CN109521409B - Cognitive radar waveform optimization method based on bat algorithm - Google Patents

Cognitive radar waveform optimization method based on bat algorithm Download PDF

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CN109521409B
CN109521409B CN201811198822.XA CN201811198822A CN109521409B CN 109521409 B CN109521409 B CN 109521409B CN 201811198822 A CN201811198822 A CN 201811198822A CN 109521409 B CN109521409 B CN 109521409B
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汪清
王昊
高丽蓉
窦同东
李萌
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Tianjin University
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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
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • 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
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
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Abstract

The invention relates to a cognitive radar technology, in order to provide a method for optimizing waveform, compared with the existing method, the calculated performance is higher, the cognitive radar waveform optimizing method based on bat algorithm of the invention, send out the signal after the target reflection at the transmitting terminal, received by the receiving terminal, calculate the scattering coefficient of the target according to the maximum posterior probability, wherein, each fictitious bat represents a feasible position of the signal, obtain the optimum optimization algorithm according to calculating the position of bat after each iteration: setting a cost function corresponding to the fitness at the position of each signal in the space; iteration is carried out through a bat algorithm, the signal waveform is changed, the mean square error calculated by comparing the actual target scattering coefficient with the estimated target scattering coefficient is gradually reduced, the best position cost is found by P after multiple iterations, and the mean square error is minimized, so that the radar waveform optimization is realized. The invention is mainly applied to the occasions of designing and manufacturing the radar.

Description

Cognitive radar waveform optimization method based on bat algorithm
Technical Field
The invention relates to a cognitive radar technology, in particular to a cognitive radar waveform optimization method based on a bat algorithm.
Background
The cognitive radar system is a closed loop system [1] composed of a transmitter, a receiver and an environment. One of the key functions of the receiver is to feed back the received environment information to the transmitter, and the transmitter optimizes the transmitted waveform according to the feedback information, thereby continuously improving the estimation and detection performance of the system. In the transmitter, the transmission waveform is changed according to the obtained information to accurately estimate the target. The primary problem with cognitive radar is waveform optimization.
Waveform optimization in cognitive radar can be used for target detection and tracking due to its functional characteristics in minimizing estimation errors. In general, existing waveform optimization problems can be summarized in several ways: maximum mutual information [2], minimum Cramer-Lo bound [3], minimum Mean Square Error (MSE) [4], maximum signal-to-interference-and-noise ratio [5] and signal-to-noise ratio [6], and an optimized ambiguity function [7], among others. These problems are all non-convex [8], and solving with the semi-positive definite relaxation (SDR) method results in inaccuracies in the solution. We generally transform these problems into convex optimization problems and solve them with semi-definite relaxation (semi-definite relaxation SDR) [9 ]. SDR is a good approximation technology and can solve many difficult optimization problems. However, when solving the optimization problem, if some constraints are abandoned, the accuracy of the result is reduced, so that other methods need to be proposed.
The natural heuristic based optimization algorithm [10] has become a hot point of research in recent years because the natural heuristic algorithm can obtain a more accurate optimization result when solving an optimization problem, particularly a non-convex optimization problem, compared with the current waveform optimization algorithm.
The bat algorithm is a meta-heuristic optimization algorithm. The method simulates the echo positioning behavior of the bat in the natural world, and realizes global search and local search by changing the pulse amplitude and the pulse frequency in time. Each virtual BAT has a random flight speed and position (problem solution), and BATs have different frequencies or wavelengths, loudness and pulse rate. When the bat finds a prey, the frequency, loudness and pulse emissivity are changed, and the best solution is selected until the target stops or the conditions are met. The BAT algorithm applies this principle and finally finds a globally optimal solution.
[1]S.Haykin,“Cognitive radar:a way of the future,”IEEE Signal Processing Magazine,vol.23,no.1,pp.30–40,Jan.2006.
[2]A.Leshem,O.Naparstek,and A.Nehorai,“Information theoretic adaptive radar waveform design for multiple extended targets,”IEEE Journal of Selected Topics in Signal Processing,vol.1,no.1,pp.42–55,Jun.2007.
[3]P.Liu,Y.Liu,and X.Wang,“A cognitive radar approach for extended target ranging,”in2017IEEE Radar Conference(RadarConf),May 2017,pp.0709–0712.
