CN104360306A - Target ship direction estimation method based on differential evolution mechanism - Google Patents

Abstract

The invention discloses a target ship direction estimation method based on a differential evolution mechanism. The method includes the following steps that firstly, a multi-variation strategy is blended in a differential evolution optimization algorithm, so that the improved differential evolution mechanism is formed, wherein the multi-variation strategy comprises three processes of variation, hybridization and selection; secondly, the improved differential evolution mechanism acquired in the first step and a likelihood function are combined and used for estimating the DOA direction of a target ship. According to the method, the multi-variation strategy and a survival of the fittest mechanism are firstly blended in the differential evolution optimization algorithm and then the improved differential evolution mechanism and the likelihood function are combined and used for estimating the DOA direction of the target ship. Tests show that the reasonability of an improved differential evolution scheme is shown through the method and the method has better optimization performance than other algorithms; in addition, the improved differential evolution scheme is applied to the target ship direction estimation method, effectiveness is achieved, and the robustness of the method is better than that of other traditional methods.

Description

A kind of target boats and ships direction estimation method based on differential evolution mechanism

Technical field

The invention belongs to signal transacting field, be specifically related to a kind of ship's fix method based on differential evolution mechanism.

Background technology

Boats and ships are a kind of important carriers of maritime traffic, due to " complexity " of marine environment and " apt to change " of weather, the safe operation of boats and ships is unavoidably affected, even cause marine accident because boats and ships itself sustain damage, once accident occurs, the azimuth information of navigating ship will provide vital science support for safety guarantee department makes maintenance accurately or searches and rescues decision-making; Moreover, in order to ensure marine operation safety, boats and ships orientation is the important evidence that makes a policy of the automatic fixation and recognition of marine intelligent transportation and ship collision prevention system especially.

Ripple in signal transacting field reaches orientation (Direction of Arrival, DOA) estimate (such as document a: prominent personage. modern signal processing [M]. Beijing: publishing house of Tsing-Hua University, 2002.), be a kind of method for estimating target azimuth formed being widely used in the aspects such as radar, sonar, missile guidance and wireless communication system, its principle is the orientation by obtaining target source to the signal analysis of antenna array receiver.Existing DOA estimation method mainly can be divided three classes: multiple signal classification (multiple signal classification, MUSIC) method is (see document: Zhang X D.Modern Signal Processing [M] .Beijing:Tsinghua University Press, 2002. and document: Zhang Y., Ng B.P.MUSIC-like DOA Estimation withoutEstimating the Number of Sources [J] .IEEE Transcations on Signal Processing, 2010, 58 (3): 1668-1669.), ESPRIT (estimating signal parameter via rotationalinvariance techniques, ESPRIT) (see document: Jensen J.R., Christensen M.G., JensenS.H.Nonlinear Least Squares Methods for Joint DOA and Pitch Estimation [J] .IEEETransactions on Audio, Speech, and Language Processing, 2013, 21 (5): 923-9333. and document: Stoica P., Gershman A.B.Maximum-likelihood DOA Estimation byData-supported Grid Search [J] .IEEE Signal Processing Letters, 2009, 6 (10): 273-275.) and maximum likelihood estimate.

Wherein, multiple signal classification MUSIC method has good robustness to noise, but it needs the fast umber of beats of Received signal strength abundant, and the gun parallax between its estimated accuracy and target source to be positioned conditions each other.ESPRIT ESPRIT can be applicable to gun parallax larger when, but it is not only to outside noise inhibiting ability difference, and as MUSIC method of estimation, require that the fast umber of beats of signal is abundant.Maximum likelihood estimate is that a kind of technology with outstanding statistical property and robustness is (see document: Volodymyr V.Improved Beamspace ESPRIT-based DOA Estimation via Pseudo-noise Resampling [C] .EuMW & EuRAD 2012, Amsterdam, 2012:238-241.), verifiedly in theory optimum target DOA orientation can be obtained by maximum likelihood method; Compare with the MUSIC method of Subspace Decomposition and ESPRIT method, based on the estimated accuracy of the DOA estimation technique of maximum likelihood not only not by the constraint of fast umber of beats, and gradation in threshold region is relatively better.But because likelihood function is a nonlinear multimodal function, optimize this objective function is a very difficult and complicated problem.

