Low-cost pseudo-bistatic passive acoustic positioning method and system

Abstract

The present application belongs to the field of underwater acoustic signal processing and underwater target positioning technology, and relates to a low-cost pseudo-bistatic passive acoustic positioning method and system. The system adopts a four-element hydrophone array in combination with a single auxiliary hydrophone to form a short-baseline pseudo-bistatic structure, and has both direction-finding and ranging capabilities. Through adaptive bearing estimation, beam signal purification, Hilbert envelope anti-multipath and weighted generalized cross-correlation time delay estimation, combined with synchronization error compensation, confidence evaluation and trajectory constraint, high-precision two-dimensional passive positioning is realized. The present application uses bearing constraint to reduce the two-dimensional positioning calculation to one-dimensional distance estimation, which significantly reduces the hardware cost and system synchronization complexity while ensuring the accuracy of angle measurement and distance measurement, effectively suppresses the shallow water multipath interference, improves the positioning stability in low signal-to-noise ratio environment, and is suitable for passive detection and positioning of underwater targets in coastal, shallow water and other waters.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic signal processing and underwater target localization technology, specifically relating to a low-cost pseudo-dual-station passive acoustic localization method and system. Background Technology

[0002] Passive acoustic positioning is a core technology for underwater target detection, unmanned vessel environmental perception, and near-shore security monitoring. It completes position calculation by receiving the target's radiated noise, without the need for active signal transmission, and has advantages such as strong concealment, low power consumption, and wide adaptability.

[0003] Existing underwater passive positioning technologies are mainly divided into two categories: one is single-array angle measurement technology, which relies solely on hydrophone arrays to estimate the target's azimuth and cannot obtain distance information. It is an underdetermined system and cannot complete two-dimensional planar positioning. The other is multi-array TDOA positioning technology, which completes positioning by constructing multiple baselines through multiple sets of distributed arrays. However, it has drawbacks such as high hardware costs, complex deployment, stringent synchronization accuracy requirements, and difficulty in large-scale application in low-cost scenarios.

[0004] In practical engineering scenarios such as lake trials, nearshore monitoring, and deployment on small unmanned platforms, the number of devices, deployment space, and hardware costs are all strictly limited. The contradiction between the inability of traditional single arrays to measure distance and the excessive cost of multiple arrays is prominent. In existing technologies, the combination of arrays and single hydrophones often adopts a direct two-dimensional joint solution method, which does not consider the impact of differences in the accuracy of different observations on the stability of the solution. Under long-distance or low signal-to-noise ratio conditions, the solution divergence or error amplification problems are prone to occur. Summary of the Invention

[0005] This invention provides a low-cost pseudo-dual-station passive acoustic positioning method and system to solve the problems of high hardware cost and complex system deployment in traditional array positioning systems.

[0006] This invention employs the following technical solution: a low-cost pseudo-dual-station passive acoustic localization method, comprising the following steps:

[0007] S1. Collect the array signal from the acquisition array unit and the single hydrophone signal from the auxiliary acquisition unit, and estimate the target azimuth angle based on the array signal;

[0008] S2. Perform beamforming processing on the array signal, extract the target direction signal, perform envelope extraction operation on the array target direction signal and the single hydrophone signal, and calculate the time delay difference between the array signal and the single hydrophone signal;

[0009] S3. Construct a target direction constraint model based on the azimuth angle, represent the target position as radial distance, construct an error function based on the time delay difference for optimization, and perform confidence evaluation and filtering on the positioning results.

[0010] Furthermore, the array received signal of the array acquisition unit satisfies:

[0011] ;

[0012] In the formula, This is the array received signal vector. It is a direction vector. For target signal, It is noise.

[0013] Furthermore, in S1, the target azimuth angle estimation adopts a signal-to-noise ratio (SNR) matching algorithm, a conventional beamforming algorithm is used when the SNR is low, and a high-resolution angle measurement algorithm is used when the SNR is high.

[0014] Furthermore, the conventional beamforming algorithm includes a conventional beamforming output as follows:

[0015] ;

[0016] In the formula, For beamforming output signal, For the corresponding The weight vector of the direction. This is the conjugate transpose. This is the array received signal vector;

[0017] The spatial spectral function is:

[0018] ;

[0019] In the formula, For conventional beamforming spatial spectrum values, For array guide vector, Let be the covariance matrix of the received signal from the array and ;

[0020] The formula for estimating the target azimuth is:

[0021] ;

[0022] In the formula, This is the estimated azimuth angle of the target.

