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

Multi-station positioning tracking method based on pitch angle Download PDF

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Publication number
CN115144851A
CN115144851A CN202210687249.9A CN202210687249A CN115144851A CN 115144851 A CN115144851 A CN 115144851A CN 202210687249 A CN202210687249 A CN 202210687249A CN 115144851 A CN115144851 A CN 115144851A
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target
target position
equation
observation
pitch angle
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关欣
于昊天
衣晓
周正
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Naval Aeronautical University
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G01S13/68—Radar-tracking systems; Analogous systems for angle tracking only

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  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • Radar Systems Or Details Thereof (AREA)

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

Multi-station positioning tracking method based on pitch angle
Technical Field
The invention belongs to the field of passive positioning, and particularly relates to a multi-station positioning and tracking method based on a pitch angle.
Background
In modern military installations, a large number of radio devices with radiation are used, and passive reconnaissance positioning systems can determine the position of the carrier by positioning the radiation source. The passive reconnaissance positioning system does not radiate electromagnetic signals, has the characteristics of strong anti-interference capability and electromagnetic concealment, and is an important means of electronic countermeasure. The passive positioning system obtains observed quantities containing target space positions, motion states and property characteristics under the condition that a target radiation source has an incoming wave signal, and the observed quantities generally include an incoming wave arrival direction, arrival time, arrival frequency, arrival amplitude and the like. In current research, pitch angle is often used as an auxiliary observation along with other observations to locate and track the target. However, in military countermeasure, due to the existence of a complex electromagnetic environment, active interference measures, limited use of equipment and the like, commonly used observation quantities such as azimuth angles and the like cannot be obtained or the measurement accuracy is poor, so that the conventional positioning method cannot play a role. When only the pitch angle is the reliable observation quantity, a multi-station positioning and tracking method based on the pitch angle has to be developed.
For example, in a normal operation mode, the height measuring radar measures the radial distance of a target by using an active radar or provides a distance parameter by using a plane radar used in cooperation with the active radar, thereby calculating the height of the target. However, in military countermeasure, the active working mode cannot be normally used and the passive working mode cannot be adopted due to special consideration, the radial distance of the target cannot be directly measured, at the moment, the observed quantity only has a pitch angle and an azimuth angle with a large error, and the target cannot be tracked and positioned by using a conventional method.
Disclosure of Invention
The invention aims to fill the blank of overcoming the prior art and provides a multi-station positioning and tracking method based on a pitch angle. 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.
The embodiment provides a multi-station positioning and tracking method based on a pitch angle, which 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.
In a specific embodiment of the present invention, the establishing a target position equation according to the pitch angles of the 4 radar observation stations to the target includes:
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 the XYZ coordinates of the target T, and 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 observatory stations;
then the observation station S i The pitch angle to the target T satisfies the observation equation set:
Figure BDA0003700088970000021
and (3) transforming the formula (1) to obtain a target position equation:
Figure BDA0003700088970000022
in a specific embodiment of the present invention, the solving the target position equation to obtain an initial solution of the target position includes:
order:
Figure BDA0003700088970000023
the target coordinates (x, y, z) are found to satisfy:
Figure BDA0003700088970000024
order:
Figure BDA0003700088970000031
obtaining:
Figure BDA0003700088970000032
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:
Figure BDA0003700088970000033
from the result of equation (9), the solution for the X and Y coordinates of the target is calculated, respectively, as:
Figure BDA0003700088970000034
Figure BDA0003700088970000035
using the results of equations (9) to (11), the initial solutions of the target positions are obtained as T 1 (x 1 ,y 1 ,z 1 ) And T 2 (x 2 ,y 2 ,z 2 )。
In a specific embodiment of the present invention, the checking the initial solution of the target position to obtain a final solution of the target position includes:
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.
The characteristics and beneficial effects of the invention
The method only utilizes the pitch angle to track and position the target, and solves the problem that under specific conditions, when most positioning methods cannot work, the target positioning and tracking with higher precision are realized under limited observation quantity; 2. the invention can enable the height measuring radar to be applied to the field of passive positioning in a passive working mode, expand the application range of the radar and improve the application value.
