CN110646792B - Radar search window setting method based on observation whistle digital telescope - Google Patents

Radar search window setting method based on observation whistle digital telescope Download PDF

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CN110646792B
CN110646792B CN201911067204.6A CN201911067204A CN110646792B CN 110646792 B CN110646792 B CN 110646792B CN 201911067204 A CN201911067204 A CN 201911067204A CN 110646792 B CN110646792 B CN 110646792B
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CN110646792A (en
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张敬卓
陈杰生
季军亮
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Air Force Engineering University of PLA
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    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a radar search window setting method based on an observation whistle digital telescope, which is used for assisting a ground radar to search and capture an aerial target more quickly and accurately. Aiming at the problems that the space condition of a digital telescope of 'observation whistle' is influenced by various factors, the information precision is low, the discreteness is large and the like, a mathematical model of the target motion rule is established, on the basis, the estimation value replaces the observation data, the target distance information is estimated by adopting a least square cross positioning algorithm, the variance between the observation value and the estimation value is obtained through calculation, the variance of the estimation error is obtained through calculation, and a radar search window is accurately set based on the variance of the estimation error. The invention can realize the purpose of quickly and accurately indicating the target.

Description

Radar search window setting method based on observation whistle digital telescope
Technical Field
The invention relates to a radar search window setting method based on an observation whistle digital telescope, which belongs to the field of low-altitude target detection.
Background
The ground radar can obtain the indication information of the target by utilizing the superior air condition or the adjacent air condition of the friend, and performs supplementary search around the indication point, thereby quickly detecting the target. Under the condition of no target indication, the radar needs to be arranged in an omnidirectional or manual mode to autonomously search aerial targets in a large range, and the target capturing period is long. In addition, the ground radar also has the problem of detection blind areas for low-altitude and ultra-low-altitude targets.
The digital telescope-based auxiliary radar detection of the ground observation whistle is a new air condition acquisition means, and the basic idea is that the ground observation whistle utilizes the digital telescope to record low-precision air condition data of a low-altitude maneuvering target, and the target positioning information is acquired and indicated to the ground radar through data processing so as to assist the ground radar to search and capture the air target. However, because the digital telescope air condition lacks distance information, the air condition quality is influenced by geography, meteorological conditions and human factors, the data error is large, and the stability is poor, no relevant technical means for processing the digital telescope air condition data and meeting the radar target indication requirement is found at present. The invention provides search window parameters for radar detection based on digital telescope air condition data.
Disclosure of Invention
The invention provides a radar search window setting method based on a digital telescope of an observation whistle, which aims to make full use of the air condition data of the digital telescope of the ground observation whistle and assist a ground radar to search and capture an aerial target more quickly and accurately.
The technical scheme of the invention is as follows:
a radar search window setting method based on an observation whistle digital telescope is characterized by comprising the following steps:
step 1) acquiring observation data of a moving target based on a single digital telescope:
continuously tracking a moving target by using a single digital telescope A, acquiring observation data and transmitting the observation data to a command information center platform end; the observation data comprises real-time azimuth angle theta and elevation angle of the moving target
Figure BDA0002259768240000026
Step 2) calculating the positioning information of the target relative to the digital telescope A:
2.1) for a non-small-route shortcut target, calculating the azimuth angle and the elevation angle estimated value of the moving target relative to the digital telescope A;
2.1.1) estimation of azimuth
Figure BDA0002259768240000021
The solution is as follows:
Figure BDA0002259768240000022
wherein, { a, tx,θxAcquiring a variation parameter of the azimuth angle of the moving target by utilizing a nonlinear function parameter estimation algorithm according to observation data;
a＝v/rxv is targetedVelocity rxA target airway shortcut is taken;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
θxthe azimuth angle parameter corresponding to the target route shortcut is obtained;
t is a time variable observed for the moving target;
2.1.2) estimation of elevation angles
Figure BDA0002259768240000023
The solution is as follows:
Figure BDA0002259768240000024
wherein, { a, b, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data; b is h/rxH is the height of the target;
2.2) for the small-route shortcut target, only the estimated value of the high and low angles of the moving target relative to the digital telescope A needs to be calculated; estimation of elevation angle
Figure BDA0002259768240000025
The solution is as follows:
Figure BDA0002259768240000031
wherein, { c, d, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data;
t is a time variable observed for the moving target;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the deviation variance of the observed data and the azimuth angle and altitude angle estimated values obtained in the step 2.1):
digital telescope A azimuth angle observation data and estimation value thereof
Figure BDA0002259768240000032
Variance of difference
Figure BDA0002259768240000033
Figure BDA0002259768240000034
Wherein the content of the first and second substances,
Figure BDA0002259768240000035
digital telescope A high-low angle observation data and estimation value thereof
Figure BDA0002259768240000036
Variance of difference
Figure BDA0002259768240000037
Figure BDA0002259768240000038
Wherein the content of the first and second substances,
Figure BDA0002259768240000039
in the formula (I), the compound is shown in the specification,
θiis tiA time azimuth observation value;
Figure BDA00022597682400000310
is tiA time azimuth angle estimation value;
Figure BDA00022597682400000311
is tiA time elevation angle observation value;
Figure BDA00022597682400000312
is tiA time elevation angle estimation value;
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
digital telescope A high-low angle observation data and estimation value thereof
Figure BDA00022597682400000313
Variance of difference
Figure BDA00022597682400000314
Figure BDA00022597682400000315
Wherein the content of the first and second substances,
Figure BDA00022597682400000316
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
4.1) for non-small-route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure BDA0002259768240000041
in the formula, v0To observe the estimate of target velocity by the whistle digital telescope a,
Figure BDA0002259768240000042
azimuth angle and elevation angle estimated values of the moving object relative to the digital telescope A are respectively obtained by 2.1.1) and 2.1.2);
the ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the target relative to the ground-centered radar are then expressed as:
Figure BDA0002259768240000043
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000044
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000045
the slant range of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000046
4.2) for small-route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure BDA0002259768240000047
in the formula, v0In order to observe the estimated value of the whistle digital telescope A to the target speed, theta (t) is the azimuth angle observed value of the moving target relative to the digital telescope A,
Figure BDA0002259768240000048
the estimated value of the elevation angle of the moving target relative to the digital telescope A is obtained by 2.2);
the ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the target relative to the ground-centered radar are then expressed as:
Figure BDA0002259768240000051
in the formula, thetaAIs the azimuthal observation of the target relative to the digital telescope a;
Figure BDA0002259768240000052
is the elevation angle estimated value of the target relative to the digital telescope A;
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000053
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000054
the slant range of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000055
step 5) calculating the variance of the estimation error:
5.1) for a non-small-route shortcut target, calculating the variance of an azimuth angle, a high-low angle and an inclined distance estimation error of the moving target relative to a ground center radar;
variance of azimuth estimation error
Figure BDA0002259768240000056
Calculated by the error transfer equation:
Figure BDA0002259768240000057
variance of high and low angle estimation error
Figure BDA0002259768240000058
Calculated by the error transfer equation:
Figure BDA0002259768240000059
the variance of the skew estimation error is
Figure BDA00022597682400000510
Calculated by the error transfer equation:
Figure BDA00022597682400000511
in the formula (I), the compound is shown in the specification,
Figure BDA00022597682400000512
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
Figure BDA0002259768240000061
the variance of the observation error of the digital telescope A is calculated in the step 3.1);
5.2) for the small-route short-cut target, only calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground center radar;
variance of high and low angle estimation error
Figure BDA0002259768240000062
Calculated by the error transfer equation:
Figure BDA0002259768240000063
the variance of the skew estimation error is
Figure BDA0002259768240000064
Calculated by the error transfer equation:
Figure BDA0002259768240000065
in the formula (I), the compound is shown in the specification,
Figure BDA0002259768240000066
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
step 6), setting a radar search window:
6.1) for non-small-way shortcuts
Setting a radar azimuth search window to (theta-n-sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure BDA0002259768240000067
the slant search window is (R-n.sigma)R,R+n·σR) The value of n is flexibly set according to the performance and the requirement of the radar;
6.2) for small-route shortcuts:
setting the radar azimuth indication as theta, wherein the high-low angle search window is as follows:
Figure BDA0002259768240000068
the slant search window is (R-n.sigma)R,R+n·σR) And the value of n is flexibly set according to the performance and the requirement of the radar.
