A distributed radiation source positioning method

Abstract

The present invention discloses a distributed radiation source positioning method, comprising: receiving reception data sent by each sensor node; the reception data is generated by each sensor node based on a radiation source signal and a signal reception model; for each grid divided in a preset search space, delay compensation is performed on the reception data of each sensing node to obtain synchronization data; using a maximum likelihood estimation algorithm, a covariance matrix U of the synchronization data under an H0 hypothesis and a covariance matrix V under an H1 hypothesis are respectively calculated; according to the covariance matrix U and the covariance matrix V, a likelihood ratio test statistic corresponding to each grid in the preset search space is calculated; after traversing each grid in the preset search space, a peak value of all likelihood ratio test statistics is determined, and a positioning result of the radiation source is obtained according to the peak value.

Description

Technical Field

[0001] The present invention belongs to the technical field of radiation source positioning, and in particular relates to a distributed radiation source positioning method. Background Art

[0002] In space electronic reconnaissance, accurately obtaining the location of the radiation source is one of the most important tasks.

[0003] Existing methods for locating emitters include TDOA (Time Difference of Arrival), FDOA (Frequency Difference of Arrival), and combined TDOA and FDOA. These methods utilize the time and / or frequency difference measurements between arrivals at different receiving stations to locate the emitter. However, measurement errors significantly impact the positioning accuracy of these methods, and positioning accuracy deteriorates rapidly as the signal-to-noise ratio decreases. In military communications, non-standard systems are increasingly being used. Communication modes such as spread spectrum, ultra-wideband, and frequency hopping offer low power spectral density and excellent concealment. Under these circumstances, non-cooperative emitter positioning is difficult and cannot meet the demands of practical applications.

[0004] Therefore, how to provide a radiation source positioning method that is easy to implement in a low signal-to-noise ratio environment, has high accuracy and can meet practical applications is an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0005] In order to solve the above problems existing in the prior art, the present invention provides a distributed radiation source positioning method. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0006] The present invention provides a distributed radiation source positioning method, which is applied to a fusion center and includes:

[0007] Receiving reception data sent by each sensor node; the reception data is generated by each sensor node based on the radiation source signal and the signal reception model;

[0008] For each grid divided in the preset search space, the received data of each sensing node is delayed compensated to obtain synchronized data;

[0009] Calculate the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis respectively using the maximum likelihood estimation algorithm;

[0010] Calculate the likelihood ratio test statistic corresponding to each grid in the preset search space according to the covariance matrix U and the covariance matrix V;

[0011] After traversing each grid in the preset search space, the peak values ​​of all likelihood ratio test statistics are determined, and the positioning result of the radiation source is obtained according to the peak values.

[0012] In one embodiment of the present invention, for each grid divided in the preset search space, the step of performing delay compensation on the received data of each sensing node to obtain synchronized data includes:

[0013] For each grid divided in the preset search space, the delay of the first perception node receiving the received data is used as a benchmark, and the delays of the remaining perception nodes relative to the first perception node are calculated respectively, and delay compensation is performed on the received data of the remaining perception nodes.

[0014] In one embodiment of the present invention, delay compensation is performed on the received data of the remaining sensing nodes according to the following formula:

[0015]

[0016] Where, represents the delay of receiving data at the jth sensing node, N represents the number of sensing nodes, represents the delay of receiving data at the first sensing node, f s represents the sampling rate, 1 represents the full 1 vector, Δτ j represents the delay compensation for the received data of the jth sensing node, j = 2, 3, ..., N, Indicates a rounding operation.

[0017] In one embodiment of the present invention, the step of calculating the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis using the maximum likelihood estimation algorithm includes:

[0018] Solve the optimization problem using the maximum likelihood estimation algorithm:

[0019]

[0020] Where R is the covariance matrix of the synchronized data y(t) to be solved, t represents the time, t=1, 2, ..., T', T' represents the preset observation time, the preset observation time is the length of the synchronization data, They represent the power of noise received by the i-th sensor node, det(·) represents the determinant of the matrix, and tr(·) represents the trace of the matrix; under the H0 hypothesis, H=0, and under the H1 hypothesis, H=[h1 h2 ...h N ] T , h irepresents the complex propagation gain from the radiation source to the i-th receiving node, i = 1, 2, 3, ..., N, and N represents the number of sensing nodes.

