Ultra-short baseline array position error and amplitude-phase error calibration method and system

Abstract

The invention discloses an ultra-short baseline array position error and amplitude-phase error calibration method and system, and relates to the technical field of underwater acoustic localization, and the method comprises the steps: sequentially numbering M array elements of an ultra-short baseline array, taking a first array element as a reference array element to establish an array coordinate system, and determining the coordinate position of each array element; the ultra-short baseline array is fixed to one end of the lifting rotating rod, the auxiliary sound source is fixed to the other end of the lifting rotating rod, the rotating angle of the ultra-short baseline array is controlled, and multiple sets of data are collected; and respectively estimating the position error of the array elements and the amplitude-phase error between the channels by using the phase difference and the covariance matrix between the receiving signals of the array elements. According to the invention, the precision of ultra-short baseline array estimation can be improved.

Description

Technical Field

[0001] The present application relates to the technical field of underwater acoustic positioning, and in particular to a method and system for calibrating position error and amplitude and phase error of an ultra-short baseline array. Background Art

[0002] The research on acoustic array calibration algorithm first appeared in the application field of microphone array. Microphones belong to the category of Wireless Acoustic Sensor Networks (WASNs), which are low-cost and difficult to detect. Compared with the working environment of microphones, the underwater measurement environment is more complex, so directly transplanting the calibration algorithm of microphone arrays to sonar arrays cannot meet the requirements of high-precision calibration.

[0003] When the ultra-short baseline array is used to estimate the target azimuth in the application domain, there is a certain deviation between the actual position of each receiving hydrophone and the theoretical position. This deviation is called array error. The causes of array error include the machining errors caused by the array manufacturing process and the fact that the geometric center of each hydrophone in the array does not completely coincide with the acoustic radiation center. Due to the small size of the ultra-short baseline array, even a millimeter-level array error will bring non-negligible relative errors, which greatly reduces the accuracy of target azimuth estimation. Therefore, the impact of array error on target azimuth estimation cannot be ignored. Before using the array to locate the target, it is essential to correct the array error.

[0004] The machining errors of the array can be corrected by precision machining or high-precision optical measurement, but this can only determine the relative position of the geometric center of the primitive, and it also brings additional costs. Compared with optical measurement, the acoustic measurement method can directly obtain the relative position of the acoustic center of each hydrophone in the array, and there is no need to purchase additional precision measurement equipment to correct the array. Therefore, the acoustic measurement method is the best choice to correct array errors and improve the working performance of the acoustic array. Summary of the invention

[0005] The purpose of the present application is to provide a method and system for calibrating position error and amplitude and phase error of an ultra-short baseline array, which can improve the accuracy of ultra-short baseline array estimation.

[0006] To achieve the above objectives, this application provides the following solutions: In a first aspect, the present application provides a method for calibrating position error and amplitude and phase error of an ultra-short baseline array, comprising the following steps: The M array elements of the ultra-short baseline array are numbered in sequence, a base array coordinate system is established with the first array element as the reference array element, and the coordinate position of each array element is determined.

[0007] Fix the ultra-short baseline array at one end of the lifting and rotating rod, and fix the auxiliary sound source at the other end. Control the rotation angle of the ultra-short baseline array and collect multiple groups of data.

[0008] Utilize the phase differences and covariance matrix among the signals received by each element to estimate the element position error and the amplitude-phase error among each channel respectively.

[0009] Optionally, establish a base array coordinate system with the first element as the reference element, specifically including: Take the first element as the origin of the coordinate system, set its amplitude gain as the reference value and the initial phase as the reference phase, and establish the base array coordinate system. The position coordinates of each element in the base array coordinate system are 。

[0010] Optionally, fix the ultra-short baseline array at one end of the lifting and rotating rod, and fix the auxiliary sound source at the other end. Control the rotation angle of the ultra-short baseline array and collect multiple groups of data, specifically including: Deploy the ultra-short baseline array and the auxiliary sound source at the same depth in the anechoic water tank.

