CN104360306B - A kind of target boats and ships direction estimation method based on differential evolution mechanism - Google Patents

Abstract

The present invention discloses a kind of target boats and ships direction estimation method based on differential evolution mechanism, it comprises the following steps: step 1: multi-Vari strategy incorporates differential evolution optimization algorithm and forms the differential evolution mechanism after improving, and multi-Vari strategy includes variation, hybridizes and select excellent three processes；Step 2: the differential evolution mechanism after the improvement of step 1 and likelihood function are combined and is applied to estimate the DOA orientation of target boats and ships.First multi-Vari strategy and " survival of the fittest " mechanism are incorporated differential evolution optimization algorithm by the present invention, then differential evolution mechanism and the likelihood function of improvement are combined and are applied to estimate the DOA orientation of target boats and ships.It is demonstrated experimentally that the method for the present invention not illustrate only the reasonability of the differential evolution scheme of improvement, and it has than some other algorithm and preferably optimizes performance；It addition, the differential evolution scheme of this improvement is applied in target boats and ships direction estimation method, not only there is effectiveness, and it has the more preferable robustness of the method more traditional than other.

Description

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

Technical field

The invention belongs to signal processing 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 " complicated " and " apt to change " of weather, the boats and ships of marine environment Safe operation be unavoidably affected, even cause marine accident because boats and ships itself sustain damage, once accident occur, The azimuth information of navigating ship will be made for safety guarantee department and safeguard or search and rescue the decision-making vital science of offer accurately Support；Moreover, in order to ensure marine operation safety, the marine intelligent transportation especially of boats and ships orientation is automatically positioned identification and boats and ships The important evidence that collision avoidance system makes a policy.

Ripple in signal processing field reaches orientation (Direction of Arrival, DOA) and estimates (such as document: Zhang Xian Reach. modern signal processing [M]. Beijing: publishing house of Tsing-Hua University, 2002.), it is that one is widely used in radar, sonar, guided missile The method for estimating target azimuth formed of the aspects such as guidance and wireless communication system, its principle is by entering the signal of antenna array receiver Row analyzes the orientation obtaining target source.Existing DOA estimation method can be divided mainly into three classes: multiple signal classification (multiple Signal classification, MUSIC) method (sees document: Zhang X D.Modern Signal Processing [M] .Beijing:Tsinghua University Press, 2002. and document: Zhang Y., Ng B.P.MUSIC- like DOA Estimation without Estimating the Number of Sources[J].IEEE Transcations on Signal Processing, 2010,58 (3): 1668-1669.), ESPRIT (estimating signal parameter via rotational invariance techniques, ESPRIT) (ginseng See document: Jensen J.R., Christensen M.G., Jensen S.H.Nonlinear Least Squares Methods for Joint DOA and Pitch Estimation[J].IEEE Transactions on Audio, Speech, and Language Processing, 2013,21 (5): 923-9333. and document: Stoica P., Gershman A.B.Maximum-likelihood DOA Estimation by Data-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 to receive the fast of signal Umber of beats is abundant, and the gun parallax between its estimated accuracy and target source to be positioned conditions each other.ESPRIT ESPRIT can be suitably used for gun parallax relatively big in the case of, but outside it is not only to noise inhibiting ability difference, and as MUSIC estimation side Method equally requires that the fast umber of beats of signal is abundant.Maximum likelihood estimate is a kind of skill with outstanding statistical property and robustness Art (sees document: Volodymyr V.Improved Beamspace ESPRIT-based DOA Estimation via Pseudo-noise Resampling [C] .EuMW&EuRAD 2012, Amsterdam, 2012:238-241.), the most The verified target DOA orientation that can be obtained optimum by method of maximum likelihood；MUSIC method and ESPRIT method with Subspace Decomposition Relatively, the estimated accuracy of the DOA estimation technique based on maximum likelihood is not retrained by fast umber of beats, and in threshold region Gradation is preferable.But, owing to likelihood function is a nonlinear multimodal function, will optimize this object function is one Individual highly difficult and complicated problem.

