CN103648164A - Time difference of arrival and Gossip algorithm based wireless sensor network distributed positioning method - Google Patents

Abstract

The invention relates to wireless sensor network distributed positioning methods and provides a time difference of arrival and Gossip algorithm based wireless sensor network distributed positioning method which aims at solving the problem that the alone time difference of arrival positioning method is low in positioning accuracy in a wireless sensor network. The time difference of arrival and Gossip algorithm based wireless sensor network distributed positioning method includes that self-position coordinates are obtained by anchor nodes; the distributed time synchronization is achieved; the anchor nodes are awoken randomly and unknown nodes are monitored; received signal time and local coordinates are saved by the awoken anchor nodes; whether signal monitoring and data saving are achieved by all the anchor nodes completely or not is judged; the anchor node j receives data of the M adjacent anchor nodes; an initial estimate value to the positions of the unknown nodes is obtained by the anchor node j; initial estimate values to the positions of the unknown nodes are obtained by all the anchor nodes; a Gossip algorithm is run to select the adjacent anchor nodes randomly and exchange positioning data; the algorithm is terminated. The time difference of arrival and Gossip algorithm based wireless sensor network distributed positioning method is applied to the wireless sensor network typical work area.

Description

A kind of wireless-sensor network distribution type localization method based on time of advent difference and Gossip algorithm

Technical field

The present invention relates to wireless-sensor network distribution type localization method.

Background technology

Wireless sensor network, as one of core technology of Internet of Things, praise one of ten large support technologies for change in future human lives.Since wireless sensor network is started by extensive concern, its location technology is the focal issue of theoretical research always.In recent years, Chinese scholars proposes multiple wireless sensor network center type or distributed location method, but it is for the situation design of unknown node (node of its position to be measured in network) positive location substantially.

The communication network that wireless sensor network is comprised of the node in a large number with functions such as data acquisition, data processing and wireless data transceivings.Typical wireless sensor network working method is that a large amount of wireless sensor nodes is arranged or shed in interested region, and wireless sensor node forms a wireless network fast by the mode of self-organizing.Each sensor node has own communication zone and by awareness apparatus, detects the information such as temperature, humidity or frequency spectrum of surrounding environment, also can be equipped with communication equipment and adjacent node and carry out short haul connection simultaneously.

Own characteristic based on above-mentioned wireless sensor network, the working region of sensor node is generally the region that the mankind such as military surveillance, road conditions detection are difficult for entering, and for the typical applied environment as sensor networks such as post-disaster reconstruction, climate monitorings, sensor node is placed in working region by the aircraft means such as shed conventionally, thereby their position is all random and unknown.Yet in many application, the data that node gathers must be just meaningful in conjunction with its residing coordinate position, thereby have great importance for the research of the location technology of wireless sensor network unknown node.

Thereby complete and measure the method positioning and be called the poor location time of advent (Time Difference of Arrival, TDOA) by arrive the time difference of nodes based on two signals.TDOA is a kind of localization method being widely adopted, and is defined as first-selected localization method at present by multiple location hardware platform.TDOA location technology has a very wide range of applications in the wireless location systems such as cellular positioning system, WCDMA technology, wireless distance finding radar, roadbed multipoint positioning, and existing researcher starts to attempt being expanded in the position application of wireless sensor network.But among wireless sensor network position application, it is lower that TDOA algorithm exists positioning precision at present, the problem that positioning performance is poor.And, at present TDOA algorithm is generally all used to realize self positive location of unknown node, not yet by its expanded application in similar military precision strike or illegally access the distributed Passive Positioning field that the wireless sensor network exemplary operation environments such as frequency spectrum radio station monitoring need.

Due to the limited communication capacity of wireless sensor node, data-handling capacity and equipment dependability, the node in wireless sensor network all adopts the mode of intensive placement conventionally.Because node density is higher, so the data that the node closing on geographical position gathers have larger redundancy conventionally.If can these data be merged, be compressed in data transmission procedure, just can significantly reduce number of packet and the grouping dimension in subsequent transmission process, thereby improve network capacity and reduce the energy consumption of node.Therefore the research about the data compression in wireless sensor network and effective transmission means just becomes a study hotspot.Under this background, be born and can be applicable to the Gossip algorithm of wireless-sensor network distribution type common recognition.Each node in this algorithm randomly with its certain selected (or certain group) adjacent node swap data, then these two (maybe this group) nodes utilize respectively protruding merge algorithm to merge these data, and fall oneself original data with new data replacement.

Gossip algorithm was proposed by people such as Tsitsiklis first as far back as 1984, and this algorithm only utilizes the local information of network node and the information of its neighbor node to carry out exchanges data, had solved the average common recognition problem under distribution occasion.In wireless sensor network, research the earliest, achievement in research is the most ripe and apply the most paired Gossip algorithm.At present, the focus that the application of the average common recognition problem based on Gossip algorithm in wireless sensor network studied especially.Different from traditional routing algorithm, Gossip routing algorithm emphasizes that the mode of carrying out exchanges data by the local information of node and neighbor node carries out Data Update, and we call iterative process one time a data updating process.Due in iterative process, only relate to the exchange of a hop neighbor nodal information and local information, so the network based on Gossip does not need Route establishment process and the maintenance process of traditional routing algorithm, also the repeating process that there is no data, this just greatly reduce network energy consumption, extended life cycle of network node.Simultaneously Gossip algorithm is a kind of random routing algorithm, has avoided the problems such as " packet loss " that cause because of channel competition in network and network congestion.And node status all in whole network is reciprocity, there is no so-called " Centroid ", has also avoided the existence of bottleneck effect.So Gossip algorithm is the good solution to distributed average common recognition problem in wireless sensor network, thereby can imagine that Gossip algorithm is also necessarily equally applicable to wireless-sensor network distribution type and locates this typical distributed problem.

