CN112903062A - Non-uniform ultrasonic array DOA estimation method - Google Patents

Non-uniform ultrasonic array DOA estimation method Download PDF

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CN112903062A
CN112903062A CN202110013623.2A CN202110013623A CN112903062A CN 112903062 A CN112903062 A CN 112903062A CN 202110013623 A CN202110013623 A CN 202110013623A CN 112903062 A CN112903062 A CN 112903062A
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薛萍
魏川博
王宏民
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Harbin University of Science and Technology
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    • G01F23/00—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm
    • G01F23/22—Indicating or measuring liquid level or level of fluent solid material, e.g. indicating in terms of volume or indicating by means of an alarm by measuring physical variables, other than linear dimensions, pressure or weight, dependent on the level to be measured, e.g. by difference of heat transfer of steam or water
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Abstract

The invention discloses a non-uniform ultrasonic array DOA estimation method, which relates to the technical field of ultrasonic arrays and comprises the following steps: calibrating an ultrasonic array structure in advance, and performing matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix; carrying out a beam forming algorithm for calibrating the inhomogeneous linear array, wherein the inhomogeneous co-prime array is introduced into the traditional beam forming algorithm; and carrying out DOA estimation on the inhomogeneous line array, wherein an array error model is established. The invention realizes the improvement of the accurate positioning of the non-uniform ultrasonic array, the self-correction of the amplitude-phase error and the mutual coupling error of the ultrasonic array signal, the accurate measurement of the dynamic liquid level in the narrow space on the basis of the accuracy of the self-correction algorithm, and the problem that the conventional ultrasonic liquid level measuring instrument cannot measure the fluctuating liquid level in the narrow space.

Description

Non-uniform ultrasonic array DOA estimation method
Technical Field
The invention relates to the technical field of ultrasonic arrays, in particular to a non-uniform ultrasonic array DOA estimation method.
Background
Ultrasonic level measurement is a traditional and at the same time very developing method. The basic principle of using ultrasonic wave to measure liquid level is based on the characteristic that ultrasonic wave is reflected on medium interface with different acoustic impedance, the echo generated by the reflection of ultrasonic wave sent by ultrasonic probe on the interface between liquid level and gas is received by probe, and the liquid level can be measured according to the time that the probe transmits ultrasonic wave and receives the ultrasonic wave again. Compared with other measuring methods, the ultrasonic liquid level measuring technology has many characteristics and advantages: ultrasonic distance measurement can realize not only contact measurement but also non-contact measurement; it not only can fix point and continuous side position, but also can conveniently provide the signal required by telemetering or telemetering. Compared with the radioactive technology, the ultrasonic technology does not need protection; compared with infrared, laser and radio distance measurement, ultrasonic distance measurement in a short distance range has the characteristics of no influence of light rays, simple structure, low cost and the like. Another outstanding advantage of ultrasonic level measurement is: the environment medium can be air, liquid or solid, and the application range is wide.
However, if a single ultrasonic sensor is used for measurement, the directivity of the ultrasonic wave is difficult to grasp, and it is difficult to correctly distinguish an effective echo signal, so that the difficulty of feature matching is increased, and the resolution of the sensor is reduced. In order to improve the resolving power of the ultrasonic sensor, a concept of an ultrasonic sensor array has been proposed. The data acquired by the ultrasonic sensor array has great practical significance for target identification, and can be applied to the aspects of robot navigation, obstacle positioning, map building (SLAM) and the like. The common ultrasonic sensor array can only obtain one-dimensional information of the obstacle, and the high-resolution array signal processing technology can obtain multi-dimensional parameter information of the obstacle. Therefore, the application of the array signal direction-finding theory to the ultrasonic sensor array has certain practical significance.