To this end, the present invention proposes a kind of target boats and ships direction estimation method based on differential evolution algorithm.Differential evolution is calculated Method be that Storn R. and Price K. propose a kind of simulate biological evolution colony's optimizing algorithm (see document: Storn R., Price K.Differential evolution—A simple and efficent adaptive 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 differential evolution to calculate One main cause of method.When utilizing its solving-optimizing problem, then parameter to be optimized is equivalent to the biology evolved, and biological Evolve and be once equivalent to an Optimized Iterative is completed for parameter to be solved.Simulation biological evolution mechanism carries out primary parameter Optimized Iterative, its process include variation, hybridize and select excellent three phases.Although numerous numerical optimization analysis example is all tested Demonstrate,prove DE than genetic algorithm (genetic algorithm, GA) and particle swarm optimization algorithm (particle swarm Optimization, PSO) algorithm has and preferably optimizes and constringency performance (sees document: Wang R.J., Zhu Y.Nonlinear dynamic system identification based on FLANN[J].Journal of Jimei University(Natural Science),2011,16(2):128-134)；But it is still excellent with other traditional intelligence colony Change algorithm and equally there is " the most precocious " deficiency that convergence rate is slow and restrains.In the DE algorithm of prototype, single Mutation Strategy adds Algorithm limits the probability into local optimum or Premature Convergence, and the thinking solving this problem 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 orientation based on differential evolution mechanism and estimates Method, current maximum likelihood estimate is optimized by it, utilizes the differential evolution mechanism based on improving to solve maximum seemingly The problem of right function, the differential evolution mechanism of improvement makes Mutation Strategy variation, solves convergence rate slow " too early with restrain Ripe " etc. deficiency；Meanwhile, the differential evolution mechanism of improvement makes whole solution procedure simplify and be easily achieved, and then it is applied to Target boats and ships orientation is estimated.

Making 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.Assume source signal s (t)=[s that n target boats and ships send₁(t),s₂(t),…,s_n(t)]^TEqual for independence each other and zero The narrow band signal of value, and remember that they the 1st angles between array element direct rays and array normal direction of arrival are θ_i(i=1, 2 ..., n), this angle is called that ripple is to orientation (angle), i.e. DOA orientation.If the 1st array element being considered as referential array, then target source Arriving non-reference array element and all can there is delay, there is a phase place with target source signal in the signal that i.e. non-reference array element receives Difference, it is ω that note i-th target source arrives the 2nd phase contrast that array element causes_i, ω_iWith θ_iBetween relation be:

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

In formula (1), λ_sFor signal wavelength,ω to be ensured_i≤ π, array element distance must is fulfilled for 2d≤λ_s.That I-th target source arrives the vector of the phase contrast composition that m array element causes and 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 m array element of arrival and cause the vector of phase contrast, By dephased for institute vector one matrix of composition, it is designated as A, it and institute directed quantity a_iRelation be:

$\begin{array}{c}A=\[a_1,a_2,...,a_n\]\\ =\left[\begin{array}{cccc}1& 1& \mathrm{...}& 1\\ e^{-{\mathrm{j\ω}}_1}& e^{-{\mathrm{j\ω}}_2}& \mathrm{...}& e^{-{\mathrm{j\ω}}_n}\\ e^{-j2{\mathrm{\ω}}_1}& e^{-j2{\mathrm{\ω}}_2}& \mathrm{...}& e^{-j2{\mathrm{\ω}}_n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ e^{-j(m-1){\mathrm{\ω}}_1}& e^{-j(m-1){\mathrm{\ω}}_1}& \mathrm{...}& 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 by m The signal that individual array element receives be designated as x (t)=[x1 (t), x2 (t) ..., xm (t)] T, then the relation between x (t) and s (t) For:

X (t)=As (t)+η (t) (4)

η (t) in formula is the most independent complex value white Gaussian noise interference signal.According to document (Li H.L., Adali T.A Class of Complex ICA Algorithms Based on the Kurtosis Cost Function[J] .IEEE Transactions on Neural Networks, 2008,19 (3): 408-419.) kurtosis defined (kurtosis) boundary can be divided into the signal of complex value and obeys super-Gaussian, the canonical of gaussian sum subalpine forests distribution or non-canonical by concept Signal, source signal si (t) (i=1,2 ..., n) for obey super-Gaussian or subalpine forests distribution canonical or non-regular complex value letter Number.Target boats and ships DOA orientation estimates that problem to be solved is exactly unknown in aliasing parameter A of source signal s (t) and receiving array In the case of, the independent statistics characteristic only according to source signal estimates each object ship from aliasing signal x (t) observed The residing DOA orientation relative to referential array of oceangoing ship, i.e. θ_i(i=1,2 ..., n).

