CN114520755A - Improved characteristic value-to-angle loading information source number estimation method - Google Patents
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Abstract
The invention discloses an improved characteristic value-to-angle loading information source number estimation method, which comprises the steps of decomposing a characteristic value of an antenna array observation signal covariance matrix, carrying out primary diagonal loading on the characteristic value, taking the diagonal loading as a geometric mean value of all the characteristic values, adding an original characteristic value and a diagonal loading value to replace the original characteristic value, recalculating the characteristic value-to-angle loading amount aiming at the characteristic value after the primary diagonal loading, carrying out secondary diagonal loading on the characteristic value after the primary diagonal loading, and determining the secondary diagonal loading amount according to the proportional relation of an array element number M and a sampling number N to ensure that the loaded characteristic value meets the condition that the ratio of the maximum value to the minimum value of a noise characteristic value is not more than 2.
Description
Technical Field
The invention relates to the technical field of signal processing, in particular to an improved characteristic value angle loading information source number estimation method.
Background
Accurate and effective determination of the number of radiation source signals in the observed signal is a necessary prerequisite for many signal processing methods, such as direction of arrival estimation, blind source separation, radiation source localization, beam forming, etc. At the present stage, researchers have researched and proposed various information source number estimation methods which are essentially based on the statistical analysis theory of observed data and moment functions thereof and mainly comprise an information theory rule method, an observed signal covariance matrix eigenvalue/singular value processing method, a Galer circle transformation method, an assumption test method, an information source number estimation method based on a random matrix theory and an information source number estimation method based on clustering effectiveness.
The accurate and fast estimation of the number of the information sources is very important, and under increasingly complex signal environments, the estimation of the number of the information sources is difficult to realize accurately, which becomes a fundamental and hotspot problem in the field of signal processing. Considering that in an actual signal environment, the proportional relationship between the antenna array number and the signal sampling number and the fact that the noise of aliasing of an observation signal is white noise or color noise are unknown, in order to improve the reliability of the information source number estimation, the information source number estimation method which is suitable for a classical asymptotic system and a general asymptotic system and is suitable for both the white noise and the color noise is required to be developed vigorously, and the reliability of the information source number estimation under the complex environment condition can be better ensured by comprehensively utilizing a plurality of methods. The invention provides an improved characteristic value angle loading source number estimation method for meeting the requirement.
Disclosure of Invention
The invention aims to provide an improved characteristic value angular loading information source number estimation method to solve the information source number estimation problem in the background technology.
In order to achieve the purpose, the invention provides the following technical scheme:
an improved eigenvalue-diagonal loading information source number estimation method comprises the steps of decomposing eigenvalues of an antenna array observation signal covariance matrix, carrying out primary diagonal loading on the eigenvalues, taking the diagonal loading as a geometric mean value of all the eigenvalues, adding an original eigenvalue and a diagonal loading value to replace the original eigenvalue, recalculating the eigenvalue-diagonal loading amount for the eigenvalue after the primary diagonal loading, carrying out secondary diagonal loading on the eigenvalue after the primary diagonal loading, and determining the secondary diagonal loading amount without a proportional relation between an array element number M and a sampling number N so that the loaded eigenvalue meets the condition that the ratio of the maximum value to the minimum value of a noise eigenvalue does not exceed 2. The actual information source number estimation method specifically comprises the following steps:
s1: setting a one-dimensional uniform linear antenna array to have M array elements, wherein M observation signals obtained by measurement are X (t), and X (t) is [ X [)1(t)，X2(t)，...，XM(t)]T(superscript)TRepresenting transposition), the sampling time t is 1,2, …, N is the number of signal samples, and the covariance matrix of the observed signal is calculated
S2: the covariance matrix r (t) is subjected to eigenvalue decomposition,
wherein the characteristic value lambdaiAnd a feature vector uiAlso called sample eigenvalues and sample eigenvectors, representing the sequence of eigenvalues as
The numerical value sequence is arranged in a value-taking size descending manner;
s3: for a sequence of characteristic values
Carrying out diagonal loading once, wherein a diagonal loading amount calculation formula is expressed as:
s4: according to the sample covariance matrix R (t) and a calculation formula of the feature value one-time diagonal loading amount, calculating a new sample covariance matrix after diagonal loading, wherein the calculation formula is represented as:
in the formula IMIs an M-dimensional identity matrix;
s5: sample covariance matrix after one diagonal loading
Decomposing the characteristic value to obtain a new characteristic value sequence
S6: for a sequence of characteristic values
And carrying out secondary diagonal loading. The diagonal loading method determination process is as follows:
1) and (3) calculating the serial number of the characteristic value with the maximum ratio of two continuous characteristic values: for the descending sequence of eigenvalues
Selecting
2) Is calculated such that
Smallest integer number of true
3) Make the second diagonal loading amount
For a sequence of characteristic values
Carrying out second diagonal loading to obtain a new characteristic value sequence
S7: for new sequences of characteristic values
And estimating the information source number by using an information theory rule method and a random matrix theory method.
