CN102325090A - Network flow estimating method - Google Patents

Abstract

The invention discloses a network flow estimating method which concretely comprises the steps of initializing, obtaining a sigma point set, predicting the state, estimating the state and updating the process. In the method, the flow matrix estimating problem is modeled into a nonlinear system which more meets the OD (Origin-Destination) flow real characteristic; the sigma point set obtained by UT (Unscented Transformation) is subjected to nonlinear transformation; the coefficient of the system sate equation needed by nonlinear transformation is obtained concretely by Chebyshev polynomial fitting instead of approximately obtaining the system state equation by the traditional local linearization; accordingly, the state equation of the system does not need to meet the available linear function approximating condition; a symmetrical sampling policy is adopted for the UT; the particle point set approaches the probability density function distribution of a nonlinear function to obtain the higher-order approximation of state estimation, the result of OD flow estimation has higher precision, and the calculating complexity of the system is reduced.

Description

A kind of network traffics method of estimation

Technical field

The invention belongs to the computer network communication technology field, particularly wherein network traffics method of estimation.

Background technology

Fast development along with Internet; Network just towards on a large scale, at a high speed, multi-service, jumbo direction develop; Control increases with the difficulty of supervising the network thereupon, and the network state parameter is regardless of all being a very important physical quantity for network management personnel, Internet Service Provider or network research personnel.

The network traffics matrix (Traffic Matrix is the important indicator of network performance parameter TM), represented in the network arbitrarily OD (Origin-Destination) to the flow between (or stream, or node), described network traffics each OD to distribution situation.Obtaining of traffic matrix can be divided into initiatively measurement and passive measurement by the cooperation mode of measuring, and can be divided into direct measurement and measure indirectly by situation about measuring.

Utilize software Netflow directly to measure the OD flow data and have a lot of problems:

(1) for obtaining the OD flow information of whole network, Netflow software must be installed on all core routers, this is a very big expense;

(2) directly need the labor router resource in the measuring process, influence router performance;

(3) be difficulty very for the data of large scale network collection with to the Treatment Analysis of measurement data.

And contribution link traffic statistics data are simply many on router, and measuring the estimated flow matrix indirectly is very popular research direction.The linear indirect problem of the link flow data utilization that obtains through collection obtains the estimation of OD flow data, and the relation between traffic matrix, routing policy, the link flow can be described through a linear equality:

Y=AX formula (1)

Wherein, Y is a matrix, the flow of all links in the expression network; X also is a matrix, the expression traffic matrix, and corresponding OD is right for the row of traffic matrix, and corresponding different OD constantly are right for row; A={a _IjBe the 0-1 matrix, expression route matrix, a _IjThe element that i is capable, j is listed as among the expression route matrix A, i ∈ 1, L, m], j ∈ [1, L, n], wherein m is the link sum, n is an OD stream sum, if j bar OD stream passes through i bar link, then a _Ij=1, otherwise a _Ij=0; Clear certain the OD traffic demand of the tabulation of A in network the set of whole links that will pass through; Y in the formula (1) and A ratio are easier to obtain: Y can measure through SNMP (Simple Network Management Protocol), and A can obtain through routing policy and network topology.But; Because real network medium chain drive test amount number is much smaller than the OD fluxion; This makes that route matrix A is not a full rank, and (1) formula has infinite many group feasible solutions, so; What the traffic matrix estimation will solve is under the situation of known link flow Y and route matrix A, to find the solution traffic matrix X, and the problem of being faced is to owe solution of inverse problems fixed, ill system.

Development along with the flow monitoring technology; If can make full use of the measurement data that can get in the flow monitoring; Directly be used to obtain OD stream the time and space correlation and need not be through hypothesis; With improving the precision that traffic matrix is estimated greatly, utilize simultaneously and directly measure the adjustment of data model that obtains, the model after the correction is used for the estimation of ensuing traffic matrix.To this problem; At document: " Vardi Y.Network Tomography:Estimating source-destination traffic intensities from link data, Journal of the American Statistical Association, 1996; 91 (433): 365-377 " propose to utilize network tomography; OD stream is modeled as Poisson distribution, uses second moment, utilize the EM algorithm to estimate the parameter of Poisson distribution model link data as inferring the right prior information of OD stream; In order to reduce the enforcement difficulty of EM algorithm under Poisson model, the use normal model has been discussed has been approached the Poisson distribution model.

