CN109031197B - A method for direct localization of radiation sources based on over-the-horizon propagation model - Google Patents

Abstract

The present invention proposes a direct radiation source positioning method based on an over-the-horizon propagation model. The method includes: a mathematical representation of a receiving model of a radiation source positioning system; solution of an analytical expression of the incident angle parameter under the over-the-horizon propagation model; Radiation source location solution for likelihood estimates. The method of the invention inherits the excellent performance of the maximum likelihood method; and does not need the data association step in the two-step positioning method; at the same time, it also avoids the approximate processing in the traditional method, and integrates the over-the-horizon propagation model in an analytical way. Solving process, so as to obtain more effective positioning results.

Description

A method for direct localization of radiation sources based on over-the-horizon propagation model

technical field

The invention belongs to the technical field of radiation source positioning technology, radar signal processing, array signal processing and parameter estimation theory, and in particular relates to a radiation source direct positioning method based on an over-the-horizon propagation model.

Background technique

Radiation source location technology is an important research topic in the fields of radar, sonar and wireless communication. For the convenience of model construction, most of the existing radiation source positioning methods limit the positioning range within the line-of-sight, and although the precise positioning of the over-the-horizon radiation source also has important research value in practice, the literature in this area is relatively scarce. . Existing literatures on the location of over-the-horizon radiation sources are all based on traditional two-step positioning algorithms. In these methods, the influence of the over-the-horizon model is usually incorporated into the error term of the line-of-sight model. Therefore, these methods In fact, it belongs to a compromise process that is robust to over-the-horizon errors.

Different from the above methods, we use the direct positioning technology to provide a radiation source positioning method under the over-the-horizon propagation model in the present invention. Compared with the two-step positioning method, this direct positioning method not only does not require the data correlation between the measurement values of each base station, but also can be better combined with the over-the-horizon propagation model, avoiding the approximation in the traditional method, so that it is more efficient. Efficiently locate over-the-horizon radiation sources.

SUMMARY OF THE INVENTION

The purpose of the present invention is to improve the limitation of the prior art, and to provide a direct positioning method of the radiation source based on the over-the-horizon propagation model, which can effectively locate the over-the-horizon radiation source.

The object of the present invention is to be realized by the following technical solutions: a method for direct positioning of radiation sources based on the over-the-horizon propagation model, comprising the following steps:

Step 1. Mathematical representation of the receiving model of the radiation source positioning system;

Step 2. Solve the analytical expression of the incident angle parameter under the over-the-horizon propagation model;

Step 3: Calculate the position of the radiation source based on the maximum likelihood estimation.

Further, the step 1 is specifically:

Suppose the earth is an ideal sphere with a radius of r, and there is a single target radiation source on the sphere; the radiation source positioning system is equipped with L base stations, and each base station contains a uniform linear array with M antenna elements; let represents the position of the radiation source in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript t represents the target, and θ _t represents the pitch angle of the target, represents the azimuth of the target; n _l (k) represents the power of The additive white Gaussian noise vector of , where k represents the k-th snapshot, and the subscript n represents the noise; s _l (k) represents the incident signal, then the received data of the l-th base station is expressed as:

in

Represents the steering vector of the array, d is the spacing of the array elements, λ is the wavelength of the incident signal, ψ _l is the angle between the incident signal and the array;

In the modeling, the array noise between different base stations is statistically independent; the coherence time of the radiation source signal is much smaller than the propagation delay difference of the signal between different base stations, that is, the signals from the same radiation source received by different base stations are statistical independent.

Further, the step 2 is specifically:

For each base station array, it is specified that the direction pointing to the north pole is the 0° direction, and the clockwise declination of the array relative to the 0° direction is represented by α _l , let represents the position of each base station in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript l represents the l-th base station, and θ _l represents the pitch angle of the base station l, represents the azimuth of base station l; in the receiving model of the radiation source positioning system described in step 1, ψ _l and There is an analytical functional relationship between:

For the ψ _l and There is an analytical functional relationship between them to solve:

(1) Coordinate system conversion:

make and Represent the positions of the target and the base station in the rectangular coordinate system, where the superscript c represents the rectangular coordinate system; according to the conversion formula between the spherical coordinate system and the rectangular coordinate system, we can get:

z _t =r cos(θ _t ) z _l =r cos(θ _l )

(2) Construct the projection matrix:

point on the sphere The tangent plane equation is:

xx _l +yy _l +zz _l =r ²

Take any two points on the tangent plane and and guarantee and The three points are not collinear; construct the vector group:

Then the projection matrix of the tangent plane is expressed as:

P _U =U(U ^H U) ^-1 U ^H

(3) Find the chord projection vector:

Let the coordinates of the North Pole be Then there are chord vectors on the two great circles of the sphere:

After projecting the two chord vectors to the tangent plane respectively, we get:

u' _0,l =P _U u _0,l u' _t,l =P _U u _t,l

(4) Calculate the included angle:

The expression of the included angle ψ _l is:

Further, the step 3 is specifically:

The joint probability density function of the data received by each base station has the following form:

in

The symbol K represents the total number of snapshots. After ignoring the constant term, the log-likelihood function of the unknown parameter is expressed as:

Among them, the estimated value of the waveform parameter is:

Substitute into the log-likelihood function and tidy up the optimized cost function for the available radiation source location estimate:

in is the projection matrix that spans the space of the steering vector, is the estimated value of the covariance matrix of the received data, and the specific expressions of the two are as follows:

The cost function is solved by means of a two-dimensional search.

The cost function of the method of the present invention is given based on the maximum likelihood estimation criterion, which inherits the excellent performance of the maximum likelihood method; at the same time, the method of the present invention does not need a data association step, and avoids the traditional method. Approximate processing. Therefore, for the radiation source localization under the condition of over-the-horizon, this method can obtain more effective target position estimation results.

Description of drawings

Fig. 1 is the flow chart of the method of the present invention;

2 is a schematic diagram of a radiation source positioning system under the condition of over-the-horizon propagation;

Figure 3 shows the results of the location of the over-the-horizon radiation source.

Detailed ways

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. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

1, the present invention proposes a method for direct positioning of radiation sources based on the over-the-horizon propagation model, comprising the following steps:

Step 1. Mathematical representation of the receiving model of the radiation source positioning system;

Step 2. Solve the analytical expression of the incident angle parameter under the over-the-horizon propagation model;

Step 3: Calculate the position of the radiation source based on the maximum likelihood estimation.

With reference to Figure 2, the step 1 is specifically:

For the convenience of expression and understanding, the symbols used are described as follows: matrices and vectors are represented by bold italic symbols; superscripts (·) ^T , (·) ^H and (·) ^-1 represent transpose, conjugate transpose and The inverse operator; the symbols ||·||, tr(·) and diag(·) represent the 2-norm, trace and diagonalization operations, respectively.

Consider the earth as an ideal sphere with radius r, and there is a single target radiation source on the sphere. The positioning system is configured with L base stations in total, and each base station includes a uniform linear array with M antenna units. make represents the position of the radiation source in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript t represents the target, and θ _t represents the pitch angle of the target, represents the azimuth of the target; n _l (k) represents the power of The additive white Gaussian noise vector of , where k represents the k-th snapshot, and the subscript n represents the noise; s _l (k) represents the incident signal, then the received data of the l-th base station can be expressed as:

in

Represents the steering vector of the array, d is the distance between the array elements, λ is the wavelength of the incident signal, and ψ _l is the angle between the incident signal and the array.

In addition, we believe that the array noise between different base stations is statistically independent in the modeling; it is considered that the coherence time of the radiation source signal is much smaller than the propagation delay difference of the signal between different base stations, that is, the same radiation received by different base stations is from the same radiation source. The signals of the sources are statistically independent.

The step 2 is specifically:

For each base station array, it is specified that the direction pointing to the north pole is the 0° direction, and the clockwise declination of the array relative to the 0° direction is represented by α _l , let represents the position of each base station in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript l represents the l-th base station, and θ _l represents the pitch angle of the base station l, represents the azimuth of base station l. In the receiving model of the radiation source positioning system described in step 1, it is noted that ψ _l is the same as There is an analytical functional relationship between:

The process of solving the above relationship is given below:

(1) Coordinate system conversion:

make and Represent the positions of the target and the base station in the rectangular coordinate system, where the superscript c represents the rectangular coordinate system; according to the conversion formula between the spherical coordinate system and the rectangular coordinate system, we can get:

z _t =r cos(θ _t ) z _l =r cos(θ _l )

(2) Construct the projection matrix:

point on the sphere The tangent plane equation is:

xx _l +yy _l +zz _l =r ²

Take any two points on the tangent plane and and guarantee and The three points are not collinear. Construct a vector group:

Then the projection matrix of the tangent plane can be expressed as:

P _U =U(U ^H U) ^-1 U ^H

(3) Find the chord projection vector:

Let the coordinates of the North Pole be Then there are chord vectors on the two great circles of the sphere:

After projecting the two chord vectors to the tangent plane respectively, we get:

u' _0,l =P _U u _0,l u' _t,l =P _U u _t,l

(4) Calculate the included angle:

The expression of the included angle ψ _l is:

The step 3 is specifically:

The joint probability density function of the data received by each base station has the following form:

in

The symbol K represents the total number of snapshots. After ignoring the constant term, the log-likelihood function of the unknown parameter can be expressed as:

Among them, the estimated value of the waveform parameter is:

Substitute into the log-likelihood function and tidy up the optimized cost function for the available radiation source location estimate:

in is the projection matrix that spans the space of the steering vector, is the estimated value of the covariance matrix of the received data, and the specific expressions of the two are as follows:

The above cost function can be solved by a two-dimensional search.

