CN103607181B - A kind of spatially distributed change exponent number adaptive system identification method - Google Patents

Abstract

The invention discloses a kind of spatially distributed change exponent number adaptive system identification method, comprising: adaptive system identification iteration initial value computing network are set and merge weight coefficient matrix. For each node in spatially distributed network, utilize the weight vector estimated information of input message, measurement information and this Nodes of previous moment of all nodes in current time adjacent area to calculate output error. For each node in spatially distributed network, reduce the exponent number of sef-adapting filter, utilize this exponent number value to recalculate output error. The adaptive updates of sef-adapting filter weight vector exponent number. The adaptive updates of sef-adapting filter weight vector weights. The Space integration of sef-adapting filter weight vector exponent number. The weights iteration of sef-adapting filter weight vector. In new sampling instant, whether evaluation algorithm reaches stable state, if reach, iteration finishes, and has completed the identification to unknown system.

Description

Identification method of space distributed variable-order self-adaptive system

Technical Field

The invention relates to the technical field of adaptive filtering and system identification, in particular to a space distributed variable-order adaptive system identification method.

Background

In system identification applications, given an unknown dynamic system, knowing the input sequence of the system and the expected output sequence with measured noise, it is necessary to estimate the unknown impulse response of the dynamic system from the input sequence and the expected output sequence, and therefore, the system identification problem can also be understood as a system impulse response parameter estimation problem. The adaptive filter can be used to estimate the unknown system impulse response, thereby completing the system identification.

Among the existing adaptive filter-based system identification methods, the Least Mean Square (LMS) system identification method is widely used because of its small calculation amount and good robustness. Then, a normalized LMS (normalized LMS, NLMS) system identification method is provided for solving the problem that the gradient noise of an LMS filter is overlarge when the amplitude of an input sequence is large; in addition, in order to solve the application problem of the identification method of the NLMS system under the condition that the order of the impact response weight vector of the system to be identified is unknown or time-varying, researchers provide an identification method of the fractional order NLMS (fractional tap-length NLMS) system, and the method has the advantages of being convenient to iterate, good in robustness, small in calculated amount and the like. However, these system identification methods can only improve the parameter estimation performance of the single-node adaptive filter. Different from the classical single-node adaptive filter system identification method, the spatial distribution type adaptive network filtering system identification method based on diffusion type information fusion forms a plurality of estimation nodes by using a plurality of sensors, wherein each node is not isolated from the estimation of the environmental parameters, and the input, measured data and parameter estimation information of adjacent nodes are used in the estimation of the environmental parameters by each node. Therefore, compared with a classical adaptive filter operated by a single node, the spatial distribution of data can be fully utilized by the spatial distribution type adaptive network filtering, the speed of parameter estimation is increased, and the accuracy of system identification is improved.

The existing spatial distribution type LMS method based on diffusion type information fusion applied in the system identification field is only suitable for the condition that the order of the impact response of an unknown system is fixed and known. When the order of the system is unknown or time-varying, the order of the filter is usually taken as a sufficiently large value, however, a large amount of calculation is necessarily brought, and meanwhile, the convergence speed of the filter is also influenced, the iteration error is increased, and the accuracy of the identification of the unknown dynamic system is reduced, so that the existing method is not suitable for the application of the system to be identified under the condition that the order of the impulse response weight vector is unknown or time-varying.

Disclosure of Invention

In order to solve the problems, the invention provides a spatial distribution type variable-order self-adaptive network filtering system identification method based on diffusion type information fusion. The identification method can effectively estimate the order and the weight of the weight vector under the condition that the order of the impact response weight vector of the system to be identified is time-varying or unknown. Meanwhile, compared with the existing single-point variable order system identification method, the distributed variable order system identification method has higher precision in the order of the weight vector and weight estimation.

The invention comprises the following steps:

the method comprises the following steps: and setting an identification iteration initial value of the self-adaptive system and calculating a network fusion weight coefficient matrix.

Step two: for each node in the space distributed network, the input information and the measurement information of all nodes in the adjacent area at the current moment and the weight vector estimation information at the node at the previous moment are utilized to calculate the output error.

Step three: for each node in the spatially distributed network, the order of the adaptive filter is reduced, and the output error is recalculated using the order value.

Step four: adaptive updating of the order of the weight vector. And for each node in the space distributed network, on the basis of the estimation order of the previous moment, calculating by using the difference between the square values of the errors output in the second step and the third step to obtain a middle estimation value of the order of the weight vector to be identified at the current moment.

