CN112697146A - Steady regression-based track prediction method - Google Patents

Steady regression-based track prediction method Download PDF

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CN112697146A
CN112697146A CN202011299772.1A CN202011299772A CN112697146A CN 112697146 A CN112697146 A CN 112697146A CN 202011299772 A CN202011299772 A CN 202011299772A CN 112697146 A CN112697146 A CN 112697146A
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prediction
coefficient
time
slope
measurement
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CN112697146B (en
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张英静
邱天
权晓岚
刘明阳
臧振宇
吴天昊
温嘉奇
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Beijing Institute of Electronic System Engineering
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C1/00—Measuring angles

Abstract

One embodiment of the invention discloses a flight path prediction method based on robust regression, which comprises the following steps: s10: acquiring a measurement value of an information source; s13: calculating a prediction coefficient; s15: calculating a weighted prediction coefficient; s17: and judging whether the iteration times are met, if so, ending, and otherwise, performing S15. According to the method, different weights are given to the measurement data according to the measurement residual errors, so that the influence of outliers on prediction is reduced, and the prediction precision is improved.

Description

Steady regression-based track prediction method
Technical Field
The present invention relates to the field of target tracking. More particularly, the invention relates to a robust regression-based flight path prediction method
Background
The target track prediction means that characteristic parameters such as the position state, the speed state and the like of the target at the current time or the future time are predicted based on the information source measurement information. The target track prediction can predict track state information in advance, and support is provided for firepower distribution and threat assessment. The traditional target track prediction adopts a least square method to carry out track fitting, however, in reality, due to the influence of climate, terrain and interference, the measured information inevitably has wild values, and the least square calculation method has to be migrated to the wild values in order to achieve the purpose of minimizing the sum of squares of residual errors, so that the prediction is inaccurate.
Disclosure of Invention
In view of the above, a first embodiment of the present invention provides a robust regression-based flight path prediction method, including:
s10: acquiring a measurement value of an information source;
s13: calculating a prediction coefficient;
s15: calculating a weighted prediction coefficient;
s17: and judging whether the iteration times are met, if so, ending, and otherwise, performing S15.
In a specific embodiment, the S10 includes:
selecting M information sources as target information sources, obtaining the measurement values of the information sources according to a sensor arranged on the target information sources,
P_t＝{R_t,A_t,E_t}
wherein, P _ t represents the M measurement set at the t-th time, R _ t represents the slope distance at the t-th time, A _ t represents the azimuth at the t-th time, and E _ t represents the pitch angle value at the t-th time.
In one embodiment, a fitting function is constructed based on the prediction coefficients, the fitting function is divided into a pitch fitting function, an azimuth fitting function, and a pitch fitting function,
the function of the skew-fit is RP ═ R β0+Rβ1t, wherein R β0And R beta1The coefficients are predicted for the fitting function.
In a specific embodiment, the S15 includes:
s151: randomly selecting moments t1, t2,. tM with measurement values, acquiring the measurement values of M target information sources at the moment with the measurement values, and calculating prediction residue values;
s153: calculating coefficient weight according to the prediction residual error;
s155: and calculating a measurement weighted prediction coefficient vector according to the coefficient weight.
In a particular embodiment, the prediction residual values include a pitch prediction residual value, an azimuth prediction residual value, and a pitch prediction residual value;
the residual value of the slope distance prediction at the time t1 is:
Re_t1＝Rβ0+Rβ1×t1-R_t1。
in a specific embodiment, the coefficient weights include a pitch coefficient weight, an azimuth coefficient weight, and a pitch coefficient weight, wherein
The slope coefficient weight at the time t1 is
Figure BDA0002786437680000021
Figure BDA0002786437680000022
Constant, Rl is the slope measurement residual measure at time t1,
Rl＝Median(|Re_t1-Median(Re_t1,Re_t2...,Re_tM)|，|Re2-Median(Re_t1,Re_t2...,Re_tM)|,...,
|Re_tM-Median(Re_t1,Re_t2...,Re_tM)|)/η,
wherein, Median is the Median of the variables; η is a constant.
In one embodiment, the measured weighted prediction coefficient vector comprises a pitch measured weighted prediction coefficient vector, an azimuth measured weighted prediction coefficient vector, and a pitch measured weighted prediction coefficient vector, wherein,
the vector of the slope measurement weighted prediction coefficient is
Figure BDA0002786437680000023
Wherein the weight vector W of the slope coefficient is
W＝[Rw_t1,Rw_t2,L,Rw_tM]T
Rw _ t2, which is the slope coefficient weight at the time t2, and Rw _ tM is the slope coefficient weight at the time tM;
actual measurement of the skew S is
S＝[R_t1，R_t2，L，R_tM]T
R _ t1 represents the slope distance at time t1, R _ t2 represents the slope distance at time t2, and R _ tM represents the slope distance at time tM
The independent variable matrix X is
Figure BDA0002786437680000024
