CN108256696B - Networking radar antenna configuration method combining state prediction and particle swarm optimization - Google Patents

Networking radar antenna configuration method combining state prediction and particle swarm optimization Download PDF

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CN108256696B
CN108256696B CN201810218028.0A CN201810218028A CN108256696B CN 108256696 B CN108256696 B CN 108256696B CN 201810218028 A CN201810218028 A CN 201810218028A CN 108256696 B CN108256696 B CN 108256696B
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张天贤
汪子钦
王远航
时巧
崔国龙
孔令讲
杨晓波
易伟
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Abstract

The invention discloses a networking radar optimization antenna configuration method based on prediction in a dynamic environment, belongs to the technical field of radar, and particularly relates to optimization configuration of networking radar sites by using a state prediction-based particle swarm optimization algorithm in the dynamic environment. The method can predict the approximate position of the radar site at the new moment according to the optimal site configuration scheme at the previous moment in the dynamic battlefield environment, and then calculate the actual optimal site configuration scheme by using a PSO (particle swarm optimization) method, thereby effectively reducing the calculation time, avoiding the waste of calculation resources and quickly obtaining the optimal configuration result of the radar site at each moment in the dynamic environment.

Description

Networking radar antenna configuration method combining state prediction and particle swarm optimization
Technical Field
The invention belongs to the technical field of radars, and particularly relates to an optimized configuration of networking radar sites by using a state prediction-based particle swarm optimization algorithm in a dynamic environment.
Background
With the development of comprehensive electronic warfare, the traditional radar working alone can not complete various tasks, the survival of the radar is also a problem to be solved urgently, and a single radar can not compete with an electronic countermeasure system. In this case, multifunctional radar networking is in force. The experts in the air and army of the united states generally consider networking to be the most promising anti-stealth, anti-interference approach. The America army has concentrated strength and preferentially arranges networking work so as to improve the monitoring and fighting capacity of the America army, and researches and continuously improves and perfects the networking of mature intelligence radar networks and guidance radars.
However, the performance of the networking radar is largely determined by the distribution of the antenna positions, and the performance of the networking radar can be obviously improved by optimizing the positions of the antennas. In recent years, Particle Swarm Optimization (PSO) is applied to solve the problem of optimizing the antenna position. However, previous researchers only studied the optimization problem of the position of the networking radar antenna under a single environment, and if the external environment changes, the obtained optimal site configuration scheme may not be applicable any more, and needs to be completely recalculated. However, in an actual battlefield, the environmental changes are divided into two types, one is irregular random change, and the other is regularly recurrent change. For the former variation, a complete recalculation each time is indeed a viable approach, but for the second, the recalculation ignores the laws between the environments, which may have a significant effect in reducing the amount of computation. The process of finding the optimal solution can be made simpler if we can find these rules and make them reasonably usable in the calculation.
Disclosure of Invention
The invention aims to research and design a particle swarm optimization method based on prediction aiming at a scheme for optimizing networking radar site configuration in a dynamic environment, and aims to solve the problem of optimization of the radar site configuration method at each moment when the environment dynamically changes within a period of time.
