CN115144851A - Multi-station positioning tracking method based on pitch angle - Google Patents

Abstract

The invention provides a multi-station positioning and tracking method based on a pitch angle, and belongs to the field of passive positioning. The method comprises the following steps: randomly selecting 4 radar observation stations, wherein 3 radar observation stations are not collinear; establishing a target position equation according to the pitch angles of the 4 radar observation stations to the target; solving the target position equation to obtain an initial solution of the target position; and checking the initial solution of the target position to obtain a final positioning result of the target position. According to the invention, only the pitch angle is utilized to position the target, so that the height measuring radar has the function of tracking and positioning the target in a passive working mode, the application field and the use scene of the height measuring radar are expanded, and the application value is higher.

Description

A Multi-station Positioning and Tracking Method Based on Elevation Angle

technical field

The invention belongs to the field of passive positioning, in particular to a multi-station positioning and tracking method based on an elevation angle.

Background technique

The radio equipment with radiation is widely used in modern military facilities, and the passive reconnaissance and positioning system can determine the position of the carrier by locating the radiation source. The passive reconnaissance and positioning system itself does not radiate electromagnetic signals, has the characteristics of strong anti-interference ability and electromagnetic concealment, and is an important means of electronic countermeasures. Under the condition that the target radiation source has the incoming wave signal, the passive positioning system obtains the observational quantity containing the target spatial position, motion state, and property characteristics, usually including the arrival direction, arrival time, arrival frequency and arrival amplitude of the incoming wave. In the current research, the pitch angle is usually used as an auxiliary observation to locate and track the target together with other observations. However, in military confrontation, due to the complex electromagnetic environment, active interference measures, and limited use of equipment, commonly used observations such as azimuth cannot be obtained or the measurement accuracy is poor, making conventional positioning methods unable to play their due role. When the only reliable observation is the pitch angle, a multi-station positioning and tracking method based on the pitch angle must be developed.

For example, in the normal working mode, the altimetry radar uses a wide beam in the horizontal direction and a narrow beam in the elevation direction to accurately measure the elevation angle, but does not perform azimuth measurement, and uses the active radar to measure the radial distance of the target or the plane radar used in conjunction with it. Provides a distance parameter to calculate the height of the target. However, in military confrontation, due to special considerations, the active working mode cannot be used normally and the passive working mode is adopted, and the radial distance of the target cannot be directly measured. At this time, only the pitch angle and the azimuth angle with a large error are observed. The target cannot be tracked.

SUMMARY OF THE INVENTION

The purpose of the present invention is to fill in and overcome the blank of the prior art, and propose a multi-station positioning and tracking method based on the pitch angle. The invention only uses the pitch angle to locate the target, so that the altimetry radar can have the function of tracking and locating the target in the passive working mode, which will expand the application field and use scene of the altimeter radar, and has high application value.

This embodiment proposes a multi-station positioning and tracking method based on an elevation angle, including:

4 radar observation stations are arbitrarily selected, 3 of which are not collinear;

According to the pitch angles of the four radar observation stations to the target, establish the target position equation;

Solving the target position equation to obtain the initial solution of the target position;

The initial solution of the target position is checked to obtain the final positioning result of the target position.

In a specific embodiment of the present invention, the establishment of the target position equation according to the pitch angles of the four radar observation stations to the target includes:

Note that the four ground observation stations are S _i (x _i , y _i , z _i ), i=1, 2, 3, 4, and _xi , y _i , and z _i represent the i-th observation station S _i respectively The XYZ coordinates of the target are marked as T(x, y, z), x, y, z represent the XYZ coordinates of the target T, and the pitch angle measured by each observation station S _i is recorded as θ _i , where S ₁ , S ₂ , S ₄ represents three non-collinear observation stations;

Then the pitch angle of the observation station _Si to the target T satisfies the observation equation set:

Transform equation (1) to get the target position equation:

In a specific embodiment of the present invention, the solution of the target position equation to obtain the initial solution of the target position includes:

make:

Get the target coordinates (x, y, z) to satisfy:

make:

get:

according to

u ₃ x+v ₃ y=p ₃ z ² +q ₃ z+c ₃ (7)

Substituting equation (6) into equation (7), we get:

(k ₁ u ₃ +k ₂ v ₃ -p ₃ )z ² +(s ₁ u ₃ +s ₂ v ₃ -q ₃ )z+(t ₁ u ₃ +t ₂ v ₃ -c ₃ )=0 (8 )

Then the solution of the Z coordinate of the target is:

According to the result of formula (9), the solutions to calculate the X and Y coordinates of the target respectively are:

Using the results of equations (9)-(11), the initial solutions of the target position are obtained as T ₁ (x ₁ , y ₁ , z ₁ ) and T ₂ (x ₂ , y ₂ , z ₂ ), respectively.

In a specific embodiment of the present invention, the testing of the initial solution of the target position to obtain the final solution of the target position includes:

If the initial solution of the target position satisfies Equation (1) and conforms to the observation information, the initial solution is the final solution of the target position.

Features and beneficial effects of the present invention

The present invention only uses the pitch angle to track and locate the target, which solves the problem of achieving high-precision target positioning and tracking under limited observation when most of the positioning methods cannot work under certain circumstances; 2. The present invention can make The altimetry radar is applied in the passive positioning field in passive working mode to expand the range of use of this type of radar and improve the application value.

Description of drawings

FIG. 1 is a schematic flowchart of a multi-station positioning and tracking method based on an elevation angle according to an embodiment of the present invention.

FIG. 2 is a geometrical schematic diagram of an observation target of an observation station in a specific embodiment of the present invention.

Detailed ways

The present invention proposes a multi-station positioning and tracking method based on an elevation angle, which is further described in detail below with reference to the accompanying drawings and specific embodiments.

An embodiment of the present invention proposes a multi-station positioning and tracking method based on an elevation angle, including:

4 radar observation stations are arbitrarily selected, 3 of which are not collinear;

According to the pitch angles of the four radar observation stations to the target, establish the target position equation;

Solving the target position equation to obtain the initial solution of the target position;

The initial solution of the target position is checked to obtain the final positioning result of the target position.

In a specific embodiment of the present invention, the overall process of the multi-station positioning and tracking method based on the pitch angle is shown in Figure 1, and includes the following steps:

1) 4 radar observation stations are arbitrarily selected, among which 3 radar observation stations are not collinear.

The present invention requires at least 4 observation stations, among which 3 observation stations are not on a straight line.

When more than 4 observation stations can be used, 4 observation stations that meet the requirement of non-collinearity can be arbitrarily selected for calculation.

2) Establish the target position equation.

A geometric schematic diagram of an observation target of an observation station in a specific embodiment of the present invention is shown in FIG. 2 . In Figure 2, the four ground observation stations selected in step 1) are respectively S _i (x _i , y _i , z _i ) (i=1, 2, 3, 4), _xi , y _i , z _i respectively Represents the XYZ coordinates of the _i -th observation station Si, the marking target is T(x, y, z), x, y, z represents the XYZ coordinates of the target T, and the pitch _angle measured by each observation station Si is marked as θ _i .

Among them, let S _i (x _i , y _i , z _i ) (i=1, 2, 4) represent 3 observation stations that are not on a straight line (no sequence requirement), and the remaining one observation station is S ₃ (x ₃ , y ₃ , z ₃ );

The pitch angle of the observation station Si ( _i =1, 2, 3, 4) to the target T satisfies the observation equations:

Transform to get the target position equation:

The equation is a system of quadratic equations in three variables, and the analytical solution of the equation cannot be directly obtained. It is necessary to reduce the power of the equation system to obtain the analytical solution of the equation.