[0011] Rotate the ultra-short baseline array through the lifting and rotating rod so that the ultra-short baseline array receives the combined signals emitted by the auxiliary sound source at each rotation angle.

[0012] Optionally, the combined signal emitted by the auxiliary sound source consists of a chirp signal and a calibration single-frequency signal with a fixed frequency.

[0013] Optionally, utilize the phase differences and covariance matrix among the signals received by each element to estimate the element position error and the amplitude-phase error among each channel respectively, specifically including: Intercept the single-frequency signal and calculate the phase differences between each element and the reference element 。

[0014] Utilize the relationship between the time delay difference of the signal arriving at each element and the phase difference, and adopt the least squares method to calculate the position of the element and the initial phase of each element 。

[0015] Calculate the amplitude gain of each element according to the covariance matrix of the signals received by the ultra-short baseline array 。

[0016] Optionally, the relationship between the time delay difference of each element and the phase difference is specifically: 。

[0017] Wherein, is the frequency of the calibration single-frequency signal, is the time delay difference between the element and the reference element, is the initial phase, is the phase difference, takes values of , takes values of .

[0018] Optionally, the calculation formula for the time delay difference is: .

[0019] Wherein, is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle.

[0020] Optionally, the least squares method is used to calculate the positions of the array elements and the initial phases of each array element, specifically including: According to the formula , calculate the positions of the array elements and the initial phases of each array element.

[0021] Wherein, the matrix , the matrix , the matrix .

[0022] Optionally, according to the covariance matrix of the signals received by the ultra-short baseline array, the amplitude gains of each array element are calculated, specifically including: According to the formula , calculate the amplitude gains of each array element.

[0023] Wherein are the elements on the diagonal of the covariance matrix.

[0024] In a second aspect, the present application provides an ultra-short baseline array position error and amplitude-phase error calibration system, including: A base array coordinate system construction module, which is used to sequentially number the M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0025] A data acquisition module, which is used to fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and collect multiple groups of data.

[0026] An error estimation module, which is used to respectively estimate the array element position error and the amplitude-phase error between each channel by using the phase difference between the signals received by each array element and the covariance matrix.

[0027] According to the specific embodiments provided by the present application, the following technical effects are disclosed: The present application provides a method and system for calibrating the position error and amplitude-phase error of an ultra-short baseline array. First, a base array coordinate system is established with the first element as the reference element, and the positions of each element are determined based on this coordinate system. Accurate element position information is the basis for subsequent error estimation and calibration, which helps to improve the positioning accuracy of the entire system. Secondly, with the help of an auxiliary sound source and a lifting and rotating rod, the rotation angle of the array can be conveniently controlled and multiple groups of data can be collected. These data include the phase differences and covariance matrix information between the received signals of each element, which are the key to estimating the element position error and the amplitude-phase error between channels. By collecting and analyzing these data, the error situation of the system can be evaluated more accurately. Finally, the present application combines the phase difference information and the covariance matrix to estimate the element position error and the amplitude-phase error between channels respectively. This method improves the accuracy and reliability of error estimation. Description of the Drawings

[0028] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can also be obtained based on these drawings.

[0029] Figure 1 It is a schematic flowchart of a method for calibrating the position error and amplitude-phase error of an ultra-short baseline array provided by an embodiment of the present application.

[0030] Figure 2 It is a flowchart of an ultra-short baseline array position and amplitude-phase error calibration algorithm provided by an embodiment of the present application.

[0031] Figure 3 It is a time-domain diagram of the signal used for array calibration provided by an embodiment of the present application.

[0032] Figure 4 It is a layout diagram of the array position calibration pool experiment provided by an embodiment of the present application.

[0033] Figure 5 It is a comparison diagram of the array calibration position and the ideal position provided by an embodiment of the present application.

[0034] Figure 6 It is a schematic diagram of the functional modules of a system for calibrating the position error and amplitude-phase error of an ultra-short baseline array provided by an embodiment of the present application. Detailed Embodiments

[0035] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts shall fall within the protection scope of the present application.