In sum, although now widely used simple TDOA localization method is very good at mobile radio networks performance, still there is the problems such as positioning precision is lower, positioning performance is limited in the application in wireless sensor network.And for using in the distributed Passive Positioning problem how to determine in the feature by wireless sensor network, also be a research blind spot at present, particularly how to complete in similar military affairs and carry out high accuracy strike for invasion unknown node, or carry out the special engineering application problems such as accurate location for the unknown radio station of illegal access frequency spectrum, be also badly in need of researcher and propose practical scheme.

Summary of the invention

The present invention is that will to solve in wireless sensor network simple TDOA localization method positioning precision low, positioning performance is limited and cannot be applicable to the problems such as this typical application scenarios of distributed Passive Positioning, and provide a kind of by the time of advent difference algorithm and Gossip algorithm organically combine and be applicable to the brand-new localization method of wireless-sensor network distribution type Passive Positioning.

Wireless-sensor network distribution type localization method poor based on the time of advent and Gossip algorithm is realized according to the following steps:

Step 1: arrange at random or artificially N anchor node in wireless sensor network coverage, each anchor node obtains self unknown coordinates (x by GPS or artificial mode of arranging _k, y _k);

Step 2: in whole wireless sensor network, all anchor nodes are realized distributed time synchronized by broadcast Gossip algorithm;

Step 3: each anchor node wakes up at each slotted random, whether monitoring unknown node occurs;

Step 4: if unknown node appearance wakes the radio signal that anchor node k will receive unknown node transmitting up, the moment t of signal received in anchor node k record _k, together with local coordinate system, be kept at (x _k, y _k, t _k);

Step 5: each anchor node wakes up successively, repeating step four, preserves until all anchor nodes all complete signal monitoring and the data of unknown node;

Step 6: the anchor node in wireless sensor network wakes up at random, suppose that anchor node j is in wake-up states, this anchor node is to all adjacent anchor node broadcasts request within the scope of communication radius, require it to return node coordinate and receive signal constantly, this anchor node starts to receive the data whether data real-time judge receive whole adjacent anchor nodes, if do not receive whole adjacent anchor node datas, continue to receive, if receive whole adjacent anchor node datas, complete the reception of data and anchor node j is received to the data of its all M adjacent anchor node are kept at this locality, obtain local data as follows

$\left[\begin{array}{ccc}{x}_0^j& y_0^j& t_0^j\end{array}\right]=\left[\begin{array}{ccc}{x}_1& y_1& t_1\\ x_1& y_2& {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_i& y_i& t_i\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_M& y_M& t_M\end{array}\right];$

Step 7: the local data that anchor node j obtains according to step 6, obtains unknown node position primary iteration value ((x according to the Taylor algorithm primary iteration location formula based on TDOA location _j(0), y _j(0)), according to the iterative process of the thresholding operation Taylor algorithm setting in advance, until obtain anchor node j for the initial estimate ((x of unknown node position _j(0), y _j(0));

Step 8: all the other anchor nodes in wireless sensor network wake up at random, according to the working method repeating step six of anchor node j and step 7, obtain this anchor node for the initial estimate of unknown node position, until all anchor nodes complete the initial estimation for unknown node position, in wireless sensor network, the unknown node position initial estimate coordinate of all anchor nodes is

$\left[\begin{array}{cc}{x}^{\&prime;}\left(0\right)& y^{\&prime;}\left(0\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& y_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right];$

Step 9: all anchor nodes obtain on the basis of this node for the initial estimate of unknown node position in wireless sensor network, the all N of a whole network anchor node moves paired Gossip algorithm, the concrete running of Gossip algorithm is as follows in pairs: suppose to be waken up at time slot t anchor node j, this anchor node is random selects an adjacent anchor node i to exchange initial estimation Value Data

$x_j^{\&prime;}(t+1)=x_i^{\&prime;}(t+1)=\frac{1}{2}(x_i^{\&prime;}\left(t\right)+x_j^{\&prime;}\left(t\right))$

$y_j^{\&prime;}(t+1)=y_i^{\&prime;}(t+1)=\frac{1}{2}(y_i^{\&prime;}\left(t\right)+y_j^{\&prime;}\left(t\right))$

The whole iterative process of paired Gossip algorithm that the whole network N anchor node moves can be expressed as follows

$z^{\&prime;}(t+1)=W\left(t\right)z^{\&prime;}\left(t\right)=\underset{n=1}{\overset{t}{\mathrm{\&Sigma;}}}W\left(n\right)z^{\&prime;}\left(0\right)$

Wherein

$z^{\&prime;}\left(t\right)=\left[\begin{array}{cc}{x}^{\&prime;}\left(t\right)& y^{\&prime;}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(t\right)& y_1^{\&prime;}\left(t\right)\\ x_2^{\&prime;}\left(t\right)& y_2^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(t\right)& y_j^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(t\right)& y_N^{\&prime;}\left(t\right)\end{array}\right];$

Step 10: judge whether Gossip algorithm reaches predefined iterations, if reach predefined iterations whole algorithm complete, in wireless sensor network, all anchor nodes complete distributed common recognition location, each anchor node obtains identical unknown node location estimation value, and the final unknown node location estimation value that the method obtains is

$z^{\&prime;}=\left[\begin{array}{cc}{x}^{\&prime;}& y^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}& y_1^{\&prime;}\\ {\mathrm{<figure-callout\; id="2"\; label="x"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">x</figure-callout>}}_2^{\&prime;}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}& y_j^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}& y_N^{\&prime;}\end{array}\right]=\frac{1}{N}\stackrel{\&RightArrow;}{1}{\stackrel{\&RightArrow;}{1}}^T\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& y_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right]$

Completed a kind of wireless-sensor network distribution type localization method based on time of advent difference and Gossip algorithm.

