CN102869026A - Distributed estimation method and system based on cooperative communication - Google Patents

Abstract

The invention discloses a distributed estimation method and a distributed estimation system based on cooperative communication. The distributed estimation method comprises the following steps: a fusion center determines cooperative node pairs according the observation quality of each sensor node towards an information source, and each cooperative node pair consists of a node with better observation quality and a node with poorer observation quality, and the two nodes are cooperative partners; the fusion center carries out transmission power distribution on each sensor node according to the current channel situation and the observation quality; each sensor node judges whether having a cooperative partner or not, if so, the two sensor nodes serving as cooperative partners for each other respectively transmit the observation information to the fusion center, and the information source is observed by nodes with better observation quality to obtain the observation information; if not, the sensor node without a cooperative partner directly transmits the observation information obtained by observing the information source to the fusion center; and the fusion center carries out fusion on the received observation information and obtains the estimation value of the information source. The distributed estimation method and the distributed estimation system based on cooperative communication are beneficial to improving of the estimation precision of a distributed estimation system.

Description

Distributed method of estimation and system based on collaboration communication

Technical field

The present invention relates to radio network technique, relate in particular to a kind of distributed method of estimation and system based on collaboration communication.

Background technology

Distributed estimation is one of important application of wireless sensor network, and distributed estimating system is observed sensor node information source in the network by a plurality of sensor nodes in the system, and according to the observation information that these nodes obtain information source is estimated.

In the existing distributed estimating system, a plurality of sensor nodes carry out independent observation to information source, and each sensor node is transferred to fusion center with the observation information that wireless channel directly obtains it, and fusion center carries out obtaining after the information fusion estimated result to information source with the observation information of a plurality of sensor nodes.Observation information is passed in the process of fusion center at sensor node, sensor node is with the broadcast mode transmission information, because signal transmission is subject to the impact of the factors such as multipath fading, noise, the observation information of some sensor nodes can not be transferred to fusion center effectively, may not be to be the higher information of observation quality even be transferred to the observation information of fusion center, thereby so that fusion center be not high to the estimated accuracy of information source yet.Therefore, need a kind of distributed method of estimation of high estimated accuracy badly.

Summary of the invention

The invention provides a kind of distributed method of estimation and system based on collaboration communication, can effectively transmit the observation information of the higher sensor node of observation quality, thereby a kind of distributed method of estimation of high estimated accuracy is provided.

First aspect of the present invention provides a kind of distributed method of estimation based on collaboration communication, comprising:

Step 1, fusion center are determined cooperative node pair according to each node to the observation quality of information source, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form, and definite result that cooperative node is right sends to corresponding node;

Step 2, described fusion center carry out transmit power allocation according to current channel conditions and observation quality to each node;

Step 3, each node judge according to the right definite result of cooperative node who receives whether self has cooperative partner, if having, then execution in step 4, otherwise execution in step 5;

Step 4, cooperative node internally mutually each other two nodes of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to described definite result, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source;

Step 5, the node that does not have a cooperative partner observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes;

Step 6, described fusion center merge the observation information that receives, and obtain the estimated value of described information source.

Another aspect of the present invention provides a kind of distributed estimating system based on collaboration communication, comprise: information source, a plurality of node and fusion center, described fusion center, be used for according to each nodes of described a plurality of nodes the observation quality of described information source being determined cooperative node pair, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form, and definite result that cooperative node is right sends to corresponding node; Also be used for the transmission channel of each node is carried out channel estimating, obtain channel conditions, and according to current channel conditions and observation quality each node is carried out transmit power allocation; And be used for the observation information that receives is merged, obtain the estimated value of described information source; Described a plurality of node, for being observed, described information source obtains observation information, cooperative node internally mutually each other two nodes of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to the right definite result of cooperative node who receives, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source; There is not the node of cooperative partner to observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes.

Technique effect of the present invention is: according to each sensor node the observation quality of information source is determined cooperative node pair by fusion center, described cooperative node to by mutually each other an observation quality of cooperative partner node and the relatively poor node of observation quality form preferably, the relatively poor node of observation quality assist observation quality preferably node carry out transfer of data, improving its signal transmission quality, thereby improve estimated accuracy; And adopt direct mode to be transferred to fusion center by not forming the observation information that the right sensor node of cooperative node also obtains its observation, thereby guarantee that fusion center takes full advantage of the observation information of nodes, obtain the more accurately estimated value of information source.

Description of drawings

Fig. 1 is the structural representation that the present invention is based on the distributed estimating system embodiment of collaboration communication;

Fig. 2 is the flow chart that the present invention is based on the distributed method of estimation embodiment of collaboration communication;

Fig. 3 is the right allocation flow figure of cooperative node in the embodiment of the invention;

Fig. 4 is the operational flowchart of transmit power allocation in the embodiment of the invention;

Fig. 5 is a kind of transmit power allocation method flow diagram in the embodiment of the invention;

Fig. 6 is the estimated accuracy simulation result test comparison figure of the present invention and prior art;

Fig. 7 is the outage probability simulation result test comparison figure of the present invention and prior art.

Embodiment

Describe the specific embodiment of the present invention in detail below in conjunction with accompanying drawing, the node in following examples is take sensor node as example, but is not limited with sensor node.

Fig. 1 is the structural representation that the present invention is based on the distributed estimating system embodiment of collaboration communication, and as shown in Figure 1, the system of the present embodiment comprises: information source θ, a plurality of sensor node i ₁₁, i ₁₂... i _K1, i _K2, j ₁... j _L-2KWith fusion center FC, wherein, fusion center, be used for according to each sensor nodes of described a plurality of sensor nodes the observation quality of described information source being determined cooperative node pair, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form, and definite result that cooperative node is right sends to corresponding sensor node; Also be used for the transmission channel of each sensor node is carried out channel estimating, obtain channel conditions, and according to current channel conditions and observation quality each sensor node is carried out transmit power allocation; And be used for the observation information that receives is merged, obtain the estimated value of described information source; Described a plurality of sensor node, for being observed, described information source obtains observation information, cooperative node internally mutually each other the two sensors node of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to the right definite result of cooperative node who receives, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source; There is not the sensor node of cooperative partner to observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes.Node i among Fig. 1 ₁₁, i ₁₂... i _K1, i _K2Two nodes that middle composition cooperative node is right are such as node i ₁₁And i ₁₂, i _K1And i _K2Respectively with observation quality node i preferably ₁₁Observe the observation information of obtaining transfer to described fusion center to described information source θ, and do not form the right node j of cooperative node ₁... j _L-2KObserve the observation information of obtaining directly transfer to described fusion center to described information source θ self, thereby fusion center can carry out information fusion to its all observation information that receive, and obtains the estimated value to information source.

Fig. 2 is the flow chart that the present invention is based on the distributed method of estimation embodiment of collaboration communication, can be carried out by above-mentioned system shown in Figure 1 in the method for the present embodiment, and the method for the present embodiment comprises:

Step 1, fusion center are determined cooperative node pair according to each sensor node to the observation quality of information source, and definite result that cooperative node is right sends to corresponding sensor node.

