Distributed passive positioning method based on spectrum whitening cross-correlation

Abstract

The invention discloses a distributed passive positioning method based on spectrum whitening cross-correlation, and belongs to the technical field of underwater sound distributed passive positioning. According to the method, the problems of low time delay inequality estimation precision and low target positioning precision caused by low-frequency strong line spectrums in ship radiation noise are solved. In order to solve the problem that a low-frequency strong line spectrum in ship radiation noise affects delay inequality estimation, a signal spectrum whitening processing method is provided, and then a distributed passive positioning method based on spectrum whitening cross correlation is provided. Aiming at the non-white characteristic of a signal power spectrum caused by a ship line spectrum and a continuous spectrum trend, an alpha filter is used for carrying out average processing on the same frequency in time to obtain the average intensity of each frequency point, and then spectrum whitening processing on the power spectrum is realized through frequency domain normalization processing. The method solves a problem that the low-frequency strong line spectrum enables the correlation function to generate multiple peaks, thereby affecting the time delay estimation precision, and improves the precision of subsequent target positioning. The method can be applied to distributed passive positioning.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic distributed passive localization technology, specifically relating to a distributed passive localization method based on spectral whitening cross-correlation. Background Technology

[0002] Distributed detection has become an important research direction in the detection field in recent years, offering advantages such as scalability, flexibility, and stability. Wide coverage can be achieved through node deployment. The basic principle is to utilize the signal characteristics (including angle of arrival and time of arrival) generated during signal transmission and reception between nodes for signal processing to calculate the target signal's position information. Time-difference-of-arrival (TDOA) positioning is simple in principle, and its feasibility and accuracy have been widely verified in cooperative target positioning. The key to TDOA positioning lies in high-precision time delay difference estimation. However, in non-cooperative passive target positioning methods based on ship radiated noise, the ship radiated noise often contains abundant low-frequency strong line spectra. These low-frequency strong line spectra severely interfere with the cross-correlation effect, causing the correlation function to produce multiple peaks. These multiple peaks reduce the accuracy of time delay difference estimation, leading to low target positioning accuracy. Therefore, removing line spectrum interference before time delay difference estimation is essential. Summary of the Invention

[0003] The purpose of this invention is to solve the problems of low time delay difference estimation accuracy and low target positioning accuracy caused by the low-frequency strong line spectrum in ship radiated noise, and to propose a distributed passive positioning method based on spectral whitening cross-correlation.

[0004] The technical solution adopted by this invention to solve the above-mentioned technical problems is: a distributed passive localization method based on spectral whitening cross-correlation, the method specifically including the following steps:

[0005] Step 1: Utilize the deployed Each node simultaneously receives ship-radiated noise signals.

[0006] Set the duration of each signal received by the node to T;

[0007] Step 2: Process the data received by each node. The segment signal is processed to obtain the time-domain received signal after spectral whitening of each node;

[0008] For the first received by node i segment signal The processing steps in step two are as follows:

[0009] Step Two: 1. Signal Perform an FFT to obtain the signal. Corresponding frequency domain signal ;

[0010] Step 22: For frequency domain signals For each frequency point result, perform separate Filtering yields the filtered frequency domain result. ;

[0011] Steps two and three: Based on the filtered frequency domain results and frequency domain signals The result after spectral whitening was obtained ;

[0012] Step 2.4: Results of Spectral Whitening Perform IFFT to obtain the time-domain received signal after spectral whitening at node i. ;

[0013] Step 3: For any two nodes, perform cross-correlation on the spectral whitening time-domain received signals corresponding to the two nodes, and obtain the time delay difference between the two nodes and the target based on the cross-correlation result;

[0014] Step 4: Calculate the target's position based on the time delay difference obtained in Step 3.

