CN103648083A - Distributed average-consensus broadcast Gossip wireless communication method - Google Patents

Abstract

The invention discloses a distributed average consensus broadcast Gossi _p wireless communication method, relating to the field of wireless communication. It is to solve the problem that the existing broadcast Gossi _p algorithm has low convergence accuracy and cannot meet the required convergence time in the case of dynamic topology, channel data link loss and data quantization. The present invention is realized based on the wireless sensor network, and the network topology and channel requirements required by the present invention are consistent with those of the BGA-1, so that the present invention has a very wide application range. The iterative process of the state value of the present invention is consistent with BGA-1, so an accompanying variable is added to save the value lost by the previous accompanying variable, and the final convergence value of the algorithm is equal to its own state value and each accompanying variable value with a certain weight Added sum. By continuously increasing the number of accompanying variables, the convergence accuracy of the algorithm can be continuously improved. The invention is applicable to the field of wireless communication.

Description

The broadcast Gossip wireless communications method of distributed average common recognition

Technical field

The present invention relates to wireless communication field.

Background technology

Along with the development of information technology, the application of communication is more and more extensive, and the form of communication also trends towards variation.The distributed common recognition problem of asking for of wherein, mainly take that wireless sensor network is medium is subject to increasing Chinese scholars and pays close attention to.So-called distributed finger in the situation that there is no Centroid,, only by it, the nodal information in can direct communications range carries out state renewal to each sensor node, finally reaches common recognition state.The features such as decentralization network is good by feat of its extensibility, height of node autonomy have obtained widely paying attention to, especially in the network of individual node limited ability, and sensor network for example.Gossip algorithm is an important branch in accidental distributed common recognition problem.Gossip algorithm is simple, efficient, has good extensibility and robustness simultaneously, has therefore emerged in the last few years many research and the application relevant to Gossip algorithm.

The people such as Hajnal in 1972 have provided the specific descriptions of Gossip problem (phone problem) first.The eighties in 20th century, Brokar etc., Tsitsiklis etc. have proposed the problem of distributed common recognition the earliest.2006, the people such as Boyd were applied to propose in distributed common recognition problem random Gossip algorithm by Gossip process, and for asynchronous time model and lock in time model done detailed analysis and contrast.In its algorithm, first independent equiprobable any one node of choosing at random in network, and in the adjacent node of this node, select arbitrarily its neighbor node to form a group node pair, thereby this group node makes the value of these two nodes be updated to two to be worth average to exchanging each other information.Constantly thereby iteration reaches distributed consistent successively.In order to overcome above-mentioned Gossip algorithm in slow this defect of convergence time, the people such as Tuncer Can Aysal have proposed a kind of Gossip algorithm (BGA-1) based on broadcast after considering the broadcast characteristic of node in 2009, this algorithm makes the convergence rate of each node have very large lifting, but the convergence result that the weak point of this algorithm is node cannot reach the average of all start node values, but stochastic convergence is near certain value average.In order to eliminate the deficiency of BGA-1 algorithm, the people such as Franceschelli improve BGA-1 algorithm, and a kind of broadcast Gossip algorithm that can converge on initial value average proposed first in 2011, here we are called BGA-2 algorithm, but the shortcoming of BGA-2 algorithm is its convergence rate, are slower than BGA-1.In the concrete analysis of above-mentioned algorithm, the required network model of BGA-1 algorithm requires relatively loose, there are some researches show that BGA-1 can restrain in the situation that dynamic topology, channel data loss of link and data quantize, but its convergence precision is undesirable.And to make BGA-2 converge to average, author think network model must be node fixing with data be error free transmission, and each node must be known the degree of self, but this model is non-existent in actual applications, has greatly affected its actual application value.Therefore, people more wish to use and a kind ofly in real network model, can restrain, and reach required precision and meet a kind of algorithm of required convergence time.