Wherein, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form,

Step 2, described fusion center carry out transmit power allocation according to current channel conditions and observation quality to each sensor node;

Step 3, each sensor node judge according to the right definite result of cooperative node who receives whether self has cooperative partner, if having, then execution in step 4, otherwise execution in step 5;

Step 4, cooperative node internally mutually each other the two sensors node of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to described definite result, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source;

Step 5, the sensor node that does not have a cooperative partner observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes;

Step 6, described fusion center merge the observation information that receives, and obtain the estimated value of described information source.

In the present embodiment, fusion center at first determines that to the observation quality of information source node and relatively poor node of observation quality form cooperative node pair preferably by an observation quality according to each sensor node in the network, and it is determined that the result sends to corresponding node, thereby receiving this, corresponding node can know self whether to have cooperative partner and self be confirmed as observation quality preferably node or the relatively poor node of observation quality as a result the time, the relatively poor node of observation quality assist observation quality preferably node carry out transfer of data, improving the preferably information transmission quality of node of observation quality, thereby improve the precision of estimating.Allow to exist a plurality of cooperative nodes pair in the network, specifically what cooperative nodes are to by the fusion center calculative determination.Specifically, when each sensor node is observed same information source in the network, its observation quality is difference to some extent, and each node also can be different to the situation of the channel of fusion center the transmission of data, when sensor node transmits observation data to fusion center, people wish can with observation quality preferably the observation information of node effectively be transferred to fusion center as far as possible, therefore, the present embodiment utilizes collaboration communication to make two sensor nodes in the network form cooperative node, and allow the good node of the poor assistance observation quality of observation quality that its observation information is transferred to fusion center, thus guarantee observation quality preferably the observation information of node can farthest effectively be transferred to fusion center.And in order to improve the utilance of observation information in the network, not forming the observation information that the right sensor node of cooperative node also obtains its observation adopts direct mode to be transferred to fusion center, guarantee that fusion center takes full advantage of the observation information of nodes, carry out information fusion according to more observation information amount, thereby obtain the more accurately estimated value of information source.

The present embodiment is determined cooperative node pair according to each sensor node to the observation quality of information source by fusion center, described cooperative node to by mutually each other an observation quality of cooperative partner node and the relatively poor node of observation quality form preferably, the relatively poor node of observation quality assist observation quality preferably node carry out transfer of data, improving its signal transmission quality, thereby improve estimated accuracy; And adopt direct mode to be transferred to fusion center by not forming the observation information that the right sensor node of cooperative node also obtains its observation, thereby guarantee that fusion center takes full advantage of the observation information of nodes, obtain the more accurately estimated value of information source.

In the above-described embodiments, the channel conditions of the transmission channel of each sensor node can carry out in real time channel estimating by fusion center and obtain channel conditions, also can obtain the channel conditions of the node of pre-stored.When obtaining the channel conditions of renewal, fusion center also comprised before execution in step 2: step 7, described fusion center carry out channel estimating to the transmission channel of each sensor node, obtain current channel conditions.Certainly, fusion center also can carry out the channel estimating of node after the complete information source estimated value of every calculating, obtain channel conditions, and this channel conditions is carried out the foundation of transmit power allocation as next fusion center.

Fig. 3 is the right allocation flow figure of cooperative node in the embodiment of the invention, and as shown in Figure 3, the right batch operation of cooperative node in the above-mentioned middle step 1 embodiment illustrated in fig. 2 specifically can comprise:

Step 11, described fusion center according to the ascending arrangement of observation noise, and are divided into observation quality preferably node set and observation quality relatively poor node set as the line of demarcation with the sensor node correspondence with the average of minimum observation noise and maximum observation noise with each sensor node.

Specifically, the observation noise variance of sensor node can reflect node to the quality of the observation quality of information source, in this step, the observation noise variance ascending order of node is arranged, and has:

And with

As the line of demarcation of distinguishing node observation performance quality, use i ₁, i ₂..., i _KThe observation quality of (variance is arranged from low to high) expression is node ID preferably, j ₁..., j _L-KThe relatively poor node ID (supposing to have in the network L node) of (variance is arranged from low to high) expression observation quality.

Step 12, described fusion center be by the linear fit mode, obtains the preferably functional relation of observation noise and the observation noise threshold value of cooperative partner node under certain observation quality condition of node of each observation quality.

Concrete grammar is as follows: describe as an example of two nodes example, at first construct a network scenarios that only has two nodes, wherein node 1 is information source node, and observation noise is known, and node 2 is the via node of observation noise the unknown.Obtain to make the observation noise threshold value (lower bound) of the more excellent via node (node 2) of systematic function after the cooperation by two kinds of transmission meanss relatively, namely fusion center obtains by computing and compares the transmission of two node disjoints and have the requirement of observing better under the condition that performance sets the observation noise of cooperative partner node.

Mode A, node 1 transmission observation information, node 2 is as via node, and both transmit 1 observation information in the collaboration communication mode.

Mode B, node 1,2 independent transmission observation information separately

Cooperation mode has following steps in A:

In first time slot, node 1 its observation information of transmission is to fusion center, and node 2 is monitored this information.

In second time slot, node 2 transfers to fusion center with the observation information of the node 1 that monitoring is obtained.

If node 2 is the via node of node 1 (observation better performances), then according to amplification forward collaboration mode of the present invention (seeing above-mentioned steps 4) and information fusion mode (seeing above-mentioned steps 6), in the situation that only consider this two nodes in the network, the signal that fusion center FC receives is the y of following formula (1) ₁And y ₂

${\mathrm{<figure-callout\; id="1"\; label="y"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">y</figure-callout>}}_1=\sqrt{{\mathrm{\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1}\mathrm{\&theta;}+(\sqrt{{\mathrm{\&alpha;}}_1{g}_1}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">n</figure-callout>}}_1+n_{c1})$

${\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">y</figure-callout>}}_2=\sqrt{{\mathrm{\&alpha;}}_2{g}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_1}\mathrm{\&theta;}+(\sqrt{{\mathrm{\&alpha;}}_2{g}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_1}{\mathrm{<figure-callout\; id="1"\; label="n"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">n</figure-callout>}}_1+\sqrt{{\mathrm{\&alpha;}}_2{g}_2}{\mathrm{<figure-callout\; id="1"\; label="n\; c"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="n\; c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">n</figure-callout>\; </figure-callout>}}_c+n_{c2})---\left(1\right)$

${\mathrm{\&alpha;}}_1=\frac{P/2}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_1^2},$ ${\mathrm{\&alpha;}}_2=\frac{P/2}{{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="1"\; label="c\; g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">c</figure-callout>}}{g}_{}{}_{\mathrm{1,2}}({\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_1^2)+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>\; </figure-callout>}\mathrm{1,2}}^2}$

P representation node institute consumed power sum wherein, α ₁The amplification coefficient of 1 pair of observation information of representation node, α ₂The amplification coefficient of the information of 2 pairs of nodes that receive 1 of representation node.g ₁, g ₂Representation node is to the channel gain of fusion center, g _1,2Channel gain between the representation node 1,2, α _cForwarding amplification coefficient when representation node 2 and node 1 cooperation, n _1,2Channel disturbance between the representation node 1,2, n ₁The observation noise of representation node 1,

Refer to corresponding noise n _xSecond moment.Stipulate that two nodes consume equal-wattage, then for the calculating of amplification factor, have:

${\mathrm{\&alpha;}}_2=\frac{(P-P_c)/2}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_2^2},$ ${\mathrm{\&alpha;}}_1=\frac{(P-P_c)/2}{{\mathrm{\&alpha;}}_{\mathrm{<figure-callout\; id="1"\; label="c\; g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">c</figure-callout>}}{g}_{}{}_{\mathrm{1,2}}({\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_2^2)+{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2}---\left(2\right)$

$P_c={\mathrm{\&alpha;}}_c({\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_2^2)$

Wherein, P _cRepresentation node 1 is transferred to oneself observation information the power of node 2

In system described in the invention, adopt following hypothesis:

1, the noise of communicating by letter of communication noise and node and fusion center FC is independent identically distributed between the node.