Compared with the prior art, the invention has the beneficial effects that: compared with the existing characteristic value-to-angle loading information theory criterion information source number estimation method, the improved characteristic value-to-angle loading information source number estimation method is applicable to the general asymptotic system with the antenna array element number and the signal sampling number being the same order of magnitude, and the noise environment can be Gaussian white noise or color noise. The invention also realizes the expansion of the application field of the random matrix theory information source number estimation method, so that the method can be applied to the color noise environment. Compared with the existing characteristic value secondary diagonal loading, the technical scheme of the invention solves the problem of threshold selection, realizes more stable secondary correction of the characteristic value, and can more accurately and effectively realize information source number estimation.
Further, in steps S3 and S6, the eigenvalue of the covariance matrix of the antenna array received signals is corrected by using a secondary diagonal loading method, which solves the problem of threshold selection and realizes more robust secondary correction of the eigenvalue compared with the existing secondary diagonal loading of the eigenvalue.
Drawings
FIG. 1 is a schematic flow chart of an improved method for estimating source number of angle loading by using a characteristic value;
fig. 2 is a graph of an experimental result of the method of the present invention under the condition of white gaussian noise without diagonal loading, where M is 10 and N is 300;
fig. 3 is a graph of an experimental result of the present invention under an environment of white gaussian noise, where M is 10 and N is 300, under a diagonal loading condition, in combination with an information theory criterion method;
fig. 4 is a graph of an experimental result of the method of the present invention under the condition of white gaussian noise, where M is 100 and N is 300, and there is no diagonal loading;
fig. 5 is a graph of an experimental result of the present invention under an environment of white gaussian noise, where M is 100 and N is 300, under a diagonal loading condition, in combination with an information theory criterion method;
fig. 6 is a graph of an experimental result of the method of the present invention under the condition of white gaussian noise without diagonal loading, where M is 300 and N is 300;
fig. 7 is a graph of an experimental result of the present invention under the condition of diagonal loading, where M is 300 and N is 300, in the white gaussian noise environment, in combination with the information theory criterion method;
fig. 8 is a graph of an experimental result of the method of the present invention under the white gaussian noise environment with no diagonal loading, where M is 310 and N is 300;
fig. 9 is a graph of an experimental result of the present invention under an environment of white gaussian noise, where M is 310 and N is 300, under a diagonal loading condition, in combination with an information theory criterion method;
fig. 10 is a graph of an experimental result of the method of the present invention in combination with the information theoretic rule under the condition of color noise, where M is 10, N is 300, and there is no diagonal loading;
fig. 11 is a graph of an experimental result of the method of the present invention under a diagonal loading condition, where M is 10 and N is 300 in a color noise environment;
fig. 12 is a graph of an experimental result of the method of the present invention in combination with the information theoretic rule under the condition of color noise, where M is 100, N is 300, and there is no diagonal loading;
fig. 13 is a graph of an experimental result of the method of the present invention under the condition of diagonal loading, where M is 100 and N is 300, in the color noise environment;
fig. 14 is a graph of an experimental result of the method of the present invention in combination with the information theoretic rule under the condition of color noise, where M is 300 and N is 300, and no diagonal loading exists;
fig. 15 is a graph of an experimental result of the method of the present invention under the condition of diagonal loading, where M is 300 and N is 300 in the color noise environment;
fig. 16 is a graph of experimental results of the method of the present invention in combination with the information theoretic rule under the condition of color noise, where M is 310 and N is 300, and no diagonal loading exists;
fig. 17 is a graph of the experimental results of the method of the present invention under the condition of diagonal loading, where M is 310 and N is 300 in the color noise environment;