Summary of the invention

The present invention is in order to solve existing broadcast Gossip algorithm in the situation that dynamic topology, channel data loss of link and data quantize, convergence precision is not high, cannot meet the problem of required convergence time, and then the broadcast Gossip wireless communications method of distributed average common recognition is provided.

The broadcast Gossip wireless communications method of distributed average common recognition, described communication means is realized based on wireless sensor network, and described communication means is:

The state value of each node and adjoint variable value in intiating radio sensor network;

In each iteration cycle, wake at random i node up, using i node as initiating node; I is more than or equal to 1 integer; Described i node broadcasted the state value x of himself in wireless sensor network _iand several adjoint variables y (t) ⁽¹⁾ _i(t), y ⁽²⁾ _i(t), y ⁽³⁾ _i(t), y ⁽⁴⁾ _i(t) ..., t represents the time;

X wherein _i(0) represent the initial condition value of i node, y ^(k) _i(0) represent k adjoint variable value of i node, y ^(k) _i(0)=0, k=1,2,3 ";

In wireless sensor network, all neighbor nodes around i node receive its current state value x of described i node broadcasts _i(t) and adjoint variable value, each node in all neighbor nodes carries out iteration to the information receiving according to it and the information of himself, obtains the state value x of next this node constantly _kand adjoint variable y (t+1) ⁽¹⁾ _k(t+1), y ⁽²⁾ _k(t+1), y ⁽³⁾ _k(t+1), y ⁽⁴⁾ _k(t+1) ...,

Each neighbor node is respectively according to himself state value and the adjoint variable value convergency value z (t) that obtains current time and next himself state value and adjoint variable value convergency value z (t+1) of obtaining next moment constantly of current time;

For each neighbor node, calculate its current time and next convergence value difference constantly, the convergence value difference corresponding when all nodes all reaches 10 ^-5during magnitude, stop iteration, realize the broadcast Gossip radio communication of distributed average common recognition; Otherwise return, carry out next iteration cycle.

Network topology required for the present invention and channel require consistent with BGA-1, make the scope of application of the present invention very extensive.The present invention's self state value iterative process is consistent with BGA-1, because BGA-1 algorithm can be lost a part of data and then cause final convergency value cannot reach average when each iteration, so constantly preserve the part value of losing the average that reaches this adjoint variable by the process consistent with state value iteration by increasing an adjoint variable.But, adjoint variable also can be lost partial data in getting the process of average, therefore can continue to increase an adjoint variable and preserve the value that an adjoint variable is lost, the final convergency value of algorithm equals the summation that state value own and each adjoint variable value are added with certain flexible strategy.This shows, by constantly increasing the number of adjoint variable, convergence of algorithm precision can improve constantly.

As shown in Figure 2, for the convergence precision of assessment algorithm, generally adopt mean square error (MSE) value of node to represent, formula is expressed as follows:

$z_{\mathrm{MSE}}\left(t\right)=\frac{1}{N}{\left|\right|z\left(t\right)-\frac{1}{\mathrm{<figure-callout\; id="1"\; label="N"\; filenames="HDA0000448218080000021.png"\; state="\{\{state\}\}">N</figure-callout>}}\stackrel{\&RightArrow;}{1}{\stackrel{\&RightArrow;}{1}}^{T}z\left(0\right)\left|\right|}_2^2$

Wherein N represents the total interstitial content in network, and z (t) represents that node is at t convergency value constantly.

Z2, z4, z6, z8 curve have represented respectively to use respectively in the present invention the MSE design sketch of 2,4,6,8 adjoint variables, the corresponding curve of pair is the MSE design sketch of the paired Gossip algorithm of standard, and BGA-1, BGA-2 curve represent respectively the MSE design sketch of BGA-1, BGA-2 algorithm.Because BGA-1 has randomness with the each convergency value of this algorithm, in order to obtain its desired effects, this emulation has been asked for respectively 10000 times the MSE value of each algorithm and the different random geometry topological structure of each employing, finally with the average of these 10000 MSE values, maps.By upper figure, can obviously be found out, along with this convergence of algorithm of increase precision of adjoint variable number is also improving constantly.