Further, before step 1), the observation data is preprocessed, specifically as follows:
A. removing repeated data in the observation data, and interpolating:
will t1The observed data of the time are recorded as
Figure BDA0002259768240000069
t2The observed data of the time are recorded as
Figure BDA00022597682400000610
tnThe observed data of the time are recorded as
Figure BDA00022597682400000611
If tiTime and tjTime of day, thetai＝θj，
Figure BDA00022597682400000612
Then order
Figure BDA00022597682400000613
The i ≠ j, i ≠ 1,2, … n, j ≠ 1,2, … n;
B. rejecting excessively deviated data in the observed data, and interpolating:
b1, continuously observing any moving target for multiple times by using a digital telescope to obtain corresponding observation data;
b2, calculating the deviation variance of the observation data with the azimuth angle and elevation angle estimation value of the moving target respectively for the observation data obtained by each continuous observation;
b3, calculating the average value of the variance of the deviation of all the observation angle data obtained in the step B2 and the angle estimation value of the moving target
Figure BDA0002259768240000071
And
Figure BDA0002259768240000072
the mean value of standard deviation is obtained by evolution
Figure BDA0002259768240000073
And
Figure BDA0002259768240000074
b4, respectively enabling the azimuth angle and the elevation angle corresponding to each moment in the observation data in the step 1) to be respectively equal to the standard deviation average value obtained in the step B3
Figure BDA0002259768240000075
And
Figure BDA0002259768240000076
making a comparison, if a certain time tkCorresponding azimuth angle thetakAnd its estimation biasThe mean value of standard deviation is greater than or equal to
Figure BDA0002259768240000077
3-5 times of the azimuth angle thetakIf the deviation is too large, let
Figure BDA0002259768240000078
If a certain time tgCorresponding high and low angles
Figure BDA0002259768240000079
Greater than or equal to the standard deviation average value
Figure BDA00022597682400000710
3-5 times of the angle of elevation, representing the elevation angle
Figure BDA00022597682400000711
If the deviation is too large, let
Figure BDA00022597682400000712
k＝1,2,…n，g＝1,2,…n。
The invention also provides another radar search window setting method based on the observation whistle digital telescope, which is characterized by comprising the following steps of:
step 1) acquiring observation data of the same moving target based on a double digital telescope:
continuously tracking the same moving target by using two digital telescopes with different coordinates, and respectively acquiring observation data; the observation data comprises real-time azimuth angle theta and elevation angle of the moving object relative to the digital telescope
Figure BDA00022597682400000713
Step 2) calculating the positioning information of the target relative to the digital telescope:
2.1) for non-small-route short-cut targets, calculating the estimated values of the azimuth angle and the elevation angle of the moving target relative to each observation whistle digital telescope;
2.1.1) estimation of azimuth
Figure BDA00022597682400000714
The solution is as follows:
Figure BDA00022597682400000715
wherein, { a, tx,θxAcquiring a variation parameter of the azimuth angle of the moving target by utilizing a nonlinear function parameter estimation algorithm according to observation data;
a＝v/rxv is the velocity of the target, rxA target airway shortcut is taken;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
θxthe azimuth angle parameter corresponding to the target route shortcut is obtained;
t is a time variable observed for the moving target;
2.1.2) estimation of elevation angles
Figure BDA0002259768240000081
The solution is as follows:
Figure BDA0002259768240000082
wherein, { a, b, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data; b is h/rxH is the height of the target;
2.2) for the small-route shortcut moving target, only the estimated value of the high and low angles of the moving target relative to each observation whistle digital telescope is needed to be calculated; estimation of elevation angle
Figure BDA0002259768240000083
The solution is as follows:
Figure BDA0002259768240000084
wherein, { c, d, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data;
t is a time variable observed for the moving target;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the deviation variance of the observed data and the azimuth angle and altitude angle estimated values obtained in the step 2.1):
single digital telescope azimuth angle observation data and estimation value thereof
Figure BDA0002259768240000085
Variance of difference
Figure BDA0002259768240000086
Figure BDA0002259768240000087
Wherein the content of the first and second substances,
Figure BDA0002259768240000088
single digital telescope observation height angle measurement data and estimation value thereof
Figure BDA0002259768240000089
Variance of difference
Figure BDA00022597682400000810
Figure BDA0002259768240000091
Wherein the content of the first and second substances,
Figure BDA0002259768240000092
in the formula (I), the compound is shown in the specification,
θiis tiA time azimuth observation value;
Figure BDA0002259768240000093
is tiA time azimuth angle estimation value;
Figure BDA0002259768240000094
is tiA time elevation angle observation value;
Figure BDA0002259768240000095
is tiA time elevation angle estimation value;
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
single digital telescope high-low angle observation data and estimation value thereof
Figure BDA0002259768240000096
Variance of difference
Figure BDA0002259768240000097
Figure BDA0002259768240000098
Wherein the content of the first and second substances,
Figure BDA0002259768240000099
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
4.1) for non-small-route shortcuts:
for the same non-small-route shortcut moving target, the slant range of the target is obtained by adopting a least square cross positioning mode, and the coordinate of the digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure BDA00022597682400000910
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure BDA00022597682400000911
Or
Figure BDA00022597682400000912
The coordinates of the target relative to the ground-centered radar are then:
Figure BDA00022597682400000913
the azimuth angle of the target relative to the ground-centered radar is:
Figure BDA0002259768240000101
the elevation angle of the target relative to the ground center radar is:
Figure BDA0002259768240000102
the target has a slope distance with respect to the ground radar:
Figure BDA0002259768240000103
in the above formula, the first and second carbon atoms are,
Figure BDA0002259768240000104
and
Figure BDA0002259768240000105
respectively obtaining an azimuth angle estimated value and a high-low angle estimated value of a target relative to the digital telescope A;
4.2) for small-route shortcuts:
for the same small-route shortcut moving target, the slant range of the target is obtained by adopting a least square cross positioning mode, and the coordinate of the digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure BDA0002259768240000106