Invention effect: by the simulation analysis of the wireless-sensor network distribution type localization method for and Gossip algorithm poor based on the time of advent proposed by the invention, can obtain as drawn a conclusion: (1) anchor node number in simulation process is set to respectively 5, 10, 20, 30, 40, 50 o'clock, positioning precision has promoted respectively 23.37%, 58.63%, 75.88%, 77.84%, 83.53%, 84.81%, thereby confirm that algorithm proposed by the invention can effectively improve the positioning precision of former algorithm really, and can find out according to simulation analysis data, along with increasing of anchor node number, positioning precision also increases thereupon, but increasing degree reduces thereupon, (2) in simulation process, Measuring Time error to standard deviation is set to respectively 3.3ns, 6.7ns, 10.0ns, 13.3ns, 16.7ns, being namely converted into corresponding range error standard deviation is respectively 1m, 2m, 3m, 4m, during 5m, positioning precision has promoted respectively 78.38%, 77.61%, 76.80%, 76.06%, 76.68%, can confirm that equally algorithm proposed by the invention can effectively improve positioning precision really, and positioning precision meets the rule reducing along with time determination error increase substantially, (3) algorithm proposed by the invention can complete distributed common recognition location, that is to say that in network, each anchor node obtains the identical estimated value for unknown node position by means of the help of paired Gossip algorithm, thereby be that good basis is established in military precision strike invasion unknown node or the wireless sensor network exemplary operation fields such as illegal unknown radio station of Real-Time Monitoring access frequency spectrum.

The present invention prepares sight to transfer to and take the distributed Passive Positioning of the unknown node field that wireless sensor network is background.Invention adopts TDOA location algorithm as basic fixed position technology, while can be selected at random adjacent node to carry out information exchange by means of Gossip algorithm and finally reach the feature of distributed average common recognition, and brand-new design goes out the wireless-sensor network distribution type difference positioning algorithm time of advent based on Gossip mechanism.Compare with traditional location algorithm, this algorithm not only possesses the advantages such as accurate positioning precision, good positioning performance, and go for completely such as the rare environment of communication spectrum for the radio station of the illegal use frequency spectrum accurate special engineering application background such as location fast, algorithm by this brand-new design can make each anchor node by Gossip algorithm, obtain the location estimation value coordinate of identical unknown node, thereby completes distributed common recognition location.

The present invention is mainly in take the engineering application that wireless sensor network is background.For example, its typical application scenarios can be the region for certain communication spectrum scarcity of resources, arranges at random or artificially the monitoring anchor node of some, to prevent illegal unknown radio station access frequency spectrum.When having unknown radio station illegally to access frequency spectrum, we monitors the radio signal that anchor node receives the transmitting of unknown radio station, and records the time of receiving signal.We monitors anchor node use Gossip algorithm and exchanges at random coordinate and time data afterwards, on each monitoring anchor node, moves TDOA location algorithm, obtains an estimated position for unknown radio station.After this our all monitoring anchor nodes participate in a Gossip process, after having moved the renewal of Gossip iteration, each monitoring anchor node reaches distributed average common recognition, that is to say that each monitoring anchor node obtains a comparatively accurate and identical unknown station location estimated coordinates, thereby complete distributed common recognition, accurately locate, the illegal unknown radio station that arrests access frequency spectrum for further implementing lays a good foundation.

At this, wanting ben is in addition, positioning precision is the important indicator that location algorithm is concerned about, mean square error (MSE) or root mean square error (RMSE) that the general conventional Measure Indexes of weighing positioning precision is positioning solution, the emulation of this algorithm launches for root mean square error.Provide mean square error and the computational methods of root mean square error in two-dimensional space location estimation below:

$\mathrm{MSE}=\frac{1}{\mathrm{MC}}\underset{h=1}{\overset{\mathrm{MC}}{\mathrm{\&Sigma;}}}{(x-x_h)}^2+{(y-y_h)}^2---\left(1\right)$

$\mathrm{RMSE}=\sqrt{\frac{1}{\mathrm{MC}}\underset{h=1}{\overset{\mathrm{MC}}{\mathrm{\&Sigma;}}}{(x-x_h)}^2+{(y-y_h)}^2}---\left(2\right)$

Wherein, MC is carried out Monte Carlo simulation number of times, and (x, y) is unknown node actual position, (x _h, y _h) be the estimated value for unknown node position that the h time l-G simulation test obtains.