The technical scheme of the invention is as follows: a networking radar optimization antenna configuration method based on prediction in a dynamic environment comprises the following steps:
step 1, adopting a prediction model of Kalman filtering according to t1The antenna optimization configuration scheme at a plurality of previous moments predicts t1A time antenna configuration scheme;
s1.1, for t1In the previous environment at a plurality of moments, the optimal antenna configuration scheme at each moment is obtained by adopting the existing antenna optimization configuration method;
s1.2, establishing t by using the optimal antenna configuration scheme at the determined moment1-a state vector at time 1;
s1.3, using t1-1 moment state vector, using prediction model of kalman filtering, predicting t1A time antenna configuration scheme state vector;
step 2, randomly initializing initial particle swarm of the particle swarm optimization algorithm to the predicted t1Around the state vector of the antenna configuration scheme at the moment;
step 3, searching and obtaining an optimal antenna configuration scheme in a variable space by using a particle swarm optimization algorithm;
firstly, establishing an external archive set for storing non-dominated particles, selecting non-dominated particles from an initial particle swarm to be stored in the external archive set, and randomly selecting one particle as a global optimal particle, wherein the position of the particle is
Figure GDA0001651510720000021
Dominance here refers to Pareto dominance; the velocity and position of all particles are updated every iteration cycle:
Figure GDA0001651510720000022
Figure GDA00016515107200000210
where w (l) is the inertial weight, decaying with increasing iteration period, and the iterative formula is: w (l) 0.9-0.5 ═ l/lmax)，lmaxIs the maximum value of the iteration cycle, c1And c2Is an acceleration constant, r1And r2Is at [0,1 ]]The random real numbers are uniformly distributed in the interior,
Figure GDA0001651510720000023
and phii(l) Representing the velocity and position of the ith particle in the l iteration period, wherein all particle velocities do not exceed Vmax，
Figure GDA0001651510720000024
Indicating the historical optimum position of the ith particle,
Figure GDA0001651510720000025
representing an optimal location of a global particle;
after each iteration, firstly calculating whether each particle in the external archive set is dominated by a newly iterated particle, and deleting the dominated particle in the external archive set; then calculating the relationship between the newly iterated particles and particles in the external archive set, and adding the newly iterated particles into the external archive set if the newly iterated particles and the particles in the external archive set are not dominant; determining a final external archive set until the maximum iteration times are reached;
selecting a particle from the external archive set according to the current actual situation as t1A time actual antenna configuration scheme;
step 4, correcting the prediction model by using the site configuration scheme of the external archive set obtained in the step 3 and combining Kalman filtering;
s4.1, selecting a plurality of particles from an external file set according to actual conditions;
s4.2, calculating the t1The time prediction error cross-correlation matrix is
Figure GDA0001651510720000026
Figure GDA0001651510720000027
A is the state transition matrix, Q is the process noise,
Figure GDA0001651510720000028
is at the t1-1 a prediction error cross-correlation matrix after time correction;
s4.3, calculating a Kalman gain matrix of
Figure GDA0001651510720000029
Figure GDA0001651510720000031
Wherein H is an observation matrix, and R is an observation noise matrix;
s4.4, selecting a plurality of particles in combination with S4.1
Figure GDA0001651510720000032
For t1And (3) correcting the station configuration scheme at the moment:
Figure GDA0001651510720000033
wherein:
Figure GDA0001651510720000034
denotes the t-th1The state vector after the time correction is carried out,
Figure GDA0001651510720000035
representing an unmodified state prediction vector;
s4.5, correcting the state error cross correlation matrix as follows:
Figure GDA0001651510720000036
wherein: and E denotes an identity matrix.
Further, in the step 1, an existing antenna optimal configuration method is adopted to obtain an optimal antenna configuration scheme at the first three moments; predicting an antenna optimal configuration scheme at the fourth time, wherein the specific operation method comprises the following steps:
the state vector of the antenna configuration scheme at the third moment is as follows:
Figure GDA0001651510720000037
wherein
Figure GDA0001651510720000038
And
Figure GDA0001651510720000039
the antenna positions in the antenna optimal configuration schemes at the first time, the second time and the third time are respectively,
Figure GDA00016515107200000310
and
Figure GDA00016515107200000311
the speed and the acceleration of the moving trend of the antenna at the third moment are respectively; estimating the site location of the antenna configuration scheme at the fourth moment:
Figure GDA00016515107200000312
Figure GDA00016515107200000313
represents the antenna configuration scheme state vector at the fourth time instant,
Figure GDA00016515107200000314
is a state transition matrix.
Further, the specific method in step 2 is to define a square or circular neighborhood around each estimated antenna position at the fourth time, the size of the neighborhood is determined according to actual conditions, the sum of the neighborhoods of the sites is the neighborhood of the antenna position at the fourth time, and the initial particle swarm is randomly initialized in the neighborhood of the antenna position at the fourth time and the initial velocity of the particles is randomly initialized.
Further, the method for determining whether a certain particle is dominated by the rest of the particles in step 3 is as follows: the coverage of the monitoring region is used as an objective function of monitoring performance, the objective function values of the monitoring regions of the two particles are compared, and if the objective function value of all the monitoring regions of a certain particle is larger than or equal to the objective function value corresponding to another particle, the other particle is called to be dominated by the particle.
Further, the method for selecting the optimal particles from the external archive set obtained in step S3 in step S4.1 is as follows:
from t1Selecting the particles with the minimum Euclidean distance to the particles Q in the time external file set, wherein the particles Q belong to the slave t1-1 particles selected in the external archive set.