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure BDA0002259768240000107
Or
Figure BDA0002259768240000108
The coordinates of the target relative to the ground-centered radar are then:
Figure BDA0002259768240000109
the azimuth angle of the target relative to the ground-centered radar is:
Figure BDA0002259768240000111
the elevation angle of the target relative to the ground center radar is:
Figure BDA0002259768240000112
the target has a slope distance with respect to the ground radar:
Figure BDA0002259768240000113
in the above formula, θAIs an azimuthal observation of the target relative to the digital telescope a,
Figure BDA0002259768240000114
is the elevation angle estimated value of the target relative to the digital telescope A;
step 5) calculating the variance of the estimation error:
5.1) for the non-small-route short-cut target, calculating the variance of the azimuth angle, the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance calculated in the step 3.1);
variance of azimuth estimation error
Figure BDA0002259768240000115
Figure BDA0002259768240000116
Variance of high and low angle estimation error
Figure BDA0002259768240000117
Figure BDA0002259768240000118
Variance of slope estimation error
Figure BDA0002259768240000119
Figure BDA00022597682400001110
In the formula (I), the compound is shown in the specification,
Figure BDA00022597682400001111
the variance of the observation errors of the digital telescopes A and B is calculated in the step 3.1);
5.2) for the small-route short-cut target, calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance obtained by the calculation in the step 3.2);
variance of high and low angle estimation error
Figure BDA0002259768240000121
Figure BDA0002259768240000122
Variance of slope estimation error
Figure BDA0002259768240000123
Figure BDA0002259768240000124
In the formula (I), the compound is shown in the specification,
Figure BDA0002259768240000125
the variance of the observation errors of the digital telescopes A and B is calculated in the step 3.2);
step 6), setting a radar search window:
6.1) for non-small-route shortcuts:
setting a radar azimuth search window to (theta-n-sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure BDA0002259768240000126
the slant search window is (R-n.sigma)R,R+n·σR) Value of nThe device is flexibly arranged according to the performance and the requirement of the radar;
6.2) for small-route shortcuts:
setting the radar azimuth indication as theta, wherein the high-low angle search window is as follows:
Figure BDA0002259768240000127
the slant search window is (R-n.sigma)R,R+n·σR) (ii) a The value of n is flexibly set according to the performance and the requirement of the radar.
Further, before step 1), data preprocessing is performed on the observation data of each digital telescope, specifically as follows:
A. removing repeated data in the observation data, and interpolating:
will t1The observed data of the time are recorded as
Figure BDA0002259768240000128
t2The observed data of the time are recorded as
Figure BDA0002259768240000129
tnThe observed data of the time are recorded as
Figure BDA00022597682400001210
If tiTime and tjTime of day, thetai＝θj，
Figure BDA00022597682400001211
Then order
Figure BDA00022597682400001212
The i ≠ j, i ≠ 1,2, … n, j ≠ 1,2, … n;
B. rejecting excessively deviated data in the observed data, and interpolating:
b1, continuously observing any moving target for multiple times by using a digital telescope to obtain corresponding observation data;
b2, calculating the deviation variance of the observation data with the azimuth angle and elevation angle estimation value of the moving target respectively for the observation data obtained by each continuous observation;
b3, calculating the average value of the variance of the deviation of all the observation angle data obtained in the step B2 and the angle estimation value of the moving target
Figure BDA0002259768240000131
And
Figure BDA0002259768240000132
the mean value of standard deviation is obtained by evolution
Figure BDA0002259768240000133
And
Figure BDA0002259768240000134
b4, respectively enabling the azimuth angle and the elevation angle corresponding to each moment in the observation data in the step 1) to be respectively equal to the standard deviation average value obtained in the step B3
Figure BDA0002259768240000135
And
Figure BDA0002259768240000136
making a comparison, if a certain time tkCorresponding azimuth angle thetakDeviation from its estimate by a value greater than or equal to the mean of standard deviation
Figure BDA0002259768240000137
3-5 times of the azimuth angle thetakIf the deviation is too large, let
Figure BDA0002259768240000138
If a certain time tgCorresponding high and low angles
Figure BDA0002259768240000139
Greater than or equal to the standard deviation average value
Figure BDA00022597682400001310
3-5 times of the angle of elevation, representing the elevation angle
Figure BDA00022597682400001311
If the deviation is too large, let
Figure BDA00022597682400001312
k＝1,2,…n，g＝1,2,…n。
The invention has the advantages that:
1. the invention can more accurately and dynamically set the radar search window and realize the purpose of quickly and accurately indicating the target.
2. According to the method, the observation data are preprocessed, repeated data and data with excessive deviation are removed, and the setting precision of the radar search window is further improved.
3. The method can acquire the target motion law parameters only by a small number of samples (5-10 observation data), and has high operation speed and strong real-time performance.
4. The air condition error estimation method can be used for evaluating the track quality of the digital telescope and providing support for the air condition recording training of the observation whistle, and the target positioning error can be used as a basis for optimizing the arrangement of the observation whistle.
5. The method can flexibly adapt to the single observation whistle or double observation whistle digital telescope air condition, and when the double observation whistle digital telescope air condition exists, the problem of insufficient information utilization of the traditional positioning algorithm is solved by adopting a least square method cross positioning method.
Drawings
FIG. 1 is a schematic diagram of the recording of air condition data by a watch whistle.
FIG. 2 is a schematic diagram of the composition of the test system.
Figure 3 is a schematic of a view of azimuth data and error estimation for a certain observation.
FIG. 4 is a schematic diagram of elevation data and error estimation for a certain observation.
Fig. 5 is a schematic diagram of some observed azimuth data.
FIG. 6 is a graph of elevation data for a certain observation.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The method for setting the radar search window provided by the invention is divided into two situations, namely an observation mode based on a single digital telescope and an observation mode based on a double digital telescope, which are respectively introduced below.