[4]Y.Yang and R.S.Blum,“Mimo radar waveform design based on mutual information and minimum mean-square error estimation,”IEEE Transactions on Aerospace and Electronic Systems,vol.43,no.1,pp.330–343,Jan.2007.
[5]X.Zhang and C.Cui,“Signal detection for cognitive radar,”Electronics Letters,vol.49,no.8,pp.559–560,Apr.2013.
[6]S.Haykin,Y.Xue,and T.N.Davidson,“Optimal waveform design for cognitive radar,”in 42nd Asilomar Conference on Signals,Systems and Computers,Oct.2008,pp.3–7.
[7]S.Shi,G.Yang,Z.Zhao,and J.Liu,“A novel radar waveform design for a low-power hf monostatic radar,”IEEE Geoscience and Remote Sensing Letters,vol.12,no.6,pp.1352–1356,Jun.2015.
[8]S.Boyd and L.Vandenberghe,Convex optimization.Cambridge university press,2004.
[9]Z.Luo,W.Ma,A.M.So,Y.Ye,and S.Zhang,“Semidefinite relaxation of quadratic optimization problems,”IEEE Signal Processing Magazine,vol.27,no.3,pp.20–34,May 2010.
[10]X.S.Yang,Nature-Inspired Optimization Algorithms,1st ed.Amsterdam,The Netherlands,The Netherlands:Elsevier Science Publishers B.V.,2014。
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a wave form optimization method based on a bat algorithm, and compared with the existing method, the calculation performance is higher. Therefore, the cognitive radar waveform optimization method based on the bat algorithm adopts the technical scheme that a signal sent by a transmitting end is received by a receiving end after being reflected by a target, the scattering coefficient of the target is calculated according to the maximum posterior probability, each virtual bat represents a feasible position of the signal and has a random flight speed, position and moving direction, and the optimal optimization algorithm is obtained according to the calculated position of the bat after each iteration: setting a cost function corresponding to the fitness at the position of each signal in the space; p represents the current position, gest represents the current global optimal position of all signals with the optimal fitness, iteration is carried out through a bat algorithm, the waveform of the signals is changed, the mean square error calculated by comparing the actual target scattering coefficient with the estimated target scattering coefficient is gradually reduced, the optimal position Gest is found by P after multiple iterations, and the mean square error is minimized, so that the optimization of the radar waveform is realized.
Specifically, the method comprises the following steps:
firstly, defining and initializing the position and speed of each bat, wherein the number of the bats is M, the position of the bats is the solution of a transmission waveform, and the position of the bats is defined as X for the waveform optimization problem i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]D is the length of the signal to be transmitted; velocity is initialized to V i ＝{v 1 ,v 2 ,v 3 ...v D At a transmission power E in order to ensure spatial randomness s Under the constraint of (i.e.
Figure GDA0001968468660000021
Randomly selecting the position of each bat;
then, the fitness of the bat is defined and initialized, and on the problem of waveform optimization, the fitness F is defined as the value of an objective function corresponding to a transmitted signal:
Figure GDA0001968468660000022
wherein: MSE minimum mean square error, fitness of F bat, tr: trace of matrix, diag: diagonal elements of the matrix, superscript H: represents the transpose of the matrix, ru: the estimated target scattering coefficient, the actual target scattering function of Rg and the superscript-1 represent matrix inversion operation;
finally, pbest and Gbest are defined and initialized, the fitness of each bat is calculated according to the initial position of the bat group, and the optimal position of each bat at the moment is determined by the position of the bat at the current moment, as follows:
Figure GDA0001968468660000023
wherein arg denotes that F (x), i.e. the minimum value of F, is maximized, and the global optimal position is the position corresponding to the minimum fitness of all bats:
Gbest＝min{Pbest}
updating the speed and position of the bat: each bat can remember the historical optimal position of the bat, each bat can know the global optimal position of all bats, and the speed and position updating of the bats is defined according to the basic principle of the bat algorithm and the characteristics of waveform optimization:
Figure GDA0001968468660000031
Figure GDA0001968468660000032
Figure GDA0001968468660000033
wherein
Figure GDA0001968468660000034
And &>
Figure GDA0001968468660000035
Represents the speed of the bat i at t +1 and t, omega is an inertia weight and can influence the search capability of the bat and be combined with the bat>
