CN106525042A - Multi-AUV synthetic location method based on combination of ant colony and extended Kalman filtering - Google Patents

Abstract

The invention aims to provide a multi- AUV synthetic location method based on combination of ant colony and extended Kalman filtering. The method comprises the steps of firstly establishing an AUV kinematic model, then conducting linearization on the AUV model, adopting a modified ant colony algorithm to conduct optimum estimations on a Q matrix and a R matrix; wherein the adoption of the modified ant colony algorithm specifically comprises the steps of at first adopting the ant colony algorithm to conduct transversal for the first time to obtain a large amount of solutions; adopting a particle swarm optimization to search a global optimum value; adopting again the ant colony algorithm to set the current solution as an initial start point of the ant colony, then choosing part of the most superior ants according to virtue or defect degrees of solutions obtained by the ants in the ant colony, and conducting weighted average to release pheromone according to virtue or defect degrees of quality of the solution; finally applying solved Q,R to an EKF, and thus location of AUV is achieved. According to the multi-AUV synthetic location method based on combination of ant colony and extended Kalman filtering, an intelligent algorithm and EFK are ingeniously combined, the problems that a noise matrix is uncertain, and hard to choose are solved, and filtering precision of EKF is improved; meanwhile, the application of combination of ant colony and extended Kalman filtering in a multi-AUV location system can sharply improve precision of the AUV location.

Description

A kind of many AUV co-locateds combined with EKF based on ant colony Method

Technical field

The present invention relates to a kind of co-located method of AUV.

Background technology

With the research continuous extension of sea area, the continuous complication of military requirement, rely solely on monomer and navigate under water Row device (AUV) works independently and will be unable to complete the set goal, therefore many AUV cooperative systems are just arisen at the historic moment, and is increasingly becoming A kind of main trend of AUV development and direction.Many AUV cooperative systems have higher requirement to positioning precision, and such as each is individual AUV will not only keep oneself high-precision positioning, but also around will understanding at the moment positional information of " partner " and from Relative position in cooperative system.If each individuality in AUV group is equipped with high-precision navigator, this is increased greatly Addition sheet.Therefore there has been proposed the co-located technology of many AUV, i.e., aid in other to match somebody with somebody using the high-precision main AUV of minority Standby inexpensive, low precision navigator realizes high-precision positioning from AUV.How by being in communication with each other between master and slave AUV An emphasis direction of domestic and international submarine navigation device navigation field research is become to improve the overall positioning precisions of many AUV.

In co-located system, in order to the degree of accuracy and precision that improve AUV positioning introduce many algorithm for estimating, extensively Use Kalman filtering.Kalman Filter Technology is developed in the sixties in 20th century, in co-located system has Zhuo Youcheng The application of effect, and EKF (EKF) is a kind of current nonlinear filtering algorithm widest in application.But use EKF carries out positioning the selection that one of topmost problem is exactly noise matrix, and the precision and convergence of positioning are to a great extent It is upper depending on priori knowledge of the user to noise matrix, that is, system noise matrix and measurement noise matrix advance planning Precision, if selecting improper, the performance of EKF will be substantially reduced, or even cisco unity malfunction.

The content of the invention

It is an object of the invention to provide can be accurately and effectively fixed by the main AUV for being furnished with high accuracy navigation equipment A kind of low many AUV co-locateds methods combined with EKF based on ant colony with from AUV positions in position.

The object of the present invention is achieved like this：

A kind of many AUV co-locateds methods combined with EKF based on ant colony of the present invention, is characterized in that：

(1) AUV kinematics models are set up

Using AUV as a particle movement, (x, y, z) is coordinates of the AUV at the k moment, and z is depth, by depth transducer Direct measurement, AUV kinematics models are described as：

In formula：x_k、x_k+1The respectively position coordinates in k, k+1 moment x direction；y_k、y_k+1Respectively k, k+1 moment y direction Position coordinates；T is the sampling period, V_kIt is the speed measured by DVL, φ_kIt is the course angle of measurement；

In this model, u is used_kRepresent [V_kφ_k]^T, then have：

In formula：WithIt is the white Gaussian noise of independent zero-mean, i.e. covarianceWithIt is also independent；The measuring value of k moment speed and course angle is represented respectively；