2, the communication noise is obeyed the Gaussian Profile with identical statistical property in the network.

3, the nodal distance fusion center is distant, and the distance between the node is very near, thus node can to regard as to the distance of fusion center be approximately uniform.

4, node is obeyed rayleigh model to the fusion center channel.

The present invention takes following simplified way to process, and to obtain the approximation of evaluated error: sensor node is densely distributed, ignores channel path loss between the node and (namely thinks g _1,2=1); Consider for the actual scene of Distributed Application, amplifying power generally will be significantly greater than interchannel noise, thereby approximate α is arranged ₂≈ 1, and communication noise and node can obtain when to pass back to the noise of communicating by letter of fusion center FC be separate between the hypothesis node:

$h={[\sqrt{{\mathrm{\&alpha;}}_1{g}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_2},\sqrt{{\mathrm{\&alpha;}}_2{g}_2}]}^{\&prime;}$

$C=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_1{g}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_2{\mathrm{\&sigma;}}_2^2+{\mathrm{\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="1"\; label="c"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">c</figure-callout>}1}^2& \sqrt{{\mathrm{\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&alpha;}}_2{g}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_2}{\mathrm{\&sigma;}}_2^2\\ \sqrt{{\mathrm{\&alpha;}}_1{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&alpha;}}_2{g}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">\; <figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>\; </figure-callout>}}_{\mathrm{1,2}}{\mathrm{\&alpha;}}_c}{\mathrm{\&sigma;}}_2^2& {\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_2^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}2}^2\end{array}\right]---\left(3\right)$

In the model of hypothesis, sensor node is densely distributed, ignores channel fading between the node and (namely thinks g _1,2=1), have:

${\mathrm{\&alpha;}}_2=\frac{P/2}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_2^2},$ ${\mathrm{\&alpha;}}_1=\frac{P/2}{{\mathrm{\&alpha;}}_2({\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_2^2)+{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2}=\frac{P/2}{P/2+{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2}---\left(4\right)$

Consider for the actual scene of Distributed Application, amplifying power generally will be significantly greater than interchannel noise, thereby approximate α is arranged ₂≈ 1; Think that node transmits additive white Gaussian noise (Additive White Gaussion Noise, the abbreviation: the AWGN noise) be same the distribution, that is: that runs into to FC

After above-mentioned formula (3) simplified and be similar to, obtain:

$h={[\sqrt{{\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1},\sqrt{{\mathrm{\&alpha;}}_2{g}_2}]}^{\&prime;}$

$C=\left[\begin{array}{cc}{\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_2^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2& {\mathrm{\&alpha;}}_2\sqrt{g_1{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2}{\mathrm{\&sigma;}}_2^2\\ {\mathrm{\&alpha;}}_2\sqrt{g_1{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2}{\mathrm{\&sigma;}}_2^2& {\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_2^2+{\mathrm{\&sigma;}}_c^2\end{array}\right]---\left(5\right)$

Under above-mentioned processing, evaluated error can be expressed as

$\mathrm{Var}\left[\widehat{\mathrm{\&theta;}}\right]={\left[h^{\&prime;}{C}^{-1}h\right]}^{-1}$

$=\frac{{\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_2{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_2^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&alpha;}}_2{g}_1{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2{\mathrm{\&sigma;}}_2^2+{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="4"\; label="c"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">c</figure-callout>}}^4}{{\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="1"\; label="g"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_1{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&alpha;}}_2{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&alpha;}}_2{g}_1{\mathrm{<figure-callout\; id="2"\; label="g"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_2{\mathrm{\&sigma;}}_{\mathrm{1,2}}^2}---\left(6\right)$

Afterwards, can obtain the average evaluated error of system under certain channel condition by the Meng Takaluo emulation mode, and obtain under certain observation quality, the via node observation noise threshold value (greater than this threshold value, then systematic function is better after the cooperation) that makes the rear systematic function of cooperation be better than not cooperating.And then, adopt the mode of linear fit, can obtain the relation of node observation noise and relaying observation noise threshold value, have:

y＝kx+b (7)

X represents the node observation noise, and y represents corresponding with it observation noise threshold value, and this formula is required threshold function table relation.

Node during step 13, described fusion center are gathered preferably to observation quality one by one in observation quality relatively poor set is sought cooperative partner node by good to poor according to observation quality.

Wherein, if the searching condition be the observation noise of the both candidate nodes in the relatively poor set of observation quality greater than the observation noise threshold value of correspondence, and this both candidate nodes is not marked as the cooperative partner node of other nodes.

In the implementation, allow i _r, r=1 ..., the K node has good cooperative partner to poor searching oneself one by one according to observation quality, and, to each node wherein, arrive the order of K at j according to s=1 _sMiddle searching (condition is the cooperative node observation noise greater than the observation noise threshold value that obtains by function in the previous step 14) meets threshold value and requires and be not labeled as the node of other node relayings or at j if find _sMiddle traversal finishes, and then finishes.If i.e. a certain i _qNode does not also have a selected set of node j that walks remaining _W1... j _We, e ∈ 1,2 ..., L-K} can not find the cooperative partner of oneself, so i _qNode afterwards is the more impossible cooperative partner that finds oneself just, because its variance to the observation noise of cooperative node has higher requirement.

The both candidate nodes that meets described searching condition that step 14, described fusion center will find is labeled as the cooperative partner node of the better node of corresponding observation quality, determine that the better node of this observation quality and this both candidate nodes are cooperative node pair, and will determine that the result sends to respectively two corresponding nodes;

Whether all nodes during step 15, observation quality are gathered are preferably sought the cooperative partner node and have been traveled through, if traveled through then execution in step 16, otherwise repeated execution of steps 13;

Step 16, described fusion center will not find the observation quality that meets described searching condition in gathering preferably node and do not meet node in the relatively poor set of the observation quality of described searching condition as the sensor node that does not have cooperative partner.

The present invention can guarantee i by above-mentioned steps _r, r=1 ..., each node of K can find and just meet the node that oneself requires, and the node that observation is good the preceding that also guaranteed to sort is preferentially searched cooperative partner, thereby has the probability that better finds cooperative node; The node of preferentially searching simultaneously cooperative partner is less demanding to observation noise, thereby the larger node of observation noise is walked in preferential choosing, thereby the node of giving the back also provides the possibility of the high as far as possible cooperative partner that finds oneself, so that more node participates in the collaboration communication, thereby be conducive to improve estimated accuracy.