For this reason, the present invention proposes a kind of target boats and ships direction estimation method based on differential evolution algorithm.A kind of colony's optimizing algorithm of simulating biological evolution that differential evolution algorithm is that Storn R. and Price K. propose is (see document: Storn R., Price K.Differential evolution-A simple and efficent adaptivescheme for global optimization over continuous spaces [R] .Berkeley:University ofCalifornia, 1996.).This optimized algorithm easily realizes, and controlled parameter is few, and this is also that we select a main cause of differential evolution algorithm.When utilizing its solving-optimizing problem, parameter so to be optimized is just equivalent to the biology of evolving, and biological evolution is once equivalent to complete an Optimized Iterative for parameter to be solved.Simulation biological evolution mechanism carries out the Optimized Iterative of primary parameter, and its process comprises variation, hybridizes and selects excellent three phases.Although numerous numerical optimization analysis example all demonstrates DE than genetic algorithm (geneticalgorithm, and particle swarm optimization algorithm (particle swarm optimization GA), PSO) algorithm have better optimize and constringency performance (see document: Wang R.J., Zhu Y.Nonlinear dynamic systemidentification based on FLANN [J] .Journal of Jimei University (Natural Science), 2011,16 (2): 128-134); But it is still the same with other traditional intelligence colony optimized algorithm exists " excessively precocious " deficiency that speed of convergence is slow and restrain.In the DE algorithm of prototype, single Mutation Strategy adds algorithm and limits probability into local optimum or Premature Convergence, and the thinking of head it off makes Mutation Strategy variation exactly.

Summary of the invention

Therefore, for above-mentioned problem, the present invention proposes a kind of target boats and ships direction estimation method based on differential evolution mechanism, it is optimized current maximum likelihood estimate, utilize the problem solving maximum likelihood function based on the differential evolution mechanism improved, the differential evolution mechanism improved makes Mutation Strategy variation, solves the deficiencies such as slow " excessively precocious " with restraining of speed of convergence; Meanwhile, the differential evolution mechanism of improvement makes whole solution procedure simplify and is easy to realize, and then it is applied to the estimation of target boats and ships orientation.

Make m and d represent array number and array element distance respectively, receiving array is positioned at the far-field region of n vessel position, and m >=n.Suppose source signal s (t)=[s that n target boats and ships send ₁(t), s ₂(t) ..., s _n(t)] ^tfor the independent each other and narrow band signal of zero-mean, and to remember that they arrive the 1st angle between array element direct rays and array normal direction be θ _i(i=1,2 ..., n), claim this angle to be that ripple is to orientation (angle), i.e. DOA orientation.If the 1st array element is considered as referential array, then target source arrives non-reference array element and all can there is delay, and namely the signal that receives of non-reference array element and target source signal exist a phase differential, and remembering that i-th target source arrives the 2nd phase differential that array element causes is ω _i, ω _iwith θ _ibetween pass be:

${\mathrm{\ω}}_i=2\mathrm{\π}\frac{d}{{\mathrm{\λ}}_s}\sin {\mathrm{\θ}}_i---\left(1\right)$

In formula (1), λ _sfor signal wavelength, ${\mathrm{\θ}}_i\∈\left[\begin{array}{cc}-\frac{\mathrm{\π}}{2}& \frac{\mathrm{\π}}{2}\end{array}\right];$ Ensure ω _i≤ π, array element distance must meet 2d≤λ _s.The vector that the phase differential that so i-th target source arrival m array element causes forms is designated as:

$a_i={[1,e^{{-\mathrm{j\ω}}_i},e^{{-j2\mathrm{\ω}}_i},\·\·\·,e^{{-j(m-1)\mathrm{\ω}}_i}]}^T---\left(2\right)$

In formula, for imaginary number.In like manner can obtain other target source signal and arrive the vector that m array element causes phase differential, vectorially form a matrix by dephased for institute, be designated as A, it and institute directed quantity a _ipass be:

$\begin{array}{c}A=[a_1,a_2,\·\·\·,a_n]\\ =\left[\begin{array}{cccc}1& 1& \·\·\·& 1\\ e^{{-\mathrm{j\ω}}_1}& e^{{-\mathrm{j\ω}}_2}& \·\·\·& e^{-j{\mathrm{\ω}}_n}\\ e^{{-j2\mathrm{\ω}}_1}& e^{{-j2\mathrm{\ω}}_2}& \·\·\·& e^{-j{2\mathrm{\ω}}_n}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ e^{{-j(m-1)\mathrm{\ω}}_1}& e^{{-j(m-1)\mathrm{\ω}}_1}& \·\·\·& e^{-j{(m-1)\mathrm{\ω}}_n}\end{array}\right]\end{array}---\left(3\right)$

A in formula (3) is Vandermonde (generalized circular matrix) matrix of m × n dimension, Rank (A)=n.If the signal that m array element receives is designated as x (t)=[x1 (t), x2 (t) ..., xm (t)] and T, the pass so between x (t) and s (t) is:

x(t)＝As(t)+η(t) (4)

η (t) in formula is mutual independently complex value white Gaussian noise undesired signal.According to document (Li H.L., AdaliT.A Class of Complex ICA Algorithms Based on the Kurtosis Cost Function [J] .IEEE Transactions on Neural Networks, 2008,19 (3): 408-419.) boundary the signal of complex value can be divided into and obeys super-Gaussian, the canonical of gaussian sum subalpine forests distribution or non-regular signal by kurtosis (kurtosis) concept defined, source signal si (t) (i=1,2,, n) for obeying the canonical of super-Gaussian or subalpine forests distribution or non-regular complex valued signals.Target boats and ships DOA estimates in orientation that problem to be solved is exactly when aliasing parameter A the unknown of source signal s (t) and receiving array, only from aliasing signal x (t) observed, estimate the residing DOA orientation relative to referential array of each target boats and ships according to the independent statistics characteristic of source signal, i.e. θ _i(i=1,2 ..., n).