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

Step 1: multi-Vari strategy is incorporated differential evolution optimization algorithm and forms the differential evolution mechanism after improving, multi-Vari Strategy includes variation, hybridizes and select excellent three processes, and solution parameter to be optimized is designated as β, and it specifically includes procedure below:

Process 11: the iterative computation formula of multi-Vari decision search next one optimization solution can change formula (5) into, by formula (5) iteration Formula obtains the more new explanation β in variation stage_m；

In formula (5), β_mFor the simulation next new solution of biomutation search, β_bestFor to optimal solution 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 The maximum of the d dimension that may solve and minima；F is the random number between [0 2],For the random number between [-1 1]；r₁、 r₂And r₃For at [1 N_sRandomly generate the sequence number of solution adjacent with i between], note r₁≠r₂≠ i, r₁≠r₂≠r₃≠i；P (l) and Being respectively different probability and the average probabilitys that may optimize solution being directly proportional from target function value, p (l) is calculated by formula (6),

Fit (β in formula (6)_l) for weighing the l solution β_lThe object function of effect of optimization；

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

K in formula (7)_sFor [1 N_sRandom integers between]；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, it Concrete formula isI 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 Hermitian (Hermitian matrix) transposition and inversion operation symbol respectively；Trace () is Matrix Calculating order operator, R_x=E [x (t) x^H(t)] it is the spatial domain covariance matrix of x (t), E [] accords with for seeking expectation computing；In order to Obtaining the target boats and ships DOA orientation of optimum (the most accurate), object function is rewritten as by weThen estimate optimum θ_i(i=1, ^, cost function 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_{ML}\right|}---\left(10\right)$

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

Process 13: select excellent: according to object function J value magnitude relationship, the β calculated from β and the process 12 of last iteration_cMiddle choosing The optimization solution made new advances；If new optimization solution is chosen as the β of last iteration, the then 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, k (l) is put_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 estimate target boats and ships DOA orientation, specifically include procedure below:

Process 21: choose up to the present optimum possible solution β from β_best；If the arrival condition of convergence, then jump into step Rapid 22；Otherwise, rebound process 11；

Step 22: select may solving of global optimum from β according to formula (10), then its element is that estimation obtains object ship The orientation of oceangoing ship.

Further, in order to more one step improves the optimization of algorithm and convergence, process 13 select excellent during, not only want root According to target function value from original β and β_cIn select new optimization solution β of future generation, also include mechanism for the survival of the fittest is incorporated difference The process of evolutionary optimization algorithm, this process does not obtain the β updated, carries out its element again by formula (8) klimit time Give possible new explanation:

β (l, d)=β_max(d)+β_min(d)-β(l,d) (8)。

The problem that the present invention is to solve orientation, target boats and ships present position, location, first by multi-Vari strategy with " winning Bad eliminate " mechanism incorporates differential evolution optimization algorithm, and then differential evolution mechanism and the likelihood function of improvement are combined and be applied to Estimate the DOA orientation of target boats and ships.It is demonstrated experimentally that the method for the present invention not illustrate only the reasonable of the differential evolution scheme of improvement Property, and it has than some other algorithm and preferably optimizes performance；It addition, the differential evolution scheme of this improvement is applied to object ship In oceangoing ship direction estimation method, not only there is effectiveness, and it has the more preferable robustness of the method 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 estimation performance of distinct methods.

Detailed description of the invention

In conjunction with the drawings and specific embodiments, the present invention is further described.

For the location of boats and ships present position, the present invention proposes a kind of target Bearing Estimation side based on differential evolution mechanism Method.First, multi-Vari strategy and good and bad elimination system are introduced differential evolution algorithm, then new differential evolution mechanism is used for excellent Change the plausible goals function estimating that ripple reaches orientation, thus reach to estimate the purpose in target boats and ships orientation.The present invention comes concrete below Illustrate method for estimating target azimuth formed based on differential evolution mechanism realizes process.