This model is described as：

X_k+1=f (x_k,u_k,w_k)=X_k+g(u_k+w_k)=f (X_k,k)+g(u_k+w_k)

In formula：X_k+1It is states of the AUV at the k+1 moment；X_k=f (X_k, k)=(x_k y_kφ)^TIt is states of the AUV at the K moment； g(u_k+w_k) it is a nonlinear terms；w_kIt is system noise, and is the white Gaussian noise with zero-mean；If Q is system noise association side Difference matrix；

In moment t_k, the distance that have received main AUV from AUV is described in horizontal space：

In formula：x_s,k,x_m,kIt is the position coordinates from AUV and main AUV k moment x direction respectively；y_s,k,y_m,kBe respectively from AUV and the position coordinates in main AUV k moment y direction；

r_kIt is their distances in horizontal space；

l_kIt is measurement noise, noise is the white Gaussian noise of zero-mean；

Let R be system measurements noise variance matrix.

Therefore this model can be described as：

r_k=h (X_k,k)+l_k

In formula：h(X_k, the distance on master and slave AUV horizontal planes k) is represented, and is had

(2) AUV models are linearized：

For AUV motion model X_k+1Formula, first by f (X_k, k) surround filter valueIt is launched into Taylor series,It is institute States of the AUV at the K moment is estimated, ignores the higher order term of more than second order, obtaining lienarized equation is：

In formula：It isWith regard toJacobian matrixes, use F_kRepresent, i.e.,：

By nonlinear function h (X_k, k) surround filter valueTransform into Taylor series,It is to be estimated by the k-1 moment AUV in the state at k moment, omit second order above item, obtain：

In formula：It is h (X_k/k-1, k) with regard to X_k/k-1Jacobian matrixes, using H_kRepresent, i.e.,：

(3) Q, R are optimized：

There are 3 state variables x in AUV kinematics models_k,y_k,φ_kWith 2 output variables x_k+1,y_k+1, then system noise Take Q=diag [Q1, Q2, Q3] respectively with the covariance matrix of measurement noise, R=diag [R1, R2], wherein Q1, Q2, Q3 be with x_k,y_k,φ_kCorresponding system noise matrix parameter；R1, R2 are and x_k+1,y_k+1Corresponding measurement noise matrix parameter；

(4) EKF is solved：

Status predication：

State of the k+1 moment from AUV is predicted by the k moment

Covariance P at k+1 moment is predicted by the k moment_k+1/k：

In formula：P_kIt is the covariance at k moment for road, Q_kIt is the system noise covariance matrix at k moment；

Update equation：

By prediction and renewal equation, Linear Estimation is proposed：

In formula：r_k+1Be the k+1 moment principal and subordinate AUV between measurement distance；It is that the master at k+1 moment is estimated by the k moment From the distance between AUV；It is the difference of k+1 moment measuring values and k moment estimates；

Gain K_k+1Equation is：

P_k+1=(I-K_k+1H_k+1)P_k+1/k

In formula：H_k+1It is h (X_k+1/k, k+1) and with regard to X_k+1/kJacobian matrixes；P_k+1It is the association side at k+1 moment for road Difference；S_k+1Represent both sums on the right of equation；

Assess the state at the k+1 moment from AUV：

The present invention can also include：

1st, the optimization of Q, R is that to Q1, Q2, Q3, R1, R2, this 5 parameters are adjusted in each sampling period, when using ant During group's algorithm, one group of parameter one paths of correspondence；When with particle cluster algorithm, one group of parameter one particle of correspondence is concrete to grasp Make step as follows：

Traveled through initially with ant group algorithm first；

Using particle cluster algorithm, global optimum is effectively obtained；

Described particle cluster algorithm adopts Crossover Strategy, that is, carry out following two steps：

A, current solution are intersected with individual extreme value；

B, current solution are intersected with colony extreme value；

Actual samples data z and estimateThe minimum target of mean square error, fitness function obj is set to：