In a specific embodiment, the parameter relationship for obtaining a certain confidence probability according to the basic parameters of the target information source is as follows:
1-p＝(1-wM)k
wherein M is the number of target information sources, p is the confidence probability, w is the proportion of the local points in the observation data, and w isMProbability that the measured data of M target information sources are local points, 1-wMIs the probability that at least one point in the measured data of M target information sources is an out-of-office point, k is the iteration number of the method, (1-w)M)kMeans that the method never chooses the probability that the M measured data are all local points;
according to the formula, obtaining the iteration times k,
Figure BDA0002786437680000031
a second embodiment of the invention provides a computer device comprising a processor and a memory stored with a computer program, the processor implementing the method according to any one of the first embodiment when executing the program.
A third embodiment of the invention provides a computer-readable storage medium, on which a computer program is stored which, when executed by a processor, implements the method according to any one of the first embodiments.
The invention has the following beneficial effects:
the invention provides a robust regression-based track prediction method, which endows different weights to measured data according to measurement residual errors, thereby reducing the influence of outliers on prediction and improving the prediction precision.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a system architecture diagram of a robust regression-based track prediction method according to an embodiment of the present invention.
FIG. 2 shows a flow diagram of a robust regression-based flight path prediction method according to an embodiment of the invention.
Fig. 3 shows a schematic structural diagram of a computer device according to another embodiment of the present invention.
Detailed Description
In order to make the technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 1, in order to implement a robust regression-based track prediction method system architecture according to an embodiment of the present invention, the system architecture may include an observation data set 101 and a server 103. The information source data set 101 includes a plurality of target information sources, where the target information sources may be any object with flight trajectory, such as an airplane and an unmanned aerial vehicle, and the server 103 is a server providing various services, such as a background server providing support for performing trajectory prediction.
As shown in fig. 2, a robust regression-based flight path prediction method includes:
s10: acquiring a measurement value of an information source;
selecting M information sources as target information sources, obtaining the measurement values of the information sources according to sensors arranged on the information sources,
P_t＝{R_t,A_t,E_t}
wherein, P _ t represents the M measurement set at the t-th time, R _ t represents the slope distance at the t-th time, A _ t represents the azimuth at the t-th time, and E _ t represents the pitch angle value at the t-th time.
S13: calculating a prediction coefficient;
s15: calculating a weighted prediction coefficient;
s151: randomly selecting moments t1, t2 and L tM with measurement values, obtaining the measurement values of M information sources at the moments with the measurement values, and calculating prediction residual values;
s153: calculating coefficient weight according to the prediction residual error;
s155: and calculating a measurement weighted prediction coefficient vector according to the coefficient weight.
S17: and judging whether the iteration times are met, if so, ending, and otherwise, performing S15.
In a specific embodiment, the track prediction is divided into a pitch prediction, an azimuth prediction and a pitch prediction, and here, the pitch prediction is taken as an example, and a person skilled in the art can obtain an azimuth prediction method and a pitch prediction method according to a step of predicting the pitch, which is not described herein in detail.
Randomly selecting one information source from M information sources as a target information source, acquiring a measurement value of the target information source,
P_t＝{R_t,A_t,E_t}
wherein, P _ t represents the M measurement set at the t-th time, R _ t represents the slope distance at the t-th time, A _ t represents the azimuth at the t-th time, and E _ t represents the pitch angle value at the t-th time.
The prediction coefficients are calculated using a least squares method,
fitting a function RP ═ R β from the slope0+Rβ1t, obtaining a fitting function with a prediction coefficient of R beta0And R beta1。
Selecting the moments t1, t2 and L tM of the target information source active measurement, obtaining the measurement values of the target information source at the moments, and calculating the prediction residual error value
The slope prediction residual value of the measured value at the t1 time is calculated as:
Re_t1＝Rβ0+Rβ1×t1-R_t1。
the slope prediction residuals Re _ t2, Re _ t3 and L Re _ tM at the time of t2, t3 and L tM can be obtained by the person skilled in the art according to the step of obtaining Re _ t1
Using the slope prediction residual value to calculate the slope coefficient weight as
Figure BDA0002786437680000051
Figure BDA0002786437680000052
Taking the slope distance as a constant value, taking the slope distance as 1.345 and Rl as a residual error measurement scale,
Rl＝Median(|Re_t1-Median(Re_t1,Re_t2...,Re_tM)|，|Re2-Median(Re_t1,Re_t2...,Re_tM)|,...,
|Re_tM-Median(Re_t1,Re_t2...,Re_tM)|)/η,
wherein, Median is the Median of the variables; eta is a constant, taken to be 0.6745.
