CN110208741B - A method of over-the-horizon single target direct positioning based on multi-array phase measurement - Google Patents

Abstract

The invention belongs to the technical field of electronic countermeasures, and specifically relates to a method for direct positioning of a single target beyond the visual range based on multi-circular array phase measurement. The present invention can extract all the information about the target position in the array flow pattern by calculating the phase difference between the received signals of different array elements of the same circular array, and establish the relationship between the phase difference and the pitch angle and azimuth angle, so that the The location points satisfying this relationship are searched in the entire observation area. In order to reduce the search dimension during the search process, the azimuth angle of the search point relative to the observation station can be brought into the above relational formula, and the optimal pitch angle can be obtained by the least square method, and then the azimuth angle and the obtained optimal pitch angle can be obtained. Put the pitch angle into the above relationship to calculate whether it conforms to the actual received signal. The beneficial effect of the present invention is that the present invention can accurately locate a single target beyond the visual distance, the method is simple, and the effect is good.

Description

A method of over-the-horizon single target direct positioning based on multi-array phase measurement

technical field

The invention belongs to the technical field of electronic countermeasures, and is a method for locating a single target through the phase difference information of different array elements of a plurality of circular arrays in a geographical coordinate system space.

Background technique

In the process of electronic reconnaissance, accurately estimating the position of the target radiation source is helpful to obtain the information of the radiation source. It is the key and main basis for high-level situation estimation and threat estimation, and it is also an important guarantee for achieving precise strikes on the target. Positioning is to approximate a certain observation area as a plane, and then use the method of plane geometry to locate and calculate the target position. This method is effective when the target and the observation area where the antenna is located are not very large relative to the curvature of the earth. However, with the continuous development of technology and the continuous expansion of the range of activities of various sea, land and air equipment, the impact of the curvature of the earth on the positioning results is increasing. At this time, the observation area can no longer be approximated as a plane for solution.

Most of the positioning algorithms based on the spherical model of the earth carry out the cross positioning of the azimuth lines on the spherical section or section to solve the position of the target, and then convert the plane position of the target to the geographic location of the target. However, the accuracy of the pitch angle of the target obtained through microwave and infrared radiation is so poor that it is impossible to measure the azimuth and pitch angle at two stations in the Cartesian coordinate system to achieve cross positioning.

Contents of the invention

In view of the above problems, the present invention proposes a single-target direct positioning scheme based on multi-circular array phase measurement in the geographic coordinate system space.

The technical scheme adopted in the present invention is:

For a stationary target, its position information is transformed into the pitch angle and azimuth angle of the target relative to the observation station, and the pitch angle and azimuth angle information are completely contained in the array flow pattern of the array receiving signal. By calculating the phase difference between the received signals of different elements of the same circular array, all the information about the target position in the array flow pattern can be extracted, and the relationship between the phase difference and the elevation angle and azimuth angle can be established, so that the entire observation The location points satisfying this relationship are searched in the area. In order to reduce the search dimension during the search process, the azimuth angle of the search point relative to the observation station can be brought into the above relational formula, and the optimal pitch angle can be obtained by the least square method, and then the azimuth angle and the obtained optimal pitch angle can be obtained. Put the pitch angle into the above relationship to calculate whether it conforms to the actual received signal. In order to eliminate position ambiguity and improve positioning accuracy, at least two antenna arrays are required. The multi-station based single target positioning model in the geographic coordinate system space is shown in Fig. 1.

Suppose there are P observation stations on the earth, the latitude and longitude of the pth observation station is: (L _p , B _p ), and the latitude and longitude of the radiation source is (L, B). The azimuth angle of the target relative to the pth observation station is θ ^p , and the elevation angle is φ ^p . The signal model shown in Figure 2 can be expressed as:

表示第p个圆阵中第m个阵元接收到的第t时刻的信号，M为每个圆阵包含的阵元数；s_p(t)表示第p个圆阵接受到信号的包络；

表示第p个圆阵中第m个阵元相对第1个阵元因为位置不同产生的相位差，R是均匀圆阵的半径，λ是接收信号的波长；

表示高斯白噪声。

Indicates the signal at time t received by the mth element in the pth circular array, M is the number of array elements contained in each circular array; sp (t) represents the envelope of the signal received by the _pth circular array ;

Indicates the phase difference between the m-th array element and the first array element in the p-th circular array due to different positions, R is the radius of the uniform circular array, and λ is the wavelength of the received signal;

represents white Gaussian noise.

