CN115219981A - Non-circular information source direct positioning method based on dimension reduction propagation operator in distributed monitoring - Google Patents

Non-circular information source direct positioning method based on dimension reduction propagation operator in distributed monitoring Download PDF

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CN115219981A
CN115219981A CN202110409494.9A CN202110409494A CN115219981A CN 115219981 A CN115219981 A CN 115219981A CN 202110409494 A CN202110409494 A CN 202110409494A CN 115219981 A CN115219981 A CN 115219981A
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circular
matrix
objective function
monitoring station
vector
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曾浩威
赖欣
张小飞
孙宇欣
张钰
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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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
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Abstract

The invention relates to the technical field of passive positioning, in particular to a non-circular information source direct positioning method based on a dimensionality reduction propagation operator in distributed monitoring. Aiming at the common non-circular signal type in the modern wireless communication system, the invention fuses non-circular phase information into an algorithm model by expanding a received signal vector so as to achieve the purposes of increasing the array aperture and improving the spatial degree of freedom; by adopting the idea of a propagation operator, a G matrix approximate to a noise subspace is obtained, and high-precision positioning of multiple targets can be realized without eigenvalue decomposition; and a dimension reduction idea is introduced to solve the problem of high complexity caused by the solution of the non-circular phase. The method avoids the problems of intermediate parameter estimation and target matching of the traditional two-step method, directly estimates the target position from the original received data layer, and effectively improves the positioning precision; the non-circular characteristics are fully utilized, the estimation precision and the spatial freedom degree of the algorithm are improved, and the complexity of the algorithm is effectively reduced by introducing a propagation operator and a dimensionality reduction idea.

Description

Non-circular information source direct positioning method based on dimension reduction propagation operator in distributed monitoring
Technical Field
The invention relates to the technical field of passive positioning, in particular to a non-circular information source direct positioning method based on a dimensionality reduction propagation operator in distributed monitoring.
Background
In the existing radiation source positioning method, most radiation source signals are treated as complex circle Gaussian signals, a signal model is too simple, and the prior information of the radiation source signal characteristics is not fully utilized, so that the high precision requirement is difficult to achieve. Researches in recent years show that the positioning accuracy of the algorithm can be improved by integrating the signal characteristics of the radiation source into the algorithm model for targeted design. Non-circular signals such as BPSK, MASK and the like are common signal types in modern communication systems, so that the research on the non-circular signal type-oriented radiation source positioning method has more general practicability and very important practical significance.
The traditional positioning mode is a two-step positioning system, namely, estimating an intermediate parameter and then performing positioning calculation. From the perspective of information theory, the existence of an intermediate processing link inevitably causes the loss of partial position information; and aiming at the situation that multiple targets exist simultaneously, an additional parameter matching link is needed, once matching errors occur, the subsequent positioning precision is reduced sharply, and the method is difficult to be applied to practical application scenes with high requirements on the positioning precision.
The direct positioning technology directly estimates the position of the radiation source through original received data, and effectively avoids the problem of parameter estimation and matching in the traditional two-step positioning system, so that the method has higher positioning precision. Because the original data information can be conveniently utilized, the direct positioning method combined with the signal characteristics can obtain better estimation performance. However, the existing direct positioning method facing to the non-circular signal type is mainly based on a subspace decomposition method, characteristic value decomposition needs to be carried out on a covariance matrix, and the algorithm complexity is high; and most algorithms simply remove non-circular phases during solving, and do not substantially carry out dimensionality reduction optimization solving on the non-circular phase search problem.
In order to solve the problems, it is necessary to research a direct positioning method which does not need subspace decomposition and has higher precision and can meet most practical application scenes, and the direct positioning method has important practical significance.
Disclosure of Invention
The invention aims to provide a non-circular information source direct positioning method based on a dimensionality reduction propagation operator in distributed monitoring, which utilizes the approximate characteristics of a propagation operator matrix and a noise subspace matrix, avoids the step of subspace decomposition to reduce algorithm complexity, simultaneously introduces the non-circular characteristics of a source signal in the process of establishing a model for achieving the purposes of increasing algorithm freedom and improving algorithm resolution, and finally directly estimates the position of a radiation source by combining the idea of direct positioning.