Array signal processing is an important branch of the signal processing field, and aims to enhance required useful signals, inhibit useless interference and noise and extract characteristic parameters contained in the signals by carrying out statistical processing on array receiving signals, so that the array signal processing has wide application in the fields of radar, sonar, voice, seismology, radio astronomy, wireless communication, medical imaging and the like. The array signal processing is realized by arranging a group of sensors which are regularly arranged according to a certain team in a space to form a sensor array so as to realize the spatial sampling of signals, and carrying out statistical signal processing on discrete observation data received by the array. Compared with the traditional single directional antenna, the layout of the array has higher resolution performance, stronger interference suppression capability, higher signal gain and more flexible beam control. Therefore, the array signal processing has received great attention and vigorous development in both theoretical research and practical application, and forms a series of important technologies including direction of arrival estimation, spatial spectrum estimation, beam forming, source localization, and the like.
The intelligent antenna system is an important system applied to the array antenna, and by combining the array antenna and the array signal processing technology, the system can adaptively change a directional diagram, so that a formed beam points to a source position, and simultaneously, a null part in the directional diagram is aligned to an interference direction. In recent years, smart antennas are widely used in the fields of digital multi-beam forming, airspace anti-interference and the like, antenna systems may be directly installed on airplanes, ships or civil systems, due to the requirement of miniaturization of equipment, antenna units become smaller gradually, arrays are also compact, mutual coupling among array antennas becomes a non-negligible problem affecting the performance of the antennas, coupling among the units affects the performance of the antennas, the direction-finding accuracy is reduced, and formed beams are directed to an undesired direction. On the other hand, in an ideal situation, both the classical DOA estimation algorithm and the adaptive beamforming algorithm can achieve respective functions, but in practical engineering application, because the sampled data is not infinitely long, estimation errors of a covariance matrix must be considered, and in addition, errors such as inconsistency of amplitude-phase characteristics of channels exist, which affect the performance of the DOA estimation and the beamforming algorithm.
Therefore, a non-uniform ultrasonic array DOA estimation method is needed.
An effective solution to the problems in the related art has not been proposed yet.
Disclosure of Invention
Aiming at the problems in the related art, the invention provides a non-uniform ultrasonic array DOA estimation method, which improves the accuracy of non-uniform ultrasonic array positioning, self-corrects the amplitude-phase error and the mutual coupling error of ultrasonic array signals, realizes the accurate measurement of dynamic liquid level in a narrow space on the basis of the accuracy of a self-correction algorithm, solves the problem that the conventional ultrasonic liquid level measuring instrument cannot measure the fluctuating liquid level in the narrow space, and overcomes the technical problems in the related art.
The technical scheme of the invention is realized as follows:
a non-uniform ultrasonic array DOA estimation method comprises the following steps:
step S1, calibrating an ultrasonic array structure in advance, wherein the ultrasonic array structure comprises a calibration frequency and an ultrasonic sensor array of a calibration signal model structure;
step S2, performing matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix;
step S3, calibrating the beam forming algorithm of the non-uniform linear array, including introducing the non-uniform co-prime array into the traditional beam forming algorithm;
and step S4, carrying out DOA estimation of the non-uniform linear array, wherein the DOA estimation comprises the establishment of an array error model.
Further, the pre-calibrating the ultrasonic array structure includes the following steps:
calibrating a set I consisting of N elements, wherein the set I is { ni, I is 1, 2,.. the. N }, and defining another set Sdiff { ni-nj, I is less than or equal to 1 and I is less than or equal to N } which is obtained by mutually differentiating all the elements in the set I, wherein the differential set of IM and N is SM, N is { Mn-Nm, N is greater than or equal to 0 and less than or equal to N-1, and M is greater than or equal to 0 and less than or equal to M-1 };
calibrating the N +2M integer to obtain a continuous integer interval of 2MN + 1;
calibrating the position of the array element, and expressing as:
S＝{Mnd,0≤n≤N-1}∪{Nmd,0≤m≤2M-1}
wherein d is the basic array element spacing unit, d is lambda/2, and lambda is the carrier wavelength.