Figure GDA0001968468660000036
And &>
Figure GDA0001968468660000037
Representing the bat positions at t +1 and t, gbest representing the global optimal position of all bats, f i Represents the search frequency, f, of bat i max And f min Represents the minimum and maximum values of the bat transmission frequency, and beta is a random number between 0 and1。
The specific steps in one example are as follows:
step 1: given dimension D of the received signal and maximum iteration number MaxDT of the whole bat algorithm, and the number M of bats;
and2, step: location X for initializing bat groups i Velocity V of i Initializing a bat population location X i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]Each element is initialized to [1, M ]]By an arbitrary integer value of (a), initializing a velocity V of the bat i ＝{v 1 ,v 2 ,v 3 ...v D Initializing global optimal solution Gbest;
and 3, step 3: according to the formula f i ＝f min +(f max -f min ) β update pulse frequency, produce pulse frequency f per bat i Initiating the frequency of pulse transmission
Figure GDA0001968468660000038
And pulse loudness>
Figure GDA0001968468660000039
And 4, step 4: updating the speed of bats
Figure GDA00019684686600000310
And position->
Figure GDA00019684686600000311
Velocity update formula
Figure GDA00019684686600000312
Location update formula
Figure GDA00019684686600000313
And 5: for each bat individual, a random number rand1 is generated, if
Figure GDA00019684686600000314
According to the formula
Figure GDA00019684686600000315
Re-disturbance generation is carried out near the current optimal individual, and the adaptive values of all the bat new positions are re-calculated;
and 6: generating a random number rand2 for each bat individual if
Figure GDA00019684686600000316
And->
Figure GDA00019684686600000317
Then the new solution is accepted and incremented>
Figure GDA00019684686600000318
Is decreased or is greater or less>
Figure GDA00019684686600000319
Wherein->
Figure GDA00019684686600000320
Indicates the pulse emission frequency at the iteration time>
Figure GDA00019684686600000321
Representing the pulse loudness at the iteration time;
and 7: and updating the global optimal solution and judging a termination condition, if so, outputting the current optimal solution, otherwise, turning to the step 3 and continuing to execute the algorithm.
The invention has the characteristics and beneficial effects that:
the method has the advantages that the waveform optimization problem can be well solved, the accuracy of waveform optimization is improved, and information is provided for the cognitive radar to better adapt to environmental changes.
In the estimation process of the cognitive radar extended target, the target scattering coefficient needs to be estimated through echo processing. In order to optimize the evaluation result, the emission waveform of the cognitive radar needs to be optimized, so that the target scattering coefficient of the received echo estimation can be closer to the actual result. The existing methods for solving the waveform optimization convert the non-convex problem into the convex optimization problem, and the result of the constraint calculation is not accurate enough due to the change. The waveform optimization method based on the bat algorithm is simple and can obtain more accurate results, and the biological heuristic algorithm is successfully applied to the cognitive radar waveform design.
In the aspect of solving result performance estimation, the simulation result shows that compared with the existing optimization method, the bat algorithm can better estimate the result. Fig. 2 is the actual Target Scattering Coefficient (TSC) and fig. 3 is the estimated target scattering coefficient after optimizing the waveform for the SDR and BAT algorithms. Fig. 4 shows the minimum Mean Square Error (MSE) of the estimated scattering coefficient of the target and the actual value, and fig. 5 shows the minimum mean square error by Kalman Filtering (KF).
Description of the drawings:
FIG. 1 is a flow chart of the algorithm.
Figure 2 actual target scattering coefficient.
Figure 3 estimates the target scattering coefficient.
Figure 4 minimum mean square error.
Fig. 5 minimum mean square error after kalman filtering.
Detailed Description
The invention belongs to the field of cognitive radar, and relates to a novel algorithm for improving cognitive radar waveform optimization. The adaptive waveform optimization algorithm is used for optimizing an adaptive waveform in a cognitive radar based on a bat algorithm to improve the estimation accuracy of a target scattering coefficient.
