A method for multi-radiation source positioning by using a drone group

Abstract

This invention discloses a method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs), comprising the following steps: multiple UAVs receiving signals from multiple radiation sources; performing Fourier transform on the signal received by each UAV to obtain frequency domain data; integrating the frequency domain data received by all UAVs and calculating the sampling covariance matrix; gridding the monitoring area and constructing a diagonal matrix related to the steering vector and transmission delay using candidate grid point location information and receiving station location information; constructing a cost function based on the sampling covariance matrix and the diagonal matrix using the MVDR criterion, and obtaining the radiation source location estimation result through spectral peak search. The method disclosed in this invention integrates data from all observation stations, constructs a cost function, performs a gridded search within a selected area, and directly extracts radiation source location information from the received signal information, achieving high-precision localization.

Description

Technical Field

[0001] This invention relates to the fields of array signal processing and passive positioning technology, and in particular to a method for multi-radiation source positioning using a swarm of unmanned aerial vehicles (UAVs). Background Technology

[0002] In recent years, electromagnetic interference incidents have occurred frequently, with radiation sources such as illegally used frequency terminals interfering with normal broadcast communications and even interfering with civil aviation communication frequencies. Given the increasingly wide monitoring areas required, ground-based monitoring platforms are greatly affected by the complex ground environment and have very poor flexibility. Unmanned aerial vehicle (UAV) platforms, on the other hand, are highly maneuverable and less affected by line-of-sight and signal multipath propagation; therefore, positioning based on UAV aerial platforms has significant practical implications.

[0003] Traditional passive positioning involves two steps. First, the receiving station estimates parameters related to the target's location using the received signal. These parameters typically include the angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA). Second, mathematical equations are established using these parameters to solve for the target's location. This two-step positioning method ignores the correlation between signals received by different receiving stations for the same target, inevitably leading to information loss during data processing and poor positioning estimation performance at low signal-to-noise ratios. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs). This method integrates data from all observation stations, constructs a cost function, performs a gridded search within a selected area, and directly extracts the radiation source location information from the received signal information, thereby achieving high-precision localization.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs) includes the following steps:

[0007] Step 1: Assume there are an unknown number of radiation sources in space. L drones carrying M-element arrays hover at a fixed point and receive signals from the multiple radiation sources respectively.

[0008] Step 2: For each UAV receiving multiple radiation source signals, divide the observation time T into J sub-segments, each with K sampled data points, and perform Fourier transform on each to obtain the signal frequency domain data.

[0009] Step 3: Integrate the frequency domain data of all signals received by the UAVs and calculate the sampling covariance matrix;

[0010] Step 4: Grid the monitoring area and construct a diagonal matrix related to the steering vector and transmission delay using grid point candidate location information and receiving station location information;

[0011] Step 5: Based on the sampling covariance matrix and the diagonal matrix, construct the cost function using the MVDR criterion, and obtain the radiation source location estimation result through spectral peak search.

[0012] In the above scheme, step 1 is specifically as follows:

[0013] Assume there are Q stationary radiation sources on the ground, and the locations of the radiation sources are p. q , q = 1,...,Q; there exist L UAVs carrying M-element uniform arrays, and the signals received by each UAV are as follows:

[0014]

[0015] r l (t) represents the signal received by the l-th UAV at time t, where b q，l a represents the unknown signal attenuation caused by path loss from the q-th radiation source to the l-th UAV; l (p q ) represents the l-th UAV array pair starting from position p q The array response of the emitted radiation source signal. Where d is the element spacing of the uniform linear array, θ q Let θ be the direction angle of arrival of the q-th radiation source signal, λ be the signal wavelength, and the coefficient be... In order to ensure ||a l (p q )||=1, M is the number of array elements; s(·) is the complex envelope of the incident signal, τ(p q ) represents the transmission delay from the q-th radiation source signal to the l-th UAV; n l (t) represents additive complex Gaussian white noise.

