CN111007457B - Radiation source direct positioning method based on block sparse Bayesian model - Google Patents

Radiation source direct positioning method based on block sparse Bayesian model Download PDF

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CN111007457B
CN111007457B CN201811166987.9A CN201811166987A CN111007457B CN 111007457 B CN111007457 B CN 111007457B CN 201811166987 A CN201811166987 A CN 201811166987A CN 111007457 B CN111007457 B CN 111007457B
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CN111007457A (en
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毛兴鹏
陈敏求
赵春雷
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Harbin Institute of 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
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
    • 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
    • G01S5/0009—Transmission of position information to remote stations
    • G01S5/0018—Transmission from mobile station to base station
    • 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
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations

Abstract

The invention provides a direct radiation source positioning method based on a block sparse Bayesian model, and belongs to the technical field of radiation source positioning. The direct positioning method of the radiation source comprises the following steps: block sparse modeling of received data; updating the posterior of the signal statistical parameter; and (5) resolving model parameters. The method provided by the invention is suitable for the condition that the radiation source signal presents a narrow-band characteristic for each base station and presents a wide-band characteristic between the base stations, and only utilizes the arrival angle information of the signal in the processing process, thereby having no receiving synchronization requirement for each base station. The method has the advantages of the block sparse Bayesian method: the target number is not required to be known, the hyper-parameter is not required to be manually set, and the positioning precision is superior to that of the conventional subspace method.

Description

Radiation source direct positioning method based on block sparse Bayesian model
Technical Field
The invention relates to a direct radiation source positioning method based on a block sparse Bayesian model, and belongs to the technical field of radiation source positioning.
Background
Radiation source location technology is an important research topic in the fields of radar, sonar and wireless communication. The traditional angle-of-arrival-based radiation source positioning method comprises two steps: the estimation of the arrival angle and the solution of the target position are carried out, so that the data association among the base stations is indispensable. Different from the traditional indirect positioning method, the direct positioning method can directly obtain the estimation result of the target position by utilizing the array received data, and avoids the measured value pairing error possibly brought by data association. However, both of the above two positioning methods require the known number of targets, and the positioning performance is drastically reduced under the conditions of low signal-to-noise ratio and small snapshot.
Disclosure of Invention
The invention provides a direct radiation source positioning method based on a block sparse Bayesian model, aiming at solving the problems that the number of targets needs to be known and the positioning performance is sharply reduced under the conditions of low signal-to-noise ratio and small snapshot in the existing positioning method. The method is suitable for the condition that the radiation source signal presents narrowband characteristics for each base station and presents broadband characteristics between the base stations, only utilizes the arrival angle information of the signal in the processing process, and has no receiving synchronization requirement for each base station. The invention discloses a direct radiation source positioning method based on a block sparse Bayesian model, which adopts the following technical scheme:
a radiation source direct positioning method based on a block sparse Bayesian model comprises the following steps:
the method comprises the following steps: for L discrete base stations and N narrow-band radiation sources in a plane, modeling received data of the L-th base station under the condition that radiation source signals are in narrow-band characteristics for each base station and in wide-band characteristics among the base stations, wherein M sensors are linearly configured for each base station, M is more than or equal to 2, L is more than or equal to 2, and N is more than or equal to 1 and less than or equal to M-1; then carrying out block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data;
step two: obtaining posterior updating of the signal statistical parameters according to the Gaussian statistical characteristics of the signals;
step three: obtaining a parameter estimation cost function in the maximum likelihood meaning by utilizing marginal probability density integral; acquiring an upper bound function of the parameter estimation cost function by utilizing an expected maximum principle, then respectively deriving the upper bound function according to the noise power and the intra-block correlation degree parameter, and correspondingly acquiring an updated expression of the noise power and the intra-block correlation degree parameter which enable the upper bound function to be minimum; obtaining another upper bound function of the parameter estimation cost function according to the Taylor expansion principle and identity transformation, and then obtaining an update expression of the inter-block sparsity parameter which enables the upper bound function to be minimum by differentiating the upper bound function according to the inter-block sparsity parameter;
step four: repeating the processes of the second step and the third step until the parameter estimation cost function is finally converged; and determining the position of the radiation source according to the peak position of the signal posterior mean value parameter.