The simulation result of doing by the present invention and analysis, can find out that the Taylor location algorithm (PGA-Taylor) based on Gossip that invention proposes can obtain optimum positioning precision.Thereby the Taylor location algorithm based on Gossip proposed by the invention is a kind ofly can obtain less positioning precision really, and can realize a kind of outstanding location algorithm of the distributed common recognition location of wireless sensor network.By verified its validity of simulating, verifying and superiority, can say that this algorithm is a kind of location algorithm being worthy to be popularized in wireless sensor network positioning field.

Accompanying drawing explanation

Fig. 1 is the flow chart of the PGA-Taylor algorithm that proposes of the present invention;

Fig. 2 is the change curve of the root mean square error in embodiment one while increasing with anchor node number; Wherein

represent Taylor,

represent PGA-Taylor;

The change curve of Fig. 3 when to be root mean square error increase with surveyed time error standard deviation; Wherein

represent Taylor,

represent PGA-Taylor.

Embodiment

Embodiment one: the wireless-sensor network distribution type localization method poor based on the time of advent and Gossip algorithm of present embodiment is realized according to the following steps:

Step 1: arrange at random or artificially N anchor node in wireless sensor network coverage, each anchor node obtains self unknown coordinates (x by GPS or artificial mode of arranging _k, y _k);

Step 2: in whole wireless sensor network, all anchor nodes are realized distributed time synchronized by broadcast Gossip algorithm;

Step 3: each anchor node wakes up at each slotted random, whether monitoring unknown node occurs;

Step 4: if unknown node appearance wakes the radio signal that anchor node k will receive unknown node transmitting up, the moment t of signal received in anchor node k record _k, together with local coordinate system, be kept at (x _k, y _k, t _k);

Step 5: each anchor node wakes up successively, repeating step four, preserves until all anchor nodes all complete signal monitoring and the data of unknown node;

Step 6: the anchor node in wireless sensor network wakes up at random, suppose that anchor node j is in wake-up states, this anchor node is to all adjacent anchor node broadcasts request within the scope of communication radius, require it to return node coordinate and receive signal constantly, this anchor node starts to receive the data whether data real-time judge receive whole adjacent anchor nodes, if do not receive whole adjacent anchor node datas, continue to receive, if receive whole adjacent anchor node datas, complete the reception of data and anchor node j is received to the data of its all M adjacent anchor node are kept at this locality, obtain local data as follows

$\left[\begin{array}{ccc}{x}_0^j& y_0^j& t_0^j\end{array}\right]=\left[\begin{array}{ccc}{x}_1& y_1& t_1\\ x_1& y_2& {\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">t</figure-callout>}}_2\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_i& y_i& t_i\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_M& y_M& t_M\end{array}\right];$

Step 7: the local data that anchor node j obtains according to step 6, obtains unknown node position primary iteration value ((x according to the Taylor algorithm primary iteration location formula based on TDOA location _j(0), y _j(0)), according to the iterative process of the thresholding operation Taylor algorithm setting in advance, until obtain anchor node j for the initial estimate ((x of unknown node position _j(0), y _j(0));

Step 8: all the other anchor nodes in wireless sensor network wake up at random, according to the working method repeating step six of anchor node j and step 7, obtain this anchor node for the initial estimate of unknown node position, until all anchor nodes complete the initial estimation for unknown node position, in wireless sensor network, the unknown node position initial estimate coordinate of all anchor nodes is

$\left[\begin{array}{cc}{x}^{\&prime;}\left(0\right)& y^{\&prime;}\left(0\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& y_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right];$

Step 9: all anchor nodes obtain on the basis of this node for the initial estimate of unknown node position in wireless sensor network, the all N of a whole network anchor node moves paired Gossip algorithm, the concrete running of Gossip algorithm is as follows in pairs: suppose to be waken up at time slot t anchor node j, this anchor node is random selects an adjacent anchor node i to exchange initial estimation Value Data

$x_j^{\&prime;}(t+1)=x_i^{\&prime;}(t+1)=\frac{1}{2}(x_i^{\&prime;}\left(t\right)+x_j^{\&prime;}\left(t\right))$

$y_j^{\&prime;}(t+1)=y_i^{\&prime;}(t+1)=\frac{1}{2}(y_i^{\&prime;}\left(t\right)+y_j^{\&prime;}\left(t\right))$

The whole iterative process of paired Gossip algorithm that the whole network N anchor node moves can be expressed as follows

$z^{\&prime;}(t+1)=W\left(t\right)z^{\&prime;}\left(t\right)=\underset{n=1}{\overset{t}{\mathrm{\&Sigma;}}}W\left(n\right)z^{\&prime;}\left(0\right)$

Wherein

$z^{\&prime;}\left(t\right)=\left[\begin{array}{cc}{x}^{\&prime;}\left(t\right)& y^{\&prime;}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(t\right)& y_1^{\&prime;}\left(t\right)\\ x_2^{\&prime;}\left(t\right)& y_2^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(t\right)& y_j^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(t\right)& y_N^{\&prime;}\left(t\right)\end{array}\right];$

Step 10: judge whether Gossip algorithm reaches predefined iterations, if reach predefined iterations whole algorithm complete, in wireless sensor network, all anchor nodes complete distributed common recognition location, each anchor node obtains identical unknown node location estimation value, and the final unknown node location estimation value that the method obtains is

$z^{\&prime;}=\left[\begin{array}{cc}{x}^{\&prime;}& y^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}& y_1^{\&prime;}\\ x_2^{\&prime;}& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}& y_j^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}& y_N^{\&prime;}\end{array}\right]=\frac{1}{N}\stackrel{\&RightArrow;}{1}{\stackrel{\&RightArrow;}{1}}^T\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& {\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right]$

Completed a kind of wireless-sensor network distribution type localization method based on time of advent difference and Gossip algorithm.