Cognitive radar has rapidly developed since its introduction. The radar target tracking system can detect and track a target in a complex radar environment (containing a large amount of clutter and various forms of interference). The cognitive radar system can obtain available information through priori knowledge, an external database and task priority, adjust the cognitive radar system according to the environment and improve the tracking, detecting, estimating and identifying performances of the system through adaptively optimizing waveforms. Therefore, waveform design is an important issue in cognitive radar research. Today, many methods for waveform optimization and design exist, but the calculation accuracy of the methods is not high enough. The invention aims to provide a wave form optimization method based on a bat algorithm, and compared with the existing method, the calculation performance is higher.
In the present invention, each bat represents a desired signal strategy, and each virtual bat has a random flight speed and position (a deployment strategy), the position and speed also representing the direction of movement of the bat. We set a fitness, or cost function, of the position of each signal in space. P denotes the current position and cost denotes the current global optimal position of all signals with the best fitness. And finding the best position after multiple iterations, and the best position is called as a global optimal solution.
The receiver utilizes the received waveform information to estimate the target scattering by using the maximum posterior probability to obtain the estimated target scattering coefficient, and comparing the estimated target scattering coefficient with the actual target scattering coefficient which is actually tested and input. And calculating the minimum mean square error between the two, taking the transmitted waveform as a variable and the minimum mean square error as a target function, and changing the transmitted waveform to realize the most accurate estimation of target information. Cost function (objective function): the minimum mean square error of the scattering coefficient and the actual scattering coefficient is estimated.
Specifically, the method comprises the following steps:
first we define and initialize the position and speed of each bat. Assuming that the number of bats is M, the location of the bats is the solution to the transmitted waveform. For the waveform optimization problem, the location of the bat is defined as X i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]D is the length of the signal to be transmitted; the velocity is initialized to V i ＝{v 1 ,v 2 ,v 3 ...v D }. This solution is a multi-dimensional vector. To ensure spatial randomness of the solution, at a transmission power E s Under the constraint of (i.e.
Figure GDA0001968468660000051
The position of each bat is randomly selected.
We then define and initialize the fitness of the bats. On the problem of waveform optimization, fitness F is defined as the value of an objective function corresponding to the transmitted signal.
Figure GDA0001968468660000052
( Defining: MSE minimum mean square error, fitness of F bat, tr: trace of matrix, diag: diagonal elements of the matrix, superscript H: represents the transpose of the matrix, ru: estimated target scattering coefficient, rg actual target scattering function. Superscript-1 representation matrix inversion operation )
Finally we define and initialize Pbest and Gbest. And calculating the appropriateness of the bats according to the initial positions of the bats, and determining the optimal position of each bat at the moment according to the position of the bat at the current moment. The following formula (arg denotes maximizing F (x), i.e., the minimum value of F)
Figure GDA0001968468660000053
The global optimal position is the position corresponding to the minimum fitness of all bats.
Gbest＝min{Pbest}
Updating the speed and position of the bat: we assume that each bat can remember its own historical optimal position, and each bat can know the global optimal position of all bats. Based on the basic principle of the bat algorithm and the characteristics of waveform optimization, we define the speed and position update of the bats
Figure GDA0001968468660000054
Figure GDA0001968468660000055
f i ＝f min +(f max -f min )×β
Wherein
Figure GDA0001968468660000056
And &>
Figure GDA0001968468660000057
The speed of the bat i at t +1 and t is shown, and omega is an inertia weight, which can affect the search capability of the bat. />
Figure GDA0001968468660000058
And &>
Figure GDA0001968468660000059
Representing the position of the bat at times t +1 and t. Gbest represents the global optimum position of all bats, f i Representing the search frequency of bat i. f. of max And f min Representing the minimum and maximum values of the bat transmission frequency. β is a random number between 0 and 1.
In summary, we introduce the bat algorithm as a calculation method. The signal sent out from the transmitting end is reflected by the target and then received by the receiving end, the scattering coefficient of the target is calculated according to the maximum posterior probability, the actual scattering coefficient of the target is compared with the estimated scattering coefficient of the target to calculate the minimum mean square error, and thus the minimum mean square error is the function of the transmitting waveform. Because the target scattering coefficient is related to the target, the closer the target scattering coefficient we estimate is to the estimated result, the more accurate it is. We therefore constantly change the waveform to minimize the mean square error.
One specific example is as follows:
a wave form optimization algorithm based on a bat algorithm comprises the following steps:
step 1, dimension D of a received signal, maximum iteration number MaxDT of the whole bat algorithm and the number M of bats are given.