The method can predict the approximate position of the radar site at the new moment according to the optimal site configuration scheme at the previous moment in the dynamic battlefield environment, and then calculate the actual optimal site configuration scheme by using a PSO (particle swarm optimization) method, thereby effectively reducing the calculation time, avoiding the waste of calculation resources and quickly obtaining the optimal configuration result of the radar site at each moment in the dynamic environment.
Drawings
Fig. 1 is a flowchart of a method for optimally configuring a radar site in a dynamic environment according to the present invention.
FIG. 2 is a flowchart illustrating the substep of step S2 according to the present invention.
FIG. 3 is a flowchart illustrating a substep of step S3 according to the present invention.
FIG. 4 is a schematic diagram of a simulation scenario according to an embodiment of the present invention.
Fig. 5 is a non-dominated solution obtained by comparing the PBPSO algorithm proposed by the present invention with the general PSO algorithm in solving the site optimization configuration problem at one moment in a dynamic environment.
Fig. 6 is a comparison of the separation distance of the optimal solution calculated by the PBPSO algorithm and the general PSO algorithm proposed by the present invention and the actual optimal solution over the entire period of time.
Detailed Description
The technical scheme adopted by the invention is based on networking radar, Kalman filtering and a multi-target PSO algorithm are used, the radar site configuration is effectively optimized, and meanwhile, the optimization calculation process can be terminated in a self-adaptive mode according to the optimization result, and the method comprises the following steps:
regarding the three initial moments as mutually independent, and calculating an optimal site configuration scheme by using a traditional PSO method. The algorithm proposed herein can then be entered:
s1, predicting a rough site optimization configuration scheme at the next moment according to the previous site optimization configuration scheme by adopting a Kalman filtering prediction model, wherein the specific operation method comprises the following steps:
the state vector of the station configuration scheme at the third moment is as follows:
Figure GDA0001651510720000041
wherein
Figure GDA0001651510720000042
And
Figure GDA0001651510720000043
the antenna positions of the optimal configuration scheme of the station at the first three moments,
Figure GDA0001651510720000044
and
Figure GDA0001651510720000045
respectively, the velocity and acceleration of the antenna movement trend at the third moment. We can make a reasonable estimate of the approximate antenna position for the site configuration scheme at time four:
Figure GDA0001651510720000051
if the environmental changes follow some law, the antenna position of the site optimal configuration at the fourth time is likely to be in the immediate vicinity of the predicted point,
Figure GDA0001651510720000052
a state transition matrix.
S2, randomly initializing initial particle swarm of the PSO algorithm around the prediction solution:
for each antenna, a square or circular neighborhood is defined around the predicted position of the antenna, and when the PSO algorithm is used for calculating the optimal solution at the moment, the initial particle swarm is initialized in the neighborhoods randomly and the initial velocity of the particles is initialized randomly. For each particle, the objective function value is obtained, and the individual optimal position of each particle is considered as the initial position, and the individual optimal value of the particle is the initial particle objective function value.
S3, searching in a variable space by using a PSO algorithm to obtain an optimal site configuration scheme:
establishing an external archive set for storing non-dominated particles, selecting non-dominated particles from an initial particle swarm to be stored in the external archive set, and randomly selecting one particle as a global optimal particle, wherein the position of the particle is
Figure GDA0001651510720000053
The dominance here refers to Pareto dominance. The velocity and position of all particles are updated every iteration cycle:
Figure GDA0001651510720000054
Figure GDA0001651510720000055
where w (l) is the inertial weight, with iteration period (maximum l)max) Is expressed as w (l) 0.9-0.5 (l/l) in terms of an iterative formulamax)，c1And c2Is an acceleration constant, r1And r2Is at [0,1 ]]The random real numbers are uniformly distributed in the interior,
Figure GDA0001651510720000056
and phii(l) Representing the velocity and position of the ith particle in the l iteration period, wherein all particle velocities do not exceed Vmax。
And calculating a corresponding objective function value for each particle again, and updating the individual optimal position. And then updating the external file set, deleting the particles in the file set which are dominated by other particles, and adding the particles in the new iteration period into the external file set if the particles in the new iteration period are not dominated by the particles in the external file set, so that the external file set is the non-dominated particle swarm. And after the maximum iteration times are reached, calculating a corresponding objective function value for each particle again, and updating the individual optimal position. And then updating the external file set, deleting the particles in the file set which are dominated by other particles, and adding the particles in the new iteration period into the external file set if the particles in the new iteration period are not dominated by the particles in the external file set, so that the external file set is the non-dominated particle swarm. And after the maximum iteration times are reached, terminating the iteration and outputting a group of Pareto Set.