[0036] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0037] Embodiment 1 As Figure 1 shown, this embodiment provides a method for calibrating the position error and amplitude-phase error of an ultra-short baseline array, including the following steps: Step 101: Number the M array elements of the ultra-short baseline array in sequence, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0038] Step 102: Fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and collect multiple groups of data.

[0039] Step 103: Use the phase difference and covariance matrix between the signals received by each array element to estimate the array element position error and the amplitude-phase error between each channel respectively.

[0040] In the present application, as Figure 2 shown in the flowchart of the method for calibrating the position error and amplitude-phase error of the ultra-short baseline array, the calibration method includes establishing a base array coordinate system, experimental data collection, data processing, and calibration result analysis. Among them, the base array coordinate system is as shown in Step 101, the experimental data collection is as shown in Step 102. Specifically, the experimental data collection includes equipment placement, array rotation, signal generation, and signal reception. The data processing includes signal synchronization, single-frequency signal interception, calculation of the initial phase of each array element position, and calculation of the amplitude gain. The calibration result analysis includes experimental data comparison.

[0041] Among them, when performing Step 101, specifically, it can be as follows: Taking the first array element as the origin of the coordinate system, setting its amplitude gain as the reference value and the initial phase as the reference phase, establish a base array coordinate system, and the position coordinates of each array element in the base array coordinate system are .

[0042] Specifically, number the M array elements of the array in sequence, take the first array element as the reference array element, establish a base array coordinate system, and represent the coordinate positions of each array element , set the reference of the amplitude gain and initial phase of the reference array element, that is , in this embodiment, a six - element circular array with a radius is selected for the error calibration example. Specifically, as shown in Figure 5 the calibration result diagram of the element positions of the uniform six - element array. The ideal positions of the elements are marked by small black circles, and the actual element positions after calibration are marked by small red circles. Among them, the first element is used as the reference element and is located at the coordinate origin. Therefore, the ideal position and the actual position completely coincide, that is, the red small circle and the black small circle overlap (only the red small circle is shown in the figure). In addition, in order to visually compare the ideal and actual element positions, a large black circle is used to enclose the two in the figure.

[0043] Among them, when performing step 102, specifically, it can be as follows: First, place the ultra - short baseline array and the auxiliary sound source at the same depth in the anechoic tank.

[0044] Then, rotate the ultra - short baseline array through the lifting and rotating rod so that the ultra - short baseline array receives the combined signals emitted by the auxiliary sound source at each rotation angle. Among them, the combined signal emitted by the auxiliary sound source is composed of a chirp signal and a calibration single - frequency signal with a fixed frequency.

[0045] Specifically, placing the ultra - short baseline array and the auxiliary sound source at the same depth in the anechoic tank can be as follows: As shown in Figure 4 the layout diagram of the calibration experimental equipment in this embodiment, which includes an ultra - short baseline array, an auxiliary sound source, a lifting and rotating rod, and a console. The ultra - short baseline array is fixed on the lifting and rotating rod, and the auxiliary sound source is fixed at the other end. The two are horizontally 6 meters apart. The array and the auxiliary sound source are both placed at a water depth of 2 meters. When the first element is aligned with the auxiliary sound source, the angle of the console of the lifting and rotating rod is set to zero. By operating the console, the array rotates by an angle , the auxiliary sound source emits signals, and the array repeatedly receives multiple groups of data.

[0046] The operator first fixes the array on the lifting and rotating rod and puts it into the water at the same depth as the auxiliary sound source at a far - field distance, ensuring that the signals emitted by the auxiliary sound source reach the array in an approximate plane - wave propagation mode. When the first element is aligned with the auxiliary sound source by controlling the rotating rod, the angle of the console of the lifting and rotating rod is set to zero.

[0047] The signal emitted by the auxiliary sound source is composed of a chirp signal and a calibration single - frequency signal with a frequency . In this embodiment, the frequency range of the chirp signal is 13 kHz~16 kHz. The frequency of the calibration single - frequency signal must be such that the half - wavelength of the signal is greater than the element spacing. In this embodiment, the element spacing is 40 mm, and kHz is selected as the calibration single - frequency signal.