Because in pairs Gossip algorithm and BGA-2 convergence of algorithm speed are slower, when the 2000th iteration, also convergence does not reach convergency value, and therefore here Main Analysis contrasts the performance of this algorithm and BGA-1 algorithm.Data and MSE performance boost formula by experiment

can obtain, while increasing respectively 2,4,6,8 adjoint variable values in this algorithm, convergence precision at least can promote 72%, 87%, 93%, 96% with respect to BGA-1 algorithm.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention;

Fig. 2 is the comparison diagram of each algorithm MSE curve.

Embodiment

Embodiment one: below in conjunction with Fig. 1, present embodiment is described, the broadcast Gossip wireless communications method of the distributed average common recognition described in present embodiment, described communication means is realized based on wireless sensor network, and described communication means is:

The state value of each node and adjoint variable value in intiating radio sensor network;

In each iteration cycle, wake at random i node up, using i node as initiating node; I is more than or equal to 1 integer; Described i node broadcasted the state value x of himself in wireless sensor network _iand several adjoint variables y (t) ⁽¹⁾ _i(t), y ⁽²⁾ _i(t), y ⁽³⁾ _i(t), y ⁽⁴⁾ _i(t) ..., t represents the time;

X wherein _i(0) represent the initial condition value of i node, y ^(k) _i(0) represent k adjoint variable value of i node, y ^(k) _i(0)=0, k=1,2,3

In wireless sensor network, all neighbor nodes around i node receive its current state value x of described i node broadcasts _i(t) and adjoint variable value, each node in all neighbor nodes carries out iteration to the information receiving according to it and the information of himself, obtains the state value x of next this node constantly _kand adjoint variable y (t+1) ⁽¹⁾ _k(t+1), y ⁽²⁾ _k(t+1), y ⁽³⁾ _k(t+1), y ⁽⁴⁾ _k(t+1) ...,

Each neighbor node is respectively according to himself state value and the adjoint variable value convergency value z (t) that obtains current time and next himself state value and adjoint variable value convergency value z (t+1) of obtaining next moment constantly of current time;

For each neighbor node, calculate its current time and next convergence value difference constantly, the convergence value difference corresponding when all nodes all reaches 10 ^-5during magnitude, stop iteration, realize the broadcast Gossip radio communication of distributed average common recognition; Otherwise return, carry out next iteration cycle.

Embodiment two: present embodiment is further qualified the broadcast Gossip wireless communications method of the distributed average common recognition described in embodiment one, in present embodiment, the state value x of i node of broadcast _i(t+1) be:

x _i(t+1)=x _i(t)，

Several adjoint variables y ⁽¹⁾ _i(t+1), y ⁽²⁾ _i(t+1), y ⁽³⁾ _i(t+1), y ⁽⁴⁾ _i(t+1) ... be respectively:

y ⁽¹⁾ _i(t+1)=y ⁽¹⁾ _i(t)；

y ⁽²⁾ _i(t+1)=y ⁽²⁾ _i(t)；

.

.

.

y ⁽ⁿ⁾ _i(t+1)=y ⁽ⁿ⁾ _i(t)。

Embodiment three: present embodiment is further qualified the broadcast Gossip wireless communications method of the distributed average common recognition described in embodiment one, in present embodiment, all neighbor nodes of i node receive after the current state value of i node, and its state value is:

$\begin{array}{cc}{x}_k(t+1)=\frac{1}{2}{x}_k\left(t\right)+\frac{1}{2}{x}_i\left(t\right),& \&ForAll;k\&Element;N_i;\end{array}$

All neighbor nodes of i node receive after the adjoint variable value of i node, and its adjoint variable value is:

$\left\{\begin{array}{cc}{y^{\left(1\right)}}_k(t+1)=\frac{1}{2}{x}_k\left(t\right)-\frac{1}{2}{x}_i\left(t\right)+\frac{1}{2}{y^{\left(1\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(1\right)}}_i\left(t\right),& \\ {y^{\left(2\right)}}_k(t+1)=\frac{1}{2}{y^{\left(1\right)}}_k\left(t\right)-\frac{1}{2}{y^{\left(1\right)}}_i\left(t\right)+\frac{1}{2}{y^{\left(2\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(2\right)}}_i\left(t\right),& \&ForAll;k\&Element;N_i,\\ {y^{\left(n\right)}}_k(t+1)=\frac{1}{2}{y^{(n-1)}}_k\left(t\right)-\frac{1}{2}{y^{(n-1)}}_i\left(t\right)+\frac{1}{2}{y^{\left(n\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(n\right)}}_i\left(t\right);& \end{array}\right.$

N wherein _irepresent the neighbor node set of i node, the adjoint variable number of i node is n.

Embodiment four: present embodiment is further qualified the broadcast Gossip wireless communications method of the distributed average common recognition described in embodiment one, in present embodiment, in whole network, remove beyond all neighbor nodes of i node, the state value of all the other all nodes is:

$\begin{array}{cc}{x}_k(t+1)=x_k\left(t\right),& \&ForAll;k\&NotElement;N_i;\end{array}$

In whole network, to remove beyond all neighbor nodes of i node, the state value of all the other all nodes is:

$\begin{array}{cc}{y^{\left(1\right)}}_k(t+1)={y^{\left(1\right)}}_k\left(t\right);& \\ {y^{\left(2\right)}}_k(t+2)={y^{\left(2\right)}}_k\left(t\right);& \&ForAll;k\&NotElement;N_i;\\ .& \\ .& \\ .& \\ {y^{\left(n\right)}}_k(t+1)={y^{\left(n\right)}}_k\left(t\right).& \end{array}$

Embodiment five: present embodiment is further qualified the broadcast Gossip wireless communications method of the distributed average common recognition described in embodiment one, in present embodiment, the convergency value z (t) of i node realizes by following formula:

$z\left(t\right)=x_k\left(t\right)+\frac{n}{n+1}{y^{\left(1\right)}}_k\left(t\right)+\frac{n-1}{n+1}{y^{\left(2\right)}}_k\left(t\right)+...+\frac{1}{n+1}{y^{\left(n\right)}}_k\left(t\right).$

Claims (5)

1. the broadcast Gossip wireless communications method of distributed average common recognition, its spy is just: described communication means is realized based on wireless sensor network, and described communication means is:

The state value of each node and adjoint variable value in intiating radio sensor network;

In each iteration cycle, wake at random i node up, using i node as initiating node; I is more than or equal to 1 integer; Described i node broadcasted the state value x of himself in wireless sensor network _iand several adjoint variables y (t) ⁽¹⁾ _i(t), y ⁽²⁾ _i(t), y ⁽³⁾ _i(t), y ⁽⁴⁾ _i(t) ..., t represents the time;

X wherein _i(0) represent the initial condition value of i node, y ^(k) _i(0) represent k adjoint variable value of i node, y ^(k) _i(0)=0, k=1,2,3

In wireless sensor network, all neighbor nodes around i node receive its current state value x of described i node broadcasts _i(t) and adjoint variable value, each node in all neighbor nodes carries out iteration to the information receiving according to it and the information of himself, obtains the state value x of next this node constantly _kand adjoint variable y (t+1) ⁽¹⁾ _k(t+1), y ⁽²⁾ _k(t+1), y ⁽³⁾ _k(t+1), y ⁽⁴⁾ _k(t+1) ...,

Each neighbor node is respectively according to himself state value and the adjoint variable value convergency value z (t) that obtains current time and next himself state value and adjoint variable value convergency value z (t+1) of obtaining next moment constantly of current time;

For each neighbor node, calculate its current time and next convergence value difference constantly, the convergence value difference corresponding when all nodes all reaches 10 ^-5during magnitude, stop iteration, realize the broadcast Gossip radio communication of distributed average common recognition; Otherwise return, carry out next iteration cycle.

