CN112945182B - Observation data-catalogue target association matching method - Google Patents

Observation data-catalogue target association matching method Download PDF

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CN112945182B
CN112945182B CN202110101532.4A CN202110101532A CN112945182B CN 112945182 B CN112945182 B CN 112945182B CN 202110101532 A CN202110101532 A CN 202110101532A CN 112945182 B CN112945182 B CN 112945182B
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李元新
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Shenzhen Weishi Xingchen Technology Co ltd
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Abstract

The invention belongs to the technical field of space situation perception, and particularly relates to an observation data-catalogue target association matching method. According to the method, a three-layer judgment model of the association between the observation data and the catalogued targets is established based on the small difference of the observation position and the forecast position of the space target in space. A first layer: performing preliminary screening on the associated targets based on the reference time space pointing parameters by using the difference between the observation position and the forecast position at the reference time; a second layer: respectively calculating observation residual errors aiming at the primary screening target, and carrying out associated target fine screening based on residual error statistical parameters; and a third layer: for the fine screening objective, the correlation results are preferred based on the optimization principle. The invention solves the problem of getting rid of the dependency of the traditional method on the initial orbit number of the observation arc section, and greatly improves the applicability to the short arc section/ultra-short arc section observation data.

Description

Observation data-catalogue target association matching method
Technical Field
The invention belongs to the technical field of space situation perception, and particularly relates to an observation data-catalogue target association matching method.
Background
With the rapid development of the aerospace technology and space application field, the number of on-orbit spacecrafts is more and more, and the situation of more severe space operation safety is faced. Under the urgent need traction of spacecraft on-orbit collision early warning and space benefit safety maintenance, the technical means of simultaneous multi-target short arc segment detection is gradually adopted for space target cataloging detection, so that the cataloging management of space targets with tens of thousands or even hundreds of thousands of scale orders is realized.
Inventory management is performed on a large batch of space targets, and firstly, the problem of association matching between each observation arc segment and an already-inventoried target (namely observation data-inventory target association matching, data-target association for short) needs to be solved. The traditional method generally adopts a correlation method based on track parameter judgment, firstly carries out initial track determination processing on an observation arc section, then compares the initial track parameters with the track parameters of an catalogued target, and optimizes a correlation result by constructing a proper judgment quantity. The correlation effect of the method is greatly influenced by the initial orbit error. When the arc length of the observation arc section is short or the measurement error is large, the precision of the corresponding initial orbit determination result is unstable, an effective association decision model cannot be constructed at the moment, and quick and accurate data-target association is difficult to realize.
By combining the requirement of large-batch space target inventory management, a universal, rapid and accurate observation data-inventory target association matching method suitable for targets with different observation arc lengths and different track heights is found, and the method is necessary for improving the space target inventory management effect.
Disclosure of Invention
The invention aims to provide an observation data-catalogued target association matching method aiming at the problems, and solves the problem of poor data-target association effect caused by too short observation arc section (or poor measurement precision).
The core of the method is to establish a three-layer judgment model for associating observation data with the catalogued targets based on the small difference of the observation positions and the forecast positions of the space targets in space. A first layer: performing primary screening by using the difference between the observation position and the forecast position at the reference moment; a second layer: respectively calculating observation residual errors aiming at the primary screening target, and carrying out fine screening based on the characteristic quantity of the observation residual errors; and a third layer: the correlation results are optimized based on the optimization principle for the fine screening objective.