Further, the matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix includes the following steps:
carrying out initialization setting in advance, wherein the initialization setting comprises setting an iteration counter and an initial value;
estimating the direction of arrival of the signal and calibrating the spatial spectrum estimate, as:
Figure RE-GDA0003024481840000031
wherein the content of the first and second substances,
Figure RE-GDA0003024481840000032
as a noise subspace, C(k)For cross-coupling error matrices, Γ(k)For the amplitude-phase error matrix, a (theta) is the signal subspace, and N maximum values of the spatial spectrum function are searched, and the corresponding angle is the estimated value of the signal arrival angle
Figure RE-GDA0003024481840000041
Estimating the amplitude-phase error matrix, stationary
Figure RE-GDA0003024481840000042
And a mutual coupling matrix C(k)Obtaining a reconstructed amplitude-phase error gamma(k+1)Which is
Figure RE-GDA0003024481840000043
Wherein g ═ Γ11,Γ22,...,ΓMM]；
Estimating the cross-coupling error matrix, fixing
Figure RE-GDA0003024481840000044
And amplitude-phase matrix gamma(k)Reconstructing the cross-coupling error matrix C(k+1)；
Calculating the direction of arrival of the signal;
performing discrimination convergence and obtaining respectively
Figure RE-GDA0003024481840000045
C(k+1)And Γ(k+1)Of an estimator of (1), its cost function JCSatisfies Jk-Jk+1>Epsilon stops the iteration, where epsilon is a given minimum.
The invention has the beneficial effects that:
the invention discloses a non-uniform ultrasonic array DOA estimation method, which comprises the steps of calibrating an ultrasonic array structure in advance, carrying out matrix reconstruction and self-correction based on a magnitude-phase error matrix and a cross-coupling error matrix, calibrating a beam forming algorithm of a non-uniform linear array, carrying out DOA estimation of the non-uniform linear array, realizing the improvement of the positioning accuracy of the non-uniform ultrasonic array, carrying out self-correction on the magnitude-phase error and the cross-coupling error of an ultrasonic array signal, realizing the accurate measurement of a dynamic liquid level in a narrow space on the basis of the accuracy of the self-correction algorithm, and solving the problem that the conventional ultrasonic liquid level measuring instrument cannot measure the fluctuating liquid level in the.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without creative efforts.
FIG. 1 is a schematic flow diagram of a non-uniform ultrasonic array DOA estimation method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a co-prime array model of a non-uniform ultrasonic array DOA estimation method according to an embodiment of the present invention;
fig. 3 is a schematic diagram of a beamforming algorithm of a non-uniform ultrasound array DOA estimation method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments that can be derived by one of ordinary skill in the art from the embodiments given herein are intended to be within the scope of the present invention.
According to an embodiment of the invention, a non-uniform ultrasound array DOA estimation method is provided.
As shown in fig. 1-3, a non-uniform ultrasound array DOA estimation method according to an embodiment of the present invention includes the following steps:
step S1, calibrating an ultrasonic array structure in advance, wherein the ultrasonic array structure comprises a calibration frequency and an ultrasonic sensor array of a calibration signal model structure;
step S2, performing matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix;
step S3, calibrating the beam forming algorithm of the non-uniform linear array, including introducing the non-uniform co-prime array into the traditional beam forming algorithm;
and step S4, carrying out DOA estimation of the non-uniform linear array, wherein the DOA estimation comprises the establishment of an array error model.
The pre-calibrating of the ultrasonic array structure comprises the following steps:
calibrating a set I consisting of N elements, wherein the set I is { ni, I is 1, 2,.. the. N }, and defining another set Sdiff { ni-nj, I is less than or equal to 1 and I is less than or equal to N } which is obtained by mutually differentiating all the elements in the set I, wherein the differential set of IM and N is SM, N is { Mn-Nm, N is greater than or equal to 0 and less than or equal to N-1, and M is greater than or equal to 0 and less than or equal to M-1 };
calibrating the N +2M integer to obtain a continuous integer interval of 2MN + 1;
calibrating the position of the array element, and expressing as:
S＝{Mnd,0≤n≤N-1}∪{Nmd,0≤m≤2M-1}
wherein d is the basic array element spacing unit, d is lambda/2, and lambda is the carrier wavelength.