[0023] Furthermore, the implementation process of the high-resolution angle measurement algorithm includes calculating the covariance matrix of the array received signal. Perform eigenvalue decomposition; the decomposition formula is as follows:

[0024] ;

[0025] In the formula, Let be the covariance matrix of the received signal of the array and , For the signal subspace, Let be a diagonal matrix formed by the eigenvalues ​​corresponding to the signal subspace. Let be a diagonal matrix formed by the eigenvalues ​​corresponding to the noise subspace. For noise subspace;

[0026] Based on noise subspace Construct a MUSIC spatial spectrum function, wherein the spatial spectrum function is:

[0027] ;

[0028] In the formula, The spatial spectrum values ​​are from a high-resolution angle measurement algorithm. For the noise subspace, For array guiding vector;

[0029] By searching for the azimuth angle that maximizes the MUSIC spatial spectrum function, the estimated target azimuth angle is obtained:

[0030] ;

[0031] In the formula, This is the estimated azimuth angle of the target.

[0032] Furthermore, the envelope extraction operation employs the Hilbert transform envelope extraction formula:

[0033] ;

[0034] In the formula, For the instantaneous envelope of the signal, The signal is after bandpass filtering. The imaginary unit, This is the Hilbert transform;

[0035] The time delay difference is calculated using a weighted generalized cross-correlation algorithm:

[0036] ;

[0037] In the formula, The weighted generalized cross-correlation function value in the frequency domain. The spectrum of the first signal. The complex conjugate of the spectrum of the second signal. For frequency domain weighting functions, It is the frequency domain time delay factor;

[0038] Synchronization error compensation is performed to address the time delay difference. The compensation formula is as follows:

[0039] ;

[0040] In the formula, This represents the actual time delay difference. To measure the time delay difference, This is due to channel synchronization deviation;

[0041] The time delay difference is converted into a sound path difference using the following formula:

[0042] ;

[0043] In the formula, For sound path difference, The speed of sound underwater. This represents the signal delay difference between the array acquisition unit and the auxiliary acquisition unit.

[0044] Furthermore, the target direction constraint model adopts pseudo-bistationary positioning geometric constraint equations:

[0045] ;

[0046] In the formula, The radial distance from the target to the center of the array. For pseudo-bistation baseline length, The target azimuth angle.

[0047] Furthermore, the confidence level of the localization results in the above steps is evaluated using the following formula:

[0048] ;

[0049] In the formula, For confidence level, The peak amplitude is the correlation value, and SNR is the signal-to-noise ratio. For the variance of azimuth variation, , , These are the weighting coefficients.

[0050] Furthermore, the array acquisition unit and the auxiliary acquisition unit are arranged along the same horizontal plane, and the baseline direction of the array acquisition unit and the auxiliary acquisition unit is perpendicular to the main distribution direction of the target, with a baseline length L≤20m.

[0051] The present invention also provides a low-cost pseudo-dual-station passive acoustic positioning system, comprising: an array acquisition unit, an auxiliary acquisition unit, a synchronous acquisition module, a signal processing module, and a positioning calculation module;

[0052] The array acquisition unit employs a hydrophone array containing at least four hydrophones to complete the acquisition and spatial sampling of the target radiated noise signal.

[0053] The auxiliary acquisition unit uses a single hydrophone deployed outside the array acquisition unit. The baseline length between the auxiliary acquisition unit and the array acquisition unit is 5m to 20m, and it is used to acquire the target radiated noise signal.

[0054] The synchronous acquisition module acquires synchronous signals from the array acquisition unit and the auxiliary acquisition unit based on the same clock source, ensuring time synchronization of the two acquisition signals.

