CN103152817B - Distributed clock synchronizing method based on broadcast Gossip algorithm - Google Patents

Abstract

A distributed clock synchronizing method based on a broadcast Gossip algorithm relates to a distributed clock synchronizing technology in a wireless sensor network, and solves the problem faced by all existing broadcast Gossip algorithms that the clock of each node is not guaranteed to converge to the average value of the initial clock of the node, such that the finally achieved synchronized clock of each node has comparatively great deviation with the average value of the initial clock of the node, which is adverse to network maintenance and data analysis. The method comprises the steps of: initializing the wireless sensor network consisting N number of nodes; ensuring each node to acquire indegree information and a scramble parameter value; setting two variables for each node; judging the state of each node; broadcasting the variable value of the node triggering an expire timer to the external neighboring nodes; updating the variable value of the node in the network; judging whether the two variables of the N number of nodes in the wireless sensor network converge to the same synchronized clock value; acquiring a clock synchronization result, and completing an iterative process. The invention can be widely used for synchronizing a distributed clock.

Description

Based on the distributed clock synchronization method of broadcast Gossip algorithm

Technical field

The present invention relates to a kind of distributed clock synchronization technology of wireless sensor network.

Background technology

The communication network that wireless sensor network is made up of the node in a large number with functions such as data acquisition, data processing and wireless data transceivings.Due to the restriction of cost and volume, these nodes all adopt powered battery usually, therefore have limited data analysis and transmittability.In many applications, need the clock synchronous of each sensor node, so that the application in the fields such as the Distributed localization of carrying out estimating such as time of advent, time division multiple access, distributed collaboration and distributed object tracking.Between node, clock synchronous can have multiple method, such as by GPS (global positioning system) or base station time service, but this method needs each sensor node to assemble GPS or cellular communication module, not only can increase the cost of equipment, also can increase their power consumption.Another method is exactly carry out distributed synchronization by switching clock information between node; but these class methods all have employed complicated Routing Protocol traditionally to carry out the exchange of clock information; so usually can due to the problem of communication delay or network capacity, cause that protocol overhead is large, convergence precision is low and the problem that convergence rate is slow.

Under above-mentioned background, be born and can be applicable to the synchronous Gossip algorithm of wireless-sensor network distribution type.In the algorithm, each node is waken up randomly, then certain (or certain group) adjacent node switching clock information that the node waken up is selected with it randomly, these two (maybe this group) nodes utilize convex merging (Convex Combination) algorithm to merge these clock informations respectively subsequently, and replace oneself original clock with new clock information.Now claim this algorithm to complete once to upgrade or an iteration.Mathematically can prove, by this algorithm, all nodes in network can realize clock synchronous (or be called achieve common recognition), and the clock of final each node equals the mean value of these node initial clock just.Therefore in wireless sensor network, apply the meaning that Gossip algorithm carries out distributed clock synchronization be: 1) avoid hot issue.Carry out clock information transmission owing to have employed random walk (Random Walk) pattern, therefore avoid that to be formed take Centroid as the fixed topology such as tree-shaped or netted of root, grouping therefore can be made better to evade hot spot region.2) protocol overhead and energy ezpenditure is reduced.Owing to not needing to carry out Route establishment and maintenance, so Gossip algorithm effectively reduces protocol overhead, and then reduce node energy consumption.In addition, all carried out before being grouped in each transmission merging compression, so number of packet greatly reduces, also effectively can reduce the energy ezpenditure of node.3) communication reliability.Owing to not needing to carry out transfer clock information by fixing end-to-end route, therefore Gossip algorithm avoids single point failure then route break problem, improves the reliability of network.4) network scalability (Scalability) is improved.Because clock information has carried out merging compression in transmittance process, thus increase node in network and only can increase the convergence of algorithm time, significantly can't increase the traffic carrying capacity of network.Therefore this algorithm can utilize Internet resources better, thus improves the autgmentability of network.5) hsrdware requirements are reduced.Tradition is communication pattern end to end, and the node in network needs buffered packet until it is correctly sent.When the nodes in network is more or traffic carrying capacity is increased sharply, node needs more time processing channel race problem, have a large amount of groupings during this to need to carry out buffer memory, this is a huge challenge for the wireless sensor node that storage capacity is very limited.And each node in Gossip algorithm only needs the clock information preserving it, once receive new clock information, the compression of two clock informations can merge by once, so it only can take the data transmit queue of finite length, and has nothing to do with the scale of network and business model.Therefore, Gossip algorithm can well adapt to architecture and the mode of operation of wireless sensor network, has good application prospect.