[0015] Furthermore, the specific process of step two is as follows:

[0016]

[0017] in, Represents the frequency domain result after filtering. Mid-frequency point The value;

[0018] Represents the frequency domain result after filtering. Mid-frequency point The value, Indicates the number of nodes i that received the first... The filtering result of the frequency domain signal corresponding to the segment signal;

[0019] Represents frequency domain signal Mid-frequency point The value;

[0020] These are the whitening filter coefficients. , This indicates the total number of frequency points.

[0021] Furthermore, the specific process of steps two and three is as follows:

[0022]

[0023] in, Indicates the result after spectral whitening. Mid-frequency point The value, .

[0024] Furthermore, the specific process of step three is as follows:

[0025] For any two nodes i and j, the result of cross-correlation between the time-domain received signal of node i after spectral whitening and the time-domain received signal of node j after spectral whitening is:

[0026]

[0027] in, This represents the time-domain received signal after the spectrum of node j has been whitened;

[0028] Indicates the time delay difference. Indicates time delay difference The corresponding cross-correlation results;

[0029] For different value corresponding Low-pass filtering is performed to obtain the cross-correlation envelope, and then the peak value of the cross-correlation envelope is... The value represents the time delay difference between node i and node j from the target. ;

[0030] in, express The absolute value of.

[0031] Furthermore, the calculation of the target's position based on the time delay difference obtained in step three specifically involves:

[0032] For a target with a known depth Z:

[0033] Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as ,but and The difference is , and The difference is ;

[0034] according to and Establish a system of equations:

[0035]

[0036] in, For equivalent speed of sound, Indicates multiplication. This represents the time delay difference between node k and node j from the target;

[0037] The established system of equations is then solved to obtain the target's position coordinates. .

[0038] Furthermore, the aforementioned and The difference for:

[0039] Let the coordinates of node i be... The coordinates of node j are: Mark the target's location coordinates as ;

[0040] .

[0041] Furthermore, the aforementioned and The difference for:

[0042] Let the coordinates of node k be... :

[0043] .

[0044] Furthermore, the calculation of the target's position based on the time delay difference obtained in step three specifically involves:

[0045] For a target with unknown depth Z:

[0046] Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as Let the distance between node p and the target be denoted as ,but and The difference is , and The difference is , and The difference is ;

[0047] Then according to , and Establish a system of equations:

[0048]

[0049] in, For equivalent speed of sound, Indicates multiplication. This represents the time delay difference between node p and node k from the target. This represents the time delay difference between node k and node j from the target;

[0050] Solving the established system of equations yields the target's position coordinates. .

[0051] Furthermore, the aforementioned and The difference , and The difference , and The difference They are respectively:

[0052] Let the coordinates of node i be... The coordinates of node j are: Mark the target's location coordinates as ,but

[0053]

[0054] Let the coordinates of node k be... ,but

[0055]

[0056] Mark the coordinates of node p as ,but

[0057] .

[0058] The beneficial effects of this invention are:

[0059] This invention addresses the impact of low-frequency strong line spectra in ship radiated noise on time delay difference estimation. It proposes a signal spectral whitening method, and further, a distributed passive positioning method based on spectral whitening cross-correlation. To address the non-whitening characteristics of the signal power spectrum caused by the ship's line spectrum and continuous spectrum trends, an α-filter is used to average the intensity of the same frequency over time to obtain the average intensity at each frequency point. Then, frequency domain normalization is applied to achieve spectral whitening of the power spectrum. This solves the problem of low-frequency strong line spectra causing multiple peaks in the correlation function, thus affecting the accuracy of time delay estimation and improving the accuracy of subsequent target positioning. Attached Figure Description

[0060] Figure 1 This is a flowchart of a distributed passive localization method based on spectral whitening cross-correlation according to the present invention;

[0061] Figure 2This is a schematic diagram comparing the power spectra of the received signal before and after spectral whitening.

[0062] Figure 3 This is a diagram showing the cross-correlation envelope results of the received signals from node 1 and node 3 before spectral whitening;

[0063] Figure 4 This is a slice of the cross-correlation envelope results of the received signals from node 1 and node 3 before spectral whitening;

[0064] Figure 5 This is a diagram showing the cross-correlation envelope of the signals received by node 1 and node 2 after spectral whitening.