[0021] In one embodiment of the present invention, under the H1 assumption, the optimization problem is solved according to the following steps:

[0022] Initialize the number of iterations k = 0, and in, is a randomly generated diagonal matrix,

[0023] Let k = k + 1;

[0024] according to Calculate the matrix And Perform eigenvalue decomposition: for The eigenvalues ​​of and for The maximum eigenvalue of

[0025] According to the maximum eigenvalue Calculate the matrix And generate any orthogonal matrix Q, where

[0026] use and Q Update

[0027]

[0028] based on S Update

[0029] based on and Update

[0030]

[0031] judge Whether the convergence condition is met; if not, return to the step of setting k=k+1; if so, output The covariance matrix V of the synchronization data under the H1 assumption is obtained.

[0032] In one embodiment of the present invention, the convergence condition is:

[0033]

[0034] Where ε represents the preset convergence accuracy.

[0035] In one embodiment of the present invention, the likelihood ratio test statistic corresponding to each grid in the preset search space is calculated according to the covariance matrix U and the covariance matrix V according to the following formula:

[0036]

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] The present invention provides a distributed radiation source positioning method. After the radiation source signal reaches each sensing node after channel fading, each sensing node transmits the received data to a fusion center. The fusion center divides the search space into a grid. The asynchronous data of the fusion center is time-delay compensated and a likelihood ratio test statistic is calculated based on the location of each search. When the search location is the actual radiation source location, the log likelihood ratio test statistic will peak, thereby achieving the positioning of the radiation source. It should be understood that existing passive positioning methods such as time difference and frequency difference positioning methods use a two-step method, that is, the first step is to extract signal parameters related to the position from the sampled signal, and then the extracted parameters are used in the second step to estimate the position of the signal source. However, under low signal-to-noise ratio (SNR), the parameter estimation error is large, resulting in a larger positioning error under low SNR conditions. The grid search-based method of the present invention does not require a parameter extraction step and can directly estimate the position of the radiation source from the received signal, thereby improving the accuracy of radiation source positioning under low SNR conditions.

[0039] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 This is a flow chart of a distributed radiation source positioning method provided by an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the spatial distribution of radiation sources and sensing nodes provided by an embodiment of the present invention;

[0042] Figure 3a 1 is a schematic diagram of a likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention;

[0043] Figure 3b is another schematic diagram of the likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention;

[0044] Figure 4a This is a curve diagram of the radiation source positioning accuracy provided by an embodiment of the present invention;

[0045] Figure 4bis another curve diagram of the radiation source positioning accuracy provided by an embodiment of the present invention;

[0046] Figure 5a is another schematic diagram of the likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention;

[0047] Figure 5b is another schematic diagram of the likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention;

[0048] Figure 6a is another curve diagram of the radiation source positioning accuracy provided by an embodiment of the present invention;

[0049] Figure 6b This is another curve diagram of the radiation source positioning accuracy provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0050] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0051] Figure 1 This is a flow chart of a distributed radiation source positioning method provided by an embodiment of the present invention. Figure 1 As shown, an embodiment of the present invention provides a distributed radiation source positioning method, including:

[0052] S1, receiving reception data sent by each sensor node; the reception data is generated by each sensor node based on the radiation source signal and the signal reception model;

[0053] S2. For each grid divided in the preset search space, delay compensation is performed on the received data of each sensing node to obtain synchronized data;

[0054] S3, using the maximum likelihood estimation algorithm to calculate the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis;

[0055] S4. Calculate the likelihood ratio test statistic corresponding to each grid in the preset search space according to the covariance matrix U and the covariance matrix V;

[0056] S5. After traversing each grid in the preset search space, determine the peak value of all likelihood ratio test statistics, and obtain the positioning result of the radiation source according to the peak value.

[0057] In the above step S2, for each grid divided in the preset search space, delay compensation is performed on the received data of each sensing node to obtain synchronized data, including:

[0058] For each grid divided in the preset search space, the delay of the first sensing node receiving the received data is used as the benchmark, and the delay of the remaining sensing nodes relative to the first sensing node is calculated respectively, and the delay compensation is performed on the received data of the remaining sensing nodes.

[0059] It should be understood that in the process of distributed detection of radiation sources, N sensing nodes obtain received data from different directions and transmit the received data to the fusion center. Therefore, the received data obtained by the fusion center is asynchronous. Therefore, in this embodiment, the fusion center compensates for the delay of the asynchronous data and converts it into synchronous data.