Gossip algorithm was proposed by people such as Tsitsiklis first in 1984, and this algorithm only utilizes the local information of network node and the information of its neighbor node to carry out exchanges data, solves the average common recognition problem under distribution occasion.Gossip algorithm can be widely used in source electricity problem, Parameter Estimation Problem, Kalman filtering etc., receives the extensive concern of academia in recent years especially.The present invention relates to the distributed average common recognition algorithm in a kind of wireless sensor network, this algorithm can make nodes all in wireless sensor network reach average common recognition state, compared with traditional algorithm, this algorithm has convergence rate faster, and be mathematically proved to be restrain and converge on average, meanwhile, this algorithm has good adaptability to the packet loss problem in actual application, topologies change problem.

Although there has been a lot of achievement in research in wireless sensor network Gossip algorithm both at home and abroad, former research has mainly laid particular emphasis on the research of paired Gossip algorithm (Pair-wise Gossip Algorithm) and geographical Gossip algorithm (Geographic Gossip Algorithm).This two classes algorithm, owing to only having selected node to carry out exchanges data when each renewal, although nodal clock therefore can be made to converge on the average of their initial clock, but can only be used for two-way link, well not utilize the broadcast characteristic of wireless channel.Several years up to date, just there is the research for broadcast Gossip algorithm (Broadcast Gossip Algorithm) in the world.In this kind of algorithm when its clock information of a node broadcasts, all nodes that can receive this clock information all can upgrade their data.Owing to not needing reverse data to exchange, so this kind of algorithm is more suitable for asymmetrical wireless channel.Meanwhile, have more node to participate in because each clock upgrades, therefore this kind of convergence of algorithm speed is faster.In addition, because broadcast Gossip algorithm no longer needs Stochastic choice adjacent node, thus make algorithm more simple and be easy to realize.Unfortunately, all in the world at present broadcast Gossip algorithm are all faced with two problems: or they can not ensure that the clock of each node converges on the mean value (i.e. average common recognition) of their initial clock; Or can mean value be converged to, but cannot mathematically prove its convergence.For the former, the synchronised clock that so each node is finally reached can have larger deviation with the average of their initial clock, is unfavorable for carrying out network operation and data analysis.And the latter is owing to mathematically can not prove its convergence, therefore the reliability of algorithm cannot be guaranteed, and this algorithm is also extremely slow from simulation analysis result convergence rate.

Summary of the invention

The present invention is faced with can not ensures that the clock of each node converges on the mean value of their initial clock to solve all at present broadcast Gossip algorithm, the synchronised clock causing each node finally to be reached can have larger deviation with the average of their initial clock, be unfavorable for carrying out network operation and data analysis problems, thus a kind of distributed clock synchronization method based on broadcast Gossip algorithm is provided.

Based on the distributed clock synchronization method of broadcast Gossip algorithm, it comprises the steps:

Step one: to the wireless sensor network initialization including N number of node, and initialization in-degree information and scrambling parameter; Wherein N is positive integer, for the in-degree information of node i, ε is scrambling parameter;

Step 2: the Two Variables of setting node, x _it present clock variable that () is node i, y _it adjoint variable that () is node i, wherein x _i(0) be the initial clock value of node i, and y _i(0)=0, namely initial time is t=0; And setting timer, the count value of described timer meets any random distribution;

Step 3: the state judging each node: then enter step 5 when node is the trigger node k regularly expired, then enter step 6 when node is the outer neighbors j receiving spot broadcasting; Otherwise continue to monitor;

Step 4: by the Two Variables value of the trigger node k that timing expires, i.e. the present clock variate-value x of trigger node k _k(t) and adjoint variable value y _kt (), utilizes spot broadcasting to be broadcast to its outer neighbors j respectively;

Step 5: the clock variable value of the node in wireless sensor network and state variable value are upgraded, and the timer of trigger node k is removed;

Step 6: judge whether the Two Variables of N number of node in wireless sensor network all converges on same synchronised clock value, and namely in wireless sensor network, the clock variable of N number of node is all identical, and the adjoint variable of N number of node is all identical; If yes then enter step 8, otherwise reset timer and return step 4;

Step 7: obtain clock synchronous result, complete iterative process.

