CN111090079A - Radar networking radiation interval optimization control method based on passive sensor cooperation - Google Patents

Radar networking radiation interval optimization control method based on passive sensor cooperation Download PDF

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CN111090079A
CN111090079A CN201911343450.XA CN201911343450A CN111090079A CN 111090079 A CN111090079 A CN 111090079A CN 201911343450 A CN201911343450 A CN 201911343450A CN 111090079 A CN111090079 A CN 111090079A
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CN111090079B (en
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佘季
姜磊
吴明宇
刘建洋
王�琦
吕超峰
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8511 Research Institute of CASIC
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention discloses a radar networking radiation interval optimization control method based on passive sensor cooperation, which comprises the following steps of: (1) all airplanes in the airplane formation are loaded with airborne phased array radars and passive sensors, the radar networking comprises N airborne phased array radars, the passive sensors can receive radiation signals from targets, and passive arrival time difference TDOA positioning is carried out by utilizing the radiation signals of the targets; (2) tracking Q motor targets which are dispersedly distributed in a two-dimensional plane by a radar networking, and constructing a motion model of the targets according to the Q motor targets; (3) obtaining BCRLB of target state estimation errors during maneuvering target tracking, and using the BCRLB to measure the prediction tracking accuracy of the maneuvering target at the next moment; (4) constructing a radar networking radiation interval optimization control model, and enabling the radar radiation times of the radar networking in the tracking process to be minimum on the premise of ensuring the tracking precision of all targets; (5) and solving the radiation interval optimization control model.

Description

Radar networking radiation interval optimization control method based on passive sensor cooperation
Technical Field
The invention belongs to an electronic countermeasure technology, and particularly relates to a radar networking radiation interval optimization control method based on passive sensor cooperation.
Background
The combat mission endowed to the advanced fighter in the future is very important, the confronted combat environment is very complex, and only when the fighter is hidden and lackluster, the fighter can be outstandingly surrounded by the complicated defense arrangement of various advanced sensors and can also survive in severe battlefield environments such as electronic interference, anti-radiation missiles and the like. The purpose of stealth is to reduce the active and passive characteristics of the target, so that an enemy sensor cannot detect or cannot accurately detect target information. In modern wars, various novel passive detection devices such as ELINT, ESM, RWR, ARM and the like are successively put into use, and the passive detection device has the advantages of long acting distance, strong concealment, difficulty in finding and the like, and the passive detection device poses serious threats to battlefield viability and defense-breaking capacity of fighters, and cannot ensure the safety of the fighters only by means of passive stealth technology. Therefore, the active stealth technology of the airplane, namely the radio frequency stealth technology, is increasingly paid more attention by domestic and foreign scholars and research institutions.
The airplane radio-frequency stealth technology is used for reducing the capabilities of passive detection equipment in intercepting, sorting, identifying and the like of radio-frequency signals by reducing the radio-frequency signal characteristics of active electronic equipment such as an airborne radar and a data link. As an important active stealth technology, the airplane radio frequency stealth technology is an important means for reducing interception probability and interception distance of a passive detection system, improving reconnaissance and anti-interference capabilities of a radar and ensuring discovery, attack and destruction of first enemies of fighters.
The airborne radar networking comprises a plurality of airborne phased array radars with different airplane platforms, different working modes and different frequency bands, data fusion and adaptive radar transmitter parameter control are carried out in a fusion center, and the tasks of searching, positioning, tracking and identifying targets can be better completed. The radio frequency stealth performance of the airborne radar networking is improved from the perspective of time resources, and is mainly reflected on optimization control of radar radiation intervals. When the target is tracked at small radiation intervals, the airborne radar networking radiates the target at high frequency to obtain echo information and update the motion state of the target, so that higher target tracking accuracy can be obtained, but the probability of the radar being found by a passive detection system is increased due to frequent radiation of the radar, and the radio frequency stealth performance of the airborne radar networking is poorer at the moment. When a large radiation interval is adopted to track a target, the target tracking precision is low, and meanwhile, the radar networking has good radio frequency stealth performance due to the fact that the radiation times are reduced.
Disclosure of Invention
The invention aims to provide a radar networking radiation interval optimization control method based on passive sensor cooperation, which can maximize the sampling interval of the radar networking to all targets on the premise that the prediction and tracking precision of all targets meets constraint conditions, namely reduce the radar radiation times and improve the radio frequency stealth performance of the radar networking.