[0048] Control the lifting and rotating rod to rotate by an angle , at each rotation angle, the auxiliary sound source emits a signal, and the array repeatedly receives multiple groups of data. The rotation angle of the array , is equivalent to the auxiliary sound source being placed at 's position.

[0049] Among them, when performing step 103, it can be specifically as follows: Intercept the single-frequency signal and calculate the phase difference between each array element and the reference array element .

[0050] Utilize the relationship between the time delay difference of the signal arriving at each array element and the phase difference, and use the least squares method to calculate the position of the array element and the initial phase of each array element .

[0051] According to the covariance matrix of the signals received by the ultra-short baseline array, calculate the amplitude gain of each array element .

[0052] Specifically, during the data processing in step 103, first synchronize the received signal using the chirp signal, and intercept a section of the calibrated single-frequency signal. The signal received by the array element is as Figure 3 shown, where the red mark is the calibrated single-frequency signal.

[0053] Then, establish the relationship between the time delay difference and the phase difference of the signal received by the array element as follows: .

[0054] Among them is the frequency of the calibrated single-frequency signal, is the time delay difference between the array element and the reference array element, is the initial phase, is the phase difference, 's value is , 's value is .

[0055] The time delay difference can be expressed by the following formula: .

[0056] Among them is the speed of sound, is the angle of rotation of the lifting and rotating rod, is the pitch angle. The array and the auxiliary sound source are placed at the same depth, so . Obtain the phase of the signal using the Fourier transform. The Fourier transform is as follows: .

[0057] .

[0058] Among them, t is time, is the time shift amount, Subtract the phase of each received signal from the phase of the reference signal to obtain the phase difference .

[0059] Arrange the above relationships to obtain the following formula: .

[0060] The matrix expression of this formula can be written as: .

[0061] Among them, is the wavelength of the calibration single-frequency signal, and its relationship with frequency and sound speed is .

[0062] Finally, use the least squares method to calculate the array element position and the initial phase , and the calculation process is shown as follows: .

[0063] Among them, the matrix , the matrix , the matrix , and H is the conjugate transpose.

[0064] Use the covariance matrix of the received signal to calculate the amplitude gain of each array element, and the calculation formula is shown as follows: .

[0065] Among them, is the element on the diagonal of the covariance matrix.

[0066] In addition, in this application, a conventional beamforming algorithm is also used for DOA estimation. Compare the DOA estimation results before and after array calibration. The comparison results of 6 groups of data are shown in Table 1. Before array calibration, the average deviation of DOA estimation is 2.26°, and after array calibration, the average deviation of DOA estimation is 0.28°. Judging from the average error, the calibration algorithm has significant estimation performance for the target azimuth angle.

[0067] Table 1 Comparison chart of azimuth angle estimation before and after array calibration

[0068] Embodiment 2 As Figure 6 described above, this embodiment provides a calibration system for the position error and amplitude-phase error of an ultra-short baseline array, including: The array coordinate system construction module 601 is used to sequentially number the M array elements of the ultra-short baseline array, establish an array coordinate system with the first array element as the reference array element, and determine the coordinate positions of each array element.

[0069] The data acquisition module 602 is used to fix the ultra-short baseline array at one end of the lifting and rotating rod, fix the auxiliary sound source at the other end, control the rotation angle of the ultra-short baseline array, and collect multiple groups of data.

[0070] The error estimation module 603 is used to respectively estimate the array element position error and the amplitude-phase error between each channel by using the phase difference and covariance matrix among the signals received by each array element.

[0071] In summary, the present application has the following technical effects: 1) In the present application, the time delay of receiving a single-frequency signal between each array element can be replaced by a phase delay. The array element position error and the initial phase error are estimated simultaneously, and the amplitude error of each channel is estimated by using the covariance matrix of the received signals. The error estimation result is accurate.

[0072] 2) In the present application, the rotation of the array is controlled by the lifting and rotating rod, avoiding the movement of the auxiliary sound source, reducing the complexity of the experimental process, and improving the performance of the calibration method.