Step five: and self-adaptive updating of the weight vector of the self-adaptive filter. And for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the middle estimator of the weight vector to be identified at the current moment by using the order estimated in the step four and the input and measurement information at the current moment.

Step six: spatial fusion of the adaptive filter weight vector orders. And for each node in the space distributed network, on the basis of the order estimation in the step four, calculating the estimated value of the order of the weight vector to be identified at the current moment by using the weight estimated in the step five.

Step seven: and (4) iterating the weight values of the weight vector of the adaptive filter. And for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the estimated value of the weight vector to be identified at the current moment by using the order estimated in the step six and the input and measurement information at the current moment.

Step eight: judging whether the algorithm reaches a steady state at a new sampling moment, and if not, re-executing the steps from the second step to the seventh step; if the system to be identified is reached, iteration is finished, the task of estimating the impulse response weight vector of the system to be identified is completed, and the unknown system is identified.

The advantages of the invention include:

(1) when the order of the impulse response weight vector of the system to be identified is unknown or time-varying, the method provided by the invention can effectively identify the order and the weight of the weight vector.

(2) Theoretical analysis and actual operation show that compared with the traditional single-point FTNLMS system identification method, the method provided by the invention has the advantages of low calculation complexity, strong operability, higher identification precision and higher identification speed.

Drawings

FIG. 1 is a schematic diagram of system identification;

FIG. 2 is a schematic diagram of a diffusion adaptive network filtering algorithm;

FIG. 3 is a flow chart of a method of the present invention;

FIG. 4 is a graph of a flooding network and a signal statistics graph for each node in the network as employed in embodiments of the present invention;

FIG. 5 is a comparison graph of the convergence curve of order and the convergence curve of Mean Square Deviation (MSD) of the method provided by the present invention when the order of the impulse response weight vector of the system to be identified is fixed, and the conventional single-point FTNLMS identification method;

FIG. 6 is a comparison graph of order convergence curves and MSD convergence curves of the method of the present invention when the order of the impulse response weight vector of the system to be identified is time-varying compared with the conventional single-point FTNLMS identification method.

Detailed Description

The present invention will be described in further detail with reference to the accompanying drawings and examples.

FIG. 1 shows a schematic diagram of system identification, in which the discrete-time signal u (i) is the system i with the time order L_optOf input vector of (2), wherein the order L_optIs an integer and represents the real order of the impulse response weight vector of the system to be identified. The conventional system identification method assumes L_optFixed and known, and therefore cannot be applied to L_optUnknown or time-varying conditions. In the method provided by the invention, L is considered to be_optUnknown and more suitable for practical application. The weight vector of the unknown system to be identified is w_optOrder of L_optD (i) is the expected signal measured at time i, u (i) and w_optIs d (i) = u^T(i)w_opt+ n (i), where n (i) is the measurement noise at time i. i time adaptive filter pair w_optThe weight vector modeled is w (i) since w_optOrder L of_optUnknown, therefore, in the method provided by the present invention, the order and weight of w (i) need to be iterated simultaneously to estimate w_opt. The output of the filter is y (i) = u^T(i) w (i), and output error e (i) = d (i) — y (i). The adaptive filter at the moment i sets a weight vector w (i) to an unknown system impact response w to be identified_optModeling is carried out, the self-adaptive algorithm automatically adjusts w (i) according to the current output error e (i), and finally converges to be close to w_optThereby completing the steady state value of w_optIs the desired E { E } of the minimized square value of the output error as the iterative cost function²(i)}。

FIG. 2 is a schematic diagram of a system identification of a distributed adaptive network filter. The basic idea of the identification of the diffusion type adaptive network filtering system is that the kth node in the network is only connected with the adjacent region N_kThe nodes in the inner are connected. In the example of fig. 2, for node k, there are 5 nodes (including the node) adjacent thereto. In each node, the impulse response of the system to be identified is estimated according to the system identification method shown in fig. 1, and the input data, the measured data and the parameter estimation values of all nodes in the neighboring region are used in the kth node iteration. Through the transmission mode, the data information of all the nodes is shared, so that the estimation speed and the estimation precision of the parameters are improved.