S4, correcting the prediction model by using the obtained optimal site configuration scheme and combining Kalman filtering:
taking the third time to the fourth time as an example, the prediction error cross-correlation matrix at the fourth time is:
Figure GDA0001651510720000061
a is the state transition matrix, Q is the process noise, and the Kalman gain matrix
Figure GDA0001651510720000062
Where H is the observation matrix and R is the observation noise matrix. Then we can combine the optimal site configuration z obtained after PSO calculation4And correcting the predicted site configuration scheme:
Figure GDA0001651510720000063
the correction to the state error cross correlation matrix is:
Figure GDA0001651510720000064
e denotes the identity matrix and the algorithm can iterate until the last moment of the dynamic environment.
Based on the embodiment, the simulation scenario of the algorithm is shown in fig. 4, assuming that two areas 1 and 2 need to be monitored, the antenna transmission power and transmission gain are 10kW and 40dB, respectively, and the simulation area is a square of 84km (each grid side length is 1.2 km). For convenience, assuming that 3 antennas need to be arranged within the site configuration area, zone 2 remains stationary and zone 1 moves vertically downward. With the coverage of the monitored area as the objective function of the monitoring performance, then
Figure GDA0001651510720000065
Wherein
Figure GDA0001651510720000066
And
Figure GDA0001651510720000067
respectively, the coverage of the area 1 and the area 2, and the larger the objective function value is, the better the monitoring performance is. In the PSO algorithm, the number N of basic parameter particles is 70, Vmax＝4，c1＝c2＝2，w＝0.4。
At the first three moments, because no prior information exists, only the optimization is carried out by using a common PSO algorithm, and a larger iteration number 200 is set. From the fourth moment, the state vector of the station configuration method at the third moment is obtained, and the optimal station configuration scheme at the fourth moment is predicted. And then optimizing the station configuration scheme at all subsequent times by using the method provided by the text, and selecting the iteration number as 15. In order to compare with the traditional method, the traditional PSO method with the same iteration number is used for optimizing the site configuration scheme at each moment. And finally comparing the results obtained by the two methods. At the fourth time, the objective functions of the site configuration schemes obtained by the two methods are shown in fig. 5, and the difference between the objective function obtained at each time and the objective function of the actual optimal scheme is shown in fig. 6. From both figures we can conclude that: the optimization effect of the traditional PSO method on the site configuration scheme at each moment in the dynamic environment is much worse than that of the method provided by the document. Moreover, with the method provided herein, errors between the obtained site optimization configuration scheme and the actual optimal site configuration scheme may gradually accumulate over time. In summary, the method can obtain the site optimization configuration scheme at each moment in a dynamic environment without much time and computing resources.

Claims (4)

1. A networking radar optimization antenna configuration method based on prediction in a dynamic environment comprises the following steps:
step 1, adopting a prediction model of Kalman filtering according to t1The antenna optimization configuration scheme at a plurality of previous moments predicts t1A time antenna configuration scheme;
s1.1, for t1In the previous environment at a plurality of moments, the optimal antenna configuration scheme at each moment is obtained by adopting the existing antenna optimization configuration method;
s1.2, establishing t by using the optimal antenna configuration scheme at the determined moment1-a state vector at time 1;
s1.3, using t1-1 moment state vector, using prediction model of kalman filtering, predicting t1A time antenna configuration scheme state vector;
step 2, randomly initializing initial particle swarm of the particle swarm optimization algorithm to the predicted t1Around the state vector of the antenna configuration scheme at the moment;
step 3, searching and obtaining an optimal antenna configuration scheme in a variable space by using a particle swarm optimization algorithm;
the method for determining whether a particle is dominated by the rest of the particles is as follows: comparing the objective function values of the monitoring areas of the two particles by taking the coverage of the monitoring areas as an objective function of monitoring performance, and if the objective function values of all the monitoring areas of a certain particle are more than or equal to the objective function value corresponding to another particle, calling that the other particle is dominated by the particle;