[0055] The signal processing module includes a position estimation submodule, a signal purification submodule, an envelope extraction submodule, and a time delay estimation submodule;

[0056] The azimuth estimation submodule estimates the target azimuth angle based on the array signal acquired by the array acquisition unit;

[0057] The signal purification submodule performs beamforming processing on the array signal acquired by the array acquisition unit based on the azimuth angle obtained by the azimuth estimation submodule to obtain the target direction signal;

[0058] The envelope extraction submodule performs envelope extraction on the target direction signal obtained by the signal purification submodule and the signal acquired by the auxiliary acquisition unit to obtain the envelope signal of the target direction signal and the signal acquired by the auxiliary acquisition unit;

[0059] The time delay estimation submodule calculates the time delay difference between the array acquisition unit and the auxiliary acquisition unit based on the envelope signal obtained by the envelope extraction submodule.

[0060] The positioning solution module applies directional constraints to the target position based on the target azimuth angle obtained by the azimuth estimation submodule, transforming the two-dimensional positioning problem into a one-dimensional distance estimation problem. It then constructs an error function based on the distance difference corresponding to the time delay difference for optimization and solution, thereby obtaining the target positioning result.

[0061] Compared with the prior art, the present invention has the following technical effects:

[0062] Extremely low hardware cost: Only one set of four-element array + a single auxiliary hydrophone is required, eliminating the need for multiple distributed arrays, reducing hardware cost by more than 60% and significantly reducing deployment difficulty; beamforming processing performs phase alignment and weighted superposition of the array's multi-channel signals in the target azimuth direction to generate an equivalent single-channel signal that matches the single hydrophone signal of the auxiliary acquisition unit, thereby constructing a dual-channel input structure for time delay estimation.

[0063] Complete positioning capability: By combining array angle measurement and pseudo-bistation time delay constraints, the underdetermined problem of a single array is transformed into a well-posed problem, and azimuth estimation, distance calculation, and two-dimensional positioning are achieved simultaneously; Strong environmental adaptability: The three-level processing of beam refinement, Hilbert envelope, and weighted GCC effectively suppresses multipath interference in shallow seas and improves the stability of time delay estimation in low signal-to-noise ratio environments.

[0064] The system is highly robust: it integrates a four-layer optimization mechanism of synchronous error compensation, adaptive angle measurement, confidence assessment, and trajectory constraint, resulting in continuous and stable positioning results with few outliers; it is also highly scalable: by changing the position of the auxiliary hydrophones or increasing the number of auxiliary hydrophones, a multi-baseline pseudo-dual-station system can be constructed to further improve positioning accuracy and coverage. Attached Figure Description

[0065] Figure 1 This is a block diagram of the overall system structure of the present invention;

[0066] Figure 2 This is a schematic diagram of the array layout and coordinate system of the present invention;

[0067] Figure 3 This is a geometric diagram illustrating the orientation-time delay joint positioning of the present invention.

[0068] Figure 4 This is a flowchart of the signal processing and positioning calculation of the present invention;

[0069] Figure 5 This is a schematic diagram illustrating the system error propagation and sensitivity of the present invention;

[0070] Figure 6 This is a diagram showing the positioning result of point A1 using a single quaternion array according to the present invention.

[0071] Figure 7 This is a diagram showing the positioning result of point A2 using a single quaternion array according to the present invention.

[0072] Figure 8 This is a diagram showing the positioning result of point A1 using a four-element array and a single hydrophone according to the present invention.

[0073] Figure 9 This is a diagram showing the positioning result of point A2 using a four-element array and a single hydrophone according to the present invention. Detailed Implementation

[0074] The present invention will be further illustrated below with reference to embodiments. These embodiments are for illustrative purposes only and are not intended to limit the invention in any way. It should be understood that the described embodiments are merely some, not all, of the embodiments described in this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0075] In this embodiment, as Figure 1 As shown, a low-cost pseudo-dual-station passive acoustic positioning system includes an array acquisition unit, an auxiliary acquisition unit, a synchronous acquisition module, a signal processing module, a synchronous error compensation module, a positioning calculation module, a confidence assessment module, a trajectory constraint module, and a result output unit. The modules work together to achieve high-precision passive positioning of underwater targets.

[0076] Figure 2 This is a schematic diagram of the array layout and coordinate system of the present invention. The array acquisition unit adopts a four-element square hydrophone array with an array element spacing of 1m, which is used to complete the acquisition of target radiated noise signals and spatial sampling. The auxiliary acquisition unit adopts a single hydrophone, which forms a long baseline structure with the array edge elements. The baseline direction is arranged approximately perpendicular to the main measuring direction of the array to improve the sensitivity of distance difference measurement.

