CN110412534B - Networking radar multi-target tracking residence time optimization method based on radio frequency stealth - Google Patents
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Abstract
The invention discloses a multi-target tracking residence time optimization method for a networking radar based on radio frequency stealth, which comprises the steps of constructing a Bayesian-Lame lower bound of a target state estimation error by taking a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables, and taking the Bayesian-Lame lower bound as a measurement index of target tracking accuracy; on the basis, the prediction tracking precision of the target at the following moment, the data processing amount of the fusion center and the radar emission resource are taken as constraint conditions, the total residence time of the minimized networking radar system is taken as an optimization target, and parameters such as radar selection, residence time, emission signal bandwidth and the like in the multi-target tracking process are optimally designed. Therefore, the tracking precision of each target in the multi-target tracking process is met, the total residence time of the networking radar system is reduced to the maximum extent, and the radio frequency stealth performance of the networking radar system during multi-target tracking is improved.
Description
Technical Field
The invention relates to the field of radar signal processing, in particular to a method for optimizing multi-target tracking residence time of a networking radar based on radio frequency stealth.
Background
In modern electronic warfare, in order to improve radio frequency stealth performance of a networking radar system, radar radiation parameter optimization design has received extensive attention. For a networking radar system, the emission parameters of the networking radar system are dynamically controllable, so that the target detection and tracking capability of the system can be improved by optimally designing the radar emission parameters, and the radio frequency stealth performance of the networking radar is improved. From the perspective of time resources, reducing the residence time of each radar transmitting beam on a target is an important measure for improving the radio frequency stealth performance of the networking radar system.
However, existing research results relate to the problem of residence time optimization during target tracking of a networking radar system, and radar selection and residence time are jointly optimized and designed under the condition that given target tracking accuracy and radar emission resources are guaranteed, so that radio frequency stealth performance during target tracking of the networking radar is improved to a certain extent. However, the existing research results only aim at a single-target tracking scene, and influence of the bandwidth of the transmitted signal on the total residence time is not considered, so that the method has certain limitations.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to provide a radio frequency stealth-based multi-target tracking residence time optimization method for a networking radar, which can solve the technical problem that the prior art only aims at a single-target tracking scene, does not consider the influence of a transmission signal bandwidth on the total residence time and has certain limitation.
The technical scheme is as follows: the invention relates to a radio frequency stealth-based networking radar multi-target tracking residence time optimization method, which comprises the following steps of:
s1: aiming at a networking radar system, constructing a Bayesian-Luo lower bound matrix which takes a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables and is used for predicting a target state estimation error, and taking the Bayesian-Luo lower bound matrix as a measurement index of target tracking accuracy; the networking radar system comprises N two-coordinate phased array radars, the space, time and frequency of all the radars are synchronous, when a multi-target is tracked, each radar can only receive and process a target echo from a self-transmitted signal, and each radar can only track one target at most at each moment;
s2: the method comprises the following steps that the predicted tracking precision of a target at the next moment, the data processing amount of a fusion center and radar emission resources are used as constraint conditions, the total residence time of a minimized networking radar system is used as an optimization target, and a networking radar multi-target tracking residence time optimization model based on radio frequency stealth is established;
s3: and solving the networking radar multi-target tracking residence time optimization model.
Further, the bayesian krame-roch lower bound matrix in step S1 is obtained according to equation (1):
in the formula (1), the acid-base catalyst,
a Bayesian Clara-Lo lower bound matrix for the kth time, qth target, which is based on the number of target cells in the target cell>
A prediction Bayesian information matrix for the kth moment and the qth target;
Is the predicted state vector of the qth target at the kth time instant, in which->
For the predicted position of the qth object at the kth time instant>
Is the abscissa of the predicted position of the kth time point, the qth object, <' > is determined by the coordinate system of the reference point>
Is the ordinate of the predicted position of the qth target at the kth time instant>
For the predicted movement speed of the qth object at the kth time instant, <' >>
For the abscissa component of the predicted movement speed of the qth object at the kth time instant, it is determined whether a reference value is greater than or equal to>
The ordinate component of the predicted movement speed of the qth target at the kth time; w is a group of q For the variance of the qth target process noise, F is the target state transition matrix, < >>
Is a Bayesian information matrix of the kth-1 moment and the qth target, device for combining or screening>
The state vector of the kth time and the qth target is obtained;
For the radar binary selection of the variable for the ith radar at the kth time instant, <' >>
Time means the kth time, the ith radar irradiates the qth target and gets it->
The time indicates that the kth time and the ith radar do not irradiate the qth target;
Is->
The jacobian matrix of (a) is,
a non-linear measurement function of the ith radar to the qth target at the kth time, N is the total number of radars, and->
And predicting the covariance matrix of the measured noise of the ith radar to the qth target at the kth moment.