Present embodiment, in step 2, broadcast Gossip algorithm is a kind of in Gossip algorithm, is different from paired Gossip algorithm, cannot guarantee finally to converge on the average of all initial values, its typical case's application has been exactly that distributed clock is synchronous;

In step 10, the iterations of the accuracy selection Gossip algorithm of the concrete network topology structure of the selective basis of iterations and demand, guarantees that algorithm can converge on initial average.

Embodiment two: present embodiment is different from embodiment one: the broadcast Gossip algorithm described in step 2 is specially:

Node in network wakes and broadcasts its state value at random up, and this state value is received by all nodes in its communication radius, and all receiving nodes upgrade its local state value according to algorithm design, and other node state values remain unchanged.Other step and parameter are identical with embodiment one.

Embodiment three: present embodiment is different from embodiment one or two:

One, TDOA location

First suppose that all anchor nodes reach distributed time synchronized by broadcast Gossip algorithm, the communication radius of anchor node is subject to the restriction of TDOA location hardware module in network, and the topological structure G (N, R) of N point wireless sensor network is by adjacency matrix Φ _ijrepresent, when i ≠ j, if anchor node i is adjacent with anchor node j, Φ _ij=1; Otherwise, Φ _ij=0; For anchor node j, definition M={i ∈ 1,2 ..., N}: Φ _ij≠ 0};

TDOA location algorithm is called again hyperbola location algorithm, thereby its mathematics mechanism is to ask for the estimated position that hyp intersection point obtains unknown node; For waking anchor node j up, its Hyperbolic Equation is

$R_{i,j}=R_i-R_j=\sqrt{{(x_i-x)}^2+{(y_i-y)}^2}-\sqrt{{(x_j-x)}^2+{(y_j-y)}^2}---\left(3\right)$

R wherein _ifor the distance of unknown node to i anchor node, R _jfor signal source arrives the distance of waking anchor node (definition anchor node j wakes anchor node up for service) up, R _i,jfor unknown node is to i anchor node and the range difference that wakes anchor node j up, R _i,j=c (t _i-t _j), wherein c is the light velocity, t _iand t _jbe respectively node i and node j receives the moment that unknown node transmits; Make therein i=1,2 ..., M, the coordinate that (x, y) is unknown node, (x _i, y _i) be the position coordinates of i anchor node, (x _j, y _j) for waking anchor node position coordinates up;

Two, Taylor algorithm

Hyperbolic Equation (3) is carried out to linearisation, adopt Taylor series expansion algorithm, Taylor series expansion algorithm is a kind of recursive algorithm that needs signal source initial estimated location, is improving the estimated position to signal source each time in recurrence by solving the local least square method solution of TDOA measure error.In actual applications, Taylor Series Expansion Method has good positioning performance conventionally.

Taylor sequence expansion needs initial estimated location, is coming improved estimator position each time in recurrence by solving the local least square method solution of TDOA measure error.For one group of TDOA measured value, first this algorithm chooses primary iteration position, specifically chooses as follows

$p={\left(G_a^T{Q}^{-1}{G}_a\right)}^{-1}{G}_a^T{Q}^{-1}h---\left(4\right)$

Wherein, the covariance matrix that Q is TDOA

$h=\frac{1}{2}\left[\begin{array}{c}{R}_{1,j}^2-x_1^2-y_1^2+x_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+y_j^2\\ {\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_{2,j}^2-x_2^2-{\mathrm{<figure-callout\; id="2"\; label="y"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_2^2+x_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="y\; j"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_j^{}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ R_{M,j}^2-x_M^2-{\mathrm{<figure-callout\; id="2"\; label="y\; M"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_M^{}+x_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">j</figure-callout>}}^2+{\mathrm{<figure-callout\; id="2"\; label="y\; j"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">y</figure-callout>}}_j^{}\end{array}\right],G_a=-\left[\begin{array}{ccc}{x}_{1,j}& y_{1,j}& R_{1,j}\\ x_{2,\mathrm{<figure-callout\; id="2"\; label="j\; y"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">j</figure-callout>}}& y_{}{}_{2,\mathrm{<figure-callout\; id="2"\; label="j\; R"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">j</figure-callout>}}& R_{}{}_{2,j}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_{M,j}& y_{M,j}& R_{M,j}\end{array}\right]$

(x in formula _i,j, y _i,j) be i anchor node and wake the coordinate difference between anchor node j up.

Taylor series expansion algorithm is chosen by following formula for the primary iteration value of unknown node position

$\left\{\begin{array}{c}{x}_j\left(0\right)=p\left(1\right)\\ y_j\left(0\right)=p\left(2\right)\end{array}\right.---\left(5\right)$

In recurrence, make next time:

x′ _j(0)=x _j(0)+△x,y′ _j(0)=y _j(0)+△y (6)

△ x, △ y choose as follows

$\mathrm{\&delta;}=\left[\begin{array}{c}\mathrm{\&Delta;x}\\ \mathrm{\&Delta;y}\end{array}\right]={\left(G_t^T{Q}^{-1}{G}_t\right)}^{-1}{G}_t^T{Q}^{-1}{h}_t---\left(7\right)$