[0060] Specifically, this embodiment takes the case where the sensing node channel is a Ricean channel as an example. When the maximum Doppler frequency deviation is 0, the complex propagation gain h from the radiation source to the i-th receiving node is i is a complex number whose modulus follows the Rice distribution, and the position of the radiation source is recorded as P s =(x0,y0), the position of the i-th sensor node is recorded as P r,i =(x i ,y i ), then the delay from the radiation source to the i-th sensing node is:

[0061]

[0062] Where c represents the speed of light, c = 3 × 10 8 .

[0063] Furthermore, the received data of the i-th sensing node is:

[0064] y i (t) = h i *s(t-τ i )+n i (t);

[0065] Where s(t) represents the radiation source signal, n i (t) represents the receiving noise of the i-th sensing node, which obeys the complex Gaussian distribution, i = 1,...,N, N represents the number of sensing nodes.

[0066] Optionally, the fusion center performs delay compensation on the received data of the remaining sensing nodes according to the following formula:

[0067]

[0068] Where, represents the delay of receiving data at the jth sensing node, N represents the number of sensing nodes, represents the delay of receiving data at the first sensing node, f s represents the sampling rate, 1 represents the full 1 vector, Δτj represents the delay compensation for the received data of the jth sensing node, j = 2, 3, ..., N, Indicates a rounding operation.

[0069] In the above step S3, the step of calculating the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis using the maximum likelihood estimation algorithm includes:

[0070] Solve the optimization problem using the maximum likelihood estimation algorithm:

[0071]

[0072] Where R is the covariance matrix of the synchronized data y(t) to be solved, t represents the time, t=1,2,...,T', T' represents the preset observation time, the preset observation time is the length of the synchronization data, denote the power of noise received by the i-th sensor node, det(·) denotes the determinant of the matrix, and tr(·) denotes the trace of the matrix. Under the H0 hypothesis, H = 0, and under the H1 hypothesis, H = [h1 h2 … h N ] T , h i represents the complex propagation gain from the radiation source to the i-th receiving node.

[0073] It should be noted that in this embodiment, the H0 assumption refers to a grid without a radiation source, and the H1 assumption refers to a grid with a radiation source. Under the H0 and H1 assumptions, the received data of the i-th sensing node at the observation time T' can be expressed as:

[0074]

[0075] Where y i (t) represents the received data of the i-th sensor node at time t, n i (t) represents the receiving noise of the i-th sensing node, which has a mean of 0 and a variance of complex Gaussian distribution and are statistically independent of each other, h i represents the complex propagation gain from the radiation source to the i-th receiving node, which is used to describe the channel propagation effect. s(t) represents the radiation source signal, t = 1, ..., T'.

[0076] Specifically, in this embodiment, the above optimization problem can be solved according to the following steps:

[0077] Initialize the number of iterations k = 0, and in, It can be a randomly generated matrix of rank 1, is a randomly generated diagonal matrix,

[0078] Let k = k + 1;

[0079] according to Calculate the matrix And Perform eigenvalue decomposition: for The eigenvalues ​​of and for The maximum eigenvalue of

[0080] According to the maximum eigenvalue Calculate the matrix And generate any orthogonal matrix Q, where

[0081] use and Q Update

[0082]

[0083] based on S Update

[0084] based on and Update

[0085]

[0086] judge Whether the convergence condition is met; if not, return to the step of setting k=k+1; if so, output The covariance matrix V of the synchronization data under the H1 assumption is obtained.

[0087] For example, the convergence condition is:

[0088]

[0089] Where ε represents the preset convergence accuracy.

[0090] Furthermore, in the above step S4, the likelihood ratio test statistic ξ corresponding to each grid in the preset search space is calculated according to the covariance matrix U and the covariance matrix V according to the following formula: GLR :

[0091]

[0092] where f(y(1),...,y(T')|V,H1) represents the joint conditional probability density function value of the observed samples under the H1 hypothesis, and f(y(1),...,y(T')|U,H0) represents the joint conditional probability density function value of the observed samples under the H0 hypothesis.

[0093] Since the likelihood ratio test statistic of the synchronous data is larger than that of the asynchronous data before delay compensation, when the searched position is the true position of the radiation source, the likelihood ratio test statistic will peak, thereby determining the positioning result of the radiation source.