[0073] 3) The method provided by the present application is applicable to array calibration with various geometric structures, such as uniform linear arrays and circular arrays.

[0074] The technical features of the above embodiments can be combined arbitrarily. For the sake of brief description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0075] In this article, specific examples are used to elaborate on the principle and implementation manner of the present application. The description of the above embodiments is only used to help understand the method and its core idea of the present application; at the same time, for those of ordinary skill in the art, according to the idea of the present application, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present application.

Claims

1. A method for calibrating position error and amplitude and phase error of an ultra-short baseline array, characterized in that: The following steps are involved: The M array elements of the ultra-short baseline array are numbered in sequence, a base array coordinate system is established with the first array element as the reference array element, and the coordinate position of each array element is determined; The ultra-short baseline array is fixed to one end of the lifting and rotating rod, and the auxiliary sound source is fixed to the other end, so as to control the rotation angle of the ultra-short baseline array and collect multiple sets of data; The array element position error and the amplitude and phase errors between channels are estimated respectively by using the phase difference and covariance matrix between the received signals of each array element.

2. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 1, characterized in that: The base array coordinate system is established with the first array element as the reference array element, including: Take the first array element as the origin of the coordinate system, set its amplitude gain as the reference value, and the initial phase as the reference phase to establish the base array coordinate system. The position coordinates of each array element in the base array coordinate system are .

3. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 1, characterized in that: The ultra-short baseline array is fixed to one end of the lifting and rotating rod, and the auxiliary sound source is fixed to the other end. The rotation angle of the ultra-short baseline array is controlled and multiple sets of data are collected, including: Place the ultra-short baseline array and the auxiliary sound source at the same depth of the anechoic pool; The ultra-short baseline array is rotated by lifting and lowering the rotating rod, so that the ultra-short baseline array receives the combined signal emitted by the auxiliary sound source at each rotation angle.

4. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 3, characterized in that: The combined signal emitted by the auxiliary sound source consists of a linear frequency modulation signal and a fixed frequency calibrated single frequency signal.

5. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 1, characterized in that: The phase difference and covariance matrix between the received signals of each array element are used to estimate the array element position error and the amplitude and phase error between each channel, including: Intercept the single-frequency signal and calculate the phase difference between each array element and the reference array element ; The relationship between the time delay difference and phase difference of the signal to each array element is used to calculate the position of the array element using the least squares method. and the initial phase of each array element ; According to the covariance matrix of the ultra-short baseline array received signal, the amplitude gain of each array element is calculated .

6. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 5, characterized in that: The relationship between the time delay difference and phase difference of each array element is as follows: ； in, To calibrate the frequency of a single-frequency signal, is the delay difference between the array element and the reference array element, is the initial phase, is the phase difference, The value of , The value of .

7. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 6, characterized in that: The calculation formula of the delay difference is: ； in, is the speed of sound, is the rotation angle of the lifting and rotating rod, is the pitch angle.

8. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 6, characterized in that: The position of the array element is calculated using the least squares method and the initial phase of each array element , specifically including: According to the formula , calculate the position of the array element and the initial phase of each array element ; Among them, the matrix ,matrix ,matrix .

9. The method for calibrating position error and amplitude and phase error of an ultra-short baseline array according to claim 1, characterized in that: According to the covariance matrix of the ultra-short baseline array received signal, the amplitude gain of each array element is calculated , specifically including: According to the formula , calculate the amplitude gain of each array element ; in are the elements on the diagonal of the covariance matrix.

10. An ultra-short baseline array position error and amplitude phase error calibration system, characterized in that: include: A base array coordinate system building module is used to sequentially number the M array elements of the ultra-short baseline array, establish a base array coordinate system with the first array element as the reference array element, and determine the coordinate position of each array element; A data acquisition module is used to fix the ultra-short baseline array to one end of the lifting and rotating rod, fix the auxiliary sound source to the other end, control the rotation angle of the ultra-short baseline array and collect multiple sets of data; The error estimation module is used to estimate the array element position error and the amplitude and phase error between each channel by using the phase difference and covariance matrix between the received signals of each array element.

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