High-precision trajectory extrapolation method and system based on instantaneous inertial coordinate system

Abstract

The present invention provides a high-precision trajectory extrapolation method and system based on an instantaneous inertial coordinate system, the method comprising: according to the prior information conditions obtained by passive radar detection, accurately considering the influence of earth gravity, earth J2 gravity, atmospheric damping and wind, and modeling the ballistic motion equation based on the geocentric instantaneous inertial coordinate system; during active radar detection, converting the radar measurement coordinate system to the geocentric instantaneous inertial coordinate system to obtain projectile measurement data; performing polynomial fitting on the projectile measurement data and the ballistic motion model, deleting points with large fitting errors in the projectile measurement data, performing reverse processing on time and speed, and using the reversely processed data to perform filtered trajectory extrapolation to reduce the trajectory extrapolation error. The present invention accurately models multiple forces, uses an inertial coordinate system to remove the influence of Coriolis inertial force on the projectile motion trajectory; deletes abnormal data through polynomial fitting, uses reverse filtering to improve reconnaissance positioning accuracy, and improves trajectory extrapolation positioning accuracy.

Description

Technical Field

[0001] The present invention relates to the technical field of ballistic target tracking, and in particular to a high-precision trajectory extrapolation method and system based on an instantaneous inertial coordinate system. Background Art

[0002] The artillery position detection and calibration radar is used to detect and track ballistic targets such as artillery, rocket launchers and ballistic missiles in the air. Based on the radar tracking data, it uses data processing and ballistic extrapolation algorithms to calculate the coordinates of the artillery position and the landing point, providing the landing point for its own ballistic calibration and providing accurate artillery position coordinate data for the command and control system to suppress fire.

[0003] Ballistic targets are affected by various complex forces during their motion, such as the gravity of the earth's center of mass, the gravity of the earth's J2 term (J2 term is the earth's dynamic shape factor), atmospheric drag, lift, Magnus force and Coriolis inertial force, etc. These forces have different effects on the trajectory, and the complexity of the force modeling and the required prior information are different.

[0004] The detection range of traditional artillery position detection radar is short, and the requirements for ranging and angle measurement accuracy are low. The trajectory extrapolation uses a simple plane model, and the motion equation of the target is established in the station-centered rectangular coordinate system taking into account the earth's gravity and damping. The trajectory is then extrapolated through sequential filtering. The extrapolation model and process are relatively simple.

[0005] However, with the rapid development of artillery position detection radar and ballistic targets, the range of firepower strike equipment continues to increase, the radar detection power continues to increase, the measurement accuracy requirements are greatly improved, and the requirements for projectile extrapolation accuracy in combat are also getting higher and higher, especially for some low-angle trajectory extrapolation accuracy. In order to improve the accuracy of trajectory extrapolation, in addition to considering the influence of gravity and atmospheric damping, it is also necessary to consider the influence of other forces. It is difficult to accurately model various forces under the traditional plane model.

[0006] Therefore, the existing artillery position detection radar trajectory extrapolation method can no longer meet the needs of long-range reconnaissance, mainly including the following difficulties and shortcomings:

[0007] 1. The ballistic motion model used is a plane model, which is too simple and the trajectory extrapolation accuracy is insufficient;

[0008] 2. The filtering process is relatively simple and does not consider the elimination of abnormal data. These abnormal data have a great impact on the accuracy of reconnaissance and calibration extrapolation. The accuracy of trajectory extrapolation decreases with the increase of forecast time. Summary of the invention

[0009] In view of this, the purpose of the present invention is to propose a high-precision trajectory extrapolation method and system based on an instantaneous inertial coordinate system, introduce the geocentric instantaneous inertial coordinate system, and accurately consider the influence of various complex forces in the geocentric instantaneous inertial coordinate system to improve the accuracy of the ballistic motion model; at the same time, by eliminating abnormal data, the influence of abnormal data is reduced, and in the filtering processing flow, forward and reverse filtering methods are respectively used according to reconnaissance and calibration to improve the accuracy of projectile trajectory extrapolation by gun position detection and calibration radar.