[0016] In the above scheme, step 2 is specifically as follows:

[0017] For each UAV receiving signals from multiple radiation sources, the observation time T is divided into J sub-segments. The frequency domain form of the received signal in the j-th sub-segment is:

[0018]

[0019]

[0020] Among them, f k It is the frequency associated with the k-th Fourier coefficient. They are the received signals rl (t), the complex envelope of the incident signal s(t), and the additive complex white Gaussian noise n l (t) in the frequency domain form at the k-th point of the j-th sub-segment;

[0021] To simplify equation (2), let

[0022] Equation (2) can be written as:

[0023]

[0024] In the above scheme, step 3 is specifically as follows:

[0025] Integrate the frequency domain data received by all drones:

[0026]

[0027] get

[0028]

[0029] in, Indicates the received signal r l (t) in the frequency domain form at the k-th point of the j-th sub-segment Includes path loss, unknown signal attenuation, and array steering vector. This represents the frequency domain form of the complex envelope of the incident signal at the k-th point of the j-th sub-segment. n represents additive complex white Gaussian noise l (t) in the frequency domain form at the k-th point of the j-th sub-segment;

[0030] Calculate the sampling covariance matrix:

[0031]

[0032] R k The sampling covariance matrix is ​​LM×LM dimensional. express The conjugate transpose of .

[0033] In the above scheme, step 4 is specifically as follows:

[0034] The monitoring area is divided into grids according to positioning requirements. An appropriate step size is selected, and the grid intersection point p(x) is chosen. ind ,y ind (x) represents the location of the candidate target radiation source. u ,y u () represents the location of the UAV in a two-dimensional plane;

[0035] Construct observations of the candidate target radiation source locations:

[0036]

[0037]

[0038] Where θ is the directional angle between the UAV and the candidate target radiation source location, τ(p) is the propagation delay between the UAV and the candidate target radiation source location, and c represents the propagation speed of the target radiation source signal;

[0039] Construct a diagonal matrix:

[0040]

[0041] in, Let d represent the array manifold of the l-th UAV receiving array caused by the radiation source signal, d be the element spacing of the uniform linear array, λ be the signal wavelength, and f be the array manifold. k It is the frequency associated with the k-th Fourier coefficient, τ l (p) represents the propagation delay between the l-th UAV and the location of the candidate target radiation source.

[0042] In the above scheme, step 5 is specifically as follows:

[0043] Based on the sampling covariance matrix and the diagonal matrix, the cost function is constructed using the MVDR criterion:

[0044]

[0045] in, This represents the unknown signal attenuation caused by path loss in all drone arrays; I L It is an L×L identity matrix, 1 M It is an M×1 unit vector. λ represents the Kronecker product; min (·) indicates solving for the minimum eigenvalue. H Indicates conjugate transpose; Λ k (p) is a diagonal matrix; R k The sampling covariance matrix is ​​LM×LM dimensional;

[0046] The matrix in the denominator of equation (10) is a Hermitian matrix. According to the properties of Hermitian matrices, equation (10) can be rewritten as:

[0047]

[0048] Where, λ max (·) indicates solving for the largest eigenvalue;

[0049] The cost function is searched within the monitoring area, and the coordinates corresponding to the peak values ​​obtained from the search are the location estimation results of the multiple radiation sources.

[0050]

[0051] The method for multi-radiation source localization using a swarm of drones provided by the above technical solution has the following beneficial effects:

[0052] 1. This method uses received signal information to estimate the location of radiation sources by constructing a cost function and performing a gridded search within a selected area. It does not require parameter estimation and location calculation, thus avoiding the problem of parameter estimation being associated with related sources in the case of multiple radiation sources.

[0053] 2. This method can locate multiple dense radiation sources of narrowband signals. By using the MVDR criterion, the number of radiation sources does not need to be known in advance, thus avoiding the model order initialization problem.

[0054] 3. In scenarios with multiple radiation sources, the MVDR criterion offers higher accuracy and resolution compared to the maximum likelihood estimator. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below.

[0056] Figure 1 This is a flowchart of a method for locating multiple radiation sources using a swarm of drones, provided by an embodiment of the present invention.

[0057] Figure 2 This is a physical scene diagram provided in an embodiment of the present invention;

[0058] Figure 3 This is a simulation positioning result diagram provided in an embodiment of the present invention. Detailed Implementation

[0059] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0060] This invention provides a method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs), such as... Figure 1 As shown, it includes the following steps:

[0061] Step 1, as follows Figure 2In the physical scenario shown, assume there are four radiation sources on the ground, located at p1(-1.5,-50), p2(1.5,-50), p3(0,-51), and p4(0,-49). Three drones equipped with a 7-element uniform array hover at a fixed point, receiving signals from multiple radiation sources. Then, the signal received by the l-th drone at time t is...

[0062]

[0063] Among them, b q，l a represents the unknown signal attenuation caused by path loss from the q-th radiation source to the l-th UAV; l (p q ) represents the l-th UAV array pair starting from position p q The array response of the emitted radiation source signal. Where d is the element spacing of the uniform linear array, θ q Let θ be the direction angle of arrival of the q-th radiation source signal, λ be the signal wavelength, and the coefficient be... In order to ensure ||a l (p q )||=1, M is the number of array elements; s(·) is the complex envelope of the incident signal, τ l (p q ) represents the transmission delay from the q-th radiation source signal to the l-th UAV; n l (t) represents additive complex Gaussian white noise.