Described in step one to the initialized process of the wireless sensor network including N number of node be:

Directed simple graph G=(V, E) is set up to the wireless sensor network including N number of node, wherein V={1,2 ..., N} is node set, and E is limit set; When node i that and if only if directly can receive grouping from node j, claim limit (i, j) ∈ E to exist, now title node i is the outer neighbour of node j, and node j is the interior neighbour of node i, and

Order with the interior neighbour of representation node i gathers and outer neighbour's set respectively, with be respectively in-degree and the out-degree of node i, symbol | X| _cthe gesture of set X is got in representative.

Described step 5: in the process that clock variable value and the state variable value of the node in wireless sensor network are upgraded:

For trigger node k, the state value of this node, adjoint variable value are sent to outer neighbors j, then the adjoint variable triggering trigger node k is set to 0;

$\left\{\begin{array}{c}{x}_k(t+1)=x_k\left(t\right)\\ y_k(t+1)=0\end{array}\right.$

In formula: x _kt () represents the clock variable of trigger node k in t, y _kt () represents the adjoint variable of trigger node k in t.

For outer neighbors j, the information according to receiving upgrades:

$\left\{\begin{array}{c}{x}_j(t+1)=(1-\frac{1}{{\mathrm{\δ}}_j^{+}})x_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_j\left(t\right)\\ y_j(t+1)=\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_j\left(t\right)-\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+(1-\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}})y_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_k\left(t\right)\end{array}\right.$

In formula: x _jt () represents the adjoint variable of outer neighbors j in t, y _jt () represents the adjoint variable of outer neighbors j in t, for the in-degree of outer neighbors j.

The value of described scrambling parameter ε is Re (ξ ₂)/2, wherein ξ ₂for the second little characteristic value of matrix L;

Described L is wherein θ is meet: if j=k and so otherwise

The present invention is based on broadcast Gossip algorithm and realize ensureing that the clock of each node converges on the mean value of their initial clock, what each node was finally reached synchronously can not have relatively large deviation problem with the average of their initial clock all the time.The present invention proposes a kind of distributed clock synchronization technology with low convergence error based on broadcast Gossip algorithm, and this algorithm can mathematically prove its convergence.When given iterations, method of the present invention has minimum convergence error, when given convergence error, method of the present invention has the fastest convergence rate, and the distributed clock synchronization method that therefore the present invention is based on broadcast Gossip algorithm has best performance in all broadcast Gossip algorithm.

Accompanying drawing explanation

Fig. 1 is the flow chart of the distributed clock synchronization method that the present invention is based on broadcast Gossip algorithm;

Fig. 2 is the simulation result of the network convergence variance of 100 nodes in embodiment one;

Fig. 3 is the simulation result of the network convergence deviation of 100 nodes in embodiment one;

Fig. 4 is the simulation result of the network convergence variance of 500 nodes in embodiment one;

Fig. 5 is the simulation result of the network convergence deviation of 500 nodes in embodiment one.

Embodiment

Embodiment one, composition graphs 1 illustrate this embodiment.