One, the description of problem

Fig. 1 is the schematic diagram that uniform line-array and ripple reach orientation, sees Fig. 1, m and d and represents array number and array element distance respectively, Receiving array is positioned at the far-field region of n vessel position, and m >=n.Assume source signal s (t)=[s that n target boats and ships send₁ (t),s₂(t),…,s_n(t)]^TFor independence each other and the narrow band signal of zero-mean, and remember that they arrive the 1st array element direct projections Angle between line and array normal direction is θ_i(i=1,2 ..., n), this angle is called that ripple is to orientation (angle), i.e. DOA side Position.If the 1st array element is considered as referential array, then all can there is delay, i.e. non-reference array element in target source arrival non-reference array element There is a phase contrast in the signal received and target source signal, note i-th target source arrives the 2nd phase contrast that array element causes For ω_i, ω_iWith θ_iBetween relation be:

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

In formula (1), λ_sFor signal wavelength,ω to be ensured_i≤ π, array element distance must is fulfilled for 2d≤λ_s.That I-th target source arrives the vector of the phase contrast composition that m array element causes and 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 m array element of arrival and cause the vector of phase contrast, By dephased for institute vector one matrix of composition, it is designated as A, it and institute directed quantity a_iRelation be:

$\begin{array}{c}A=\[a_1,a_2,...,a_n\]\\ =\left[\begin{array}{cccc}1& 1& \mathrm{...}& 1\\ e^{-{\mathrm{j\ω}}_1}& e^{-{\mathrm{j\ω}}_2}& \mathrm{...}& e^{-{\mathrm{j\ω}}_n}\\ e^{-j2{\mathrm{\ω}}_1}& e^{-j2{\mathrm{\ω}}_2}& \mathrm{...}& e^{-j2{\mathrm{\ω}}_n}\\ .& .& .& .\\ .& .& .& .\\ .& .& .& .\\ e^{-j(m-1){\mathrm{\ω}}_1}& e^{-j(m-1){\mathrm{\ω}}_1}& \mathrm{...}& 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 m array element is received Signal be designated as x (t)=[x₁(t),x₂(t),…,x_m(t)] T, then the relation between x (t) and s (t) is:

X (t)=As (t)+η (t) (4)

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

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

2.1, the differential evolution mechanism of multi-Vari strategy

Differential evolution algorithm is a kind of colony's optimizing algorithm simulating biological evolution that Storn R. and Price K. proposes (see document: Storn R., Price K.Differential evolution A simple and efficent adaptive 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 us Select a main cause of differential evolution algorithm.When utilizing its solving-optimizing problem, then parameter to be optimized be equivalent to into The biology changed, and biological evolution is once equivalent to complete an Optimized Iterative for parameter to be solved.Simulation biological evolution machine Reason carries out the Optimized Iterative of primary parameter, and its process includes variation, hybridizes and select excellent three phases.Although numerous numerical value Optimize analysis example and all demonstrate DE than genetic algorithm (genetic algorithm, GA) and particle swarm optimization algorithm (particle swarm optimization, PSO) algorithm has preferably optimization and constringency performance and (sees document Wang R.J.,Zhu Y.Nonlinear dynamic system identification based on FLANN[J].Journal of Jimei University(Natural Science),2011,16(2):128-134.)；But it is still traditional with other Equally there is " the most precocious " deficiency that convergence rate is slow and restrains in intelligent group optimized algorithm.Single variation in the DE algorithm of prototype Strategy adds algorithm and limits the probability into local optimum or Premature Convergence, and the thinking solving this problem makes Mutation Strategy various exactly Change.Solution parameter to be optimized is designated as β by the present invention, it is proposed that the iterative computation formula of multi-Vari decision search next one optimization solution can Change into:

In formula (5), β_mFor the simulation next new solution of biomutation search, β_bestFor to optimal solution 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 maximum and the minima of the d dimension that may solve；F is the random number between [0 2],Between [-1 1] Random number；r₁、r₂And r₃For at [1 N_sRandomly generate the sequence number of solution adjacent with i between], note r₁≠r₂≠ i, r₁≠r₂≠r₃ ≠i；P (l) andBeing respectively different probability and the average probabilitys that may optimize solution being directly proportional from target function value, p (l) is by formula (6) it is calculated,

Fit (β in formula (6)_l) for weighing the l solution β_lThe object function of effect of optimization.

Crossing phase produces the iteration of new explanation and is described by formula (7).

K in formula (7)_sFor [1 N_sRandom integers between]；For the random number produced between [0 1], C_RFor hybridization Rate, its span is in [0 1].