In order better to follow the trail of the non-stationary of OD stream; Approach the non-stationary of OD stream with first-order Markov process; Propose to use bayes method to find the solution traffic matrix at document " Tebaldi C; West M.Bayesian inference on network traffic using link count data.Journal of the American Statistical Association, 1998,93 (442): 557～576 "; These class methods are based upon on matrix theory and the statistical mathematics basis, utilize tomographic inversion to find the solution the network traffics matrix.Wherein, at document " A.Soule, K.Salamatian; A.Nucci; et al.Traffic matrix tracking using Kalman filters.ACM SIGMETRICS Performance Evaluation Review, 2005,33 (3): 24-31 " the Kalman filtered method has been proposed; Utilize the systemtheoretical state-space model of dynamic linear to represent the variation of system, regard OD stream as the basic status of network traffics system.Because OD stream is dynamic change in time, so state space also changes.

Based on the OD flow method of estimation of Kalman filter, be based on the linear dynamic system of state model; And because the most system of real world all is non-linear, the nonlinear model that the OD flow is estimated can better embody OD flow estimation model characteristic.When system when being non-linear, it is difficult obtaining the complete description of system equation, often adopts linear approximation to obtain suboptimum and estimates.When system has strong nonlinearity, can introduce bigger linearisation error, influence the precision that the OD flow is estimated; Need calculate partial derivative matrix simultaneously, increase the computation complexity of system.

Summary of the invention

The objective of the invention is to have proposed a kind of network traffics method of estimation in order to solve existing the problems referred to above that exist based on the OD flow method of estimation of Kalman filter.

Technical scheme of the present invention is: a kind of network traffics method of estimation comprises the steps:

S1. initialization, the network link flow and the right network traffics data of source-destination node of acquisition random time section, the prior distribution of supposing the network traffics that source-destination node is right is a Gaussian distribution, tries to achieve the initial condition average With covariance matrix P ₀, be used to ask for the weight sampling point set of initial time 0.

S2. obtain the σ point set, adopt tasteless conversion to obtain σ point set σ _iAnd corresponding weights W _i, wherein, i=0, L, 2n _x, each σ point all is the n of moment t _xDimension OD stream stochastic regime vector, n _xBe integer, the dimension of expression OD stream, 2n _xThe number of+1 expression state sampled point; The σ point set that obtains is carried out nonlinear transformation through system state equation, obtain conversion σ point set afterwards: χ _{T, t-1}=f (χ _T-1, ω _T-1), wherein, χ _T-1={ χ _{I, t, t-1}, i=0, L, 2n _xThe t-1 that obtains of sampling σ point set constantly before the expression conversion, χ _{T, t-1}={ χ _{I, t, t-1}, i=0, L, 2n _xRepresent the t-1 σ point set constantly that conversion sampling afterwards obtains, said system state equation is X _t=f (X _T-1, ω _T-1), wherein, X _tExpression t is n constantly _xMaintain the system state vector, ω _T-1Expression t-1 n constantly _xMaintain system state-noise vector, f representes current time and next system mode vector nonlinear relation constantly;

S3. status predication, the σ point set after the conversion that step S2 is obtained carries out weighted, obtains the one-step prediction state

Covariance matrix P with the one-step prediction state _{T, t-1}:

$\left\{\begin{array}{c}{\hat{X}}_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·{\mathrm{\χ}}_{i,t,t-1}\\ P_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·({\mathrm{\χ}}_{i,t,t-1}-{\hat{X}}_{t,t-1}){({\mathrm{\χ}}_{i,t,t-1}-\widehat{X_{t,t-1}})}^T+Q_t\end{array}\right.,$ Wherein, the transposition computing of " T " representing matrix, Q _tThe covariance matrix of expression system mode noise; By the one-step prediction state

Obtain step link flow prediction

Wherein, A _tExpression t is route matrix constantly, V _tExpression t is measure error constantly;

S4. state estimation is measured flow Y according to t moment link _t, obtain t moment link flow evaluated error and be expressed as

Trying to achieve corresponding covariance matrix is S _t=A _tP _{T, t-1}A _t+ R _t, wherein, R _tBe measure error V _tCovariance matrix, calculate the filter gain matrix K _t:

Upgrade OD stream predicted state, obtain t OD stream estimated value constantly Variance matrix P with OD stream estimated value _tAs follows:

S5: process is upgraded, when any link flow estimation error variance surpasses predefined threshold value, then execution in step S1-S4 constantly at continuous several.