The technical solution for realizing the purpose of the invention is as follows: a radar networking radiation interval optimization control method based on passive sensor cooperation comprises the following steps:
the method comprises the following steps: all airplanes in the airplane formation are loaded with airborne phased array radars and passive sensors, the radar networking comprises N airborne phased array radars, the passive sensors can receive radiation signals from targets and carry out passive time difference of arrival (TDOA) positioning by utilizing the radiation signals of the targets;
step two: tracking Q motor targets which are dispersedly distributed in a two-dimensional plane by a radar networking, and constructing a motion model of the targets according to the Q motor targets;
step three: obtaining BCRLB of target state estimation errors during maneuvering target tracking, and using the BCRLB to measure the prediction tracking accuracy of the maneuvering target at the next moment;
step four: constructing a radar networking radiation interval optimization control model, and enabling the radar radiation times of the radar networking in the tracking process to be minimum on the premise of ensuring the tracking precision of all targets;
step five: and solving the radiation interval optimization control model.
Compared with the prior art, the invention has the remarkable advantages that: by optimizing the radar radiation intervals when the airborne radar networking tracks multiple targets, the radar radiation times of the radar networking can be reduced while the target tracking performance is ensured, the radio frequency stealth performance of the radar networking is effectively improved, and the tracking accuracy of all targets is ensured.
Drawings
FIG. 1 is a flow chart of a multi-target tracking strategy.
Fig. 2 is a graph of the target irradiation mark and the irradiation interval when M is 1, where fig. (a) is target 1 and fig. (b) is target 2.
Fig. 3 is a graph of the target irradiation mark and the irradiation interval when M is 2, where fig. (a) is target 1 and fig. (b) is target 2.
Detailed Description
The present invention is described in further detail below with reference to the attached drawing figures.
The invention relates to a radar networking radiation interval optimization control method based on passive sensor cooperation, which comprises the following steps of:
the method comprises the following steps: all airplanes in the airplane formation are loaded with airborne phased array radars and passive sensors, the radar networking comprises N airborne phased array radars, the passive sensors can receive radiation signals from targets, and passive arrival time difference TDOA positioning is carried out by utilizing the radiation signals of the targets, and the method specifically comprises the following steps:
all aircraft platforms of the airborne radar networking are loaded with passive sensors (x)i,yi) The position coordinates of the ith passive sensor are represented, i is more than or equal to 1 and less than or equal to N, and the distance between the target q and each passive sensor at the moment k
Figure BDA00023327141700000320
Comprises the following steps:
Figure BDA0002332714170000031
wherein ,
Figure BDA0002332714170000032
is the position of the target q at time k. Assuming that the passive sensor 1 is the master station, the rest are passive transmissionsThe sensors are secondary stations, and the time difference between the arrival of the signals radiated by the target q at the moment k at the primary station and the arrival at each secondary station
Figure BDA0002332714170000033
Comprises the following steps:
Figure BDA0002332714170000034
where c is the electromagnetic wave propagation velocity. The formula (1) can be substituted into the formula (2):
Figure BDA0002332714170000035
the above equation is N-1 hyperbolic equations, and the position of the target q at the moment k can be determined according to the focus of the hyperbolic curves. Will be provided with
Figure BDA0002332714170000036
As an observation value of the passive sensor networking observation model, the observation model can be expressed as:
Figure BDA0002332714170000037
wherein ,
Figure BDA0002332714170000038
is a non-linear transfer function, and
Figure BDA0002332714170000039
Figure BDA00023327141700000310
for the passive sensor network at the moment k to measure the error of the target q,
Figure BDA00023327141700000311
is a mean of zero and a variance of
Figure BDA00023327141700000312
The white gaussian noise of (a) is,
Figure BDA00023327141700000313
can be calculated as:
Figure BDA00023327141700000314
wherein ,
Figure BDA00023327141700000315
is composed of
Figure BDA00023327141700000316
The standard deviation of the observed error of (a),
Figure BDA00023327141700000317
is composed of
Figure BDA00023327141700000318
And
Figure BDA00023327141700000319
the correlation coefficient of (2).