The matrix reconstruction and self-correction are carried out based on the amplitude-phase error matrix and the cross-coupling error matrix, and the method comprises the following steps:
carrying out initialization setting in advance, wherein the initialization setting comprises setting an iteration counter and an initial value;
estimating the direction of arrival of the signal and calibrating the spatial spectrum estimate, as:
Figure RE-GDA0003024481840000051
wherein the content of the first and second substances,
Figure RE-GDA0003024481840000052
as a noise subspace, C(k)For cross-coupling error matrices, Γ(k)For the amplitude-phase error matrix, a (theta) is the signal subspace, and N maximum values of the spatial spectrum function are searched, and the corresponding angle is the estimated value of the signal arrival angle
Figure RE-GDA0003024481840000053
Estimating the amplitude-phase error matrix, stationary
Figure RE-GDA0003024481840000054
And a mutual coupling matrix C(k)Obtaining a reconstructed amplitude-phase error gamma(k+1)Which is
Figure RE-GDA0003024481840000055
Wherein g ═ Γ11,Γ22,...,ΓMM]；
Estimating the cross-coupling error matrix, fixing
Figure RE-GDA0003024481840000061
And amplitude-phase matrix gamma(k)Reconstructing the cross-coupling error matrix C(k+1)；
Calculating the direction of arrival of the signal;
performing discrimination convergence and obtaining respectively
Figure RE-GDA0003024481840000062
C(k+1)And Γ(k+1)Of an estimator of (1), its cost function JCSatisfies Jk-Jk+1>Epsilon stops the iteration, where epsilon is a given minimum.
By means of the technical scheme, the ultrasonic liquid level measuring instrument performs matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix by calibrating the ultrasonic array structure in advance, performs the beam forming algorithm of the non-uniform linear array, performs DOA estimation of the non-uniform linear array, realizes improvement of positioning accuracy of the non-uniform ultrasonic array, performs self-correction of amplitude-phase errors and cross-coupling errors of ultrasonic array signals, realizes accurate measurement of dynamic liquid level in a narrow space on the basis of accuracy of the self-correction algorithm, and solves the problem that the conventional ultrasonic liquid level measuring instrument cannot measure fluctuating liquid level in the narrow space.
In addition, specifically, as shown in fig. 2, the step of pre-calibrating the ultrasonic array structure includes a difference set: defining a set I consisting of N elements, wherein the set I is { ni, I is 1, 2,.. the. N }, defining another set Sdiff which is obtained by mutually differentiating all the elements in the set I, wherein the set Sdiff is { ni-nj, 1 is less than or equal to I, and I is less than or equal to N }, and defining a new set Sdu which is obtained by removing repeated items in S as a differential set due to the existence of repeated items in the set Sdiff. If there is a pair of reciprocal prime numbers M and N, a set is defined, expressed as:
IM,N＝{Mn，0≤n≤N-1}{Nm，0≤m≤M-1}
then by definition, the differential set of IM, N is represented as:
SM,N＝{Mn-Nm，0≤n≤N-1，0≤m≤M-1}。
coprime theorem: from the above definition, when M and N are in a relatively prime relationship, the element intervals in the set SM, N are [ -N (M-1), M (N-1) ], but are not consecutive integers within this range, and in order to extract consecutive parts of the elements for practical application, the following co-prime theorem is proposed by scholars: if there is a pair of reciprocal numbers M and N and M < N, defining an integer k ∈ 0, MN ], then two positive integers M ∈ [0, 2M-1] and N ∈ [0, N-1] must be present such that k ═ Nm-MN holds for the integer k in any interval [0, MN ], and likewise two positive integers M ∈ [0, 2M-1] and N ∈ [0, N-1] must be present such that k ═ MN-MN holds for the integer k in any interval [ -MN,0 ]. Specifically, the values of M and N can be continuously adjusted, so that k traverses all integer values in the interval of [ -MN, MN ], and a continuous integer interval of 2MN +1 can be obtained only by N +2M integers.