A kind of target boats and ships direction estimation method based on differential evolution mechanism of the present invention, comprises the following steps:

Step 1: multi-Vari strategy is incorporated differential evolution optimization algorithm and form the differential evolution mechanism after improving, multi-Vari strategy comprises variation, hybridizes and selects excellent three processes, and solution parameter to be optimized is designated as β, and it specifically comprises following process:

Process 11: the iterative computation formula of the next optimization solution of multi-Vari decision search can change formula (5) into, by the iterative more new explanation β obtaining the variation stage of formula (5) _m;

In formula (5), β _mfor the solution that simulation biomutation search is next new, β _bestfor optimum solution extremely so far; L=1 ..., N _s, N _sfor biological scale of evolving; D=1 ..., D, D are the dimension of parameter to be solved, β _max(d) and β _mind () is respectively maximal value and the minimum value of the d dimension that may separate; F is the random number between [0 2], is the random number between [-1 1]; r ₁, r ₂and r ₃for at [1 N _s] between the random sequence number producing solution adjacent with i, attention r ₁≠ r ₂≠ i, r ₁≠ r ₂≠ r ₃≠ i; P (i) and be respectively probability and the average probability of the different possibility optimization solutions be directly proportional from target function value, p (i) is calculated by formula (6),

$\begin{array}{cc}p\left(l\right)=\frac{\mathrm{fit}\left({\mathrm{\β}}_l\right)}{\underset{l=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}\mathrm{fit}\left({\mathrm{\β}}_l\right)}& l=1,^,N_s\end{array}---\left(6\right);$

Fit (β in formula (6) _l) be measurement l solution β _lthe objective function of effect of optimization;

Process 12: hybridization: by the iterative more new explanation β obtaining crossing phase of formula (7) _c, and calculate their corresponding objective function J according to formula (9)-(10);

K in formula (7) _sfor [1 N _s] between random integers; for the random number produced between [0 1], C _rfor hybrid rate, its span is in [0 1];

$J_{\mathrm{ML}}=\mathrm{trace}\left(P_A^{\⊥}{R}_X\right)---\left(9\right)$

Formula (9) is for estimating n DOA orientation θ _ilikelihood function, in formula (9), for the projection matrix of noise subspace, its concrete formula is i is the unit matrix of m × n dimension, A ^*=(A ^ha) ^-1a ^hfor complex matrix A broad sense pseudo inverse matrix, " H " of pre-super and "-1 " represent respectively Hermitian (Hermitian matrix) transposition and inversion operation symbol; Trace () is Matrix Calculating order operational symbol, R _x=E [x (t) x ^h(t)] be the spatial domain covariance matrix of x (t), E [] accords with for asking expectation computing; In order to obtain the target boats and ships DOA orientation of optimum (namely the most accurate), objective function is rewritten as by we then estimate optimum θ _ithe cost function of (i=1, ^, n) is formula (10):

$\widehat{\mathrm{\θ}}=[{\widehat{\mathrm{\θ}}}_1,{\widehat{\mathrm{\θ}}}_2,\·\·\·,{\widehat{\mathrm{\θ}}}_n]=\underset{\mathrm{\θ}}{\arg \max }J=\frac{1}{c+\left|J_{\mathrm{ML}}\right|}---\left(10\right)$

In formula (10), ︱ ︱ accords with for asking signed magnitude arithmetic(al); C>0 is arbitrary constant, as J → c,

Process 13: select excellent: according to objective function J value magnitude relationship, from the β that β and the process 12 of last iteration calculate _cin select new optimization solution; If new optimization solution is chosen as the β of last iteration, then the corresponding biological k (l) that evolves _count=k (l) _count+ 1, for k (l) _count>k _limitβ produce its new explanation according to formula (8); Otherwise, put k (l) _count=0;

β(l,d)＝β _max(d)+β _min(d)-β(l,d) (8)；

Step 2: the differential evolution mechanism after the improvement of step 1 and likelihood function are combined and is applied to the DOA orientation of estimating target boats and ships, specifically comprise following process:

Process 21: choose from β and up to the present optimumly may separate β _best; If the arrival condition of convergence, then jump into step 22; Otherwise, rebound process 11;

Step 22: select may separating of global optimum according to formula (10) from β, then its element is the orientation estimating to obtain target boats and ships.

Further, in order to more a step improves the optimization of algorithm and convergence, process 13 select in excellent process, not only will according to target function value from original β and β _cin select new optimization solution β of future generation, also comprise process mechanism for the survival of the fittest being incorporated differential evolution optimization algorithm, this process does not obtain the β of renewal to klimit time, again gives possible new explanation by formula (8) to its element:

β(l,d)＝β _max(d)+β _min(d)-β(l,d) (8)。

The present invention is in order to solve the problem in orientation, localizing objects boats and ships present position, first multi-Vari strategy and " survival of the fittest " mechanism are incorporated differential evolution optimization algorithm, then the differential evolution mechanism of improvement and likelihood function being combined is applied to the DOA orientation of estimating target boats and ships.Experiment proves, method of the present invention not illustrate only the rationality of the differential evolution scheme of improvement, and it has better Optimal performance than some other algorithm; In addition, the differential evolution scheme of this improvement is applied in target boats and ships direction estimation method, not only has validity, and it has the method better robustness more traditional than other.

