nth observation time slot, if the th... If a radiation source is in a radiating state, then If the first The radiation source is in a non-radiative state, that is ; It is in the In the observation time slot, the first The second quick snapshot observed the first The radiation signal from a radiation source It is zero-mean complex Gaussian white noise, and its covariance matrix is... Prior knowledge, For noise variance, express 3D identity matrix; Indicates the first Within the first observation time slot The array steering vector of the radiation sources is expressed as follows: (2) in, It is a natural constant. The imaginary unit, It is the wave vector; Indicates the first The array element in the first Each observation time slot relative to the location of the observation station The relative position coordinates of can be expressed as: (3) in, This indicates that the origin is the first array element, and the direction of the line connecting adjacent array elements is... x The axis and the perpendicular direction of the line connecting the array elements are: y The axis is obtained according to the right-hand screw rule. z In the local coordinate system of the array of axes, the first The position coordinates of each element, rotation matrix Depends on the first Array attitude angle (pitch angle) within each observation time slot Azimuth Roll angle ).

[0027] wave vector It is given by the following formula: (4) Step 2: Design the super-resolution direct localization spatial spectrum.

[0028] Based on the received signal model established in step 1, formula (1), the received signal is defined. Lag The spatiotemporal correlation matrix at time t is Assuming the noise is zero-mean complex Gaussian white noise, the following holds true: (5) Among them, array manifold matrix Since the radiation sources are uncorrelated, the spatiotemporal correlation matrix of the radiation sources can be written as: (6) in, For the first Each radiation source has a time delay The autocorrelation function under the following conditions For the first Each radiation source in all A collection of radiation signals from each observation time slot .structure Different delays Different time delays Substituting into formula (5) yields the spatiotemporal correlation matrix of this delay. ,in The corresponding element is: (7) The above equation has a joint diagonalization structure and is related to the array manifold matrix. Zhang Cheng shares the same space; therefore, this is utilized. The joint diagonalization structure of the spatiotemporal correlation matrices can determine the array manifold matrix. The value space is used to locate and estimate the radiation source.

[0029] For the For every radiation source, there always exists a vector. With and except Other The value spaces spanned by the array guide vectors are orthogonal; therefore, we can obtain: (8) in, Indicates the first The location of the radiation source ;So: (9) In the formula, It is a scalar; the above formula shows that if the variable It is the actual location of the radiation source. Then there always exists a scalar. Make and They are collinear, that is: (10) The above formula applies to all delays All of these conditions hold true, and different observation time slots are independent. Therefore, the positioning problem can be transformed into the following optimization problem: (11) Among them, variables The location of the radiation source to be estimated. For variables The corresponding array steering vector; where It is a vector The vector formed by calculation, It is a scalar The vector formed; , yes and A set. For a given variable , and All are about The function; to avoid trivial solutions ,right Added constraints .

[0030] Obviously, due to and Since these are unknown interference parameters, directly solving them using the above formula requires a multi-dimensional search, resulting in high computational complexity and making it difficult to implement. To reduce the computational load, we consider changing the position parameter variable... Decoupled from other parameters, only information about the variable is obtained. The simple cost function.

[0031] Expanding the above equation, we get: (12) in: (13) (14) The equality constraints and the objective function are combined into a single Lagrange function using the Lagrange multiplier method: (15) in, It is a Lagrange multiplier.

[0032] Fixed variables and vector For the Lagrange function in the above equation Regarding vectors Find the first-order partial derivative and set it to zero, then we get: (16) The solution yields: (17) Substituting formula (17) into formula (12), the optimization problem can be simplified to: (18) Minimizing the above expression is equivalent to minimizing the expression itself. The process of maximizing; Perform eigenvalue decomposition: (19) in, Indicates the first 1 eigenvalue, ; It is the corresponding number Let eigenvectors; for A linear combination of vectors yields: (20) In the formula, From Selected from 1 eigenvector ; For the corresponding A linear combination of weights; substituting the above formula into... have to: (twenty one) in, For the corresponding of One eigenvalue; due to yes The largest eigenvalue can be obtained as follows: (twenty two) By constraints have to: (twenty three) Substituting it into inequality (22), then The maximum value is: (twenty four) If and only if When the above equation holds true, the formula can be further simplified to: (25) in, This represents finding the largest eigenvalue of the matrix; therefore, the spatial spectrum for direct localization of multiple radiation sources is constructed as follows: (26) Step 3, receive state binary clustering.

[0033] To obtain an accurate and robust location spectrum, it is necessary to identify and remove the corresponding idle reception time slot interference terms in the denominator of formula (26), i.e., to estimate the radiation reception state parameters of the radiation source. The initial direct location spatial spectrum is constructed as follows: (27) in, The minimum number of radiation time slots for the radiation source; (28) in, Indicates descending order. express Take the first one after sorting in descending order The first item Term; Position spectrum function in equation (26) above It can be represented as: (29) Without any prior information In practice, this is unknown; since the cost function is established using the array's manifold vector information, which includes the location information of the target radiation source signal, calculating the cost function only within a single time slot would lead to multiple solutions. Therefore, based on the requirement of uniqueness in radiation source location estimation, it is initialized as follows: .