Further, in the above formula (1), W q Obtained by the formula (2):
in the formula (2), the reaction mixture is,
process noise Strength for the qth targetAnd degree, T is a target tracking sampling interval.
Further, in the formula (1),
obtained by the formula (3):
in the formula (3), the reaction mixture is,
a predicted Fisher information matrix of the prior information of the kth time and the qth target,
and the Fisher information matrix is the measured data of the ith radar to the qth target at the kth moment.
Further, the
Obtained by the formula (4):
in the formula (4), the reaction mixture is,
represents a pair->
And (4) making expectations.
Further, the
Obtained by the formula (5): />
In the formula (5), the reaction mixture is,
is->
In the mean square error of the evaluation of>
For the predicted distance between the kth time, the ith radar and the qth target>
Is->
In the mean square error of the evaluation of>
And predicting the direction angle of the ith radar to the qth target at the kth moment.
Further, the
And &>
Obtained by the formula (6):
in the formula (6), the reaction mixture is,
c =3 × 10 for the effective bandwidth of the transmitted signal of the ith radar to the qth target at the kth time 8 m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture, and/or>
And predicting the signal-to-noise ratio of the echo irradiated to the q-th target by the ith radar at the kth moment.
Further, the
Obtained by the formula (7):
in the formula (7), the reaction mixture is,
dwell time, T, of the ith radar on the qth target at the kth time rpt Is the pulse repetition period of the radar, P t Is the transmission power of radar, G t Gain for radar transmitting antenna, G r Gain of radar receiving antenna, G RP For processing gain, T, of radar receivers o For noise temperature of radar receivers, F rad Is the noise figure, k, of the radar receiver B Is Boltzmann constant, σ q Is the radar cross section of the qth target>
The bandwidth of a matched filter in the receiver of the ith radar for the qth target at the kth instant is combined>
Is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, theta 3dB Is the 3dB transmit and receive antenna beamwidth.
Further, the
Obtained by the formula (8):
in the formula (8), the reaction mixture is,
for the predicted distance between the kth time, the ith radar and the qth target>
Predicting direction angle of the ith radar to the qth target for the kth time, (x) i ,y i ) Is the position coordinate, x, of the ith radar i Is the abscissa, y, of the ith radar i The ordinate of the ith radar.
Further, in step S2, the multi-target tracking residence time optimization model of the networking radar is as shown in formula (9):
in the formula (9), the reaction mixture is,
the effective bandwidth of the signal transmitted by the ith radar to the qth target for the kth time, Q being the total number of targets, and->
For the dwell time of the qth target illumination by the ith radar at the kth time instant, <' >>
Is a matrix
Row 1, column 1 element->
Is a matrix->
Element of row 3, column 3, F max Estimating a threshold value for a lower bound of mean square error for each target position, -determining a mean square error for each target position based on the estimated threshold value>
For the total amount of data transmitted by the radar to the fusion center at the kth moment,
the data volume which needs to be transmitted to the fusion center and is related to the qth target for the ith moment and the ith radar, rho is more than or equal to 1 and is an oversampling coefficient, V is the area of a given observation area, and c =3 × 10 8 m/s is the speed of light, and>
effective bandwidth of a transmitted signal of the ith radar to the qth target at the kth moment, wherein epsilon is data processing rate of a fusion center and beta min For the lower limit of the bandwidth of the transmitted signal, beta max For upper limit of the bandwidth of the transmitted signal>
For upper limits of the dwell time of the radar irradiated target, <' >>
And M is less than or equal to N, which is the lower limit of the residence time of the radar irradiated target.
Has the advantages that: the invention discloses a multi-target tracking residence time optimization method for a networking radar based on radio frequency stealth, which comprises the steps of constructing a Bayesian-Roman lower bound of a target state estimation error by taking a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables, and taking the Bayesian-Roman lower bound as a measurement index of target tracking accuracy; on the basis, the prediction tracking precision of the target at the following moment, the data processing amount of the fusion center and the radar emission resource are taken as constraint conditions, the total residence time of the minimized networking radar system is taken as an optimization target, and parameters such as radar selection, residence time, emission signal bandwidth and the like in the multi-target tracking process are optimally designed. Therefore, the tracking precision of each target in the multi-target tracking process is met, the total residence time of the networking radar system is reduced to the maximum extent, and the radio frequency stealth performance of the networking radar system during multi-target tracking is improved.