fig. 18 is a graph of an experimental result of the present invention under the condition of white gaussian noise environment, where M is 10 and N is 300, and no diagonal loading is performed, in combination with a random matrix theory method;
fig. 19 is a graph of an experimental result of the present invention under the condition of diagonal loading, where M is 10 and N is 300, in the white gaussian noise environment, in combination with the random matrix theory method;
fig. 20 is a graph of an experimental result of the present invention under the condition of white gaussian noise environment, where M is 200 and N is 300, and no diagonal loading is performed in combination with a random matrix theory method;
fig. 21 is a graph showing the experimental results of the present invention under the condition of diagonal loading in white gaussian noise environment with M being 200 and N being 300, in combination with the random matrix theory method;
fig. 22 is a graph of an experimental result of the present invention under the condition of white gaussian noise environment, where M is 310, N is 300, and no diagonal loading is performed, in combination with a random matrix theory method;
fig. 23 is a graph of an experimental result of the present invention under the condition of diagonal loading in white gaussian noise environment with M being 310 and N being 300, in combination with a random matrix theory method;
fig. 24 is a graph of an experimental result of the present invention combining a random matrix theory method under a color noise environment, where M is 10, N is 300, and there is no diagonal loading;
fig. 25 is a graph of an experimental result of the diagonal loading in the color noise environment under the condition that M is 10 and N is 300 in combination with the random matrix theory method according to the present invention;
FIG. 26 illustrates a method of the present invention incorporating random matrix theory. Under the color noise environment, M is 200, N is 300, and an experimental result graph under the condition of no diagonal loading is obtained;
fig. 27 is a graph of an experimental result of the present invention combining a random matrix theory method under a color noise environment, where M is 200, N is 300, and diagonal loading is performed;
fig. 28 is a graph of an experimental result of the present invention combining a random matrix theory method under a color noise environment, where M is 310, N is 300, and there is no diagonal loading;
fig. 29 is a graph of the experimental result of the diagonal loading under the color noise environment with M being 310 and N being 300, in combination with the random matrix theory method.
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, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1-29, the present invention provides a technical solution: an improved eigenvalue-diagonal loading information source number estimation method comprises the steps of decomposing eigenvalues of an antenna array observation signal covariance matrix, carrying out primary diagonal loading on the eigenvalues, taking the diagonal loading as a geometric mean value of all the eigenvalues, adding an original eigenvalue and a diagonal loading value to replace the original eigenvalue, recalculating the eigenvalue-diagonal loading amount for the eigenvalue after the primary diagonal loading, carrying out secondary diagonal loading on the eigenvalue after the primary diagonal loading, and determining the secondary diagonal loading amount without a proportional relation between an array element number M and a sampling number N so that the loaded eigenvalue meets the condition that the ratio of the maximum value to the minimum value of a noise eigenvalue does not exceed 2.
From the above description, the assumed conditions in the mathematical model are specifically as follows:
(1) assuming an incident signal: suppose K far-field signals are from direction θ1，…，θKIncident on an array of M sensors, and an array observation signal at time t is X (t) and is expressed as:
wherein X (t) ═ X1(t)，X2(t)，...，XM(t)]T(superscript)TRepresenting transposition) into an array observation signal vector, a (θ)k) Is an array direction vector, A (theta) ═ a (theta)1)，a(θ2)，…，a(θK)]Is a matrix of directional vectors, theta ═ theta1，θ2，…，θK]TIs the incoming wave angle parameter vector of the signal, s (t) ═ s1(t)，s2(t)，…，sK(t)]TFor the incident signal vector, w (t) ═ w1(t)，w2(t)，…，wM(t)]TFor an additive noise vector, the sampling time t is 1,2, …, and N is the number of signal samples. Incident signals are mutually independent narrow-band steady signals, and satisfy the mean value E { s (t) } ═ 0 and a covariance matrix
Wherein
Is the power of the k-th signal.