In formula：M represents number of cycles；

Ant group algorithm is reused, current disaggregation is set to into the initial starting point of ant colony, is then obtained according to ant in ant colony Solution quality quality, from the outstanding ant in part is wherein selected, the good and bad degree for then solving by them is carried out weighted average and is released Pheromones are put, to explore the ability of optimal solution after strengthening ant：

Current disaggregation is set to into the initial starting point of ant colony, after all ants build and complete one group of parameter, letter Breath element evaporation is operated as the following formula：

In formula：τ_ijRepresent t i parameter and the pheromones intensity on j parameter side；The evaporation rate of ρ representative informations element； E is the set for assigning power side；Threshold function tables of the τ (λ _ f) for λ-branching factor, which is defined as：

In formula：τ_minValue is 1/Cⁿⁿ, CⁿⁿIt is the square mean error amount obtained by arest neighbors method；τ (t) is iterations t Function：τ (t)=0.9* (1/ (ρ * C^bs)-τ_ij(t))/ρ；

In current iteration, the ant (r≤ω -1) of ranking r updates information cellulose content on its path according to following formula：

In formula：It is given by：

T^rThe path set up in current iteration by the ant of ranking r；C^rFor the length in path.

Now the renewal rule of pheromones is：

In formula：Bs is iteration optimum ant or optimum ant so far；

The invoked frequency of optimum ant is given by so far:

All the time t be iterations；

If τ after updating_ij≥1/ρC^bs, then make τ_ij=1/ ρ C^bs(i, j=1,2,3 ... n).

Advantage of the invention is that：Intelligent algorithm is dexterously combined by the present invention with EKF, not only solves noise matrix Uncertain, the difficult problem for selecting, and improve the filtering accuracy of EKF, be applied in the alignment system of many AUV, carry significantly The high accuracy to positioning from AUV so that high accuracy navigation equipment need not be equipped with from AUV, cost is reduced.

Description of the drawings

Fig. 1 is AUV primary and secondary structure schematic diagrames；

Fig. 2 is principal and subordinate's AUV positional information schematic diagrames；

Fig. 3 is to compare analogous diagram from the Actual path of AUV with the estimated path for improving EKF, EKF；

Fig. 4 is the partial enlarged drawing in Fig. 3；

Fig. 5 is that the EKF position errors of AUV compare analogous diagram；

Specific embodiment

Illustrate below in conjunction with the accompanying drawings and the present invention is described in more detail：

With reference to Fig. 1-5, the present invention comprises the steps：

Step one：Set up AUV kinematics models

Step1:

AUV is considered as a particle movement, (x, y, z) is coordinates of the AUV at the k moment.Z is depth.Z can be passed by depth Sensor direct measurement, does not consider it in this invention.AUV kinematics models are described as：

In formula：

x_k, x_k+1The position coordinates in respectively k, k+1 moment x direction；

y_k, y_k+1The position coordinates in respectively k, k+1 moment y direction.

T is the sampling period, V_kIt is the speed measured by DVL, φ_kIt is the course angle of measurement.

In this model, u is used_kRepresent [V_kφ_k]^T, then have：

In formula：

WithIt is the white Gaussian noise of independent zero-mean, i.e. covarianceWithIt is also independent.

The measuring value of k moment speed and course angle is represented respectively.

This model is described as：

X_k+1=f (x_k,u_k,w_k)=X_k+g(u_k+w_k)=f (X_k,k)+g(u_k+w_k) (3)

In formula：

X_k+1It is states of the AUV at the k+1 moment；

X_k=f (X_k, k)=(x_k y_kφ)^TIt is states of the AUV at the K moment；

g(u_k+w_k) it is a nonlinear terms；

w_kIt is system noise, and is the white Gaussian noise with zero-mean；

If Q is system noise covariance matrix.

Step2:

In moment t_k, algorithm can be reduced to 2 dimensions from 3-dimensional using depth transducer, then as shown in Figure 2, be have received from AUV The distance of main AUV is described in horizontal space：

In formula：

x_s,k,x_m,kIt is the position coordinates from AUV and main AUV k moment x direction respectively；

y_s,k,y_m,kIt is the position coordinates from AUV and main AUV k moment y direction respectively；

r_kIt is their distances in horizontal space；

l_kIt is measurement noise, noise is the white Gaussian noise of zero-mean；

Let R be system measurements noise variance matrix.