Based on the distributed clock synchronization method of broadcast Gossip algorithm, it comprises the steps:

Step one: to the wireless sensor network initialization including N number of node, and initialization in-degree information and scrambling parameter; Wherein N is positive integer, for the in-degree information of node i, ε is scrambling parameter;

Step 2: the Two Variables of setting node, x _it present clock variable that () is node i, y _it adjoint variable that () is node i, wherein x _i(0) be the initial clock value of node i, and y _i(0)=0, namely initial time is t=0; And setting timer, the count value of described timer meets any random distribution;

Step 3: the state judging each node: then enter step 5 when node is the trigger node k regularly expired, then enter step 6 when node is the outer neighbors j receiving spot broadcasting; Otherwise continue to monitor;

Step 4: by the Two Variables value of the trigger node k that timing expires, i.e. the present clock variate-value x of trigger node k _k(t) and adjoint variable value y _kt (), utilizes spot broadcasting to be broadcast to its outer neighbors j respectively;

Step 5: the clock variable value of the node in wireless sensor network and state variable value are upgraded, and the timer of trigger node k is removed;

Step 6: judge whether the Two Variables of N number of node in wireless sensor network all converges on same synchronised clock value, and namely in wireless sensor network, the clock variable of N number of node is all identical, and the adjoint variable of N number of node is all identical; If yes then enter step 8, otherwise reset timer and return step 4;

Step 7: obtain clock synchronous result, complete iterative process.

Operation principle: the present invention utilizes broadcast Gossip algorithm to obtain the clock synchronous of wireless sensor network, and in this algorithm, the clock value of each node is not only restrained, and converges on the average of their initial clock.Mathematically can also prove, if scrambling parameter ε value is Re (ξ ₂)/2, so proposed algorithm has the fastest convergence rate.

The method of this patent has convergence rate or better convergence precision faster than every other broadcast Gossip algorithm.When given iterations, this method convergence error in all broadcast Gossip algorithm is minimum; When given convergence error, this method convergence rate is the fastest.When practical application, distributed clock synchronization weighs performance index by these two parameters.Or the iterations of limiting network interior joint, or the error of given convergence.Meet one of these two conditions, algorithm is just thought and has been restrained.

Concrete steps of the present invention are in detail:

Step one: to the wireless sensor network initialization including N number of node, and initialization in-degree information and scrambling parameter; Wherein N is positive integer, for the in-degree information of node i, ε is scrambling parameter;

For the wireless sensor network having N number of node, an oriented free hand drawing G=(V, E) can be modeled as, V={1 here, 2 ..., N} is node set, and E is limit set.When node i that and if only if directly can receive grouping from node j, just claim limit (i, j) ∈ E exists, and now title node i is the outer neighbour (Out-neighbor) of node j, and node j is the interior neighbour (In-neighbor) of node i.In the present invention, the existence from ring will do not allowed, namely like this, even if when node sends grouping, it oneself can receive by wireless channel the grouping that it sends, also will directly abandon.Definition with the interior neighbour of representation node i gathers and outer neighbour's set respectively, and defines with for in-degree (In-degree, graph theory term represent quantity adjacent in a node) and the out-degree (Out-degree, graph theory term represent the outer adjacent quantity of a node) of node i, symbol here | X| _cthe gesture (i.e. the quantity of element in set) of set X is got in representative.

In-degree information is divided into two kinds of modes to obtain according to radio sensing network topological structure: it is as follows that the mode that (1) obtains voluntarily obtains in-degree information process: the grouping that its surroundings nodes of each node listens sends, thus can know the neighbor information around it.Such node just can obtain the quantity of its adjacent node by the mode intercepted, thus obtains in-degree information; (2) directly setting means obtains in-degree information.If network topology structure is fairly simple, time nodes is less, also directly can set the in-degree information of each node.If network is random distribution, so preferably just adopt the mode obtaining in-degree information voluntarily.

Step 2: the Two Variables of setting node, x _it present clock variable that () is node i, y _it adjoint variable that () is node i, wherein x _i(0) be the initial clock value of node i, and y _i(0)=0, namely initial time is t=0; And setting timer, the count value of described timer meets any random distribution;

Each node i in network all preserves Two Variables, and one is its present clock variable x _it (), another is adjoint variable y _i(t).Wherein x _i(0) be the initial clock value of each node, and specify y _i(0)=0.