The invention relates to a space distribution type variable-order self-adaptive system identification method based on diffusion type information fusion, a flow chart is shown in figure 3, and the method comprises the following steps:

the method comprises the following steps: and setting an identification iteration initial value of the self-adaptive system and calculating a network fusion weight coefficient matrix. Specifically, the initial value of the weight iteration of the identification weight vector of the adaptive system is generally set as a zero vector, and the initial value of the order iteration of the weight vector is set as L_minI.e. byN_k,0=L_min,Wherein,is N_k,0Wiry column vector, weight vector representing initial time estimate at node k, N_k,0Representing the order of the weight vector estimated at the initial instant at node k, 0 representing a zero vector of the same dimension, a symbolAnd P is the total number of nodes of the network. The design principle is L_min>Δ, wherein Δ ≈ 0.1L_optIs a positive integer and is used to avoid the algorithm converging on a suboptimal order. In the embodiment of the invention, two network fusion weight coefficient matrixes need to be calculated and are respectively self-adaptive updating weight coefficient matrixesThe method is used for distributing the measurement information and the input information of the adjacent nodes at the moment i. Spatial fusion weight coefficient matrixFor fusing the weight vector estimates at neighboring nodes. The two satisfy the following relations respectively:

1^TC=1^T,C1=1,1^TB=1^T（1）

where 1 is a P × 1-dimensional column vector. C and B were calculated by the following methods, respectively:

calculation of c from McStobes rule_l,_kThe method comprises the following steps:

wherein n is_kRepresents N_kOperation max (-) shows the maximum value of the section to which the node belongs, operation ∑ (-) shows the summation, the symbol ∈ shows that the node belongs to the latter, and N_k/{ k } denotes N_kExcept for the k node. The node k and the node l can exchange information and are called connection; the condition that the node k and the node l cannot interact with each other is called unconnected; k = l indicates that node k and node l are one node.

B is calculated by the principle of correlation_l,kThe method comprises the following steps:

as can be seen from equations (2) and (3), the method provided in the embodiment of the present invention only needs to transmit the measurement, input and estimation information in the neighboring areas.

Step two: for each node in the spatially distributed network, an output error is calculated using input information and measurement information of all nodes in the neighboring area at the current time and weight vector estimation information at the node at the previous time (the output error is calculated according to the initial value zero vector at time 1), where the measurement information is the measured amplitude of the desired signal. Specifically, taking node k as an example, let the current time be i (i ≧ 1), and take N_kThe output error of the current time at the node l is calculated by the weight vector estimated at the node k at the previous time (i-1 time) at any node l in the region

$e_{l,N_{k,i-1}}\left(w_k(i-1)\right)=d_l\left(i\right)-u_{l,N_{k,i-1}}^T\left(i\right)w_{k,N_{k,i-1}}(i-1)---\left(4\right)$

By the same token, obtain N_kOutput errors at other nodes within the region. Wherein,represents the weight vector estimated at the i-1 time at the node k at the i time node lThe calculated output error. N is a radical of_k,i-1Representing the order of the weight vector estimated at time i-1 at node k.The weight vector estimate information for the node at the previous time is N_k,i-1Dimension column vector, representationThe weight vector estimated at time i-1 at node k. d_l(i) For measurement information, representing the expected signal at node l at time i,for the input information, is N_k,i-1Wiry vector representing the first N of the input sequence at time i node l_k,i-1And (4) each element.

Step three: for each node in the spatially distributed network, the order of the adaptive filter is reduced, and the output error is recalculated using the order value. Specifically, taking node k as an example, and setting the current time as i time, take N_kWhen the order of any node l in the area is reduced to N_k,i-1- Δ, recalculated (4)

$e_{l,N_{k,i-1}-\mathrm{\Δ}}\left(w_k(i-1)\right)=d_l\left(i\right)-u_{l,N_{k,i-1}-\mathrm{\Δ}}^T\left(i\right)w_{k,N_{k,i-1}-\mathrm{\Δ}}(i-1)---\left(5\right)$

Wherein the subscript N_k,i-1- Δ represents the first N of the corresponding vector_k,i-1-a elements.

Step four: adaptive updating of the order of the weight vector. And for each node in the space distributed network, on the basis of the estimation order of the previous moment, calculating by using the difference between the square values of the errors output in the second step and the third step to obtain a middle estimation value of the order of the weight vector to be identified at the current moment. Specifically, taking node k as an example, assuming the current time as i time, N is set_kThe squared differences calculated at all nodes (4) (5) in the region are distributed using the k-th column of the adaptively updated weight coefficient matrix C to correct the fractional order estimated at time i-1 by the following method:

$\begin{array}{c}{M}_{k,f}\left(i\right)=N_{k,f}(i-1)-{\mathrm{\α}}_k-\\ {\mathrm{\γ}}_k\underset{l\∈N_k}{\mathrm{\Σ}}{c}_{l,k}(e_{l,N_{k,i-1}}^2\left(w_k(i-1)\right)-e_{l,N_{k,i-1}-\mathrm{\Δ}}^2\left(w_k(i-1)\right))\end{array}---\left(6\right)$

wherein M is_k,f(i)>0 represents the intermediate estimate of the fractional order at time i at node k. N is a radical of_k,f(i-1)>0 represents the estimation quantity of the fractional order at the i-1 moment at the node k, and the initial value of the iteration of the estimation quantity is L_min。α_kFor the leakage coefficient at node k, frequent changes in the order, γ, due to adaptive noise can be avoided_kIs the iteration step size of the order at node k. Equation (6) shows that, in the system identification method provided by the embodiment of the present invention, the order is always iterated along the direction in which the square value of the output error is reduced. The intermediate estimation value of the i moment order at the node k is as follows:

and satisfy L_min<M_k,i. Wherein M is_k,i>0 is an integerAnd represents the intermediate estimate of the i time order at node k.Indicating a rounding down. Is a small integer threshold value, and is used for preventing M when the iteration noise of the order is large_k,iFrequently changing. Equation (7) shows that, in the system identification method provided in the embodiment of the present invention, the integer order is changed only when the fractional order is accumulated to a certain degree.

Step five: and self-adaptive updating of the weight vector of the self-adaptive filter. And for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the middle estimator of the weight vector to be identified at the current moment by using the order estimated in the step four and the input and measurement information at the current moment. Specifically, taking node k as an example, let the current time be i time, and take M_k,iAs the order of the adaptive filter iteration at this time, take the first M of the estimated weight vector at i-1 time at node k_k,iCalculating the neighboring region N by one element_kAnd the product of the output error and the input vector is distributed by using the kth column of the self-adaptive updating weight coefficient matrix C to correct the weight vector estimated at the moment i-1, wherein the method comprises the following steps:

$\begin{array}{c}{\mathrm{\&psi;}}_{k,M_{k,i}}\left(i\right)=w_{k,M_{k,i}}(i-1)+\\ {\mathrm{\&mu;}}_k\underset{l\&Element;N_k}{\mathrm{\&Sigma;}}{c}_{l,k}\frac{u_{l,M_{k,i}}\left(i\right)}{u_{l,M_{k,i}}^T\left(i\right)u_{l,M_{k,i}}\left(i\right)+\mathrm{\&epsiv;}}(d_l\left(i\right)-u_{l,M_{k,i}}^T\left(i\right)w_{k,M_{k,i}}(i-1))\end{array}---\left(8\right)$

wherein,is a M_k,iAnd the VilsleDeg vector represents the intermediate estimator of the weight vector to be identified at the node k at the moment i.Is a M_k,iWiry column vector, representing the top M of the estimated weight vector at time i-1 at node k_k,iAnd (4) each element. If M is_k,i>N_k,i-1,In the iteration of (8), the order of the original estimation weight vector is increased by adopting a zero filling method. Mu.s_kIs the iteration step size of the weight vector weight at the k node, operation (·)^TIndicates to find the transpose, 0<<<1 to avoid a denominator of 0.Is a M_k,iWiki vector, representing the top M of the input sequence at time i node l_k,iAnd (4) each element.

Step six: spatial fusion of the adaptive filter weight vector orders. For each node in the space distributed network, on the basis of the estimation order of the step four, the weight value estimated in the step five is utilizedAnd calculating the estimated value of the order of the weight vector to be identified at the current moment. Specifically, taking node k as an example, assuming the current time as time i, N is obtained through (8) operation_kAfter the weight vectors estimated at all nodes in the region, defining a delta-dimensional vector at each node as the first M of the estimated weight vector at each node_k,iCalculating k nodes and N of the last delta elements in the elements_kThe squares of the euclidean norms of the vector differences at all nodes in the region are distributed through the kth column of the spatial fusion weight coefficient matrix B to correct the fractional order obtained by the calculation of (6), and the method is as follows:

$N_{k,f}\left(i\right)=M_{k,f}\left(i\right)-{\mathrm{\&gamma;}}_k\underset{l\&Element;N_k}{\mathrm{\&Sigma;}}{b}_{l,k}{\left|\right|{\mathrm{\&psi;}}_{k,\mathrm{\&Delta;}|M_{k,i}}^{\&prime;}\left(i\right)-{\mathrm{\&psi;}}_{l,\mathrm{\&Delta;}|M_{k,i}}^{\&prime;}\left(i\right)\left|\right|}^2---\left(9\right)$