Single-number telescope-based observation mode
The method for setting the radar search window specifically comprises the following steps:
step 1) acquiring observation data of a moving target based on a single digital telescope:
a single observation whistle digital telescope A continuously tracks a moving target, acquires observation data and transmits the observation data to a command information center platform end; the observation data comprises real-time azimuth angle theta and elevation angle of the moving target
Figure BDA0002259768240000141
Step 2) calculating the positioning information of the target relative to the digital telescope:
2.1) for non-small-way short-cut objects, it is necessary to calculate an estimate of the azimuth of the moving object relative to the digital telescope A
Figure BDA0002259768240000142
Estimation of elevation angle
Figure BDA0002259768240000143
According to the geometric relationship between the target and the observation whistle in the schematic diagram of recording the air situation of the observation whistle in the figure 1, the angle change rule of the moving target is deduced by utilizing the triangle correlation theorem:
2.1.1) estimation of azimuth
Figure BDA0002259768240000144
The solution is as follows:
Figure BDA0002259768240000145
wherein, { a, tx,θxIs the variation parameter of the azimuth angle of the moving target in short timeThe motion state of the target in the interval is kept unchanged, and then the target can be obtained by utilizing a nonlinear function parameter estimation algorithm according to the observation data. The invention adopts Levenberg-Marquardt (LM) method, according to the azimuth data in the observation data, through iterative search, obtain the above formula optimum parameter group { a, tx,θxGet an estimate of the azimuth angle therefrom
Figure BDA0002259768240000151
Optimal parameter set { a, tx,θxThe specific estimation method comprises the following steps:
first, a function e is constructedθAnd
Figure BDA0002259768240000152
then search through the known azimuth and elevation observation data using Levenberg-Marquardt algorithm such that function eθAnd
Figure BDA0002259768240000153
minimized parameter set { a, tx,θxAnd { a, b, t }xObtaining a motion rule parameter of the moving target;
Figure BDA0002259768240000154
Figure BDA0002259768240000155
wherein:
theta (t) is a specific parameter optimal azimuth angle change rule function to be searched and solved; theta is an observed value of the azimuth angle of the moving target;
Figure BDA0002259768240000156
obtaining the optimal high-low angle change rule function of the specific parameters for searching;
Figure BDA0002259768240000157
and (4) obtaining the observed value of the elevation angle of the moving target. 2.1.2) estimation of elevation angles
Figure BDA0002259768240000158
The solving method of (1):
Figure BDA0002259768240000159
wherein, { a, b, txAnd the parameters are the variation parameters of the elevation angle of the moving target, are similar to the azimuth angle, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to the observation data.
2.2) for the moving target with a short-cut small navigation path, only the estimated value of the high and low angles of the moving target relative to the digital telescope A needs to be calculated
Figure BDA00022597682400001510
Estimation of elevation angle
Figure BDA00022597682400001511
The solution is as follows:
Figure BDA00022597682400001512
wherein, { c, d, txAnd the parameters are the variation parameters of the elevation angle of the moving target, are similar to the azimuth angle, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to the observation data.
Optimal parameter set { c, d, txThe specific estimation method is as follows:
first construct a function
Figure BDA0002259768240000161
Then using LM algorithm, searching the function through the known high and low angle observation data
Figure BDA0002259768240000162
Minimized parameter set { c, d, txGet the moving targetA high-low angle change rule parameter;
Figure BDA0002259768240000163
wherein the content of the first and second substances,
Figure BDA0002259768240000164
the optimal high-low angle change law function of the specific parameters is obtained by searching,
Figure BDA0002259768240000165
the observed value of the elevation angle of the moving target is obtained;
step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the deviation variance of the observation data and the azimuth angle and altitude angle estimated values obtained in the step 2.1) by using the following formula:
for a set of observation time series θ ═ θ1,θ2,…,θnAnd
Figure BDA0002259768240000166
the sequence of observation errors can be found:
Δθ＝{Δθ1,Δθ2,…,Δθn}
Figure BDA0002259768240000167
in the formula (I), the compound is shown in the specification,
Figure BDA0002259768240000168
digital telescope azimuth angle observation data and estimation value thereof
Figure BDA0002259768240000169
Variance of difference
Figure BDA00022597682400001610
Figure BDA00022597682400001611
Wherein the content of the first and second substances,
Figure BDA00022597682400001612
high-low angle observation data and estimation value thereof of digital telescope
Figure BDA00022597682400001613
Variance of difference
Figure BDA00022597682400001614
Figure BDA00022597682400001615
Wherein the content of the first and second substances,
Figure BDA00022597682400001616
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
observing time series for a set of high and low angles
Figure BDA00022597682400001617
The sequence of observation errors can be found:
Figure BDA00022597682400001618
in the formula (I), the compound is shown in the specification,
Figure BDA00022597682400001619
high-low angle observation data and estimation value thereof of digital telescope
Figure BDA0002259768240000171
Variance of difference
Figure BDA0002259768240000172
Figure BDA0002259768240000173
Wherein the content of the first and second substances,
Figure BDA0002259768240000174
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
4.1) for non-small route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure BDA0002259768240000175
in the formula, v0In order to observe the estimated value of the sentinel digital telescope A to the target speed, which is a key parameter influencing the target slope distance estimation precision, the target slope distance needs to be estimated according to the target type, as the low altitude penetration target usually adopts a high-speed horizontal linear motion mode, the target speed in engineering can be 190 plus 240m/s, the specific value is determined by the observation sentinel according to experience,
Figure BDA0002259768240000176
respectively an azimuth angle estimated value and a high-low angle estimated value of the moving object relative to the digital telescope A.
The ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the moving target with respect to the ground-centered radar can then be expressed as:
Figure BDA0002259768240000177
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000178
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000179
the slant range of the moving target relative to the ground center radar is as follows:
Figure BDA00022597682400001710
4.2) for small-route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure BDA0002259768240000181
in the formula, v0In order to observe the estimated value of the whistle digital telescope A to the target speed, theta (t) is the azimuth angle observed value of the moving target relative to the digital telescope A,
Figure BDA0002259768240000182
the estimated value of the elevation angle of the moving target relative to the digital telescope A is obtained by 2.2);
the ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the target relative to the ground-centered radar are then expressed as:
Figure BDA0002259768240000183
in the formula, thetaAIs an azimuthal observation of the target relative to the digital telescope a,
Figure BDA0002259768240000184
is the elevation angle estimated value of the target relative to the digital telescope A;
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000185
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000186
the slant range of the moving target relative to the ground center radar is as follows:
Figure BDA0002259768240000187
step 5) calculating the variance of the estimation error:
5.1) for non-small-route short-cut targets, calculating the variance of the estimation errors of azimuth angles, elevation angles and slope distances of the moving targets relative to the ground center radar:
the geographic coordinate of the digital telescope, the azimuth angle and the elevation angle of an observed target have certain errors, and due to an error propagation mechanism, the calculation of the azimuth angle, the elevation angle and the slant range of the target relative to a ground center radar is necessarily influenced by the positioning error and the observation error of the digital telescope; the positioning error of the digital telescope is very small, only 2-3 meters, and the influence of the positioning error relative to the observation error is negligible, so the variance of the azimuth angle estimation error
Figure BDA0002259768240000191
Calculated by the error transfer equation:
Figure BDA0002259768240000192
variance of high and low angle estimation error
Figure BDA0002259768240000193
Calculated by the error transfer equation:
Figure BDA0002259768240000194
the variance of the skew estimation error is
Figure BDA0002259768240000195
Calculated by the error transfer equation:
Figure BDA0002259768240000196
in the formula (I), the compound is shown in the specification,
Figure BDA0002259768240000197
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
Figure BDA0002259768240000198
the variance of the observation error of the digital telescope A is calculated in the step 3.1);
5.2) for the small-route short-cut target, only calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground center radar;
variance of high and low angle estimation error
Figure BDA0002259768240000199
Calculated by the error transfer equation:
Figure BDA00022597682400001910
the variance of the skew estimation error is
Figure BDA00022597682400001911
Calculated by the error transfer equation:
Figure BDA00022597682400001912
in the formula (I), the compound is shown in the specification,
Figure BDA00022597682400001913
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
step 6), setting a radar search window:
for non-small-route shortcuts, the radar search window may be set to be theta,
Figure BDA00022597682400001914
And R is the midpoint, a plurality of times of the upper and lower sigmaθ、
Figure BDA00022597682400001915
And σRSo that the radar azimuth search window is set to (theta-n · sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure BDA0002259768240000201
the slant search window is (R-n.sigma)R,R+n·σR). The value of n is flexibly set according to the performance and the requirement of the radar.