[0094] The distributed radiation source positioning method provided by the present invention is further illustrated below through simulation experiments.

[0095] Specifically, Figure 2 This is a schematic diagram of the spatial distribution of the radiation source and the sensing node provided by an embodiment of the present invention. The radiation source signal adopts BPSK (Binary Phase Shift Keying) modulation. The simulation scenario and simulation parameter settings are shown in Table 1:

[0096] Table 1 Distributed radiation source positioning simulation parameter settings

[0097] Parameter name parameter Grid Search Space Ω={(x,y)|x∈[-25km,25km],y∈[-25km,25km]} Radiation source signal modulation method BPSK / QPSK Radiation source signal baud rate 100kBaud True radiation source location [-15Km,0] Position of each sensing node <![CDATA[P r ={(x,y)|x∈[0km,25km],y∈[-25km,25km]}]]> Reference signal-to-noise ratio at 5km / dB -11:5 Sampling rate 600kHz Monte Carlo simulation times 40

[0098] Figure 3a and Figure 3b is a schematic diagram of the likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention, wherein: Figure 3a The average signal-to-noise ratio shown is -25.3dB, Figure 3b The average signal-to-noise ratio shown is 14.3dB. Figure 3a-3b As shown in Figure 3, the value of the likelihood ratio test statistic increases with the increase of the signal-to-noise ratio. The larger the signal-to-noise ratio, the more obvious the peak.

[0099] Figure 4a and Figure 4b is a schematic diagram of a curve showing the positioning accuracy of a radiation source provided by an embodiment of the present invention, wherein: Figure 4a The location of the radiation source is on the grid point, and the width of the search grid is 2.5 km. Figure 4b The location of the radiation source is not on the grid point. The width of the search grid is 0.5 km. The radiation source signal uses BPSK (Binary Phase Shift Keying) modulation. Figure 4a-4b , the positioning error will decrease as the average signal-to-noise ratio of each receiving node increases. When the position of the radiation source is exactly on the grid point, the positioning error is 0.

[0100] Figure 5a and Figure 5b is a schematic diagram of the likelihood ratio test statistic under different signal-to-noise ratios provided by an embodiment of the present invention, wherein: Figure 5a The average signal-to-noise ratio shown is -25.3dB, Figure 5b The average signal-to-noise ratio shown is 14.3dB. Figure 5a-5b As shown in Figure 3, the value of the likelihood ratio test statistic increases with the increase of the signal-to-noise ratio. The larger the signal-to-noise ratio, the more obvious the peak.

[0101] Figure 6a and Figure 6b is a curve diagram of the radiation source positioning accuracy provided by an embodiment of the present invention, Figure 6a The location of the radiation source is on a grid point. The width of the search grid is 2.5 km. The radiation source signal is modulated using QPSK (Quadrature Phase Shift Keying). Figure 6b The location of the radiation source is not on the grid point, and the width of the search grid is 0.5 km. Figure 5a-5b As shown in the figure, the positioning error decreases as the average signal-to-noise ratio of each receiving node increases. When the position of the radiation source is exactly on the grid point, the positioning error is 0.

[0102] In a predefined simulation scenario, this example analyzes the impact of the average signal-to-noise ratio (SNR) of each sensing node on positioning accuracy. As shown in the figure, positioning error decreases as the SNR increases, and the GLR test statistic at the peak also increases with the SNR. When the radiation source signal uses different modulation methods, the positioning accuracy curves vary with the average SNR of each node, showing essentially the same trend.

[0103] It can be seen from the above embodiments that the beneficial effects of the present invention are:

[0104] The present invention provides a distributed radiation source positioning method. After the radiation source signal reaches each sensing node after channel fading, each sensing node transmits the received data to a fusion center. The fusion center divides the search space into a grid. The asynchronous data of the fusion center is time-delay compensated and a likelihood ratio test statistic is calculated based on the location of each search. When the search location is the actual radiation source location, the log likelihood ratio test statistic will peak, thereby achieving the positioning of the radiation source. It should be understood that existing passive positioning methods such as time difference and frequency difference positioning methods use a two-step method, that is, the first step is to extract signal parameters related to the position from the sampled signal, and then the extracted parameters are used in the second step to estimate the position of the signal source. However, under low signal-to-noise ratio (SNR), the parameter estimation error is large, resulting in a larger positioning error under low SNR conditions. The grid search-based method of the present invention does not require a parameter extraction step and can directly estimate the position of the radiation source from the received signal, thereby improving the accuracy of radiation source positioning under low SNR conditions.