Further, the process of establishing the block sparse model of the received data in the first step includes:
the first step is as follows: arranging L discrete base stations in a plane, wherein each base station is linearly provided with M sensors and N narrow-band radiation sources, M is more than or equal to 2, L is more than or equal to 2, and N is more than or equal to 1 and less than or equal to M-1; the transmit signal is represented as: sn(t) (1. ltoreq. N. ltoreq.N), N representing a signal number index; the radiation source position coordinate is represented by a position vector pn(N is more than or equal to 1 and less than or equal to N) is determined; using l to represent the base station number index, the received data of the ith base station is represented as:
Figure BDA0001821367840000021
wherein the content of the first and second substances,
Figure BDA0001821367840000022
wherein, wl,nIs an unknown complex parameter representing the channel fading from the nth radiation source to the l base station; gaussian distributed random vector nl(t) represents array noise; a isl(pn) For array steering vectors, τl(pn) For propagation delay of the signal,. psil(pn) Is the phase delay of the signal between two adjacent sensors;
under the condition that the radiation source signal has a narrow-band characteristic for each base station and a wide-band characteristic between the base stations, the signals received by different base stations from the same radiation source are modeled into different signals which are independent of each other, and a receiving model is determined as follows:
x(t)＝Φsss(t)+n(t)
wherein the content of the first and second substances,
Figure BDA0001821367840000023
Figure BDA0001821367840000024
Figure BDA0001821367840000025
Figure BDA0001821367840000026
wherein, the upper label (·)sRepresenting base station modeling parameters; phisRepresents the total steering matrix;
Figure BDA0001821367840000027
a steering matrix representing an nth radiation source; sl,n(t) represents the nth signal received by the nth base station;
the second step is that: performing block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data, wherein the block sparse model of the received data is as follows:
Figure BDA0001821367840000031
wherein the content of the first and second substances,
Figure BDA0001821367840000032
Figure BDA0001821367840000033
Figure BDA0001821367840000034
wherein Q represents the number of atoms of the sparse dictionary; the upper line represents the model parameters under the sparse frame;
Figure BDA0001821367840000035
representing a block sparse dictionary;
Figure BDA0001821367840000036
representing the q block in the dictionary;
Figure BDA0001821367840000037
representative signal
Figure BDA0001821367840000038
A probability density function of;
Figure BDA0001821367840000039
representing the mean as a zero vector and the covariance matrix as
Figure BDA00018213678400000310
Gaussian distribution of gammaqTo characterize the parameters of inter-block sparsity,
Figure BDA00018213678400000311
is a parameter characterizing the degree of correlation within a block.
Further, the posterior updating of the signal statistical parameter in the second step includes:
according to the Gaussian statistical characteristics of the signals:
Figure BDA00018213678400000312
wherein the content of the first and second substances,
γ＝[γ1,γ2,...,γQ]T
the posterior update expression of the obtained signal statistical parameters is as follows:
Figure BDA00018213678400000313
Figure BDA00018213678400000314
wherein the content of the first and second substances,
Figure BDA00018213678400000315
wherein λ represents the noise power;
Figure BDA00018213678400000316
a posterior mean of the representative signal;
Figure BDA00018213678400000317
a posterior covariance matrix representing the signal;
Figure BDA00018213678400000318
a prior covariance matrix representing the signal; i represents a unit array.