[0010] The present invention provides a high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system, comprising the following steps:

[0011] Based on the prior information conditions obtained by passive radar detection, the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind are accurately considered, and the earth's center instantaneous inertial coordinate system is introduced to model the ballistic motion equation and construct a ballistic motion model;

[0012] The modeling of the present invention adds the influence of the earth's J2 gravity and wind, which improves the accuracy of the ballistic motion model compared to the existing model that only focuses on considering the earth's gravity and atmospheric damping.

[0013] When the radar is actively detecting, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system through coordinate conversion, and the measurement coordinates are converted to the geocentric instantaneous inertial coordinates to obtain the projectile measurement data;

[0014] Specifically, the use of the geocentric instantaneous inertial coordinate system can provide a stable reference benchmark that is not affected by the rotation of the earth, thereby improving the data position accuracy of the measurement point.

[0015] The projectile measurement data is polynomially fitted with the ballistic motion model, points with large fitting errors in the projectile measurement data are deleted, abnormal data are eliminated, and then the projectile measurement data is reversely processed in terms of time and speed, and the data after reverse processing is used for filtering trajectory extrapolation.

[0016] By eliminating abnormal data, the influence of abnormal data on the extrapolation accuracy of reconnaissance and calibration can be avoided, and the problem of the continuous decrease of trajectory extrapolation accuracy with the increase of prediction time can be avoided, thereby reducing the trajectory extrapolation error.

[0017] Furthermore, the method for converting the radar measurement coordinate system to the geocentric instantaneous inertial coordinate system comprises the following steps:

[0018] The radar measurement coordinates ( , , ) converted to radar rectangular coordinates , radar measurement coordinates ( , , ) to radar rectangular coordinates The conversion relationship is:

[0019] (1)

[0020] In formula (1), For distance, is the azimuth angle, is the pitch angle;

[0021] The radar rectangular coordinates Convert to station center coordinates The station center coordinate system is a coordinate system that rotates with the earth with the station center as the origin. Center coordinates of the station The conversion relationship is:

[0022] (2)

[0023] In formula (2), is the latitude of the radar station, is the longitude of the radar station, the rotation matrix function involved in the conversion , and for:

[0024] ;

[0025] ;

[0026] (3)

[0027] In formula (3), Representation vector R Around x Axis rotation θ The transformation of angle, Representation vector R Around y Axis rotation θ The transformation of angle, Representation vector R Around z Axis rotation θ Transformation of angles;

[0028] Calculate the geocentric rectangular coordinates of the radar station and convert the station center coordinates Convert to geocentric rectangular coordinates ;

[0029] The calculation expression of the geocentric rectangular coordinates of the radar station is:

[0030] (4)

[0031] In formula (4) , , are the longitude, latitude, and altitude of the radar station. and are the equatorial radius and flattening corresponding to the earth reference ellipsoid used at the radar station location;

[0032] The conversion relationship from station center coordinates to geocentric rectangular coordinates is:

[0033] (5)

[0034] Geocentric rectangular coordinates Convert to geocentric instantaneous inertial coordinates ,include:

[0035] The time of taking the first observation data is Moment, choice The coordinate system that coincides with the geocentric rectangular coordinate system at all times and does not rotate with the earth is taken as the geocentric instantaneous inertial coordinate system. The coordinate conversion relationship is:

[0036] ;

[0037] (6)

[0038] In formula (6), The data time that needs to be converted into coordinates, in seconds; is the Earth's rotation rate, .

[0039] Furthermore, the ballistic motion model that introduces the earth's center instantaneous inertial coordinate system to model the ballistic motion equation is:

[0040] (7)

[0041] In formula (7), is the position of the projectile in the instantaneous inertial coordinate system of the Earth's center, is the velocity of the projectile in the instantaneous inertial coordinate system at the center of the Earth, The Earth J2 term is included; is the atmospheric damping coefficient, is the wind speed in the instantaneous inertial coordinate system at the center of the earth.