The technical scheme of the invention is as follows:
an observation data-inventory target association matching method comprises the following steps:
s1, acquiring observation data: acquiring all n-point observation data of an observation arc section to be correlated through an observation station with known position coordinates, wherein the corresponding observation time is tiI ═ 1,2, …, n; the method comprises the following steps of dividing observation data into two types, wherein the first type is pure angle measurement type observation data, and the second type is distance measurement combined angle measurement type observation data;
s2, calculating the space direction vector of each point observation data
Figure GDA0003555396840000021
Generating a measurement matrix P:
for the first type of observation data, for the orientation/pitch type angle measurement data, the spatial orientation vector is calculated by the following formula:
Figure GDA0003555396840000022
wherein A isiIs tiAzimuth measurement of time of day, EiIs tiA pitch measurement at a time; (ZR)iIs tiA transformation matrix from a time observation station coordinate system to a ground-fixed coordinate system; (HG)iIs tiAt the moment J2000.0, a conversion matrix from an inertial coordinate system to a ground-fixed coordinate system is formed, and superscript T represents matrix transposition operation;
for astronomical right ascension/astronomical declination angle measurement data, a spatial orientation vector is calculated by the following formula:
Figure GDA0003555396840000023
wherein alpha isiIs tiAstronomical right ascension measurement at time, deltaiIs tiAn astronomical declination measurement at a time;
for the second type of observation, the spatial orientation vector is calculated by:
Figure GDA0003555396840000024
Figure GDA0003555396840000025
Figure GDA0003555396840000026
where ρ isiIs tiThe observed value of the distance at the moment of time,
Figure GDA0003555396840000027
is tiThe position vector of the observation station in the J2000.0 inertial coordinate system at the moment,
Figure GDA0003555396840000028
is tiObserving a position vector of the station in a ground-fixed coordinate system at a moment;
spatial pointing vector using point-by-point computation
Figure GDA0003555396840000031
Generating a measurement matrix P:
Figure GDA0003555396840000032
s3, calculating a space orientation vector of the reference time:
constructing a characteristic polynomial matrix by adopting a quadratic polynomial fitting model:
Figure GDA0003555396840000033
wherein, Δ ti＝ti-tref，tref＝tmFor the purpose of reference to the time of day,
Figure GDA0003555396840000034
symbol [ 2 ]]For rounding operation;
defining a polynomial fitting coefficient matrix:
Figure GDA0003555396840000035
and (3) solving a fitting coefficient by adopting a least square estimation method:
C＝(ATA)-1AT·P
and calculating a spatial orientation vector of the reference moment by using the fitting coefficient result:
Figure GDA0003555396840000036
s4, performing associated target primary screening based on the spatial orientation parameters at the reference moment:
setting all the cataloged targets as initial candidate targets, acquiring the number of tracks of all the initial candidate targets, and setting the number of the initial candidate targets to be N0All the initial candidate targets are numbered in sequence according to Arabic numerals;
starting from an initial candidate target with the number 1, the following steps are sequentially executed:
s41, performing track extrapolation prediction according to the track number of the current initial candidate target, and calculating the target position at the reference time
Figure GDA0003555396840000041
According to the type of the measured data, calculating the forecast space directional vector of the initial candidate target I
Figure GDA0003555396840000042
For the first type of observation:
Figure GDA0003555396840000043
wherein the content of the first and second substances,
Figure GDA0003555396840000044
is a reference time tmA position vector of the time observation station in a J2000.0 inertial coordinate system;
for the second type of observation:
Figure GDA0003555396840000045
s42, judging whether the current initial candidate target passes the primary screening, if so, adding the current target into a primary candidate set, otherwise, adding 1 to the number of the current initial candidate target, and returning to the step S41 until the number is N0Step S5 is entered; the specific method for judging whether the current initial candidate target passes the initial screening comprises the following steps:
for the first type of observation data, the judgment condition is that:
θ≤gθ
Figure GDA0003555396840000046
where, | | is the vector modulo operation, gθPointing the vector to a consistency decision threshold;
for the second type of observation data, the judgment conditions are as follows:
Figure GDA0003555396840000047
Figure GDA0003555396840000048
wherein, gθPointing the vector to a consistency decision threshold, grA vector magnitude consistency judgment threshold;
s5, counting the number of the primary candidate sets and setting the number as N1(ii) a Judgment of N1If yes, the flag association result is 0, and the process proceeds to step S8; otherwise, go to step S6;
s6, performing associated target fine screening based on the observation residual characteristic parameters:
setting the catalogued targets in the primary candidate set as primary candidate targets, numbering the primary candidate targets in the primary candidate set according to Arabic numerals, and sequentially executing the following steps from the primary candidate target with the number of 1:
s61, using the number of the current primary candidate target to do track extrapolation forecast, calculating the target position corresponding to each observation time
Figure GDA0003555396840000051
S62, calculating the actual measurement space pointing vector of each observation point
Figure GDA0003555396840000052
And forecasting spatial pointing vectors
Figure GDA0003555396840000053
For the first type of observation:
Figure GDA0003555396840000054
Figure GDA0003555396840000055
for the second type of observation:
Figure GDA0003555396840000056
Figure GDA0003555396840000057
s63, judging whether the current primary candidate target passes the fine screening, if so, adding the current target into a secondary candidate set, otherwise, adding 1 to the number of the current primary candidate target, and returning to the step S61 until the number is N0Step S7 is entered; the specific method for judging whether the current primary candidate target passes through the fine screening comprises the following steps:
for the first type of observation data, the judgment condition is that:
Figure GDA0003555396840000058
Figure GDA0003555396840000059
Figure GDA0003555396840000061
Figure GDA0003555396840000062
Figure GDA0003555396840000063
Figure GDA0003555396840000064
wherein, gsdev_θ、grmse_θ、
Figure GDA0003555396840000065
Respectively, an angle observation residual standard deviation, a root mean square error and a Slope decision threshold, Sdev (theta) is the angle observation residual standard deviation, Rmse (theta) is the angle observation residual root mean square error, Slope (theta) is the angle observation residual Slope, and coefficients
Figure GDA0003555396840000066
Solving by first order polynomial fitting:
Figure GDA0003555396840000067
Figure GDA0003555396840000068
Figure GDA0003555396840000069
Figure GDA00035553968400000610
wherein, Δ ti＝ti-t1Is the relative observation time;
for the second type of observation data, the judgment conditions are as follows:
Figure GDA00035553968400000611
Figure GDA00035553968400000612
Figure GDA00035553968400000613
Figure GDA0003555396840000071
Figure GDA0003555396840000072
Figure GDA0003555396840000073
wherein, gsdev_△、grmse_△、gslope_△Respectively as position observation residual standard deviation, root mean square error and Slope decision threshold, Sdev (delta) is position observation residual standard deviation, Rmse (delta) is position observation residual root mean square error, Slope (delta) is position observation residual Slope, coefficient
Figure GDA0003555396840000074
Solving through first-order polynomial fitting;
Figure GDA0003555396840000075
Figure GDA0003555396840000076
Figure GDA0003555396840000077
s7, counting the number of the secondary candidate sets, and setting the number as N2(ii) a Judgment of N2If yes, the flag association result is 0, and the process proceeds to step S9; otherwise, go to step S8;
s8, setting the cataloged targets in the secondary candidate set as secondary candidate targets, and starting from N2Selecting a target with the minimum observation residual root mean square error from the secondary candidate targets, recording the number of the target, and identifying the target as a correlation result;
and S9, returning the association result identification and ending the association.
The invention has the beneficial effects that: according to the invention, the spatial orientation parameters of the observation arc section are directly constructed, and the association matching between the observation arc section and the cataloged target can be accurately and efficiently completed based on the three-layer judgment of the combination of the spatial orientation parameters and the residual statistical parameters. Wherein:
1. the initial screening association decision quantity constructed by the reference time space pointing vector is adopted for association initial screening, so that the dependence of the traditional method on the number of observation arc initial rails is eliminated, and the applicability to short arc section/ultra-short arc section observation data is greatly improved;
2. the influence of factors such as measurement errors, track prediction errors, track extrapolation model errors and the like is fully considered, and the association fine screening is carried out by adopting the characteristic quantity combined judgment of observation residual statistical standard deviation, root mean square errors, slopes and the like, so that the data-target association accuracy is improved;
3. the method has strong universality and is suitable for data-target association processing of various types of angle measurement data of the sky/foundation and combined angle measurement data of distance measurement.
Drawings
FIG. 1 is a flow chart of data-target association based on joint decision of spatial orientation parameters and residual statistical parameters;
Detailed Description
The technical scheme of the invention is further described in detail by combining the attached drawings:
the implementation scheme of the invention mainly comprises four parts, namely reference time space pointing parameter construction based on polynomial fitting, associated target primary screening based on the reference time space pointing parameter, associated target fine screening based on residual statistical parameter, and associated target optimization.
