CN111948608A - Underwater sound multipath signal arrival time difference estimation method based on sparse modeling - Google Patents

Underwater sound multipath signal arrival time difference estimation method based on sparse modeling Download PDF

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CN111948608A
CN111948608A CN202010816503.1A CN202010816503A CN111948608A CN 111948608 A CN111948608 A CN 111948608A CN 202010816503 A CN202010816503 A CN 202010816503A CN 111948608 A CN111948608 A CN 111948608A
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time difference
time
sparse
signals
underwater
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CN111948608B (en
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张贞凯
江峰
林云航
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Suzhou High Airlines Intellectual Property Rights Operation Co ltd
Yunnan Poly Tiantong Underwater Equipment Technology Co ltd
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Jiangsu University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/18—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using ultrasonic, sonic, or infrasonic waves
    • G01S5/22—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements

Abstract

The invention discloses an underwater acoustic multipath signal arrival time difference estimation method based on sparse modeling, which comprises the following steps of: (1) the underwater target transmits the acoustic signals to a reference sensor and other sensors by sending the acoustic signals, wherein the acoustic signals received by the sensors contain non-line-of-sight time delay information such as sea surface reflection, curve propagation and the like; (2) carrying out time reversal processing on signals received by a reference sensor, carrying out convolution operation on the signals subjected to time reversal and signals received by other sensors respectively, and carrying out discrete Fourier transform on all the signals subjected to convolution; (3) the sampling time is symmetrically extended to the negative half axis and thinned such that the time interval from zero to the maximum sampling time is extended to the negative half axis. And carrying out sparse reconstruction on the obtained signal by utilizing the thinned sampling time, extracting all time difference parameters of the sparse signal by using an orthogonal matching tracking method, and applying the extracted time difference parameters to TDOA positioning.