[0042] The ballistic motion model constructed by the present invention adopts the instantaneous inertial coordinate system of the center of the earth, so there is no Coriolis non-inertial force, which improves the accuracy of the model. The Coriolis non-inertial force is related to the mass, rotation speed and rotation radius of the object. Due to the existence of rotation, the earth is not an inertial system, but a rotating reference system, so the movement of particles on the ground will be affected by the Coriolis force (Coriolis force). The Coriolis force in the field of earth science is a component of the Coriolis force in the direction along the surface of the earth.

[0043] Furthermore, the method of performing polynomial fitting of the projectile measurement data and the ballistic motion model comprises:

[0044] The midpoint of the projectile measurement data is selected as the reference point, and the data of the measurement point is fitted using the following second-order polynomial:

[0045] (8)

[0046] In formula (8), , and The projectile targets are Position, velocity and acceleration at a given moment.

[0047] The polynomial fitting method approximates the relationship between a set of data points through a polynomial equation, so that the fitted polynomial equation is as consistent as possible with the actual data. By fitting the main trends of the data of the measurement points, the influence of random noise is reduced.

[0048] Furthermore, the method of deleting points with large fitting errors in the projectile measurement data and eliminating abnormal data includes:

[0049] The position fitting residual of the data of each measuring point is calculated, and the root mean square value of the position fitting deviation is counted. According to 5 times the root mean square value as the threshold, the measuring points with large fitting residual are deleted.

[0050] The present invention determines whether the polynomial fitting has the problem of overfitting or underfitting by analyzing the residual, deletes the measurement points with large fitting residual, and avoids fitting errors.

[0051] Furthermore, the method for performing filtering trajectory extrapolation using the reversely processed data includes:

[0052] The data time of the remaining measurement points after deleting the measurement points with large fitting residuals is adopted Reverse processing to obtain , the calculation formula is:

[0053] (9)

[0054] In formula (9), For the The data time of each measurement point, is the time of the last measurement point. The measurement points are sorted in ascending order of time after reverse processing for subsequent filter trajectory extrapolation.

[0055] Reverse processing refers to the transformation in which the spatial coordinate remains unchanged while the time coordinate changes its sign. It is a transformation that replaces the time variable describing the physical process with its negative quantity, that is, a transformation that reverses the process. The measurement points are sorted in ascending order of time after reverse processing, thereby achieving accurate ballistic extrapolation.

[0056] Furthermore, the method for filtering trajectory extrapolation includes:

[0057] The introduced geocentric instantaneous inertial coordinate system and the constructed ballistic motion model are used for filtering to estimate the position, velocity and damping coefficient of the projectile target, and the ballistic motion model is used for trajectory extrapolation to calculate the gun position or landing point of the projectile.

[0058] The present invention is based on the geocentric instantaneous inertial coordinate system and a newly constructed ballistic motion model, and adopts reverse filtering to filter and remove abnormal measurement points and measurement data, thereby improving the accuracy and reliability of trajectory prediction.

[0059] The present invention also provides a high-precision trajectory extrapolation system based on an instantaneous inertial coordinate system, which executes the high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system as described above, including:

[0060] Building a ballistic motion model module: It is used to accurately consider the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind based on the prior information conditions obtained by passive radar detection, introduce the geocentric instantaneous inertial coordinate system to model the ballistic motion equation, and build a ballistic motion model;

[0061] Coordinate conversion module: used for active radar detection, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system through coordinate conversion, and the measurement coordinates are converted to the geocentric instantaneous inertial coordinates to obtain the projectile measurement data;

[0062] Trajectory extrapolation module: used to perform polynomial fitting on the projectile measurement data and the ballistic motion model, delete points with large fitting errors in the projectile measurement data, eliminate abnormal data, and then perform reverse processing on the projectile measurement data in terms of time and speed, and use the reverse processed data to perform filtered trajectory extrapolation.

[0063] The present invention also provides a computer-readable storage medium having a computer program stored thereon, and when the program is executed by a processor, the steps of the high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system as described above are implemented.