firstly, establishing an external archive set for storing non-dominated particles, and selecting the non-dominated particles from an initial particle swarmStoring the particles in an external archive set, and randomly selecting one particle as a global optimal particle, wherein the position of the particle is
Figure FDA0003199590920000011
Dominance here refers to Pareto dominance; the velocity and position of all particles are updated every iteration cycle:
Figure FDA0003199590920000012
Figure FDA0003199590920000013
where w (l) is the inertial weight, decaying with increasing iteration period, and the iterative formula is: w (l) 0.9-0.5 ═ l/lmax)，lmaxIs the maximum value of the iteration cycle, c1And c2Is an acceleration constant, r1And r2Is at [0,1 ]]The random real numbers are uniformly distributed in the interior,
Figure FDA0003199590920000014
and phii(l) Representing the velocity and position of the ith particle in the l iteration period, wherein all particle velocities do not exceed Vmax，
Figure FDA0003199590920000015
Indicating the historical optimum position of the ith particle,
Figure FDA0003199590920000016
representing an optimal location of a global particle;
after each iteration, firstly calculating whether each particle in the external archive set is dominated by a newly iterated particle, and deleting the dominated particle in the external archive set; then calculating the relationship between the newly iterated particles and particles in the external archive set, and adding the newly iterated particles into the external archive set if the newly iterated particles and the particles in the external archive set are not dominant; determining a final external archive set until the maximum iteration times are reached;
selecting a particle from the external archive set according to the current actual situation as t1A time actual antenna configuration scheme;
step 4, correcting the prediction model by using the site configuration scheme of the external archive set obtained in the step 3 and combining Kalman filtering;
s4.1, selecting a plurality of particles from an external file set according to actual conditions;
s4.2, calculating the t1The time prediction error cross-correlation matrix is
Figure FDA0003199590920000021
Figure FDA0003199590920000022
A is the state transition matrix, Q is the process noise,
Figure FDA0003199590920000023
is at the t1-1 a prediction error cross-correlation matrix after time correction;
s4.3, calculating a Kalman gain matrix of
Figure FDA0003199590920000024
Figure FDA0003199590920000025
Wherein H is an observation matrix, and R is an observation noise matrix;
s4.4, selecting a plurality of particles in combination with S4.1
Figure FDA0003199590920000026
For t1And (3) correcting the station configuration scheme at the moment:
Figure FDA0003199590920000027
wherein:
Figure FDA0003199590920000028
denotes the t-th1The state vector after the time correction is carried out,
Figure FDA0003199590920000029
representing an unmodified state prediction vector;
s4.5, correcting the state error cross correlation matrix as follows:
Figure FDA00031995909200000210
wherein: and E denotes an identity matrix.
2. The networking radar optimization antenna configuration method based on prediction in the dynamic environment as claimed in claim 1, wherein the existing antenna optimization configuration method is adopted in the step 1 to obtain the optimal antenna configuration scheme at the first three moments; predicting an antenna optimal configuration scheme at the fourth time, wherein the specific operation method comprises the following steps:
the state vector of the antenna configuration scheme at the third moment is as follows:
Figure FDA00031995909200000211
wherein
Figure FDA00031995909200000212
And
Figure FDA00031995909200000213
the antennas at the first, second and third time points respectivelyThe position of each antenna in the preferred configuration,
Figure FDA00031995909200000214
and
Figure FDA00031995909200000215
the speed and the acceleration of the moving trend of the antenna at the third moment are respectively; estimating the site location of the antenna configuration scheme at the fourth moment:
Figure FDA0003199590920000031
Figure FDA0003199590920000032
represents the antenna configuration scheme state vector at the fourth time instant,
Figure FDA0003199590920000033
is a state transition matrix.
3. The method according to claim 1, wherein the step S4.1 of selecting the optimal particles from the external archive set obtained in step 3 comprises:
from t1Selecting the particles with the minimum Euclidean distance to the particles Q in the time external file set, wherein the particles Q belong to the slave t1-1 particles selected in the external archive set.
4. The method as claimed in claim 2, wherein the specific method in step 2 is to define a square or circular neighborhood around each estimated antenna position at the fourth time, the size of the neighborhood is determined according to practical conditions, the sum of the neighborhoods of the sites is the neighborhood of the antenna position at the fourth time, and initialize the initial particle swarm in the neighborhood of the antenna position at the fourth time and initialize the initial velocity of the particles randomly.
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