Further, the model parameter calculation process in step three includes:
the first step is as follows: obtaining a parameter estimation cost function under the maximum likelihood meaning by utilizing marginal probability density integral, wherein the parameter estimation cost function is as follows:
Figure BDA00018213678400000319
wherein T represents the sampling fast beat number;
Figure BDA00018213678400000320
representing an unknown parameter set;
the second step is that: according to an expectation maximum theory, determining an upper bound function of the parameter estimation cost function, wherein the upper bound function of the parameter estimation cost function is as follows:
Figure BDA0001821367840000041
wherein, the upper scale theta(old)Representing the last updated parameter value;
the third step: determining an updated expression of λ that minimizes an upper bound function by derivation, the updated expression of λ that minimizes the upper bound function being:
Figure BDA0001821367840000042
the fourth step: obtained by derivation
Figure BDA0001821367840000043
Update expression of (1), the
Figure BDA0001821367840000044
The update expression of (a) is as follows:
Figure BDA0001821367840000045
wherein the content of the first and second substances,
Figure BDA0001821367840000046
represents
Figure BDA0001821367840000047
The q-th block of (a),
Figure BDA0001821367840000048
represents
Figure BDA0001821367840000049
The q block matrix on the diagonal;
the fifth step: performing Taylor expansion according to a first term in the parameter estimation cost function, and obtaining the first term Taylor expansion as follows:
Figure BDA00018213678400000410
wherein the content of the first and second substances,
Figure BDA00018213678400000411
represents
Figure BDA00018213678400000412
Q is the atomic index of the sparse dictionary;
Figure BDA00018213678400000413
represents
Figure BDA00018213678400000414
The last update value of (a);
Figure BDA00018213678400000415
represents gammaqThe last update value of (a);
and a sixth step: and carrying out identity transformation on a second term in the parameter estimation cost function to obtain an identity transformation expression of the second term, wherein the identity transformation expression of the second term is as follows:
Figure BDA00018213678400000416
the seventh step: according to the third stepThe fifth step and the sixth step determine another upper bound function
Figure BDA00018213678400000417
The another upper bound function
Figure BDA00018213678400000418
The expression of (a) is:
Figure BDA00018213678400000419
eighth step: updating expression pass pair of parameter gamma
Figure BDA00018213678400000420
The derivation yields that the expression of the qth element of the parameter γ is:
Figure BDA0001821367840000051
the invention has the beneficial effects that:
the cost function of the direct radiation source positioning method based on the block sparse Bayesian model is given based on the block sparse Bayesian model, and the method does not need to know the number of targets and manually set the hyper-parameters; compared with the traditional method, the method provided by the invention has higher positioning performance and does not need data association.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Figure 2 is a schematic view of a radiation source positioning system.
Fig. 3 shows the positioning performance simulation result.
Detailed Description
The present invention will be further described with reference to the following specific examples, but the present invention is not limited to these examples.
Example 1:
a direct radiation source positioning method based on a block sparse bayesian model, as shown in fig. 1, the direct radiation source positioning method includes:
the method comprises the following steps: for L discrete base stations and N narrow-band radiation sources in a plane, modeling received data of the L-th base station under the condition that radiation source signals are in narrow-band characteristics for each base station and in wide-band characteristics among the base stations, wherein M sensors are linearly configured for each base station, M is more than or equal to 2, L is more than or equal to 2, and N is more than or equal to 1 and less than or equal to M-1; then carrying out block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data;
step two: obtaining posterior updating of the signal statistical parameters according to the Gaussian statistical characteristics of the signals;
step three: obtaining a parameter estimation cost function in the maximum likelihood meaning by utilizing marginal probability density integral; acquiring an upper bound function of the parameter estimation cost function by utilizing an expected maximum principle, then respectively deriving the upper bound function according to the noise power and the intra-block correlation degree parameter, and correspondingly acquiring an updated expression of the noise power and the intra-block correlation degree parameter which enable the upper bound function to be minimum; obtaining another upper bound function of the parameter estimation cost function according to the Taylor expansion principle and identity transformation, and then obtaining an update expression of the inter-block sparsity parameter which enables the upper bound function to be minimum by differentiating the upper bound function according to the inter-block sparsity parameter;
step four: repeating the processes of the second step and the third step until the parameter estimation cost function is finally converged; and determining the position of the radiation source according to the peak position of the signal posterior mean value parameter.