[0065] Figure 6 This is a diagram showing the cross-correlation envelope of the signals received by node 1 and node 3 after spectral whitening.

[0066] Figure 7 This is a diagram showing the cross-correlation envelope of the signals received by nodes 2 and 3 after spectral whitening.

[0067] Figure 8 This is a slice of the cross-correlation envelope results of the received signals from nodes 1 and 2, nodes 1 and 3, and nodes 2 and 3 after spectral whitening.

[0068] Figure 9 This is a comparison chart of the target trajectory localization results before and after spectral whitening. Detailed Implementation

[0069] Specific implementation method one: Combining Figure 1 This embodiment describes a distributed passive localization method based on spectral whitening cross-correlation, which specifically includes the following steps:

[0070] Step 1: Utilize the deployed A node with a known location simultaneously receives the ship's radiated noise signal. The node can be located on the water surface or underwater. In this invention, a submersible moor is used as an example.

[0071] Set the duration of each signal received by the node to T;

[0072] Step 2: Each node receives the first... After the segment signal, the first segment received by each node is processed separately. The segment signal is processed to obtain the time-domain received signal after spectral whitening of each node;

[0073] For the first received by node i segment signal The processing steps in step two are as follows:

[0074] Step Two: 1. Signal Perform FFT (Fourier Transform) to obtain the signal Corresponding frequency domain signal ;

[0075] Step 22: For frequency domain signals For each frequency point result, perform separate Filtering yields the filtered frequency domain result. ;

[0076] Steps two and three: Based on the filtered frequency domain results and frequency domain signals The result after spectral whitening was obtained ;

[0077] Step 2.4: Results of Spectral Whitening Perform IFFT (Inverse Fourier Transform) to obtain the time-domain received signal after spectral whitening at node i. ;

[0078] Step 3: For any two nodes, perform cross-correlation on the spectral whitening time-domain received signals corresponding to the two nodes, and obtain the time delay difference between the two nodes and the target based on the cross-correlation result;

[0079] Step 4: Calculate the target's position based on the time delay difference obtained in Step 3.

[0080] This invention first sets the duration of each signal segment received by a node to be T. Then, all deployed nodes simultaneously begin receiving ship radiated noise signals. Because each node acquires signals synchronously, when the acquisition time reaches T, each node simultaneously completes the acquisition of the first signal segment; when the acquisition time reaches 2T, each node simultaneously completes the acquisition of the second signal segment, and so on. Furthermore, this invention uses the simultaneous acquisition of the first signal segment by each node as the basis for... Taking a segment signal as an example, when each node completes the first segment... After acquiring the segment signal, based on the first segment received by each node... The first segment of the signal is performed The target position is calculated in this way. After each node collects a segment of signal, it can calculate its current position. The trajectory formed by connecting the calculated target positions is the target's trajectory.

[0081] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One. The specific process of step two is as follows:

[0082]

[0083] in, Represents the frequency domain result after filtering. Mid-frequency point The value;

[0084] Represents the frequency domain result after filtering. Mid-frequency point The value, Indicates the number of nodes i that received the first... The filtering result of the frequency domain signal corresponding to the segment signal;

[0085] Represents frequency domain signal Mid-frequency point The value;

[0086] These are the whitening filter coefficients. , This indicates the total number of frequency points.

[0087] The other steps and parameters are the same as in Specific Implementation Method 1.

[0088] Whitening filter coefficients in this embodiment The smaller the value, the smoother the filtered result; however, when the whitening filter coefficient... If the value is too small, severe lag will occur; it is usually set to... The value of is no greater than 0.5.

[0089] For the first segment of signal received by node i, initialization is performed before filtering. The value at each frequency point is 0.

[0090] Specific Implementation Method Three: This implementation method is a further limitation of Specific Implementation Method Two. The specific process of steps two and three is as follows:

[0091]

[0092] in, Indicates the result after spectral whitening. Mid-frequency point The value, .