Fig. 4 is the operational flowchart of transmit power allocation in the embodiment of the invention, and as shown in Figure 4, in above-mentioned embodiment shown in Figure 2, the distribution of through-put power specifically can comprise in the described step 2:

Step 21, the division right according to cooperative node of described fusion center, calculate and definite cooperative node to the opening state of the sensor node that does not have cooperative partner;

Step 22, to the cooperative node opened to carrying out transmit power allocation with the sensor node that does not have cooperative partner;

Step 23, to the cooperative node opened to the channel conditions according to the internal two sensors node of cooperative node, the two sensors node is carried out the reallocation of internal transmission power;

Step 24, the opening state of each node and the through-put power correspondence of distribution are sent to each sensor node, so that each node determines whether to transmit observation information according to described opening state and according to the through-put power transmission observation information of distributing.

In the aforesaid operations step, fusion center is in calculating, cooperative node is become a node to equivalence, after fusion center carries out preliminary transmit power allocation to the node opened (comprise the node that do not have cooperative partner and cooperative node to), again two internal nodes of cooperative node are carried out transmit power allocation, opening state and through-put power with each node sends to each sensor node at last, each node determines whether the transmission of the value of participation measurement information according to the opening state that receives, and according to the through-put power that is assigned with accordingly observation information be transferred to fusion center.

Power division process and resolution principle that following labor is above-mentioned.

At first systematic function is analyzed, cooperative node represents with K number in the system, and the node that then all participates in cooperation can be used i ₁₁, i ₁₂..., i _K1, i _K2Indicate, wherein i _R1Represent that r cooperative node is to central observation performance node preferably, i _R2Expression i _R1Partner node; Remaining node all adopts oneself observation, and the mode of operation of forward pass fusion center FC is used j ₁, j ₂..., j _L-2KExpression.The observation information that fusion center receives can be expressed to be become:

$y_{i_{11}}=\sqrt{{\mathrm{\&alpha;}}_{i_{11}}{\mathrm{<figure-callout\; id="11"\; label="g\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}}\mathrm{\&theta;}+(n_{i_{11}}\sqrt{{\mathrm{\&alpha;}}_{i_{11}}{\mathrm{<figure-callout\; id="11"\; label="g\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}}+n_{{\mathrm{ci}}_{11}})$

$y_{i_{12}}=\sqrt{{\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{12}}{\mathrm{<figure-callout\; id="1"\; label="g\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&alpha;}}_{i_{11}}}\mathrm{\&theta;}+(n_{i_{11}}\sqrt{{\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{12}}{\mathrm{<figure-callout\; id="1"\; label="g\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&alpha;}}_{i_{11}}}+\sqrt{{\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{12}}}{n}_{i_{1}M}+n_{{\mathrm{ci}}_{12}})$

$....$

$y_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}=\sqrt{{\mathrm{\&alpha;}}_{i_{K1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_K}}\mathrm{\&theta;}+(n_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}\sqrt{{\mathrm{\&alpha;}}_{i_{K1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_K}}+n_{{\mathrm{ci}}_{K1}})$ (8)

$y_{i_{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}2}}=\sqrt{{\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K2}}{g}_{i_K}{\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}}\mathrm{\&theta;}+(n_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}\sqrt{{\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K2}}{g}_{i_K}{\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}}+\sqrt{{\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K2}}}{n}_{i_K,M}+n_{{\mathrm{ci}}_{12}})$

${\mathrm{<figure-callout\; id="1"\; label="y\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">y</figure-callout>}}_{j_{}}=\sqrt{{\mathrm{\&alpha;}}_{j_1}{\mathrm{<figure-callout\; id="1"\; label="g\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{j_{}}}\mathrm{\&theta;}+{\mathrm{<figure-callout\; id="1"\; label="n\; cj"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">n</figure-callout>}}_{{\mathrm{cj}}_{}}+\sqrt{{\mathrm{\&alpha;}}_{j_1}{g}_{j_1}}{\mathrm{<figure-callout\; id="1"\; label="n\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">n</figure-callout>}}_{j_{}}$

$....$

$y_{j_{L-2K}}=\sqrt{{\mathrm{\&alpha;}}_{j_{L-2K}}{g}_{j_{L-2K}}}\mathrm{\&theta;}+n_{{\mathrm{cj}}_{L-2K}}+\sqrt{{\mathrm{\&alpha;}}_{j_{L-2K}}{g}_{j_{L-2K}}}{n}_{j_{L-2K}}$

Subscript i wherein _{M, n}Represent n right node of m cooperative node in the i sequence (cooperative node is to sequence), j _kRepresent k node in the j sequence (non-cooperative node sequence).

Represent r cooperative node to the channel gain between two nodes,

Represent r cooperative node to the interchannel noise of communication between two nodes,

Represent r cooperative node between channel gain, subscript i _R1, i _R2Represent respectively r node and the bad node of observation quality that cooperative node centering observation quality is good.

So, the covariance of observation can represent to become:

$C=\left[\begin{array}{cccccccc}{C}_{i_{11}}& {\mathrm{<figure-callout\; id="1"\; label="R\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">R</figure-callout>}}_{i_{}}& & & & & & 0\\ R_{i_1}& {\mathrm{<figure-callout\; id="12"\; label="C\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">C</figure-callout>}}_{i_{}}& & & & & & \\ & & ...& & & & & \\ & & & C_{i_{K1}}& R_{i_K}& & & \\ & & & R_{i_K}& C_{i_{K2}}& & & \\ & & & & & {\mathrm{<figure-callout\; id="1"\; label="C\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{j_{}}& & \\ & & & & & & ...& \\ 0& & & & & & & C_{j_{L-2K}}\end{array}\right]---\left(9\right)$

$C_{i_{11}}={\mathrm{\&alpha;}}_{i_{11}}{\mathrm{<figure-callout\; id="11"\; label="g\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&sigma;}}_{i_{11}}^2+{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="11"\; label="ci"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">ci</figure-callout>}}_{11}}^2,$ $C_{i_{12}}={\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{12}}{\mathrm{<figure-callout\; id="1"\; label="g\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&alpha;}}_{i_{11}}{\mathrm{\&sigma;}}_{i_{11}}^2+{\mathrm{\&alpha;}}_{i_{12}}{\mathrm{<figure-callout\; id="12"\; label="g\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&sigma;}}_{i_1}^2+{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="12"\; label="ci"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">ci</figure-callout>}}_{12}}^2$

${\mathrm{<figure-callout\; id="1"\; label="R\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">R</figure-callout>}}_{i_{}}={\mathrm{\&alpha;}}_{i_{11}}\sqrt{{\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{11}}{g}_{i_1}{g}_{i_{12}}}{\mathrm{\&sigma;}}_{i_{11}}^2,$ $R_{i_K}={\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}\sqrt{{\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K1}}{g}_{i_K}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_K}}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}^2$