For convenience of presentation and understanding, the following notations are used to describe in unison: the matrix and vector are represented in bold italic notation; superscript (·)T、(·)HAnd (·)-1Respectively representing transposition, conjugate transposition and inversion operation characters; the symbols, | |, tr (·) and diag (·) respectively represent determinant taking 2 norms, trace taking and diagonalization operation;
the first step of establishing the block sparse model of the received data includes:
the first step is as follows: as shown in FIG. 2, L discrete base stations are arranged in a plane, and each base station is linearly provided with M sensors and N narrow-band radiation sources, wherein M is greater than or equal to 2, L is greater than or equal to 2, and N is greater than or equal to 1 and less than or equal to M-1;the transmit signal is represented as: sn(t) (1. ltoreq. N. ltoreq.N), N representing a signal number index; the radiation source position coordinate is represented by a position vector pn(N is more than or equal to 1 and less than or equal to N) is determined; using l to represent the base station number index, the received data of the ith base station is represented as:
Figure BDA0001821367840000061
wherein the content of the first and second substances,
Figure BDA0001821367840000062
wherein, wl,nIs an unknown complex parameter representing the channel fading from the nth radiation source to the l base station; gaussian distributed random vector nl(t) represents array noise; a isl(pn) For array steering vectors, τl(pn) For propagation delay of the signal,. psil(pn) Is the phase delay of the signal between two adjacent sensors;
under the condition that the radiation source signal has a narrow-band characteristic for each base station and a wide-band characteristic between the base stations, the signals received by different base stations from the same radiation source are modeled into different signals which are independent of each other, and a receiving model is determined as follows:
x(t)＝Φsss(t)+n(t)
wherein the content of the first and second substances,
Figure BDA0001821367840000063
Figure BDA0001821367840000064
Figure BDA0001821367840000065
Figure BDA0001821367840000066
wherein, the upper label (·)sRepresenting base station modeling parameters; phisRepresents the total steering matrix;
Figure BDA0001821367840000067
a steering matrix representing an nth radiation source; sl,n(t) represents the nth signal received by the nth base station;
the second step is that: performing block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data, wherein the block sparse model of the received data is as follows:
Figure BDA0001821367840000071
wherein the content of the first and second substances,
Figure BDA0001821367840000072
Figure BDA0001821367840000073
Figure BDA0001821367840000074
wherein Q represents the number of atoms of the sparse dictionary; the upper line represents the model parameters under the sparse frame;
Figure BDA0001821367840000075
representing a block sparse dictionary;
Figure BDA0001821367840000076
representing the q block in the dictionary;
Figure BDA0001821367840000077
representative signal
Figure BDA0001821367840000078
A probability density function of;
Figure BDA0001821367840000079
representing the mean as a zero vector and the covariance matrix as
Figure BDA00018213678400000710
Gaussian distribution of gammaqTo characterize the parameters of inter-block sparsity,
Figure BDA00018213678400000711
is a parameter characterizing the degree of correlation within a block.
Step two, the posterior updating of the signal statistical parameters comprises the following steps:
according to the Gaussian statistical characteristics of the signals:
Figure BDA00018213678400000712
wherein the content of the first and second substances,
γ＝[γ1,γ2,...,γQ]T
the posterior update expression of the obtained signal statistical parameters is as follows:
Figure BDA00018213678400000713
Figure BDA00018213678400000714
wherein the content of the first and second substances,
Figure BDA00018213678400000715
wherein λ represents the noise power;
Figure BDA00018213678400000716
a posterior mean of the representative signal;
Figure BDA00018213678400000717
a posterior covariance matrix representing the signal;
Figure BDA00018213678400000718
a prior covariance matrix representing the signal; i represents a unit array.