[0093] The other steps and parameters are the same as in Specific Implementation Method Two.

[0094] This implementation method divides the original spectrum by... The smooth spectral background of the filtered output can cancel out the line spectrum in the continuous spectrum, thereby improving the accuracy of time delay difference estimation.

[0095] Specific Implementation Method Four: This implementation method is a further limitation of Specific Implementation Method Three. The specific process of step three is as follows:

[0096] For any two nodes i and j, the result of cross-correlation between the time-domain received signal of node i after spectral whitening and the time-domain received signal of node j after spectral whitening is:

[0097]

[0098] in, This represents the time-domain received signal after the spectrum of node j has been whitened;

[0099] Indicates the time delay difference. Indicates time delay difference The corresponding cross-correlation results;

[0100] For different value corresponding Low-pass filtering is performed to obtain the cross-correlation envelope, and then the peak value of the cross-correlation envelope is... The value represents the time delay difference between node i and node j from the target. ;

[0101] in, express The absolute value of.

[0102] The other steps and parameters are the same as in Specific Implementation Method 3.

[0103] Specific Implementation Method Five: This implementation method further defines Specific Implementation Method Four. Specifically, the calculation of the target's position based on the time delay difference obtained in step three is as follows:

[0104] For a target with a known depth Z: to determine the target's x-coordinate and y-coordinate, a system of equations is required, meaning that when the target depth Z is known, this invention requires at least three nodes. When multiple nodes are deployed, the target's current position can be calculated by arbitrarily selecting three nodes from the deployed nodes.

[0105] Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as ,but and The difference is , and The difference is ;

[0106] Multiplying the extracted time delay difference estimate by the speed of sound yields the distance difference. Therefore, the distance difference between any two nodes relative to the target can be expressed by an equation. and Establish a system of equations:

[0107]

[0108] in, For equivalent speed of sound, Indicates multiplication. This represents the time delay difference between node k and node j from the target, and the calculation process is the same as in Implementation Method Four;

[0109] The established system of equations is then solved to obtain the target's position coordinates. .

[0110] The other steps and parameters are the same as in Specific Implementation Method Four.

[0111] For example, methods for solving systems of equations include, but are not limited to, the following:

[0112] make , , , , , , The system of equations for determining the location of the radiation source target is obtained. ,in:

[0113]

[0114] Since the coordinates of each node are known, the target's coordinates can be obtained by solving the above system of equations. .

[0115] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Method Five, wherein... and The difference for:

[0116] Let the coordinates of node i be... The coordinates of node j are: Assuming the target's position remains unchanged during the period the node receives the signal, the target's coordinates are denoted as follows: ;

[0117]

[0118] The other steps and parameters are the same as in Specific Implementation Method 5.

[0119] Specific Implementation Method Seven: This implementation method is a further limitation of Specific Implementation Method Six, wherein... and The difference for:

[0120] Let the coordinates of node k be... :

[0121]

[0122] The other steps and parameters are the same as in Specific Implementation Method Six.

[0123] Specific Implementation Method Eight: This implementation method further defines Specific Implementation Method Four. Specifically, the calculation of the target's position based on the time delay difference obtained in step three is as follows:

[0124] For a target with an unknown depth Z: This invention requires at least 4 nodes to be arranged. When multiple nodes are arranged, the current position of the target can be calculated by arbitrarily selecting 4 nodes from the arranged nodes.

[0125] Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as Let the distance between node p and the target be denoted as ,but and The difference is , and The difference is , and The difference is ;

[0126] Then according to , and Establish a system of equations:

[0127]

[0128] in, This represents the time delay difference between node p and node k from the target. This represents the time delay difference between node k and node j from the target. The calculation process for the time delay difference is the same as in Specific Implementation Method Four.

[0129] Solving the established system of equations yields the target's position coordinates. .

[0130] The other steps and parameters are the same as in Specific Implementation Method Four.