Therefore this model can be described as：

r_k=h (X_k,k)+l_k (5)

In formula：

h(X_k, the distance on master and slave AUV horizontal planes k) is represented, and is had

Step 2：Linearisation AUV models

Step1：

For AUV motion models (3) formula, first by f (X_k, k) surround filter value(It is estimated AUV in K The state at quarter) it is launched into Taylor series, and ignore the higher order term of more than second order, obtaining lienarized equation is：

In formula：

It isWith regard toJacobian matrixes, this patent adopts F_kRepresent.I.e.：

Step2:

For system measurements equation (5) formula, by nonlinear function h (X_k, k) surround filter value(It is by k-1 States of the AUV that moment estimates at the k moment) Taylor series are transformed into, and second order above item is omitted, obtain：

In formula：

It is h (X_k/k-1, k) with regard to X_k/k-1Jacobian matrixes, this patent adopts H_kRepresent, i.e.,：

Step 3：Optimization Q, R

There are 3 state variables x in AUV state equations (1)_k,y_k,φ_kWith 2 output variables x_k+1,y_k+1(because φ_k+1 =φ_k, so patent is no longer by φ_k+1As an output variable), then the covariance matrix of system noise and measurement noise divides Q=diag [Q1, Q2, Q3], R=diag [R1, R2] are not taken.Wherein Q1, Q2, Q3 are and x_k,y_k,φ_kCorresponding system noise square Battle array parameter；R1, R2 are and x_k+1,y_k+1Corresponding measurement noise matrix parameter.

The optimization of noise matrix is exactly that to more than, 5 parameters are adjusted in each sampling period.When using ant group algorithm When, one group of parameter one paths of correspondence；When with particle cluster algorithm, one group of parameter one particle of correspondence.Concrete operation step It is as follows：

Step1:Traveled through initially with ant group algorithm first；

Step2:Using particle cluster algorithm, global optimum is effectively obtained.

Critical operational information：

Here particle cluster algorithm employs Crossover Strategy, that is, carry out following two steps：

(1) current solution is intersected with individual extreme value；

(2) current solution is intersected with colony extreme value；

Target in the present invention is actual samples data z and estimateMean square error it is minimum, therefore, fitness function Obj is set to：

In formula：

M represents number of cycles, and M too conferences cause the operating time oversize, then the general values of M are 600～1400.

Step3:Ant group algorithm is reused, current disaggregation the initial starting point of ant colony is set to into, then according to ant in ant colony The quality of the quality of the solution that ant obtains, from the classic ant in part is wherein selected, the good and bad degree for then solving by them is adding Weight average release pheromone, to explore the ability of optimal solution after strengthening ant.

Critical operational information：

Current disaggregation is set to into the initial starting point of ant colony, is built in all ants and is completed one group of parameter (Yi Tiaolu Footpath) after, pheromones evaporation is operated by (11) formula：

In formula：

τ_ijRepresent t i parameter and the pheromones intensity on j parameter side；

The evaporation rate of ρ representative informations element；

E is the set for assigning power side；

Threshold function tables of the τ (λ _ f) for λ-branching factor, which is defined as：

In formula：

τ_minGeneral value is 1/Cⁿⁿ, CⁿⁿIt is the square mean error amount obtained by arest neighbors method；

Functions of the τ (t) for iterations t：τ (t)=0.9* (1/ (ρ * C^bs)-τ_ij(t))/ρ；

In current iteration, the ant (r≤ω -1) of ranking r needs to update pheromones on its path and contain according to (13) formula Amount：

In formula：

It is given by：

T^rThe path set up in current iteration by the ant of ranking r；

C^rFor the length in path.

So, now the renewal rule of pheromones is：

In formula：

Bs is iteration optimum ant or optimum ant so far.

The invoked frequency of optimum ant is given by (16) formula so far:

All the time t be iterations.

If τ after updating_ij≥1/ρC^bs, then make τ_ij=1/ ρ C^bs(i, j=1,2,3 ... n).