Step 3: the state judging each node: then enter step 5 when node is the trigger node k regularly expired, then enter step 6 when node is the outer neighbors j receiving spot broadcasting; Otherwise continue to monitor;

Step 4: by the Two Variables value of the trigger node k that timing expires, i.e. the present clock variate-value x of trigger node k _k(t) and adjoint variable value y _kt (), utilizes spot broadcasting to be broadcast to its outer neighbors j respectively;

Step 5: the clock variable value of the node in wireless sensor network and state variable value are upgraded, and the timer of trigger node k is removed;

The detailed process of these its variablees of node updates is as follows:

For trigger node k, the state value of this node, adjoint variable value are sent to outer neighbors j, then the adjoint variable triggering trigger node k is set to 0;

$\left\{\begin{array}{c}{x}_k(t+1)=x_k\left(t\right)\\ y_k(t+1)=0\end{array}\right.$

In formula: x _kt () represents the clock variable of trigger node k in t, y _kt () represents the adjoint variable of trigger node k in t.

For outer neighbors j, the information according to receiving upgrades:

$\left\{\begin{array}{c}{x}_j(t+1)=(1-\frac{1}{{\mathrm{\δ}}_j^{+}})x_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_j\left(t\right)\\ y_j(t+1)=\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_j\left(t\right)-\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+(1-\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}})y_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_k\left(t\right)\end{array}\right.$

In formula: x _jt () represents the adjoint variable of outer neighbors j in t, y _jt () represents the adjoint variable of outer neighbors j in t, for the in-degree of outer neighbors j.

For other node have:

$\left\{\begin{array}{c}{x}_l(t+1)=x_l\left(t\right)\\ y_l(t+1)=y_l\left(t\right)\end{array}\right.,$

Namely other nodes l only carries out the clock renewal of oneself.

In above-mentioned iterative algorithm, x (t+1) is mainly used to store the synchronised clock estimated value stored by each iterative process interior joint; Y (t+1) is used for storing the deviation between each iterative process interior joint synchronised clock estimated value and actual value; ε is scrambling parameter, and by changing this parameter, algorithm will have different convergence rates, after can discuss its value in detail.Because above-mentioned algorithm is typical linear iterative algorithm, therefore can state by the form of matrix, namely

$\left[\begin{array}{c}x(t+1)\\ y(t+1)\end{array}\right]=W_k\left(t\right)\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]---\left(1\right)$

Here matrix of a linear transformation W _kt the lower footnote k of () represents the renewal of current clock and is initiated by node k.

Step 6: judge whether the Two Variables of N number of node in wireless sensor network all converges on same synchronised clock value, and namely in wireless sensor network, the clock variable of N number of node is all identical, and the adjoint variable of N number of node is all identical; If yes then enter step 8, otherwise reset timer and return step 4;

For broadcast Gossip algorithm, when the renewal of any t, certain node k only having this renewal to activate broadcasts its state value, and only has the outer neighbors of node k just can receive this state value and carry out state updating.Therefore, node is only had in network take part in current state value with limit (j, k) ∈ E to upgrade.Based on this reason, the node in figure G all can be retained but all deleted on the limit beyond (j, k) ∈ E, and construct a new figure G _k.Then be this new figure G _kgenerate corresponding spot broadcasting weighted adjacent matrix spot broadcasting weighting indegree matrix with spot broadcasting weighting Laplacian Matrix for ease of describing, provide the concrete definition of these three kinds of matrixes below.

Spot broadcasting weighted adjacent matrix each element in this matrix meet: if j=k and so otherwise

Spot broadcasting weighting indegree matrix each element in this matrix meet: if so otherwise

Spot broadcasting weighting Laplacian Matrix here represent complete 1 vector and Diag (v) represents a diagonal matrix and its diagonal element is the corresponding element of vector v.

These three kinds of weighting matrixs are respectively:

${\hat{A}}_2\left(\mathrm{\θ}\right)=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0.5& 0& 0\end{array}\right],$ ${\hat{D}}_2\left(\mathrm{\β}\right)=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& 0.5\end{array}\right],$ ${\hat{L}}_2\left(\mathrm{\θ}\right)=\left[\begin{array}{cccc}0& 0& 0& 0\\ 0& 0& 0& 0\\ 0& -1& 1& 0\\ 0& 0.5& 0& 0.5\end{array}\right]$

Utilize this three kinds of matrixes, can by transformation matrix W _kt () describes with following formula.