The radar search window should be set to
Figure BDA0002259768240000202
And R is a midpoint which is several times the upper and lower
Figure BDA0002259768240000203
And σRThe range of intervals, therefore, the high-low angle search window is:
Figure BDA0002259768240000204
the slant search window is (R-n.sigma)R,R+n·σR) (ii) a The value of n is flexible according to the performance and the requirement of the radarAnd (4) setting. And setting the radar azimuth indication as theta, and performing small-range search by taking the theta as a center.
Observation mode based on double digital telescopes
The method for setting the radar search window specifically comprises the following steps:
step 1) acquiring observation data of the same moving target based on a double digital telescope:
two observation whistles with different coordinates continuously track the same moving target by using respective digital telescopes to respectively acquire observation data; the observation data comprises real-time azimuth angle theta and elevation angle of the moving object relative to the digital telescope
Figure BDA0002259768240000205
Step 2) calculating the positioning information of the target relative to the digital telescope:
2.1) for non-small-route short-cut targets, calculating the estimated values of the azimuth angle and the elevation angle of the moving target relative to each observation whistle digital telescope;
2.1.1) estimation of azimuth
Figure BDA0002259768240000206
The solution is as follows:
Figure BDA0002259768240000207
wherein, { a, tx,θxAnd acquiring the azimuth angle change parameters of the moving target by utilizing a nonlinear function parameter estimation algorithm according to the observation data.
2.1.2) estimation of elevation angles
Figure BDA0002259768240000208
The solution is as follows:
Figure BDA0002259768240000209
in the formula, { a,b,txthe parameters are the variation parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data, and the specific method is the same as the estimation method in the single digital telescope observation mode.
2.2) for the small-route shortcut moving target, only the estimated value of the high and low angles of the moving target relative to each observation whistle digital telescope is needed to be calculated; estimation of elevation angle
Figure BDA0002259768240000211
The solution is as follows:
Figure BDA0002259768240000212
wherein, { c, d, txThe parameters are the variation parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data, and the specific method is the same as the estimation method in the single digital telescope observation mode.
Step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the variance of the deviation of the observed data and the azimuth angle and altitude angle estimated values obtained in the step 2.1):
single digital telescope azimuth angle observation data and estimation value thereof
Figure BDA0002259768240000213
Variance of difference
Figure BDA0002259768240000214
Figure BDA0002259768240000215
Wherein the content of the first and second substances,
Figure BDA0002259768240000216
single digital telescope observation height angle measurement data and estimation value thereof
Figure BDA0002259768240000217
Variance of difference
Figure BDA0002259768240000218
Figure BDA0002259768240000219
Wherein the content of the first and second substances,
Figure BDA00022597682400002110
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
single digital telescope high-low angle observation data and estimation value thereof
Figure BDA00022597682400002111
Variance of difference
Figure BDA00022597682400002112
Figure BDA00022597682400002113
Wherein the content of the first and second substances,
Figure BDA00022597682400002114
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
for the same non-small-route shortcut moving target, the method adopts a cross positioning mode to obtain the slant range of the target, the invention adopts a least square cross positioning algorithm to estimate the slant range of the target, and the coordinate of a digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure BDA0002259768240000221
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure BDA0002259768240000222
Or
Figure BDA0002259768240000223
The coordinates of the target relative to the ground-centric radar can be expressed as:
Figure BDA0002259768240000224
the azimuth angle of the target relative to the ground-centered radar is:
Figure BDA0002259768240000225
the elevation angle of the target relative to the ground center radar is:
Figure BDA0002259768240000226
the target has the following slant range relative to the ground center radar:
Figure BDA0002259768240000227
in the above formula, the first and second carbon atoms are,
Figure BDA0002259768240000228
and
Figure BDA0002259768240000229
respectively telescopic for the target relative to the numberAn estimated value of the azimuth angle and an estimated value of the elevation angle of the mirror A;
4.2) for small-route shortcuts:
for the same small-route shortcut moving target, the slant range of the target is obtained by adopting a least square cross positioning mode, and the coordinate of the digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure BDA0002259768240000231
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure BDA0002259768240000232
Or
Figure BDA0002259768240000233
The coordinates of the target relative to the ground-centered radar are then:
Figure BDA0002259768240000234
the azimuth angle of the target relative to the ground-centered radar is:
Figure BDA0002259768240000235
the elevation angle of the target relative to the ground center radar is:
Figure BDA0002259768240000236
the target has a slope distance with respect to the ground radar:
Figure BDA0002259768240000237
in the above formula, θAIs an azimuthal observation of the target relative to the digital telescope a,
Figure BDA0002259768240000238
is the elevation angle estimated value of the target relative to the digital telescope A;
step 5) calculating the variance of the estimation error:
5.1) for the non-small-route short-cut target, calculating the variance of the azimuth angle, the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance calculated in the step 3.1);
variance of azimuth estimation error
Figure BDA0002259768240000241
Figure BDA0002259768240000242
Variance of high and low angle estimation error
Figure BDA0002259768240000243
Figure BDA0002259768240000244
Variance of slope estimation error
Figure BDA0002259768240000245
Figure BDA0002259768240000246
In the formula (I), the compound is shown in the specification,
Figure BDA0002259768240000247
the variance of the observation errors of the digital telescopes A and B can be calculated by 3.1).
5.2) for the small-route short-cut target, calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance obtained by the calculation of 3.2);
variance of high and low angle estimation error
Figure BDA0002259768240000248
Figure BDA0002259768240000249
Variance of slope estimation error
Figure BDA00022597682400002410
Figure BDA00022597682400002411
Step 6), setting a radar search window:
6.1) for non-small-route shortcuts:
the radar search window should be set at θ,
Figure BDA00022597682400002412
And R is the midpoint, a plurality of times of the upper and lower sigmaθ、
Figure BDA00022597682400002413
And σRSo that the radar azimuth search window is set to (theta-n · sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure BDA0002259768240000251
slant search windowThe mouth is (R-n. sigma.)R,R+n·σR) (ii) a The value of n is flexibly set according to the performance and the requirement of the radar.
6.2) for small-route shortcuts:
the radar search window should be set to
Figure BDA0002259768240000252
And R is a midpoint which is several times the upper and lower
Figure BDA0002259768240000253
And σRThe range of intervals, therefore, the high-low angle search window is:
Figure BDA0002259768240000254
the slant search window is (R-n.sigma)R,R+n·σR) (ii) a The value of n is flexibly set according to the performance and the requirement of the radar. And setting the radar azimuth indication as theta, and performing small-range search by taking the theta as a center.