Step 4：EKF is solved

Step1:Status predication：

State of the k+1 moment from AUV is predicted by the k momentEquation is：

Step2:Covariance P at k+1 moment is predicted by the k moment_k+1/k, equation is：

In formula：

P_kIt is the covariance at k moment for road；

Q_kIt is the system noise covariance matrix at k moment.

Step3:Update equation：

By prediction and renewal equation, it is proposed that Linear Estimation：

In formula：

r_k+1Be the k+1 moment principal and subordinate AUV between measurement distance；

It is the distance between the principal and subordinate AUV for being estimated the k+1 moment by the k moment；

It is the difference of k+1 moment measuring values and k moment estimates.

Gain K_k+1Equation is：

P_k+1=(I-K_k+1H_k+1)P_k+1/k (21)

In formula：

H_k+1It is h (X_k+1/k, k+1) and with regard to X_k+1/kJacobian matrixes；

P_k+1It is the covariance at k+1 moment for road；

S_k+1Both sums on the right of equation are represented only.

Step4:Assess the state at the k+1 moment from AUV：

Name a specific example：

Assume that master and slave AUV is located in the same horizontal plane, and main AUV initial headings angle be 45, forward speed is 2.23m/s, Original position is (100,150)；Do at the uniform velocity turning motion from AUV, speed is 1.4m/s, original position for (100,100).System Process noise takesMeasurement noise takesMore The new cycle is T=1s.Simulation result is as shown in Figure 3.

Fig. 4 is the partial enlarged drawing in Fig. 3.Can be from Fig. 3, find out red route representative in 4 is that improved EKF estimates Path, blue then be EKF estimated paths, black is the real navigation route from AUV.The deviation phase of red route and black route It is substantially little much compared with blue route.

The EKF position errors of Fig. 5 AUV.Can be from Fig. 3, find out red line representative in 4 is that improved EKF estimates to miss Difference, blue then be EKF evaluated errors, green is error in measurement.Three is in contrast, it is evident that red line fluctuation is little, and error is little.

This example shows：From AUV at the uniform velocity curvilinear motion when, the filter effect of conventional EKF is evidently poor, error substantially compared with Greatly, preferably, error no significant difference is this based on ant colony so as to further demonstrate that for the EKF filter effects and based on innovatory algorithm The many AUV co-locateds optimized algorithms combined with EKF show more outstanding in terms of precision and reliability, More accurately can position from the position of AUV.

Claims (2)

1. a kind of many AUV co-locateds methods combined with EKF based on ant colony, is characterized in that：

(1) AUV kinematics models are set up

Using AUV as a particle movement, (x, y, z) is coordinates of the AUV at the k moment, and z is depth, direct by depth transducer Measurement, AUV kinematics models are described as：

$\left\{\begin{array}{c}{x}_{k+1}=x_k+T\·V_k\·cos\left({\mathrm{\φ}}_k\right)\\ y_{k+1}=y_k+T\·V_k\·sin\left({\mathrm{\φ}}_k\right)\\ {\mathrm{\φ}}_{k+1}={\mathrm{\φ}}_k\end{array}\right.$

In formula：x_k、x_k+1The respectively position coordinates in k, k+1 moment x direction；y_k、y_k+1The respectively position in k, k+1 moment y direction Coordinate；T is the sampling period, V_kIt is the speed measured by DVL, φ_kIt is the course angle of measurement；

In this model, u is used_kRepresent [V_k φ_k]^T, then have：

$u_k=\left[\begin{array}{c}{V}_k\\ {\mathrm{\φ}}_k\end{array}\right]=\left[\begin{array}{c}{V}_{m_k}+{\mathrm{\ω}}_{v_k}\\ {\mathrm{\φ}}_{m_k}+{\mathrm{\ω}}_{{\mathrm{\φ}}_k}\end{array}\right]$

In formula：WithIt is the white Gaussian noise of independent zero-mean, i.e. covarianceWithIt is also independent；Respectively Represent the measuring value of k moment speed and course angle；