[0064] The present invention also provides a computer device, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system as described above are implemented.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The high-precision trajectory extrapolation method and system based on the instantaneous inertial coordinate system provided by the present invention adopt the geocentric instantaneous inertial coordinate system, can accurately model various forces, describe the motion equation of the projectile in the geocentric instantaneous inertial coordinate system, accurately consider the influence of the geocentric gravity, atmospheric damping, the earth's J2 gravity and wind, and adopt the geocentric instantaneous inertial coordinate system to eliminate the influence of the Coriolis inertial force on the projectile motion trajectory; delete abnormal data through polynomial fitting, reduce the influence of abnormal data on the reconnaissance and correction extrapolation accuracy; adopt reverse filtering to improve the reconnaissance positioning accuracy, reduce the prediction time, and effectively improve the trajectory extrapolation positioning accuracy and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Various other advantages and benefits will become apparent to those of ordinary skill in the art by reading the following detailed description of the preferred embodiment.The drawings are only for the purpose of illustrating the preferred embodiments and are not to be construed as limiting the invention.

[0068] In the attached picture:

[0069] Figure 1 This is a diagram of the high-precision trajectory extrapolation design architecture of a gun position detection and calibration radar based on the geocentric instantaneous inertial coordinate system according to an embodiment of the present invention;

[0070] Figure 2 It is a flow chart of converting the coordinates measured by the artillery position detection radar to the geocentric instantaneous inertial coordinates according to an embodiment of the present invention;

[0071] Figure 3 is a processing flow chart of filtered trajectory extrapolation according to an embodiment of the present invention;

[0072] Figure 4 It is a flow chart of the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system of the present invention;

[0073] Figure 5 The present invention is a flow chart for converting the radar measurement coordinate system and the earth-centered instantaneous inertial coordinate system;

[0074] Figure 6 The figure is a schematic diagram of the structure of a computer device according to an embodiment of the present invention. DETAILED DESCRIPTION

[0075] Exemplary embodiments will be described in detail herein, examples of which are shown in the accompanying drawings. When the following description refers to the drawings, the same numbers in different drawings represent the same or similar elements unless otherwise indicated. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the present disclosure. Instead, they are merely examples of devices and products consistent with some aspects of the present disclosure as detailed in the appended claims.

[0076] The terms used in this disclosure are for the purpose of describing specific embodiments only and are not intended to limit the disclosure. The singular forms of "a", "said" and "the" used in this disclosure and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0077] It should be understood that although the terms first, second, third, etc. may be used in the present disclosure to describe various information, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of the present disclosure, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0078] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0079] The embodiment of the present invention provides a high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system. Figure 4 As shown, the following steps are included:

[0080] S1. Based on the prior information conditions obtained by passive radar detection, the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind are accurately considered, and the earth's center instantaneous inertial coordinate system is introduced to model the ballistic motion equation and construct a ballistic motion model;

[0081] In this embodiment, the ballistic motion model constructed is:

[0082] (7)

[0083] In formula (7), is the position of the projectile in the instantaneous inertial coordinate system of the Earth's center, is the velocity of the projectile in the instantaneous inertial coordinate system at the center of the Earth, is the atmospheric damping coefficient, is the wind speed in the instantaneous inertial coordinate system at the center of the earth.

[0084] The ballistic motion model constructed in this embodiment adopts the geocentric instantaneous inertial coordinate system, and there is no Coriolis non-inertial force.

[0085] S2. When the radar is actively detecting, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system (such as Figure 2 As shown in the figure), the measurement coordinates are converted to the instantaneous inertial coordinates of the center of the earth to obtain the projectile measurement data;

[0086] Specifically, the method for converting the radar measurement coordinate system to the geocentric instantaneous inertial coordinate system includes the following steps (eg Figure 5 shown):

[0087] S21, the radar measurement coordinates ( , , ) converted to radar rectangular coordinates , radar measurement coordinates ( , , ) to radar rectangular coordinates The conversion relationship is:

[0088] (1)

[0089] In formula (1), For distance, is the azimuth angle, is the pitch angle;

[0090] S22, the radar rectangular coordinates Convert to station center coordinates , radar rectangular coordinates Center coordinates of the station The conversion relationship is:

[0091] (2)

[0092] In formula (2), is the latitude of the radar station, is the longitude of the radar station, the rotation matrix function involved in the conversion , and for:

[0093] ;

[0094] ;

[0095] (3)