Drawings
Fig. 1 is a schematic flow chart of a multi-station positioning and tracking method based on a pitch angle in an embodiment of the present invention.
FIG. 2 is a geometric diagram of an observation station observing an object in accordance with an embodiment of the present invention.
Detailed Description
The invention provides a multi-station positioning and tracking method based on a pitch angle, which is further described in detail below by combining the accompanying drawings and specific embodiments.
The embodiment of the invention provides a multi-station positioning and tracking method based on a pitch angle, which 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.
In an embodiment of the present invention, the overall process of the multi-station positioning and tracking method based on pitch angle is shown in fig. 1, and includes the following steps:
1) 4 radar survey stations were arbitrarily chosen, with 3 radar survey stations being non-collinear.
The present invention requires at least 4 observatory stations, where there are 3 observatory stations that are not in a straight line.
When more than 4 observation stations are available, 4 observation stations meeting the non-collinear requirement can be arbitrarily selected for calculation.
2) And establishing a target position equation.
A schematic geometric view of an observation station observing an object in an embodiment of the present invention is shown in fig. 2. In fig. 2, the 4 ground observation stations selected in step 1) are respectively represented as S 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 。
Wherein, let S i (x i ,y i ,z i ) (i =1,2,4) represents 3 stations that are not on a straight line (no order requirement), with the remaining station being S-station 3 (x 3 ,y 3 ,z 3 )；
Observation station S i (i =1,2,3,4) the pitch angle to target T satisfies the observation equation set:
Figure BDA0003700088970000051
and transforming to obtain a target position equation:
Figure BDA0003700088970000052
the formula is a ternary quadratic equation set, the analytical solution of the equation cannot be directly solved, and the analytical solution of the equation can be solved only by performing power reduction processing on the equation set.
3) Solving the target position equation to obtain a target position; the specific method comprises the following steps:
first step of parameter replacement
Order:
Figure BDA0003700088970000053
where cot is cotangent, i.e., cos/sin.
The target coordinates (x, y, z) satisfying the equation can be obtained by simplifying the deformation:
Figure BDA0003700088970000054
performing second-step parameter substitution:
Figure BDA0003700088970000055
by simplifying the deformation:
Figure BDA0003700088970000061
according to
u 3 x+v 3 y＝p 3 z 2 +q 3 z+c 3 (7)
Bringing equation (6) into equation (7) yields an 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)
from the practical significance of the observation system, a quadratic equation with one element has at least 1 root.
The solution to the Z coordinate of the target is calculated as:
Figure BDA0003700088970000062
from the result of equation (9), the solution for the X and Y coordinates of the target is calculated as:
Figure BDA0003700088970000063
Figure BDA0003700088970000064
using the results of equations (9) to (11), the possible positions of the targets are obtained as T 1 (x 1 ,y 1 ,z 1 ) And T 2 (x 2 ,y 2 ,z 2 )。
4) And 3) checking the target position obtained in the step 3).
In the embodiment of the invention, the following 2 detection conditions are adopted to eliminate false alarms caused by target wrong position solutions:
firstly, the correct target position needs to meet an observation equation set;
the correct target location must be consistent with other information. For example, when the height finding radar detects a target, the target is within the horizontal broad beam range of the height finding radar, thereby limiting the target bearing to a range of intervals that can be used to verify the correct target position.
Through inspection, the method of the embodiment certainly removes an error position and only reserves 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:
Figure FDA0003700088960000011
and (3) transforming the formula (1) to obtain a target position equation:
Figure FDA0003700088960000012
3. the method of claim 2, wherein solving the target position equation to obtain an initial solution for the target position comprises:
order:
Figure FDA0003700088960000021
obtaining target coordinates (x, y, z) satisfying:
Figure FDA0003700088960000022
order:
Figure FDA0003700088960000023
obtaining:
Figure FDA0003700088960000024
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:
Figure FDA0003700088960000025
from the result of equation (9), the solution for the X and Y coordinates of the target is calculated as:
Figure FDA0003700088960000026
Figure FDA0003700088960000027
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.
CN202210687249.9A 2022-06-17 2022-06-17 Multi-station positioning tracking method based on pitch angle Pending CN115144851A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115616578A (en) * 2022-12-05 2023-01-17 成都航空职业技术学院 Radar detection method and device for unmanned aerial vehicle

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115616578A (en) * 2022-12-05 2023-01-17 成都航空职业技术学院 Radar detection method and device for unmanned aerial vehicle

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