[0105] In the description of the present invention, the terms "first" and "second" are used for descriptive purposes only and should not be understood to indicate or imply relative importance or implicitly specify the number of the technical features indicated. Therefore, a feature specified as "first" or "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0106] Descriptions with reference to the terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0107] Although the present application is described herein in conjunction with various embodiments, in the process of implementing the claimed application, those skilled in the art can understand and implement other variations of the disclosed embodiments by reviewing the drawings, the disclosure, and the appended claims.

[0108] The above is a further detailed description of the present invention in conjunction with specific preferred embodiments, and the specific implementation of the present invention should not be considered to be limited to these descriptions. For those skilled in the art to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all of these should be considered to fall within the scope of protection of the present invention.

Claims

1. A distributed radiation source positioning method, characterized in that: Applications in fusion centers include: Receiving reception data sent by each sensor node; the reception data is generated by each sensor node based on the radiation source signal and the signal reception model; For each grid divided in the preset search space, the received data of each sensing node is delayed compensated to obtain synchronized data; Calculate the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis respectively using the maximum likelihood estimation algorithm; Calculate the likelihood ratio test statistic corresponding to each grid in the preset search space according to the covariance matrix U and the covariance matrix V; After traversing each grid in the preset search space, the peak values ​​of all likelihood ratio test statistics are determined, and the positioning result of the radiation source is obtained according to the peak values.

2. The distributed radiation source positioning method according to claim 1, characterized in that: For each grid divided in the preset search space, delay compensation is performed on the received data of each sensing node to obtain synchronized data, including: For each grid divided in the preset search space, the delay of the first perception node receiving the received data is used as a benchmark, and the delays of the remaining perception nodes relative to the first perception node are calculated respectively, and delay compensation is performed on the received data of the remaining perception nodes.

3. The distributed radiation source positioning method according to claim 2, characterized in that: The delay compensation for the received data of the remaining sensing nodes is performed according to the following formula: Where, represents the delay of receiving data at the jth sensing node, N represents the number of sensing nodes, represents the delay of receiving data at the first sensing node, f s represents the sampling rate, 1 represents the full 1 vector, Δτ j represents the delay compensation for the received data of the jth sensing node, j = 2, 3, ..., N, Indicates a rounding operation.

4. The distributed radiation source positioning method according to claim 1, characterized in that: The step of calculating the covariance matrix U of the synchronization data under the H0 hypothesis and the covariance matrix V under the H1 hypothesis using the maximum likelihood estimation algorithm includes: Solve the optimization problem using the maximum likelihood estimation algorithm: Where R is the covariance matrix of the synchronized data y(t) to be solved, t represents the time, t=1, 2, ..., T', T' represents the preset observation time, the preset observation time is the length of the synchronization data, denote the power of noise received by the i-th sensor node, det(·) denotes the determinant of the matrix, and tr(·) denotes the trace of the matrix. Under the H0 hypothesis, H = 0, and under the H1 hypothesis, H = [h1 h2 … h N ] T , h i represents the complex propagation gain from the radiation source to the i-th receiving node, i = 1, 2, 3, ..., N, and N represents the number of sensing nodes.

5. The distributed radiation source positioning method according to claim 4, characterized in that: Under the H1 assumption, the optimization problem is solved as follows: Initialize the number of iterations k = 0, and in, is a randomly generated diagonal matrix, Let k = k + 1; according to Calculate the matrix And Perform eigenvalue decomposition: for The eigenvalues ​​of and for The maximum eigenvalue of According to the maximum eigenvalue Calculate the matrix And generate any orthogonal matrix Q, where use and Q Update based on S Update based on and Updated judge Whether the convergence condition is met; if not, return to the step of setting k=k+1; if so, output The covariance matrix V of the synchronization data under the H1 assumption is obtained.

6. The distributed radiation source positioning method according to claim 5, characterized in that: The convergence condition is: Where ε represents the preset convergence accuracy.

7. The distributed radiation source positioning method according to claim 6, characterized in that: According to the covariance matrix U and the covariance matrix V, the likelihood ratio test statistic corresponding to each grid in the preset search space is calculated according to the following formula:

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