[0131] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Method Eight, wherein... and The difference , and The difference , and The difference They are respectively:

[0132] Let the coordinates of node i be... The coordinates of node j are: Assuming the target's position remains unchanged during the period the node receives the signal, the target's coordinates are denoted as follows: ,but

[0133]

[0134] Let the coordinates of node k be... ,but

[0135]

[0136] Mark the coordinates of node p as ,but

[0137]

[0138] The other steps and parameters are the same as in Specific Implementation Method 8.

[0139] Simulation Experiment

[0140] Simulation conditions: When the target depth is known (this simulation assumes the target depth is 0), the coordinates of the nodes are assumed to be (-1000 m, 1250 m, 2500 m), (-500 m, -1500 m, 2500 m), and (1250 m, 250 m, 2500 m), respectively. The continuous spectrum bandwidth is 100~300 Hz, the continuous spectrum signal-to-noise ratio is -5 dB, the line spectrum frequencies are 120 Hz, 130 Hz, 140 Hz, 150 Hz, 160 Hz, and 170 Hz, the line spectrum level signal-to-noise ratio is 20 dB (input signal-to-noise ratio within a 1 Hz bandwidth), and the target velocity along the x-direction is 2 m / s. The duration of each signal segment is 5 s, and the whitening filter coefficient is 0.2.

[0141] Simulation Results: This invention performs localization simulation on broadband noise target signals containing line spectra and provides analysis results.

[0142] Depend on Figure 2 A comparison of the power spectra of the received signals before and after spectral whitening shows that the line spectral components in the broadband noise signal are canceled out after spectral whitening. Figure 3The cross-correlation envelope results of the received signals from nodes 1 and 3 before spectral whitening show that when line spectrum clusters exist, the cross-correlation output exhibits a significant periodic multi-peak phenomenon. According to the properties of Fourier transform, a discrete period in the frequency domain corresponds to a discrete period in the time domain. According to Wiener-Khinchin's theorem, the power spectrum and cross-correlation function of a signal are Fourier transform pairs. Line spectrum clusters exhibiting harmonic relationships can be considered as discrete (the line spectrum only has values ​​at certain frequencies) and periodic (exhibiting a certain harmonic relationship with a certain fundamental frequency). Therefore, the cross-correlation function obtained from its inverse Fourier transform must also have periodic discreteness, thus exhibiting equally spaced multi-peaks. Figure 4 As can be seen from the slice of the cross-correlation envelope results of the received signals of node 1 and node 3 before spectral whitening, the true correlation peak may lead to the corresponding time delay estimation error due to the multi-peak phenomenon. Figure 5 This is a diagram showing the cross-correlation envelope of the received signals from node 1 and node 2 after spectral whitening. Figure 6 This is a diagram showing the cross-correlation envelope of the signals received by node 1 and node 3 after spectral whitening. Figure 7 This is a diagram showing the cross-correlation envelope of the received signals from node 2 and node 3 after spectral whitening. Figure 8 This is a slice of the cross-correlation envelope results of the received signals from nodes 1 and 2, 1 and 3, and 2 and 3 after spectral whitening. Figure 5 , Figure 6 , Figure 7 and Figure 8 It is evident that the cross-correlation results after spectral whitening eliminate the influence of multi-peaks and improve the accuracy of time delay estimation. From Figure 9 A comparison of the target trajectory localization results before and after spectral whitening shows that the localization accuracy of the signal after spectral whitening is greatly improved compared with that of the signal without spectral whitening. The feasibility of the method of the present invention is verified by simulation experiments.