And2, initializing the position Xi of the bat group and the speed Vi of the bat. Initializing a bat population location X i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]Each element is initialized to [1, M ]]Any integer value of (a). Initializing a velocity V of the bat i ＝{v 1 ,v 2 ,v 3 ...v D }. InitialAnd (4) transforming the global optimal solution Gbest.
Step 3, according to the formula f i ＝f min +(f max -f min ) X beta update frequency, generating pulse frequency f of each bat i . And initializing the transmission frequency of the generated pulse frequency
Figure GDA0001968468660000061
And pulse loudness->
Figure GDA0001968468660000062
And calculating an objective function value and an optimal solution during initialization. The pulse loudness is related to the random disturbance generated by the generated random numbers, and the position of the bat can be updated by comparing the generated random numbers with the pulse frequency and the pulse intensity.
Step 4, updating the speed of the bat
Figure GDA0001968468660000063
And &>
Figure GDA0001968468660000064
Step 5, generating a random number rand1 for each bat individual, if so
Figure GDA0001968468660000065
According to the speed update and the position update of the last step, the vicinity of the current optimal individual is subjected to re-perturbation to generate X i And recalculating the objective function values of all the bat new positions.
Step 6, generating random number rand2 for each bat individual, if
Figure GDA0001968468660000066
And->
Figure GDA0001968468660000067
Then the new solution is accepted and increased>
Figure GDA0001968468660000068
Decrease->
Figure GDA0001968468660000069
Step 7, updating global optimal solution Gbest
And 8, judging whether the iteration times are reached or the global optimal solution is obtained, if so, outputting the current optimal solution, otherwise, turning to the step 3, and continuing to execute the algorithm.
The invention is further described in detail below with reference to the attached drawings and specific examples.
As shown in fig. 1.
A cognitive radar waveform optimization method based on a bat algorithm comprises the following steps:
step 1: given the dimension D of the received signal and the maximum number of iterations MaxDT of the entire bat algorithm, and the number of bats M.
Step 2: location X for initializing bat group i Velocity V of i . Initializing a bat population location X i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]Each element is initialized to [1, M ]]Any integer value of (a). Initializing a speed V of the bat i ＝{v 1 ,v 2 ,v 3 ...v D }. And initializing the global optimal solution Gbest.
And step 3: according to the formula f i ＝f min +(f max -f min ) β update pulse frequency, produce pulse frequency f per bat i Initiating the frequency of pulse transmission
Figure GDA00019684686600000610
And pulse loudness->
Figure GDA00019684686600000611
And 4, step 4: updating bat speed
Figure GDA00019684686600000612
And position->
Figure GDA00019684686600000613
Velocity update formula
Figure GDA00019684686600000614
Location update formula
Figure GDA00019684686600000615
And 5: for each bat individual, a random number rand1 is generated, if
Figure GDA0001968468660000071
According to the formula
Figure GDA0001968468660000072
And re-perturbing the generation near the current optimal individual. And recalculating the adaptive values of all the new bat positions. />
Step 6: generating a random number rand2 for each bat individual if
Figure GDA0001968468660000073
And->
Figure GDA0001968468660000074
Then the new solution is accepted and incremented>
Figure GDA0001968468660000075
Is decreased or is greater or less>
Figure GDA0001968468660000076
Wherein->
Figure GDA0001968468660000077
Indicates the pulse emission frequency at the iteration time>
Figure GDA0001968468660000078
Indicating the loudness of the pulses at that iteration time.
And 7: and updating the global optimal solution and judging a termination condition, if so, outputting the current optimal solution, otherwise, turning to the step 3 and continuing to execute the algorithm.

