A method and system for calibrating a full-space acoustic vector sensor array
By employing a hierarchical calibration strategy and a physical information neural network, position and orientation errors are gradually decoupled, solving the problems of high computational complexity and error coupling in existing technologies. This achieves efficient calibration of the full-space acoustic vector sensor array and improves the array's DOA estimation accuracy.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NANJING UNIV
- Filing Date
- 2026-01-21
- Publication Date
- 2026-05-29
Smart Images
Figure CN122120686A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of acoustic signal processing and sensor array technology, and relates to a method and system for calibrating a full-space acoustic vector sensor array. Background Technology
[0002] Calibration of acoustic vector sensor arrays is a key issue in acoustic signal processing. Existing technologies can be mainly divided into the following categories: statistical inference methods (such as maximum likelihood estimation and Bayesian methods), subspace and matrix factorization methods, and traditional optimization and evolutionary algorithms. While these methods are effective under specific conditions, they have significant limitations when facing complex scenarios with full-space errors (i.e., coupled position and orientation errors).
[0003] The closest existing technology and its shortcomings: Unconditional maximum likelihood estimators and adaptive calibration methods applying the ML framework to acoustic vector sensors suffer from high computational complexity and sensitivity to signal-to-noise ratio (SNR). ML methods require solving high-dimensional parameters through nonlinear optimization, and their non-convexity makes them prone to getting trapped in local optima. Furthermore, the computational cost increases exponentially with the number of array elements. At high SNRs, optimization stalls easily, necessitating auxiliary techniques such as attenuation diagonal loading, which further increases the algorithm's complexity.
[0004] Eigenvalue decomposition methods based on the Hadamard product of the covariance matrix and gain-phase error calibration methods utilizing the orthogonality of signal subspaces rely on specific array structures, and high-dimensional matrix decomposition is computationally expensive. Subspace methods require the assumption that the array has a uniform, linear, or decomposable geometry (such as Toeplitz blocks), which cannot be satisfied by arbitrarily arranged vector arrays. Furthermore, covariance matrix decomposition is computationally inefficient for multi-channel vector arrays.
[0005] Methods combining weed invasion optimization and particle swarm optimization, along with weighted least squares algorithms, suffer from contradictions in convergence speed and parameter sensitivity, and are limited by linear assumptions. While evolutionary algorithms can avoid local optima, they require numerous iterations, are sensitive to initial parameter settings, and exhibit poor stability in practical engineering. Least squares methods, based on linear error models, cannot handle nonlinear projection distortion caused by orientation errors.
[0006] The root causes of existing technological shortcomings and the difficulty in solving them: 1. Error Coupling Position error affects high-frequency performance through phase difference, while orientation error affects low-frequency performance through direction cosine. Existing methods often assume that errors are independent or only deal with a single type of error. In practical applications, position error affects the incident angle of near-field sound sources to a certain extent.
[0007] 2. The curse of dimensionality in high-dimensional parameter spaces Tetrahedral arrays require simultaneous estimation of 33 error parameters (9 positions + 24 orientations), and traditional methods suffer from low optimization efficiency due to the large search space. Summary of the Invention
[0008] The purpose of this invention is to overcome the shortcomings of the prior art and to propose a calibration method and system for a full-space acoustic vector sensor array.
[0009] In view of this, the present invention proposes a method for calibrating a full-space acoustic vector sensor array, comprising: Step 1: Construct an acoustic vector sensor array including multiple vector sensors, and arrange at least three non-coplanar calibration sound sources around the array; Step 2: Acquire acoustic signals received by multiple vector sensors and perform frequency domain processing to obtain frequency domain data for the array sound pressure channel and the particle velocity channel; Step 3: Based on the frequency domain data of the array acoustic pressure channels, construct a first loss function with phase difference information as the physical constraint, and output the position error parameters of each vector sensor in the array by training the established position error estimation neural network; Step 4: Update the array's geometric model based on the position error parameters, and calculate the incident azimuth and elevation angles of the calibration sound source relative to each array element based on the updated geometric model; Step 5: Based on the incident azimuth and elevation angles, and the frequency domain data of the particle velocity channel, construct a second loss function with energy projection information as the physical constraint. Train the established orientation error estimation neural network to output the orientation error parameters of each channel of each vector sensor in the array. Step 6: Complete array calibration using position error parameters and orientation error parameters.