(2) Assuming array observed signals: the superimposed noise in the array observation signal vector is additive noise and is independent of the signal.
(3) Assuming the number of incident signals: the number of incident signals is smaller than the number of array elements and the number of samples at the same time, namely K < min (M, N).
(4) Assuming an ideal state for broadcasting: the signals are propagated in an ideal space, and the array sensor has omnidirectional consistency.
The actual information source number estimation method specifically comprises the following steps:
s1: setting an antenna array, and calculating a covariance matrix R (t);
setting an antenna array to have M array elements, wherein M observation signals obtained by measurement are X (t), and X (t) is [ X [)1(t)，X2(t)，...，XM(t)]T(superscript)TRepresenting transposition), the sampling time t is 1,2, …, N is the number of signal samples, and the covariance matrix of the observed signal is calculated
S2: decomposing the eigenvalue of the covariance matrix;
the covariance matrix r (t) is subjected to eigenvalue decomposition,
wherein the characteristic value lambdaiAnd a feature vector uiAlso called sample eigenvalues and sample eigenvectors, representing the sequence of eigenvalues as
Which is a sequence of values arranged in descending order of magnitude of the value.
S3: diagonally loading a characteristic value sequence;
for a sequence of characteristic values
And carrying out diagonal loading once, wherein a diagonal loading amount calculation formula is expressed as follows:
s4: computing new sample covariance matrices
According to the sample covariance matrix R (t) and a calculation formula of the feature value one-time diagonal loading amount, calculating a new sample covariance matrix after diagonal loading, wherein the calculation formula is represented as:
in the formula IMIs an M-dimensional identity matrix.
S5: calculating a new sample characteristic sequence value;
sample covariance matrix after one diagonal loading
Decomposing the characteristic value to obtain a new characteristic value sequence
S6: carrying out diagonal loading on a new characteristic value sequence;
for a sequence of characteristic values
And carrying out secondary diagonal loading. The diagonal loading method determination process is as follows: 1) and (3) calculating the serial number of the characteristic value with the maximum ratio of two continuous characteristic values: for the descending sequence of eigenvalues
Selecting
2) Is calculated such that
Smallest integer number of true
3) Make the second diagonal loading amount
For a sequence of characteristic values
Carrying out second diagonal loading to obtain a new characteristic value sequence
S7: estimating and calculating the number of information sources;
for new sequences of characteristic values
And estimating the information source number by using an information theory rule method and a random matrix theory method.
The invention is further described below in conjunction with experimental test charts.
1. Setting experimental conditions:
the experimental verification of the invention is carried out under the simulation condition of a computer, and MATLAB R2010a is adopted as simulation software. In order to fully verify the effectiveness of the invention, the technical scheme of the invention is compared with the technical scheme of the literature, and four groups of experimental tests are carried out.
Example 1: the technology of the invention is combined with the information theory criterion method (BIC, AIC, MDL, KIC), and the estimation effect comparison under the Gaussian white noise environment is carried out by directly adopting the information theory criterion method (BIC, AIC, MDL, KIC). The radiation source signals are set as:
1)s1is BPSK signal, the code element width is 10/31 mus, the carrier frequency is 10 MHz;
2)s2is a CW signal, the sub-pulse width is 15 mus, and the carrier frequency is 10 MHz;
3)s3the LFM signal has the pulse width of 10+10 · rand (1) mus, the initial frequency of 10MHz and the frequency modulation bandwidth of 10/(1+ rand (1)) MHz;
4)s4the MPSK signal is obtained by Franke coding, the code element width is 0.4 mus, and the carrier frequency is 50 MHz.