[0034] The region of interest (the area where the radiation source may be located, obtained from prior information or speculation, or the area to be detected) is divided into grids, and the initial direct location spatial spectrum of each grid point is calculated. Then, using the CFAR detection criterion, detection estimation is performed on the initial positioning spatial spectrum to obtain the number of radiation sources and the initial location information of each radiation source in this scenario. This involves dividing a region into grids, creating multiple location points. Each Each location corresponds to a direct location spatial spectrum. If at a certain position A large peak (forming a peak in the 3D image) indicates the presence of a radiation source at that location, and its corresponding... This is the location of the radiation source.

[0035] The above solution location only utilizes Due to the short observation time of each observation slot, the accuracy of radiation source location is not high, and the number of radiation slots for each radiation source is usually greater than [a certain number]. To further improve positioning accuracy and spatial spectrum resolution, it is necessary to estimate the number of radiation time slots for each radiation source separately and use more data received by the radiation time slot array to solve for the location of the radiation sources. For the The initial location information of each radiation source was obtained using the K-means clustering method. place spectral values ​​at each location They are clustered into two categories, where the larger value corresponds to the radiated reception time slot and the smaller value corresponds to the idle reception time slot, i.e.: (30) in, This indicates that K-means clustering is being performed. and These are the center values ​​for the two categories (radiated reception slots and idle reception slots), respectively. and This represents the number of radiation time slots for the corresponding category; based on the cluster center distance, non-intermittent radiation sources are identified according to the following criteria: (31) in, It is a priori set discrimination threshold, which gives the minimum requirement for the relative difference between the two categories; if the discrimination condition is met, the current radiation source is an intermittent radiation source, otherwise it is a continuous radiation source.

[0036] When the radiation source type is determined to be an intermittent radiation source, it is necessary to avoid non-radiative time slots from entering the location spatial spectrum calculation. Therefore, the number of radiation time slots should be updated first according to the result of formula (30). for Then, according to formula (27), Replace with Update the spatial spectral function to Finally, based on the new spatial spectral function Estimate the location of the radiation source; when the radiation source type is determined to be a non-intermittent radiation source, it means that all observation time slots of the radiation source are in a radiating state, and the location of the radiation source can be estimated based on the original spatial spectrum function of formula (26). The location of the radiation source estimated using all radiation time slots is compared with the result estimated in the initial positioning spatial spectrum. It has higher positioning accuracy and spatial resolution.

[0037] Example: The scenario established by this invention for a motion observation station to detect intermittent radiation source signals is as follows: Figure 1 As shown, a single satellite observation station was set up to observe the radiation source for 12 time slots. The coordinates were derived from STK, and the specific locations are shown in Table 1. There are two radiation sources in the scenario, located at (30.3147°N, 140.2126°E) and (30.6124°N, 140.5853°E) respectively, with transmission carrier frequencies... A BPSK signal with a frequency of 1 GHz, a code rate of 1000 bps, and a bandwidth of 1.5 kHz has the following radiated probabilities: , (i.e., in all observation time slots) In China, there are a total of Each time slot receives the corresponding intermittent radiation source signal.

[0038] Table 1. Specific positions of the satellite in different observation time slots.

[0039] A local coordinate system was constructed with (30.45°N, 140.4°E) as the origin, and a positioning search was performed within a range of -25km to 25km. The signal-to-noise ratio was set to 10dB, and the number of snapshots was 64. The method flow is as follows: Figure 2 As shown. In this embodiment, based on the requirement of uniqueness in radiation source location estimation, the following is set: .

[0040] The location results of each radiation source in this embodiment are shown in the figure below. Figures 3-5 As shown in the figure, it can be seen that the method of this application can locate both intermittent and continuous radiation sources. With the same observation scene set, a fixed number of snapshots of 128, and a signal-to-noise ratio ranging from -10dB to 10dB, 200 Monte Carlo analyses were performed in 5dB increments. The root mean square error at each signal-to-noise ratio was statistically analyzed, and the positioning performance diagram is shown below. Figure 6 It can be seen that, compared with the improved MVDR method, this method has higher positioning accuracy.

[0041] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A robust method for direct localization of multiple intermittent radiation sources without requiring source number estimation, characterized in that, include: First, a model of the received signals of the observation station under the scenario of multiple intermittent radiation sources is constructed; Secondly, based on the received signal model, a multi-source direct location spatial spectrum is constructed using the spatiotemporal correlation matrix of the received signal at different lag times. Finally, an initial direct location spatial spectrum is constructed using the number of radiation time slots. The radiation source states are sorted based on the spatial location of the radiation source, and the radiation source type is determined by binary clustering of spectral values ​​under all observation time slots. For intermittent radiation sources, the radiation source location is estimated by updating the number of radiation time slots in the initial direct location spatial spectrum according to the clustering results. For non-intermittent radiation sources, the radiation source location is estimated using the multi-source direct location spatial spectrum.