Wherein

$h_t=\left[\begin{array}{c}{R}_{1,j}-R_1+{\mathrm{<figure-callout\; id="2"\; label="R\; j\; R"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_j& \\ R_{}{}_{2,j}-{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_2+R_j\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ R_{M,j}-R_M+R_j\end{array}\right],G_t=\left[\begin{array}{cc}(x_j-x)/R_j-(x_1-x)/R_1& (y_j-y)/R_j-(y_1-y)/R_1\\ (x_j-x)/R_j-(x_2-x)/R_2& (y_j-y)/R_j-(y_2-y)/{\mathrm{<figure-callout\; id="2"\; label="R"\; filenames="HDA0000441780080000031.png"\; state="\{\{state\}\}">R</figure-callout>}}_2\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ (x_j-x)/R_j-(x_M-x)/R_M& (y_j-y)/R_j-(y_M-y)/R_M\end{array}\right]$

Repeat above process, until △ x, △ y are enough little, meet certain thresholding:

Wherein ε is a very little positive number, now ((x ' _j(0), y ' _j(0)) be anchor node j for the initial estimate of unknown node position.

Other step and parameter are identical with embodiment one or two.

Embodiment four: present embodiment is different from one of embodiment one to three:

Assumed wireless sensor network has N sensor node, and each sensor node j is carved with a state value a when t _j(t), t=1,2,

In the Gossip algorithm incipient stage, be t=0, each sensor node j need to obtain the state value a of oneself according to task _j(0), this value can be the value of information of any pre-monitoring; Subsequently, in wireless sensor network any sensor node j can moment t by random activate and and it select at random possess state value a _i(t) adjacent sensors node i swap status value, exemplary formula is

$a_j(t+1)=a_i(t+1)=\frac{1}{2}(a_i\left(t\right)+a_j\left(t\right))---\left(9\right)$

The state of all the sensors node in wireless sensor network is represented with a N dimensional vector a (t), for the ease of research, (9) formula is rewritten into vectorial form:

A (t+1)=W (t) a (t) (10) wherein W (t) is a random matrix, and it depends primarily on the sensor node being waken up in time slot t, has so just obtained the general mathematics model of classical paired Gossip algorithm.From algorithm model, can find out, the realization of classical clean culture Gossip algorithm is in pairs very simple, and key issue is that its convergence has also obtained theoretical proof., the object of Gossip algorithm is exactly by few iterations of trying one's best, and makes the state value of each node j in network all converge on the average of all the sensors node initial condition value $(1/N){\mathrm{\&Sigma;}}_{m=1}^N{a}_m\left(0\right).$

Other step and parameter are identical with one of embodiment one to three.

Emulation experiment:

This emulation positions algorithm simulating in the two dimensional surface of 100m * 100m, supposes that unknown node position coordinates is for (20m, 20m).TDOA time determination error meets the Gaussian Profile of zero-mean, and Taylor algorithm iteration thresholding is set to ε=10 ^-8.Figure of description 2 for respectively to anchor node number N=5,10,20,30,40,50 situation is carried out emulation, this emulation anchor node position random arrangement within the scope of 100m * 100m.Root-mean-square error curve when the present invention draws respectively original Taylor algorithm and the Taylor location algorithm (PGA-Taylor) based on Gossip and increases along with anchor node number, the data in whole emulation are to carry out the result that obtains after 1000 independent experiments are averaged.This emulation experiment anchor node number in simulation process is set to respectively 5,10,20,30,40,50 o'clock, positioning precision has promoted respectively 23.37%, 58.63%, 75.88%, 77.84%, 83.53%, 84.81%, thereby confirm that PGA-Taylor algorithm proposed by the invention can effectively improve the positioning precision of former algorithm really, and can find out according to simulation analysis data, along with increasing of anchor node number, positioning precision also increases thereupon, but increasing degree reduces thereupon.Figure of description 3 be fixed anchor nodes number N=20 and anchor node position also within the scope of 100m * 100m during random distribution, the emulation that situation about changing with time determination error standard deviation for root-mean-square error is carried out.Still be respectively Taylor algorithm and the PGA-Taylor algorithm root-mean-square error curve while becoming large along with time determination error, whole emulation experiment is also to carry out the result of 1000 independent experiments after average.In this simulation process, Measuring Time error to standard deviation is set to respectively 3.3ns, 6.7ns, 10.0ns, 13.3ns, 16.7ns, namely being converted into corresponding range error standard deviation is respectively 1m, 2m, 3m, 4m, during 5m, positioning precision has promoted respectively 78.38%, 77.61%, 76.80%, 76.06%, 76.68%, can confirm that equally algorithm proposed by the invention can effectively improve positioning precision really, and positioning precision meets the rule reducing along with time determination error increase substantially.