wherein N is_k,f(i)>0 represents the fractional order estimated at node k at time i.Andis a delta-dimensional column vector and respectively represents the front M of the intermediate estimator of the weight vector obtained by the operation (8) at the node k and the node l_k,iThe last delta element of the elements. And when the order of the node l is smaller than the order of the node k, increasing the order by adopting a zero filling method. The operation | · | | represents solving the euclidean norm. Equation (9) shows that in the method provided by the embodiment of the present invention, the iteration of the order is always along the direction of decreasing the euclidean norm of the difference between the estimated weight vectors of each node in the network and each node in the neighboring area. The estimated value of the i moment order at the node k is as follows:

and satisfy L_min<N_k,i。

Step seven: adaptive filterAnd iterating the weight values of the weight vectors. And for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the estimated value of the weight vector to be identified at the current moment by using the order estimated in the step six and the input and measurement information at the current moment. Specifically, taking node k as an example, let the current time be i time, and take N_k,iAs the order of the adaptive filter iteration at this moment, the recalculation (8) is obtained:

$\begin{array}{c}{\mathrm{\&psi;}}_{k,N_{k,i}}\left(i\right)=w_{k,N_{k,i}}(i-1)+\\ {\mathrm{\&mu;}}_k\underset{l\&Element;N_k}{\mathrm{\&Sigma;}}{c}_{l,k}\frac{u_{l,N_{k,i}}\left(i\right)}{u_{l,N_{k,i}}^T\left(i\right)u_{l,N_{k,i}}\left(i\right)+\mathrm{\&epsiv;}}(d_l\left(i\right)-u_{l,N_{k,i}}^T\left(i\right)w_{k,N_{k,i}}(i-1))\end{array}---\left(11\right)$

distributing adjacent region N by using kth column of spatial fusion weight coefficient matrix B_kAll nodes in the node are obtained by calculation (11)The estimate of the weight vector at the node k at time i is obtained by:

$w_{k,N_{k,i}}\left(i\right)=\underset{l\&Element;N_k}{\mathrm{\&Sigma;}}{b}_{l,k}{\mathrm{\&psi;}}_{l,N_{l,i}}\left(i\right)---\left(12\right)$

step eight: at the new sampling time, judging whether the algorithm reaches the steady state (the algorithm reaches the steady state refers to the mean square value of the output errorConstant), if not, re-executing the steps two to seven; if the system to be identified is reached, iteration is finished, the task of estimating the impulse response weight vector of the system to be identified is completed, and the unknown system is identified.

Example (b): a diffused adaptive network is constructed according to fig. 4 (a). The total node number P =7, the measurement noise sequence and the input sequence are both zero-mean independent white noise sequences with the same distribution, and the two sequences are independent. The noise variance is var (n) =0.02, and operation var (·) represents variance. The variance and signal-to-noise ratio (SNR) of the input sequence at each node in the network is shown in fig. 4 (b). The SNR unit is decibel (dB), and is calculated from a variance ratio of a desired signal to an interference signal in the desired output signal, and the specific calculation method is as follows:

${\mathrm{SNR}}_k=101g\frac{\mathrm{var}\left(u_{k,L_{\mathrm{opt}}}^T\left(i\right)w_{\mathrm{opt}}\right)}{\mathrm{var}\left(n\left(i\right)\right)}---\left(13\right)$

wherein the SNR_kRepresenting the SNR at node k, and the operation lg {. cndot.) represents base-10 logarithm. In addition, the weight of the impulse response weight vector of the system to be identified is taken from a white noise sequence with zero mean value independent and same distribution, and the sequence variance is 0.01. In order to test the identification capability of the method provided by the embodiment of the invention on the system impact response, two simulation experiments are provided: simulation one is the discrimination of fixed orderIdentifying an experiment, wherein the order of an impact response weight vector of a system to be identified is set to be 100; and simulating an identification experiment with a time-varying order, and setting the order of the impact response weight vector of the system to be identified to be 80 from 100 at the 3000 th sampling moment.

Firstly, setting an identification iteration initial value of the self-adaptive system and calculating a network fusion weight coefficient matrix. Specifically, Δ =10 is set, and the lower limit of the order estimation is L_min= 20. The initial iteration value of the weight vector of the adaptive filter is 20-dimensional zero vector, and the initial iteration value of the order is 20. Calculating the self-adaptive updating weight coefficient matrix C and the spatial fusion weight coefficient matrix B of the identification method of the distributed FTNLMS system according to the step (2) and the step (3) respectively

$C=\left[\begin{array}{ccccccc}0.3& 0& 1/6& 1/6& 0& 1/5& 1/6\\ 0& 5/12& 0& 1/6& 1/4& 0& 1/6\\ 1/6& 0& 1/6& 1/6& 1/6& 1/6& 1/6\\ 1/6& 1/6& 1/6& 1/6& 1/6& 0& 1/6\\ 0& 1/4& 1/6& 1/6& 5/12& 0& 0\\ 1/5& 0& 1/6& 0& 0& 7/15& 1/6\\ 1/6& 1/6& 1/6& 1/6& 0& 1/6& 1/6\end{array}\right]---\left(14\right)$