Beneficial effect of the present invention: the inventive method is modeled as a non linear system with the traffic matrix estimation problem, more meets the genuine property of OD flow.Concrete through UT conversion acquisition σ point set; Then the σ point set that obtains is carried out nonlinear transformation through system state equation; System state equation specifically obtains coefficient through the Chebyshev polynomials match; The state equation of system replaced the existing approximate system state equation that obtains of local linearization that utilizes, so can satisfy the condition of useable linear function approximation; The symmetric sampling strategy has been adopted in UT conversion wherein, with the probability density function profiles that the particle point set approaches nonlinear function, obtains the more high-order approximation of state estimation, makes OD flow results estimated that higher precision arranged.Tasteless Kalman filtering does not require that system is an approximately linear, need not adopt linearisation approximate yet; It utilizes the symmetric sampling strategy based on Gauss's priori, and the probability density function of nonlinear function is similar to, and can make the solving precision of nonlinear function statistic reach 2 rank, has improved the precision that the OD flow is estimated, has reduced computation complexity.

Description of drawings

Fig. 1 is the small-sized star-network that two sub-net are connected to a router.

Fig. 2 is a network traffics method of estimation particular flow sheet of the present invention.

Embodiment

Below in conjunction with accompanying drawing and concrete embodiment the present invention is done further elaboration.

For the ease of understanding, earlier the foundation of OD flow estimation model is set forth technical scheme of the present invention.

The knowledge of tomography Network Based, through the link measurement data of SNMP acquisition and the relation between the OD flow, the measurement equation that obtains non linear system is following:

Y _t=A _tX _t+ V _tFormula (2)

Y _tFlow is measured in the expression link of t constantly, is obtained X by the SNMP data _tExpression t OD flow vector constantly, A _tExpression t route matrix constantly is if j bar OD stream is through i bar link, then A _tCapable, the j column element a of i _Ij Be 1, otherwise be 0; Because in the process of data collection, can produce error, so introduced random process V _tThe expression measure error; All parameters all are defined on the discrete time point.

Introduce in the face of network tomography down:

The link flow matrix notation of l*T dimension is Y _L*T, l is the link number, and T is a moment number, and the route matrix of l*k dimension is expressed as A _L*k, need be from Y _L*T=A _L*kX _K*TIn find the solution and obtain immeasurablel OD traffic matrix, and k＞l generally, k is the number of OD stream.

The linear equation of the star-network route matrix of Fig. 1 is following:

$\left[\begin{array}{c}y(1,t)\\ y(2,t)\\ y(3,t)\end{array}\right]\left[\begin{array}{cccc}1& 1& 0& 0\\ 0& 0& 1& 1\\ 1& 0& 1& 0\end{array}\right]\left[\begin{array}{c}x(1,t)\\ x(2,t)\\ x(3,t)\\ x(4,t)\end{array}\right]$ Formula (3)

(1, the t) link flow of expression from node 1 to router comprises from node 1 going out to be sent back to the OD flow of self and 2 the flow from node 1 to node y; (2, the t) link flow of expression from node 2 to router comprises from node 2 going out to be sent back to the OD flow of self and 1 the flow from node 2 to node y; Y (3, t) expression link flow of 1 from the router to the node, comprise from node 2 to node 1 OD flow and from node 1 to it self OD flow.

Measure flow from l known independent link, estimate k immesurable OD flow; Because k＞l, this system owes fixed, so need extra constraints to obtain the unique solution of equation.

The prior distribution of known OD stream is a Gaussian distribution, and network OD is flowed the state of regarding system as, and then traffic matrix has been represented the state of whole network, and the state equation of non linear system is represented as follows:

X _t=f (X _T-1, ω _T-1) formula (4)

X _tExpression t is n constantly _xMaintain the system state vector, ω _T-1Expression n _xMaintain system state-noise vector.