[0077] A low-cost pseudo-bistation passive acoustic localization method includes the following steps:

[0078] With the center of the array acquisition unit as the origin O, The axis runs along the baseline direction of the array and the auxiliary hydrophone. The axis points in the main detection direction of the water area, and the target position can be represented by polar coordinates. or rectangular coordinates It means that among them The radial distance from the target to the center of the array. The target azimuth angle.

[0079] The array received signal model uses the following formula:

[0080] ;

[0081] In the formula, This is the array received signal vector. It is a direction vector. For target signal, It is noise.

[0082] The synchronous acquisition module uses a unified multi-channel NI acquisition card to acquire data, achieving synchronous sampling of the four hydrophone signals from the array acquisition unit and the one hydrophone signal from the auxiliary acquisition unit. All channels maintain a consistent sampling rate, effectively eliminating measurement errors caused by clock asynchrony. This embodiment requires only single-baseline synchronization, significantly reducing system synchronization complexity and implementation cost compared to multi-array positioning systems.

[0083] The azimuth estimation submodule in the signal processing module adaptively selects the array processing algorithm based on the signal-to-noise ratio of the input signal to achieve the target azimuth angle. Accurate estimates:

[0084] When the input signal has a high signal-to-noise ratio (SNR ≥ 3dB in this embodiment), the MUSIC high-resolution angle measurement algorithm is used:

[0085] ;

[0086] In the formula, The spatial spectrum values ​​are from a high-resolution angle measurement algorithm. This is the estimated azimuth angle of the target.

[0087] ;

[0088] In the formula, The spatial spectrum values ​​are from a high-resolution angle measurement algorithm. For the noise subspace, For array guiding vector;

[0089] When the input signal has a low signal-to-noise ratio (SNR < 3dB), the conventional beamforming algorithm used is as follows:

[0090] ;

[0091] In the formula, Estimate the target azimuth angle;

[0092] ;

[0093] In the formula, For conventional beamforming spatial spectrum values, For array guide vector, Let be the covariance matrix of the received signal of the array and ;

[0094] The signal purification submodule in the signal processing module calculates the target azimuth angle based on the output of the azimuth estimation submodule. The array signal acquired by the array acquisition unit is processed by beamforming to suppress noise and interference in non-target directions, thereby obtaining a high-purity target direction signal.

[0095] The envelope extraction submodule in the signal processing module first performs bandpass filtering on the target direction signal and the signal acquired by the auxiliary acquisition unit, and then uses Hilbert transform to extract the instantaneous envelope of the signal.

[0096] ;

[0097] In the formula, For the instantaneous envelope of the signal, The signal is after bandpass filtering. The imaginary unit, This is the Hilbert transform;

[0098] Using the envelope signal for subsequent correlation calculations can effectively reduce the impact of phase distortion caused by multipath propagation in shallow seas on time delay estimation.

[0099] like Figure 4 As shown, the time delay estimation submodule in the signal processing module uses the weighted generalized cross-correlation method to calculate the time delay difference between the two envelope signals:

[0100] ;

[0101] In the formula, The weighted generalized cross-correlation function value in the frequency domain. The spectrum of the first signal. The complex conjugate of the spectrum of the second signal. For frequency domain weighting functions, It is the frequency domain time delay factor;

[0102] In this embodiment, the weight function A function for the amplitude of the signal spectrum is selected to improve the identification accuracy of correlation peaks under low signal-to-noise ratio. At the same time, subsampling interpolation technology is used to achieve high-precision time delay estimation.

[0103] like Figure 5 As shown, the synchronization error compensation module estimates the time deviation between the array acquisition unit and the auxiliary acquisition unit in real time using a reference signal. Then, the delay difference calculated by the delay estimation submodule is compensated and corrected according to the compensation formula:

[0104] ;

[0105] In the formula, This represents the actual time delay difference. To measure the time delay difference, This is due to channel synchronization deviation;

[0106] Compensation is provided to compensate for time delay differences, thereby eliminating the impact of hardware channel time delay errors on positioning accuracy.

[0107] Figure 3 This is the geometric relationship diagram of the orientation-time delay joint positioning of the present invention. The positioning solution module first calculates the compensated actual time delay difference according to the conversion formula. Converted to path difference :

[0108] ;

[0109] In the formula, For sound path difference, The speed of sound underwater. In this embodiment, the signal delay difference between the array acquisition unit and the auxiliary acquisition unit is... =1502m / s.

