CN112272385B - Multi-task adaptive network for non-negative parameter vector estimation - Google Patents

Multi-task adaptive network for non-negative parameter vector estimation Download PDF

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CN112272385B
CN112272385B CN202011390047.5A CN202011390047A CN112272385B CN 112272385 B CN112272385 B CN 112272385B CN 202011390047 A CN202011390047 A CN 202011390047A CN 112272385 B CN112272385 B CN 112272385B
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CN112272385A (en
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王紫璇
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Suzhou University
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Abstract

The invention discloses a multi-task self-adaptive network for non-negative parameter vector estimation, and belongs to the field of wireless sensor networks. The network is divided into a plurality of clusters, the parameter vector estimated by each cluster is the same, the parameter vectors estimated by different clusters are different, but certain similarity exists between the clusters. At the same time, each node in the network needs to satisfy a non-negative constraint due to the constraints of some engineering applications. The adaptive filter contained in each node adopts a multitask non-negative cubic absolute value method to cooperatively estimate the parameters, so that higher convergence speed is obtained.

Description

Multi-task adaptive network for non-negative parameter vector estimation
Technical Field
The invention discloses a multi-task adaptive network for non-negative parameter vector estimation, in particular relates to a multi-task non-negative cubic absolute value method for parameter estimation, and belongs to the field of wireless sensor networks.
Background
An adaptive network is a communication network consisting of a plurality of nodes dispersed over an area, each node being equipped with an adaptive filter for adaptively estimating an unknown parameter vector. At present, the application of a multitask self-adaptive network is very wide, and each node in the network can perform independent operation by using the interactive information of adjacent nodes, so that the accuracy of the identification of the whole network is improved. Multitasking adaptive networks have been widely used in machine learning, computer networking, and other applications.
According to different cooperation modes of nodes, the network can be divided into three adaptive network types of an incremental type, a diffusion type and a probability type. Based on various structures and adaptive filtering frameworks, scholars propose a series of distributed network algorithms. In 2013, chen et al proposed a Multitask Diffusion least mean square algorithm (abbreviated as MD-LMS) [ Multitask Diffusion Adaptation over Networks [ J ]. IEEE Journal of Selected Topics in Signal Processing,2013, PP (99): 1-1 ], which effectively expanded the application range of the adaptive network.
In some physical phenomena, such as concentration fields, demographics, etc., the parameter vectors in a multitasking adaptive network need to satisfy non-negative constraints. The adaptive filtering algorithm under the non-negative constraint condition is essentially to solve the optimization problem under the constraint condition. In 2011, chen et al proposed a non-negative Least Mean Square Algorithm (abbreviated as NNLMS) [ non-negative Least-Mean-Square Algorithm [ J ]. Signal Processing,2011,59 (11): 5225-5235 ], enriching the theory of the adaptive filter.
However, the existing multitask diffusion LMS algorithm and multitask diffusion RLS algorithm are only suitable for identifying unconstrained parameter vectors. Therefore, an efficient method for non-negative parameter vector identification of a multitask adaptive network needs to be found. Meanwhile, the main indexes for measuring the performance of the adaptive network comprise convergence speed and steady state maladjustment, wherein the convergence speed determines the time required by the adaptive network to estimate the unknown parameter vector, and the steady state maladjustment determines the accuracy which can be achieved by the adaptive network to estimate the unknown parameter vector. Therefore, the proposed algorithm also requires a faster convergence rate or lower steady state imbalance than the conventional least mean square algorithm.
Disclosure of Invention
In order to solve the above-mentioned defects, the present invention aims to: the method supplements the blank of the existing identification of the non-negative parameter vector of the multitask network, and simultaneously can obtain low steady state offset.
In order to realize the scheme, the invention adopts the following technical scheme:
a multi-tasking adaptive network for non-negative parameter vector estimation, characterized by:
the multitask self-adaptive network is composed of K nodes, the network is divided into Q clusters, the parameter vector estimated by each cluster is the same, the parameter vectors estimated by different clusters are different, and each node comprises a self-adaptive filter;
the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the correlation among parameter vectors of different task clusters is ensured; the adaptive filter is used for carrying out parameter estimation on the information of the node. The correlation between the parameter vectors of different task clusters is described as that the parameter vectors of different task clusters have difference and maintain similarity to a certain extent.
Furthermore, the multitask adaptive network adopts a multitask non-negative cubic absolute value method to estimate the unknown parameter vector.
Further, the parameter estimation specifically includes the following steps:
s1: solving joint matrix C, similarity matrix rho and system joint parameters of network
Figure GDA0003978820890000021
In a multitask adaptive network, a neighborhood of node k is defined as N k ，N k The cluster where the node k is located is C (k). For nodes in the same cluster, a joint matrix C epsilon i is defined K×K Each of which is a joint parameter
Figure GDA0003978820890000022
Satisfy the requirement of
Figure GDA0003978820890000023
For nodes in different clusters, defining a similarity matrix rho epsilon i K ×K Each similarity parameter thereof->
Figure GDA0003978820890000024
Satisfy->
Figure GDA0003978820890000025
Preferably, in order to simplify the system combination parameters, a value is taken>
Figure GDA0003978820890000026
S2: generating a joint estimate ψ of node k at time n +1 for an unknown parameter k (n+1),k∈{1,2,…,K}
By w k (n) represents the estimation of the unknown parameter by node k at time n,
Figure GDA0003978820890000027
is represented by w k (n) a diagonal matrix with diagonal elements, the input signal at node k at time n being x k (n), error->
Figure GDA0003978820890000028
The joint estimation ψ of node k at time n +1 for the unknown parameters k (n + 1) is represented by the formula
Figure GDA0003978820890000031
Generating, wherein mu and eta are step length parameters;
s3: generating the latest estimation w of the unknown parameters by the node k at the moment n +1 k (n+1),k∈{1,2,…,K}
By using
Figure GDA0003978820890000032
Representing node>
Figure GDA0003978820890000033
The joint estimation of the unknown parameters at time n +1 can then be used
Figure GDA0003978820890000034
A latest estimate of the unknown parameter at time n +1 is generated for node k.
Advantageous effects