[0010] As an improvement to the above method, the at least three non-coplanar calibration sound sources in step 1 satisfy the full rank of the Jacobian matrix and have a unique solution.
[0011] As an improvement to the above method, the first loss function in step 3 for:
[0012] in, The normalized correlation matrix, i and j The first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List, The superscript T represents the transpose of the matrix, which is the ideal sound pressure channel steering vector. Indicates conjugate.
[0013] As an improvement to the above method, the position error estimation neural network in step 3 adopts a physical information-based neural network, which is a fully connected network with two hidden layers and uses the Tanh activation function. During training, the first loss function is minimized through the Adam optimizer.
[0014] As an improvement to the above method, the second loss function in step 5 for:
[0015] in, The normalized energy projection matrix, The vector is the guiding vector for the velocity channel of an ideal particle. The superscript T denotes the transpose of the matrix. Indicates conjugate. i and j The first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List.
[0016] As an improvement to the above method, the orientation error estimation neural network in step 5 adopts a physical information-based neural network, which is a fully connected network with two hidden layers, uses the Tanh activation function, and minimizes the second loss function through the Adam optimizer during training.
[0017] On the other hand, the present invention provides a full-space acoustic vector sensor array calibration system, comprising: An array building module is used to build an acoustic vector sensor array including multiple vector sensors and to arrange at least three non-coplanar calibration sound sources around the array; The frequency domain processing module is used to acquire acoustic signals received by multiple vector sensors and perform frequency domain processing to obtain frequency domain data for the array sound pressure channel and the particle velocity channel. A position error estimation neural network training module is established to construct a first loss function with phase difference information as a physical constraint based on the frequency domain data of the array sound pressure channel. By training the established position error estimation neural network, the position error parameters of each vector sensor in the array are output. The array update module is used to update the array's geometric model according to the position error parameters, and calculate the incident azimuth and elevation angles of the calibration sound source relative to each array element based on the updated geometric model. A training module for establishing an orientation error estimation neural network is used to construct a second loss function with energy projection information as a physical constraint based on the incident azimuth and elevation angles and the frequency domain data of the particle velocity channel. By training the established orientation error estimation neural network, the orientation error parameters of each channel of each vector sensor in the array are output. The array calibration module is used to perform array calibration using position error parameters and orientation error parameters.
[0018] Compared with the prior art, the advantages of the present invention are: 1. Significantly improved computational efficiency The Physical-Informed Neural Network (PINN) reduces the parameter search space through physical constraints, avoiding high-dimensional matrix factorization (such as subspace methods) or global random search (such as evolutionary algorithms), and its loss function converges rapidly within 200 steps. It achieves error parameter convergence within 500 iterations, calibrating position errors to the millimeter level and orientation errors to the sub-angular level.
[0019] 2. Error decoupling and full-space calibration capability The hierarchical calibration strategy leverages the independence of phase-energy physics (high-frequency phase is sensitive to position, and low-frequency energy is sensitive to orientation) to overcome parameter interference in traditional joint optimization. It achieves completely decoupled estimation of position and orientation errors, supporting full-space error calibration for arbitrary array configurations without assuming element orthogonality or known positions.