And

$B=\left[\begin{array}{ccccccc}5/27& 0& 5/31& 5/31& 0& 5/21& 5/31\\ 0& 2/10& 0& 4/31& 2/10& 0& 4/31\\ 6/27& 0& 6/31& 6/31& 3/10& 6/21& 6/31\\ 6/27& 3/10& 6/31& 6/31& 3/10& 0& 6/31\\ 0& 2/10& 4/31& 4/31& 2/10& 0& 0\\ 4/27& 0& 4/31& 0& 0& 4/21& 4/31\\ 6/27& 3/10& 6/31& 6/31& 0& 6/21& 6/31\end{array}\right]---\left(15\right)$

in order to show the superiority of the method, the method is compared with the traditional single-point FTNLMS system identification method. In the single-point FTNLMS system identification method, a self-adaptive updating weight coefficient matrix C = I and a spatial fusion weight coefficient matrix B = I are set, wherein I is a 7-dimensional unit matrix.

Next, at each sampling time, the weight vector of the adaptive filter at that time is calculated in accordance with (4) to (12).

Finally, judging whether the algorithm reaches a steady state or not, if not, continuing to execute the steps (4) to (12) to obtain a weight vector of the adaptive filter at the current moment; and if the system reaches the steady state, finishing the estimation task of the impulse response weight vector of the system to be identified, and realizing the identification of the unknown system.

In the implementation process, the parameters are set in two simulations as follows, wherein the leakage coefficient of each node is α =0.008, =2 and =10^-4. The iteration step size mu =0.3 of the weight vector weight at each node. In simulation one, the order iteration step size γ =20 at each node, and in simulation two, γ changes from 20 to 18 at the 3000 th sampling moment.

In the simulation process, a Mean Square Deviation (MSD) performance index is adopted to compare various filtering methods, the performance index represents the identification degree of the weight vector estimated by the adaptive filter at each sampling moment to a real weight vector, and the specific calculation method is as follows:

${\mathrm{MSD}}_k\left(i\right)=101g\left\{\frac{1}{N}\underset{j=1}{\overset{N}{\mathrm{\&Sigma;}}}\right[\mathrm{\&rho;}{\left|\right|w_{\mathrm{opt}}-w_k^{\left(j\right)}(i-1)\left|\right|}^2+(1-\mathrm{\&rho;}){\left|\right|w_{\mathrm{opt}}-w_k^{\left(j\right)}\left(i\right)\left|\right|}^2\left]\right\}---\left(16\right)$

wherein, MSD_k(i) Representing MSD at time i at node k. N =100 is the MonteCarlo number of times, and each MonteCarlo simulation runs 2500 sampling cycles in the first simulation; in simulation two, a total of 8000 sample periods were run for each MonteCarlo simulation. Further, equation (16) indicates that exponential smoothing processing is adopted in each MonteCarlo simulation and the smoothing coefficient is ρ = 0.99. Upper label(j) The weight vector of the adaptive filter in the jth MonteCarlo simulation is shown. In both simulations, k =3, namely the output result at the node 3 is selected as the basis to compare the performance of the distributed and single-point FTNLMS system identification methods based on the diffusion type adaptive network. The smaller the steady state MSD estimated for the weight vector is, the higher the representation identification precision is, and the better the steady state performance of the algorithm is; the faster the MSD curve reaches the steady state value, the faster the characterization recognition speed, and the better the transient performance of the algorithm.

Effects achieved by the embodiments of the present invention will be described below with reference to the drawings. FIGS. 5 and 6 show the comparison results of the order convergence curve and MSD convergence curve of the method of the present invention and the conventional single-point FTNLMS system identification method when the order of the impulse response weight vector of the system to be identified is fixed and time-varying, respectively; as can be seen from fig. 5 and 6, for the distributed type adaptive network, in order identification (for example, fig. 5 (a) and 6 (a)) and weight identification (for example, fig. 5 (b) and 6 (b)) of a weight vector with a fixed order or a time-varying order, compared with the conventional single-point FTNLMS system identification method, the distributed FTNLMS system identification method can greatly improve the identification accuracy and the identification speed of the algorithm. In addition, the system identification method provided by the embodiment of the invention only needs to transmit the measurement, input and estimation information in the adjacent areas, so that the method has the characteristics of small measurement amount and strong operability.