The invention adopts the following technical scheme for solving the technical problems:
the direct positioning method based on the dimension reduction propagation operator is provided, and the basic idea is as follows: receiving signals from K non-circular radiation sources by monitoring stations arranged at N different positions, and sampling the signals to obtain an original received signal matrix; then considering the non-circular phase of the signal, expanding a received signal matrix, calculating the expanded covariance matrix of the received signals of all the monitoring stations, and constructing a G matrix and a sub-targeting function by utilizing the idea of a propagation operator; then, performing dimensionality reduction on the sub-objective function, solving the non-circular phase dimensionality reduction problem by a Lagrange multiplier method, fusing G matrixes and sub-functions of all monitoring stations, and constructing a final direct positioning method objective function based on dimensionality reduction and a propagation operator; and finally, performing spectral peak search solving on the final objective function, and estimating the position of the non-circular radiation source.
The invention is characterized by comprising the following steps:
step 1: in a two-dimensional plane, monitoring stations arranged at N different positions receive signals from K non-circular radiation sources and sample the received signals;
step 2: considering the non-circular phase of a radiation source signal, expanding a received signal vector, respectively calculating the expanded covariance matrix of the received signals of different monitoring stations, and constructing a G matrix and a sub-objective function by utilizing the idea of a propagation operator;
and 3, step 3: carrying out dimension reduction on the sub-objective function, solving the non-circular phase dimension reduction problem by a Lagrange multiplier method, fusing G matrixes of all monitoring stations, and constructing a final direct positioning method objective function based on dimension reduction and a propagation operator;
and 4, step 4: and (5) carrying out spectral peak search solving on the final objective function, and estimating the position of the non-circular radiation source.
As a further optimization scheme of the non-circular information source direct positioning method based on the dimensionality reduction propagation operator in distributed monitoring, in step 1, a received signal z of an nth monitoring station at a jth sampling moment n (j) Is composed of
Figure BDA0003023588910000021
In the formula, z n (j) Is the received signal vector of the nth monitoring station at the jth sampling moment, K is the number of non-circular radiation sources,
Figure BDA0003023588910000022
for the signal steering vector of the antenna array incident on the nth monitoring station for the kth radiation source,
Figure BDA0003023588910000023
is the angle of incidence, u, of the k radiation source to the n monitoring station n ＝[x n ,y n ] T For monitoring station position, p k ＝[x k ,y k ] T For the position of the radiation source, M is the number of the array elements, d is the spacing between the array elements, λ is the signal wavelength, s n,k (j) The signal waveform of the kth radiation source at the jth sampling snapshot time is received by the nth monitoring station,
Figure BDA0003023588910000031
and (3) assuming that the noise is complex round Gaussian white noise which is independent from the signal for the noise vector of the antenna array of the nth monitoring station at the jth sampling moment, and the target source signals are not related to each other.
As a further optimization scheme of the non-circular information source direct positioning method based on the dimensionality reduction propagation operator in distributed monitoring, the specific steps of combining the non-circular phase extension received signal vector and constructing the G matrix and the sub-target function by utilizing the idea of the propagation operator in the step 2 are as follows:
step 2.1, considering the non-circular phase of the signal, expanding the received signal vector:
Figure BDA0003023588910000032
in the formula, r n (j) Extended received signal vector for the nth monitoring station, A n (p) is the direction matrix of the nth monitoring station,
Figure BDA0003023588910000033
in order to expand the direction matrix,
Figure BDA0003023588910000034
for the extended steering vector of the nth monitoring station,
Figure BDA0003023588910000035
for the non-circular phase of the k-th radiation source,
Figure BDA0003023588910000036
is a non-circular phase matrix, s n (j) Is a source signal vector;
step 2.2, estimating the extended covariance matrix of the received signals of each monitoring station according to the following formula:
Figure BDA0003023588910000037
in the formula (I), the compound is shown in the specification,
Figure BDA0003023588910000038
the extended covariance matrix for the signal received by the nth monitoring station,
Figure BDA0003023588910000039
an expanded received signal matrix of the nth monitoring station is adopted, and J is a sampling fast beat number;
and 2.3, combining the idea of the propagation operator to construct a G matrix and a sub-objective function:
for the extended covariance matrix
Figure BDA0003023588910000041
Is divided into blocks, i.e.
Figure BDA0003023588910000042
Is composed of
Figure BDA0003023588910000043
First K columns of (2), Q n Is composed of
Figure BDA0003023588910000044
Last 2M-K columns of (c), then the operator matrix is propagated
Figure BDA0003023588910000045
Is shown as
Figure BDA0003023588910000046
Thus, a G matrix is constructed
Figure BDA0003023588910000047
In the formula I 2M-K Is a unit matrix of (2M-K) × (2M-K)
Further construct sub-goal functions as follows
Figure BDA0003023588910000048
Wherein the content of the first and second substances,
Figure BDA0003023588910000049
for the n-th sub-objective function,
Figure BDA00030235889100000410
is the spread signal manifold vector for the nth monitoring station at the time of the search, p is the location vector,
Figure BDA00030235889100000411
and theta is the signal incident angle.