Accompanying drawing explanation

Fig. 1 is the schematic diagram that uniform line-array and ripple reach orientation;

Fig. 2 is the planisphere of canonical signal;

Fig. 3 is the planisphere of non-canonical signal;

Fig. 4 a is Different Optimization convergence of algorithm curve (source signal of canonical distribution);

Fig. 4 b is Different Optimization convergence of algorithm curve (source signal of non-canonical distribution);

Fig. 5 is the planisphere of mixed type signal;

Fig. 6 is the schematic diagram of the estimated performance of distinct methods.

Embodiment

Now the present invention is further described with embodiment by reference to the accompanying drawings.

For the location of boats and ships present position, the present invention proposes a kind of method for estimating target azimuth formed based on differential evolution mechanism.First, multi-Vari strategy and good and bad elimination system are introduced differential evolution algorithm, then new differential evolution mechanism is used for the plausible goals function that optimal estimating ripple reaches orientation, thus reaches the object in estimating target boats and ships orientation.The present invention below specifically sets forth the implementation procedure of the method for estimating target azimuth formed based on differential evolution mechanism.

One, the description of problem

Fig. 1 is the schematic diagram that uniform line-array and ripple reach orientation, represents array number and array element distance respectively see Fig. 1, m and d, and receiving array is positioned at the far-field region of n vessel position, and m >=n.Suppose source signal s (t)=[s that n target boats and ships send ₁(t), s ₂(t) ..., s _n(t)] ^tfor the independent each other and narrow band signal of zero-mean, and to remember that they arrive the 1st angle between array element direct rays and array normal direction be θ _i(i=1,2 ..., n), claim this angle to be that ripple is to orientation (angle), i.e. DOA orientation.If the 1st array element is considered as referential array, then target source arrives non-reference array element and all can there is delay, and namely the signal that receives of non-reference array element and target source signal exist a phase differential, and remembering that i-th target source arrives the 2nd phase differential that array element causes is ω _i, ω _iwith θ _ibetween pass be:

${\mathrm{\ω}}_i=2\mathrm{\π}\frac{d}{{\mathrm{\λ}}_s}\sin {\mathrm{\θ}}_i---\left(1\right)$

In formula (1), λ _sfor signal wavelength, ${\mathrm{\θ}}_i\∈\left[\begin{array}{cc}-\frac{\mathrm{\π}}{2}& \frac{\mathrm{\π}}{2}\end{array}\right];$ Ensure ω _i≤ π, array element distance must meet 2d≤λ _s.The vector that the phase differential that so i-th target source arrival m array element causes forms is designated as:

$a_i={[1,e^{{-\mathrm{j\ω}}_i},e^{{-j2\mathrm{\ω}}_i},\·\·\·,e^{{-j(m-1)\mathrm{\ω}}_i}]}^T---\left(2\right)$

In formula, for imaginary number.In like manner can obtain other target source signal and arrive the vector that m array element causes phase differential, vectorially form a matrix by dephased for institute, be designated as A, it and institute directed quantity a _ipass be:

$\begin{array}{c}A=[a_1,a_2,\·\·\·,a_n]\\ =\left[\begin{array}{cccc}1& 1& \·\·\·& 1\\ e^{{-\mathrm{j\ω}}_1}& e^{{-\mathrm{j\ω}}_2}& \·\·\·& e^{-j{\mathrm{\ω}}_n}\\ e^{{-j2\mathrm{\ω}}_1}& e^{{-j2\mathrm{\ω}}_2}& \·\·\·& e^{-j{2\mathrm{\ω}}_n}\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ \·& \·& \·& \·\\ e^{{-j(m-1)\mathrm{\ω}}_1}& e^{{-j(m-1)\mathrm{\ω}}_1}& \·\·\·& e^{-j{(m-1)\mathrm{\ω}}_n}\end{array}\right]\end{array}---\left(3\right)$

A in formula (3) is the Vandermonde matrix of m × n dimension, Rank (A)=n.If the signal that m array element receives is designated as x (t)=[x ₁(t), x ₂(t) ..., x _m(t)] T, the pass so between x (t) and s (t) is:

x(t)＝As(t)+η(t) (4)

η (t) in formula is mutual independently complex value white Gaussian noise undesired signal.According to document (Li H.L., AdaliT.A Class of Complex ICA Algorithms Based on the Kurtosis Cost Function [J] .IEEE Transactions on Neural Networks, 2008,19 (3): 408-419.) boundary the signal of complex value can be divided into and obeys super-Gaussian, the canonical of gaussian sum subalpine forests distribution or non-regular signal, source signal s by kurtosis (kurtosis) concept defined _i(t) (i=1,2 ..., n) for obeying the canonical of super-Gaussian or subalpine forests distribution or non-regular complex valued signals.Target boats and ships DOA estimates in orientation that problem to be solved is exactly when aliasing parameter A the unknown of source signal s (t) and receiving array, only from aliasing signal x (t) observed, estimate the residing DOA orientation relative to referential array of each target boats and ships according to the independent statistics characteristic of source signal, i.e. θ _i(i=1,2 ..., n).