For the two modes, in order to further improve the accuracy of the setting of the radar window, the observation data can be preprocessed before the step 2); the method for preprocessing the observation data of the single digital telescope comprises the following steps:
A. removing repeated data in the observation data, and interpolating:
will t1The observed data of the time are recorded as
Figure BDA0002259768240000255
t2The observed data of the time are recorded as
Figure BDA0002259768240000256
tnThe observed data of the time are recorded as
Figure BDA0002259768240000257
If tiTime and tjTime of day, thetai＝θj，
Figure BDA0002259768240000258
Then order
Figure BDA0002259768240000259
The i ≠ j, i ≠ 1,2, … n, j ≠ 1,2, … n;
B. rejecting excessively deviated data in the observed data, and interpolating:
b1, continuously observing any moving target for multiple times by using a digital telescope to obtain corresponding observation data;
b2, calculating the deviation variances of the observation data and the azimuth angle and elevation angle estimated values of the moving target by respectively using the formula in the step 2.2) for the observation data obtained by each continuous observation;
b3, calculating the average value of the variance of the deviation of all the observation angle data obtained in the step B2 and the angle estimation value of the moving target
Figure BDA00022597682400002510
And
Figure BDA00022597682400002511
the mean value of standard deviation is obtained by evolution
Figure BDA00022597682400002512
And
Figure BDA00022597682400002513
b4, respectively enabling the azimuth angle and the elevation angle corresponding to each moment in the observation data in the step 1) to be respectively equal to the standard deviation average value obtained in the step B3
Figure BDA00022597682400002514
And
Figure BDA00022597682400002515
making a comparison, if a certain time tkCorresponding azimuth angle thetakDeviation from its estimate by a value greater than or equal to the mean of standard deviation
Figure BDA00022597682400002516
3-5 times of the azimuth angle thetakIf the deviation is too large, let
Figure BDA00022597682400002517
If a certain time tgCorresponding high and low angles
Figure BDA00022597682400002518
Greater than or equal to the standard deviation average value
Figure BDA0002259768240000261
3-5 times of the angle of elevation, representing the elevation angle
Figure BDA0002259768240000262
If the deviation is too large, let
Figure BDA0002259768240000263
k＝1,2,…n，g＝1,2,…n。
As shown in fig. 2, the testing system for implementing the method of the present invention includes 6 modules, which are a data recording and preprocessing module based on a digital telescope, a target motion law parameter estimation module, an air observation error statistic module, a target relative center radar positioning module, an air observation error transmission module, and a radar target indication window setting module.
And the data recording and preprocessing module is mainly used for recording the low-altitude target air condition data and preprocessing the air condition data.
And the target motion rule parameter estimation module determines the angle change parameters of the target according to the moving target azimuth angle and high-low angle change rule and a nonlinear function parameter estimation method through target azimuth angle and high-low angle data recorded by the digital telescope.
And the air observation error statistic module is used for calculating the variance of the current observation error of the digital telescope in real time.
And the target relative center radar positioning module estimates positioning information (azimuth angle, elevation angle and slope distance) of the target relative to the ground center radar according to observation data of the observation whistle digital telescope.
And the air observation error transfer module is used for calculating the positioning error of the target relative to the ground center radar according to the observation error of the digital telescope and an error transfer formula.
And the radar target indication window setting module is used for reasonably setting a radar search window according to the target positioning information and the target positioning error and assisting the radar to quickly capture the aerial target.
For the judgment of whether the target is a small-route shortcut target or a non-small-route shortcut target, the following method is adopted:
estimating a target motion rule by using N observation points, wherein the value of N is related to the target speed and the observation sampling period, the suggested value of N is 5-10, and if the azimuth angles of the N observation points meet the following conditions: thetai+N-1-θi∈(θl,θu)，θiIs the azimuth angle (i.e. t) of the ith observation pointiAzimuthal observation of time), θi+N-1Is the azimuth angle (i.e. t) of the i + N-1 th observation pointi+N-1Azimuthal observation of time), θlIs a lower limit value of θuIf the target is the upper limit value, the moving target is considered to be a small navigation path shortcut target, otherwise, the moving target is a non-small navigation path shortcut target.

Claims (4)

1. A radar search window setting method based on an observation whistle digital telescope is characterized by comprising the following steps:
step 1) acquiring observation data of a moving target based on a single digital telescope:
continuously tracking a moving target by using a single digital telescope A, acquiring observation data and transmitting the observation data to a command information center platform end; the observation data comprises real-time azimuth angle theta and elevation angle of the moving target
Figure FDA0002259768230000011
Step 2) calculating the positioning information of the target relative to the digital telescope A:
2.1) for a non-small-route shortcut target, calculating the azimuth angle and the elevation angle estimated value of the moving target relative to the digital telescope A;
2.1.1) estimation of azimuth
Figure FDA0002259768230000012
The solution is as follows:
Figure FDA0002259768230000013
wherein, { a, tx,θxAcquiring a variation parameter of the azimuth angle of the moving target by utilizing a nonlinear function parameter estimation algorithm according to observation data;
a＝v/rxv is the velocity of the target, rxA target airway shortcut is taken;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
θxthe azimuth angle parameter corresponding to the target route shortcut is obtained;
t is a time variable observed for the moving target;
2.1.2) estimation of elevation angles
Figure FDA0002259768230000014
The solution is as follows:
Figure FDA0002259768230000015
wherein, { a, b, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data; b is h/rxH is the height of the target;
2.2) for the small-route shortcut target, only the estimated value of the high and low angles of the moving target relative to the digital telescope A needs to be calculated; estimation of elevation angle
Figure FDA0002259768230000016
The solution is as follows:
Figure FDA0002259768230000021
wherein, { c, d, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data;
t is a time variable observed for the moving target;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the deviation variance of the observed data and the azimuth angle and altitude angle estimated values obtained in the step 2.1):
digital telescope A azimuth angle observation data and estimation value thereof
Figure FDA0002259768230000022
Variance of difference
Figure FDA0002259768230000023
Figure FDA0002259768230000024
Wherein the content of the first and second substances,
Figure FDA0002259768230000025
digital telescope A high-low angle observation data and estimation value thereof
Figure FDA0002259768230000026
Variance of difference
Figure FDA0002259768230000027
Figure FDA0002259768230000028
Wherein the content of the first and second substances,
Figure FDA0002259768230000029
in the formula (I), the compound is shown in the specification,
θiis tiA time azimuth observation value;
Figure FDA00022597682300000210
is tiA time azimuth angle estimation value;
Figure FDA00022597682300000211
is tiA time elevation angle observation value;
Figure FDA00022597682300000212
is tiA time elevation angle estimation value;
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
digital telescope A high-low angle observation data and estimation value thereof
Figure FDA00022597682300000213
Variance of difference
Figure FDA00022597682300000214
Figure FDA00022597682300000215
Wherein the content of the first and second substances,
Figure FDA00022597682300000216
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
4.1) for non-small-route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure FDA0002259768230000031