[0020] 3. Generalizability and engineering applicability The calibration unit is processed independently (the smallest unit is a single array element), requiring no prior knowledge of the global array geometry. The method can be extended to non-concurrent vector arrays or underwater acoustic systems, solving the problem of limitations imposed by structural assumptions (such as uniform linear arrays) in traditional methods. Attached Figure Description
[0021] Figure 1 This is a schematic diagram of the orientation error projection of the three-axis mass velocity channel in a single-vector sensor; Figure 2 This is a schematic diagram of a PINN-based acoustic vector array calibration network structure; Figure 3 This is a schematic diagram of the array and calibration sound source setup; Figure 4 It is the convergence curve of the estimated position error of the vector sensor on the x-axis; Figure 5 It is the convergence curve of the estimated orientation error of the vector sensor at the origin; Figure 6 It is the DOA estimation of the calibration array under different SNR; Figure 7 It is the DOA estimation of the calibrated array elevation angle under different SNR. Detailed Implementation
[0022] This application provides a hierarchical calibration method for acoustic vector arrays based on a Physical-Informed Neural Network (PINN). The core of this method lies in guiding the neural network training through physical constraints, gradually decoupling and estimating position and orientation errors. The specific steps of the technical solution are as follows: 1. Design of a graded calibration framework A phased strategy is adopted, first calibrating the position error and then calibrating the orientation error to avoid parameter coupling: Position error calibration stage: Input: Frequency domain received data from the array's acoustic pressure channels.
[0023] Physical constraints: A loss function is constructed using the phase information of the sound pressure channel correlation matrix. Normalized correlation matrix. Compared with the ideal phase difference model Differences as constraints:
[0024] in, The normalized correlation matrix, i and j The first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List, The superscript T represents the transpose of the matrix, which is the ideal sound pressure channel steering vector. Indicates conjugate.
[0025] Neural network structure: Fully connected network (input is spatiotemporal coordinates, output is 9-dimensional position error parameters), hidden layers use Tanh activation function, and loss function is minimized by Adam optimizer.
[0026] Convergence criteria: At least three non-collinear calibration sources are required to ensure that the Jacobian matrix is full rank and the solution is unique.
[0027] Orientation error calibration phase: Input: Array data after position calibration, with a focus on the particle velocity channel.
[0028] Physical constraints: Using the normalized energy ratio of sound pressure to construct a loss function to constrain the consistency between the energy projection and the ideal model:
[0029] in, The normalized energy projection matrix, The vector is the guiding vector for the velocity channel of an ideal particle. The superscript T denotes the transpose of the matrix. Indicates conjugate. i and jThe first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List.
[0030] Neural network structure: similar to a position calibration network, the output is a 24-dimensional orientation error parameter (azimuth and pitch angle error).
[0031] Convergence condition: At least three non-coplanar calibration sound sources are required to ensure that the vector dot product equation has a unique solution.
[0032] like Figure 1 The figure shown is a schematic diagram of the orientation error projection of the three-axis mass velocity channel in a single-vector sensor; Figure 2 This is a schematic diagram of a PINN-based acoustic vector array calibration network structure.
[0033] 2. Physical information embedding and training mechanism Key innovation: The array manifold physical equations (element delay and amplitude relationship) are used as soft-constraint embedding loss functions to replace pure data-driven black-box learning.
[0034] Training process: Step 1: Perform a Fourier transform on the received data to extract the phase and energy information of the frequency domain correlation matrix.
[0035] Step 2: Prioritize the optimization of the position calibration network, and update the array geometry model after outputting error parameters.
[0036] Step 3: The orientation calibration network performs energy constraint optimization based on the updated incident angle.
[0037] Step 4: Jointly verify the DOA estimation performance of the calibrated array (e.g., using the MUSIC algorithm).
[0038] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.
[0039] Example 1 This embodiment provides a full-space acoustic vector sensor array calibration method, which uses Python for data processing and employs a PINN-based acoustic vector array calibration method. Specific steps include: (1) Set up a tetrahedral array consisting of four vector sensors, and set up calibration sound sources in the axial direction as follows: Figure 3 As shown; the coordinates of the pairwise elements follow a truncated normal distribution. Positional error, truncated at m; Add a truncated normal distribution to the particle velocity channel. The orientation error, truncated at ; z The velocity channel of the axial mass is quite special because its initial pitch angle is... Since the azimuth angle is arbitrary, its orientation error is set to a uniform distribution. , .