As can be seen from the above embodiments, for a diffusion type adaptive network, when the order of the impulse response weight vector of the system to be identified is unknown or time-varying, the method provided by the present invention can effectively identify the order and the weight of the weight vector; compared with the existing identification method of the variable-order system, the method provided by the invention has the advantages of low calculation complexity, strong operability, higher identification precision and higher identification speed.

Claims (1)

1. A method for identifying a space distributed variable-order self-adaptive system is characterized by comprising the following steps:

the method comprises the following steps: setting an identification iteration initial value of the self-adaptive system and calculating a network fusion weight coefficient matrix;

is provided with $w_{k,N_{k,0}}\left(0\right)=0,$ $N_{k,0}=L_{\min },\&ForAll;k=1,2,...,P,$ Wherein,is N_k,0Wiry column vector, weight vector representing initial time estimate at node k, N_k,0Representing the order of the weight vector estimated at the initial instant at node k, 0 representing a zero vector of the same dimension, a symbolRepresents arbitrary taking in the belonged interval, P is the total node number of the network, L_minMore than delta, delta is a positive integer, and an adaptive updating weight coefficient matrix is setC is used for distributing the measurement information and the input information of the adjacent nodes at the moment i; setting a spatial fusion weight coefficient matrixB is used for fusing weight vector estimators at adjacent nodes, and B and C satisfy:

1^TC＝1^T,C1＝1,1^TB＝1^T

wherein 1 is a P × 1-dimensional column vector;

wherein n is_kRepresents N_kThe number of nodes in (1), max (·) represents the maximum value of the section to which the node belongs, operation Σ (·) represents the summation, reference ∈ represents that the node belongs to the latter, and N_k/{ k } denotes N_kNodes other than the k node; the node k and the node l can exchange information and are called connection; the condition that the node k and the node l cannot interact with each other is called unconnected; k ═ l denotes that node k and node l are one node;

step two: for each node in the spatial distributed network, calculating a first output error by using input information and measurement information of all nodes in an adjacent area at the current moment and weight vector estimation information at the node at the previous moment, wherein the weight vector estimation information at the node at the previous moment is obtained through the iteration initial value;

the current moment is moment i, wherein i is more than or equal to 1, and N is taken_kCalculating a first output error of a current moment at any node l in the area as follows:

$e_{l,N_{k,i-1}}\left(w_k\right(i-1\left)\right)=d_l\left(i\right)-u_{l,N_{k,i-1}}^T\left(i\right)w_{k,N_{k,i-1}}(i-1)$

wherein N is_k,i-1Representing the order of the weight vector estimated at the i-1 moment at the node k;is N_k,i-1The wiry column vector represents a weight vector estimated at the i-1 moment at the node k; d_l(i) The measurement information is used for representing an expected signal at a node l at the moment i;for the input information is N_k,i-1Wiry vector representing the first N of the input sequence at time i node l_k,i-1An element;

step three: for each node in the spatial distributed network, reducing the order of the adaptive filter, and recalculating a second output error by using the order value;

get N_kWhen the order of any node l in the area is reduced to N_k,i-1- Δ, calculating a second output error of

$e_{l,N_{k,i-1}-\mathrm{\&Delta;}}\left(w_k\right(i-1\left)\right)=d_l\left(i\right)-u_{l,N_{k,i-1}-\mathrm{\&Delta;}}^T\left(i\right)w_{k,N_{k,i-1}-\mathrm{\&Delta;}}(i-1)$

Wherein the subscript N_k,i-1- Δ represents the first N of the corresponding vector_k,i-1-a number of elements;

step four: for each node in the space distributed network, on the basis of the estimation order at the previous moment, calculating to obtain a middle estimation value of the order of the weight vector to be identified at the current moment by using the difference between the square values of the first output error and the second output error and the network fusion weight coefficient matrix;

calculating the intermediate estimation value of the fraction order at the i moment at the node k as follows:

$\begin{array}{c}{M}_{k,f}\left(i\right)=N_{k,f}(i-1)-{\mathrm{\&alpha;}}_k-\\ {\mathrm{\&gamma;}}_k\underset{l\&Element;N_k}{\&Sigma;}{c}_{l,k}\left(e_{l,N_{k,i-1}}^2\right(w_k\left(i-1\right))-e_{l,N_{k,i-1}-\mathrm{\&Delta;}}^2(w_k\left(i-1\right)\left)\right)\end{array}$

wherein M is_k,f(i) The value > 0 represents the intermediate estimation value of the fractional order at the i moment at the node k; n is a radical of_k,f(i-1) > 0 represents the estimator of the fractional order at the node k at the moment i-1, and the initial iteration value of the estimator is L_min；α_kIs a nodeLeakage coefficient at k, gamma_kThe iteration step length of the order at the node k;