Two, the target boats and ships orientation based on differential evolution mechanism is estimated

2.1, the differential evolution mechanism of multi-Vari strategy

A kind of colony's optimizing algorithm of simulating biological evolution that differential evolution algorithm is that Storn R. and Price K. propose is (see document: Storn R., Price K.Differential evolution-A simple and efficentadaptive scheme for global optimization over continuous spaces [R] .Berkeley:University of California, 1996.).This optimized algorithm easily realizes, and controlled parameter is few, and this is also that we select a main cause of differential evolution algorithm.When utilizing its solving-optimizing problem, parameter so to be optimized is just equivalent to the biology of evolving, and biological evolution is once equivalent to complete an Optimized Iterative for parameter to be solved.Simulation biological evolution mechanism carries out the Optimized Iterative of primary parameter, and its process comprises variation, hybridizes and selects excellent three phases.Although numerous numerical optimization analysis example all demonstrates DE than genetic algorithm (genetic algorithm, and particle swarm optimization algorithm (particle swarm optimization GA), PSO) algorithm have better optimize and constringency performance (see document Wang R.J., Zhu Y.Nonlinear dynamicsystem identification based on FLANN [J] .Journal of Jimei University (NaturalScience), 2011,16 (2): 128-134.); But it is still the same with other traditional intelligence colony optimized algorithm exists " excessively precocious " deficiency that speed of convergence is slow and restrain.In the DE algorithm of prototype, single Mutation Strategy adds algorithm and limits probability into local optimum or Premature Convergence, and the thinking of head it off makes Mutation Strategy variation exactly.Solution parameter to be optimized is designated as β by the present invention, and the iterative computation formula that we propose the next optimization solution of multi-Vari decision search can change into:

In formula (5), β _mfor the solution that simulation biomutation search is next new, β _bestfor optimum solution extremely so far; L=1 ..., N _s, wherein N _sfor biological scale of evolving; D=1 ..., D, wherein D is the dimension of parameter to be solved, β _max(d) and β _mind () is respectively maximal value and the minimum value of the d dimension that may separate; F is the random number between [0 2], is the random number between [-1 1]; r ₁, r ₂and r ₃for at [1 N _s] between the random sequence number producing solution adjacent with i, attention r ₁≠ r ₂≠ i, r ₁≠ r ₂≠ r ₃≠ i; P (i) and be respectively probability and the average probability of the different possibility optimization solutions be directly proportional from target function value, p (i) is calculated by formula (6),

$\begin{array}{cc}p\left(l\right)=\frac{\mathrm{fit}\left({\mathrm{\β}}_l\right)}{\underset{l=1}{\overset{\mathrm{Ns}}{\mathrm{\Σ}}}\mathrm{fit}\left({\mathrm{\β}}_l\right)}& l=1,^,N_s\end{array}---\left(6\right)$

Fit (β in formula (6) _l) be measurement l solution β _lthe objective function of effect of optimization.

The iteration that crossing phase produces new explanation is described by formula (7).

K in formula (7) _sfor [1 N _s] between random integers; for the random number produced between [0 1], C _rfor hybrid rate, its span is in [0 1].

In order to more a step improves optimization and the convergence of algorithm, the excellent stage of selecting of the DE algorithm that we propose not only will according to target function value from original β and β _cin select new optimization solution β of future generation, the mechanism of " survival of the fittest " of also introducing is to k _limitthe secondary β not obtaining upgrading, gives possible new explanation by formula (8) again to its element.

β(l,d)＝β _max(d)+β _min(d)-β(l,d) (8)

2.2, the target boats and ships DOA orientation based on differential evolution mechanism is estimated

The estimation in target DOA orientation comprises a number of targets n and n θ _iestimation two gordian techniquies.Target boats and ships number n by document (Wang Rongjie. owe to determine the research [D] of blind source separating and self-adaptive complex blind source separation algorithm. Guangzhou: Zhongshan University, 2012.) intersection test technology estimation mutually, this is repeated no more herein; Estimate n DOA orientation θ _ilikelihood function be formula (9).