Drawings
FIG. 1 is a flow chart of a genetic algorithm based on non-linear programming in an embodiment of the present invention;
FIG. 2 is a diagram illustrating a multi-target motion trajectory and a networking radar spatial distribution diagram according to an embodiment of the present invention;
FIG. 3 is a diagram of radar selection and signal bandwidth allocation for target 1 in accordance with an embodiment of the present invention;
FIG. 4 is a diagram of radar selection versus signal bandwidth allocation for target 2 in accordance with an embodiment of the present invention;
FIG. 5 is a diagram of radar selection versus dwell time assignments for target 1 in accordance with an embodiment of the present invention;
FIG. 6 is a diagram of radar selection versus dwell time allocation for target 2 in accordance with an embodiment of the present invention;
FIG. 7 is a comparison graph of multi-target tracking errors under different algorithms in accordance with an embodiment of the present invention;
fig. 8 is a comparison graph of the total residence time of the networked radar systems under different algorithms in the embodiment of the present invention.
Detailed Description
The specific embodiment discloses a radio frequency stealth-based method for optimizing multi-target tracking residence time of a networking radar, which comprises the following steps:
s1: constructing a Bayesian Clary-Rous lower bound matrix which takes a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables and is used for predicting target state estimation errors aiming at a networking radar system, and taking the Bayesian Clary-Rous lower bound matrix as a measurement index of target tracking accuracy; the networking radar system comprises N two-coordinate phased array radars, the space, time and frequency of all the radars are synchronous, when a plurality of targets are tracked, each radar can only receive and process target echoes from self-emitted signals, and each radar can only track one target at most at each moment;
s2: the method comprises the following steps that the predicted tracking precision of a target at the next moment, the data processing amount of a fusion center and radar emission resources are used as constraint conditions, the total residence time of a minimized networking radar system is used as an optimization target, and a networking radar multi-target tracking residence time optimization model based on radio frequency stealth is established;
s3: and solving the networking radar multi-target tracking residence time optimization model.
The Bayesian Classmei-Rou lower bound matrix in the step S1 is obtained according to the formula (1):
in the formula (1), the reaction mixture is,
a Bayesian Classman-Luo lower bound matrix for the kth time, qth objective, <' > is based on>
A prediction Bayesian information matrix for the kth moment and the qth target;
Is the predicted state vector of the qth target at the kth time instant, in which->
For the predicted position of the qth object at the kth time instant>
Is the abscissa of the predicted position of the kth time point, the qth object>
Is the ordinate of the predicted position of the qth target at the kth time instant>
For the predicted movement speed of the qth object at the kth time instant, <' >>
For the abscissa component of the predicted movement speed of the qth object at the kth time instant, it is determined whether a reference value is greater than or equal to>
The ordinate component of the predicted movement speed of the qth target at the kth time; w q For the variance of the qth target process noise, F is the target state transition matrix, based on>
A Bayesian information matrix for the kth-1 time, qth object, <' >>
The state vector of the kth time and the qth target is obtained;
Binary selection of variables for the radar at the kth time instant, i-th radar>
Time means the kth time, the ith radar irradiates the qth target, and>
the time indicates that the kth time and the ith radar do not irradiate the qth target;
Is->
The jacobian matrix of (a) is,
a non-linear measurement function of the ith radar to the qth target at the kth time, N being the total number of radars, and->
And (4) predicting a covariance matrix of the measured noise of the ith radar to the qth target at the kth moment.
In the formula (1), W q Obtained by the formula (2):
in the formula (2), the reaction mixture is,
and T is the process noise intensity of the qth target, and the target tracking sampling interval.