[0064] The location information of the radiation source is reflected in the received signal in two ways: one is the array manifold, which is related to the angle of arrival of the signal emitted by the radiation source; the other is the transmission delay, which is related to the distance from the radiation source to the receiving station.

[0065] Step 2: For each UAV receiving multiple radiation source signals, divide the observation time T into J sub-segments, each with K sampled data points, and perform Fourier transform on each to obtain the signal frequency domain data.

[0066] In this embodiment, sampling is performed at 150kHz. The received signal in the j-th sub-segment is in the frequency domain as follows:

[0067]

[0068] Among them, f k It is the frequency associated with the k-th Fourier coefficient. They are the received signals r l (t), the complex envelope of the incident signal s(t), and the additive complex white Gaussian noise n l (t) in the frequency domain form at the k-th point of the j-th sub-segment;

[0069] To simplify equation (2), let

[0070] Equation (2) can be written as:

[0071]

[0072] Step 3: Integrate the frequency domain data of all signals received by the UAVs and calculate the sampling covariance matrix;

[0073] Specifically as follows:

[0074] Integrate the frequency domain data received by all drones:

[0075]

[0076] get

[0077]

[0078] in, Indicates the received signal r l (t) in the frequency domain form at the k-th point of the j-th sub-segment Includes path loss, unknown signal attenuation, and array steering vector. This represents the frequency domain form of the complex envelope of the incident signal at the k-th point of the j-th sub-segment. n represents additive complex white Gaussian noise l (t) in the frequency domain form at the k-th point of the j-th sub-segment;

[0079] Calculate the sampling covariance matrix:

[0080]

[0081] R k The sampling covariance matrix is ​​LM×LM dimensional. express The conjugate transpose of .

[0082] In this embodiment, the received signal covariance matrix of each UAV is replaced by the sampling covariance matrix.

[0083] Step 4: Grid the monitoring area and construct a diagonal matrix related to the steering vector and transmission delay using grid point candidate location information and receiving station location information;

[0084] In this embodiment, the monitoring area is divided into grids with x-coordinates ranging from -2.5km to 2.5km and y-coordinates ranging from -52km to -47.5km, with an interval of 0.125km. The grid intersection point p(x) is selected. ind ,y ind (x) represents the location of the candidate target radiation source. u,y u () represents the location of the UAV in a two-dimensional plane;

[0085] Construct observations of the candidate target radiation source locations:

[0086]

[0087]

[0088] Where θ is the directional angle between the UAV and the candidate target radiation source location, τ(p) is the propagation delay between the UAV and the candidate target radiation source location, and c represents the propagation speed of the target radiation source signal;

[0089] Construct a diagonal matrix:

[0090]

[0091] in, Let d represent the array manifold of the l-th UAV receiving array caused by the radiation source signal, d be the element spacing of the uniform linear array, λ be the signal wavelength, and f be the array manifold. k It is the frequency associated with the k-th Fourier coefficient, τ l (p) represents the propagation delay between the l-th UAV and the location of the candidate target radiation source.

[0092] Step 5: Based on the sampling covariance matrix and the diagonal matrix, construct the cost function using the MVDR criterion, and obtain the radiation source location estimation result through spectral peak search;

[0093] Specifically as follows:

[0094] Based on the sampling covariance matrix and the diagonal matrix, the cost function is constructed using the MVDR criterion:

[0095]

[0096] in, This represents the unknown signal attenuation caused by path loss in all drone arrays; I L It is an L×L identity matrix, 1 M It is an M×1 unit vector. λ represents the Kronecker product; min (·) indicates solving for the minimum eigenvalue. H Indicates conjugate transpose; Λ k (p) is a diagonal matrix; R k The sampling covariance matrix is ​​LM×LM dimensional;

[0097] The matrix in the denominator of equation (10) is a Hermitian matrix. According to the properties of Hermitian matrices, equation (10) can be rewritten as:

[0098]

[0099] Where, λ max (·) indicates solving for the largest eigenvalue;

[0100] The cost function is searched within the monitoring area, and the coordinates corresponding to the peak values ​​obtained from the search are the location estimation results of the multiple radiation sources.