As a further optimization scheme of the non-circular information source direct positioning method based on the dimensionality reduction propagation operator in distributed monitoring, the step 3 of solving the non-circular phase dimensionality reduction problem by adopting a lagrange multiplier method and constructing a final objective function comprises the following detailed steps:
step 3.1, separating and expanding non-circular phase information and target position information in the received signal vector:
Figure BDA00030235889100000412
in the formula (I), the compound is shown in the specification,
Figure BDA00030235889100000413
the kth spread pilot vector representing the nth monitoring station,
Figure BDA00030235889100000414
a position information matrix representing the kth radiation source,
Figure BDA00030235889100000415
a non-circular phase information vector representing the kth radiation source,
Figure BDA00030235889100000416
a non-circular phase for the kth radiation source;
the nth sub-objective function in step 2.3 above is then equivalent to
Figure BDA00030235889100000417
Is also equivalent to
Figure BDA00030235889100000418
Order to
Figure BDA0003023588910000051
Then
Figure BDA0003023588910000052
It can be seen that for non-circular phase parameters
Figure BDA0003023588910000053
In other words, the solution of the sub-objective function belongs to the quadratic optimization problem, and let e = [1,0 =] T Then, then
Figure BDA0003023588910000054
This then translates into the following convex optimization problem:
Figure BDA0003023588910000055
solving by adopting a Lagrange multiplier method, and constructing the following functions:
Figure BDA0003023588910000056
in the formula (I), the compound is shown in the specification,
Figure BDA0003023588910000057
representing the lagrangian objective function of the,
Figure BDA0003023588910000058
is a phase vector, W n And (p) is a position search matrix corresponding to the nth monitoring station, and eta is a multiplier. Make the above formula pair
Figure BDA0003023588910000059
Is zero, i.e.
Figure BDA00030235889100000510
Then the
Figure BDA00030235889100000511
Where μ is the multiplier coefficient, W n (p) -1 Searching matrix W for position corresponding to nth monitoring station n (p) the inverse;
and is composed of
Figure BDA00030235889100000512
Get μ = 1/(e) H W n (p) -1 e) Is thus
Figure BDA00030235889100000513
The nth sub-objective function is converted into
Figure BDA00030235889100000514
And 3.2, constructing a final objective function by the G matrixes of all monitoring stations:
comprehensively considering G matrix and sub-objective function of all monitoring stations, and constructing final objective function, namely f RDNCPM-DPD (p)：
Figure BDA00030235889100000515
As a further optimization scheme of the non-circular information source direct positioning method based on the dimensionality reduction propagation operator in distributed monitoring, the step 4 specifically comprises the following steps:
for the final objective function f after dimensionality reduction RDNCPM-DPD And (p) searching spectral peaks, wherein coordinates corresponding to the K maximum peak values are estimated values of the positions of the non-circular radiation sources.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
(1) the non-circular characteristic of the radiation source signal is utilized, and the positioning precision is effectively improved;
(2) and the idea of propagation operator and dimension reduction processing is combined, so that the algorithm complexity is reduced.
(3) The spatial degree of freedom of the algorithm is increased, and more information sources can be estimated simultaneously;
(4) the source resolution is higher, and the requirement of a more complex actual scene can be met.
Drawings
FIG. 1 is a flow chart of an implementation of a method for directly positioning a non-circular information source based on a dimensionality reduction propagation operator in distributed monitoring according to the present invention;
FIG. 2 is a view of a multi-non-circular radiation source positioning scenario in accordance with the present invention;
FIG. 3 is a peak diagram of the positioning spectrum of the RDNCPM-DPD method of the present invention;
FIG. 4 is a comparison graph of the calculation time before and after dimensionality reduction of the RDNCPM-DPD method of the present invention;
FIG. 5 is a graph comparing the performance of the Capon-based direct positioning algorithm, the PM-based direct positioning algorithm, the two-step positioning algorithm and the RDNCPM-DPD method of the present invention under different array element numbers;
FIG. 6 is a graph comparing the performance of the Capon-based direct positioning algorithm, the PM-based direct positioning algorithm, the two-step positioning algorithm and the RDNCPM-DPD method of the present invention under different signal-to-noise ratios;
FIG. 7 is a performance comparison chart of the Capon-based direct positioning algorithm, the PM-based direct positioning algorithm, the two-step positioning algorithm and the RDNCPM-DPD method of the present invention under different snapshot numbers.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. In the drawings, components are exaggerated for clarity.