Description

Underwater sound multipath signal arrival time difference estimation method based on sparse modeling
Technical Field
The invention belongs to the field of underwater sound source positioning, and particularly relates to an underwater sound multipath signal arrival time difference estimation method based on sparse modeling.
Background
The underwater sound source positioning is a key technology of an underwater wireless sensor network, and is a guarantee for long-time underwater operation of an autonomous underwater vehicle, an unmanned underwater vehicle and the like.
In complex marine environments, underwater acoustic signals are often accompanied by severe noise interference and multipath effects, which make positioning underwater sound sources difficult. The positioning of the time difference of arrival has the advantages of high complexity, low positioning requirement and the like, thereby becoming a main method for positioning the underwater sound source. The time difference of arrival parameter extracted from the underwater acoustic signal becomes the first problem of positioning, and the most common time difference of arrival estimation method is a mutual fuzzy function. The mutual ambiguity function can quickly solve the time difference of arrival parameters of the signals, but the precision is greatly reduced under the condition of high noise.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide an underwater acoustic multipath signal arrival time difference estimation method based on sparse modeling, which is used for solving the problems.
The technical scheme is as follows: the invention relates to an underwater acoustic multipath signal arrival time difference estimation method based on sparse modeling, which comprises the following steps of:
(1) the underwater target transmits the acoustic signals to the reference sensor and other sensors;
(2) carrying out time reversal processing on signals received by a reference sensor, carrying out convolution operation on the signals subjected to time reversal and signals received by other sensors respectively, and carrying out discrete Fourier transform on all the signals subjected to convolution;
(3) the sampling time is symmetrically expanded to a negative half shaft and then refined, sparse reconstruction is carried out on the obtained signals by utilizing the refined sampling time, all time difference parameters of the sparse signals are extracted by an orthogonal matching tracking method, and the extracted time difference parameters are applied to TDOA positioning.
Further, in step (1), the sensor receives signals as follows
When the underwater target transmits a carrier wave s (t), the underwater acoustic signal received by the sensor i (i ═ 1,2, …, N) is as follows
Figure BDA0002632927200000011
In the formula betai,kFor the gain of the kth path, τi,kIs the time delay of the kth path, K is the number of multipaths, wi(t) is a noise function;
the number of the sensors is N +1, the sensor 0 is a reference sensor, and the sound wave signal received by the reference sensor is expressed as
Figure BDA0002632927200000021
In the formula beta0,dIs the gain, τ, of the d-th path0,dTime delay of the D-th path, D is the number of multipaths, w0(t) is a noise function.
Further, in step (2), the time reversal of the underwater acoustic signal is as follows
For y0Is processed by time reversal to obtain
Figure BDA0002632927200000022
Where represents the convolution operation, (t) is the unit impulse function,
for acoustic signal yiAnd y'0Is obtained by convolution operation
Figure BDA0002632927200000023
Wherein w (t) is a noise function obtained by discrete Fourier transform of equation (4)
Figure BDA0002632927200000024
Wherein M is 0,1, …, M-1, M is the number of sampling points, fcIs the carrier frequency, Δ f is the sampling interval, W (m) is the discrete Fourier transform of w (t), where the discrete Fourier transform of s (t) is S (m).
Further, in step (3), the sampling time is refined as follows
The sampling time of the signal is p, and the sampling time is thinned
Figure BDA0002632927200000025
Wherein n is a positive integer greater than ten thousand, such that
Figure BDA0002632927200000026
Sufficiently small and n is much greater than KD;
Figure BDA0002632927200000027
representing contained relationships between collections.
Further, in step (3), the sparse reconstruction of the signal is as follows
By equation (6), constructing a sparse matrix is written as
Figure BDA0002632927200000031
Where E' is an M × (2n +1) -dimensional matrix, the matrix equation is thus represented as
Y＝SE′B′+W＝θB′+W (8)
In the formula
Y＝[Yi,0(0),Yi,0(1),…,Yi,0(M-1)]T (9)
S＝diag([S(0)S(0),…,S(M-1)S(-M+1)]) (10)
Figure BDA0002632927200000032
W＝[W(0),W(1),…,W(M-1)]T (12)
θ is an unknown quantity SE 'and B'; equation (8) is solved by an orthogonal matching pursuit algorithm, β2n+1Is the amplitude of the virtual path, the number of lines of B' corresponds to the set of delay differences
Figure BDA0002632927200000033
Set the row number and time difference of all non-zero terms of B
Figure BDA0002632927200000034
One-to-one correspondence, the first row of B' corresponds to the time difference-p; the extracted time difference parameter is multiplied by the TDOA measured value required by the underwater sound velocity to determine the positioning.