[0040] (2) Three calibration sound sources sequentially played a 30 dB 800 Hz sine wave signal and collected it for 10 s. The signal was then processed in the frequency domain to retain the 800 Hz narrowband signal and the correlation matrix of the sound pressure channel was calculated. and normalized energy projection matrix .
[0041] (3) The neural network model for estimating position error is constructed as follows: two hidden layers are set, each with 64 neurons, and the Tanh function is used for activation to satisfy the universal approximation theorem; the output layer is set to 9 dimensions, corresponding to the 9 position parameters for estimating position error; the Adam optimizer is selected with a learning rate of 0.05, and the training parameters are weighted. To avoid convergence to virtual element positions symmetric about the calibration sound source plane, the loss function described in formula (6) is obtained through 500 iterations. x The convergence curve of the estimation error of the position error of the on-axis vector sensor is as follows: Figure 4 As shown.
[0042] (4) The azimuth angle of the calibration signal relative to each array element is calculated based on the ideal array element position, the array element position error estimate, and the calibration sound source position. and pitch angle The neural network model for estimating the orientation error is constructed as follows: two hidden layers are set, each with 64 neurons, activated by the Tanh function to satisfy the universal approximation theorem; the output layer is set to 24 dimensions, corresponding to the 24 positional parameters for estimating the orientation error; the training iterations are 500, the Adam optimizer is selected, and the learning rate is 0.05. The convergence curve of the estimated orientation error of the origin vector sensor is obtained by performing 500 iterations according to the loss function described in formula (7). Figure 5 As shown.
[0043] (5) Perform 1000 Monte Carlo simulations, each time using a different random error to ensure the adaptability of the algorithm; calculate the mean and variance of the position error and orientation error estimates for 1000 simulations, as shown in Table 1.
[0044] Table 1 Error Quantification Table
[0045] (6) To verify the calibration effect of the error, two sets of DOA estimation simulations were set up with different signal frequencies and different SNRs. In the spatial coordinate system... A calibration sound source was placed to play an 800 Hz narrowband signal with an SNR of 0 dB or 30 dB. Azimuth and elevation angles (DOA) were estimated using the MUSIC algorithm, employing the original error array, an ideal array, and the original error array calibrated with estimated error parameters. Figure 6 and Figure 7 As shown.
[0046] (7) In the spatial coordinate system A calibration source was placed to play a 200 Hz or 2 kHz narrowband signal with an SNR of 30 dB. Azimuth and elevation angles (DOA) were estimated using the MUSIC algorithm, employing the original error array, an ideal array, and the original error array calibrated with estimated error parameters.
[0047] Therefore, the PINN-based acoustic vector array calibration method can largely correct the position and orientation errors caused by the vector array, thereby improving the accuracy of vector array DOA estimation.
[0048] Example 2 Embodiment 2 of the present invention provides a full-space acoustic vector sensor array calibration system, implemented based on the method of Embodiment 1. The system includes: An array building module is used to build an acoustic vector sensor array including multiple vector sensors and to arrange at least three non-coplanar calibration sound sources around the array; The frequency domain processing module is used to acquire acoustic signals received by multiple vector sensors and perform frequency domain processing to obtain frequency domain data for the array sound pressure channel and the particle velocity channel. A position error estimation neural network training module is established to construct a first loss function with phase difference information as a physical constraint based on the frequency domain data of the array sound pressure channel. By training the established position error estimation neural network, the position error parameters of each vector sensor in the array are output. The array update module is used to update the array's geometric model according to the position error parameters, and calculate the incident azimuth and elevation angles of the calibration sound source relative to each array element based on the updated geometric model. A training module for establishing an orientation error estimation neural network is used to construct a second loss function with energy projection information as a physical constraint based on the incident azimuth and elevation angles and the frequency domain data of the particle velocity channel. By training the established orientation error estimation neural network, the orientation error parameters of each channel of each vector sensor in the array are output. The array calibration module is used to perform array calibration using position error parameters and orientation error parameters. It is worth noting that in the embodiments of the above system, the modules included are divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be achieved; in addition, the specific names of each functional module are only for easy differentiation and are not used to limit the scope of protection of the present invention.