${\mathrm{<figure-callout\; id="1"\; label="C\; i\; K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{i_K}={\mathrm{\&alpha;}}_{i_{K1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_K}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}^2+{\mathrm{\&sigma;}}_{{\mathrm{ci}}_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}^2,$ ${\mathrm{<figure-callout\; id="2"\; label="C\; i\; K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">C</figure-callout>}}_{i_K}={\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K2}}{g}_{i_K}{\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}^2+{\mathrm{\&alpha;}}_{i_{K2}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; k"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_k}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}}}^2+{\mathrm{\&sigma;}}_{{\mathrm{ci}}_{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}2}}^2$

${\mathrm{<figure-callout\; id="1"\; label="C\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">C</figure-callout>}}_{j_{}}={\mathrm{\&alpha;}}_{j_1}{\mathrm{<figure-callout\; id="1"\; label="g\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{j_{}}{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">j</figure-callout>}}_1}^2+{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="1"\; label="cj"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">cj</figure-callout>}}_1}^2,$ $C_{j_{L-2K}}={\mathrm{\&alpha;}}_{j_{L-2K}}{g}_{j_{L-2K}}{\mathrm{\&sigma;}}_{j_{L-2\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}}}^2+{\mathrm{\&sigma;}}_{{\mathrm{cj}}_{L-2\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}}}^2$

Represent K node between the variance of interchannel noise;

Represent the observation noise variance of K the better node of node centering observation quality;

Represent K node between channel gain.

Following formula (9) can be simplified and become:

$C=\left[\begin{array}{cccccc}{\mathrm{<figure-callout\; id="1"\; label="B\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">B</figure-callout>}}_{i_{}}& & & & & 0\\ & ...& & & & \\ & & B_{i_{\mathrm{<figure-callout\; id="1"\; label="K\; C\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}}}& & & \\ & & & C_{j_{}}{{}_1}_{}& & \\ & & & & ...& \\ 0& & & & & C_{j_{L-2K}}\end{array}\right]$ $B_{i_r}=\left[\begin{array}{cc}{C}_{i_{r1}}& R_{\mathrm{ir}}\\ R_{\mathrm{ir}}& C_{i_{r2}}\end{array}\right]---\left(10\right)$

Further obtain:

$C^{-1}={\left[\begin{array}{cccccc}{B}_{i_1}^{-1}& & & & & 0\\ & ...& & & & \\ & & B_{i_K}^{-1}& & & \\ & & & C_{j_1}^{-1}& & \\ & & & & ...& \\ 0& & & & & C_{j_{L-2K}}^{-1}\end{array}\right]}_{L-K,L-K}$

$\mathrm{Var}\left[\widehat{\mathrm{\&theta;}}\right]={\left[h^{\&prime;}{C}^{-1}h\right]}^{-1}$

$h=[\sqrt{{\mathrm{\&alpha;}}_{i_{11}}{\mathrm{<figure-callout\; id="11"\; label="g\; i"\; filenames="HDA00001766614500021.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}},\sqrt{{\mathrm{\&alpha;}}_{i_{12}}{g}_{i_{12}}{\mathrm{<figure-callout\; id="1"\; label="g\; i"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_{}}{\mathrm{\&alpha;}}_{i_{11}}},...,\sqrt{{\mathrm{\&alpha;}}_{i_{K1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_K}},\sqrt{{\mathrm{\&alpha;}}_{i_{K2}}{g}_{i_{K2}}{g}_{i_K}{\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">K</figure-callout>}1}}},$

$\sqrt{{\mathrm{\&alpha;}}_{j_1}{\mathrm{<figure-callout\; id="1"\; label="g\; j"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{j_{}}},...,\sqrt{{\mathrm{\&alpha;}}_{j_{L-2K}}{g}_{j_{L-2K}}}{]}^{\&prime;}$

Consider that channel gain is regarded 1 hypothesis as between the node, namely have:

$g_{i_p}=1,p=1,...,K$ So have

$\left|B_{i_p}\right|={\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{\mathrm{\&alpha;}}_{i_{p2}}{g}_{i_{p1}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}^2{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">p</figure-callout>}}}^2+{\mathrm{\&alpha;}}_{i_{p1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}^2{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="ci\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">ci</figure-callout>}}_p}^2+{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="1"\; label="ci\; p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">ci</figure-callout>}}_p}^2{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="ci\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">ci</figure-callout>}}_p}^2$

$+{\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{\mathrm{\&alpha;}}_{i_{p2}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}^2{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="1"\; label="ci\; p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">ci</figure-callout>}}_p}^2+{\mathrm{\&alpha;}}_{i_{p2}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">p</figure-callout>}}}^2{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="1"\; label="ci\; p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">ci</figure-callout>}}_p}^2,p=1,...,K$

$\left|C_{j_q}\right|={\mathrm{\&alpha;}}_{j_q}{g}_{j_q}{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="j\; q"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">j</figure-callout>}}_q}^2+{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="cj\; q"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">cj</figure-callout>}}_q}^2,q=1,...,L-K$

We suppose that noise all is independent identically distributed, and are transmitting under the environment, and the interchannel noise between the node is identical to the FC interchannel noise with node, thereby has: ${\mathrm{\&sigma;}}_{{\mathrm{ci}}_{a1}}^2={\mathrm{\&sigma;}}_{{\mathrm{ci}}_{a2}}^2={\mathrm{\&sigma;}}_{i_b}^2={\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="cj\; d"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">cj</figure-callout>}}_d}^2={\mathrm{\&sigma;}}^2,$

a，b＝1，......，K；d＝1，......L-2K

$\left|B_{i_p}\right|={\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{\mathrm{\&alpha;}}_{i_{p2}}{g}_{i_{p1}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{p1}}{\mathrm{<figure-callout\; id="1"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}}_1}^2{\mathrm{\&sigma;}}^2+$

${\mathrm{\&alpha;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}{\mathrm{\&alpha;}}_{i_{p2}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}_{i_{\mathrm{<figure-callout\; id="1"\; label="p"\; filenames="HDA00001766614500012.png"\; state="\{\{state\}\}">p</figure-callout>}1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{p2}}{\mathrm{<figure-callout\; id="2"\; label="g\; i\; p"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">g</figure-callout>}}_{i_p}{\mathrm{\&sigma;}}^4{\mathrm{\&sigma;}}^4,p=1,...,K$

$\left|C_{j_q}\right|={\mathrm{\&alpha;}}_{j_q}{g}_{j_q}{\mathrm{\&sigma;}}_{{\mathrm{<figure-callout\; id="2"\; label="j\; q"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">j</figure-callout>}}_q}^2+{\mathrm{\&sigma;}}^2,q=1,...,L-K$

Be approximately 1 through channel gain between above-mentioned hypothesis and consideration node, and with communication noise σ in the system ²Expression, so, evaluated error can represent to become:

$\mathrm{Var}\left[\widehat{\mathrm{\&theta;}}\right]={[\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}{h_{i_r}}^{\&prime;}{B}_{i_r}^{-1}{h}_{i_r}+\underset{s=1}{\overset{K}{\mathrm{\&Sigma;}}}{h_{j_s}}^{\&prime;}{C}_{j_s}^{-1}{h}_{j_s}]}^{-1}$