Obtain the complete description of non linear system by formula (2), (4):

$\left\{\begin{array}{c}{X}_t=f(X_{t-1},{\mathrm{\ω}}_{t-1})\\ Y_t=A_t{X}_t+V_t\end{array}\right.$ Formula (5)

State-noise ω and measurement noise V _tBe the zero-mean white Gaussian noise, and uncorrelated mutually, covariance matrix is respectively Q _tAnd R _t

Network traffics method of estimation flow chart of the present invention is as shown in Figure 2, specifically comprises the steps:

S1. initialization, the network link flow and the right network traffics data of source-destination node of acquisition random time section, the prior distribution of supposing the network traffics that source-destination node is right is a Gaussian distribution, tries to achieve the initial condition average

With covariance matrix P ₀, be used to ask for the weight sampling point set of initial time 0;

S2. obtain the σ point set, adopt tasteless conversion to obtain σ point set σ _iAnd corresponding weights W _i, wherein, i=0, L, 2n _x, each σ point all is the n of moment t _xDimension OD stream stochastic regime vector, n _xBe the dimension of integer representation OD stream, 2n _xThe number of+1 expression state sampled point; The σ point set that obtains is carried out nonlinear transformation through system state equation, and it is following to obtain conversion σ point set afterwards: χ _{T, t-1}=f (χ _T-1, ω _T-1), χ _T-1={ χ _{I, t-1}, i=0, L, 2n _xThe t-1 that obtains of the sampling of expression before conversion σ point set constantly, χ _{T, t-1}={ χ _{I, t, t-1}, i=0, L, 2n _xRepresent the t-1 moment σ point set that conversion sampling afterwards obtains, said system state equation is X _t=f (X _T-1, ω _T-1), wherein, X _tExpression t is n constantly _xMaintain the system state vector, ω _T-1Expression t-1 n constantly _xMaintain system state-noise vector, f representes current time and next system mode vector nonlinear relation constantly;

S3. status predication, the σ point set after the conversion that step S2 is obtained carries out weighted, obtains the covariance matrix of one-step prediction state and one-step prediction state:

$\left\{\begin{array}{c}{\hat{X}}_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·{\mathrm{\χ}}_{i,t,t-1}\\ P_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·({\mathrm{\χ}}_{i,t,t-1}-{\hat{X}}_{t,t-1}){({\mathrm{\χ}}_{i,t,t-1}-\widehat{X_{t,t-1}})}^T+Q_t\end{array}\right.,$ Wherein, the transposition computing of " T " representing matrix, Q _tThe covariance matrix of expression system mode noise; Obtain step link flow prediction by the one-step prediction state:

A _tExpression t is route matrix constantly, V _tExpression t is measure error constantly;

S4. state estimation is measured flow Y according to moment t link _t, obtaining constantly, t link flow evaluated error is expressed as

Trying to achieve corresponding covariance matrix is S _t=A _tP _{T, t-1}A _t+ R _t, R _tBe measure error V _tCovariance matrix.

Calculating the filter gain matrix is:

Upgrade OD stream predicted state, obtain the OD stream estimated value of t constantly

Variance matrix P with OD stream estimated value _tAs follows:

S5. process is upgraded, when any link flow estimation error variance surpasses predefined threshold value, then execution in step S1-S4 constantly at continuous several.

Specify below:

UKF filter (Unscented Kalman Filter) has two kinds of processing modes to noise: first kind expands to system mode with state-noise and observation noise; Utilize same system model to estimate; Shortcoming is that the dimension of system becomes big, and it is many that the sampling number that needs becomes; Second kind of non-extended mode do not need expanding system dimension and sampling number; Here adopt the estimation of the UKF filter realization OD flow of non-extended mode.

In step S1, suppose that the prior distribution of OD stream is a Gaussian distribution, obtain the initial numerical characteristic of OD flow:

K=0, ${\stackrel{\‾}{X}}_0=E\left[X_0\right],$ $P_0=E\left[(X_0-{\stackrel{\‾}{X}}_0){(X_0-{\stackrel{\‾}{X}}_0)}^T\right]$ Formula (6)

Here " random time section " specifically is taken as 24 hours.Consider that mainly network traffics have temporal correlation to a certain degree, get the data on flows of a day (24 hours) and ask for OD traffic figure characteristic, the substantive characteristics of OD flow relatively can be described.

In step S2, adopt tasteless conversion to obtain σ point set and corresponding weights W _i, obtain 2n _x+ 1 σ point, each σ point all are t OD stream mode vectors constantly, and it is following to obtain the σ point set:

$\left\{\begin{array}{c}{\mathrm{\χ}}_{t-1}=\begin{array}{}\end{array}\left[\begin{array}{ccc}{\stackrel{\‾}{X}}_{t-1}& {\stackrel{\‾}{X}}_{t-1}-{\left(\sqrt{(n_x+k)P_x}\right)}_i& {\stackrel{\‾}{X}}_{t-1}+{\left(\sqrt{(n_x+k)P_x}\right)}_i\end{array}\right]\\ W_{t-1}=[W_0,W_i=1/[2(n_x+k)],W_{i+n_x}=1/[2(n_x+k)\left]\right]\end{array}\right.i=1,K,n_x$ Formula (7)

Do simple declaration in the face of tasteless conversion (Unscented Transformation) down.