Step two: the radar networking tracks Q motor-driven targets which are dispersedly distributed in a two-dimensional plane, and a motion model of the targets is constructed according to the Q motor-driven targets, and the method specifically comprises the following steps:
there are Q discretely distributed maneuvering targets in a two-dimensional plane, and the motion model of the Q-th target can be described as:
Figure BDA0002332714170000041
wherein ,
Figure BDA0002332714170000042
is the state vector of the target q at time k,
Figure BDA0002332714170000043
and
Figure BDA0002332714170000044
respectively at the time k for the target qF represents a target state transition matrix, the movement trajectory of the maneuvering target is composed of a uniform velocity model and a coordinated turning model, and the corresponding target state transition matrices can be respectively represented as:
uniform motion model:
Figure BDA0002332714170000045
coordinating a turning model:
Figure BDA0002332714170000046
where T denotes an observation time interval and ω denotes a turning factor. WqThe process noise representing the target Q may be assumed to be zero as the mean and Q as the varianceqWhite gaussian noise, QqCan be expressed as:
Figure BDA0002332714170000047
wherein ,
Figure BDA0002332714170000048
the process noise strength for target q.
Step three: the BCRLB of the target state estimation error during the maneuvering target tracking is obtained to measure the prediction tracking accuracy of the maneuvering target at the next moment, and the method comprises the following specific steps:
obtaining a forecast Bayesian Information Matrix (BIM) of the target q state at the moment k according to the forecast probability and the forecast value of the target state of each model of the target q
Figure BDA0002332714170000051
Comprises the following steps:
Figure BDA0002332714170000052
wherein ,
Figure BDA0002332714170000053
the BIM of the target q state at time k-1,
Figure BDA0002332714170000054
and
Figure BDA0002332714170000055
the predicted values of the covariance matrix and the Jacobian matrix of the measured noise of the target q at the moment k are respectively measured by the radar ijState transition matrix, Q, representing the target model jqIs the variance of the process noise and is,
Figure BDA0002332714170000056
is the predicted probability of the model j,
Figure BDA0002332714170000057
an index is assigned to the radar,
Figure BDA0002332714170000058
indicating that the radar i is illuminating the target q at time k,
Figure BDA0002332714170000059
indicating that the radar i does not irradiate the target q at the moment k;
the predicted BiM inversion of the target q state yields a predicted Bayesian Clarithrome boundary (BCRLB) of the target q at time k
Figure BDA00023327141700000510
Figure BDA00023327141700000511
Step four: the method comprises the following steps of constructing a radar networking radiation interval optimization control model, and enabling the radar radiation times of the radar networking in the tracking process to be minimum on the premise of ensuring the tracking precision of all targets, wherein the method specifically comprises the following steps:
step 4-1, irradiation target selection model
And (3) establishing an optimization control model of the target irradiation index by taking the condition that the prediction tracking precision of all targets at the moment k meets the requirement as a constraint condition and the minimum number of targets needing irradiation as a target function:
Figure BDA00023327141700000512
wherein ,
Figure RE-GDA00024212842800000513
the lower bound of the mean square error is estimated for the predicted position of the target q at time k,
Figure RE-GDA00024212842800000514
prediction of BCRLB, F for target at time kmaxIs preset
Figure RE-GDA00024212842800000515
The threshold value of (a) is set,
Figure RE-GDA0002421284280000061
is an index of the target irradiation,
Figure RE-GDA0002421284280000062
indicating that the target q needs to be illuminated at time k,
Figure RE-GDA0002421284280000063
indicating that the target q need not be illuminated at time k. The optimal result of all target tracking indexes at the moment k can be obtained by solving the above formula
Figure RE-GDA0002421284280000064
Step 4-2, selecting a model by a radar distribution mode
According to the obtained vk,optAnd establishing an optimization control model of radar distribution indexes by taking the highest sum of the prediction tracking precision of the target to be irradiated at the moment k as a target function:
Figure BDA0002332714170000065
wherein ,
Figure BDA0002332714170000066
an index is assigned to the radar,
Figure BDA0002332714170000067
the target which represents that the time k needs to be irradiated is fixedly irradiated by M radars, M is more than or equal to 1 and less than or equal to N,
Figure BDA0002332714170000068
the method includes the steps that each radar irradiates one target at most simultaneously, and the result of the radar distribution index at the k moment is obtained by solving the optimization control model of the above formula