The positioning spectrum obtained by the direct positioning method of the radiation source based on the over-the-horizon propagation model is shown in FIG. 3 . It can be seen that the method of the present invention successfully locates an over-the-horizon target.

A method for direct positioning of radiation sources based on the over-the-horizon propagation model provided by the present invention has been described above in detail. In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only It is used to help understand the method of the present invention and its core idea; at the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific embodiments and application scope. The contents of the description should not be construed as limiting the present invention.

Claims (3)

1. a radiation source direct positioning method based on a trans-horizon propagation model, is characterized in that, comprises the steps: Step 1. Mathematical representation of the receiving model of the radiation source positioning system; Step 2. Solve the analytical expression of the incident angle parameter under the over-the-horizon propagation model; Step 3: Calculate the position of the radiation source based on the maximum likelihood estimation; The step 1 is specifically: Suppose the earth is an ideal sphere with a radius of r, and there is a single target radiation source on the sphere; the radiation source positioning system is equipped with L base stations, and each base station contains a uniform linear array with M antenna elements; let represents the position of the radiation source in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript t represents the target, and θ _t represents the pitch angle of the target, represents the azimuth of the target; n _l (k) represents the power of The additive white Gaussian noise vector of , where k represents the k-th snapshot, and the subscript n represents the noise; s _l (k) represents the incident signal, then the received data of the l-th base station is expressed as: in Represents the steering vector of the array, d is the spacing of the array elements, λ is the wavelength of the incident signal, ψ _l is the angle between the incident signal and the array; In the modeling, the array noise between different base stations is statistically independent; the coherence time of the radiation source signal is much smaller than the propagation delay difference of the signal between different base stations, that is, the signals from the same radiation source received by different base stations are statistical independent. 2. a kind of radiation source direct positioning method based on Transcendent line of sight propagation model according to claim 1, is characterized in that, described step 2 is specifically: For each base station array, it is specified that the direction pointing to the north pole is the 0 ^° direction, and the clockwise declination of the array relative to the 0 ^° direction is represented by α _l , let represents the position of each base station in the spherical coordinate system, where the superscript s represents the spherical coordinate system, the subscript l represents the l-th base station, and θ _l represents the pitch angle of the base station l, represents the azimuth of base station l; in the receiving model of the radiation source positioning system described in step 1, ψ _l and There is an analytical functional relationship between: For the ψ _l and There is an analytical functional relationship between them to solve: (1) Coordinate system conversion: make and Represent the positions of the target and the base station in the rectangular coordinate system, where the superscript c represents the rectangular coordinate system; according to the conversion formula between the spherical coordinate system and the rectangular coordinate system, we can get: z _t =rcos(θ _t )z _l =rcos(θ _l ) (2) Construct the projection matrix: point on the sphere The tangent plane equation is: xx _l +yy _l +zz _l =r ² Take any two points on the tangent plane and and guarantee and The three points are not collinear; construct the vector group: Then the projection matrix of the tangent plane is expressed as: P _U =U(U ^H U) ^-1 U ^H (3) Find the chord projection vector: Let the coordinates of the North Pole be Then there are chord vectors on the two great circles of the sphere: After projecting the two chord vectors to the tangent plane respectively, we get: u' _0,l =P _U u _0,l u' _t,l =P _U u _t,l (4) Calculate the included angle: The expression of the included angle ψ _l is: 3. a kind of radiation source direct positioning method based on Transcendent line of sight propagation model according to claim 2, is characterized in that, described step 3 is specifically: The joint probability density function of the data received by each base station has the following form: in The symbol K represents the total number of snapshots. After ignoring the constant term, the log-likelihood function of the unknown parameter is expressed as: Among them, the estimated value of the waveform parameter is: Substitute into the log-likelihood function and tidy up the optimized cost function for the available radiation source location estimate: in is the projection matrix that spans the space of the steering vector, is the estimated value of the covariance matrix of the received data, and the specific expressions of the two are as follows: The cost function is solved by means of a two-dimensional search.