FIG. 1 is a flow chart of a method for directly positioning a non-circular information source based on a dimension reduction propagation operator in distributed monitoring, wherein N monitoring stations arranged at different positions receive signals from K non-circular radiation sources, perform signal sampling, and fuse all snapshot data to obtain a received signal matrix; considering the non-circular phase of the signal, expanding a received signal matrix, respectively calculating the expanded covariance matrices of the received signals of different monitoring stations, and constructing a G matrix and a sub-targeting function by utilizing the idea of a propagation operator; carrying out dimensionality reduction on the sub-objective function, solving the non-circular phase dimensionality reduction problem by a Lagrange multiplier method, fusing G matrixes of all monitoring stations, and constructing a final direct positioning method objective function based on dimensionality reduction and a propagation operator; and carrying out spectral peak search solving on the final objective function, and estimating the position of the non-circular radiation source, wherein the specific steps are as follows:
step 1: monitoring stations arranged at N different positions receive signals from K non-circular radiation sources and sample the received signals:
as shown in FIG. 2, assuming that K incoherent far-field narrow bands are incident to N monitoring stations arranged at different positions in a two-dimensional plane, each monitoring station is provided with an M-element uniform linear array, and a non-circular radiation source and the monitoring stations are respectively positioned at p k ＝[x k ,y k ] T (K =1,2, \ 8230;, K) and u n ＝[x n ,y n ] T (N =1,2, \8230;, N), the received signal z of the nth monitoring station at the J (J =1,2, \8230;, J) th sampling instant n (j) Comprises the following steps:
Figure BDA0003023588910000071
in the formula, z n (j) Is the received signal vector of the nth monitoring station at the jth sampling moment, K is the number of non-circular radiation sources,
Figure BDA0003023588910000072
the signal steering vector for the antenna array incident on the nth monitoring station for the kth radiation source,
Figure BDA0003023588910000073
is the incident angle from the k radiation source to the n monitoring station, d is the array element spacing, lambda is the signal wavelength, s n,k (j) The signal waveform of the kth radiation source at the jth sampling snapshot time is received by the nth monitoring station,
Figure BDA0003023588910000074
and assuming the noise to be complex round Gaussian white noise independent from the signal for the noise vector of the antenna array of the nth monitoring station at the jth sampling moment.
Step 2: considering the non-circular phase of a radiation source signal, expanding a received signal vector, respectively calculating the expanded covariance matrix of the received signals of different monitoring stations, and constructing a G matrix and a sub-objective function by utilizing the idea of a propagation operator:
according to the characteristics of the maximum non-circular rate signal, the following can be obtained:
Figure BDA0003023588910000075
in the formula, s n (j) The source signal vector at the jth sampling instant for the nth monitoring station,
Figure BDA0003023588910000076
is a non-circular phase matrix and is,
Figure BDA0003023588910000077
for the non-circular phase of the k-th radiation source,
Figure BDA0003023588910000078
a real envelope for the source signal vector;
therefore, the received signal vector r of the nth monitoring station at the jth sampling moment n (j) Comprises the following steps:
Figure BDA0003023588910000081
in the formula (I), the compound is shown in the specification,
Figure BDA0003023588910000082
is a direction matrix of the nth monitoring station, s n (j) In the form of a vector of the source signal,
Figure BDA0003023588910000083
in order to extend the direction matrix,
Figure BDA0003023588910000084
an extended steering vector for the nth monitoring station;
the extended covariance matrix of the nth observation station passes
Figure BDA0003023588910000085
The calculation is carried out in such a way that,
Figure BDA0003023588910000086
an expanded received signal matrix of the nth monitoring station is obtained, and J is a sampling fast beat number;
combining the idea of propagation operator to expand covariance matrix
Figure BDA0003023588910000087
Is divided into blocks, i.e.