Figure BDA0002332714170000069
Wherein
Figure BDA00023327141700000610
Step five: solving the radiation interval optimization control model, which specifically comprises the following steps:
the first item in the predicted BIM of the maneuvering target is only related to the BIM of the target state at the k-1 moment and is not related to the radar distribution mode at the k moment, and the first item can be inverted to obtain the BCRLB of the target state estimation error when the target state is predicted by the prior information
Figure BDA00023327141700000611
Figure BDA00023327141700000612
wherein ,
Figure BDA00023327141700000613
BIM, F for target q State at time k-1jState transition matrix, Q, representing target model jqIs the variance of the process noise and is,
Figure BDA00023327141700000614
prediction for target model jProbability;
constructing a target position estimation mean square error lower bound based on prior information
Figure RE-GDA00024212842800000615
Can see as long as
Figure RE-GDA00024212842800000616
Is established, then
Figure RE-GDA00024212842800000617
Is bound to be established, wherein
Figure RE-GDA0002421284280000071
Is the lower bound of the mean square error of the target predicted position estimate, FmaxThe threshold value of the lower bound of the mean square error is estimated for the target position, and the irradiation target selection optimization control model can be equivalently:
Figure BDA0002332714170000072
wherein ,
Figure BDA0002332714170000073
is a target illumination index;
aiming at the specific situation that the target needing to be irradiated at each moment is fixed and irradiated by M radars, M is more than or equal to 1 and less than or equal to N, if
Figure BDA0002332714170000074
Indicating that the target q need not be illuminated if
Figure BDA0002332714170000075
And (3) representing that the target q needs to be irradiated, calculating the estimation mean square error lower bound of all possible radar combinations on the predicted position of the target to be irradiated, and obtaining the optimal result of the radar distribution index by using an enumeration method.
Example 1
A simulation scene for an airborne radar networking tracking maneuvering target is designed, the number of radars in the airborne radar networking is N-6, the number of targets in the airborne radar networking is Q-2, system parameters of all radars are the same, and the parameter setting is shown in table 1.
TABLE 1 airborne radar networking parameter settings
Figure BDA0002332714170000076
The observation time interval T is 3s and the tracking process duration is 300 s. The motion model set of the target comprises uniform-speed motion, left-turning motion and right-turning motion, and the threshold of target tracking precision is Fmax＝30m。
Fig. 2 and fig. 3 show the irradiation marks and irradiation time intervals of each target by the onboard radar networking in the process of tracking the target in the monte carlo experiment for a certain time when each target is irradiated by one radar and each target is irradiated by two radars respectively. The simulation result shows that the radiation interval of the optimized airborne radar networking to the target is not fixed to be 3s any more, the radiation interval is often larger than 3s, and the maximum radiation interval can reach 12 s.
The simulation result can be obtained, and the method can reduce the number of radar radiation times of the airborne radar networking in the tracking process on the premise of ensuring the target tracking precision, thereby improving the radio frequency stealth performance of the multi-target tracking of the airborne radar networking system.

Claims (6)

1. A radar networking radiation interval optimization control method based on passive sensor cooperation is characterized by comprising the following steps:
the method comprises the following steps: all airplanes in the airplane formation are loaded with airborne phased array radars and passive sensors, the radar networking comprises N airborne phased array radars, the passive sensors can receive radiation signals from targets, and passive arrival time difference TDOA positioning is carried out by utilizing the radiation signals of the targets;
step two: tracking Q motor targets which are dispersedly distributed in a two-dimensional plane by a radar networking, and constructing a motion model of the targets according to the Q motor targets;
step three: obtaining BCRLB of target state estimation errors during maneuvering target tracking, and using the BCRLB to measure the prediction tracking accuracy of the maneuvering target at the next moment;
step four: constructing a radar networking radiation interval optimization control model, and enabling the radar radiation times of the radar networking in the tracking process to be minimum on the premise of ensuring the tracking precision of all targets;
step five: and solving the radiation interval optimization control model.