[0096] In formula (3), Representation vector R Aroundx Axis rotation θ The transformation of angle, Representation vector R Around y Axis rotation θ The transformation of angle, Representation vector R Around z Axis rotation θ Transformation of angles;

[0097] S23, calculate the geocentric rectangular coordinates of the radar station, and convert the station center coordinates Convert to geocentric rectangular coordinates ;

[0098] The calculation expression of the geocentric rectangular coordinates of the radar station is:

[0099] (4)

[0100] In formula (4) , , are the longitude, latitude, and altitude of the radar station. and are the equatorial radius and flattening corresponding to the earth reference ellipsoid used at the radar station location;

[0101] The conversion relationship from station center coordinates to geocentric rectangular coordinates is:

[0102] (5)

[0103] S24, the geocentric rectangular coordinates Convert to geocentric instantaneous inertial coordinates ,include:

[0104] The time of taking the first observation data is Moment, choice The coordinate system that coincides with the geocentric rectangular coordinate system at all times and does not rotate with the earth is taken as the geocentric instantaneous inertial coordinate system. The coordinate conversion relationship is:

[0105] ;

[0106] (6)

[0107] In formula (6), The data time that needs to be converted into coordinates, in seconds; is the Earth's rotation rate, .

[0108] S3, performing polynomial fitting on the projectile measurement data and the ballistic motion model, deleting points with large fitting errors in the projectile measurement data, eliminating abnormal data, and then performing reverse processing on the projectile measurement data in terms of time and speed, and using the reversely processed data to perform filtered trajectory extrapolation, thereby reducing the trajectory extrapolation error (such as Figure 3 as shown).

[0109] The method of performing polynomial fitting of the projectile measurement data and the ballistic motion model is:

[0110] The midpoint of the projectile measurement data is selected as the reference point, and the data of the measurement point is fitted using the following second-order polynomial:

[0111] (8)

[0112] In formula (8), , and The projectile targets are Position, velocity and acceleration at a given moment.

[0113] The method of deleting points with large fitting errors in the projectile measurement data and eliminating abnormal data is as follows:

[0114] The position fitting residual of the data of each measuring point is calculated, and the root mean square value of the position fitting deviation is counted. According to 5 times the root mean square value as the threshold, the measuring points with large fitting residual are deleted.

[0115] The method of using the reverse processed data to perform filtered trajectory extrapolation is:

[0116] The data time of the remaining measurement points after deleting the measurement points with large fitting residuals is adopted Reverse processing to obtain , the calculation formula is:

[0117] (9)

[0118] In formula (9), For the The data time of each measurement point, is the time of the last measurement point. The measurement points are sorted in ascending order of time after reverse processing for subsequent filter trajectory extrapolation.

[0119] The method of filtering trajectory extrapolation is:

[0120] The introduced geocentric instantaneous inertial coordinate system and the constructed ballistic motion model are used for filtering to estimate the position, velocity and damping coefficient of the projectile target, and the ballistic motion model is used for trajectory extrapolation to calculate the gun position or landing point of the projectile.

[0121] Figure 1 The high-precision ballistic design architecture of the gun position detection and correction radar based on the geocentric instantaneous inertial coordinate system of this embodiment is shown.

[0122] The embodiment of the present invention also provides a high-precision trajectory extrapolation system based on an instantaneous inertial coordinate system, which executes the high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system as described above, including:

[0123] Building a ballistic motion model module: It is used to accurately consider the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind based on the prior information conditions obtained by passive radar detection, introduce the geocentric instantaneous inertial coordinate system to model the ballistic motion equation, and build a ballistic motion model;

[0124] Coordinate conversion module: used for active radar detection, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system through coordinate conversion, and the measurement coordinates are converted to the geocentric instantaneous inertial coordinates to obtain the projectile measurement data;

[0125] Trajectory extrapolation module: used to perform polynomial fitting on the projectile measurement data and the ballistic motion model, delete points with large fitting errors in the projectile measurement data, eliminate abnormal data, and then perform reverse processing on the projectile measurement data in terms of time and speed, and use the reverse processed data to perform filtered trajectory extrapolation.