This model is described as：

X_k+1=f (x_k,u_k,w_k)=X_k+g(u_k+w_k)=f (X_k,k)+g(u_k+w_k)

In formula：X_k+1It is states of the AUV at the k+1 moment；X_k=f (X_k, k)=(x_k y_k φ)^TIt is states of the AUV at the K moment；g (u_k+w_k) it is a nonlinear terms；w_kIt is system noise, and is the white Gaussian noise with zero-mean；If Q is system noise association side Difference matrix；

In moment t_k, the distance that have received main AUV from AUV is described in horizontal space：

$r_k=\sqrt{{(x_{s,k}-x_{m,k})}^2+{(y_{s,k}-y_{m,k})}^2}+l_k$

In formula：x_s,k,x_m,kIt is the position coordinates from AUV and main AUV k moment x direction respectively；y_s,k,y_m,kBe respectively from AUV and The position coordinates in main AUV k moment y direction；

r_kIt is their distances in horizontal space；

l_kIt is measurement noise, noise is the white Gaussian noise of zero-mean；

Let R be system measurements noise variance matrix.

Therefore this model can be described as：

r_k=h (X_k,k)+l_k

In formula：h(X_k, the distance on master and slave AUV horizontal planes k) is represented, and is had

(2) AUV models are linearized：

For AUV motion model X_k+1Formula, first by f (X_k, k) surround filter valueIt is launched into Taylor series,It is estimated States of the AUV at the K moment, ignores the higher order term of more than second order, obtains lienarized equation and is：

$X_{k+1}=f({\hat{X}}_k,k)+\frac{\∂f}{\∂{\hat{X}}_k}\[X_k-{\hat{X}}_k\]+g(u_k+w_k)$

In formula：It isWith regard toJacobian matrixes, use F_kRepresent, i.e.,：

$F_k=\frac{\∂f}{\∂{\hat{X}}_k}=\frac{\∂f({\hat{X}}_k,k)}{\∂X_k}{|}_{X_k={\hat{X}}_k},$

By nonlinear function h (X_k, k) surround filter valueTransform into Taylor series,It is the AUV estimated by the k-1 moment In the state at k moment, second order above item is omitted, is obtained：

$r_k=h({\hat{X}}_{k/k-1},k)+\frac{\∂h}{\∂X_k}{|}_{{\hat{X}}_{k/k-1}}\[X_k-{\hat{X}}_{k/k-1}\]+l_k$

In formula：It is h (X_k/k-1, k) with regard to X_k/k-1Jacobian matrixes, using H_kRepresent, i.e.,：

$H_k=\frac{\∂h}{\∂X_k}{|}_{{\hat{X}}_{k/k-1}}$

(3) Q, R are optimized：

There are 3 state variables x in AUV kinematics models_k,y_k,φ_kWith 2 output variables x_k+1,y_k+1, then system noise and amount The covariance matrix for surveying noise takes Q=diag [Q1, Q2, Q3] respectively, and R=diag [R1, R2], wherein Q1, Q2, Q3 are and x_k, y_k,φ_kCorresponding system noise matrix parameter；R1, R2 are and x_k+1,y_k+1Corresponding measurement noise matrix parameter；

(4) EKF is solved：

Status predication：

State of the k+1 moment from AUV is predicted by the k moment

${\hat{X}}_{k+1/k}=f(x_k,u_k,0)$

Covariance P at k+1 moment is predicted by the k moment_k+1/k：

$P_{k+1/k}=F_k\·P_k\·F_k^T+H_k\·Q_k\·H_k^T$

In formula：P_kIt is the covariance at k moment for road, Q_kIt is the system noise covariance matrix at k moment；

Update equation：

By prediction and renewal equation, Linear Estimation is proposed：

${\tilde{r}}_{k+1}=r_{k+1}-{\hat{r}}_{k+1/k}$

In formula：r_k+1Be the k+1 moment principal and subordinate AUV between measurement distance；It is that the principal and subordinate AUV at k+1 moment is estimated by the k moment Between distance；It is the difference of k+1 moment measuring values and k moment estimates；