$J_{\mathrm{ML}}=\mathrm{trace}\left(P_A^{\⊥}{R}_X\right)---\left(9\right)$

In formula (9), for the projection matrix of noise subspace, its concrete formula is i is the unit matrix of m × n dimension, A ^*=(A ^ha) ^-1a ^hfor complex matrix A broad sense pseudo inverse matrix, " H " of pre-super and "-1 " represent respectively Hermitian transposition and inversion operation symbol; Trace () is Matrix Calculating order operational symbol, R _x=E [x (t) x ^h(t)] be the spatial domain covariance matrix of x (t), E [] accords with for asking expectation computing.The estimating target that intelligent optimization algorithm and plausible goals function combined is in the method in the DOA orientation of position, is exactly corresponding n θ when utilizing the JML the minimization of object function in intelligent excellent Algorithm for Solving formula (9) in fact _ivalue, but this thinking can only obtain θ usually _ithe secondary figure of merit, in order to obtain the target boats and ships DOA orientation of optimum (namely the most accurate), objective function is rewritten as by we then estimate optimum θ _ithe cost function of (i=1, ^, n) is formula (10).

$\widehat{\mathrm{\θ}}=[{\widehat{\mathrm{\θ}}}_1,{\widehat{\mathrm{\θ}}}_2,\·\·\·,{\widehat{\mathrm{\θ}}}_n]=\underset{\mathrm{\θ}}{\arg \max }J=\frac{1}{c+\left|J_{\mathrm{ML}}\right|}---\left(10\right)$

In formula (10), ︱ ︱ accords with for asking signed magnitude arithmetic(al); C>0 is arbitrary constant, as J → c, c herein elects 1 as.

If solution β to be optimized for differential evolution algorithm is defined as DOA orientation θ, the performing step applied based on the DOA estimation principle localizing objects boats and ships anticounterfeiting methods of differential evolution mechanism is summed up as follows:

Step 1. initialization maximum iteration time k _max, k _limit, C _r, do not obtain record k (l) count of more excellent solution, evolve biological scale NS and the dimension D of solution to be optimized; At [β _min(d) β _max(d)] between produce β (l, d) initial value at random, l=1,2 ..., N _s; D=1,2 ..., D;

Step 2. is by the iterative more new explanation β obtaining the variation stage of formula (5) _m;

Step 3. is by the iterative more new explanation β obtaining crossing phase of formula (6) _c, and calculate their corresponding objective function J according to formula (9)-(10);

Step 4. according to objective function J value magnitude relationship, from the β that β and Step 3. of last iteration calculates _cin select new optimization solution; If new optimization solution is chosen as the β of last iteration, then the corresponding biological k (l) that evolves _count=k (l) _count+ 1, for k (l) _count>k _limitβ produce its new explanation according to formula (7); Otherwise, put k (l) _count=0;

Step 5. chooses and up to the present optimumly may separate β from β _best; If the arrival condition of convergence, then jump into Step 6; Otherwise, rebound Step 2;

Step 6. selects may separating of global optimum according to formula (10) from β, then its element is the orientation estimating to obtain target boats and ships.

3, simulation analysis

In order to investigate the effect of the differential evolution algorithm majorized function of the multi-Vari strategy of Section 2, choosing target boats and ships and sending and obey canonical distribution and non-canonical distribution signal two source signals and test.

Obeying at source signal 3 points of level signals chosen in canonical distribution emulation experiment is: r (t) and produce at random between [0 1] and [-π π] respectively; s ₂t () is 16QAM signal; s ₃the similar s of production method of (t) signal ₁t (), its r (t) produces at random according to Poisson distribution.Their planisphere as shown in Figure 2, s ₁(t) and s ₂t () is the complex signal of obeying subalpine forests distribution, and s ₃t () is for obeying the complex signal of super-Gaussian distribution; The orientation sending boats and ships present position corresponding to these 3 signals is θ=[10 ° 45 °-45 °].

Obeying at source signal 3 signals chosen in non-canonical distributed simulation is: s ₁(t) and s ₂t () can be expressed as s _r(t)+js _i(t), s ₁(t) and s ₂t the real part of () and imaginary part produce at random according to Poisson distribution and Gamma distribution respectively, and the real part in each moment and imaginary part inequality, the plural source signal obtained all obeys super-Gaussian distribution; s ₃t () is for obeying the bpsk signal of subalpine forests distribution; As shown in Figure 3, the orientation sending boats and ships present position corresponding to these 3 signals is θ=[-10 ° 45 °-45 °] to their planisphere.

Be optimized except utilizing the objective function J of algorithm to them herein, by algorithm herein and document (StornR., Price K.Differential evolution-A simple and efficent adaptive scheme for globaloptimization over continuous spaces [R] .Berkeley:University of California, 1996.) the DE optimized algorithm of mesarcs, document (Rahnamayan S., Tizhoosh H.R., Salama M.A.Opposition-based differential evolution [J] .IEEE Transactions on EvolutionaryComputation, 2008, 12 (1): 64-79.) the DE optimized algorithm improved in and document (Kennedy J., Eberhart R.C.Particle swarm optimization [C] .Proceedings of IEEE InternationalConference on Neural Networks, Perth, 1995:1942-1948.) in the experimental result of PSO optimized algorithm compare and emulate, in addition, the innovatory algorithm of DE or some relevant intelligent optimization algorithms are mentioned in current numerous document, in view of research emphasis herein, this is repeated no more herein.Fig. 4 is that four kinds of Different Optimization algorithms are to estimating the convergence curve that the likelihood function of DOA is optimized, can the optimization convergence capabilities of intuitive analysis algorithms of different by this curve, note the average for independent operating 30 emulation experiments, array number m=8, MABC in figure is document (Rahnamayan S., Tizhoosh H.R., Salama M.A.Opposition-based differential evolution [J] .IEEE Transactions on EvolutionaryComputation, 2008, 12 (1): 64-79.) the DE optimized algorithm of a kind of improvement proposed in, and IDE algorithm is innovatory algorithm in this paper, the optimum configurations that IDE, MDE and DE tri-kinds of algorithms are relevant is formula (11), and the relative parameters setting of PSO optimized algorithm is formula (12).