[0126] The embodiment of the present invention further provides a computer device, Figure 6 is a schematic diagram of the structure of a computer device provided by an embodiment of the present invention; see the accompanying drawings Figure 6 As shown, the computer device includes: an input device 23, an output device 24, a memory 22 and a processor 21; the memory 22 is used to store one or more programs; when the one or more programs are executed by the one or more processors 21, the one or more processors 21 implement the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system provided in the above embodiment; wherein the input device 23, the output device 24, the memory 22 and the processor 21 can be connected via a bus or other means, Figure 6 The example of connecting through bus is taken in the following.

[0127] The memory 22 is a readable and writable storage medium of a computing device, which can be used to store software programs and computer executable programs, such as program instructions corresponding to the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system described in the embodiment of the present invention; the memory 22 can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required for a function; the data storage area can store data created according to the use of the device, etc.; in addition, the memory 22 can include a high-speed random access memory, and can also include a non-volatile memory, such as at least one disk storage device, a flash memory device, or other non-volatile solid-state storage device; in some instances, the memory 22 can further include a memory remotely arranged relative to the processor 21, and these remote memories can be connected to the device via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0128] The input device 23 may be used to receive input digital or character information, and to generate key signal input related to user settings and function control of the device; the output device 24 may include a display device such as a display screen.

[0129] The processor 21 executes various functional applications and data processing of the device by running the software programs, instructions and modules stored in the memory 22, that is, realizes the above-mentioned high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system.

[0130] The computer device provided above can be used to execute the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system provided in the above embodiment, and has corresponding functions and beneficial effects.

[0131] The embodiment of the present invention also provides a storage medium containing computer executable instructions, which are used to execute the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system as provided in the above embodiment when executed by a computer processor. The storage medium is any of various types of memory devices or storage devices, and the storage medium includes: installation media, such as CD-ROM, floppy disk or tape device; computer system memory or random access memory, such as DRAM, DDRRAM, SRAM, EDORAM, Rambus RAM, etc.; non-volatile memory, such as flash memory, magnetic media (such as hard disk or optical storage); registers or other similar types of memory components, etc.; the storage medium may also include other types of memory or a combination thereof; in addition, the storage medium may be located in a first computer system in which the program is executed, or may be located in a different second computer system, the second computer system is connected to the first computer system via a network (such as the Internet); the second computer system may provide program instructions to the first computer for execution. The storage medium includes two or more storage media that can reside in different locations (for example, in different computer systems connected via a network). The storage medium can store program instructions (for example, specifically implemented as a computer program) that can be executed by one or more processors.

[0132] Of course, the storage medium containing computer executable instructions provided in an embodiment of the present invention is not limited to the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system as described in the above embodiment, and can also execute related operations in the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system provided in any embodiment of the present invention.

[0133] So far, the technical solutions of the present invention have been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

[0134] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system, characterized in that: The following steps are involved: Based on the prior information conditions obtained by passive radar detection, the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind are accurately considered, and the earth's center instantaneous inertial coordinate system is introduced to model the ballistic motion equation and construct a ballistic motion model; When the radar is actively detecting, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system through coordinate conversion, and the measurement coordinates are converted to the geocentric instantaneous inertial coordinates to obtain the projectile measurement data; Performing polynomial fitting on the projectile measurement data and the ballistic motion model, deleting points with large fitting errors in the projectile measurement data, eliminating abnormal data, and then performing reverse processing on the projectile measurement data in terms of time and speed, and using the reversely processed data to perform filtered trajectory extrapolation; The ballistic motion model that introduces the geocentric instantaneous inertial coordinate system to model the ballistic motion equation is: （7） In formula (7), is the position of the projectile in the instantaneous inertial coordinate system of the Earth's center, is the velocity of the projectile in the instantaneous inertial coordinate system at the center of the Earth, is the atmospheric damping coefficient, is the speed of wind in the instantaneous inertial coordinate system at the center of the earth; The method of performing polynomial fitting of the projectile measurement data and the ballistic motion model comprises: The midpoint of the projectile measurement data is selected as the reference point, and the data of the measurement point is fitted using the following second-order polynomial: （8） In formula (8), , and The projectile targets are Position, velocity and acceleration at each moment; The method of deleting points with large fitting errors in the projectile measurement data and eliminating abnormal data includes: Calculate the position fitting residual of the data of each measuring point, and count the root mean square value of the position fitting deviation, and delete the measuring points with large fitting residual according to 5 times the root mean square value as the threshold; The method for performing filtering trajectory extrapolation using the reversely processed data includes: The data time of the remaining measurement points after deleting the measurement points with large fitting residuals is adopted Reverse processing to obtain , the calculation formula is: （9） In formula (9), For the The data time of each measurement point, is the time of the last measurement point. The measurement points are sorted in ascending order of time after reverse processing for subsequent filter trajectory extrapolation.