2. The robust multi-intermittent radiation source direct localization method without source number estimation as described in claim 1, characterized in that, The scenario described in the method includes a moving observation station and multiple fixed radiation sources, with the observation station performing multiple array snapshots in each observation time slot; The received signal model is characterized using the array steering vector, the radiation state of the radiation source, the radiation signal, and noise.

3. The robust multi-intermittent radiation source direct localization method without source number estimation as described in claim 1, characterized in that, Based on the received signal model, the received signal is defined. Lag The spatiotemporal correlation matrix at time t is Assuming the noise is zero-mean complex Gaussian white noise, the following holds true: ; in, Let be the array manifold matrix; since the radiation sources are uncorrelated, the spatiotemporal correlation matrix of the radiation sources is written as: ; in, For the first Each radiation source has a time delay The autocorrelation function under the given conditions; construction Different delays Different time delays Substitution The spatiotemporal correlation matrix of this delay is obtained. ; It has a joint diagonalization structure and is associated with the array manifold matrix. Zhang Cheng shares the same space; then utilize this The joint diagonalization structure of the spatiotemporal correlation matrices can determine the array manifold matrix. The value space is used to locate and estimate the radiation source.

4. The robust multi-intermittent radiation source direct localization method without source number estimation as described in claim 1, characterized in that, For the For every radiation source, there always exists a vector. With except the first Within the first observation time slot Array steering vector of each radiation source Other The value spaces spanned by the array guide vectors are orthogonal; therefore, we can obtain: ； in, Indicates the first The location of the radiation source ;So: ； In the formula, It is a scalar; the above formula shows that if the variable It is the actual location of the radiation source. Then there always exists a scalar. Make and They are collinear, that is: ； The above formula applies to all delays All of these conditions hold true, and different observation time slots are independent. Therefore, the positioning problem can be transformed into the following optimization problem: Among them, variables The location of the radiation source to be estimated. For variables The corresponding array steering vector; where It is a vector The vector formed by calculation, It is a scalar The vector formed; , yes and A set of.

5. The robust multi-intermittent radiation source direct localization method without source number estimation as described in claim 1, characterized in that, The optimization problem is expanded, and the equality constraints and objective function are combined into a single Lagrange function using the Lagrange multiplier method; by applying vectors Solve the problem to simplify the optimization process; the final constructed spatial spectrum of direct localization of multiple radiation sources is as follows: ； in, , Parameter superscript , Represent the conjugate transpose and the pseudo-inverse, respectively. This indicates finding the largest eigenvalue of a matrix.

6. The robust multi-intermittent radiation source direct localization method without source number estimation according to claim 1, characterized in that, The initial direct location spatial spectrum is constructed as follows: ； in, The initial number of radiation time slots for the radiation source; in, Indicates descending order. express Take the first one after sorting in descending order The first item Term; Position spectral function Represented as: for Set an initial value, divide the region of interest into grids, and calculate the initial direct localization spatial spectrum of each grid point. Then, by using the CFAR detection criterion, detection and estimation are performed on the initial positioning spatial spectrum to obtain the number of radiation sources and the initial location information of each radiation source in the scenario.

7. The robust multi-intermittent radiation source direct localization method without source number estimation according to claim 1, characterized in that, For the The initial location information of each radiation source was obtained using the K-means clustering method. place spectral values ​​at each location They are clustered into two categories, with the larger value corresponding to the radiation receiving time slot and the smaller value corresponding to the idle receiving time slot: in, and These are the center values ​​of the radiation receiving time slot and the idle receiving time slot, respectively. and This represents the number of radiation time slots for the corresponding category; based on the cluster center distance, non-intermittent radiation sources are identified according to the following criteria: in, It is a pre-set discrimination threshold; if the discrimination condition is met, the current radiation source is an intermittent radiation source, otherwise it is a continuous radiation source.

8. The robust multi-intermittent radiation source direct localization method without source number estimation according to claim 7, characterized in that, When the radiation source type is determined to be an intermittent radiation source, it is necessary to prevent non-radiative time slots from entering the positioning spatial spectrum calculation. Therefore, the number of radiation time slots in the initial direct positioning spatial spectrum is updated to... The location of the radiation source is estimated based on the new spatial spectrum function; when the radiation source type is identified as a non-intermittent radiation source, the location of the radiation source is estimated directly by using the multi-radiation source direct positioning spatial spectrum.

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the robust multi-intermittent radiation source direct localization method without source number estimation as described in any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the robust multi-intermittent radiation source direct localization method without source number estimation as described in any one of claims 1-8.

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