$W_k\left(t\right)=\left[\begin{array}{cc}I-{\hat{L}}_k\left(\mathrm{\θ}\right),& \mathrm{\ϵ}{\hat{D}}_k\left(\mathrm{\β}\right)\\ {\hat{L}}_k\left(\mathrm{\θ}\right),& I-e_k{e}_k^T-{\mathrm{\ϵ}\hat{D}}_k\left(\mathrm{\β}\right)+{\hat{A}}_k\left(\mathrm{\θ}\right)\end{array}\right]---\left(2\right)$

Here I is unit matrix, and e _kfor the base vector of standard, namely it except a kth element be except 1, all the other elements are all 0.Can verify here with be respectively complete 1 column vector and full 0 column vector.If therefore vector x (t) and y (t) converge on respectively with (c is a constant here), so whole iterative algorithm just enters a fixed point, and after this state value of vector x (t) and y (t) can not change, thus enter convergence state.And now all nodes achieve common recognition, namely for arbitrary two node i and j, lim _{t → ∞}x _i(t)=lim _{t → ∞}x _j(t).It may be noted that if links all in network is all bi-directional symmetrical, so have arbitrary node now can prove, in this algorithm, the clock value of each node is not only restrained, and converges on the average of their initial clock.

Step 7: obtain clock synchronous result, complete iterative process.

Discuss from mathematical theory:

If scrambling parameter ε value is Re (ξ ₂)/2, so proposed algorithm has the fastest convergence rate, here ξ ₂for the second little characteristic value of matrix L.Utilize matrix perturbance theory and Markov matrix theory, following two conclusions can be obtained.

Conclusion 1. propose algorithm and can ensure that each node can reach clock synchronous according to mathematic expectaion, namely

$\underset{t\→\∞}{\lim }E\left(\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]\right)=\underset{t\→\∞}{\lim }E\left(\underset{j=0}{\overset{t}{\mathrm{\Π}}}W\left(j\right)\right)\left[\begin{array}{c}x\left(0\right)\\ y\left(0\right)\end{array}\right]$

$=\underset{t\→\∞}{\lim }{\stackrel{\‾}{W}}^t\left[\begin{array}{c}x\left(0\right)\\ y\left(0\right)\end{array}\right]$

$=\left[\begin{array}{c}\stackrel{\→}{1}\\ \stackrel{\→}{0}\end{array}\right]\left[\begin{array}{cc}{\mathrm{\ω}}_1^T& {\mathrm{\ω}}_2^T\end{array}\right]\left[\begin{array}{c}x\left(0\right)\\ y\left(0\right)\end{array}\right]---\left(3\right)$

$=\left({\mathrm{\ω}}_1^{T}x\left(0\right)\right)\left[\begin{array}{c}\stackrel{\→}{1}\\ \stackrel{\→}{0}\end{array}\right]$

Here, it is because each matrix W that this formula is set up _kt () is independent identically distributed random matrix.Utilize character and the matrix perturbance theory of Markov matrix, can matrix be proved eigenvalue of maximum be 1, and be one single; And the mould of its all the other characteristic values is all less than 1, so the long-pending convergence of this Matris Spectral, convergence result is as shown in formula (3), wherein vectorial ${\left[\begin{array}{cc}{\mathrm{\ω}}_1^T& {\mathrm{\ω}}_2^T\end{array}\right]}^T$ With ${\left[\begin{array}{cc}{\stackrel{\→}{1}}^T& {\stackrel{\→}{0}}^T\end{array}\right]}^T$ Be respectively matrix corresponding to left eigenvector and the right characteristic vector of characteristic value 1, and meet normalizing condition $\left[\begin{array}{cc}{\mathrm{\ω}}_1^T& {\mathrm{\ω}}_2^T\end{array}\right]{\left[\begin{array}{cc}{\stackrel{\→}{1}}^T& {\stackrel{\→}{0}}^T\end{array}\right]}^T=1.$ Be not difficult to find out from formula (3), the clock of all nodes finally converges on value