2. The high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system according to claim 1 is characterized in that: The method for converting the radar measurement coordinate system to the geocentric instantaneous inertial coordinate system comprises the following steps: The radar measurement coordinates ( , , ) converted to radar rectangular coordinates , radar measurement coordinates ( , , ) to radar rectangular coordinates The conversion relationship is: （1） In formula (1), For distance, is the azimuth angle, is the pitch angle; The radar rectangular coordinates Convert to station center coordinates , radar rectangular coordinates Center coordinates of the station The conversion relationship is: （2） In formula (2), is the latitude of the radar station, is the longitude of the radar station, the rotation matrix function involved in the conversion , and for: ； ； （3） In formula (3), Representation vector R Around x Axis rotation θ The transformation of angle, Representation vector R Around y Axis rotation θ The transformation of angle, Representation vector R Around z Axis rotation θ Transformation of angles; Calculate the geocentric rectangular coordinates of the radar station and convert the station center coordinates Convert to geocentric rectangular coordinates ; The calculation expression of the geocentric rectangular coordinates of the radar station is: （4） In formula (4) , , are the longitude, latitude, and altitude of the radar station. and are the equatorial radius and flattening corresponding to the earth reference ellipsoid used at the radar station location; The conversion relationship from station center coordinates to geocentric rectangular coordinates is: （5） Geocentric rectangular coordinates Convert to geocentric instantaneous inertial coordinates ,include: The time of taking the first observation data is Moment, choice The coordinate system that coincides with the geocentric rectangular coordinate system at all times and does not rotate with the earth is taken as the geocentric instantaneous inertial coordinate system. The coordinate conversion relationship is: ； （6） In formula (6), The data time that needs to be converted into coordinates, in seconds; is the Earth's rotation rate, .

3. The high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system according to claim 1 is characterized in that: The method for filtering trajectory extrapolation includes: The introduced geocentric instantaneous inertial coordinate system and the constructed ballistic motion model are used for filtering to estimate the position, velocity and damping coefficient of the projectile target, and the ballistic motion model is used for trajectory extrapolation to calculate the gun position or landing point of the projectile.

4. A high-precision trajectory extrapolation system based on an instantaneous inertial coordinate system, which executes a high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system as claimed in any one of claims 1 to 3, characterized in that: include: Building a ballistic motion model module: It is used to accurately consider the influence of the earth's gravity, the earth's J2 gravity, atmospheric damping and wind based on the prior information conditions obtained by passive radar detection, introduce the geocentric instantaneous inertial coordinate system to model the ballistic motion equation, and build a ballistic motion model; Coordinate conversion module: used for active radar detection, the radar measurement coordinate system is converted to the geocentric instantaneous inertial coordinate system through coordinate conversion, and the measurement coordinates are converted to the geocentric instantaneous inertial coordinates to obtain the projectile measurement data; Trajectory extrapolation module: used to perform polynomial fitting on the projectile measurement data and the ballistic motion model, delete points with large fitting errors in the projectile measurement data, eliminate abnormal data, and then perform reverse processing on the projectile measurement data in terms of time and speed, and use the reverse processed data to perform filtered trajectory extrapolation.

5. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the high-precision trajectory extrapolation method based on an instantaneous inertial coordinate system described in any one of claims 1 to 3 are implemented.

6. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of the high-precision trajectory extrapolation method based on the instantaneous inertial coordinate system as described in any one of claims 1 to 3 are implemented.

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