2. The method for optimizing and controlling the radiation interval of the radar networking based on the passive sensor cooperation as claimed in claim 1, wherein in the first step, all the airplanes in the formation of the airplanes are loaded with the airborne phased array radar and the passive sensor, the radar networking comprises N portions of airborne phased array radars, the passive sensor can receive the radiation signals from the target, and the passive sensor can perform the passive time difference of arrival TDOA positioning by using the radiation signals of the target, and the method comprises the following specific steps:
all aircraft platforms of the airborne radar networking are loaded with passive sensors (x)i,yi) Is the position coordinate of the ith passive sensor, wherein i is more than or equal to 1 and less than or equal to N, and the distance between the target q and each passive sensor at the moment k
Figure FDA0002332714160000016
Comprises the following steps:
Figure FDA0002332714160000011
wherein ,
Figure FDA0002332714160000012
the position of the target q at the moment k; assuming that the passive sensor 1 is a main station and the other passive sensors are auxiliary stations, the time difference between the arrival of the signal radiated by the target q at the moment k at the main station and the arrival at each auxiliary station
Figure FDA0002332714160000013
Comprises the following steps:
Figure FDA0002332714160000014
wherein c is the propagation speed of the electromagnetic wave; the formula (1) can be substituted into the formula (2):
Figure FDA0002332714160000015
the formula is N-1 hyperbolic equations, and the position of the target q at the moment k can be determined according to the focus of the hyperbolic curves; will be provided with
Figure FDA0002332714160000021
As an observation value of the passive sensor networking observation model, the observation model can be expressed as:
Figure FDA0002332714160000022
wherein ,
Figure FDA0002332714160000023
is a non-linear transfer function, and
Figure FDA0002332714160000024
Figure FDA0002332714160000025
for the passive sensor network at the moment k to measure the error of the target q,
Figure FDA0002332714160000026
is a mean of zero and a variance of
Figure FDA0002332714160000027
The white gaussian noise of (a) is,
Figure FDA0002332714160000028
can be calculated as:
Figure FDA0002332714160000029
wherein ,
Figure FDA00023327141600000210
is composed of
Figure FDA00023327141600000211
The standard deviation of the observed error of (a),
Figure FDA00023327141600000212
is composed of
Figure FDA00023327141600000213
And
Figure FDA00023327141600000214
the correlation coefficient of (2).
3. The radar networking radiation interval optimization control method based on passive sensor cooperation according to claim 1, wherein in the second step, the radar networking tracks Q mobile targets which are dispersedly distributed in a two-dimensional plane, and a motion model of the targets is constructed according to the tracked mobile targets, specifically as follows:
there are Q discretely distributed maneuvering targets in a two-dimensional plane, and the motion model of the Q-th target can be described as:
Figure FDA00023327141600000215
wherein Q is 1., Q,
Figure FDA00023327141600000216
is the state vector of the target q at time k,
Figure FDA00023327141600000217
and
Figure FDA00023327141600000218
the position and the speed of the target q at the moment k are respectively shown, F represents a target state transition matrix, the motion track of the maneuvering target is composed of a uniform velocity model and a coordinated turning model, and the corresponding target state transition matrices can be respectively shown as follows:
uniform motion model:
Figure FDA00023327141600000219
coordinating a turning model:
Figure FDA0002332714160000031
wherein T represents an observation time interval, and ω represents a turning factor; wqThe process noise, representing the target Q, can be assumed to be zero as the mean and Q as the varianceqWhite gaussian noise, QqCan be expressed as:
Figure FDA0002332714160000032
wherein ,
Figure FDA0002332714160000033
the process noise strength for target q.