Conclusion 2. carry algorithm second moment convergence, i.e. the limit exist, wherein $m\left(t\right)={\left[\begin{array}{cc}{x\left(t\right)}^T& {y\left(t\right)}^T\end{array}\right]}^T-(1/N){\left[\begin{array}{cc}{\stackrel{\→}{1}}^T& {\stackrel{\→}{0}}^T\end{array}\right]}^T\left[\begin{array}{cc}{\stackrel{\→}{1}}^T& {\stackrel{\→}{1}}^T\end{array}\right]{\left[\begin{array}{cc}{x\left(0\right)}^T& {y\left(0\right)}^T\end{array}\right]}^T$ Represent the Two Variables value of each node and the difference of all node initializaing variable mean value when each clock upgrades.

Comprehensive conclusion 1 and conclusion 2 known, clock synchronization algorithm of carrying not only can be restrained according to probability, and convergence error bounded, and therefore algorithm mathematically can prove its convergence.

For the ease of comparing, show and existing two kinds of broadcast Gossip algorithm will distinguish called after BGA-1 and BGA-2 in the world, and the algorithm (called after BBGA) proposed in they and the present invention carrying out Performance comparision.Wherein BGA-1 can prove algorithmic statement, but algorithm can not converge on the broadcast Gossip algorithm of initial clock average; And BGA-2 does not prove its constringent broadcast Gossip algorithm by mathematical measure.In performance evaluation below, in network, there are 100 or 500 nodes, and generate random geometry figure by them.Have employed two kinds of different scrambling parameter configurations in emulation, wherein BBGA-opt represents scrambling parameter ε and gets optimal value Re (ξ ₂)/2; And BBGA-0.5 represents scrambling parameter ε value 0.5.The performance of parser is carried out below respectively from convergence rate and convergence error two aspects.

1) convergence rate

In order to analyze convergence rate, first define the evaluation criterion of convergence rate, i.e. variance

Be not difficult to find out from formula (4), the variance of the clock variable that each node keeps when q (t) has measured each iteration.When node is built consensus, q (t) will converge to 0.Therefore, the speed speed that q (t) converges on 0 can be used for the convergence rate of measure algorithm.

2) convergence error

In order to analyze convergence error, departure function can be defined

If an algorithm can ensure the average converging on all node initial clock, so r (t) will converge on 0; Otherwise the size of r (t) convergency value just determines the size of convergence error.Therefore departure function r (t) can be used for the convergence error of measure algorithm.

Fig. 2 and Fig. 4 is the simulation result at 100 nodes and 500 meshed network convergence variance between algorithm, and this simulation result indicates convergence of algorithm speed simultaneously.Fig. 2 and Fig. 5 is the simulation result at 100 nodes and 500 meshed network convergence deviations between algorithm, and this simulation result indicates convergence of algorithm error simultaneously.As can be seen from simulation result, BGA-1 convergence rate is the fastest, but this is cost to the maximum with convergence error.BGA-2 convergence rate is the slowest, but convergence precision is the highest.BBGA algorithm proposed by the invention, no matter scrambling parameter gets optimal value or 0.5, and their performance is all between BGA-1 and BGA-2.Obviously, the performance of BBGA-opt is better than BBGA-0.5, but the optimization of scrambling parameter needs to know topology of networks in advance, so be only suitable for small-scale application.

To sum up, for distributed clock synchronization, due to the average not needing the clock of each node finally strictly to converge on their initial clock, as long as this convergency value meets certain required precision.Be not difficult to find out from above simulation analysis, algorithm proposed by the invention is better than BGA-1 in convergence precision, in convergence rate, be better than BGA-2, be therefore the equilibrium between convergence rate and convergence precision, more meets the application requirement of distributed clock synchronization algorithm.Meanwhile, have simple and easy to do due to BBGA-0.5 and be applicable to large scale network application, therefore there is optimum engineering practice and be worth.