Assume that the noise satisfies:

为噪声方差，δ(t)为冲激函数，t与t1代表时刻，T为总的采样时间。in,

is the noise variance, δ(t) is the impulse function, t and t1 represent the time, and T is the total sampling time.

Find the correlation function of the received signals of the two array element channels k and l in the circular array p

For k≠l, the phase angle of the correlation function r _kl (t) in the sense of time statistics is:

Putting the above formula into matrix form is:

in,

Divide the measurement area of the observatory station into Q×N grids, each grid point represents a position coordinate (x _q , y _n ) in the latitude-longitude plane of the target, q=1,2,...,Q, n=1, 2,...,N. Let the latitude and longitude corresponding to this position be (L ^q , B ⁿ ), 1≤q≤Q, 1≤n≤N, and the latitude and longitude of the center of the pth circular array is (L _p , B _p ), 1≤p≤P (P is the total number of circular arrays).

Use the following formula to calculate the azimuth of the search point position (L ^q ,B ⁿ ) relative to the center of the p-th circular array (L _p ,B _p )

b _p,q,n = sin B _p sin B ⁿ +cos B _p cos B ⁿ cos(L _p -L ^q ) (10)

带入(6)式，用最小二乘法求搜索点位置(L^q,Bⁿ)的俯仰角的最优解：Will

Putting it into formula (6), use the least square method to find the optimal solution of the pitch angle of the search point position (L ^q , B ⁿ ):

Put (13) into (6) to get the error of the search point relative to the pth observation station:

为

的投影正交补矩阵，其为幂等矩阵，即

并满足

here

for

The projection orthogonal complement matrix of is an idempotent matrix, namely

and meet

In the same way, the error of the search point relative to all observation stations can be obtained, and the overall error can be calculated:

Take the inverse of the error as the cost function for the search point:

The latitude and longitude of the final destination are:

The beneficial effect of the present invention is that the present invention can accurately locate a single target beyond the visual distance, the method is simple, and the effect is good.

Description of drawings

Fig. 1 is the direct positioning model diagram of multi-circle array in the spherical model;

Fig. 2 is a receiving signal model;

Fig. 3 is the flow chart of the over-the-horizon single target direct positioning algorithm based on multi-circle array phase measurement;

Figure 4 is a single-target pseudo-spectrogram generated by a rough search;

Figure 5 is the single-target pseudo-spectrogram generated by the fine search.

Figure 6 shows the positioning error under different signal-to-noise ratios.

Detailed ways

The present invention is described in detail below in conjunction with embodiment:

Example

In this example, matlab is used to verify the above-mentioned over-the-horizon single target direct positioning algorithm scheme of multi-array phase measurement. For the sake of simplicity, the following assumptions are made on the algorithm model:

1. All observatories and targets are on the Earth's surface;

2. The signals received by all observation stations have the same signal-to-noise ratio;

3. All engineering errors are added to the equivalent noise;

4. Assume that the target is stationary or moving at a very low speed;

Step 1. Set the area where the target is located: the longitude is from 90° to 110°, the latitude is from 20° to 40°, the target longitude and latitude are (101.667,31.667), and the unit is degree. Use 3 fixed observation stations to locate the above target, all observation stations are also distributed in this area, the latitude and longitude are: (95,25), (105,25), (100,35), the unit is degree. It is assumed that the noise of the observation station obeys a Gaussian distribution with a mean value of zero, and the noise between different array elements of each observation station is independent of each other;

Step 2. Time synchronization is done to the M channel array antenna receiving system of each observation station, and the radio signal data of the target radiation is collected according to the Nyquist sampling theorem to obtain the array signal data;

k,l＝1,2,…,M,(k≠l)p＝1,…,P；Step 3. Perform cross-correlation processing on the received signals between different channels of the same observation station to obtain the phase difference of signals between different channels

k,l=1,2,...,M,(k≠l)p=1,...,P;

q,n表示当前搜索的格子的位置，p表示第p个观测站；Step 4. Divide the observation area into Q×N (20×20 for this simulation) grid, and calculate the azimuth of the vertex position of the grid relative to each observation station

q, n represent the position of the currently searched grid, and p represents the pth observation station;