$\left\{\begin{array}{c}{k}_{\max }=500\\ C_R=0.5\\ N_S=20\end{array}\right.---\left(11\right)$

From the result compared four kinds of Different Optimization algorithms of Fig. 4, the IDE algorithm that the present invention proposes has better effect of optimization than MDE algorithm, DE algorithm and PSO algorithm; This also illustrates that the thinking that be used for improve the Optimal performance of related algorithm mutual by multi-Vari strategy in improved differential evolution algorithm and " survival of the fittest " selection method that the present invention proposes is feasible, and Case Simulation experimental result also reaches re-set target.

The source signal constellation chosen in the emulation experiment of checking based on the target boats and ships DOA orientation validity of differential evolution mechanism as shown in Figure 5, s ₁(t)=s _r(t)+js _i(t), real part and imaginary part produce at random according to Poisson distribution, and the real part in each moment and imaginary part inequality, it obeys the non-canonical signal of super-Gaussian distribution; for obeying the canonical signal of subalpine forests distribution, r (t) produces at random according to Gamma distribution, and (t) produces at random between [-π π]; s ₃t () is for obeying the 16QAM canonical signal of super-Gaussian distribution; s ₄t () is for obeying the non-canonical signal of BPSK of subalpine forests distribution; The orientation sending boats and ships present position corresponding to these 4 signals is θ=[10 °-10 ° 45 °-45 °], and the optimum configurations that differential evolution optimization algorithm is relevant is formula (14).In addition, also by this algorithm and document (Zhang Y., Ng B.P.MUSIC-like DOA Estimation withoutEstimating the Number of Sources [J] .IEEE Transcations on Signal Processing, 2010, 58 (3): 1668-1669.) based on the algorithm of MUSIC in, document (Volodymyr V.ImprovedBeamspace ESPRIT-based DOA Estimation via Pseudo-noise Resampling [C] .EuMW & EuRAD 2012, Amsterdam, based on the algorithm of ESPRIT and document (Li M.H. 2012:238-241.), Lu Y.L.Accrate Direction-of-Arrival Estimation of Multiple SourcesUsing a Genetic Approach [J] .Wireless Communcations and Mobile Computing, 2005, 5 (3): 343-353.) algorithm being objective function with class maximum likelihood function in carries out emulation and compares.In order to the effect that distinct methods is estimated is estimated in quantitative test, adopt formula (15) to evaluate the performance of algorithms of different, utilize them to the estimated result under different signal to noise ratio (S/N ratio) (Signal to Noise Ratio, SNR) as figure institute 6 shows.

$\left\{\begin{array}{c}{k}_{\max }=1000\\ C_R=0.5\\ N_S=20\end{array}\right.---\left(14\right)$

$\mathrm{Rmse}=\sqrt{\frac{1}{\mathrm{Kn}}\underset{i}{\mathrm{\Σ}}{({\mathrm{\θ}}_i-{\widehat{\mathrm{\θ}}}_i)}^2}---\left(15\right)$

K in formula (15) is the number of times of emulation experiment.

As shown in Figure 6, as high s/n ratio (i.e. SNR >=0dB), the quality that method herein and other method are estimated the DOA of target boats and ships is very close; But as low signal-to-noise ratio (i.e. SNR<0dB), the performance of the target boats and ships DOA direction estimation method based on differential evolution mechanism herein is obviously better than other method.Shown in this paperly to utilize the differential evolution mechanism improved and estimate that the plausible goals function of DOA combine the orientation of estimating target boats and ships present position is feasible by this simulation experiment result.

The present invention adopts such scheme, in order to solve the problem in orientation, localizing objects boats and ships present position, first multi-Vari strategy and " survival of the fittest " mechanism are incorporated differential evolution optimization algorithm, then the differential evolution mechanism of improvement and likelihood function being combined is applied to the DOA orientation of estimating target boats and ships.In emulation experiment, indicated the rationality of the differential evolution scheme of improvement on the one hand by the test result of the likelihood function of obeying in canonical distribution and non-canonical distribution two kinds of situations source signal, and it has better Optimal performance than some other algorithm; Estimate that the simulation experiment result not illustrate only the validity of the target boats and ships direction estimation method based on differential evolution mechanism of proposition by canonical and non-canonical mixed type source signal DOA orientation on the other hand, and it have the method better robustness more traditional than other.