The skew measurement residual measures Rw _ t2, Rw _ t3 and L Rw _ tM at the time t2, t3 and L tM can be calculated by the person skilled in the art according to the step of obtaining Rw _ t 1.
Calculating a weighted prediction coefficient vector of the slope measure as
Figure BDA0002786437680000053
Wherein the weight vector W of the slope coefficient is
W＝[Rw_t1,Rw_t2,L,Rw_tM]T.
Actual measurement of the skew S is
S＝[R_t1，R_t2，L，R_tM]T
The independent variable matrix X is
Figure BDA0002786437680000054
After the slope measurement weighted prediction coefficient vector of one information source is calculated, adding one to the iteration times, then judging whether the iteration times are met, if not, selecting one information source to calculate the slope measurement weighted prediction coefficient vector of the new information source until the iteration times are met.
The parameter relationship for obtaining a certain confidence probability according to the basic parameters of the target information source is as follows:
1-p＝(1-wM)k
wherein M is the number of target information sources, p is the confidence probability, w is the proportion of the local points in the observation data, and w isMProbability that the measured data of M target information sources are local points, 1-wMIs the probability that at least one point in the measured data of M target information sources is an out-of-office point, k is the iteration number of the method, (1-w)M)kMeans that the method never chooses the probability that the M measured data are all local points;
according to the formula, obtaining the iteration times k,
Figure BDA0002786437680000055
another embodiment of the present invention provides a computer readable storage medium having stored thereon a computer program, which when executed by a processor, implements any combination of one or more computer readable media in a practical application. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the present embodiment, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.
As shown in fig. 3, another embodiment of the present invention provides a schematic structural diagram of a computer device. The computer device 12 shown in FIG. 3 is only an example and should not impose any limitation on the scope of use or functionality of embodiments of the present invention.
As shown in FIG. 3, computer device 12 is in the form of a general purpose computing device. The components of computer device 12 may include, but are not limited to: one or more processors or processing units 16, a system memory 28, and a bus 18 that couples various system components including the system memory 28 and the processing unit 16.
Bus 18 represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, such architectures include, but are not limited to, Industry Standard Architecture (ISA) bus, micro-channel architecture (MAC) bus, enhanced ISA bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus.
Computer device 12 typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer device 12 and includes both volatile and nonvolatile media, removable and non-removable media.
The system memory 28 may include computer system readable media in the form of volatile memory, such as Random Access Memory (RAM)30 and/or cache memory 32. Computer device 12 may further include other removable/non-removable, volatile/nonvolatile computer system storage media. By way of example only, storage system 34 may be used to read from and write to non-removable, nonvolatile magnetic media (not shown in FIG. 3, and commonly referred to as a "hard drive"). Although not shown in FIG. 3, a magnetic disk drive for reading from and writing to a removable, nonvolatile magnetic disk (e.g., a "floppy disk") and an optical disk drive for reading from or writing to a removable, nonvolatile optical disk (e.g., a CD-ROM, DVD-ROM, or other optical media) may be provided. In these cases, each drive may be connected to bus 18 by one or more data media interfaces. Memory 28 may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the invention.
A program/utility 40 having a set (at least one) of program modules 42 may be stored, for example, in memory 28, such program modules 42 including, but not limited to, an operating system, one or more application programs, other program modules, and program data, each of which examples or some combination thereof may comprise an implementation of a network environment. Program modules 42 generally carry out the functions and/or methodologies of the described embodiments of the invention.
Computer device 12 may also communicate with one or more external devices 14 (e.g., keyboard, pointing device, display 24, etc.), with one or more devices that enable a user to interact with computer device 12, and/or with any devices (e.g., network card, modem, etc.) that enable computer device 12 to communicate with one or more other computing devices. Such communication may be through an input/output (I/O) interface 22. Also, computer device 12 may communicate with one or more networks (e.g., a Local Area Network (LAN), a Wide Area Network (WAN), and/or a public network such as the Internet) via network adapter 20. As shown in FIG. 3, the network adapter 20 communicates with the other modules of the computer device 12 via the bus 18. It should be understood that although not shown in FIG. 3, other hardware and/or software modules may be used in conjunction with computer device 12, including but not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data backup storage systems, among others.
The processor unit 16 executes various functional applications and data processing by executing programs stored in the system memory 28, for example, to implement a ranac-based dense object tracking method provided by the embodiment of the present invention.
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be included within the scope of the present invention.