[0110] Then, the sound path difference Substituting the pseudo-bistationary positioning geometric constraint equations:

[0111] ;

[0112] In the formula, The radial distance from the target to the center of the array. For pseudo-bistation baseline length, The target azimuth angle;

[0113] The positioning solution module is based on azimuth angle. By constructing polar coordinate constraints, the two-dimensional target localization problem is transformed into a one-dimensional distance estimation problem along the azimuth direction. The radial distance of the target is then achieved by minimizing the cost function. Estimate:

[0114] ;

[0115] In the formula, To locate the cost function in the solution process, The radial distance from the target to the center of the array acquisition unit. The theoretical distance difference function is determined by geometric relationships. , This is a weighting coefficient, which can be adjusted according to actual working conditions; This is the initial estimate for array ranging.

[0116] In this embodiment, by pre-constructing a mapping table of azimuth, radial distance, and distance difference, and combining it with numerical optimization methods to solve for the target radial distance r, the instability of analytical solutions under long-distance conditions is avoided, thus improving the reliability of the positioning solution.

[0117] The confidence assessment module calculates the confidence level of the location results according to the confidence calculation formula:

[0118] ;

[0119] In the formula, For confidence level, The peak amplitude is the correlation value, and SNR is the signal-to-noise ratio. For the variance of azimuth variation, , , These are the weighting coefficients.

[0120] The positioning results are filtered or updated based on confidence levels. When the confidence level is lower than a set threshold, the current positioning result is rejected or its weight in trajectory updates is reduced. The trajectory constraint module constrains the positioning results at consecutive time points based on the continuity of target motion, eliminating abnormal data that do not meet kinematic constraints, thereby further improving the stability and reliability of the positioning results.

[0121] Experimental environment parameters

[0122] To verify the practical feasibility of the system of the present invention, a passive acoustic positioning experiment was conducted in a near-shore environment, under the following specific conditions:

[0123] Experimental water area: shallow open sea area near the coast of Qingdao, with a water depth of 6m, a water temperature of 12℃, and an underwater sound speed of 1502m / s; the equivalent sound level of the environmental background noise is 28dB, and the seabed sand has no strong reflection interference.

[0124] Hardware deployment parameters

[0125] Array acquisition unit: a four-element square hydrophone array with an element spacing of 1m and the array center placed at a depth of 1m underwater;

[0126] Auxiliary acquisition unit: a single hydrophone, deployed at a depth of 1m underwater, with a baseline length of 10m from the center of the array, and the baseline forming a 90° angle with the main beam pointing of the array (vertically deployed).

[0127] Synchronous acquisition module: multi-channel NI acquisition card, sampling rate 48kHz, synchronization accuracy ±1μs, 5-channel synchronous acquisition (4-channel array + 1-channel auxiliary).

[0128] Target and input parameters

[0129] Target: Electric underwater unmanned vehicle, radiated noise frequency band 400Hz~2.5kHz, travel speed 2m / s;

[0130] Preset target locations: rectangular coordinates A1 (60m, 60m), rectangular coordinates A2 (120m, 120m);

[0131] Operating signal-to-noise ratio: 3dB;

[0132] Acquisition configuration: 5 seconds for each frame, 20 frames are collected continuously and the average is calculated.

[0133] Signal processing parameters

[0134] Filtering: 8th order Butterworth bandpass filter 400Hz~2.5kHz;

[0135] Azimuth estimation: 3dB high signal-to-noise ratio, using the MUSIC high-resolution algorithm, with a spectral peak search step size of 0.1°;

[0136] Envelope extraction: Hilbert transform is used to extract the instantaneous envelope;

[0137] Delay estimation: GCC-PHAT weighted generalized cross-correlation, subsampling interpolation accuracy 1 / 100 of the sampling points;

[0138] Synchronization compensation: Reference signal calibration, channel deviation compensation accuracy ±0.05μs;

[0139] Location calculation: Least squares optimization, iterative accuracy 0.1m.