Claims (5)

1., based on the distributed clock synchronization method of broadcast Gossip algorithm, it is characterized in that it comprises the steps:

Step one: to the wireless sensor network initialization including N number of node, and initialization in-degree information and scrambling parameter; Wherein N is positive integer, for the in-degree information of node i, ε is scrambling parameter;

Step 2: the Two Variables of setting node, x _it present clock variable that () is node i, y _it adjoint variable that () is node i, wherein x _i(0) be the initial clock value of node i, and y _i(0)=0, namely initial time is t=0; And setting timer, the count value of described timer meets any random distribution;

Step 3: the state judging each node: then enter step 4 when node is the trigger node k regularly expired, then enter step 5 when node is the outer neighbors j receiving spot broadcasting; Otherwise continue to monitor;

Step 4: by the Two Variables value of the trigger node k that timing expires, i.e. the present clock variate-value x of trigger node k _k(t) and adjoint variable value y _kt (), utilizes spot broadcasting to be broadcast to its outer neighbors j respectively;

Step 5: the clock variable value of the node in wireless sensor network and state variable value are upgraded, and the timer of trigger node k is removed;

Step 6: judge whether the Two Variables of N number of node in wireless sensor network all converges on same synchronised clock value, and namely in wireless sensor network, the clock variable of N number of node is all identical, and the adjoint variable of N number of node is all identical; If yes then enter step 7, otherwise reset timer and return step 3;

Step 7: obtain clock synchronous result, complete iterative process.

2. according to claim 1 based on broadcast Gossip algorithm distributed clock synchronization method, it is characterized in that described in step one to the initialized process of the wireless sensor network including N number of node be:

Oriented simple unidirectional relationship G=(V, E) is set up to the wireless sensor network including N number of node, wherein V={1,2 ..., N} is node set, and E is limit set; When node i that and if only if directly can receive grouping from node j, claim limit (i, j) ∈ E to exist, now title node i is the outer neighbour of node j, and node j is the interior neighbour of node i, and

Order $N_i^{+}:=\{j\∈V:(i,j)\∈E\}$ With $N_i^{-}:=\{k\∈V:(k,j)\∈E\}$ The interior neighbour of representation node i gathers and outer neighbour's set respectively, with be respectively in-degree and the out-degree of node i, symbol | X| _cthe gesture of set X is got in representative.

3. the distributed clock synchronization method based on broadcast Gossip algorithm according to claim 2, is characterized in that described step 5: in the process upgrade clock variable value and the state variable value of the node in wireless sensor network:

For trigger node k, the state value of this node, adjoint variable value are sent to outer neighbors j, then the adjoint variable triggering trigger node k is set to 0;

$\left\{\begin{array}{c}{x}_k(t+1)=x_k\left(t\right)\\ y_k(t+1)=0\end{array}\right.$

In formula: x _kt () represents the clock variable of trigger node k in t, y _kt () represents the adjoint variable of trigger node k in t.

4. the distributed clock synchronization method based on broadcast Gossip algorithm according to claim 3, is characterized in that described step 5: in the process upgrade clock variable value and the state variable value of the node in wireless sensor network:

For outer neighbors j, the information according to receiving upgrades:

$\left\{\begin{array}{c}{x}_j(t+1)=(1-\frac{1}{{\mathrm{\δ}}_j^{+}})x_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_j\left(t\right)\\ y_j(t+1)=\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_j\left(t\right)-\frac{1}{{\mathrm{\δ}}_j^{+}}{x}_k\left(t\right)+(1-\mathrm{\ϵ}\frac{1}{{\mathrm{\δ}}_j^{+}})y_j\left(t\right)+\frac{1}{{\mathrm{\δ}}_j^{+}}{y}_k\left(t\right)\end{array}\right.$

In formula: x _jt () represents the adjoint variable of outer neighbors j in t, y _jt () represents the adjoint variable of outer neighbors j in t, for the in-degree of outer neighbors j.

5. the distributed clock synchronization method based on broadcast Gossip algorithm according to claim 1, is characterized in that the value of scrambling parameter ε described in step one is Re (ξ ₂)/2, wherein ξ ₂for the second little characteristic value of matrix L;

Described L is wherein θ is if meet j=k and so otherwise ${\mathrm{\θ}}_{i,j}^{\left(k\right)}=0.$