in the formula, v0To observe the estimate of target velocity by the whistle digital telescope a,
Figure FDA0002259768230000032
azimuth angle and elevation angle estimated values of the moving object relative to the digital telescope A are respectively obtained by 2.1.1) and 2.1.2);
the ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the target relative to the ground-centered radar are then expressed as:
Figure FDA0002259768230000033
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000034
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000035
the slant range of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000036
4.2) for small-route shortcuts:
the slant distance of the moving object relative to the digital telescope A is as follows:
Figure FDA0002259768230000037
in the formula, v0In order to observe the estimated value of the whistle digital telescope A to the target speed, theta (t) is the azimuth angle observed value of the moving target relative to the digital telescope A,
Figure FDA0002259768230000038
the estimated value of the elevation angle of the moving target relative to the digital telescope A is obtained by 2.2);
the ground center radar is taken as the origin of a ground rectangular coordinate system, and the coordinate of the digital telescope A is (x)A,yA,zA) The coordinates of the target relative to the ground-centered radar are then expressed as:
Figure FDA0002259768230000041
in the formula, thetaAIs the azimuthal observation of the target relative to the digital telescope a;
Figure FDA0002259768230000042
is the elevation angle estimated value of the target relative to the digital telescope A;
the azimuth angle of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000043
the elevation angle of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000044
the slant range of the moving target relative to the ground center radar is as follows:
Figure FDA0002259768230000045
step 5) calculating the variance of the estimation error:
5.1) for a non-small-route shortcut target, calculating the variance of an azimuth angle, a high-low angle and an inclined distance estimation error of the moving target relative to a ground center radar;
variance of azimuth estimation error
Figure FDA0002259768230000046
Calculated by the error transfer equation:
Figure FDA0002259768230000047
variance of high and low angle estimation error
Figure FDA0002259768230000048
Calculated by the error transfer equation:
Figure FDA0002259768230000049
the variance of the skew estimation error is
Figure FDA00022597682300000410
Calculated by the error transfer equation:
Figure FDA00022597682300000411
in the formula (I), the compound is shown in the specification,
Figure FDA00022597682300000412
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
Figure FDA0002259768230000051
the variance of the observation error of the digital telescope A is calculated in the step 3.1);
5.2) for the small-route short-cut target, only calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground center radar;
variance of high and low angle estimation error
Figure FDA0002259768230000052
Calculated by the error transfer equation:
Figure FDA0002259768230000053
the variance of the skew estimation error is
Figure FDA0002259768230000054
Calculated by the error transfer equation:
Figure FDA0002259768230000055
in the formula (I), the compound is shown in the specification,
Figure FDA0002259768230000056
estimating the variance of the deviation for the target speed, wherein the variance is a preset value and is used as a known quantity;
step 6), setting a radar search window:
6.1) for non-small-way shortcuts
Setting a radar azimuth search window to (theta-n-sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure FDA0002259768230000057
the slant search window is (R-n.sigma)R,R+n·σR) The value of n is flexibly set according to the performance and the requirement of the radar;
6.2) for small-route shortcuts:
setting the radar azimuth indication as theta, wherein the high-low angle search window is as follows:
Figure FDA0002259768230000058
the slant search window is (R-n.sigma)R,R+n·σR) And the value of n is flexibly set according to the performance and the requirement of the radar.
2. The observation whistle digital telescope-based radar search window setting method as claimed in claim 1, wherein: before step 1), preprocessing observation data, specifically as follows:
A. removing repeated data in the observation data, and interpolating:
will t1The observed data of the time are recorded as
Figure FDA0002259768230000059
t2The observed data of the time are recorded as
Figure FDA00022597682300000510
…，tnThe observed data of the time are recorded as
Figure FDA00022597682300000511
If tiTime and tjTime of day, thetai＝θj，
Figure FDA00022597682300000512
Then order
Figure FDA00022597682300000513
The i ≠ j, i ≠ 1,2, … n, j ≠ 1,2, … n;
B. rejecting excessively deviated data in the observed data, and interpolating:
b1, continuously observing any moving target for multiple times by using a digital telescope to obtain corresponding observation data;
b2, calculating the deviation variance of the observation data with the azimuth angle and elevation angle estimation value of the moving target respectively for the observation data obtained by each continuous observation;
b3, calculating the average value of the variance of the deviation of all the observation angle data obtained in the step B2 and the angle estimation value of the moving target
Figure FDA0002259768230000061
And
Figure FDA0002259768230000062
the mean value of standard deviation is obtained by evolution
Figure FDA0002259768230000063
And
Figure FDA0002259768230000064
b4, respectively enabling the azimuth angle and the elevation angle corresponding to each moment in the observation data in the step 1) to be respectively equal to the standard deviation average value obtained in the step B3
Figure FDA0002259768230000065
And
Figure FDA0002259768230000066
making a comparison, if a certain time tkCorresponding azimuth angle thetakDeviation from its estimate by a value greater than or equal to the mean of standard deviation
Figure FDA0002259768230000067
3-5 times of the azimuth angle thetakIf the deviation is too large, let
Figure FDA0002259768230000068
If a certain time tgCorresponding high and low angles
Figure FDA0002259768230000069
Greater than or equal to the standard deviation average value
Figure FDA00022597682300000610
3-5 times of the angle of elevation, representing the elevation angle
Figure FDA00022597682300000611
If the deviation is too large, let
Figure FDA00022597682300000612
k＝1,2,…n，g＝1,2,…n。
3. A radar search window setting method based on an observation whistle digital telescope is characterized by comprising the following steps:
step 1) acquiring observation data of the same moving target based on a double digital telescope:
continuously tracking the same moving target by using two digital telescopes with different coordinates, and respectively acquiring observation data; the observation data comprises real-time azimuth angle theta and elevation angle of the moving object relative to the digital telescope
Figure FDA00022597682300000613
Step 2) calculating the positioning information of the target relative to the digital telescope:
2.1) for non-small-route short-cut targets, calculating the estimated values of the azimuth angle and the elevation angle of the moving target relative to each observation whistle digital telescope;
2.1.1) estimation of azimuth
Figure FDA00022597682300000614
The solution is as follows:
Figure FDA00022597682300000615
wherein, { a, tx,θxIs the variation parameter of the azimuth angle of the moving target according toObserving data, and obtaining by utilizing a nonlinear function parameter estimation algorithm;
a＝v/rxv is the velocity of the target, rxA target airway shortcut is taken;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
θxthe azimuth angle parameter corresponding to the target route shortcut is obtained;
t is a time variable observed for the moving target;
2.1.2) estimation of elevation angles
Figure FDA0002259768230000071
The solution is as follows:
Figure FDA0002259768230000072
wherein, { a, b, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data; b is h/rxH is the height of the target;
2.2) for the small-route shortcut moving target, only the estimated value of the high and low angles of the moving target relative to each observation whistle digital telescope is needed to be calculated; estimation of elevation angle
Figure FDA0002259768230000073
The solution is as follows:
Figure FDA0002259768230000074
wherein, { c, d, txThe parameters are the change parameters of the high and low angles of the moving target, and are obtained by utilizing a nonlinear function parameter estimation algorithm according to observation data;
t is a time variable observed for the moving target;