In order to more one step improves the optimization of algorithm and convergence, it is proposed that excellent stage of selecting of DE algorithm not only will basis Target function value is from original β and β_cIn select new optimization solution β of future generation, the mechanism of " survival of the fittest " that also introduces is to k_limitSecondary Do not obtain the β updated, again give possible new explanation by formula (8) to its element.

β (l, d)=β_max(d)+β_min(d)-β(l,d) (8)

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

The estimation in target DOA orientation includes number of targets n and n θ_iTwo key technologies of estimation.Target boats and ships number n can lead to Cross 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 is tested technology mutually and is estimated, repeats no more this herein；Estimate n DOA orientation θ_iLikelihood function be formula (9)。

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

In formula (9),For the projection matrix of noise subspace, its concrete formula isI is the unit of m × n dimension Matrix, 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 operator, R_x=E [x (t) x^H(t)] it is the sky of x (t) Territory covariance matrix, E [] accords with for seeking expectation computing.At estimation target that intelligent optimization algorithm and plausible goals function are combined In the method in the DOA orientation of position, when utilizing the JML the minimization of object function in intelligent excellent Algorithm for Solving formula (9) the most exactly Corresponding n θ_iValue, but this thinking is typically only capable to obtain θ_iThe secondary figure of merit, in order to obtain the target of optimum (the most accurate) Boats and ships DOA orientation, object function is rewritten as by weThen estimate optimum θ_i(i=1, ^, cost function 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_{ML}\right|}---\left(10\right)$

In formula (10), for asking signed magnitude arithmetic(al) to accord with；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, DOA based on differential evolution mechanism is applied to estimate The step that realizes of meter principle location target boats and ships anticounterfeiting methods is summed up as follows:

Step 1. initializes 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 randomly generate β (l, d) initial value, 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 they phases according to formula (9)-(10) The object function J answered；

Step 4. is according to object function J value magnitude relationship, the β calculated from β and Step 3. of last iteration_cIn select new Optimization solution；If new optimization solution is chosen as the β of last iteration, the then 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, k (l) is put_count=0；

Step 5. chooses up to the present optimum possible solution β from β_best；If the arrival condition of convergence, then jump into Step 6；Otherwise, rebound Step 2；

Step 6. selects may solving of global optimum according to formula (10) from β, then its element is that estimation obtains object ship The orientation of oceangoing ship.

3, simulation analysis

In order to investigate the effect of the differential evolution algorithm majorized function of the multi-Vari strategy of Section 2, choose target boats and ships and send out Take and test from Canonical Distribution and non-canonical distribution signal two source signals.

3 chosen in source signal obeys Canonical Distribution emulation experiment signal respectively is:r (t) andRandomly generate between [0 1] and [-π π] respectively；s₂T () is 16QAM signal；s₃The production method of (t) signal Similar s₁T (), its r (t) randomly generates according to Poisson distribution.Their planisphere is as in figure 2 it is shown, s₁(t) and s₂T () is clothes From the complex signal of subalpine forests distribution, and s₃T () is for obeying the complex signal of super-Gaussian distribution；Send these 3 signals corresponding The orientation of boats and ships present position is θ=[10 ° 45 °-45 °].

3 signals chosen in source signal obeys non-canonical distributed simulation are: s₁(t) and s₂T () can be expressed as s_R (t)+js_I(t), s₁(t) and s₂T the real part of () and imaginary part randomly generate according to Poisson distribution and Gamma distribution respectively, and each moment Real part and imaginary part inequality, the plural source signal obtained all obeys super-Gaussian distribution；s₃T () is for obeying the BPSK of subalpine forests distribution Signal；Their planisphere is as it is shown on figure 3, the orientation that sends boats and ships present position corresponding to these 3 signals is θ=[-10 ° 45° -45°]。