Claims (2)

1. A cognitive radar waveform optimization method based on a bat algorithm is characterized in that a signal sent by a transmitting end is received by a receiving end after being reflected by a target, a target scattering coefficient is calculated according to the maximum posterior probability, wherein each virtual bat represents a feasible position of the signal and has a random flight speed, position and moving direction, and an optimal optimization algorithm is obtained according to the calculated position of the bat after each iteration: the position of each bat in the space is provided with an objective function corresponding to the fitness; p represents the current position, gbest represents the current global optimal position of all bats with optimal fitness, iteration is carried out through a bat algorithm, the signal waveform is changed, the mean square error calculated by comparing the actual target scattering coefficient with the estimated target scattering coefficient is gradually reduced, the optimal position Gbest is found by P after multiple iterations, the mean square error is minimum, and therefore radar waveform optimization is achieved; the method comprises the following specific steps:
firstly, defining and initializing the position and speed of each bat, wherein the number of the bats is M, the position of the bats is the solution of a transmission waveform, and the position of the bats is defined as X for the waveform optimization problem i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]D is the length of the signal to be transmitted; velocity is initialized to V i ＝{v 1 ,v 2 ,v 3 ...v D At a transmission power E in order to guarantee spatial randomness of the solution s Under the constraint of (2), i.e.
Figure FDA0003899470890000011
Randomly selecting the position of each bat;
the fitness of the bat is then defined and initialized, and on the problem of waveform optimization, the fitness F is defined as the value of the objective function corresponding to the transmitted signal:
Figure FDA0003899470890000012
wherein: MSE represents the minimum mean square error, F represents the fitness of the bat, tr: trace of matrix, diag: diagonal elements of the matrix, superscript H: representing the transpose of a matrix, R u : estimated scattering coefficient of the object, R g Representing the actual target scattering function, and superscript-1 representing matrix inversion operation;
finally, pbest and Gbest are defined and initialized, the fitness of each bat is calculated according to the initial position of the bat group, and the optimal position of each bat at the moment is determined by the position of the bat at the current moment, as follows:
Figure FDA0003899470890000013
wherein arg denotes maximizing F (x), i.e. the minimum value of F, and the global optimal position is the position corresponding to the minimum fitness of all bats:
Gbest＝min{Pbest}
updating the speed and position of the bat: each bat can remember the historical optimal position of the bat, each bat can know the global optimal position of all bats, and the speed and position updating of the bats is defined according to the basic principle of the bat algorithm and the characteristics of waveform optimization:
Figure FDA0003899470890000014
Figure FDA0003899470890000015
f i ＝f min +(f max -f min )×β
wherein V i t+1 And V i t The speed of the bat i at t +1 and t is shown, omega is an inertia weight, the searching capability of the bat is influenced,
Figure FDA0003899470890000016
and &>
Figure FDA0003899470890000017
Representing the bat positions at t +1 and t moments, gbest representing the global optimal positions of all bats, f i Represents the search frequency, f, of bat i max And f min Represents the minimum and maximum values of the bat search frequency, and is a random number between 0 and 1.
2. The bat algorithm-based cognitive radar waveform optimization method of claim 1, further comprising the following specific steps:
step 1: given the dimension D of the received signal and the maximum iteration number MaxDT of the whole bat algorithm, and the number M of bats;
and2, step: location X for initializing bat group i And velocity V i Initializing bat group location X i ＝{X 1 ,X 2 ,X 3 ...X D }，i∈[1,M]Each element is initialized to [1, M ]]By an arbitrary integer value of (a), initializing a velocity V of the bats group i ＝{v 1 ,v 2 ,v 3 ...v D }, initializing a global optimal position Gbest;
and 3, step 3: according to the formula f i ＝f min +(f max -f min ) β update search frequency, generate search frequency f for each bat i Initialization of the pulse emission frequency r i 0 And pulse loudness
Figure FDA0003899470890000021
And 4, step 4: updating the speed V of the bat i t And position
Figure FDA0003899470890000022
Velocity update formula
Figure FDA0003899470890000023
Location update formula
Figure FDA0003899470890000024
And 5: for each bat individual, a random number rand1 is generated, if rand1>r i t According to the formula
Figure FDA0003899470890000025
Regenerating disturbance near the current optimal individual, and recalculating the fitness of the new positions of all bats;
and 6: generating a random number rand2 for each bat individual, if rand
Figure FDA0003899470890000026
And->
Figure FDA0003899470890000027
Then accept this new solution and increase r i t Is decreased or is greater or less than>
Figure FDA0003899470890000028
Wherein r is i t Indicates the pulse emission frequency at the iteration time>
Figure FDA0003899470890000029
Representing the pulse loudness at the iteration time;
and 7: and updating the global optimal position and judging a termination condition, if so, outputting the current optimal solution, otherwise, turning to the step 3 and continuing to execute.
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