$h_{i_r}=[\sqrt{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}},\sqrt{{\mathrm{\&alpha;}}_{i_{r2}}{g}_{i_{r2}}{\mathrm{\&alpha;}}_{i_{r1}}}{]}^{\&prime;}r=1,...,K---\left(11\right)$

$h_{j_s}={\left[\sqrt{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}}\right]}^{\&prime;},s=1,...,L-K$

On power division is found the solution, at first power division there are not the node of cooperative partner and cooperative node pair to each, two nodes that again cooperative node cooperated to participation to the power division that obtains afterwards, consider that cooperative node is to only according to dividing according to the channel quality, and under the hypothesis formerly, channel between the node can be thought independent identically distributed variable, thereby, although under a secondary channel is realized, node can be different to inner power division, in the long run, the power of two node acquisitions is identical, thereby to node to when carrying out power division, for the ease of the analysis of problem, can think that the power that two cooperative partner obtain is identical; Further, because the signal energy that channel fading is left in the basket, the noise energy of communicating by letter in practice is far smaller than communication between node between node can have:

Consider in real system afterwards

Following simplification is then arranged:

${h_{i_r}}^{\&prime;}{B}_{i_t}^{-1}{h}_{i_r}$

$=\frac{(a_{i_{r1}}{g}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}^2))}{({\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2{\mathrm{\&sigma;}}^2+g_{i_{r2}}{\mathrm{\&sigma;}}^4+{\mathrm{\&sigma;}}^4)}---\left(12\right)$

$\&ap;\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}^2}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2{\mathrm{\&sigma;}}^2+{\mathrm{\&sigma;}}^4}=\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&sigma;}}^2}$

r＝1，...，K

Former equation (11) is approximated as follows simplification, has:

$\mathrm{Var}\left[\widehat{\mathrm{\&theta;}}\right]\&ap;{[\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&sigma;}}^2}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}}{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}{\mathrm{\&sigma;}}_{j_s}^2+{\mathrm{\&sigma;}}^2}]}^{-1}---\left(13\right)$

Optimization problem can be described as follows:

$\underset{{\mathrm{\&alpha;}}_{i_{r1}},{\mathrm{\&alpha;}}_{j_s}}{\min }{[\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&sigma;}}^2}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}}{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}{\mathrm{\&sigma;}}_{j_s}^2+{\mathrm{\&sigma;}}^2}]}^{-1}$

$s.t.\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}(P_{i_{r1}}+P_{i_{r2}})+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}{P}_{\mathrm{js}}\&le;P_{\mathrm{tot}}$

${{\mathrm{\&alpha;}}^{\&prime;}}_{i_{i1}}\&GreaterEqual;0,{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}\&GreaterEqual;0,r=1,...K;s=1,...L-2K$

Wherein: $P_{i_{r1}}={\mathrm{\&alpha;}}_{i_{r1}}({\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2+{\mathrm{\&sigma;}}_{i_{r1}}^2)={{\mathrm{\&alpha;}}^{\&prime;}}_{i_{i1}}(1+\frac{{\mathrm{\&sigma;}}_{i_{r1}}^2}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2})={{\mathrm{\&alpha;}}^{\&prime;}}_{i_{i1}}(1+{\mathrm{\&gamma;}}_{i_{r1}}^{-1}),$ (14)

$P_{j_s}={{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}(1+{\mathrm{\&gamma;}}_{j_s}^{-1}),$ $P_{i_{r2}}={{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}(1+{\mathrm{\&gamma;}}_{i_{r1}}^{-1})+{\mathrm{\&sigma;}}^2$

According to the hypothesis of front, be not difficult:

So optimization problem can be transformed into:

$\underset{{\mathrm{\&alpha;}}_{i_{r1}},{\mathrm{\&alpha;}}_{j_s}}{\min }{[\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&sigma;}}^2}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}}{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}{\mathrm{\&sigma;}}_{j_s}^2+{\mathrm{\&sigma;}}^2}]}^{-1}$

$s.t.\underset{r=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}}{\mathrm{\&Sigma;}}}2{{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}(1+{\mathrm{\&gamma;}}_{i_{r1}}^{-1})+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}(1+{\mathrm{\&gamma;}}_{j_s}^{-1})\&le;P_{\mathrm{tot}},$

${{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}\&GreaterEqual;0,{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}\&GreaterEqual;0,r=1,...K;s=1,...L-2K$

P wherein _TotGross power for the nodes transmission.

Further, this optimization problem can be converted into following equivalents:

$\underset{{\mathrm{\&alpha;}}_{i_{r1}},{\mathrm{\&alpha;}}_{j_s}}{\min }-\left(\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}}{{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r2}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&alpha;}}_{i_{r1}}{g}_{i_{r1}}{\mathrm{\&sigma;}}_{i_{r1}}^2+{\mathrm{\&sigma;}}^2}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}}{{\mathrm{\&alpha;}}_{j_s}{g}_{j_s}{\mathrm{\&sigma;}}_{j_s}^2+{\mathrm{\&sigma;}}^2}\right)$

$s.t.\underset{r=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="HDA00001766614500012.png,HDA00001766614500051.png"\; state="\{\{state\}\}">K</figure-callout>}}{\mathrm{\&Sigma;}}}2{{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}(1+{\mathrm{\&gamma;}}_{i_{r1}}^{-1})+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}(1+{\mathrm{\&gamma;}}_{j_s}^{-1})\&le;P_{\mathrm{tot}}---\left(15\right)$

${{\mathrm{\&alpha;}}^{\&prime;}}_{i_{i1}}\&GreaterEqual;0,{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}\&GreaterEqual;0,r=1,...K;s=1,...L-2K$

To find the solution in order further simplifying, to adopt Equivalent Thought, have:

$-\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2}(\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}(s_{i_{r1}}+s_{i_{r2}})}{{{\mathrm{\&alpha;}}^{\&prime;}}_{i_{r1}}(s_{i_{r1}}+s_{i_{r2}}){\mathrm{\&gamma;}}_{i_r}^{-1}+1}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}{\mathrm{\&gamma;}}_{j_s}^{-1}+1})$

$=-\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2}(\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{z_r}{s}_{z_r}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{z_r}{s}_{z_r}{\mathrm{\&gamma;}}_{z_r}^{-1}+1}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}{\mathrm{\&gamma;}}_{j_s}^{-1}+1})$

For equivalent node, have:

Structure α ' _Mv, v=1 ..., L-K,

Order: ${{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}=\left\{\begin{array}{c}2{{\mathrm{\&alpha;}}^{\&prime;}}_{z_v},v=1,...,K\\ {{\mathrm{\&alpha;}}^{\&prime;}}_{j_{v-K}},v=K+1,...,L-K\end{array}\right.---\left(16\right)$