2. the broadcast Gossip wireless communications method of distributed average common recognition according to claim 1, is characterized in that: the state value x of i node of broadcast _i(t+1) be:

x _i(t+1)=x _i(t)，

Several adjoint variables y ⁽¹⁾ _i(t+1), y ⁽²⁾ _i(t+1), y ⁽³⁾ _i(t+1), y ⁽⁴⁾ _i(t+1) ... be respectively:

y ⁽¹⁾ _i(t+1)=y ⁽¹⁾ _i(t)；

y ⁽²⁾ _i(t+1)=y ⁽²⁾ _i(t)；

.

.

.

y ⁽ⁿ⁾ _i(t+1)=y ⁽ⁿ⁾ _i(t)。

3. the broadcast Gossip wireless communications method of distributed average common recognition according to claim 1, is characterized in that: all neighbor nodes of i node receive after the current state value of i node, and its state value is:

$\begin{array}{cc}{x}_k(t+1)=\frac{1}{2}{x}_k\left(t\right)+\frac{1}{2}{x}_i\left(t\right),& \&ForAll;k\&Element;N_i;\end{array}$

All neighbor nodes of i node receive after the adjoint variable value of i node, and its adjoint variable value is:

$\left\{\begin{array}{cc}{y^{\left(1\right)}}_k(t+1)=\frac{1}{2}{x}_k\left(t\right)-\frac{1}{2}{x}_i\left(t\right)+\frac{1}{2}{y^{\left(1\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(1\right)}}_i\left(t\right),& \\ {y^{\left(2\right)}}_k(t+1)=\frac{1}{2}{y^{\left(1\right)}}_k\left(t\right)-\frac{1}{2}{y^{\left(1\right)}}_i\left(t\right)+\frac{1}{2}{y^{\left(2\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(2\right)}}_i\left(t\right),& \&ForAll;k\&Element;N_i,\\ {y^{\left(n\right)}}_k(t+1)=\frac{1}{2}{y^{(n-1)}}_k\left(t\right)-\frac{1}{2}{y^{(n-1)}}_i\left(t\right)+\frac{1}{2}{y^{\left(n\right)}}_k\left(t\right)+\frac{1}{2}{y^{\left(n\right)}}_i\left(t\right);& \end{array}\right.$

N wherein _irepresent the neighbor node set of i node, the adjoint variable number of i node is n.

4. the broadcast Gossip wireless communications method of distributed average common recognition according to claim 1, is characterized in that: in whole network, remove beyond all neighbor nodes of i node, the state value of all the other all nodes is:

$\begin{array}{cc}{x}_k(t+1)=x_k\left(t\right),& \&ForAll;k\&NotElement;N_i;\end{array}$

In whole network, to remove beyond all neighbor nodes of i node, the state value of all the other all nodes is:

$\begin{array}{cc}{y^{\left(1\right)}}_k(t+1)={y^{\left(1\right)}}_k\left(t\right);& \\ {y^{\left(2\right)}}_k(t+2)={y^{\left(2\right)}}_k\left(t\right);& \&ForAll;k\&NotElement;N_i;\\ .& \\ .& \\ .& \\ {y^{\left(n\right)}}_k(t+1)={y^{\left(n\right)}}_k\left(t\right).& \end{array}$

5. the broadcast Gossip wireless communications method of distributed average common recognition according to claim 1, is characterized in that: the convergency value z (t) of i node realizes by following formula:

$z\left(t\right)=x_k\left(t\right)+\frac{n}{n+1}{y^{\left(1\right)}}_k\left(t\right)+\frac{n-1}{n+1}{y^{\left(2\right)}}_k\left(t\right)+...+\frac{1}{n+1}{y^{\left(n\right)}}_k\left(t\right).$

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