Compared with the scheme in the prior art, the invention has the advantages that: the method of the invention can not only keep the multitask self-adaptive network to have high convergence speed, but also ensure that the multitask self-adaptive network obtains low steady state imbalance. The method can be widely applied to computer networks, distributed machine learning, disaster early warning, target positioning and cognitive radio.
Drawings
The invention is further described below with reference to the following figures and examples:
FIG. 1 is a schematic diagram of a multitasking adaptive network;
fig. 2 is a diagram of a multitasking adaptive network connection of a 4-task cluster and 20 nodes used in the embodiment;
a weight parameter vector value schematic diagram of a 4-task cluster used in the embodiment of fig. 3;
FIG. 4 illustrates a network mean square deviation curve using Gaussian noise as input in an embodiment;
the network mean square deviation curve at the input is used in the embodiment of fig. 5 with uniform noise.
Detailed Description
Examples
To better illustrate the objects and advantages of the present invention, the following detailed description of the invention is provided in conjunction with the accompanying drawings and examples. The following section further illustrates the above embodiments in conjunction with specific examples. It should be understood that these examples are for illustrative purposes and are not intended to limit the scope of the present invention. The conditions employed in the examples may be adjusted to suit the particular application, and the conditions not specified are typically those used in routine experimentation.
In this embodiment, an unknown parameter vector is identified by using an adaptive network (abbreviated as MD-NNLMAT) of the MD-NNLMAT method, and the performance of the unknown parameter vector is compared with the performance of the adaptive network (abbreviated as MD-NNLMS) using the MD-NNLMS method, where the MD-NNLMS method is obtained by using a mean square error as a cost function. The performance of the normalized mean square deviation NMSD with respect to the different methods is evaluated by
Figure GDA0003978820890000041
The unit is decibel (dB), wherein
Figure GDA0003978820890000042
All experimental curves were results averaged 20 times for the optimal solution without negative values. Fig. 2 is a schematic diagram of a multitasking adaptive network used in the experiment, which includes 4 task clusters and 20 nodes. Because of the similarity between adjacent clusters, a linear model is used>
Figure GDA0003978820890000043
Picking a cluster>
Figure GDA0003978820890000044
The weight parameter vector of (1), FIG. 3 is trueThe parameter vectors of different clusters used in the experiment are not identical, and each cluster selected parameter vector is not identical, but contains the same original parameter vector w * Therefore, the parameter value taking condition of the multitask adaptive network is reasonably reflected.
The principle of the invention is as follows: and designing a multi-task self-adaptive method under a non-negative constraint condition by adopting the KKT condition and the theory of a diffusion method.
In this embodiment, the adaptive network using the MD-NNLMAT method is used to pair unknown parameter vectors w o Performing an estimation comprising the steps of:
s1: solving joint matrix C, similarity matrix rho and system joint parameters of network
Figure GDA0003978820890000045
In a multitasking adaptive network, a neighborhood of node k (including k) is defined as N k The cluster in which the node k is located is C (k). For nodes in the same cluster, defining a joint matrix C epsilon i K×K Each of which is a joint parameter
Figure GDA0003978820890000046
Satisfy the requirements of
Figure GDA0003978820890000047
For nodes in different clusters, defining a similarity matrix rho epsilon i K ×K Each similarity parameter thereof->
Figure GDA0003978820890000048
Satisfy->
Figure GDA0003978820890000049
To simplify the system combination parameters, take>
Figure GDA00039788208900000410
S2: generating a joint estimate psi of node k at time instant n +1 on the unknown parameter k (n+1),k∈{1,2,…,K}
By w k (n) represents the estimation of the unknown parameter by node k at time n,
Figure GDA00039788208900000411
is represented by w k (n) the elements are diagonal matrices of diagonal elements, and the input signal at node k at time n is x k (n), error->
Figure GDA00039788208900000412
Then node k jointly estimates psi the unknown parameters at time instant n +1 k (n + 1) is represented by the formula
Figure GDA0003978820890000051
Generating, wherein mu and eta are step length parameters; />
S3: generating a latest estimate w of unknown parameters at time n +1 for node k k (n+1),k∈{1,2,…,K}
By using
Figure GDA0003978820890000052
Representing node>
Figure GDA0003978820890000053
The joint estimation of the unknown parameters at time n +1 can then be used
Figure GDA0003978820890000054
A latest estimate of the unknown parameter at time n +1 is generated for node k.
In this embodiment, the parameter vector to be estimated is a vector with a negative value and a length of M =20, w * The vector value is 0.8, 0.6, 0.5, 0.2, 0.3, 0.2, 0.7, 0.6, 0.5, 0.4, -0.3, 0.6, 0.1, 0.5, 0.7, 0.3, -0.2. The filters in all nodes are of the same length. For joint parameters
Figure GDA0003978820890000055
And a similarity parameter>
Figure GDA0003978820890000056
In that we use the averaging rule in unison, i.e. </or >>
Figure GDA0003978820890000057
In this embodiment, gaussian noise is used as input, and the mean value is 0.5 and the standard deviation is 0.1; the system noise is respectively selected from Gaussian noise and uniform noise with the average value of 0.05 and the standard deviation of 0.001.
In this embodiment, the parameters are selected as follows:
s1: when the system noise is Gaussian noise, the step length of the MD-NNLMS method is set to be mu =0.015, eta =0.001, and the step length of the MD-NNLMAT method is set to be mu =0.024, eta =0.001; when the input is uniform noise, the step size using the MD-NNLMS method is taken to be μ =0.015, η =0.001, and the step size using the MD-NNLMAT method is taken to be μ =0.024, η =0.001.
Fig. 4 and 5 are normalized mean square deviation curves for gaussian noise and uniform noise, respectively, as system noise. The experimental results show that: under the same steady state maladjustment condition, the multitask self-adaptive network based on the MD-NNLMAT method has the fastest convergence speed.
The multi-task adaptive network for estimating the non-negative parameter vector of the embodiment is composed of K nodes, the network is divided into Q clusters, the parameter vector estimated by each cluster is the same, the parameter vectors estimated by different clusters are different, and each node comprises an adaptive filter; the clusters are used for simulating the parameter distribution condition of the multi-task system, so that the correlation among parameter vectors of different task clusters is ensured; the adaptive filter is used for carrying out parameter estimation on the information of the node. The related expression among the parameter vectors of different task clusters is that the parameter vectors of different task clusters have differences and keep similarity to a certain extent. The multitasking adaptive network in the above embodiments is sometimes also referred to as a multitasking adaptive filter.
The above embodiments are merely illustrative of the technical ideas and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All modifications made according to the spirit of the main technical scheme of the invention are covered in the protection scope of the invention.