[0140] Complete the array and auxiliary hydrophone deployment according to the parameters, and calibrate the synchronous acquisition module;

[0141] Control the unmanned vessel to hover at preset positions A1 (60m, 60m) and A2 (120m, 120m);

[0142] Simultaneous acquisition of 20 frames of array + auxiliary hydrophone signals;

[0143] Frame-by-frame execution: Filtering → Azimuth estimation → Beam refinement → Envelope extraction → Delay estimation → Synchronization compensation;

[0144] Substituting the orientation constraint model, the two-dimensional positioning is transformed into a one-dimensional distance optimization solution;

[0145] Confidence assessment + trajectory filtering, output the final result.

[0146] Figure 6 The image shows the positioning result of point A1 using a single quaternion array according to the present invention. When only a single quaternion array is used, the root mean square error (RMSE) of positioning A1(60, 60) is 46.92m. Figure 7 The image shows the positioning result of point A2 using a single quaternion array according to the present invention. When only a single quaternion array is used, the root mean square error (RMSE) of positioning A2(120, 120) is 78.25m. Figure 8 The diagram shows the positioning result of point A1 using a quad array and a single hydrophone according to the present invention. After introducing the assistance of a single hydrophone, the root mean square error (RMSE) of positioning A1(60, 60) was reduced to 1.26m. Figure 9 The diagram shows the positioning result of point A2 using a four-element array and a single hydrophone according to the present invention. After introducing the assistance of a single hydrophone, the root mean square error (RMSE) of positioning A2(120, 120) is reduced to 1.81m.

[0147] Depend on Figures 6 to 9 It can be seen that the average estimated angle is 45.72°, the azimuth error is 0.16°, the root mean square error (RMSE) of the positioning of A1(60,60) with a single quaternion array is 46.92m, and the root mean square error (RMSE) of the positioning of A2(120,120) is 78.25m; after introducing the single hydrophone, the positioning results of the quaternion array plus the single hydrophone are A1(60,60) with a root mean square error (RMSE) of 1.26m and A2(120,120) with a root mean square error (RMSE) of 1.81m.

[0148] In this embodiment, under typical shallow sea conditions, the positioning error is <2m and the azimuth error is <0.2°. The system can stably achieve high-precision passive positioning of underwater targets, meeting the engineering requirements for near-shore monitoring and unmanned platform deployment. This verifies the engineering feasibility and robustness of the method of this invention under low-cost conditions.

[0149] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A low-cost pseudo-bistation passive acoustic localization method, characterized in that, Includes the following steps: S1. Collect the array signal from the acquisition array unit and the single hydrophone signal from the auxiliary acquisition unit, and estimate the target azimuth angle based on the array signal; The target azimuth angle estimation adopts a signal-to-noise ratio (SNR) matching algorithm, a conventional beamforming algorithm is used when the SNR is low, and a high-resolution angle measurement algorithm is used when the SNR is high. The conventional beamforming output is: ； In the formula, For beamforming output signal, For the corresponding The weight vector of the direction. This is the conjugate transpose. This is the array received signal vector; The spatial spectral function is: ； In the formula, For conventional beamforming spatial spectrum values, For array guide vector, Let be the covariance matrix of the received signal of the array and ; The formula for estimating the target azimuth is: ； In the formula, This is the estimated azimuth angle of the target. The implementation process of the high-resolution angle measurement algorithm includes calculating the covariance matrix of the array received signal. Perform eigenvalue decomposition; the decomposition formula is as follows: ； In the formula, Let be the covariance matrix of the received signal of the array and , For the signal subspace, Let be a diagonal matrix formed by the eigenvalues ​​corresponding to the signal subspace. Let be a diagonal matrix formed by the eigenvalues ​​corresponding to the noise subspace. For noise subspace; Based on noise subspace Construct a MUSIC spatial spectrum function, wherein the spatial spectrum function is: ； In the formula, The spatial spectrum values ​​are from a high-resolution angle measurement algorithm. For the noise subspace, For array guiding vector; By searching for the azimuth angle that maximizes the MUSIC spatial spectrum function, the estimated target azimuth angle is obtained: ； In the formula, This is the estimated azimuth angle of the target. S2. Perform beamforming processing on the array signal, extract the target direction signal, perform envelope extraction operation on the array target direction signal and the single hydrophone signal, and calculate the time delay difference between the array signal and the single hydrophone signal; S3. Construct a target direction constraint model based on the azimuth angle, represent the target position as radial distance, construct an error function based on the time delay difference for optimization, and perform confidence evaluation and filtering on the positioning results.