带入(13)式中求得有关俯仰角的最优解

Step 5. Put

into (13) to obtain the optimal solution for the pitch angle

Step 6. Calculate the error of the search point relative to the pth observation station according to formula (14)

Step 7. Accumulate the errors of the search point relative to all observation stations to obtain C ^q,n ;

Step 8. Find the reciprocal Q ^q,n of C ^q, n, and use Q ^q,n to draw a pseudo-spectrum of a single target. The peak point is the positioning result of the rough search, that is, the longitude and latitude of the target (L',B') ;

Step 9. Continue to use the method from step 4 to step 8 to search within the range with (L', B') as the center and a difference of 2 degrees in latitude and longitude, and then the precise positioning result of the target can be obtained.

Direct positioning effect of over-the-horizon target based on uniform circular array array:

As shown in Figure 4, the observation area is roughly divided. From the figure, it can be seen that the pseudo peak map of the target appears in the observation area, and the position of the peak is the preliminary positioning result of the target. From the rough search results, the approximate location of the target can be determined, so that the search range can be narrowed down, and a more detailed search can be performed on this range. It can be seen from Figure 5 that the precise positioning result of the target is obtained. Figure 6 shows the variation trend of positioning error with signal-to-noise ratio.

Claims (1)

1. a kind of beyond-the-line-of-sight single target direct location method based on multicircular array phase measurement, it is characterized in that, may further comprise the steps: S1. Suppose there are P observation circular arrays on the earth, the latitude and longitude of the pth circular array is: (L _p , B _p ), the latitude and longitude of the radiation source is (L, B), and the azimuth of the target relative to the pth observation station The angle is θ ^p , the pitch angle is φ ^p , and the signal model is established as:

Indicates the signal at time t received by the mth element in the pth circular array, M is the number of array elements contained in each circular array; sp (t) represents the envelope of the signal received by the _pth circular array ;

Indicates the phase difference between the m-th array element and the first array element in the p-th circular array due to different positions, R is the radius of the uniform circular array, and λ is the wavelength of the received signal;

Represents Gaussian white noise; S2. Perform time synchronization on the M-channel array antenna receiving system of each observation station, collect the radio signal data radiated by the target according to the Nyquist sampling theorem, and obtain the array signal data; S3. Perform cross-correlation processing on the received signals between different channels of the same circular array to obtain the phase difference of signals between different channels:

Let the noise satisfy:

1≤k≤M, 1≤l≤M, 1≤t, t1≤T in,

is the noise variance, δ(t) is the impulse function, t and t1 represent the time, and T is the total sampling time; Then the correlation function of the received signals of two different array element channels k and l in the circular array p

For k≠l, the phase angle of the correlation function r _kl (t) in the sense of time statistics is:

Arranged into matrix form as:

in

S4. Divide the circular array measurement area into Q×N grids, each grid point represents a position coordinate (x _q , y _n ) in the target latitude-longitude plane, q=1,2,...,Q,n= 1,2,...,N, let the latitude and longitude corresponding to this position be (L ^q , B ⁿ ), 1≤q≤Q, 1≤n≤N, and the latitude and longitude of the center of the pth circular array is (L _p ,B _p ), 1≤p≤P; use the following formula to calculate the azimuth of the search point position (L ^q , B ⁿ ) relative to the center of the p-th circular array (L _p , B _p )

b _p,q,n = sinB _p sinB ⁿ +cosB _p cosB ⁿ cos(L _p -L ^q )

S5. Will

bring in

Use the least squares method to find the optimal solution of the pitch angle of the search point position (L ^q , B ⁿ ):

S6. Calculate the error of the search point relative to the pth observation station

for

The projection orthogonal complement matrix of is an idempotent matrix, namely

and meet

S7. Accumulate the errors of the search point relative to all observation stations, and get C _(q,n) :

1≤q≤Q,1≤n≤N S8. Find the reciprocal Q (q, n) of C _{( q, n)}

Use Q _{(q, n)} to draw the pseudo-spectrum of a single target, and the peak point is the positioning result of the rough search, that is, the longitude and latitude (L', B') of the target; S9. Continue to use the method from step S4 to step S8 to search within the range with (L', B') as the center and a difference of 2 degrees in latitude and longitude, and obtain the final positioning result of the target

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