Except utilizing algorithm herein that their object function J is optimized, by algorithm herein and document (Storn R., Price K.Differential evolution—A simple and efficent adaptive scheme for global optimization 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 Evolutionary Computation, 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 International Conference on Neural Networks, Perth, 1995:1942-1948.) in PSO optimize The experimental result of algorithm compares and emulates, additionally, mention the innovatory algorithm of DE or relevant some in current numerous document Intelligent optimization algorithm, in view of research emphasis herein, repeats no more herein to this.Fig. 4 is that four kinds of Different Optimization algorithms are to estimation The convergence curve that the likelihood function of DOA is optimized, can intuitively analyze the optimization convergence capabilities of algorithms of different by this curve, Note the average for 30 emulation experiments of independent operating, array number m=8, the MABC in figure be document (Rahnamayan S., Tizhoosh H.R.,Salama M.A.Opposition-based differential evolution[J].IEEE Transactions on Evolutionary Computation, 2008,12 (1): 64-79.) the middle a kind of improvement proposed DE optimized algorithm, and IDE algorithm is innovatory algorithm in this paper；The parameter that tri-kinds of algorithms of IDE, MDE and DE are relevant is set to Formula (11), and the relative parameters setting of PSO optimized algorithm is formula (12).

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

Knowable to the result comparing four kinds of Different Optimization algorithms of Fig. 4, the IDE algorithm that the present invention proposes compares MDE Algorithm, DE algorithm and PSO algorithm have better effect of optimization；This also illustrates that what the present invention proposed passes through improved differential evolution The effect that in algorithm, multi-Vari strategy is mutual with " survival of the fittest " selection method improves the thinking of the optimization performance of related algorithm Being feasible, Case Simulation experimental result has also reached target.

The source signal chosen in verifying the emulation experiment of target boats and ships DOA orientation based on differential evolution mechanism effectiveness Constellation is as it is shown in figure 5, s₁(t)=s_R(t)+js_IT (), real part and imaginary part randomly generate according to Poisson distribution, and the reality in each moment Portion and imaginary part inequality, it obeys the non-canonical signal of super-Gaussian distribution；Sub-high for obeying The canonical signal of this distribution, r (t) randomly generates according to Gamma distribution,Randomly generate between [-π π]；s₃T () is super for obeying The 16QAM canonical signal of Gauss distribution；s₄T () is for obeying the BPSK non-canonical signal of subalpine forests distribution；Send this 4 signals pair The orientation of the boats and ships present position answered is θ=[10 °-10 ° 45 °-45 °], and the parameter that differential evolution optimization algorithm is relevant is arranged For formula (14).Additionally, also by this algorithm and document (Zhang Y., Ng B.P.MUSIC-like DOA Estimation without Estimating the Number of Sources[J].IEEE Transcations on Signal Processing, 2010,58 (3): 1668-1669.) algorithm based on MUSIC, document (Volodymyr V.Improved in Beamspace ESPRIT-based DOA Estimation via Pseudo-noise Resampling[C].EuMW& EuRAD 2012, Amsterdam, 2012:238-241.) in algorithm based on ESPRIT and document (Li M.H., Lu Y.L.Accrate Direction-of-Arrival Estimation of Multiple Sources Using a Genetic Approach[J].Wireless Communcations and Mobile Computing,2005,5(3): In 343-353.), algorithm with class maximum likelihood function as object function carries out emulation and compares.In order to difference is estimated in quantitative analysis The effect that method is estimated, uses formula (15) to evaluate the performance of algorithms of different, utilizes them at different signal to noise ratio (Signal To Noise Ratio, SNR) under estimated result such as figure institute 6 show.

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

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

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

It will be appreciated from fig. 6 that as high s/n ratio (i.e. SNR >=0dB), methods herein and other method are to target boats and ships DOA estimate quality very close to；But as low signal-to-noise ratio (i.e. SNR < 0dB), object ship based on differential evolution mechanism herein The method that the performance of oceangoing ship DOA direction estimation method is substantially better than other.Shown in this paper by this simulation experiment result The plausible goals function utilizing the differential evolution mechanism improved and estimation DOA combines and estimates the side of target boats and ships present position Position is feasible.

The present invention uses such scheme, in order to solve to position the problem in orientation, target boats and ships present position, first by changeable Different strategy and " survival of the fittest " mechanism incorporate differential evolution optimization algorithm, then by the differential evolution mechanism improved and likelihood function Combine and be applied to estimate the DOA orientation of target boats and ships.In emulation experiment, on the one hand by source signal is obeyed Canonical Distribution The reasonability of the differential evolution scheme of improvement is indicated with the test result of the likelihood function in the case of non-Canonical Distribution two kinds, and It has than some other algorithm and preferably optimizes performance；On the other hand by canonical and non-canonical mixed type source signal DOA Orientation estimates that the simulation experiment result not illustrate only the target boats and ships direction estimation method based on differential evolution mechanism of proposition Effectiveness, and it has the more preferable robustness of the method more traditional than other.