3) Solve the target position equation to obtain the target position; the specific method is:

Do the first step of parameter substitution

make:

where cot is the cotangent, or cos/sin.

By simplifying the deformation, the target coordinates (x, y, z) can be obtained to satisfy the equation:

Do the second step parameter substitution:

By simplifying the deformation, we get:

according to

u ₃ x+v ₃ y=p ₃ z ² +q ₃ z+c ₃ (7)

Substitute equation (6) into equation (7) to obtain the equation that the target height satisfies:

(k ₁ u ₃ +k ₂ v ₃ -p ₃ )z ² +(s ₁ u ₃ +s ₂ v ₃ -q ₃ )z+(t ₁ u ₃ +t ₂ v ₃ -c ₃ )=0 (8 )

According to the practical significance of the observation system, the quadratic equation of one variable has at least one root.

The solution to calculate the Z coordinate of the target is:

According to the result of formula (9), the solutions to calculate the X and Y coordinates of the target respectively are:

Using the results of equations (9)-(11), the possible target positions are obtained as T ₁ (x ₁ , y ₁ , z ₁ ) and T ₂ (x ₂ , y ₂ , z ₂ ) respectively.

4) Check the target position obtained in step 3).

In the embodiment of the present invention, the following 2 test conditions are adopted to eliminate the false alarm caused by the target wrong position solution:

First, the correct target position must satisfy the observation equations;

Second, the correct target location must be consistent with other intelligence. For example, when the altimetry radar detects a target, the target is within the horizontal wide beam range of the altimeter radar, thereby limiting the target azimuth within a certain range, which can be used to check the correct target position.

Through inspection, the method of this embodiment will definitely remove an erroneous position and retain only one position, and the reserved position is the final target positioning result.

Claims (4)

1. A multi-station positioning and tracking method based on a pitch angle is characterized by comprising the following steps:

randomly selecting 4 radar observation stations, wherein 3 radar observation stations are not collinear;

establishing a target position equation according to the pitch angles of the 4 radar observation stations to the target;

solving the target position equation to obtain an initial solution of the target position;

and checking the initial solution of the target position to obtain a final positioning result of the target position.

2. The method of claim 1, wherein establishing a target position equation based on the pitch angles of the 4 radar observation stations to the target comprises:

recording the 4 ground observation stations as S respectively _i (x _i ,y _i ,z _i )，i＝1,2,3,4，x _i ,y _i ,z _i Respectively represent the ith observation station S _i Let T (x, y, z), x, y, z represent XYZ coordinates of the target T, each observation station S _i The measured pitch angle is recorded as theta _i In which S is ₁ ，S ₂ ，S ₄ Representing 3 non-collinear observation stations;

then the observation station S _i The pitch angle to the target T satisfies the observation equation set:

and (3) transforming the formula (1) to obtain a target position equation:

3. the method of claim 2, wherein solving the target position equation to obtain an initial solution for the target position comprises:

order:

obtaining target coordinates (x, y, z) satisfying:

order:

obtaining:

according to

u ₃ x+v ₃ y＝p ₃ z ² +q ₃ z+c ₃ (7)

Bringing formula (6) into formula (7) yields:

(k ₁ u ₃ +k ₂ v ₃ -p ₃ )z ² +(s ₁ u ₃ +s ₂ v ₃ -q ₃ )z+(t ₁ u ₃ +t ₂ v ₃ -c ₃ )＝0 (8)

the solution for the Z coordinate of the target is then:

from the result of equation (9), the solution for the X and Y coordinates of the target is calculated as:

using the results of equations (9) - (11), the initial solutions to the target position are T ₁ (x ₁ ,y ₁ ,z ₁ ) And T ₂ (x ₂ ,y ₂ ,z ₂ )。

4. The method of claim 3, wherein the examining the initial solution of the target location to obtain a final solution of the target location comprises:

and if the initial solution of the target position meets the formula (1) and accords with the observation information, the initial solution is the final solution of the target position.

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