Thereby have,

$-\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2}(\underset{r=1}{\overset{K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{z_r}{s}_{z_r}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{z_r}{s}_{z_r}{\mathrm{\&gamma;}}_{z_r}^{-1}+1}+\underset{s=1}{\overset{L-2K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{j_s}{s}_{j_s}{\mathrm{\&gamma;}}_{j_s}^{-1}+1})=-\frac{1}{{\mathrm{\&sigma;}}_{\mathrm{\&theta;}}^2}\left(\underset{v=1}{\overset{L-K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_{\mathrm{mv}}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_{\mathrm{mv}}{\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1}+1}\right)$

Wherein,

$s_{\mathrm{mv}}=\left\{\begin{array}{c}{s}_{z_v}/2,v=1,...,K\\ s_{j_{v-K}},v=K+1,...,L-K\end{array}\right.;$ ${\mathrm{\&gamma;}}_{\mathrm{mv}}=\left\{\begin{array}{c}{\mathrm{\&gamma;}}_{i_v},v=1,...,K\\ {\mathrm{\&gamma;}}_{j_{v-K}},v=K+1,...,L-K\end{array}\right.$

And definition: η _Mv=s _Mv/ (1+ γ _Mv) v=1 ..., L-K

The optimization problem of this moment just can be explained and become:

$\underset{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}}{\min }-\underset{v=1}{\overset{L-K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_{\mathrm{mv}}}{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_{\mathrm{mv}}{\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1}+1},v=1,...,L-K$

$s.t.P_{\mathrm{tot}}=\underset{v=1}{\overset{L-K}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}(1+{\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1}),v=1,...,L-K---\left(17\right)$

α′ _mv≥0，v＝1，...，L-K

The structure Lagrange multiplier has:

$G({{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}};{\mathrm{\&lambda;}}_0,{\mathrm{\&mu;}}_m)=$

$-\underset{v=1}{\overset{L-K}{\mathrm{\&Sigma;}}}\frac{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_v}{{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}{s}_{\mathrm{mv}}+1}-{\mathrm{\&lambda;}}_0(P_{\mathrm{tot}}-\underset{j=1}{\overset{L-K}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mj}}(1+{\mathrm{\&gamma;}}_{\mathrm{mj}}^{-1}))-\underset{l=1}{\overset{L-K}{\mathrm{\&Sigma;}}}{\mathrm{\&mu;}}_{\mathrm{ml}}{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{ml}}---\left(18\right)$

Constraints can be expressed as:

α′ _mv≥0 v＝1，...，L-K

μ _mvα′ _mv＝0 v＝1，...，L-K

μ _mv≥0 v＝1，...，L-K

$-\frac{s_{\mathrm{mv}}^{-1}}{{({\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1}{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}+s_{\mathrm{mv}}^{-1})}^2}+{\mathrm{\&lambda;}}_0(1+{\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1})-{\mathrm{\&mu;}}_{\mathrm{mv}}=0,\&ForAll;v---\left(19\right)$

$P_{\mathrm{tot}}=\underset{v=1}{\overset{L-K}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}(1+{\mathrm{\&gamma;}}_{\mathrm{mv}}^{-1})$

According to above-mentioned network analysis, simplification and approximate statement, following concrete solution procedure can be arranged in step 2 practical application, Fig. 5 is a kind of transmit power allocation method flow diagram in the embodiment of the invention, as shown in Figure 5, its operation comprises:

Step 201, the fusion center division right according to node are determined

And η _MvAccording to size ordering, and the sequence that will newly line up represents with a, namely satisfies condition: ${\mathrm{\&eta;}}_{a_1}\&GreaterEqual;{\mathrm{\&eta;}}_{a_2}\&GreaterEqual;...\&GreaterEqual;{\mathrm{\&eta;}}_{a_{L-K}};$

Step 202, introducing function f (k):

$f\left(k\right)=\sqrt{\frac{{\mathrm{\&eta;}}_{a_k}}{{\mathrm{\&lambda;}}_0}}-1=\frac{\sqrt{{\mathrm{\&eta;}}_{a_k}}B\left(k\right)}{A\left(k\right)}-1,k=1,...,L-K$

${\mathrm{\&lambda;}}_0={\left(\frac{A=\left(K_1\right)}{B\left(K_1\right)}\right)}^2,$ $A=\left(k\right)=\underset{v=1}{\overset{k}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&gamma;}}_{a_v}}{\sqrt{{\mathrm{\&eta;}}_v}},$ $B\left(k\right)=\underset{v=1}{\overset{k}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&gamma;}}_{a_v}}{{\mathrm{\&eta;}}_v}{P}_{\mathrm{tot}}---\left(20\right)$

From 1 to L-K traversal, find the solution f (k) value.

Step 203, judge whether to exist a K ₁, satisfy f (K ₁)＞0 and f (K ₁+ 1)≤0, if exist, go to step 204, otherwise execution in step 205;

Step 204, according to K ₁Node is opened or closed and determine: as k≤K ₁The time, corresponding node is open-minded, as k＞K ₁The time, corresponding node opening state is closed, and goes to step 206;

Step 205, make node all open-minded;

Step 206, node or the right through-put power of cooperative node are distributed according to following formula (21)

${{\mathrm{\&alpha;}}^{\&prime;}}_{\mathrm{mv}}=\frac{{\mathrm{\&gamma;}}_{\mathrm{mv}}}{s_{\mathrm{mv}}}{(\sqrt{\frac{{\mathrm{\&eta;}}_{\mathrm{mv}}}{{\mathrm{\&lambda;}}_0}}-1)}^{+}\&ForAll;v---\left(21\right)$

Step 207, cooperative node are reallocated to internal power.

On the basis of above-mentioned steps 201-206, to cooperative node to internal power on principle $P_{i_{r1}}:P_{i_{r2}}=s_{i_{r1}}^2:s_{i_{r2}}^2$ Reallocate.

Step 208, fusion center transfer to each sensor node with opening state and through-put power.

In the above embodiment of the present invention, described step 4 specifically can comprise:

Step 41, the internal phase of cooperative node each other two nodes of cooperative partner judge it self is preferably node or the relatively poor node of observation quality of observation quality according to described definite result, if observation quality is node preferably, then execution in step 42, otherwise execution in step 43;

Step 42, the through-put power of distributing according to described fusion center are transferred to described fusion center after observing the observation information of obtaining amplify to described information source self;

Step 43, the observation information after monitoring this cooperative node centering observation quality node amplifying preferably, obtain the noisy copy of the observation information after the described amplification, and will be transferred to described fusion center after the described noisy copy amplification according to the through-put power that described fusion center distributes.

Described step 6 is specifically as follows: all observation information that described fusion center will receive adopt linear optimal to carry out information fusion without bias estimation, obtain the estimated value of described information source.

In the implementation, can calculate as follows estimation:

y＝hθ+v

$\widehat{\mathrm{\&theta;}}={\left[h^{\&prime;}{R}^{-1}h\right]}^{-1}{h}^{\&prime;}{R}^{-1}y---\left(22\right)$

Wherein first equation is expressed the observation information that receives and the linear relationship of information source, the covariance matrix of the R Representative errors in second equation.