Although specifically showing and describe the present invention in conjunction with preferred embodiment, but those skilled in the art should be bright In vain, in the spirit and scope of the present invention limited without departing from appended claims, in the form and details can be right The present invention makes a variety of changes, and is protection scope of the present invention.

Claims (3)

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

Step 1: multi-Vari strategy is incorporated differential evolution optimization algorithm and forms the differential evolution mechanism after improving, multi-Vari strategy Including variation, hybridize and select excellent three processes；

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

Wherein, in described step 1, solution parameter to be optimized being designated as β, it specifically includes procedure below:

Process 11: the iterative computation formula of multi-Vari decision search next one optimization solution is formula (5), is become by formula (5) is iterative The more new explanation β in different stage_m；

In formula (5), β_mFor the simulation next new solution of biomutation search, β_bestFor to optimal solution 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 and may solve D dimension maximum and minima；F is the random number between [02],For the random number between [-11]；r₁、r₂And r₃For [1N_sRandomly generate the sequence number of solution adjacent with i between], note r₁≠r₂≠ i, r₁≠r₂≠r₃≠i；P (l) andIt is respectively and mesh The difference that offer of tender numerical value is directly proportional may optimize the probability and average probability solved, and p (l) is calculated by formula (6),

$p\left(l\right)=\frac{fit\left({\mathrm{\&beta;}}_l\right)}{\underset{l=1}{\overset{Ns}{\&Sigma;}}fit\left({\mathrm{\&beta;}}_l\right)},l=1,^,N_s---\left(6\right);$

Fit (β in formula (6)_l) for weighing the l solution β_lThe object function of effect of optimization；

Process 12: hybridization: by the iterative more new explanation β obtaining crossing phase of formula (7)_c, and calculate they phases according to formula (9)-(10) The object function J answered；

K in formula (7)_sFor [1N_sRandom integers between]；For the random number produced between [01], C_RFor hybrid rate, taking of it Value scope is in [01]；

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

Formula (9) is for estimating n DOA orientation θ_iLikelihood function, in formula (9),For the projection matrix of noise subspace, it is concrete Formula isI is the unit matrix of m × n dimension, A^*=(A^HA)^-1A^HFor complex matrix A broad sense pseudo inverse matrix, upper left Target " H " and "-1 " represent Hermitian transposition and inversion operation symbol respectively；Trace () is Matrix Calculating order operator, R_x= E[x(t)x^H(t)] it is the spatial domain covariance matrix of x (t), E [] accords with for seeking expectation computing；Object function is rewritten asThen estimate optimum θ_i(i=1, ^, cost function n) is formula (10):

$\widehat{\mathrm{\&theta;}}=\&lsqb;{\widehat{\mathrm{\&theta;}}}_1,{\widehat{\mathrm{\&theta;}}}_2,...,{\widehat{\mathrm{\&theta;}}}_n\&rsqb;=\underset{\mathrm{\&theta;}}{\mathrm{argmax}}J=\frac{1}{c+\left|J_{ML}\right|}---\left(10\right)$

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

Process 13: select excellent: according to object function J value magnitude relationship, the β calculated from β and the process 12 of last iteration_cIn select new Optimization solution；If new optimization solution is chosen as the β of last iteration, the then 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, k (l) is put_count=0；

β (l, d)=β_max(d)+β_min(d)-β(l,d) (8)。

Target boats and ships direction estimation method the most according to claim 1, it is characterised in that: in described step 2, specifically include Procedure below:

Process 21: choose up to the present optimum possible solution β from β_best；If the arrival condition of convergence, then jump into step 22； Otherwise, rebound process 11；

Step 22: select may solving of global optimum from β according to formula (10), then its element is to estimate to obtain target boats and ships Orientation.

Target boats and ships direction estimation method the most according to claim 1, it is characterised in that: in described process 13, also include Mechanism for the survival of the fittest incorporates the process of differential evolution optimization algorithm, and this process is to k_limitThe secondary β not obtaining updating, by formula (8) element to it gives possible new explanation again:

β (l, d)=β_max(d)+β_min(d)-β(l,d) (8)。