4. The radar networking radiation interval optimization control method based on passive sensor cooperation according to claim 1, wherein in step three, a BCRLB of a target state estimation error during maneuvering target tracking is obtained to measure a prediction tracking accuracy of a maneuvering target at a next moment, and specifically the following is:
according to the prediction probability and the target state prediction value of each model of the target q, the prediction of the target q state at the moment k is obtained
Figure FDA0002332714160000034
Comprises the following steps:
Figure FDA0002332714160000035
wherein ,
Figure FDA0002332714160000036
the BIM of the target q state at time k-1,
Figure FDA0002332714160000037
and
Figure FDA0002332714160000038
the predicted values of the covariance matrix and the Jacobian matrix of the measured noise of the target q at the moment k are respectively measured by the radar ijState transition matrix, Q, representing the target model jqIs the variance of the process noise and is,
Figure FDA0002332714160000039
is the predicted probability of the model j,
Figure FDA00023327141600000310
an index is assigned to the radar,
Figure FDA00023327141600000311
indicating that the radar i is illuminating the target q at time k,
Figure FDA00023327141600000312
indicating that the radar i does not irradiate the target q at the moment k;
the predicted BCRLB of the target q at the moment k can be obtained by inverting the predicted BIM of the target q state:
Figure FDA0002332714160000041
5. the method for optimizing and controlling the radiation interval of the radar networking based on the passive sensor cooperation as claimed in claim 1, wherein in the fourth step, a radar networking radiation interval optimization and control model is constructed, so that the number of radar radiation times of the radar networking in the tracking process can be minimized on the premise of ensuring the tracking accuracy of all targets, and the method specifically comprises the following steps:
step 4-1, irradiation target selection model
And (3) establishing an optimization control model of the target irradiation index by taking the condition that the prediction tracking precision of all targets at the moment k meets the requirement as a constraint condition and the minimum number of targets needing irradiation as a target function:
Figure FDA0002332714160000042
wherein ,
Figure FDA0002332714160000043
the lower bound of the mean square error is estimated for the predicted position of the target q at time k,
Figure FDA0002332714160000044
prediction of BCRLB, F for target at time kmaxIs preset
Figure FDA0002332714160000045
The threshold value of (a) is set,
Figure FDA0002332714160000046
is an index of the target irradiation,
Figure FDA0002332714160000047
indicating that the target q needs to be illuminated at time k,
Figure FDA0002332714160000048
indicating that the target q is not required to be irradiated at time k; the optimal result of all target tracking indexes at the moment k can be obtained by solving the above formula
Figure FDA0002332714160000049
Step 4-2, selecting a model by a radar distribution mode
According to the obtained vk,optAnd establishing an optimization control model of radar distribution indexes by taking the highest sum of the prediction tracking precision of the target to be irradiated at the moment k as a target function:
Figure FDA00023327141600000410
wherein ,
Figure FDA0002332714160000051
an index is assigned to the radar,
Figure FDA0002332714160000052
the target which represents that the time k needs to be irradiated is fixedly irradiated by M radars, M is more than or equal to 1 and less than or equal to N,
Figure FDA0002332714160000053
the method includes the steps that each radar irradiates one target at most simultaneously, and the result of the radar distribution index at the k moment is obtained by solving the optimization control model of the above formula
Figure FDA0002332714160000054
wherein
Figure FDA0002332714160000055
6. The radar networking radiation interval optimization control method based on passive sensor cooperation according to claim 1, wherein in the fifth step, a radiation interval optimization control model is solved, specifically as follows:
the first item in the predicted BIM of the maneuvering target is only related to the BIM of the target state at the moment k-1 and is not related to the radar distribution mode at the moment k, and the first item can be inverted to obtain the state of the target predicted by the prior informationError of target state estimation
Figure RE-FDA0002421284270000056
Figure RE-FDA0002421284270000057
wherein ,
Figure RE-FDA0002421284270000058
BIM, F for target q State at time k-1jState transition matrix, Q, representing the target model jqIs the variance of the process noise and is,
Figure RE-FDA0002421284270000059
is the predicted probability of the target model j;
constructing a target position estimation mean square error lower bound based on prior information
Figure RE-FDA00024212842700000510
Can see as long as
Figure RE-FDA00024212842700000511
Is established, then
Figure RE-FDA00024212842700000512
Is bound to be established, wherein
Figure RE-FDA00024212842700000513
Is the lower bound of the mean square error of the target predicted position estimate, FmaxThe threshold value of the lower bound of the mean square error is estimated for the target position, and the irradiation target selection optimization control model can be equivalently:
Figure RE-FDA00024212842700000514
wherein ,
Figure RE-FDA00024212842700000515
is a target illumination index;
aiming at the specific situation that the target needing to be irradiated at each moment is fixed and irradiated by M radars, M is more than or equal to 1 and less than or equal to N, if
Figure RE-FDA00024212842700000516
Indicating that the target q need not be illuminated if
Figure RE-FDA00024212842700000517
And (3) representing that the target q needs to be irradiated, calculating the estimation mean square error lower bound of all possible radar combinations on the predicted position of the target to be irradiated, and obtaining the optimal result of the radar distribution index by using an enumeration method.
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