Estimated accuracy and outage probability are two important technical indicators of distributed estimating system, and estimated accuracy adopts the Monte Carlo mode to obtain, the computational methods reference formula (22) in once realizing.The system that refers to outage probability satisfies the probability of certain evaluated error index, expresses as shown in the formula (23):

${\mathrm{<figure-callout\; id="0"\; label="P\; D"\; filenames="HDA00001766614500051.png"\; state="\{\{state\}\}">P</figure-callout>}}_{D_{}}=\mathrm{Prob}\left\{\mathrm{Vav}\right[\widehat{\mathrm{\&theta;}}]>D_0\}---\left(23\right)$

D wherein ₀Refer to the evaluated error index.

By adopting the cooperation among the present invention to estimate mechanism, can obtain than existing general distributed estimation and adopt the node estimated accuracy that directly transmission and power division Optimization Mechanism are higher and lower outage probability.

Fig. 6 is the estimated accuracy simulation result test comparison figure of the present invention and prior art; Fig. 7 is the outage probability simulation result test comparison figure of the present invention and prior art.Wherein, the Cui Optimization Mechanism refers to and adopts node directly to transmit the mechanism of optimizing with power division, but general distributed estimation mode refers to and adopts node directly to transmit the mechanism that does not adopt power division to optimize, from the simulation results of the two, the present invention has lower evaluated error under the identical condition of transmission gross power, have lower outage probability, be that estimated accuracy of the present invention is higher, thereby promoted the performance of estimating system.

One of ordinary skill in the art will appreciate that: all or part of step that realizes said method embodiment can be finished by the relevant hardware of program command, aforesaid program can be stored in the computer read/write memory medium, this program is carried out the step that comprises said method embodiment when carrying out; And aforesaid storage medium comprises: the various media that can be program code stored such as ROM, RAM, magnetic disc or CD.

It should be noted that at last: above embodiment is only in order to technical scheme of the present invention to be described but not limit it, although with reference to preferred embodiment the present invention is had been described in detail, those of ordinary skill in the art is to be understood that: it still can be made amendment or be equal to replacement technical scheme of the present invention, and these modifications or be equal to replacement and also can not make amended technical scheme break away from the spirit and scope of technical solution of the present invention.

Claims (8)

1. the distributed method of estimation based on collaboration communication is characterized in that, comprising:

Step 1, fusion center are determined cooperative node pair according to each node to the observation quality of information source, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form, and definite result that cooperative node is right sends to corresponding node;

Step 2, described fusion center carry out transmit power allocation according to current channel conditions and observation quality to each node;

Step 3, each node judge according to the right definite result of cooperative node who receives whether self has cooperative partner, if having, then execution in step 4, otherwise execution in step 5;

Step 4, cooperative node internally mutually each other two nodes of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to described definite result, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source;

Step 5, the node that does not have a cooperative partner observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes;

Step 6, described fusion center merge the observation information that receives, and obtain the estimated value of described information source.

2. method according to claim 1 is characterized in that, before the described step 2, also comprises:

Step 7, described fusion center carry out channel estimating to the transmission channel of each node, obtain channel conditions.

3. method according to claim 1 and 2 is characterized in that, described step 1 specifically comprises:

Step 11, described fusion center according to the ascending arrangement of observation noise, and are divided into observation quality preferably node set and observation quality relatively poor node set as the line of demarcation with the node correspondence with the average of minimum observation noise and maximum observation noise with each node;

Step 12, described fusion center be by the linear fit mode, obtains the preferably functional relation of observation noise and the observation noise threshold value of cooperative partner node under certain observation quality condition of node of each observation quality;

Node during step 13, described fusion center are gathered preferably to observation quality one by one in observation quality relatively poor set is sought cooperative partner by good to poor according to observation quality, if the searching condition be the observation noise of the both candidate nodes in the relatively poor set of observation quality greater than the observation noise threshold value of correspondence, and this both candidate nodes is not marked as the cooperative partner of other nodes;

The both candidate nodes that meets described searching condition that step 14, described fusion center will find is labeled as the preferably cooperative partner of node of corresponding observation quality, determine this observation quality preferably node and this both candidate nodes be cooperative node pair, and will determine that the result sends to respectively two corresponding nodes;

If all nodes during step 15 observation quality is gathered are preferably sought cooperative partner and do not traveled through, then execution in step 13.

4. method according to claim 3 is characterized in that, also comprises after the described step 15:

If all nodes during step 16 observation quality is gathered are preferably sought cooperative partner nodes and have been traveled through, then described fusion center will not find the observation quality that meets described searching condition in gathering preferably node and do not meet node in the relatively poor set of the observation quality of described searching condition as the node that does not have cooperative partner.

5. method according to claim 1 and 2 is characterized in that, described step 4 specifically comprises:

Step 41, the internal phase of cooperative node each other two nodes of cooperative partner judge it self is preferably node or the relatively poor node of observation quality of observation quality according to described definite result, if observation quality is node preferably, then execution in step 42, otherwise execution in step 43;

Step 42, the through-put power of distributing according to described fusion center are transferred to described fusion center after observing the observation information of obtaining amplify to described information source self;

Step 43, the observation information after monitoring this cooperative node centering observation quality node amplifying preferably, obtain the noisy copy of the observation information after the described amplification, and will be transferred to described fusion center after the described noisy copy amplification according to the through-put power that described fusion center distributes.

6. method according to claim 1 and 2 is characterized in that, described step 6 is specially: all observation information that described fusion center will receive adopt linear optimal to carry out information fusion without bias estimation, obtain the estimated value of described information source.

7. method according to claim 1 and 2 is characterized in that, described step 2 specifically comprises:

Step 21, the division right according to cooperative node of described fusion center, calculate and definite cooperative node to the opening state of the sensor node that does not have cooperative partner;

Step 22, to the cooperative node opened to carrying out transmit power allocation with the node that does not have cooperative partner;

Step 23, to the cooperative node opened to the channel conditions according to internal two nodes of cooperative node, two nodes are carried out the reallocation of internal transmission power;

Step 24, the opening state of each node and the through-put power correspondence of distribution are sent to each node, so that each node determines whether to transmit observation information according to described opening state and according to the through-put power transmission observation information of distributing.

8. distributed estimating system based on collaboration communication comprises: information source, a plurality of node and fusion center, it is characterized in that,

Described fusion center, be used for according to each nodes of described a plurality of nodes the observation quality of described information source being determined cooperative node pair, described cooperative node to by mutually each other an observation quality of cooperative partner preferably node and the relatively poor node of observation quality form, and definite result that cooperative node is right sends to corresponding node; Also be used for the transmission channel of each node is carried out channel estimating, obtain channel conditions, and according to current channel conditions and observation quality each node is carried out transmit power allocation; And be used for the observation information that receives is merged, obtain the estimated value of described information source;

Described a plurality of node, for being observed, described information source obtains observation information, cooperative node internally mutually each other two nodes of cooperative partner determine observation quality preferably node and the relatively poor node of observation quality according to the right definite result of cooperative node who receives, and the through-put power of distributing according to described fusion center respectively with observation quality preferably node observe the observation information of obtaining transfer to described fusion center to described information source; There is not the node of cooperative partner to observe the observation information of obtaining directly transfer to described fusion center to described information source self according to the through-put power that described fusion center distributes.

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