Has the advantages that: the method for estimating the arrival time difference of the underwater acoustic multipath signals based on sparse modeling can effectively solve the problem of estimation of the arrival time difference of the multipath signals in underwater sound source positioning, and has the advantages of high complexity and high precision.
Drawings
FIG. 1 is a graph of acoustic propagation of an underwater target;
FIG. 2 is a block diagram of underwater multipath signal time difference of arrival estimation;
FIG. 3 an underwater acoustic signal;
Detailed Description
As shown in fig. 1 to 3, the target transmits acoustic waves to the plurality of sensors, and the acoustic signals may be multipath signals of straight line propagation, curved line propagation, sea surface reflection, or the like. The invention discloses an underwater acoustic multipath signal arrival time difference estimation method based on sparse modeling, which comprises the following steps of:
(1) the underwater target transmits the acoustic signals to a reference sensor and other sensors by sending the acoustic signals, wherein the acoustic signals received by the sensors contain non-line-of-sight time delay information such as sea surface reflection, curve propagation and the like;
(2) carrying out time reversal processing on signals received by a reference sensor, carrying out convolution operation on the signals subjected to time reversal and signals received by other sensors respectively, and carrying out discrete Fourier transform on all the signals subjected to convolution;
(3) the sampling time is symmetrically extended to the negative half axis and thinned such that the time interval from zero to the maximum sampling time is extended to the negative half axis. And carrying out sparse reconstruction on the obtained signal by utilizing the thinned sampling time, extracting all time difference parameters of the sparse signal by using an orthogonal matching tracking method, and applying the extracted time difference parameters to TDOA positioning.
Further, in the step (1), the sensor receives the signal as follows
When the underwater target transmits a carrier wave s (t), the underwater acoustic signal received by the sensor i (i ═ 1,2, …, N) is as follows
Figure BDA0002632927200000041
In the formula betai,kFor the gain of the kth path, τi,kIs the time delay of the kth path, K is the number of multipaths, wi(t) is a noise function;
the number of the sensors is N +1, the sensor 0 is a reference sensor, and the sound wave signal received by the reference sensor is expressed as
Figure BDA0002632927200000042
In the formula beta0,dIs the gain, τ, of the d-th path0，dTime delay of the D-th path, D is the number of multipaths, w0(t) is a noise function.
Equations (1) and (2) are rewritten as
Figure BDA0002632927200000043
Figure BDA0002632927200000044
Where represents the convolution operation and (t) is the unit impulse function.
Further, in the step (2), for y0Is processed by time reversal to obtain
Figure BDA0002632927200000045
For acoustic signal yiAnd y'0Is obtained by convolution operation
Figure BDA0002632927200000051
Where w (t) is a noise function obtained by discrete Fourier transform of equation (6)
Figure BDA0002632927200000052
Wherein M is 0,1, …, M-1, M is the number of sampling points, fcIs the carrier frequency, Δ f is the sampling interval, W (m) is the discrete Fourier transform of w (t), where the discrete Fourier transform of s (t) is S (m).
Further, in step (3), the thinning of the sampling time and the sparse reconstruction of the signal are as follows
Equation (7) of step (2) is written in the form of a matrix as follows
Y＝SEB+W (8)
In the formula
Y＝[Yi,0(0)，Yi，0(1),…,Yi,0(M-1)]T (9)
S＝diag([S(0)S(0),…,S(M-1)S(-M+1)]) (10)
Figure BDA0002632927200000053
Figure BDA0002632927200000054
W＝[W(0),W(1),…,W(M-1)]T (13)
Where matrix E is an M by KD dimensional matrix and vector B has dimension KD.
From the matrix equation, both equations (11) and (12) contain delay parameters, so that sparse reconstruction of equation (11) is required. The sampling time of the signal is p, the sampling time is thinned, and the result is shown as follows
Figure BDA0002632927200000055
Where n is a positive integer large enough (n is generally greater than ten thousand, the larger n the more accurate the time difference estimate, but the system load will also increase) so that
Figure BDA0002632927200000056
Sufficiently small and n is much greater than KD;
Figure BDA0002632927200000057
representing contained relationships between collections; here, it is considered to reverse the time such that the time interval from the zero time to the maximum sampling time extends to the negative half-axis.
By equation (14), the matrix E is thinned out, and the thinned matrix is written as
Figure BDA0002632927200000061
Where E' is an M × (2n +1) -dimensional matrix, the new matrix equation is thus expressed as
Y＝SE′B′+W＝θB′+W (16)
In the formula
Figure BDA0002632927200000062
θ is an unknown quantity SE 'and B'.
Equation (16) is solved by an orthogonal matching pursuit algorithm, β2n+1Is the amplitude of the virtual path, the number of lines of B' corresponds to the set of delay differences
Figure BDA0002632927200000063
Set the row number and time difference of all non-zero terms of B
Figure BDA0002632927200000064
One-to-one correspondence, the first row of B' corresponds to the time difference-p; the extracted time difference parameter multiplied by the underwater sound velocity is the TDOA measurement required for positioning.