In the formula (1), the reaction mixture is,
obtained by the formula (3):
in the formula (3), the reaction mixture is,
a prediction Fisher information matrix of the prior information of the kth time and the qth target,
and the Fisher information matrix is the measured data of the kth radar to the qth target at the kth moment.
in the formula (4), the reaction mixture is,
represents a pair->
And (4) making expectations.
in the formula (5), the reaction mixture is,
is->
Is estimated mean square error, based on the mean square error value of the signal>
For the predicted distance between the kth time, the ith radar and the qth target>
Is->
Is estimated mean square error, based on the mean square error value of the signal>
And predicting the direction angle of the ith radar to the qth target at the kth moment.
in the formula (6), the reaction mixture is,
c =3 × 10 for the effective bandwidth of the transmitted signal of the ith radar to the qth target at the kth time 8 m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture, and/or>
And predicting the signal-to-noise ratio of the echo irradiated by the ith radar to the qth target at the kth moment.
in the formula (7), the reaction mixture is,
the dwell time of the irradiation of the qth target by the ith radar at the kth time, T rpt For the pulse repetition period of the radar, P t Is the transmission power of radar, G t Gain for the radar transmitting antenna, G r Gain of radar receiving antenna, G RP For processing gain of radar receiver, T o As noise temperature of radar receiver, F rad Is the noise figure, k, of the radar receiver B Is Boltzmann constant, σ q Is the radar cross section of the qth target, device for combining or screening>
The bandwidth of the matched filter in the receiver of the i-th radar for the q-th target at the k-th instant is->
Is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, theta 3dB Is the 3dB transmit and receive antenna beamwidth.
in the formula (8), the reaction mixture is,
for the predicted distance between the kth time, the ith radar and the qth target>
For the k time and the ith radar to the q target prediction direction angle, (x) i ,y i ) Is the position coordinate, x, of the ith radar i Is the abscissa, y, of the ith radar i The ordinate of the ith radar.
In the step S2, the multi-target tracking residence time optimization model of the networking radar is shown as a formula (9):
in the formula (9), the reaction mixture is,
the effective bandwidth of a transmitted signal of the ith radar to the qth target at the kth moment, wherein Q isA total number of targets>
For the dwell time of the qth target illumination by the ith radar at the kth time instant, <' >>
Is a matrix->
Row 1, column 1 element->
Is a matrix->
Element of row 3, column 3, F max Estimate a threshold value of the lower bound of the mean square error for each target position, <' >>
For the sum of the data transmitted by the radar to the fusion center at the kth time, based on the sum of the data transmitted by the radar to the fusion center>
The data volume which needs to be transmitted to the fusion center and is related to the qth target for the ith moment and the ith radar, rho is more than or equal to 1 and is an oversampling coefficient, V is the area of a given observation area, and c =3 × 10 8 m/s is the speed of light, and>
effective bandwidth of the transmitted signal of the ith radar to the qth target at the kth moment, epsilon is data processing rate of the fusion center, beta min For the lower limit of the bandwidth of the transmitted signal, beta max For upper limiting of the bandwidth of the transmitted signal>
For upper bounds on radar exposure target dwell times>
And M is less than or equal to N, which is the lower limit of the residence time of the radar irradiated target.
The model shown in the formula (9) is solved by adopting a two-step decomposition method and a genetic algorithm based on nonlinear programming, and the solving process is as follows:
(a) First, for a given satisfied constraint for the qth target
In the radar assignment mode of (1), equation (9) may be rewritten to include only the variable ≥>
And &>
In the form of (1). In addition, assuming that the fusion center processes the same amount of relevant data for each target to ensure that all targets have enough information, equation (9) can be simplified as follows:
in the formula, beta total The sum of the signal bandwidths transmitted for all radars illuminating a single target.
(b) Secondly, as the formula (10) is a non-convex and non-linear constraint optimization problem, the genetic algorithm based on non-linear programming is adopted to solve the problem. A flow chart of a genetic algorithm based on nonlinear programming is shown in fig. 1. The population initialization module initializes the population according to the solved problem, the fitness value calculation module calculates the fitness value of chromosomes in the population according to the fitness function, the fitness value is selected, crossed and mutated to be a search operator of the genetic algorithm, N is a fixed value, when the number of times of evolution is a multiple of N, the evolution is accelerated by adopting a nonlinear optimization method, and the nonlinear optimization uses the current chromosome value to search the local optimum value of the problem by adopting a function fminimax.
(c) Finally, based on passing through the non-linear gaugeSelecting radar selection, residence time and transmitted signal bandwidth value of each target under a designated radar distribution mode by the genetic algorithm, and selecting the radar selection which enables the total residence time of the networking radar system to be minimum
Dwell time->
And an emission signal bandwidth>
As the optimal solution for the model.
The number of the radars in the networking radar system is assumed to be N =6, the number of the targets is assumed to be Q =2, and the working parameters of the radars are the same. The remaining parameter settings are shown in table 1.