Claims (1)

1. A multi-tasking adaptive network for non-negative parameter vector estimation, characterized by:
the multitask self-adaptive network is composed of K nodes and comprises Q clusters,
the parameter vectors estimated by each cluster are the same, the parameter vectors estimated by different clusters are different, and each node comprises a self-adaptive filter; the cluster is used for simulating the parameter distribution condition of the multi-task system so as to ensure the correlation of parameter vectors of different task clusters;
the adaptive filter is used for carrying out parameter estimation on the information of the node, the adaptive filter adopts a multitask non-negative cubic absolute value method to carry out estimation on an unknown parameter vector,
comprises the following steps:
s1: solving joint matrix C, similarity matrix rho and system joint parameter a of network lk ，
In a multitask adaptive network, a neighborhood of node k is defined as N k ，N k The method comprises the following steps that a node k is included, a cluster where the node k is located is C (k), and for nodes in the same cluster, a joint matrix C epsilon i is defined K×K Each of which is associated with a parameter c lk Satisfy c lk ≥0,
Figure FDA0003978820880000011
Defining a similarity matrix rho epsilon i for nodes in different clusters in the S1 K×K Each of the similarity parameters ρ thereof kl Satisfy the requirements of
Figure FDA0003978820880000012
Selecting a lk ＝c kl ；
S2: generating a joint estimation psi of unknown parameters by node k at the time n +1 k (n+1),k∈{1,2,…,K}
By w k (n) denotes node k is atThe estimation of the unknown parameter at time n,
Figure FDA0003978820880000013
is represented by w k (n) the elements are diagonal matrices of diagonal elements, and the input signal at node k at time n is x k (n), error->
Figure FDA0003978820880000014
Then node k jointly estimates psi the unknown parameters at time instant n +1 k (n + 1) is represented by the formula
Figure FDA0003978820880000015
Generating, wherein mu and eta are step length parameters;
s3: generating the latest estimation w of the unknown parameters by the node k at the moment n +1 k (n+1),k∈{1,2,…,K}
By psi l (n + 1) represents the joint estimation of unknown parameters by node l at the time n +1
Figure FDA0003978820880000016
A latest estimate of the unknown parameter at time n +1 is generated for node k. />
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