The signal source number K is 4, the array element number of the array antenna is respectively set to be M10, 100, 300 and 310, the steering matrix A is generated by a random function randn, the sampling frequency is 120MHz, the number of signal sampling points is N300, Gaussian white noise is superposed on a mixed signal, the variation range of the signal-to-noise ratio is-10 dB to 30dB, the step length is 2dB, 200 times of Monte Carlo simulation is carried out on each signal-to-noise ratio, and the experimental result is shown in figures 3 to 10.
FIGS. 2-9 show the results of experiments performed in white Gaussian noise environment with the inventive technique combined with information theoretic criterion methods (BIC, AIC, MDL, KIC). It can be seen from fig. 2 and fig. 3 that at this time, M/N is less than 1, the relationship between the number of antenna array elements and the number of samples meets the requirement of the classical asymptotic system, under the condition of gaussian white noise, the estimation of the number of information sources can be accurately realized under the condition of a certain signal-to-noise ratio based on the technology of the present invention in combination with the information theory criterion method and the directly applied information theory criterion method, and the required signal-to-noise ratio condition is higher when the technology is applied than when the technology of the present invention is not applied. In the case of figures 4 and 5 of the drawings,
the relation between the array element number and the sample number of the antenna array approximately meets the requirements of a classical asymptotic system, the technology can achieve good estimation effect when being applied and combined with a method which does not apply the technology and an information theory criterion method, and the required signal-to-noise ratio condition has no obvious difference. In the case of the figures 6-9,
array element number and sample of antenna arrayThe relation of the number meets the requirement of a general asymptotic system, the accurate estimation of the information source number can be stably realized at a lower signal-to-noise ratio by applying the technology of the invention and combining the information theory criterion method, but the estimation fails by applying the technology of the invention and only adopting the information theory criterion method.
Experiment two: the technology of the invention is combined with the information theory criterion method (BIC, AIC, MDL, KIC) and the estimation effect under the color noise environment is directly realized by adopting the information theory criterion method (BIC, AIC, MDL, KIC). The signal source is the same as in experiment one. The source number K is 4, the array antenna element number is set to M10, 100, 300, 310, respectively, the steering matrix a is generated by a random function randn, the sampling frequency is 120MHz, the signal sampling point number is N300, the mixed signal is superimposed with color noise, and the elements of the covariance matrix are given by the following formula:
wherein sigmanIs an adjustable parameter, is used for setting the signal-to-noise ratio of an observation signal, the change range of the signal-to-noise ratio is-10 dB to 40dB, the step length is 4dB, 200 times of Monte Carlo simulation is carried out on each signal-to-noise ratio, and the experimental result is shown in a graph of 10-17.
As can be seen from fig. 10 and 11, at this time, M/N is less than 1, the relationship between the array element number of the antenna array and the sample number meets the requirement of the classical asymptotic system, and under the condition of color noise, the estimation of the signal source number can be accurately realized under the condition of a certain signal-to-noise ratio based on the technology of the present invention in combination with the information theory criterion method; without the application of the present invention, accurate estimation of the number of sources cannot be achieved. In fig. 12 and 13, M/N is 1/3, the relationship between the antenna array element number and the sample number approximately meets the requirement of the classical asymptotic system, and when the technique of the present invention is applied in combination with the information theory criterion method, a good signal source number estimation effect can be achieved, otherwise the signal source number estimation fails. In fig. 14-17, M/N is greater than or equal to 1, the relationship between the number of antenna array elements and the number of samples meets the requirements of a general asymptotic system, and by applying the technical scheme of the present invention in combination with the information theory criterion method, accurate estimation of the number of information sources can be realized robustly at a lower signal-to-noise ratio, while the estimation of the number of information sources is erroneous without applying the technique of the present invention.