Step three, the model parameter calculating process comprises the following steps:
the first step is as follows: obtaining a parameter estimation cost function under the maximum likelihood meaning by utilizing marginal probability density integral, wherein the parameter estimation cost function is as follows:
Figure BDA00018213678400000719
wherein T represents the sampling fast beat number;
Figure BDA0001821367840000081
representing an unknown parameter set;
the second step is that: according to an expectation maximum theory, determining an upper bound function of the parameter estimation cost function, wherein the upper bound function of the parameter estimation cost function is as follows:
Figure BDA0001821367840000082
wherein, the upper scale theta(old)Representing the last updated parameter value;
the third step: determining an updated expression of λ that minimizes an upper bound function by derivation, the updated expression of λ that minimizes the upper bound function being:
Figure BDA0001821367840000083
the fourth step: obtained by derivation
Figure BDA0001821367840000084
Update expression of (1), the
Figure BDA0001821367840000085
The update expression of (a) is as follows:
Figure BDA0001821367840000086
wherein the content of the first and second substances,
Figure BDA0001821367840000087
represents
Figure BDA0001821367840000088
The q-th block of (a),
Figure BDA0001821367840000089
represents
Figure BDA00018213678400000810
The q block matrix on the diagonal;
the fifth step: performing Taylor expansion according to a first term in the parameter estimation cost function, and obtaining the first term Taylor expansion as follows:
Figure BDA00018213678400000811
wherein the content of the first and second substances,
Figure BDA00018213678400000812
represents
Figure BDA00018213678400000813
Q is the atomic index of the sparse dictionary;
Figure BDA00018213678400000814
represents
Figure BDA00018213678400000815
The last update value of (a);
Figure BDA00018213678400000816
represents gammaqThe last update value of (a);
and a sixth step: and carrying out identity transformation on a second term in the parameter estimation cost function to obtain an identity transformation expression of the second term, wherein the identity transformation expression of the second term is as follows:
Figure BDA00018213678400000817
the seventh step: determining another upper bound function according to the fifth step and the sixth step
Figure BDA00018213678400000818
The another upper bound function
Figure BDA00018213678400000819
The expression of (a) is:
Figure BDA0001821367840000091
eighth step: updating expression pass pair of parameter gamma
Figure BDA0001821367840000092
The derivation yields that the expression of the qth element of the parameter γ is:
Figure BDA0001821367840000093
the direct radiation source positioning method based on the block sparse Bayesian model is suitable for the condition that radiation source signals are narrow-band for each base station and wide-band between the base stations, and only the arrival angle information of the signals is utilized in the processing process, thereby meeting the requirement of no-reception synchronization of each base station.
The mean square error curve of the positioning result obtained by using the direct positioning method of the radiation source based on the block sparse Bayesian model is shown in FIG. 3, and the simulation conditions are as follows: the radiation source locations are at (0, -0.5) and (0,0.5) km, and the base stations are at (-3, -3), (-3,3), (3, -3) and (3,3) km. The array element interval is half wavelength, and the receiving signal-to-noise ratio is 20 dB; the attenuation factors of the signals to the stations are respectively set as: w is a1＝[1.1,0.5]，w2＝[1.5,1.3]，w3＝[0.8,0.7]And w4＝[0.4,1.6](ii) a Incident signal is given by 100The frequency of the signal is randomly generated within the bandwidth range; taking 10 observation snapshots to give a simulation, and changing the signal-to-noise ratio from 0dB to 25 dB; according to the simulation result, the positioning mean square error of the method provided by the invention is superior to that of the existing direct positioning method.
Although the present invention has been described with reference to the preferred embodiments, it should be understood that various changes and modifications can be made therein by those skilled in the art without departing from the spirit and scope of the invention as defined in the appended claims.