[0049] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to the embodiments, those skilled in the art should understand that modifications or equivalent substitutions to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.
Claims
1. A method for calibrating a full-space acoustic vector sensor array, comprising: Step 1: Construct an acoustic vector sensor array that includes multiple vector sensors, and arrange at least three non-coplanar calibration sound sources around the array; Step 2: Acquire acoustic signals received by multiple vector sensors and perform frequency domain processing to obtain frequency domain data for the array sound pressure channel and the particle velocity channel; Step 3: Based on the frequency domain data of the array acoustic pressure channels, construct a first loss function with phase difference information as the physical constraint, and output the position error parameters of each vector sensor in the array by training the established position error estimation neural network; Step 4: Update the array's geometric model based on the position error parameters, and calculate the incident azimuth and elevation angles of the calibration sound source relative to each array element based on the updated geometric model; Step 5: Based on the incident azimuth and elevation angles, and the frequency domain data of the particle velocity channel, construct a second loss function with energy projection information as the physical constraint. Train the established orientation error estimation neural network to output the orientation error parameters of each channel of each vector sensor in the array. Step 6: Complete array calibration using position error parameters and orientation error parameters.
2. The full-space acoustic vector sensor array calibration method according to claim 1, characterized in that, The at least three non-coplanar calibration sound sources in step 1 satisfy the requirement of a full-rank Jacobian matrix and have a unique solution.
3. The full-space acoustic vector sensor array calibration method according to claim 1, characterized in that, The first loss function in step 3 for: ； in, The normalized correlation matrix, i and j The first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List, The superscript T represents the transpose of the matrix, which is the ideal sound pressure channel steering vector. Indicates conjugate.
4. The full-space acoustic vector sensor array calibration method according to claim 1, characterized in that, The position error estimation neural network in step 3 adopts a physical information-based neural network, which is a fully connected network with two hidden layers and uses the Tanh activation function. During training, the first loss function is minimized through the Adam optimizer.
5. The full-space acoustic vector sensor array calibration method according to claim 1, characterized in that, The second loss function in step 5 for: ； in, The normalized energy projection matrix, The vector is the guiding vector for the velocity channel of an ideal particle. The superscript T denotes the transpose of the matrix. This indicates the conjugate transpose. i and j The first element represents the frequency domain covariance matrix of the sound pressure channel receiver. i Line number j List.
6. The full-space acoustic vector sensor array calibration method according to claim 5, characterized in that, The orientation error estimation neural network in step 5 is a physics-based neural network, which is a fully connected network with two hidden layers and uses the Tanh activation function. During training, the second loss function is minimized through the Adam optimizer.
7. A full-space acoustic vector sensor array calibration system, characterized in that, include: An array building module is used to build an acoustic vector sensor array including multiple vector sensors and to arrange at least three non-coplanar calibration sound sources around the array; The frequency domain processing module is used to acquire acoustic signals received by multiple vector sensors and perform frequency domain processing to obtain frequency domain data for the array sound pressure channel and the particle velocity channel. A position error estimation neural network training module is established to construct a first loss function with phase difference information as a physical constraint based on the frequency domain data of the array sound pressure channel. By training the established position error estimation neural network, the position error parameters of each vector sensor in the array are output. The array update module is used to update the array's geometric model according to the position error parameters, and calculate the incident azimuth and elevation angles of the calibration sound source relative to each array element based on the updated geometric model. A training module for establishing an orientation error estimation neural network is used to construct a second loss function with energy projection information as a physical constraint based on the incident azimuth and elevation angles and the frequency domain data of the particle velocity channel. By training the established orientation error estimation neural network, the orientation error parameters of each channel of each vector sensor in the array are output. and The array calibration module is used to perform array calibration using position error parameters and orientation error parameters.