txthe time corresponding to the target flying to the navigation shortcut is obtained;
step 3) calculating the variance of the deviation of the observed value and the estimated value:
3.1) for the non-small-route shortcut target, calculating the deviation variance of the observed data and the azimuth angle and altitude angle estimated values obtained in the step 2.1):
single digital telescope azimuth angle observation data and estimation value thereof
Figure FDA0002259768230000075
Variance of difference
Figure FDA0002259768230000076
Figure FDA0002259768230000081
Wherein the content of the first and second substances,
Figure FDA0002259768230000082
single digital telescope observation height angle measurement data and estimation value thereof
Figure FDA0002259768230000083
Variance of difference
Figure FDA0002259768230000084
Figure FDA0002259768230000085
Wherein the content of the first and second substances,
Figure FDA0002259768230000086
in the formula (I), the compound is shown in the specification,
θiis tiA time azimuth observation value;
Figure FDA0002259768230000087
is tiA time azimuth angle estimation value;
Figure FDA0002259768230000088
is tiA time elevation angle observation value;
Figure FDA0002259768230000089
is tiA time elevation angle estimation value;
3.2) for the small-route shortcut target, only calculating the variance of the deviation of the observed data and the elevation angle estimated value obtained in the step 2.2):
single digital telescope high-low angle observation data and estimation value thereof
Figure FDA00022597682300000810
Variance of difference
Figure FDA00022597682300000811
Figure FDA00022597682300000812
Wherein the content of the first and second substances,
Figure FDA00022597682300000813
step 4), calculating the azimuth angle, the elevation angle and the slope distance of the moving target relative to the ground center radar:
4.1) for non-small-route shortcuts:
for the same non-small-route shortcut moving target, the slant range of the target is obtained by adopting a least square cross positioning mode, and the coordinate of the digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure FDA00022597682300000814
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure FDA00022597682300000815
Or
Figure FDA00022597682300000816
The coordinates of the target relative to the ground-centered radar are then:
Figure FDA0002259768230000091
the azimuth angle of the target relative to the ground-centered radar is:
Figure FDA0002259768230000092
the elevation angle of the target relative to the ground center radar is:
Figure FDA0002259768230000093
the target has a slope distance with respect to the ground radar:
Figure FDA0002259768230000094
in the above formula, the first and second carbon atoms are,
Figure FDA0002259768230000095
and
Figure FDA0002259768230000096
respectively the azimuth angle estimated value of the target relative to the digital telescope AAnd elevation angle estimates;
4.2) for small-route shortcuts:
for the same small-route shortcut moving target, the slant range of the target is obtained by adopting a least square cross positioning mode, and the coordinate of the digital telescope A is recorded as (x)A,yA,zA) The coordinate of the digital telescope B is (x)B,yB,zB) Solving the following formula:
AX＝Y
wherein the content of the first and second substances,
Figure FDA0002259768230000097
the least squares solution of the target slope distance is then:
X＝(ATA)-1ATY
an estimate of the target's skew angle with respect to the digital telescopes A and B is then obtained
Figure FDA0002259768230000098
Or
Figure FDA0002259768230000099
The coordinates of the target relative to the ground-centered radar are then:
Figure FDA0002259768230000101
the azimuth angle of the target relative to the ground-centered radar is:
Figure FDA0002259768230000102
the elevation angle of the target relative to the ground center radar is:
Figure FDA0002259768230000103
the target has a slope distance with respect to the ground radar:
Figure FDA0002259768230000104
in the above formula, θAIs an azimuthal observation of the target relative to the digital telescope a,
Figure FDA0002259768230000105
is the elevation angle estimated value of the target relative to the digital telescope A;
step 5) calculating the variance of the estimation error:
5.1) for the non-small-route short-cut target, calculating the variance of the azimuth angle, the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance calculated in the step 3.1);
variance of azimuth estimation error
Figure FDA0002259768230000106
Figure FDA0002259768230000107
Variance of high and low angle estimation error
Figure FDA0002259768230000108
Figure FDA0002259768230000109
Variance of slope estimation error
Figure FDA00022597682300001010
Figure FDA00022597682300001011
In the formula (I), the compound is shown in the specification,
Figure FDA0002259768230000111
the variance of the observation errors of the digital telescopes A and B is calculated in the step 3.1);
5.2) for the small-route short-cut target, calculating the variance of the elevation angle and the slope distance estimation error of the moving target relative to the ground radar according to an error transfer formula based on the observation error variance obtained by the calculation in the step 3.2);
variance of high and low angle estimation error
Figure FDA0002259768230000112
Figure FDA0002259768230000113
Variance of slope estimation error
Figure FDA0002259768230000114
Figure FDA0002259768230000115
In the formula (I), the compound is shown in the specification,
Figure FDA0002259768230000116
the variance of the observation errors of the digital telescopes A and B is calculated in the step 3.2);
step 6), setting a radar search window:
6.1) for non-small-route shortcuts:
setting a radar azimuth search window to (theta-n-sigma)θ,θ+n·σθ) The high and low angle search window is:
Figure FDA0002259768230000117
the slant search window is (R-n.sigma)R,R+n·σR) The value of n is flexibly set according to the performance and the requirement of the radar;
6.2) for small-route shortcuts:
setting the radar azimuth indication as theta, wherein the high-low angle search window is as follows:
Figure FDA0002259768230000118
the slant search window is (R-n.sigma)R,R+n·σR) (ii) a The value of n is flexibly set according to the performance and the requirement of the radar.
4. The observation whistle digital telescope-based radar search window setting method as claimed in claim 3, wherein: before step 1), respectively preprocessing the observation data of each digital telescope, specifically as follows:
A. removing repeated data in the observation data, and interpolating:
will t1The observed data of the time are recorded as
Figure FDA0002259768230000121
t2The observed data of the time are recorded as
Figure FDA0002259768230000122
…，tnThe observed data of the time are recorded as
Figure FDA0002259768230000123
If tiTime and tjTime of day, thetai＝θj，
Figure FDA0002259768230000124
Then order
Figure FDA0002259768230000125
The i ≠ j, i ≠ 1,2, … n, j ≠ 1,2, … n;
B. rejecting excessively deviated data in the observed data, and interpolating:
b1, continuously observing any moving target for multiple times by using a digital telescope to obtain corresponding observation data;
b2, calculating the deviation variance of the observation data with the azimuth angle and elevation angle estimation value of the moving target respectively for the observation data obtained by each continuous observation;
b3, calculating the average value of the variance of the deviation of all the observation angle data obtained in the step B2 and the angle estimation value of the moving target
Figure FDA0002259768230000126
And
Figure FDA0002259768230000127
the mean value of standard deviation is obtained by evolution
Figure FDA0002259768230000128
And
Figure FDA0002259768230000129
b4, respectively enabling the azimuth angle and the elevation angle corresponding to each moment in the observation data in the step 1) to be respectively equal to the standard deviation average value obtained in the step B3
Figure FDA00022597682300001210
And
Figure FDA00022597682300001211
making a comparison, if a certain time tkCorresponding azimuth angle thetakDeviation from its estimate by a value greater than or equal to the mean of standard deviation
Figure FDA00022597682300001212
3-5 times of the azimuth angle thetakIf the deviation is too large, let
Figure FDA00022597682300001213
If a certain time tgCorresponding high and low angles
Figure FDA00022597682300001214
Greater than or equal to the standard deviation average value
Figure FDA00022597682300001215
3-5 times of the angle of elevation, representing the elevation angle
Figure FDA00022597682300001216
If the deviation is too large, let
Figure FDA00022597682300001217
k＝1,2,…n，g＝1,2,…n。
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