Although specifically show in conjunction with preferred embodiment and describe the present invention; but those skilled in the art should be understood that; not departing from the spirit and scope of the present invention that appended claims limits; can make a variety of changes the present invention in the form and details, be protection scope of the present invention.

Claims (4)

1., based on a target boats and ships direction estimation method for differential evolution mechanism, comprise the following steps:

Step 1: multi-Vari strategy is incorporated differential evolution optimization algorithm and form the differential evolution mechanism after improving, multi-Vari strategy comprises variation, hybridizes and selects excellent three processes;

Step 2: the differential evolution mechanism after the improvement of step 1 and likelihood function are combined and is applied to the DOA orientation of estimating target boats and ships.

2. target boats and ships direction estimation method according to claim 1, is characterized in that: in described step 1, and solution parameter to be optimized is designated as β, and it specifically comprises following process:

Process 11: the iterative computation formula of the next optimization solution of multi-Vari decision search is formula (5), by the iterative more new explanation β obtaining the variation stage of formula (5) _m;

In formula (5), β _mfor the solution that simulation biomutation search is next new, β _bestfor optimum solution extremely so far; L=1 ..., N _s, N _sfor biological scale of evolving; D=1 ..., D, D are the dimension of parameter to be solved, β _max(d) and β _mind () is respectively maximal value and the minimum value of the d dimension that may separate; F is the random number between [0 2], is the random number between [-1 1]; r ₁, r ₂and r ₃for at [1 N _s] between the random sequence number producing solution adjacent with i, attention r ₁≠ r ₂≠ i, r ₁≠ r ₂≠ r ₃≠ i; P (i) and be respectively probability and the average probability of the different possibility optimization solutions be directly proportional from target function value, p (i) is calculated by formula (6), $\begin{array}{cc}p\left(l\right)=\frac{\mathrm{fit}\left({\mathrm{\&beta;}}_l\right)}{\underset{l=1}{\overset{\mathrm{Ns}}{\mathrm{\&Sigma;}}}\mathrm{fit}\left({\mathrm{\&beta;}}_l\right)}& l=1,^,N_s---\left(6\right);\end{array}$

Fit (β in formula (6) _l) be measurement l solution β _lthe objective function of effect of optimization;

Process 12: hybridization: by the iterative more new explanation β obtaining crossing phase of formula (7) _c, and according to formula (9)-(10)

Calculate their corresponding objective function J;

K in formula (7) _sfor [1 N _s] between random integers; for the random number produced between [0 1], C _rfor hybrid rate, its span is in [0 1];

$J_{\mathrm{ML}}=\mathrm{trace}\left(P_A^{\&perp;}{R}_x\right)---\left(9\right)$

Formula (9) is for estimating n DOA orientation θ _ilikelihood function, in formula (9), for the projection matrix of noise subspace, its concrete formula is i is the unit matrix of m × n dimension, A ^*=(A ^ha) ^-1a ^hfor complex matrix A broad sense pseudo inverse matrix, " H " of pre-super and "-1 " represent respectively Hermitian transposition and inversion operation symbol; Trace () is Matrix Calculating order operational symbol, R _x=E [x (t) x ^h(t)] be the spatial domain covariance matrix of x (t), E [] accords with for asking expectation computing; Objective function is rewritten as then estimate optimum θ _ithe cost function of (i=1, ^, n) is formula (10):

$\widehat{\mathrm{\&theta;}}=[{\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_2,\&CenterDot;\&CenterDot;\&CenterDot;,{\widehat{\mathrm{\&theta;}}}_n]=\underset{\mathrm{\&theta;}}{\arg \max }J=\frac{1}{c+\left|J_{\mathrm{ML}}\right|}---\left(10\right)$

In formula (10), ︱ ︱ accords with for asking signed magnitude arithmetic(al); C>0 is arbitrary constant, as J → c,

Process 13: select excellent: according to objective function J value magnitude relationship, from the β that β and the process 12 of last iteration calculate _cin select new optimization solution; If new optimization solution is chosen as the β of last iteration, then the corresponding biological k (l) that evolves _count=k (l) _count+ 1, for k (l) _count>k _limitβ produce its new explanation according to formula (8); Otherwise, put k (l) _count=0;

β(l,d)＝β _max(d)+β _min(d)-β(l,d) (8)。

3. target boats and ships direction estimation method according to claim 2, is characterized in that: in described step 2, specifically comprises following process:

Process 21: choose from β and up to the present optimumly may separate β _best; If the arrival condition of convergence, then jump into step 22; Otherwise, rebound process 11;

Step 22: select may separating of global optimum according to formula (10) from β, then its element is the orientation estimating to obtain target boats and ships.

4. target boats and ships direction estimation method according to claim 2, is characterized in that: in described process 13, also comprise process mechanism for the survival of the fittest being incorporated differential evolution optimization algorithm, this process is to k _limitthe secondary β not obtaining upgrading, gives possible new explanation by formula (8) again to its element:

β(l,d)＝β _max(d)+β _min(d)-β(l,d) (8)。