Claims (3)

1. A direct radiation source positioning method based on a block sparse Bayesian model is characterized by comprising the following steps:
the method comprises the following steps: for L discrete base stations and N narrow-band radiation sources in a plane, modeling received data of the L-th base station under the condition that radiation source signals are in narrow-band characteristics for each base station and in wide-band characteristics among the base stations, wherein M sensors are linearly configured for each base station, M is more than or equal to 2, L is more than or equal to 2, and N is more than or equal to 1 and less than or equal to M-1; then carrying out block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data;
step two: obtaining posterior updating of the signal statistical parameters according to the Gaussian statistical characteristics of the signals;
step three: obtaining a parameter estimation cost function in the maximum likelihood meaning by utilizing marginal probability density integral; acquiring an upper bound function of the parameter estimation cost function by utilizing an expected maximum principle, then respectively deriving the upper bound function according to the noise power and the intra-block correlation degree parameter, and correspondingly acquiring an updated expression of the noise power and the intra-block correlation degree parameter which enable the upper bound function to be minimum; obtaining another upper bound function of the parameter estimation cost function according to the Taylor expansion principle and identity transformation, and then obtaining an update expression of the inter-block sparsity parameter which enables the upper bound function to be minimum by differentiating the upper bound function according to the inter-block sparsity parameter;
the model parameter calculation process comprises the following steps:
the first step is as follows: obtaining a parameter estimation cost function under the maximum likelihood meaning by utilizing marginal probability density integral, wherein the parameter estimation cost function is as follows:
Figure FDA0002641924650000011
wherein T represents the sampling fast beat number;
Figure FDA0002641924650000012
representing an unknown parameter set;
the second step is that: according to an expectation maximum theory, determining an upper bound function of the parameter estimation cost function, wherein the upper bound function of the parameter estimation cost function is as follows:
Figure FDA0002641924650000013
wherein, the upper scale theta(old)Representing the last updated parameter value;
the third step: determining an updated expression of λ that minimizes an upper bound function by derivation, the updated expression of λ that minimizes the upper bound function being:
Figure FDA0002641924650000014
the fourth step: obtained by derivation
Figure FDA0002641924650000015
Update expression of (1), the
Figure FDA0002641924650000016
The update expression of (a) is as follows:
Figure FDA0002641924650000021
wherein the content of the first and second substances,
Figure FDA0002641924650000022
represents
Figure FDA0002641924650000023
The q-th block of (a),
Figure FDA0002641924650000024
represents
Figure FDA0002641924650000025
The q block matrix on the diagonal;
the fifth step: performing Taylor expansion according to a first term in the parameter estimation cost function, and obtaining the first term Taylor expansion as follows:
Figure FDA0002641924650000026
wherein the content of the first and second substances,
Figure FDA0002641924650000027
represents
Figure FDA0002641924650000028
Q is the atomic index of the sparse dictionary;
Figure FDA0002641924650000029
represents
Figure FDA00026419246500000210
The last update value of (a);
Figure FDA00026419246500000211
represents gammaqThe last update value of (a);
and a sixth step: and carrying out identity transformation on a second term in the parameter estimation cost function to obtain an identity transformation expression of the second term, wherein the identity transformation expression of the second term is as follows:
Figure FDA00026419246500000212
the seventh step: determining another upper bound function according to the fifth step and the sixth step
Figure FDA00026419246500000213
The another upper bound function
Figure FDA00026419246500000214
The expression of (a) is:
Figure FDA00026419246500000215
eighth step: updating expression pass pair of parameter gamma
Figure FDA00026419246500000216
The derivation yields that the expression of the qth element of the parameter γ is:
Figure FDA00026419246500000217
wherein, x (t) is the received data of all base stations; λ represents the noise power; i represents an identity matrix;
Figure FDA00026419246500000218
representing a block sparse dictionary;
Figure FDA00026419246500000219
a prior covariance matrix representing the signal;
Figure FDA00026419246500000220
a parameter representing intra-block correlation;
Figure FDA00026419246500000221
indicating that the building block is thinSparse modeled signal components;
Figure FDA00026419246500000222
a posterior mean representing the signal;
Figure FDA00026419246500000223
a posterior covariance matrix representing the signal; gamma rayqIs a parameter characterizing the sparsity between blocks;
Figure FDA00026419246500000225
representing the q block in the dictionary;
step four: repeating the processes of the second step and the third step until the parameter estimation cost function is finally converged; and determining the position of the radiation source according to the peak position of the signal posterior mean value parameter.