Experiment three: the technology of the invention is combined with a source number estimation method (BN-AIC, KN [9], RMT-AIC) based on a random matrix theory, and experimental results are compared under the environment of Gaussian white noise. The radiation source signals are set as:
1)s1is BPSK signal, the code element width is 10/31 mus, the carrier frequency is 10 MHz;
2)s2is a CW signal, the sub-pulse width is 15 mus, and the carrier frequency is 10 MHz;
3)s3the LFM signal has the pulse width of 10+10 · rand (1) mus, the initial frequency of 10MHz and the frequency modulation bandwidth of 10/(1+ rand (1)) MHz;
4)s4is FSK signal, 13 bit Barker code, the code element width is 10/13 mus, the frequency of two code elements is 25MHz and 50MHz respectively;
5)s5the MPSK signal is obtained by Franke coding, the code element width is 0.4 mus, and the carrier frequency is 50 MHz.
The source number K is 5, the array antenna element number is set to M10, 200, 310, respectively, the steering matrix a is generated by a random function randn, the sampling frequency is 120MHz, and the signal sampling point number is N300. The variation range of the signal-to-noise ratio is-10 dB to 40dB, the step length is 4dB, 200 Monte Carlo simulations are carried out on each signal-to-noise ratio, and the experimental results are shown in FIGS. 18 to 23.
It can be seen from fig. 18 and 19 that at this time, M/N is less than 1, the relationship between the array element number of the antenna array and the sample number meets the requirement of the classical asymptotic system, and under the condition of white gaussian noise, based on the technology of the present invention combined with the random matrix theory method, when the signal-to-noise ratio reaches 20dB, the source number estimation can be realized with the approaching probability 1; the random matrix theory method is directly applied, and when the signal-to-noise ratio reaches 10dB, the three methods can realize the information source number estimation with the probability of 1. In the case of the figures 20 and 21,
the relation between the array element number and the sample number of the antenna array approximately meets the requirement of a classical asymptotic system, and when the technology of the invention is combined with a random matrix theory method, the estimation accuracy of the three methods is improved along with the increase of the signal-to-noise ratio, and when the signal-to-noise ratio is increased to more than about-5 dB, the estimation accuracy can reach the approximate accuracyThe ratio is 1. The method directly adopts a random matrix method, BN-AIC and KN can realize source number estimation with a probability of 1 when the signal-to-noise ratio reaches above about 0dB, and RMT-AIC can realize source number estimation with a probability of 1 when the signal-to-noise ratio is required to reach above 5 dB. In the case of figures 22 and 23 of the drawings,
the relation between the array element number of the antenna array and the sample number meets the requirement of a general asymptotic system, and when the technology of the invention is combined with a random matrix theory method, the three methods can realize accurate estimation of the information source number with the probability of 0.95 when the signal-to-noise ratio reaches more than-5 dB; by directly adopting a random matrix theory method, the BN-AIC and KN methods can realize accurate estimation of the information source number by the probability 1 when the signal-to-noise ratio reaches more than 2dB, and the RMT-AIC can realize accurate estimation of the information source number by the probability 1 when the signal-to-noise ratio is about more than 5 dB.
Experiment four: the technology of the invention is combined with a source number estimation method (BN-AIC, KN and RMT-AIC) based on a random matrix theory, experimental results are compared under a color noise environment, and radiation source signals are the same as those in the experiment III.
The source number K is 5, the array antenna element number is set to M10, 200, 310, respectively, the steering matrix a is generated by a random function randn, the sampling frequency is 120MHz, the signal sampling point number is N300, the observation signal is superimposed with spatial color noise, and the elements of the covariance matrix are given by the following formula:
wherein σnIs an adjustable parameter, is used for setting the signal-to-noise ratio of an observation signal, has the signal-to-noise ratio variation range of-10 dB to 40dB and the step length of 4dB, and carries out 200 times of Monte Carlo simulation on each signal-to-noise ratio, and the experimental result is shown in a graph 24-29. As can be seen from FIGS. 24 and 25, when M/N < 1, the relationship between the number of antenna elements and the number of samples meets the requirement of the classical asymptotic system, and under the condition of color noise, when the signal-to-noise ratio reaches above about 18dB based on the technology of the present invention combined with the stochastic matrix theory methodThe estimation of the information source number can be realized with the accuracy rate of not less than 90 percent; without the application of the present technique, the three methods fail to estimate. In the case of the figures 26 and 27,
the relation between the array element number of the antenna array and the sample number approximately meets the requirement of a classical asymptotic system, and by combining the technology of the invention and a random matrix theory method, when the signal-to-noise ratio reaches above about 17dB, the three methods can accurately realize the estimation of the information source number with the probability of 1; without the adoption of the technology of the invention, the information source number estimation can not be accurately realized. In the case of the figures 28 and 29,
the relation between the array element number of the antenna array and the sample number meets the requirement of a general asymptotic system, and by applying the technology of the invention and a random matrix theory method, when the signal-to-noise ratio reaches more than 8dB, the BN-AIC method and the RMT-AIC method can accurately realize the information source number estimation with the probability of 1 when the signal-to-noise ratio reaches more than 10 dB; without the adoption of the technology of the invention, the information source number estimation can not be accurately realized.