Tasteless conversion is based on that the symmetric sampling strategy of Gaussian distribution realizes; Its main thought is through obtaining deterministic sampling point set (σ point set); Catch the statistical property that input OD stream mode distributes; Each sampled point is carried out nonlinear transformation respectively, the statistical property of the random vector after the weighted calculation after the acquisition nonlinear transformation.

Consider a n _xDimension OD stream random vector X supposes that the average of X does

Variance is P _X, through a Nonlinear and Random equation

Obtain a non-linear stochastic vector Y that OD stream is corresponding,

Y=g (X) formula (8)

Use UT to calculate the statistical property of Y, at first obtain a 2n _x+ 1OD flow weight sampling point set S _i={ W _i, χ _i, the symmetric sampling strategy can be caught true average of priori and the variance of OD flow vector X, as follows:

${\mathrm{\χ}}_0=\stackrel{\‾}{X}$ W ₀＝k/(n _x+k) i＝0

${\mathrm{\χ}}_i=\stackrel{\‾}{X}+{\left(\sqrt{(n_x+k)P_x}\right)}_i$ W _i＝1/{2(n _x+k)} i＝1，K，n _x

${\mathrm{\χ}}_i=\stackrel{\‾}{X}-{\left(\sqrt{(n_x+k)P_x}\right)}_i$ W _i＝1/{2(n _x+k)} i＝n _x+1，K，2n _x

${\mathrm{\Σ}}_{i=0}^{2n_x}{W}_i=1$ Formula (9)

Here k is a scale parameter,

Be matrix (n _x+ k) P _xSubduplicate i column or row, W _iIt is the weight that i is ordered.Each σ point is through the σ point y behind the non-linear function transformation _iFor:

y _i=g (χ _i) i=0, K, 2n _xFormula (10)

The average and the variance that can obtain the σ point set Y after the conversion are following:

$\left\{\begin{array}{c}\stackrel{\‾}{Y}=\underset{i=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_i{y}_i\\ P_Y=\underset{i=0}{\overset{2n_x}{\mathrm{\Σ}}}{W}_i(y_i-\stackrel{\‾}{Y}){(y_i-\stackrel{\‾}{Y})}^T\end{array}\right.$ Formula (11)

Average of estimating and variance can reach the precision of the three rank Taylor series expansions of nonlinear function g (X) for any nonlinear function.

In step S2, the prediction of OD stream mode is carried out nonlinear transformation with the σ point that obtains through system state equation, and it is following to obtain Nonlinear Processing σ point set afterwards:

χ _{T, t-1}=f (χ _T-1, ω _T-1) formula (12)

Through the σ point set after the conversion is carried out weighted, obtain the one-step prediction state Covariance matrix P with the one-step prediction state _{T, t-1}:

$\left\{\begin{array}{c}{\hat{X}}_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·{\mathrm{\χ}}_{i,t,t-1}\\ P_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·({\mathrm{\χ}}_{i,t,t-1}-{\hat{X}}_{t,t-1}){({\mathrm{\χ}}_{i,t,t-1}-\widehat{X_{t,t-1}})}^T+Q_t\end{array}\right.$ Formula (13)

By the step predicted state link to get step flow projections

Specifically adopt the Chebyshev polynomials matched curve to confirm that system state equation is used for nonlinear transformation here.

Chebyshev polynomial of the first kind:

T ₀(x)=1, T ₁(x)=and x, L, T _N+1(x)=2xT _n(x)-T _N-1(x) formula (14)

Choose Chebyshev's node:

$x_k=\mathrm{Cos}\frac{2k-1}{2n+2}\·\mathrm{\π},k=\mathrm{1,2},L,n+1$ Formula (15)

Wherein n is the exponent number of match,

The non-linear system status The Representation Equation is:

F (x)=a ₀T ₀(x)+a ₁T ₁(x)+L+a _nT _n(x) formula 16)

Utilize the Chebyshev polynomials approximating method, obtain the formula that embodies of non-linear system status equation, concrete steps are following:

S31: independent variable mapping

Obtain 24 hours network OD data on flows collection { (X _I-1, X _i), try to achieve the scope of OD data on flows, obtain interpolation interval [a, b], linear transformation is to interval [1,1], as follows:

$X_i=\frac{1}{2}[(b-a)X_i^{\′}+(b+a)]i=\mathrm{1,2},L,t$ Formula (17)

S32: try to achieve Chebyshev's node

If the polynomial fitting number of times is n, obtain Chebyshev n+1 order polynomial n+1 zero point w ' _i, as follows

$w_i^{\′}=\mathrm{Cos}\left(\frac{2k-1}{2n+2}\mathrm{\π}\right)k=\mathrm{1,2},L,n+1$ Formula (18)

In the substitution formula (17), obtain Chebyshev's node w _iFor

$w_i=\frac{1}{2}(a+b)+\frac{b-a}{2}\mathrm{Cos}\left(\frac{2k-1}{2n+2}\mathrm{\π}\right),k=\mathrm{1,2},L,n+1$ Formula (19)

S33: ask fitting coefficient a _k

$\left\{\begin{array}{c}{a}_0=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{X}_i^{\′}\\ a_k=\frac{2}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{T}_i\left(w_i\right)x_i^{\′}\end{array}\right.k=\mathrm{1,2},L,n$ Formula (20)

S34: with Chebyshev polynomials match OD stream non-linear system status equation, as follows:

X _i=f (X _I-1, W _I-1)=a ₀T ₀(X _I-1)+a ₁T ₁(X _I-1)+L a _nT _n(X _I-1)+W _I-1I=1,2, L, t formula (21)

In step S4, according to t link measurement constantly flow, obtaining constantly, t link flow evaluated error is expressed as

Trying to achieve corresponding covariance matrix is S _t=A _tP _{T, t-1}A _t+ R _t

Calculate the filter gain matrix K _tFor:

$K_t=P_{t,t-1}{A}_t^T{S}_t^{-1}$ Formula (22)

Upgrade OD stream predicted state, the OD stream estimated value that obtains t constantly is following with the variance matrix that OD flows estimated value:

formula (23)

In step S5; OD traffic matrix model can change along with the time; Here can select when any link flow estimation error variance and surpass threshold value continuous ten moment; It is the covariance matrix of moment t link flow evaluated error

that threshold settings is

); In next collection that starts OD flow/data of 24 hours constantly, the OD discharge model is proofreaied and correct.

Provide posteriority evaluated error covariance matrix, i.e. the variance matrix P of OD stream estimated value _tDerivation following:

Definition by the evaluated error covariance matrix can get:

$P_t=\mathrm{cov}(X_t-{\hat{X}}_t)$

$=\mathrm{cov}[X_t-{\hat{X}}_{t,t-1}-K_t\left({Y_t-A}_t{\hat{X}}_{t,t-1}\right)]$

$=\mathrm{cov}[X_t-{\hat{X}}_{t,t-1}-K_t(A_t{X}_t+V_t-A_t{\hat{X}}_{t,t-1})]$

$=(I-K_t{A}_t)P_{t,t-1}{(I-K_t{A}_t)}^T+K_t{R}_t{K}_t^T$ Formula (24)

Obtaining OD stream least mean-square error estimates; Promptly try to achieve the filter gain matrix of satisfied ; Because OD stream mean square error equals the error covariance matrix trace that OD stream is estimated; Promptly to try to achieve and make evaluated error covariance matrix mark get the filter gain matrix of minimum value, derive as follows:

Formula (24) is launched as follows:

$P_t=P_{t,t-1}-K_t{A}_t{P}_{t,t-1}{P}_{t,t-1}{A}_t{K}_t^T+K_t{S}_t{K}_t^T$ Formula (25)

Ask the local derviation of evaluated error covariance matrix mark to get:

$\frac{\∂\mathrm{Tr}\left(P_t\right)}{\∂K_t}=-2{\left(A_t{P}_{t,t-1}\right)}^T+2K_t{S}_t$ Formula (26)

Order-2 (A _tP _{T, t-1}) ^T+ 2K _tS _t=0, try to achieve

$K_t=P_{t,t-1}{A}_t^T{S}_t^{-1}$ Formula (27)

By formula (27) but simplified style (25) be:

P _t=P _{T, t-1}-K _tA _tP _{T, t-1}Formula (28)