Claims (4)

1. a wireless-sensor network distribution type localization method for and Gossip algorithm poor based on the time of advent, is characterized in that based on differing from the time of advent and the wireless-sensor network distribution type localization method of Gossip algorithm is realized according to the following steps:

Step 1: arrange at random or artificially N anchor node in wireless sensor network coverage, each anchor node obtains self unknown coordinates (x by GPS or artificial mode of arranging _k, y _k);

Step 2: in whole wireless sensor network, all anchor nodes are realized distributed time synchronized by broadcast Gossip algorithm;

Step 3: each anchor node wakes up at each slotted random, whether monitoring unknown node occurs;

Step 4: if unknown node appearance wakes the radio signal that anchor node k will receive unknown node transmitting up, the moment t of signal received in anchor node k record _k, together with local coordinate system, be kept at (x _k, y _k, t _k);

Step 5: each anchor node wakes up successively, repeating step four, preserves until all anchor nodes all complete signal monitoring and the data of unknown node;

Step 6: the anchor node in wireless sensor network wakes up at random, suppose that anchor node j is in wake-up states, this anchor node is to all adjacent anchor node broadcasts request within the scope of communication radius, require it to return node coordinate and receive signal constantly, this anchor node starts to receive the data whether data real-time judge receive whole adjacent anchor nodes, if do not receive whole adjacent anchor node datas, continue to receive, if receive whole adjacent anchor node datas, complete the reception of data and anchor node j is received to the data of its all M adjacent anchor node are kept at this locality, obtain local data as follows

$\left[\begin{array}{ccc}{x}_0^j& y_0^j& t_0^j\end{array}\right]=\left[\begin{array}{ccc}{x}_1& y_1& t_1\\ x_1& y_2& t_2\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_i& y_i& t_i\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_M& y_M& t_M\end{array}\right];$

Step 7: the local data that anchor node j obtains according to step 6, obtains unknown node position primary iteration value ((x according to the Taylor algorithm primary iteration location formula based on TDOA location _j(0), y _j(0)), according to the iterative process of the thresholding operation Taylor algorithm setting in advance, until obtain anchor node j for the initial estimate ((x of unknown node position _j(0), y _j(0));

Step 8: all the other anchor nodes in wireless sensor network wake up at random, according to the working method repeating step six of anchor node j and step 7, obtain this anchor node for the initial estimate of unknown node position, until all anchor nodes complete the initial estimation for unknown node position, in wireless sensor network, the unknown node position initial estimate coordinate of all anchor nodes is

$\left[\begin{array}{cc}{x}^{\&prime;}\left(0\right)& y^{\&prime;}\left(0\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& y_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right];$

Step 9: all anchor nodes obtain on the basis of this node for the initial estimate of unknown node position in wireless sensor network, the all N of a whole network anchor node moves paired Gossip algorithm, the concrete running of Gossip algorithm is as follows in pairs: suppose to be waken up at time slot t anchor node j, this anchor node is random selects an adjacent anchor node i to exchange initial estimation Value Data

$x_j^{\&prime;}(t+1)=x_i^{\&prime;}(t+1)=\frac{1}{2}(x_i^{\&prime;}\left(t\right)+x_j^{\&prime;}\left(t\right))$

$y_j^{\&prime;}(t+1)=y_i^{\&prime;}(t+1)=\frac{1}{2}(y_i^{\&prime;}\left(t\right)+y_j^{\&prime;}\left(t\right))$

The whole iterative process of paired Gossip algorithm that the whole network N anchor node moves can be expressed as follows

$z^{\&prime;}(t+1)=W\left(t\right)z^{\&prime;}\left(t\right)=\underset{n=1}{\overset{t}{\mathrm{\&Sigma;}}}W\left(n\right)z^{\&prime;}\left(0\right)$

Wherein

$z^{\&prime;}\left(t\right)=\left[\begin{array}{cc}{x}^{\&prime;}\left(t\right)& y^{\&prime;}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}\left(t\right)& y_1^{\&prime;}\left(t\right)\\ x_2^{\&prime;}\left(t\right)& y_2^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(t\right)& y_j^{\&prime;}\left(t\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(t\right)& y_N^{\&prime;}\left(t\right)\end{array}\right];$

Step 10: judge whether Gossip algorithm reaches predefined iterations, if reach predefined iterations whole algorithm complete, in wireless sensor network, all anchor nodes complete distributed common recognition location, each anchor node obtains identical unknown node location estimation value, and the final unknown node location estimation value that the method obtains is

$z^{\&prime;}=\left[\begin{array}{cc}{x}^{\&prime;}& y^{\&prime;}\end{array}\right]=\left[\begin{array}{cc}{x}_1^{\&prime;}& y_1^{\&prime;}\\ x_2^{\&prime;}& y_2^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}& y_j^{\&prime;}\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}& y_N^{\&prime;}\end{array}\right]=\frac{1}{N}\stackrel{\&RightArrow;}{1}{\stackrel{\&RightArrow;}{1}}^T\left[\begin{array}{cc}{x}_1^{\&prime;}\left(0\right)& y_1^{\&prime;}\left(0\right)\\ x_2^{\&prime;}\left(0\right)& y_2^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_j^{\&prime;}\left(0\right)& y_j^{\&prime;}\left(0\right)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ x_N^{\&prime;}\left(0\right)& y_N^{\&prime;}\left(0\right)\end{array}\right]$

Completed a kind of wireless-sensor network distribution type localization method based on time of advent difference and Gossip algorithm.

2. the wireless-sensor network distribution type localization method of a kind of and Gossip algorithm poor based on the time of advent according to claim 1, is characterized in that the broadcast Gossip algorithm described in step 2 is specially:

Node in network wakes and broadcasts its state value at random up, and this state value is received by all nodes in its communication radius, and all receiving nodes upgrade its local state value according to algorithm design, and other node state values remain unchanged.