Table 1 simulation parameter settings
The initial position of the target 1 is (-100, -10) km and flies at a constant speed of (1300, 530) m/s, the initial position of the target 2 is (100, 90) km and flies at a constant speed of (-1300, -530) m/s, and the process noise intensity of the two targets is 15. Assuming airborne radar networking sampling interval T =3s, the tracking process duration is 150s. The maximum value of the residence time is
Minimum value equal to radar pulse repetition period T r . The maximum value of the bandwidth of the radar emission signal is beta max =1.9MHz, minimum value β min =0.1MHz. The preset tracking accuracy threshold is F max ＝30m。
The multi-target motion trajectory and networking radar spatial distribution diagram is shown in fig. 2, the radar selection and signal bandwidth allocation diagram of the target 1 is shown in fig. 3, the radar selection and signal bandwidth allocation diagram of the target 2 is shown in fig. 4, the radar selection and residence time allocation diagram of the target 1 is shown in fig. 5, and the radar selection and residence time allocation diagram of the target 2 is shown in fig. 6. As can be seen from fig. 2 to 6, in the target tracking process, along with the movement of the target, the networking radar system preferentially selects a radar close to the target to irradiate the target; meanwhile, the bandwidth and the residence time of the radar emission signal tend to be distributed to the selected radar far away from the target, so that the total residence time of the networking radar system is ensured to be shortest.
The multi-target tracking Error ratio under different algorithms is shown in fig. 7, where a target tracking Root Mean Square Error (RMSE) is defined as:
in the formula, N MC For the number of monte carlo experiments,
is the estimated position of the target obtained in the nth Monte Carlo experiment, where N is set MC =100. As can be seen from fig. 2 and 7, the proposed algorithm can better meet the tracking accuracy requirements of all targets.
The total residence time ratio of the networked radar systems under different algorithms is shown in fig. 8. As can be seen from fig. 8, compared with the bandwidth uniform distribution algorithm, the provided algorithm enables the networking radar system to have shorter total residence time, thereby further improving the radio frequency stealth performance of the networking radar during multi-target tracking.
According to the simulation result, the method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth can adaptively optimize and adjust parameters such as radar selection, residence time, emission signal bandwidth and the like in the multi-target tracking process under the condition of meeting the target prediction tracking precision, the fusion center data processing amount and the radar emission resource constraint at the next moment, minimize the total residence time of the networking radar system, and effectively improve the radio frequency stealth performance of the networking radar system during the multi-target tracking.
Claims (8)
1. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth is characterized by comprising the following steps of: the method comprises the following steps:
s1: constructing a Bayesian Clary-Rous lower bound matrix which takes a radar binary selection variable, radar residence time and transmitted signal bandwidth as independent variables and is used for predicting target state estimation errors aiming at a networking radar system, and taking the Bayesian Clary-Rous lower bound matrix as a measurement index of target tracking accuracy; the networking radar system comprises N two-coordinate phased array radars, the space, time and frequency of all the radars are synchronous, when a plurality of targets are tracked, each radar can only receive and process target echoes from self-emitted signals, and each radar can only track one target at most at each moment;
the bayesian krame-luo lower bound matrix is obtained according to equation (1):
in the formula (1), the reaction mixture is,
a Bayesian Classman-Luo lower bound matrix for the kth time, qth objective, <' > is based on>
A prediction Bayesian information matrix for the kth moment and the qth target;
Is the predicted state vector of the qth target at the kth time instant, in which->
For the predicted position of the qth object at the kth time instant>
Is the abscissa of the predicted position of the kth time point, the qth object>
As the ordinate of the predicted position of the qth object at the kth time,
for the predicted movement speed of the kth, qth object at a time instant>
For the abscissa component of the predicted movement speed of the qth object at the kth time instant, it is determined whether a reference value is greater than or equal to>
The ordinate component of the predicted movement speed of the qth target at the kth time; w is a group of q For the variance of the qth target process noise, F is the target state transition matrix, based on>
A Bayesian information matrix for the kth-1 time, qth object, <' >>
The state vector of the kth moment and the qth target is obtained;
Binary selection of variables for the radar at the kth time instant, i-th radar>
Time means the kth time, the ith radar irradiates the qth target and gets it->
The time indicates that the kth time and the ith radar do not irradiate the qth target;
Is->
The jacobian matrix of (a) is,
a non-linear measurement function of the ith radar to the qth target at the kth time, N is the total number of radars, and->
A prediction covariance matrix of the measured noise of the ith radar to the qth target at the kth moment;