[0143] The above examples of the present invention are merely illustrative of the computational model and process of the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is impossible to exhaustively list all possible implementations here. Any obvious variations or modifications derived from the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. A distributed passive localization method based on spectral whitening cross-correlation, characterized in that, The method specifically includes the following steps: Step 1: Utilize the deployed Each node simultaneously receives ship-radiated noise signals. Set the duration of each signal received by the node to T; Step 2: Process the data received by each node. The segment signal is processed to obtain the time-domain received signal after spectral whitening of each node; For the first received by node i segment signal The processing steps in step two are as follows: Step Two:

1. Signal Perform an FFT to obtain the signal. Corresponding frequency domain signal ; Step 22: For frequency domain signals For each frequency point result, do the following: Filtering yields the filtered frequency domain result. ; Steps two and three: Based on the filtered frequency domain results and frequency domain signals The result after spectral whitening was obtained ; Step 2.4: Results of Spectral Whitening Perform IFFT to obtain the time-domain received signal after spectral whitening at node i. ; Step 3: For any two nodes, perform cross-correlation on the spectral whitening time-domain received signals corresponding to the two nodes, and obtain the time delay difference between the two nodes and the target based on the cross-correlation result; Step 4: Calculate the target's position based on the time delay difference obtained in Step 3.

2. The distributed passive localization method based on spectral whitening cross-correlation according to claim 1, characterized in that, The specific process of step two is as follows: in, Represents the frequency domain result after filtering. Mid-frequency point The value; Represents the frequency domain result after filtering. Mid-frequency point The value, Indicates the number of nodes i that received the first... The filtering result of the frequency domain signal corresponding to the segment signal; Represents frequency domain signal Mid-frequency point The value; These are the whitening filter coefficients. , This indicates the total number of frequency points.

3. The distributed passive localization method based on spectral whitening cross-correlation according to claim 2, characterized in that, The specific process of steps two and three is as follows: in, Indicates the result after spectral whitening. Mid-frequency point The value, .

4. The distributed passive localization method based on spectral whitening cross-correlation according to claim 3, characterized in that, The specific process of step three is as follows: For any two nodes i and j, the result of cross-correlation between the time-domain received signal after spectral whitening at node i and the time-domain received signal after spectral whitening at node j is: in, This represents the time-domain received signal after the spectrum of node j has been whitened; Indicates the time delay difference. Indicates time delay difference The corresponding cross-correlation results; For different value corresponding Low-pass filtering is performed to obtain the cross-correlation envelope, and then the peak value of the cross-correlation envelope is... The value represents the time delay difference between node i and node j from the target. ; in, express The absolute value of.

5. The distributed passive localization method based on spectral whitening cross-correlation according to claim 4, characterized in that, The calculation of the target's position based on the time delay difference obtained in step three is specifically as follows: For a target with a known depth Z: Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as ,but and The difference is , and The difference is ; according to and Establish a system of equations: in, For equivalent speed of sound, Indicates multiplication. This represents the time delay difference between node k and node j from the target; The established system of equations is then solved to obtain the target's position coordinates. .

6. The distributed passive localization method based on spectral whitening cross-correlation according to claim 5, characterized in that, The and The difference for: Let the coordinates of node i be... The coordinates of node j are: Mark the target's location coordinates as ; 。 7. A distributed passive localization method based on spectral whitening cross-correlation according to claim 6, characterized in that, The and The difference for: Let the coordinates of node k be... : 。 8. A distributed passive localization method based on spectral whitening cross-correlation according to claim 4, characterized in that, The calculation of the target's position based on the time delay difference obtained in step three is specifically as follows: For a target with unknown depth Z: Let the distance between node i and the target be denoted as Let the distance between node j and the target be denoted as Let the distance between node k and the target be denoted as Let the distance between node p and the target be denoted as ,but and The difference is , and The difference is , and The difference is ; Then according to , and Establish a system of equations: in, For equivalent speed of sound, Indicates multiplication. This represents the time delay difference between node p and node k from the target. This represents the time delay difference between node k and node j from the target; Solving the established system of equations yields the target's position coordinates. .

9. A distributed passive localization method based on spectral whitening cross-correlation according to claim 8, characterized in that, The and The difference , and The difference , and The difference They are respectively: Let the coordinates of node i be... The coordinates of node j are: Mark the target's location coordinates as ,but Let the coordinates of node k be... ,but Mark the coordinates of node p as ,but 。

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