Figure BDA0003023588910000088
Figure BDA0003023588910000089
Is composed of
Figure BDA00030235889100000810
First K columns of (2), Q n Is composed of
Figure BDA00030235889100000811
Last 2M-K columns of (C), then the operator matrix is propagated
Figure BDA00030235889100000812
Expressed as:
Figure BDA00030235889100000813
thus, a G matrix is constructed
Figure BDA00030235889100000814
In the formula I 2M-K Is a unit matrix of (2M-K) × (2M-K)
Further construct sub-goal functions as follows
Figure BDA00030235889100000815
Wherein the content of the first and second substances,
Figure BDA00030235889100000816
for the nth sub-objective function,
Figure BDA0003023588910000091
the spread signal manifold vector for the nth monitoring station at the time of the search, p is the location vector,
Figure BDA00030235889100000918
and theta is the non-circular phase and theta is the signal incident angle.
And 3, step 3: carrying out dimensionality reduction on the sub-objective function, solving the non-circular phase dimensionality reduction problem by a Lagrange multiplier method, fusing G matrixes of all monitoring stations, and constructing a final direct positioning method objective function based on dimensionality reduction and a propagation operator:
due to the influence of non-circular phase, the searching dimension is too large when the sub-objective function is solved in the step 2, dimension reduction solving is carried out on the sub-objective function, and the expanded guide vector is rewritten through matrix transformation
Figure BDA0003023588910000092
Separating the position information from the non-circular phase information:
Figure BDA0003023588910000093
in the formula (I), the compound is shown in the specification,
Figure BDA0003023588910000094
the kth spread pilot vector representing the nth monitoring station,
Figure BDA0003023588910000095
a position information matrix representing the kth radiation source,
Figure BDA0003023588910000096
a non-circular phase information vector representing the kth radiation source,
Figure BDA0003023588910000097
represents the non-circular phase of the kth radiation source;
therefore, the nth sub-objective function in step 2 is equivalent to
Figure BDA0003023588910000098
Is also equivalent to
Figure BDA0003023588910000099
Order to
Figure BDA00030235889100000910
Then
Figure BDA00030235889100000911
It can be seen that for non-circular phase parameters
Figure BDA00030235889100000912
In other words, the solution of the sub-objective function belongs to the quadratic optimization problem, let e = [1,0 =] T Then, then
Figure BDA00030235889100000913
This then translates into the following convex optimization problem:
Figure BDA00030235889100000914
solving by adopting a Lagrange multiplier method, and constructing the following functions:
Figure BDA00030235889100000915
in the formula (I), the compound is shown in the specification,
Figure BDA00030235889100000916
representing the lagrangian objective function of the signal,
Figure BDA00030235889100000917
is a phase vector, W n And (p) is a position search matrix corresponding to the nth monitoring station, and eta is a multiplier. Order the above type is to
Figure BDA00030235889100001012
Is zero, i.e.
Figure BDA0003023588910000101
Then
Figure BDA0003023588910000102
Where μ is the multiplier coefficient, W n (p) -1 Searching matrix W for position corresponding to nth monitoring station n (p) the inverse;
and is composed of
Figure BDA0003023588910000103
Get μ = 1/(e) H W n (p) -1 e) Is thus
Figure BDA0003023588910000105
The nth sub-objective function translates to:
Figure BDA0003023588910000106
comprehensively considering G matrix and sub-objective function of all monitoring stations, and constructing final objective function, namely f RDNCPM-DPD (p)：
Figure BDA0003023588910000107
And 4, step 4: and (3) carrying out spectral peak search solving on the final objective function, and estimating the position of the non-circular radiation source:
for the final objective function f after dimensionality reduction RDNCPM-DPD And (p) searching spectral peaks, wherein coordinates corresponding to the K maximum peak values are estimated values of the positions of the non-circular radiation sources.
The performance of the method is better than that of the existing algorithm through simulation verification. Simulation analysis was performed using MATLAB, with Root Mean Square Error (RMSE) as a criterion for evaluating performance, which is defined as follows:
Figure BDA0003023588910000108
wherein K is the number of non-circular signal sources, MN is the number of Monte Carlo simulation experiments,
Figure BDA0003023588910000109
as an estimate of the position of the radiation source, (x) k ,y k ) The true value of the radiation source position.
FIG. 3 is a peak map of the positioning spectrum of RDNCPM-DPD according to the method of the present invention, where the number of radiation sources K =4, and the radiation sources are located at p 1 ＝[-800,800] T 、p 2 ＝[200,500] T 、p 3 ＝[400,1000] T And p 4 ＝[1000,0] T (unit is m, the same applies below) corresponding to a non-circular phase
Figure BDA00030235889100001010
And
Figure BDA00030235889100001011
the number of monitoring stations N =5, u respectively 1 ＝[-1000,-500] T 、u 2 ＝[-800,-700] T 、u 3 ＝[-200,-500] T 、u 4 ＝[200,-700] T And u 5 ＝[600,-500] T M =3 uniform linear arrays are placed on the monitoring stations, each monitoring station samples fast-beat number J =400, signal-to-noise ratioIs 20dB. As can be seen from the spectrum peak chart of the simulation result, the invention can realize the simultaneous positioning of multiple targets even under the condition that the number of array elements is less than that of radiation sources.