s2: the method comprises the following steps that the predicted tracking precision of a target at the next moment, the data processing amount of a fusion center and radar emission resources are used as constraint conditions, the total residence time of a minimized networking radar system is used as an optimization target, and a networking radar multi-target tracking residence time optimization model based on radio frequency stealth is established;
the networking radar multi-target tracking residence time optimization model is shown as formula (9):
in the formula (9), the reaction mixture is,
the effective bandwidth of the signal transmitted by the ith radar to the qth target for the kth time, Q being the total number of targets, and->
For the dwell time of the qth target illumination by the ith radar at the kth time instant, <' >>
Is a matrix->
Row 1, column 1 element->
Is a matrix->
Element of row 3, column 3, F max Estimate a threshold value of the lower bound of the mean square error for each target position, <' >>
For the sum of data transmitted by the radar to the fusion center at the k-th time instant, the value is greater than>
The data volume which needs to be transmitted to the fusion center and is related to the qth target for the ith moment and the ith radar, rho is more than or equal to 1 and is an oversampling coefficient, V is the area of a given observation area, and c =3 × 10 8 m/s is the speed of light, and>
effective bandwidth of a transmitted signal of the ith radar to the qth target at the kth moment, wherein epsilon is data processing rate of a fusion center and beta min For the lower limit of the bandwidth of the transmitted signal, beta max For upper limit of the bandwidth of the transmitted signal>
For upper bounds on radar exposure target dwell times>
The lower limit of the residence time of the radar irradiated target is set, and M is less than or equal to N;
s3: and solving the networking radar multi-target tracking residence time optimization model.
2. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 1, characterized in that: in the formula (1), W q Obtained by the formula (2):
in the formula (2), the reaction mixture is,
and T is the process noise intensity of the qth target, and T is the target tracking sampling interval.
3. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 1, characterized in that: in the formula (1), the reaction mixture is,
obtained by the formula (3): />
In the formula (3), the reaction mixture is,
a prediction Fisher information matrix of the prior information of the kth time and the qth target,
and the Fisher information matrix is the measured data of the kth radar to the qth target at the kth moment.
4. According to the claimsSolving 3 the multi-target tracking residence time optimization method for the networking radar based on the radio frequency stealth is characterized in that: the above-mentioned
Obtained by the formula (4):
in the formula (4), the reaction mixture is,
represents a pair->
And (4) making the expectation.
5. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 3, wherein: the above-mentioned
Obtained by the formula (5):
in the formula (5), the reaction mixture is,
is->
In the mean square error of the evaluation of>
For the predicted distance between the kth time, the ith radar and the qth target>
Is->
In the mean square error of the evaluation of>
And predicting the direction angle of the ith radar to the qth target at the kth moment.
6. The radio frequency stealth-based networking radar multi-target tracking residence time optimization method according to claim 5, characterized in that: the above-mentioned
And &>
Obtained by the formula (6):
in the formula (6), the reaction mixture is,
c =3 × 10 for the effective bandwidth of the transmitted signal of the ith radar to the qth target at the kth time 8 m/s is the speed of light, lambda is the radar operating wavelength, gamma is the antenna aperture, and/or>
And predicting the signal-to-noise ratio of the echo irradiated by the ith radar to the qth target at the kth moment.
7. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 6,the method is characterized in that: the above-mentioned
Obtained by the formula (7):
in the formula (7), the reaction mixture is,
the dwell time of the irradiation of the qth target by the ith radar at the kth time, T rpt For the pulse repetition period of the radar, P t Is the transmission power of radar, G t Gain for radar transmitting antenna, G r Gain of radar receiving antenna, G RP For processing gain, T, of radar receivers o As noise temperature of radar receiver, F rad Is the noise figure, k, of the radar receiver B Is Boltzmann constant, σ q Is the radar cross section of the qth target>
The bandwidth of the matched filter in the receiver of the i-th radar for the q-th target at the k-th instant is->
Is the angle difference between the true azimuth of the qth target and the beam pointing angle of the ith radar to the qth target, θ 3dB Is the 3dB transmit and receive antenna beamwidth.
8. The method for optimizing the multi-target tracking residence time of the networking radar based on the radio frequency stealth as claimed in claim 1, wherein: the described
Obtained by the formula (8):
in the formula (8), the reaction mixture is,
for the predicted distance between the kth time, the ith radar and the qth target>
Predicting direction angle of the ith radar to the qth target for the kth time, (x) i ,y i ) Is the position coordinate, x, of the ith radar i Is the abscissa, y, of the ith radar i The ordinate of the ith radar. />
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