Claims (5)

1. The method for estimating the underwater acoustic multipath signal arrival time difference based on sparse modeling is characterized by comprising the following steps of:
(1) the underwater target transmits the acoustic signals to the reference sensor and other sensors;
(2) carrying out time reversal processing on signals received by a reference sensor, carrying out convolution operation on the signals subjected to time reversal and signals received by other sensors respectively, and carrying out discrete Fourier transform on all the signals subjected to convolution;
(3) the sampling time is symmetrically expanded to a negative half shaft and then refined, sparse reconstruction is carried out on the obtained signals by utilizing the refined sampling time, all time difference parameters of the sparse signals are extracted by an orthogonal matching tracking method, and the extracted time difference parameters are applied to TDOA positioning.
2. The method for estimating underwater acoustic multipath signal arrival time difference based on sparse modeling according to claim 1, wherein in step (1), the sensor receives the signals as follows
When the underwater target transmits a carrier wave s (t), the underwater acoustic signal received by the sensor i (i ═ 1,2, …, N) is as follows
Figure FDA0002632927190000011
In the formula betai,kFor the gain of the kth path, τi,kIs the time delay of the kth path, K is the number of multipaths, wi(t) is a noise function;
the number of the sensors is N +1, the sensor 0 is a reference sensor, and the sound wave signal received by the reference sensor is expressed as
Figure FDA0002632927190000012
In the formula beta0,dIs the gain, τ, of the d-th path0,dTime delay of the D-th path, D is the number of multipaths, w0(t) is a noise function.
3. The method for estimating underwater acoustic multipath signal arrival time difference based on sparse modeling as claimed in claim 1, wherein in step (2), the time reversal of the underwater acoustic signal is as follows
For y0Is processed by time reversal to obtain
Figure FDA0002632927190000013
Where represents the convolution operation, (t) is the unit impulse function,
for acoustic signal yiAnd y'0Is obtained by convolution operation
Figure FDA0002632927190000014
Wherein w (t) is a noise function obtained by discrete Fourier transform of equation (4)
Figure FDA0002632927190000021
Wherein M is 0,1, …, M-1, M is the number of sampling points, fcIs the carrier frequency, Δ f is the sampling interval, W (m) is the discrete Fourier transform of w (t), where the discrete Fourier transform of s (t) is S (m).
4. The underwater acoustic multipath signal arrival time difference estimation method based on sparse modeling as claimed in claim 1, wherein in step (3), the sampling time is refined as follows
The sampling time of the signal is p, and the sampling time is thinned
Figure FDA0002632927190000022
Wherein n is a positive integer greater than ten thousand, such that
Figure FDA0002632927190000023
Sufficiently small and n is much greater than KD;
Figure FDA0002632927190000024
representing contained relationships between collections.
5. The method for estimating underwater acoustic multipath signal arrival time difference based on sparse modeling as claimed in claim 1, wherein in step (3), the sparse reconstruction of the signal is as follows
By equation (6), constructing a sparse matrix is written as
Figure FDA0002632927190000025
Where E' is an M × (2n +1) -dimensional matrix, the matrix equation is thus represented as
Y＝SE′B′+W＝θB′+W (8)
In the formula
Y＝[Yi,0(0),Yi,0(1),…,Yi，0(M-1)]T (9)
S＝diag([S(0)S(0)，…，S(M-1)S(-M+1)]) (10)
Figure FDA0002632927190000026
W＝[W(0),W(1),…,W(M-1)]T (12)
θ is an unknown quantity SE 'and B'; equation (8) is solved by an orthogonal matching pursuit algorithm, β2n+1Is the amplitude of the virtual path, the number of lines of B' corresponds to the set of delay differences
Figure FDA0002632927190000027
Set the row number and time difference of all non-zero terms of B
Figure FDA0002632927190000031
One-to-one correspondence, the first row of B' corresponds to the time difference-p; the extracted time difference parameter is multiplied by the TDOA measured value required by the underwater sound velocity to determine the positioning.
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