[0101]

[0102] The visual localization result obtained from the search result spectrum peak in this embodiment is as follows: Figure 3 As shown. The localization method provided by this invention combines observations received from all UAVs and ends with a cost function that depends only on the location of the target radiation source, overcoming the problem of associating estimated parameters with their associated sources. When the signal-to-noise ratio is low or the sources are dense, using MVDR (Minimum Variance Distortionless Response) can produce better resolution by generating spectral peaks (or heatmaps) to determine the number and location of radiation sources.

[0103] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs), characterized in that, Includes the following steps: Step 1: Assume there are an unknown number of radiation sources in space. A carrier The drones in the array hovered at a fixed point and received signals from multiple radiation sources. Step 2, for each UAV received a plurality of radiation source signals, in the observation time , divided into sub-segments, each segment has sample data, respectively, Fourier transform, get signal frequency domain data; Step 3: Integrate the frequency domain data of all signals received by the UAVs and calculate the sampling covariance matrix; Step 4: Grid the monitoring area and construct a diagonal matrix related to the steering vector and transmission delay using grid point candidate location information and receiving station location information; Step 5: Based on the sampling covariance matrix and the diagonal matrix, construct the cost function using the MVDR criterion, and obtain the radiation source location estimation result through spectral peak search; Step 4 is as follows: The monitoring area is divided into grids according to positioning requirements, an appropriate step size is selected, and grid intersections are chosen. The location of the candidate target radiation source. This represents the location of the drone in a two-dimensional plane. Construct observations of the candidate target radiation source locations: （7）； （8）； in, The directional angle between the UAV and the location of the candidate target radiation source. Let c be the propagation delay between the UAV and the candidate target radiation source location, and let c represent the propagation speed of the target radiation source signal. Construct a diagonal matrix: （9）； in, Indicates the first The array manifold of a UAV receiver array caused by the radiation source signal. The element spacing of a uniform linear array. For the signal wavelength, Is with the first The frequency related to the Fourier coefficients For the first Propagation delay between the location of the drone and the candidate target radiation source; The number of array elements; Step 5 is described in detail below: Based on the sampling covariance matrix and the diagonal matrix, the cost function is constructed using the MVDR criterion: （10）； in, This represents the unknown signal attenuation caused by path loss in all drone arrays; , for identity matrix yes Unit vector, Indicates the Kronecker product; This indicates the search for the minimum eigenvalue. Indicates conjugate transpose; It is a diagonal matrix; for 3D sampling covariance matrix; The matrix in the denominator of equation (10) is a Hermitian matrix. According to the properties of Hermitian matrices, equation (10) can be rewritten as: （11）； wherein denotes solving the largest eigenvalue; The cost function is searched within the monitoring area, and the coordinates corresponding to the peak values ​​obtained from the search are the location estimation results of the multiple radiation sources. （12）。 2. The method for multi-radiation source localization using a swarm of unmanned aerial vehicles (UAVs) according to claim 1, characterized in that, Step 1 is described in detail as follows: Assuming the ground has There is a stationary radiation source, and the location of the radiation source is... ; There is a plurality of drones carrying a uniform array of elements, each drone receiving a signal respectively: （1）； For the first The signals received by the drone at time t, where Indicates the first The signal from the radiation source to the first The unknown signal attenuation caused by path loss in a drone; Indicates the first A drone array from location The array response of the emitted radiation source signal. ,in, The element spacing of a uniform linear array. For the first The direction angle of arrival of the radiation source signal For the signal wavelength, the coefficients are... In order to ensure , The number of array elements; The complex envelope of the incident signal, For the first The signal from the radiation source to the first The transmission delay of a single drone; Vector representation of additive complex Gaussian white noise.

3. The method of claim 2, wherein, Step 2 is described in detail below: For each UAV receiving signals from multiple radiation sources, during the observation time Inside, divided into The sub-segment, in the... The received signal frequency domain form of each sub-segment is: （2）； in, Is with the first The frequency related to the Fourier coefficients , , Receiving signals respectively Complex envelope of incident signal Additive white Gaussian noise In the The first sub-segment Frequency domain form of a single point; To simplify equation (2), let , Equation (2) can be written as: （3）。 4. The method of claim 3, wherein, Step 3 is as follows: Integrate the frequency domain data received by all drones: （4）； get （5） in, Indicates received signal In the The first sub-segment Frequency domain form of a point, Includes path loss, unknown signal attenuation, and array steering vector. The complex envelope of the incident signal is represented in the th... The first sub-segment Frequency domain form of a point, This represents additive complex white Gaussian noise. In the The first sub-segment Frequency domain form of a single point; Calculate the sampling covariance matrix: （6）； For the covariance matrix of the samples, denotes the conjugate transpose.

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