Claims (10)

1. A robust regression-based flight path prediction method is characterized by comprising the following steps:
s10: acquiring a measurement value of an information source;
s13: calculating a prediction coefficient;
s15: calculating a weighted prediction coefficient;
s17: and judging whether the iteration times are met, if so, ending, and otherwise, performing S15.
2. The method according to claim 1, wherein the S10 includes:
selecting M information sources as target information sources, obtaining the measurement values of the information sources according to a sensor arranged on the target information sources,
P_t＝{R_t,A_t,E_t}
wherein, P _ t represents the M measurement set at the t-th time, R _ t represents the slope distance at the t-th time, A _ t represents the azimuth at the t-th time, and E _ t represents the pitch angle value at the t-th time.
3. The method of claim 1, wherein a fitting function is constructed based on the prediction coefficients, the fitting function being divided into a pitch fitting function, an azimuth fitting function, and a pitch fitting function,
the function of the skew-fit is RP ═ R β0+Rβ1t, wherein R β0And R beta1The coefficients are predicted for the fitting function.
4. The method according to claim 1, wherein the S15 includes:
s151: randomly selecting moments t1, t2,. tM with measurement values, acquiring the measurement values of M target information sources at the moment with the measurement values, and calculating prediction residue values;
s153: calculating coefficient weight according to the prediction residual error;
s155: and calculating a measurement weighted prediction coefficient vector according to the coefficient weight.
5. The method of claim 1, wherein the prediction residual values comprise a pitch prediction residual value, an azimuth prediction residual value, and a pitch prediction residual value;
the residual value of the slope distance prediction at the time t1 is:
Re_t1＝Rβ0+Rβ1×t1-R_t1。
6. the method of claim 1, wherein the coefficient weights comprise a pitch coefficient weight, an azimuth coefficient weight, and a pitch coefficient weight, wherein
The slope coefficient weight at the time t1 is
Figure FDA0002786437670000011
Figure FDA0002786437670000012
Constant, Rl is the slope measurement residual measure at time t1,
Rl＝Median(|Re_t1-Median(Re_t1,Re_t2...,Re_tM)|，|Re2-Median(Re_t1,Re_t2...,Re_tM)|,...,|Re_tM-Median(Re_t1,Re_t2...,Re_tM)|)/η,
wherein, Median is the Median of the variables; η is a constant.
7. The method of claim 1 wherein the measured weighted prediction coefficient vector comprises a pitch measured weighted prediction coefficient vector, an azimuth measured weighted prediction coefficient vector, and a pitch measured weighted prediction coefficient vector, wherein,
the vector of the slope measurement weighted prediction coefficient is
Figure FDA0002786437670000021
Wherein the weight vector W of the slope coefficient is
W＝[Rw_t1,Rw_t2,L,Rw_tM]T
Rw _ t2, which is the slope coefficient weight at the time t2, and Rw _ tM is the slope coefficient weight at the time tM;
actual measurement of the skew S is
S＝[R_t1，R_t2，L，R_tM]T
R _ t1 represents the slope distance at time t1, R _ t2 represents the slope distance at time t2, and R _ tM represents the slope distance at time tM
The independent variable matrix X is
Figure FDA0002786437670000022
8. The method of claim 1,
the parameter relationship for obtaining a certain confidence probability according to the basic parameters of the target information source is as follows:
1-p＝(1-wM)k
wherein M is the number of target information sources, p is the confidence probability, w is the proportion of the local points in the observation data, and w isMMeasurements for M target information sourcesAccording to the probability of being local interior points, 1-wMIs the probability that at least one point in the measured data of M target information sources is an out-of-office point, k is the iteration number of the method, (1-w)M)kMeans that the method never chooses the probability that the M measured data are all local points;
according to the formula, obtaining the iteration times k,
Figure FDA0002786437670000023
9. a computer device comprising a processor and a memory having stored thereon a computer program, characterized in that the processor, when executing the program, implements the method according to any of claims 1-7.
10. A computer-readable storage medium, on which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1-7.
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