2. The method for directly positioning the radiation source according to claim 1, wherein the step one of establishing the block sparse model of the received data comprises:
the first step is as follows: arranging L discrete base stations in a plane, wherein each base station is linearly provided with M sensors and N narrow-band radiation sources, M is more than or equal to 2, L is more than or equal to 2, and N is more than or equal to 1 and less than or equal to M-1; the transmit signal is represented as: sn(t) (1. ltoreq. N. ltoreq.N), N representing a signal number index; the radiation source position coordinate is represented by a position vector pn(N is more than or equal to 1 and less than or equal to N) is determined; using l to represent the base station number index, the received data of the ith base station is represented as:
Figure FDA0002641924650000031
wherein the content of the first and second substances,
Figure FDA0002641924650000032
wherein, wl,nIs an unknown complex parameter representing the channel fading from the nth radiation source to the l base station; gaussian distributed random vector nl(t) watchArray noise is shown; a isl(pn) For array steering vectors, τl(pn) For propagation delay of the signal,. psil(pn) Is the phase delay of the signal between two adjacent sensors;
under the condition that the radiation source signal has a narrow-band characteristic for each base station and a wide-band characteristic between the base stations, the signals received by different base stations from the same radiation source are modeled into different signals which are independent of each other, and a receiving model is determined as follows:
x(t)＝Φsss(t)+n(t)
wherein the content of the first and second substances,
Figure FDA0002641924650000033
Figure FDA0002641924650000034
Figure FDA0002641924650000035
Figure FDA0002641924650000036
wherein, the upper label (·)sRepresenting base station modeling parameters; phisRepresents the total steering matrix;
Figure FDA0002641924650000037
a steering matrix representing an nth radiation source; sl,n(t) represents the nth signal received by the nth base station;
the second step is that: performing block sparse Bayesian expansion on the receiving model to obtain a block sparse model of the received data, wherein the block sparse model of the received data is as follows:
Figure FDA0002641924650000041
wherein the content of the first and second substances,
Figure FDA0002641924650000042
Figure FDA0002641924650000043
Figure FDA0002641924650000044
wherein Q represents the number of atoms of the sparse dictionary; the upper line represents the model parameters under the sparse frame;
Figure FDA0002641924650000045
representing a block sparse dictionary;
Figure FDA0002641924650000046
representing the q block in the dictionary;
Figure FDA0002641924650000047
representative signal
Figure FDA0002641924650000048
A probability density function of;
Figure FDA0002641924650000049
representing the mean as a zero vector and the covariance matrix as
Figure FDA00026419246500000410
Gaussian distribution of gammaqTo characterize the parameters of inter-block sparsity,
Figure FDA00026419246500000411
is a parameter characterizing the degree of correlation within a block.
3. The direct radiation source positioning method according to claim 1, wherein the posterior updating of the signal statistical parameters in step two comprises:
according to the Gaussian statistical characteristics of the signals:
Figure FDA00026419246500000412
wherein the content of the first and second substances,
γ＝[γ1,γ2,...,γQ]T
the posterior update expression of the obtained signal statistical parameters is as follows:
Figure FDA00026419246500000413
Figure FDA00026419246500000414
wherein the content of the first and second substances,
Figure FDA00026419246500000415
wherein λ represents the noise power;
Figure FDA00026419246500000416
a posterior mean of the representative signal;
Figure FDA00026419246500000417
a posterior covariance matrix representing the signal;
Figure FDA00026419246500000418
a prior covariance matrix representing the signal; i represents a unit array.
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