(I) constructing reference time space pointing parameters
The reference time is typically chosen to be the observation time of the middle data point of the observation arc. In order to reduce the influence of the measurement outlier, polynomial fitting is carried out by adopting all observation arc section data, and the spatial pointing parameter of the reference moment is calculated.
1. Spatial orientation parameter definition
For pure goniometric observation data (class i), the spatial orientation parameters are defined as orientation vectors pointing from the observation station to the spatial target; for range-finding joint goniometric observation (class ii), the spatial orientation parameter is defined as the distance vector from the earth's center to the spatial target. Both types of vectors are defined in a J2000.0 inertial coordinate system, the former is defined as a standing-center rectangular coordinate system, and the latter is defined as a ground-center rectangular coordinate system. The two types of space direction vectors are respectively:
Figure GDA0003555396840000081
Figure GDA0003555396840000082
2. calculation of spatial orientation parameters corresponding to different types of measurement data
For the azimuth/elevation angle measurement data, the calculation formula of the space direction vector corresponding to each observation point is as follows:
Figure GDA0003555396840000091
wherein A is an azimuth measurement value, and E is a pitch measurement value; (ZR) is a transformation matrix from a coordinate system of the measuring station to a ground-fixed coordinate system; (HG) is a conversion matrix from the J2000.0 inertial coordinate system to the earth-fixed coordinate system, and superscript T represents the matrix transposition operation.
For the astronomical right ascension/astronomical declination angle measurement data, the calculation formula of the space direction vector corresponding to each observation point is as follows:
Figure GDA0003555396840000092
wherein, alpha is an astronomical right ascension measurement value, and delta is an astronomical declination measurement value;
for the measurement data of distance measurement/angle measurement (azimuth/elevation), the calculation formula of the space direction vector corresponding to each observation point is as follows:
Figure GDA0003555396840000093
wherein the content of the first and second substances,
Figure GDA0003555396840000094
is the position vector of the observation station in the earth-fixed coordinate system.
3. Reference time spatial pointing parameter calculation
Fitting the multi-point observation data in the observation arc section by using a quadratic polynomial to obtain a space pointing vector of the reference moment.
Using n observation points (corresponding observation times are t respectively)1,t2,…,tn) Respectively calculate corresponding spatial directional vectors
Figure GDA0003555396840000095
Generating a measurement matrix P:
Figure GDA0003555396840000096
constructing a characteristic polynomial matrix by adopting a quadratic polynomial fitting model:
Figure GDA0003555396840000101
wherein, Δ ti＝ti-tref，tref＝tmFor the purpose of reference to the time of day,
Figure GDA0003555396840000102
symbol [ 2 ]]Is a rounding operation.
Defining a polynomial fitting coefficient matrix:
Figure GDA0003555396840000103
and (3) solving a fitting coefficient by adopting a least square estimation method:
C＝(ATA)-1AT·P (9)
and calculating a spatial orientation vector of the reference moment by using the fitting coefficient result:
Figure GDA0003555396840000104
(II) performing associated target primary screening based on reference time space pointing parameters
Respectively carrying out orbit extrapolation prediction on all catalogued targets (initial candidate targets) by using corresponding orbit roots, and calculating the position vector of the inertial system of the target at the reference moment
Figure GDA0003555396840000105
Generating a corresponding forecast spatial directional vector; constructing a preliminary screening association judgment conditional expression by using the reference time space pointing vector; and the catalogued targets meeting the judgment conditions are used as primary candidate targets for subsequent further association fine screening through primary screening.
1. Target association primary screen for class I observation data
For class i observation data, the predictor space pointing vector is:
Figure GDA0003555396840000106
wherein the content of the first and second substances,
Figure GDA0003555396840000107
is the inertial system position vector of the measuring station at the reference moment.
The preliminary screening association decision quantity constructed by using the reference time space direction vector is as follows:
Figure GDA0003555396840000111
wherein, | | is a vector modulo operation.