Gain K_k+1Equation is：

$K_{k+1}=P_{k+1/k}{H}_{k+1}^T{S}_{k+1}^{-1}$

P_k+1=(I-K_k+1H_k+1)P_k+1/k

$S_{k+1}=H_{k+1}{P}_{k+1/k}{H}_{k+1}^T+R_{k+1}$

In formula：H_k+1It is h (X_k+1/k, k+1) and with regard to X_k+1/kJacobian matrixes；P_k+1It is the covariance at k+1 moment for road；S_k+1 Represent both sums on the right of equation；

Assess the state at the k+1 moment from AUV：

${\hat{X}}_{k+1}={\hat{X}}_{k+1/k}+K_{k+1}{\tilde{r}}_{k+1}.$

2. a kind of many AUV co-located sides combined with EKF based on ant colony according to claim 1 Method, is characterized in that：

The optimization of Q, R is that to Q1, Q2, Q3, R1, R2, this 5 parameters are adjusted in each sampling period, when using ant group algorithm When, one group of parameter one paths of correspondence；When with particle cluster algorithm, one group of parameter one particle of correspondence, concrete operation step It is as follows：

Traveled through initially with ant group algorithm first；

Using particle cluster algorithm, global optimum is effectively obtained；

Described particle cluster algorithm adopts Crossover Strategy, that is, carry out following two steps：

A, current solution are intersected with individual extreme value；

B, current solution are intersected with colony extreme value；

Actual samples data z and estimateThe minimum target of mean square error, fitness function obj is set to：

$obj=\frac{1}{M}\underset{k=1}{\overset{M}{\Σ}}{\[z\left(k\right)--\hat{z}\left(k\right)\]}^2$

In formula：M represents number of cycles；

Ant group algorithm is reused, current disaggregation is set to into the initial starting point of ant colony, the solution for then being obtained according to ant in ant colony Quality quality, from the outstanding ant in part is wherein selected, then by they solve good and bad degree come weighted average release believe Breath element, to explore the ability of optimal solution after strengthening ant：

Current disaggregation is set to into the initial starting point of ant colony, after all ants build and complete one group of parameter, pheromones Evaporation is operated as the following formula：

${\mathrm{\τ}}_{ij}\←(1-\mathrm{\ρ})\×{\mathrm{\τ}}_{ij}+\mathrm{\ρ}*\mathrm{\τ}(\mathrm{\λ}\_f),\∀(i,j)\∈E$

In formula：τ_ijRepresent t i parameter and the pheromones intensity on j parameter side；The evaporation rate of ρ representative informations element；E is Assign the set on power side；Threshold function tables of the τ (λ _ f) for λ-branching factor, which is defined as：

In formula：τ_minValue is 1/Cⁿⁿ, CⁿⁿIt is the square mean error amount obtained by arest neighbors method；Letters of the τ (t) for iterations t Number：τ (t)=0.9* (1/ (ρ * C^bs)-τ_ij(t))/ρ；

In current iteration, the ant (r≤ω -1) of ranking r updates information cellulose content on its path according to following formula：

${\mathrm{\τ}}_{ij}\←{\mathrm{\τ}}_{ij}+2*r/(\mathrm{\ω}*(\mathrm{\ω}-1\left)\right)*{\mathrm{\Δ\τ}}_{ij}^r,\∀(i,j)\∈T^r$

In formula：It is given by：

T^rThe path set up in current iteration by the ant of ranking r；C^rFor the length in path.

Now the renewal rule of pheromones is：

${\mathrm{\τ}}_{ij}\←{\mathrm{\τ}}_{ij}+\underset{r=2}{\overset{\mathrm{\ω}-1}{\Σ}}2*(\mathrm{\ω}-r)/(\mathrm{\ω}*(\mathrm{\ω}-1\left)\right)*{\mathrm{\Δ\τ}}_{ij}^r+2/w*{\mathrm{\Δ\τ}}_{ij}^{bs}$

In formula：Bs is iteration optimum ant or optimum ant so far；

The invoked frequency of optimum ant is given by so far:

All the time t be iterations；

If τ after updating_ij≥1/ρC^bs, then make τ_ij=1/ ρ C^bs(i, j=1,2,3 ... n).