Network traffics matrix estimation method of the present invention has been realized the OD traffic matrix estimation problem based on non linear system, has following advantage:

(1) the traffic matrix estimation problem is modeled as a non linear system, more meets OD flow genuine property;

(2) the σ point set that obtains through the UT conversion is carried out nonlinear transformation; The coefficient of the system state equation that nonlinear transformation is required specifically obtains through the Chebyshev polynomials match; Replace the existing approximate system state equation that obtains of local linearization that utilizes, therefore do not needed the state equation of system to satisfy the condition of useable linear function approximation;

(3) because the symmetric sampling strategy has been adopted in the UT conversion,, obtain the more high-order approximation of state estimation, make OD flow results estimated that higher precision arranged with the probability density function profiles that the particle point set approaches nonlinear function.

Those of ordinary skill in the art will appreciate that embodiment described here is in order to help reader understanding's principle of the present invention, should to be understood that protection scope of the present invention is not limited to such special statement and embodiment.Those of ordinary skill in the art can make various other various concrete distortion and combinations that do not break away from essence of the present invention according to these teachings disclosed by the invention, and these distortion and combination are still in protection scope of the present invention.

Claims (3)

1. a network traffics method of estimation is characterized in that, comprises the steps:

S1. initialization, the network link flow and the right network traffics data of source-destination node of acquisition random time section, the prior distribution of supposing the network traffics that source-destination node is right is a Gaussian distribution, tries to achieve the initial condition average With covariance matrix P ₀, be used to ask for the weight sampling point set of initial time 0.

S2. obtain the σ point set, adopt tasteless conversion to obtain σ point set σ _iAnd corresponding weights W _i, wherein, i=0, L, 2n _x, each σ point all is the n of moment t _xDimension OD stream stochastic regime vector, n _xBe integer, the dimension of expression OD stream, 2n _xThe number of+1 expression state sampled point; The σ point set that obtains is carried out nonlinear transformation through system state equation, obtain conversion σ point set afterwards: χ _{T, t-1}=f (χ _T-1, ω _T-1), wherein, χ _T-1={ χ _{I, t, t-1}, i=0, L, 2n _xThe t-1 that obtains of sampling σ point set constantly before the expression conversion, χ _{T, t-1}={ χ _{I, t, t-1}, i=0, L, 2n _xRepresent the t-1 σ point set constantly that conversion sampling afterwards obtains, said system state equation is X _t=f (X _T-1, ω _T-1), wherein, X _tExpression t is n constantly _xMaintain the system state vector, ω _T-1Expression t-1 n constantly _xMaintain system state-noise vector, f representes current time and next system mode vector nonlinear relation constantly;

S3. status predication, the σ point set after the conversion that step S2 is obtained carries out weighted, obtains the one-step prediction state Covariance matrix P with the one-step prediction state _{T, t-1}:

$\left\{\begin{array}{c}{\hat{X}}_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·{\mathrm{\χ}}_{i,t,t-1}\\ P_{t,t-1}=\underset{i=0}{\overset{2n_x+1}{\mathrm{\Σ}}}{W}_i\·({\mathrm{\χ}}_{i,t,t-1}-{\hat{X}}_{t,t-1}){({\mathrm{\χ}}_{i,t,t-1}-\widehat{X_{t,t-1}})}^T+Q_t\end{array}\right.,$ Wherein, the transposition computing of " T " representing matrix, Q _tThe covariance matrix of expression system mode noise; By the one-step prediction state

Obtain step link flow prediction

Wherein, A _tExpression t is route matrix constantly, V _tExpression t is measure error constantly;

S4. state estimation is measured flow Y according to t moment link _t, obtain t moment link flow evaluated error and be expressed as

Trying to achieve corresponding covariance matrix is S _t=A _tP _{T, t-1}A _t+ R _t, wherein, R _tBe measure error V _tCovariance matrix, calculate the filter gain matrix K _t:

Upgrade OD stream predicted state, obtain t OD stream estimated value constantly

Variance matrix P with OD stream estimated value _tAs follows:

S5: process is upgraded, when any link flow estimation error variance surpasses predefined threshold value, then execution in step S1-S4 constantly at continuous several.

2. network traffics method of estimation according to claim 1 is characterized in that, the random time section described in the step S1 was specially 24 hours.

3. network traffics method of estimation according to claim 1 is characterized in that, the system state equation described in the step S3 specifically adopts the Chebyshev polynomials matched curve to confirm.

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