The preliminary screening association judgment condition formula is as follows:
θ≤gθ (13)
wherein, gθThe vectors are directed to a consistency decision threshold.
2. Target association preliminary screening of class II observation data
For class ii observation data, the predictor space pointing vector is:
Figure GDA0003555396840000112
the preliminary screening association decision quantity constructed by utilizing the reference time space direction vector is as follows:
Figure GDA0003555396840000113
the preliminary screening association judgment condition formula is as follows:
Figure GDA0003555396840000114
wherein, gθPointing the vector to a consistency decision threshold, grAnd the vector amplitude consistency judgment threshold is obtained.
(III) performing associated target fine screening based on observation residual characteristic parameters
For each candidate target passing through the preliminary screening, calculating the spatial position/speed of the inertial system of the target at each observation moment point by using the corresponding track number to obtain a forecast spatial direction vector (calculated value C); and comparing the vector with a space orientation vector (measured value O) corresponding to an actual observation result to obtain an observation residual error (O-C) vector. Calculating statistical parameters of the generated observation residual vector sequence, and constructing a fine screening association judgment condition formula; and (4) carrying out fine screening on the candidate cataloging targets meeting the judgment condition, and entering a subsequent association optimization link (secondary candidate targets).
1. Track extrapolation prediction
Generating a matched orbit extrapolation model by using the orbit number, carrying out orbit extrapolation prediction, and calculating to obtain a position velocity vector time sequence of the target inertial system at each observation time
Figure GDA0003555396840000121
2. Target associated fine screen for class I observation data
For class i observation data, the predictor space pointing vector is:
Figure GDA0003555396840000122
wherein the content of the first and second substances,
Figure GDA0003555396840000123
in order to predict the spatial position vector,
Figure GDA0003555396840000124
is the inertial system position vector of the survey station at a specific observation time.
Constructing a fine screening associated decision quantity by using a space direction vector predicted value and an actual measurement value and taking an angle observation residual error as a parameter:
Figure GDA0003555396840000125
and respectively calculating characteristic parameters of the angle observation residual time sequence. The method comprises the following steps: residual standard deviation Sdev (theta), residual root mean square error Rmse (theta) and residual Slope (theta). Wherein:
Figure GDA0003555396840000126
Figure GDA0003555396840000127
Figure GDA0003555396840000128
solving coefficients by fitting a first order polynomial
Figure GDA0003555396840000129
The specific method comprises the following steps:
Figure GDA00035553968400001210
Figure GDA00035553968400001211
Figure GDA00035553968400001212
Figure GDA0003555396840000131
wherein, Δ ti＝ti-t1Is the relative observation time.
The fine screening association judgment condition formula is as follows:
Figure GDA0003555396840000132
wherein, gsdev_θ、grmse_θ、
Figure GDA0003555396840000133
The judgment thresholds are respectively angle observation residual standard deviation, root mean square error and slope。
3. Target-associated fine screen for class II observation data
For class ii observation data, the predictor space pointing vector is:
Figure GDA0003555396840000134
wherein, among others,
Figure GDA0003555396840000135
to predict the spatial location vector.
Constructing a fine screening associated decision quantity by using a space direction vector predicted value and an actual measurement value and taking a position observation residual error as a parameter:
Figure GDA0003555396840000136
and respectively calculating characteristic parameters of the position observation residual time sequence. The method comprises the following steps: residual standard deviation Sdev (Δ), residual root mean square error Rmse (Δ), and residual Slope (Δ). Wherein:
Figure GDA0003555396840000137
Figure GDA0003555396840000138
Figure GDA0003555396840000139
solving coefficients by fitting a first order polynomial
Figure GDA00035553968400001310
The specific method comprises the following steps:
Figure GDA00035553968400001311
Figure GDA0003555396840000141
Figure GDA0003555396840000142
Figure GDA0003555396840000143
wherein, Δ ti＝ti-t1Is the relative observation time.
The fine screening association judgment condition formula is as follows:
Figure GDA0003555396840000144
wherein, gsdev_△、grmse_△、gslope_△The standard deviation of the position observation residual error, the root mean square error and the slope judgment threshold are respectively.