Co-prime array: a pair of mutually prime numbers M and N is defined, and M < N, then a mutually prime array with a physical array element number of N +2M (the actual physical array element number is N +2M-1 since the first array element is shared).
In summary, by means of the above technical scheme of the present invention, an ultrasonic array structure is calibrated in advance, a matrix reconstruction and self-correction are performed based on a magnitude-phase error matrix and a mutual coupling error matrix, a beam forming algorithm of the non-uniform linear array is calibrated, DOA estimation of the non-uniform linear array is performed, accuracy in positioning of the non-uniform ultrasonic array is improved, self-correction of a magnitude-phase error and a mutual coupling error of an ultrasonic array signal is performed, accurate measurement of a dynamic liquid level in a narrow space is achieved on the basis of accuracy of a self-correction algorithm, and the problem that an existing ultrasonic liquid level measuring instrument cannot measure a fluctuating liquid level in the narrow space is solved.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (3)

1. A non-uniform ultrasonic array DOA estimation method is characterized by comprising the following steps:
calibrating an ultrasonic array structure in advance, wherein the ultrasonic array structure comprises a calibration frequency and an ultrasonic sensor array of a calibration signal model structure;
performing matrix reconstruction and self-correction based on the amplitude-phase error matrix and the cross-coupling error matrix;
carrying out a beam forming algorithm for calibrating the inhomogeneous linear array, wherein the inhomogeneous co-prime array is introduced into the traditional beam forming algorithm;
and carrying out DOA estimation on the inhomogeneous line array, wherein an array error model is established.
2. The non-uniform ultrasonic array DOA estimation method according to claim 1, wherein said pre-calibrating the ultrasonic array structure comprises the steps of:
calibrating a set I consisting of N elements, wherein the set I is { ni, I is 1, 2,.. the. N }, and defining another set Sdiff { ni-nj, I is less than or equal to 1 and I is less than or equal to N } which is obtained by mutually differentiating all the elements in the set I, wherein the differential set of IM and N is SM, N is { Mn-Nm, N is greater than or equal to 0 and less than or equal to N-1, and M is greater than or equal to 0 and less than or equal to M-1 };
calibrating the N +2M integer to obtain a continuous integer interval of 2MN + 1;
calibrating the position of the array element, and expressing as:
S＝{Mnd,0≤n≤N-1}∪{Nmd,0≤m≤2M-1}
wherein d is the basic array element spacing unit, d is lambda/2, and lambda is the carrier wavelength.
3. The non-uniform ultrasound array DOA estimation method according to claim 1, wherein said step of performing matrix reconstruction and self-correction based on magnitude-phase error matrix and cross-coupling error matrix comprises the steps of:
carrying out initialization setting in advance, wherein the initialization setting comprises setting an iteration counter and an initial value;
estimating the direction of arrival of the signal and calibrating the spatial spectrum estimate, as:
Figure RE-FDA0003024481830000011
wherein the content of the first and second substances,
Figure RE-FDA0003024481830000012
as a noise subspace, C(k)For cross-coupling error matrices, Γ(k)For the amplitude-phase error matrix, a (theta) is the signal subspace, and N maximum values of the spatial spectrum function are searched, and the corresponding angle is the estimated value of the signal arrival angle
Figure RE-FDA0003024481830000013
Estimating the amplitude-phase error matrix, stationary
Figure RE-FDA0003024481830000014
And a mutual coupling matrix C(k)Obtaining a reconstructed amplitude-phase error gamma(k+1)Which is
Figure RE-FDA0003024481830000015
Wherein g ═ Γ11,Γ22,...,ΓMM]；
Estimating the cross-coupling error matrix, fixing
Figure RE-FDA0003024481830000016
And amplitude-phase matrix gamma(k)Reconstructing the cross-coupling error matrix C(k+1)；
Calculating the direction of arrival of the signal;
performing discrimination convergence and obtaining respectively
Figure RE-FDA0003024481830000017
C(k+1)And Γ(k+1)Of an estimator of (1), its cost function JCSatisfies Jk-Jk +1>Epsilon stops the iteration, where epsilon is a given minimum.
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