With the above embodiments, the simulation results are analyzed as follows:
the combination of the method and the information theory criterion type information source number estimation method or the random matrix theory method is compared with the combination, and the method can realize the information source number estimation under the color noise environment. If the scheme of the invention is not adopted, the information theory criterion method can not be suitable for the general asymptotic system, and the information theory criterion method can be suitable for the information source number estimation under the general asymptotic system by adopting the scheme of the invention. Therefore, the invention is a great improvement to the existing source number estimation method.
Although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that various changes in the embodiments and/or modifications of the invention can be made, and equivalents and modifications of some features of the invention can be made without departing from the spirit and scope of the invention.
Claims (1)
1. An improved eigenvalue-diagonal loading information source number estimation method comprises the steps of decomposing eigenvalues of an antenna array observation signal covariance matrix, carrying out primary diagonal loading on the eigenvalues, taking the diagonal loading as a geometric mean value of all the eigenvalues, adding an original eigenvalue and a diagonal loading value to replace the original eigenvalue, recalculating the eigenvalue-diagonal loading amount for the eigenvalue after the primary diagonal loading, carrying out secondary diagonal loading on the eigenvalue after the primary diagonal loading, and determining a secondary diagonal loading amount without a proportional relation between an array element number M and a sampling number N so that the loaded eigenvalue meets the condition that the ratio of the maximum value to the minimum value of a noise eigenvalue is not more than 2; the actual information source number estimation method specifically comprises the following steps:
s1: setting a one-dimensional uniform linear antenna array to have M array elements, wherein M observation signals obtained by measurement are X (t), and X (t) is [ X [)1(t),X2(t),…,XM(t)]T(superscript)TRepresenting transposition), the sampling time t is 1,2, …, N is the number of signal samples, and the covariance matrix of the observed signal is calculated
S2: the covariance matrix r (t) is subjected to eigenvalue decomposition,
wherein the characteristic value lambdaiAnd a feature vector uiAlso called sample eigenvalues and sample eigenvectors, representing the sequence of eigenvalues as
The numerical value sequence is arranged in a value-taking size descending manner;
s3: for a sequence of characteristic values
Carrying out diagonal loading once, wherein a diagonal loading amount calculation formula is expressed as:
s4: according to the sample covariance matrix R (t) and a calculation formula of the feature value one-time diagonal loading amount, calculating a new sample covariance matrix after diagonal loading, wherein the calculation formula is represented as:
in the formula IMIs an M-dimensional identity matrix;
s5: for a sample covariance matrix after one diagonal loading
Decomposing the characteristic value to obtain a new characteristic value sequence
S6: for a sequence of characteristic values
Carrying out secondary diagonal loading; the diagonal loading method determination process is as follows:
1) calculating the serial number of the characteristic value with the maximum ratio of two continuous characteristic values: for the descending sequence of eigenvalues
Selecting
2) Is calculated such that
Smallest integer number of true
3) Make the second diagonal loading amount
For a sequence of characteristic values
Carrying out second diagonal loading to obtain a new characteristic value sequence
S7: for new sequences of characteristic values
And estimating the information source number by using an information theory rule method and a random matrix theory method.
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