3. the wireless-sensor network distribution type localization method of a kind of and Gossip algorithm poor based on the time of advent according to claim 1 and 2, is characterized in that the Taylor algorithm of locating based on TDOA described in step 7 is specially:

One, TDOA location

First suppose that all anchor nodes reach distributed time synchronized by broadcast Gossip algorithm, the communication radius of anchor node is subject to the restriction of TDOA location hardware module in network, and the topological structure G (N, R) of N point wireless sensor network is by adjacency matrix Φ _ijrepresent, when i ≠ j, if anchor node i is adjacent with anchor node j, Φ _ij=1; Otherwise, Φ _ij=0; For anchor node j, definition M={i ∈ 1,2 ..., N}: Φ _ij≠ 0};

For waking anchor node j up, its Hyperbolic Equation is

$R_{i,j}=R_i-R_j=\sqrt{{(x_i-x)}^2+{(y_i-y)}^2}-\sqrt{{(x_j-x)}^2+{(y_j-y)}^2}---\left(1\right)$

R wherein _ifor the distance of unknown node to i anchor node, R _jfor signal source arrives the distance of waking anchor node up, R _i,jfor unknown node is to i anchor node and the range difference that wakes anchor node j up, R _i,j=c (t _i-t _j), wherein c is the light velocity, t _iand t _jbe respectively node i and node j receives the moment that unknown node transmits; Make therein i=1,2 ..., M, the coordinate that (x, y) is unknown node, (x _i, y _i) be the position coordinates of i anchor node, (x _j, y _j) for waking anchor node position coordinates up;

Two, Taylor algorithm

Adopt Taylor algorithm to carry out linearisation to Hyperbolic Equation (1), Taylor sequence expansion needs initial estimated location, in recurrence, by solving the local least square method solution of TDOA measure error, coming improved estimator position each time, for one group of TDOA measured value, first this algorithm chooses primary iteration position, specifically chooses as follows

$p={\left(G_a^T{Q}^{-1}{G}_a\right)}^{-1}{G}_a^T{Q}^{-1}h---\left(2\right)$

Wherein, the covariance matrix that Q is TDOA

$h=\frac{1}{2}\left[\begin{array}{c}{R}_{1,j}^2-x_1^2-y_1^2+x_j^2+y_j^2\\ R_{2,j}^2-x_2^2-y_2^2+x_j^2+y_j^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ R_{M,j}^2-x_M^2-y_M^2+x_j^2+y_j^2\end{array}\right],G_a=-\left[\begin{array}{ccc}{x}_{1,j}& y_{1,j}& R_{1,j}\\ x_{2,j}& y_{2,j}& R_{2,j}\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;& \&CenterDot;\\ x_{M,j}& y_{M,j}& R_{M,j}\end{array}\right]$

(x in formula _i,j, y _i,j) be i anchor node and wake the coordinate difference between anchor node j up;

Taylor algorithm is chosen by following formula for the primary iteration value of unknown node position

$\left\{\begin{array}{c}{x}_j\left(0\right)=p\left(1\right)\\ y_j\left(0\right)=p\left(2\right)\end{array}\right.---\left(3\right)$

In recurrence, make next time:

x′ _j(0)=x _j(0)+△x,y′ _j(0)=y _j(0)+△y (4)

△ x, △ y choose as follows

$\mathrm{\&delta;}=\left[\begin{array}{c}\mathrm{\&Delta;x}\\ \mathrm{\&Delta;y}\end{array}\right]={\left(G_t^T{Q}^{-1}{G}_t\right)}^{-1}{G}_t^T{Q}^{-1}{h}_t---\left(5\right)$

Wherein

$h_t=\left[\begin{array}{c}{R}_{1,j}-R_1+R_j\\ R_{2,j}-R_2+R_j\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ R_{M,j}-R_M+R_j\end{array}\right],G_t=\left[\begin{array}{cc}(x_j-x)/R_j-(x_1-x)/R_1& (y_j-y)/R_j-(y_1-y)/R_1\\ (x_j-x)/R_j-(x_2-x)/R_2& (y_j-y)/R_j-(y_2-y)/R_2\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ (x_j-x)/R_j-(x_M-x)/R_M& (y_j-y)/R_j-(y_M-y)/R_M\end{array}\right]$

Repeat above process, until △ x, △ y are enough little, meet and set thresholding:

Wherein ε is a very little positive number, now ((x ' _j(0), y ' _j(0)) be anchor node j for the initial estimate of unknown node position.

4. the wireless-sensor network distribution type localization method of a kind of and Gossip algorithm poor based on the time of advent according to claim 1 and 2, is characterized in that described in step 9, paired Gossip algorithm is specially:

Assumed wireless sensor network has N sensor node, and each sensor node j is carved with a state value a when t _j(t), t=1,2,

In the Gossip algorithm incipient stage, be t=0, each sensor node j need to obtain the state value a of oneself according to task _j(0); Subsequently, in wireless sensor network any sensor node j can moment t by random activate and and it select at random possess state value a _i(t) adjacent sensors node i swap status value, exemplary formula is

$a_j(t+1)=a_i(t+1)=\frac{1}{2}(a_i\left(t\right)+a_j\left(t\right))---\left(7\right)$

The state of all the sensors node in wireless sensor network is represented with a N dimensional vector a (t), (7) formula is rewritten into vectorial form:

a(t+1)=W(t)a(t) (8)

Wherein W (t) is a random matrix, it depends primarily on the sensor node being waken up in time slot t, obtain the classical general mathematics model of Gossip algorithm in pairs, Gossip algorithm is by few iterations of trying one's best, and makes the state value of each node in network all converge on the average of all the sensors node initial condition value

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