(IV) associated target preference determination
And if a plurality of candidate targets (secondary candidate targets) exist after fine screening, selecting and determining a final correlation result according to the principle of minimum root mean square error of the observed residual error.
The specific implementation mode of carrying out data-target association based on the joint judgment of the space pointing parameter and the residual error statistical parameter is that firstly, each point observation data in an observation arc section is utilized to generate a reference moment space pointing vector; secondly, performing primary screening on the associated targets based on the space pointing parameters by using the space position forecasting result of the catalogued targets at the reference moment; respectively calculating the spatial position of each primary candidate cataloged target at each observation moment, and calculating the measured value and the calculated value of the space direction vector, so as to obtain an observation residual sequence related to the space direction vector; carrying out statistical parameter solving on the observation residual sequence to obtain a statistical standard deviation, a root mean square error and a slope, and carrying out associated target fine screening based on the residual statistical parameters; and finally, selecting the catalogue target with the minimum observation residual error root-mean-square error from the secondary candidate catalogue targets obtained after fine screening, and outputting the catalogue target as a final correlation result. The specific steps are shown in figure 1:
1) reading in all n-point observation data of the observation arc segment to be correlated, and recording observation time t corresponding to each group of observation datai(i＝1,2,…,n)。
2) Reading the attribute parameters of the observation station equipment corresponding to the observation arc section, wherein the attribute parameters comprise station address coordinates, measurement types, measurement errors and the like; and setting parameters such as a correlation decision threshold and the like.
3) According to the type of the measurement data, the spatial orientation vector of the observation data at each point is calculated by using the formula (3), the formula (4) or the formula (5), and a measurement matrix P is generated.
4) According to equation (8), a characteristic polynomial matrix a is calculated.
5) And (4) solving a space directional vector fitting coefficient matrix C by adopting a least square estimation method according to the formula (9).
6) According to (10), a spatial orientation vector of the reference time is calculated
Figure GDA0003555396840000151
7) Reading all initial candidate target track number, recording initial candidate target number N0。
8) The initial candidate target number I is set to 1.
9) Performing track extrapolation prediction by using the track number of the initial candidate target I, and calculating the target position at the reference time
Figure GDA0003555396840000152
10) Calculating a forecast spatial orientation vector of the initial candidate target I according to the measurement data type by using the formula (11) or (14)
Figure GDA0003555396840000153
11) And calculating a preliminary screening association decision quantity by using the formula (12) or (15) according to the type of the measurement data.
12) And (4) judging whether the initial candidate target I passes the primary screening or not by using the formula (13) or (16) according to the type of the measured data. And if so, adding the target I into the primary candidate set.
13) And the initial screening candidate target serial number I is I + 1. Judging whether I exceeds N0(ii) a If not, turning to step 9); if yes, recording the number N of primary candidate targets1。
14) If N is present1If yes, identifying the association result as 0 (no association result), and going to step 23); otherwise, the primary candidate target sequence number J is set to 1.
15) Performing track extrapolation prediction by using the track number of the primary candidate target J, and calculating the target position corresponding to each observation time
Figure GDA0003555396840000154
16) Calculating the actual measurement space pointing vector of each observation point according to the measurement data type by using the formula (11) or (14)
Figure GDA0003555396840000155
Calculating the forecast space directional vector of the primary candidate target J by using the formula (17) or (24)
Figure GDA0003555396840000156
17) The observation residual θ of each observation point is calculated by the equation (18) or (25) according to the type of the measurement dataiOr deltai(i＝1,2,…,n)。
18) The observation residual statistical standard deviation, root mean square error and slope are calculated using equations (19) - (22) or equations (26) - (29) depending on the type of measurement data.
19) And (4) judging whether the primary candidate target J passes the fine screening or not by using the formula (23) or (30) according to the type of the measured data. And if so, adding the target J into the secondary candidate set.
20) Fine screening candidate target sequence number J ═J + 1. Judging whether J exceeds N1(ii) a If not, turning to step 15); if yes, recording the number N of secondary candidate targets2。
21) If N is present2If it is 0, the association result is identified as 0 (no association result), and the process goes to step 23).