2. The low-cost pseudo-dual-station passive acoustic localization method according to claim 1, characterized in that, The array received signal of the array acquisition unit satisfies: ； In the formula, This is the array received signal vector. It is a direction vector. For target signal, It is noise.

3. The low-cost pseudo-dual-station passive acoustic localization method according to claim 1, characterized in that, The envelope extraction operation uses the Hilbert transform envelope extraction formula: ； In the formula, For the instantaneous envelope of the signal, The signal is after bandpass filtering. The imaginary unit, This is the Hilbert transform; The time delay difference is calculated using a weighted generalized cross-correlation algorithm: ； In the formula, The weighted generalized cross-correlation function value in the frequency domain. The spectrum of the first signal. The complex conjugate of the spectrum of the second signal. For frequency domain weighting functions, It is the frequency domain time delay factor; Synchronization error compensation is performed to address the time delay difference. The compensation formula is as follows: ； In the formula, This represents the actual time delay difference. To measure the time delay difference, This is due to channel synchronization deviation; The time delay difference is converted into a sound path difference using the following formula: ； In the formula, For sound path difference, The speed of sound underwater. This represents the signal delay difference between the array acquisition unit and the auxiliary acquisition unit.

4. The low-cost pseudo-bistation passive acoustic localization method according to claim 1, characterized in that, The target orientation constraint model adopts pseudo-bistation positioning geometric constraint equations: ； In the formula, The radial distance from the target to the center of the array. For pseudo-bistation baseline length, The target azimuth angle.

5. The low-cost pseudo-dual-station passive acoustic localization method according to claim 1, characterized in that, The confidence level of the localization results in the above steps is assessed using the following formula: ； In the formula, For confidence level, The peak amplitude is the correlation value, and SNR is the signal-to-noise ratio. For the variance of azimuth variation, , , These are the weighting coefficients.

6. The low-cost pseudo-bistation passive acoustic localization method according to claim 1, characterized in that, The array acquisition unit and the auxiliary acquisition unit are arranged along the same horizontal plane. The baseline direction of the array acquisition unit and the auxiliary acquisition unit is perpendicular to the main distribution direction of the target, and the baseline length L≤20m.

7. A low-cost pseudo-bistatic passive acoustic positioning system employing the low-cost pseudo-bistatic passive acoustic positioning method according to any one of claims 1 to 6, characterized in that, include: The system comprises an array acquisition unit, an auxiliary acquisition unit, a synchronous acquisition module, a signal processing module, and a positioning and calculation module. The array acquisition unit employs a hydrophone array containing at least four hydrophones to complete the acquisition and spatial sampling of the target radiated noise signal. The auxiliary acquisition unit uses a single hydrophone deployed outside the array acquisition unit. The baseline length between the auxiliary acquisition unit and the array acquisition unit is 5m to 20m, and it is used to acquire the target radiated noise signal. The synchronous acquisition module acquires synchronous signals from the array acquisition unit and the auxiliary acquisition unit based on the same clock source, ensuring time synchronization of the two acquisition signals. The signal processing module includes a position estimation submodule, a signal purification submodule, an envelope extraction submodule, and a time delay estimation submodule; The azimuth estimation submodule estimates the target azimuth angle based on the array signal acquired by the array acquisition unit; The signal purification submodule performs beamforming processing on the array signal acquired by the array acquisition unit based on the azimuth angle obtained by the azimuth estimation submodule to obtain the target direction signal; The envelope extraction submodule performs envelope extraction on the target direction signal obtained by the signal purification submodule and the signal acquired by the auxiliary acquisition unit to obtain the envelope signal of the target direction signal and the signal acquired by the auxiliary acquisition unit; The time delay estimation submodule calculates the time delay difference between the array acquisition unit and the auxiliary acquisition unit based on the envelope signal obtained by the envelope extraction submodule. The positioning solution module applies directional constraints to the target position based on the target azimuth angle obtained by the azimuth estimation submodule, transforming the two-dimensional positioning problem into a one-dimensional distance estimation problem. It then constructs an error function based on the distance difference corresponding to the time delay difference for optimization and solution, thereby obtaining the target positioning result.

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