FIG. 4 is a comparison chart of calculation time before and after dimension reduction of RDNCPM-DPD in the method of the present invention under different snapshot numbers. Assuming that the number of radiation sources Q =3, respectively, is located at p 1 ＝[-800,800] T 、p 2 ＝[0,500] T And p 3 ＝[800,1000] T (unit is m, the same below) corresponding to the non-circular phase
Figure BDA0003023588910000111
And
Figure BDA0003023588910000112
the number of monitoring stations N =5, u respectively 1 ＝[-1000,-500] T 、u 2 ＝[-700,-200] T 、u 3 ＝[-200,-500] T 、u 4 ＝[100,-300] T And u 5 ＝[900,-700] T The array element number M =6, the sampling fast beat number J of each monitoring station is stepped from 50 to 300 at intervals of 50, and the signal-to-noise ratio is 20dB. As can be seen from the simulation result, the dimension reduction method adopted by the invention can obviously shorten the calculation time of the algorithm and improve the practicability of the algorithm.
FIG. 5 is a graph comparing the performance of the direct positioning algorithm based on Capon, the direct positioning algorithm based on PM, the two-step positioning algorithm and the RDNCPM-DPD method of the present invention with the change of the array elements. Assuming that the number of radiation sources K =3, p is each 1 ＝[-800,800] T 、p 2 ＝[0,500] T And p 3 ＝[800,1000] T (unit is m, the same applies below) corresponding to a non-circular phase
Figure BDA0003023588910000113
And
Figure BDA0003023588910000114
the number of monitoring stations N =5, u respectively 1 ＝[-1000,100] T 、u 2 ＝[-800,-300] T 、u 3 ＝[-200,-200] T 、u 4 ＝[200,-500] T And u 5 ＝[600,-100] T The number of array elements of the uniform linear arrays arranged on the monitoring stations is respectively 3, 5, 7 and 9, the sampling fast beat number J =100 of each monitoring station, the signal-to-noise ratio is 20dB, and the number of simulation experiments MN =200 of Monte Carlo. As can be seen from the figure, even if the number of array elements is equal to the number of radiation sources, the RDNCPM-DPD method can still realize positioning, and the corresponding positioning error is always smaller than that of a two-step positioning algorithm and a PM-based direct positioning algorithm, so that the estimation accuracy is improved while the spatial degree of freedom is increased; with the increase of the array elements, the performance of the Capon-based direct positioning algorithm is gradually improved to be superior to that of the method, and the increase of the array elements consolidates the stability of the covariance matrix, so that the Capon-based direct positioning algorithm for constructing the objective function by directly utilizing the inverse matrix of the covariance matrix has higher precision advantage.
Fig. 6 is a graph comparing the performance of the Capon-based direct positioning algorithm, the PM-based direct positioning algorithm, the two-step positioning algorithm, and the RDNCPM-DPD method of the present invention with the change of the signal-to-noise ratio. Assuming that the number of radiation sources K =3, p is each 1 ＝[-800,800] T 、p 2 ＝[0,500] T And p 3 ＝[800,200] T (unit is m, the same applies below) corresponding to a non-circular phase
Figure BDA0003023588910000121
And
Figure BDA0003023588910000122
the number of monitoring stations N =5, u respectively 1 ＝[-1000,-500] T 、u 2 ＝[-500,-500] T 、u 3 ＝[0,-500] T 、u 4 ＝[500,-500] T And u 5 ＝[500,-500] T The sampling fast beat number J =100 for each monitoring station, the signal-to-noise ratio is stepped from-5 dB to 30db at 5dB intervals, and the number of monte Carlo simulation experiments MN =200. As can be seen from simulation results, along with the increase of the signal to noise ratio, the positioning performance of the invention is always superior to that of a direct positioning algorithm and a two-step positioning algorithm based on PM, and the direct positioning algorithm is verified to be relative to the two-step positioning algorithmPerformance advantages of the bit algorithm and the introduction of non-circular features improve the performance of the algorithm; but the estimation accuracy is less than Capon-based direct localization algorithms at high signal-to-noise ratios because the covariance matrix is more susceptible to signal-to-noise ratios than the propagation operators.