22) From N2And selecting the target with the minimum observation residual root mean square error from the secondary candidate targets, recording the number of the target, and identifying the target as a correlation result.
23) And returning the association result identifier and exiting.
The design implementation method for performing data-target association based on joint decision of the spatial directional parameters and the residual statistical parameters is finished.

Claims (1)

1. An observation data-inventory target association matching method is characterized by comprising the following steps:
s1, acquiring observation data: acquiring all n-point observation data of an observation arc section to be correlated through an observation station with known position coordinates, wherein the corresponding observation time is tiI ═ 1,2, …, n; the method comprises the following steps of dividing observation data into two types, wherein the first type is pure angle measurement type observation data, and the second type is distance measurement combined angle measurement type observation data;
s2, calculating the space direction vector of each point observation data
Figure FDA0003555396830000011
Generating a measurement matrix P:
for the first type of observation data, for the orientation/pitch type angle measurement data, the spatial orientation vector is calculated by the following formula:
Figure FDA0003555396830000012
wherein A isiIs tiAzimuth measurement of time of day, EiIs tiA pitch measurement at a time; (ZR)iIs tiA transformation matrix from a time observation station coordinate system to a ground-fixed coordinate system; (H)G)iIs tiAt the moment J2000.0, a conversion matrix from an inertial coordinate system to a ground-fixed coordinate system is formed, and superscript T represents matrix transposition operation;
for astronomical right ascension/astronomical declination angle measurement data, a spatial orientation vector is calculated by the following formula:
Figure FDA0003555396830000013
wherein alpha isiIs tiAstronomical right ascension measurement at time, deltaiIs tiAn astronomical declination measurement at a time;
for the second type of observation, the spatial orientation vector is calculated by:
Figure FDA0003555396830000014
Figure FDA0003555396830000015
Figure FDA0003555396830000016
where ρ isiIs tiThe observed value of the distance at the moment,
Figure FDA0003555396830000017
is tiThe position vector of the observation station in the J2000.0 inertial coordinate system at the moment,
Figure FDA0003555396830000021
is tiObserving a position vector of the station in a ground-fixed coordinate system at a moment;
spatial pointing vector using point-by-point computation
Figure FDA0003555396830000022
Generating a measurement matrix P:
Figure FDA0003555396830000023
s3, calculating a space orientation vector of the reference time:
constructing a characteristic polynomial matrix by adopting a quadratic polynomial fitting model:
Figure FDA0003555396830000024
wherein, Δ ti＝ti-tref，tref＝tmFor the purpose of reference to the time of day,
Figure FDA0003555396830000025
symbol [ 2 ]]For rounding operation;
defining a polynomial fitting coefficient matrix:
Figure FDA0003555396830000026
and (3) solving a fitting coefficient by adopting a least square estimation method:
C＝(ATA)-1AT·P
and calculating a spatial orientation vector of the reference moment by using the fitting coefficient result:
Figure FDA0003555396830000027
s4, performing associated target primary screening based on the spatial orientation parameters at the reference moment:
setting all the cataloged targets as initial candidate targets, acquiring the number of tracks of all the initial candidate targets, and setting the number of the initial candidate targets to be N0And for all initial candidatesThe targets are numbered in sequence according to Arabic numbers;
starting from an initial candidate target with the number 1, the following steps are performed in sequence:
s41, performing track extrapolation prediction according to the track number of the current initial candidate target, and calculating the target position at the reference time
Figure FDA0003555396830000031
According to the type of the measured data, calculating the forecast space directional vector of the initial candidate target I
Figure FDA0003555396830000032
For the first type of observation:
Figure FDA0003555396830000033
wherein the content of the first and second substances,
Figure FDA0003555396830000034
is a reference time tmA position vector of the time observation station in a J2000.0 inertial coordinate system;
for the second type of observation:
Figure FDA0003555396830000035
s42, judging whether the current initial candidate target passes the primary screening, if so, adding the current target into a primary candidate set, otherwise, adding 1 to the number of the current initial candidate target, and returning to the step S41 until the number is N0Step S5 is entered; the specific method for judging whether the current initial candidate target passes the initial screening comprises the following steps:
for the first type of observation data, the judgment condition is that:
θ≤gθ
Figure FDA0003555396830000036
where, | | is the vector modulo operation, gθPointing the vector to a consistency decision threshold;
for the second type of observation data, the judgment conditions are as follows:
Figure FDA0003555396830000037
Figure FDA0003555396830000038
wherein, gθPointing the vector to a consistency decision threshold, grA vector magnitude consistency judgment threshold;
s5, counting the number of the primary candidate sets and setting the number as N1(ii) a Judgment of N1If yes, the flag association result is 0, and the process proceeds to step S8; otherwise, go to step S6;
s6, performing associated target fine screening based on the observation residual characteristic parameters:
setting the cataloged targets in the primary candidate set as primary candidate targets, numbering the primary candidate targets in the primary candidate set according to Arabic numerals, and sequentially executing the following steps from the primary candidate target with the number of 1:
s61, using the number of the current primary candidate target to do track extrapolation forecast, calculating the target position corresponding to each observation time
Figure FDA0003555396830000041
S62, calculating the actual measurement space pointing vector of each observation point
Figure FDA0003555396830000042
And forecasting spatial pointing vectors
Figure FDA0003555396830000043
For the first type of observation:
Figure FDA0003555396830000044
Figure FDA0003555396830000045
for the second type of observation:
Figure FDA0003555396830000046
Figure FDA0003555396830000047
s63, judging whether the current primary candidate target passes the fine screening, if so, adding the current target into a secondary candidate set, otherwise, adding 1 to the number of the current primary candidate target, and returning to the step S61 until the number is N0Step S7 is entered; the specific method for judging whether the current primary candidate target passes through the fine screening comprises the following steps:
for the first type of observation data, the judgment condition is that:
Figure FDA0003555396830000048
Figure FDA0003555396830000049
Figure FDA0003555396830000051
Figure FDA0003555396830000052
Figure FDA0003555396830000053
Figure FDA0003555396830000054
wherein, gsdev_θ、grmse_θ、
Figure FDA0003555396830000055
Respectively an angle observation residual standard deviation, a root mean square error and a Slope decision threshold, Sdev (theta) is the angle observation residual standard deviation, Rmse (theta) is the angle observation residual root mean square error, Slope (theta) is the angle observation residual Slope, and a coefficient vector is solved through first-order polynomial fitting
Figure FDA0003555396830000056
Thereby obtaining
Figure FDA0003555396830000057
Coefficient of (2)
Figure FDA0003555396830000058
And
Figure FDA0003555396830000059
Figure FDA00035553968300000510
Figure FDA00035553968300000511
Figure FDA00035553968300000512
Figure FDA00035553968300000513
wherein, Δ ti＝ti-t1Is the relative observation time;
for the second type of observation data, the judgment condition is that:
Figure FDA00035553968300000514
Figure FDA00035553968300000515
Figure FDA0003555396830000061
Figure FDA0003555396830000062
Figure FDA0003555396830000063
Figure FDA0003555396830000064
wherein, gsdev_△、grmse_△、gslope_△Respectively as position observation residual standard deviation, root mean square error and Slope decision threshold, Sdev (delta) is position observation residual standard deviation, Rmse (delta) is position observation residual root mean square error, Slope (delta) is position observation residual Slope, and coefficient vector is solved by first-order polynomial fitting
Figure FDA0003555396830000065
Thereby obtaining
Figure FDA0003555396830000066
Coefficient of (2)
Figure FDA0003555396830000067
And
Figure FDA0003555396830000068
Figure FDA0003555396830000069
Figure FDA00035553968300000610
Figure FDA00035553968300000611
s7, counting the number of the secondary candidate sets, and setting the number as N2(ii) a Judgment of N2If yes, the flag association result is 0, and the process proceeds to step S9; otherwise, go to step S8;
s8, setting the cataloged targets in the secondary candidate set as secondary candidate targets, and starting from N2Selecting a target with the minimum observation residual root mean square error from the secondary candidate targets, recording the number of the target, and identifying the target as a correlation result;
and S9, returning the association result identification and ending the association.
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