the intermediate estimation value of the i moment order at the node k is as follows:

and satisfy M_k,i＞L_minWherein M is_k,i> 0 is an integer, represents an intermediate estimate of the order at time i at node k,represents rounding down; is a small integer threshold value, and is used for preventing M when the iteration noise of the order is large_k,iFrequent changes;

step five: for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the middle estimator of the weight vector to be identified at the current moment by using the middle estimation value of the order, the input information and the measurement information at the current moment;

calculating the intermediate estimator of the weight vector to be identified at the node k at the time i as follows:

$\begin{array}{c}{\mathrm{\&psi;}}_{k,M_{k,i}}\left(i\right)=w_{k,M_{k,i}}(i-1)+\\ {\mathrm{\&mu;}}_k\underset{l\&Element;N_k}{\&Sigma;}{c}_{l,k}\frac{u_{l,M_{k,i}}\left(i\right)}{u_{l,M_{k,i}}^T\left(i\right)u_{l,M_{k,i}}\left(i\right)+\mathrm{\&epsiv;}}\left(d_l\right(i)-u_{l,M_{k,i}}^T(i\left)w_{k,M_{k,i}}\right(i-1\left)\right)\end{array}$

wherein,is a M_k,iThe wiry column vector represents the middle estimator of the weight vector to be identified at the node k at the moment i;is a M_k,iWiry column vector, representing the top M of the estimated weight vector at time i-1 at node k_k,iAn element; if it isIn the iteration of the formula, the order of the original estimation weight vector is increased by adopting a zero filling method; mu.s_kIs the iteration step size of the weight vector weight at the k node, operation (·)^TThe transposition is obtained, 0 < 1;is a M_k,iWiki vector, representing the top M of the input sequence at time i node l_k,iAn element;

step six: for each node in the space distributed network, calculating an estimated value of the order of the weight vector to be identified at the current moment by using the intermediate estimator of the weight;

calculating the fraction order estimated at the node k at the moment i as follows:

$N_{k,f}\left(i\right)=M_{k,f}\left(i\right)-{\mathrm{\&gamma;}}_k\underset{l\&Element;N_k}{\&Sigma;}{b}_{l,k}\left|\right|{\mathrm{\&psi;}}_{k,\mathrm{\&Delta;}|M_{k,i}}^{\&prime;}\left(i\right)-{\mathrm{\&psi;}}_{l,\mathrm{\&Delta;}|M_{k,i}}^{\&prime;}\left(i\right)|{|}^2$

wherein N is_k,f(i) The fraction order estimated at the node k at the moment i is more than 0;andfor delta-dimensional column vectors, respectivelyFront M showing intermediate estimates of weight vectors at node k and node l_k,iThe last delta element of the elements; if the order of the node l is smaller than the order of the node k, increasing the order by adopting a zero filling method; operating the expression of the integer | · | |, solving the Euclidean norm;

and calculating the estimated value of the i moment order at the node k as follows:

and satisfy L_min＜N_k,i；

Step seven: for each node in the space distributed network, on the basis of the weight estimation at the previous moment, calculating the estimation value of the weight vector to be identified at the current moment by using the estimation value of the order, the input information and the measurement information at the current moment;

with N_k,iAs the order of the adaptive filter iteration at this time, the estimator of the weight vector at the k node at time i is calculated as:

$w_{k,N_{k,i}}\left(i\right)=\underset{l\&Element;N_k}{\&Sigma;}{b}_{l,k}{\mathrm{\&psi;}}_{l,N_{l,i}}\left(i\right);$

wherein,

$\begin{array}{c}{\mathrm{\&psi;}}_{k,N_{k,i}}\left(i\right)=w_{k,N_{k,i}}(i-1)+\\ {\mathrm{\&mu;}}_k\underset{l\&Element;N_k}{\&Sigma;}{c}_{l,k}\frac{u_{l,N_{k,i}}\left(i\right)}{u_{l,N_{k,i}}^T\left(i\right)u_{l,N_{k,i}}\left(i\right)+\mathrm{\&epsiv;}}\left(d_l\right(i)-u_{l,N_{k,i}}^T(i\left)w_{k,N_{k,i}}\right(i-1\left)\right)\end{array};$

step eight: judging whether the algorithm reaches a steady state at a new sampling moment, and if so, finishing the identification of the unknown system; and if the algorithm is judged not to reach the steady state, adding 1 to i, and then executing the steps from two to seven.