FIG. 7 is a graph comparing the performance of the direct positioning algorithm based on Capon, the direct positioning algorithm based on PM, the two-step positioning algorithm and the RDNCPM-DPD method of the present invention varying with the number of snapshots. Assuming that the number of radiation sources K =3, p is each 1 ＝[-800,800] T 、p 2 ＝[0,500] T And p 3 ＝[800,1000] T (unit is m, the same applies below) corresponding to a non-circular phase
Figure BDA0003023588910000123
And
Figure BDA0003023588910000124
the number of monitoring stations N =5, each u 1 ＝[-1000,100] T 、u 2 ＝[-800,-300] T 、u 3 ＝[-200,-200] T 、u 4 ＝[200,-500] T And u 5 ＝[600,-100] T The sampling fast-beat number J of each observation position is stepped from 50 to 300 at intervals of 50, the signal-to-noise ratio is 5dB, and the simulation experiment number of Monte Carlo is MN =100. It can be seen from the figure that, under the signal-to-noise ratio, the positioning performance of the invention is continuously improved along with the increase of the number of snapshots, and the positioning accuracy is higher than that of a Capon-based direct positioning algorithm, a PM-based direct positioning algorithm and a two-step positioning algorithm.
The above embodiments are only for illustrating the technical idea of the present invention and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made on the basis of the technical solution of the present invention according to the technical idea of the present invention should be included in the scope of the present invention.

Claims (5)

1. A non-circular information source direct positioning method based on a dimensionality reduction propagation operator in distributed monitoring is characterized by comprising the following steps:
step 1), in a two-dimensional plane, receiving signals from K non-circular radiation sources by N monitoring stations arranged at different positions, and sampling the received signals;
step 2), considering the non-circular phase of the radiation source signal, expanding the received signal vector, respectively calculating the expanded covariance matrix of the received signals of different monitoring stations, and constructing a G matrix and a sub-objective function by using the idea of a propagation operator;
step 3), performing dimensionality reduction on the sub-objective function, solving the non-circular phase dimensionality reduction problem by a Lagrange multiplier method, fusing G matrixes of all monitoring stations, and constructing a final direct positioning method objective function based on dimensionality reduction and a propagation operator;
and 4) carrying out spectral peak search solving on the final objective function, and estimating the position of the non-circular radiation source.
2. The method for non-circular source direct positioning based on dimension reduction propagation operator in distributed monitoring as claimed in claim 1, wherein in step 1), the received signal z of the nth monitoring station at the jth sampling moment is n (j) Is composed of
Figure FDA0003023588900000011
In the formula, z n (j) Is the received signal vector of the nth monitoring station at the jth sampling moment, K is the number of non-circular radiation sources,
Figure FDA0003023588900000012
the signal steering vector for the antenna array incident on the nth monitoring station for the kth radiation source,
Figure FDA0003023588900000013
is the angle of incidence, u, of the k radiation source to the n monitoring station n ＝[x n ,y n ] T For monitoring station position, p k ＝[x k ,y k ] T For the radiation source position, M is the number of array elements, and d is the array elementSpacing, λ signal wavelength, s n,k (j) The signal waveform of the kth radiation source at the jth sampling snapshot time is received by the nth monitoring station,
Figure FDA0003023588900000014
and assuming the noise to be complex round Gaussian white noise independent from the signal for the noise vector of the antenna array of the nth monitoring station at the jth sampling moment.
3. The method for directly positioning a non-circular information source based on a dimensionality reduction propagation operator in distributed monitoring according to claim 2, wherein the specific steps of combining the non-circular phase extension received signal vector and constructing the G matrix and the subgoal function by using the idea of the propagation operator in the step 2) are as follows:
step 2.1), the non-circular phase of the signal is considered, and the received signal vector is expanded:
Figure FDA0003023588900000015
in the formula, r n (j) Extended received signal vector for nth monitoring station, A n (p) is the direction matrix of the nth monitoring station,
Figure FDA0003023588900000021
in order to extend the direction matrix,
Figure FDA0003023588900000022
extended steering vector for the nth monitoring station, a n (p k ) In order to guide the vector, the vector is,
Figure FDA0003023588900000023
for the non-circular phase of the k-th radiation source,
Figure FDA0003023588900000024
is a non-circular phase matrix, s n (j) Is a source signal vector;
step 2.2), estimating an extended covariance matrix of the received signals of each monitoring station according to the following formula:
Figure FDA0003023588900000025
in the formula (I), the compound is shown in the specification,
Figure FDA0003023588900000026
the extended covariance matrix of the received signal for the nth monitoring station,
Figure FDA0003023588900000027
an expanded received signal matrix of the nth monitoring station, wherein J is a sampling fast beat number;
step 2.3), combining the idea of a propagation operator, constructing a G matrix and a sub-objective function:
for the extended covariance matrix
Figure FDA0003023588900000028
Is divided into blocks, i.e.
Figure FDA0003023588900000029
Is composed of
Figure FDA00030235889000000210
First K rows of (A), Q n Is composed of
Figure FDA00030235889000000211
Last 2M-K columns of (C), then the operator matrix is propagated
Figure FDA00030235889000000212
Is shown as
Figure FDA00030235889000000213
Thus constructing a G matrix
Figure FDA00030235889000000214
In the formula I 2M-K Is a unit matrix of (2M-K) × (2M-K)
Further construct sub-goal functions as follows
Figure FDA00030235889000000215
Wherein the content of the first and second substances,
Figure FDA00030235889000000216
for the nth sub-objective function,
Figure FDA00030235889000000217
is the spread signal manifold vector for the nth monitoring station at the time of the search, p is the location vector,
Figure FDA00030235889000000218
and theta is the non-circular phase and theta is the signal incident angle.
4. The method for directly positioning the non-circular information source based on the dimensionality reduction propagation operator in the distributed monitoring according to claim 3, wherein the detailed steps of solving the non-circular phase dimensionality reduction problem and constructing the final objective function by using a Lagrange multiplier method in the step 3) are as follows:
step 3.1), separating the non-circular phase information and the target position information in the expanded received signal vector:
Figure FDA0003023588900000031
in the formula (I), the compound is shown in the specification,
Figure FDA0003023588900000032
the kth spread pilot vector representing the nth monitoring station,
Figure FDA0003023588900000033
a position information matrix representing the kth radiation source,
Figure FDA0003023588900000034
a non-circular phase information vector representing the kth radiation source,
Figure FDA0003023588900000035
a non-circular phase for the kth radiation source;
so that the nth sub-objective function as defined in claim 3 is equivalent to
Figure FDA0003023588900000036
Is also equivalent to
Figure FDA0003023588900000037
Order to
Figure FDA0003023588900000038
Then
Figure FDA0003023588900000039
It can be seen that for non-circular phase parameters
Figure FDA00030235889000000310
In other words, the solution of the sub-objective function belongs to the quadratic optimization problem, and let e = [1,0 =] T Then, then
Figure FDA00030235889000000311
This then translates into the following convex optimization problem:
Figure FDA00030235889000000312
solving by adopting a Lagrange multiplier method, and constructing the following functions:
Figure FDA00030235889000000313
in the formula (I), the compound is shown in the specification,
Figure FDA00030235889000000314
representing the lagrangian objective function of the signal,
Figure FDA00030235889000000315
is a phase vector, W n (p) searching a matrix for the position corresponding to the nth monitoring station, wherein eta is a multiplier; order the above type is to
Figure FDA00030235889000000316
Is zero, i.e.
Figure FDA00030235889000000317
Then
Figure FDA00030235889000000318
Where μ is the multiplier coefficient, W n (p) -1 Searching matrix W for position corresponding to nth monitoring station n (p) inversion;
and is composed of
Figure FDA00030235889000000319
Get μ = 1/(e) H W n (p) -1 e) Is thus
Figure FDA00030235889000000320
The nth sub-objective function translates to:
Figure FDA00030235889000000321
step 3.2), G matrixes of all monitoring stations are constructed, and a final objective function is constructed:
comprehensively considering G matrix and sub-objective function of all monitoring stations, and constructing final objective function, namely f RDNCPM-DPD (p)：
Figure FDA0003023588900000041
5. The method for non-circular source direct localization based on dimension reduction propagation operator in distributed monitoring according to claim 4, wherein the detailed steps of the step 4) are as follows:
for the final objective function f after dimensionality reduction RDNCPM-DPD And (p) searching spectral peaks, wherein coordinates corresponding to the K maximum peak values are estimated values of the positions of the non-circular radiation sources.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115825863A (en) * 2022-12-16 2023-03-21 南京航空航天大学 Method for quickly and directly positioning non-circular signal under impact noise
CN115825863B (en) * 2022-12-16 2023-12-29 南京航空航天大学 Method for rapidly and directly positioning non-circular signal under impact noise

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