CN106019217A - AOA-based two-dimensional wireless sensor network semi-definite programming positioning method - Google Patents

Abstract

The invention relates to an AOA-based two-dimensional wireless sensor network semi-definite programming positioning method comprising the following steps: assuming that there is no obstruction between a reference node and a target node to be positioned in a wireless sensor network, and measuring the angle of arrival of each signal; converting the angles of arrival of the signals into distance information between the nodes; converting a problem of wireless sensor network target node positioning into a mathematical optimization problem of maximum likelihood estimate MLE and solving the problem, and providing an optimized objective function for subsequent steps; introducing redundant variables to convert the mathematical optimization problem of maximum likelihood estimate MLE into a constrained optimization problem; converting the obtained constrained optimization problem into a semi-definite programming SDP convex optimization problem using a mini-max criterion and a semi-definite relaxation SDR method, and getting an optimal solution, thus completing positioning of the target node. Through the method, the precision of target node positioning is improved.

Description

Two dimensional wireless sensor network Semidefinite Programming localization method based on AOA

Technical field

The invention belongs to wireless sensor network positioning field, relate to Semidefinite Programming (SDP) convex optimization method based on AOA Application in the two dimensional wireless sensor network target node locating measured.

Background technology

In recent years, wireless sensor network (WSNs) in target tracking, intrusion detection, efficiency route, underground and was surveyed under water The application in the various fields such as survey is obtained for and develops rapidly.Wireless sensor network location is by the reference node of distribution in network Cooperation between point completes the location to destination node.Localization method mainly includes four kinds, respectively time of arrival (toa) (TOA), Signal arrival time difference (TDOA), accept signal energy (RSS) and direction of arrival (AOA).For different localization methods, fixed Position degree of accuracy and location complexity are two principal elements that Design Orientation system is considered.

Typically, wireless sensor network positioning system is broadly divided into two parts.Part I is that docking receipts signal parameter enters Row is measured, and mainly includes TOA, TDOA, RSS and AOA.In the middle of RSS model, signal energy measured value is easily by the shadow of environment noise Ringing, this can cause the biggest measurement error.TOA model and TDOA model are typically extensive at view distance environment Application comparison, but should Model needs to meet internodal time synchronized, higher to hardware requirement, improves location cost.By contrast, AOA positions mould Type can complete the estimation to direction of arrival by array antenna, it is not necessary to meets time synchronized between node, and hardware device is wanted Ask relatively low, thus reduce the location cost to destination node.Part II is to complete based on above direction of arrival measured value Location to destination node.Stansfield proposes a kind of Stansfield location algorithm, and this algorithm is it needs to be determined that destination node And the range information between reference mode.Also having a kind of PLS algorithm, this algorithm is biased estimation, and along with pendulous frequency Increase deviation will not reduce.In order to overcome this shortcoming, some scholars propose maximum-likelihood estimation (MLE), but, this calculation Method not only it needs to be determined that the initial value of an iterative, is additionally, since tan and has high non-linearity, and iterative is easy Obtain local optimum, reduce the positioning precision to destination node.

Summary of the invention

The present invention provides a kind of two dimensional wireless sensor network based on AOA that can improve the positioning precision to destination node Network Semidefinite Programming localization method.Technical scheme is as follows:

A kind of two dimensional wireless sensor network Semidefinite Programming localization method based on AOA, including following step:

1) it is located in wireless sensor network and between reference mode and destination node to be positioned, there is not shelter, the most not There is non line-of-sight communication, set up xy rectangular coordinate system, measure each direction of arrival；

2) direction of arrival is converted into internodal range information, calculates destination node X and reference mode X_iBetween Range information d_i；

3) by wireless sensor network target node locating problem being converted into the mathematical optimization of maximal possibility estimation MLE Problem solves, and provides the object function optimized for subsequent step, and object function is:

$\tilde{X}=\underset{X}{\min }\underset{i=1}{\overset{N}{\Σ}}{f}_i$

f_i=(d_i-r_i)²

In formula,For the estimated value of destination node, r_iFor destination node X to reference mode X_iActual range.

4) on the basis of the fresh target function that the 3rd step obtains, by introducing redundant variables y_s=X^TMaximum likelihood is estimated by X The mathematical optimization problem of meter MLE is converted into constrained optimization problems, wherein, and X^TThe transposition of representing matrix X；

5) by application minimax criterion and semidefinite decoding SDR method, the constrained optimization problems obtained is turned further Turn to the convex optimization problem of Semidefinite Programming SDP, by using integrated SeDuMi method in Matlab tool kit to try to achieve half set pattern Draw the optimal solution of the convex optimization problem of SDP, thus complete the location to destination node.

The range information that first the signal angle information obtained be converted between destination node and reference mode by the present invention； Then, based on the range information obtained, this orientation problem is converted into maximal possibility estimation (MLE) optimization problem, passes through meanwhile Introduce redundant variables, and combine minimax criterion and this optimization problem is converted into half set pattern by semidefinite decoding (SDR) method Draw (SDP) convex optimization problem.This method is possible not only to the impact reducing internodal time synchronization problem to positioning performance, also may be used To obtain the globally optimal solution of optimization problem, thus improve the positioning precision to destination node.

Accompanying drawing explanation

Fig. 1 schematic network structure.

Fig. 2 triangle relation figure.

The positioning performance of Fig. 3 algorithms of different compares.

Detailed description of the invention

Two dimensional wireless sensor network reference mode in this method uses oval distribution form such as Fig. 1, i.e. reference Inserting knot is in a rectangular region, and wherein, destination node is set to X=[0,25], and reference mode number is set to 6, reference The position coordinates of node is expressed as: X₁=[-100,0], X₂=[-50,100], X₃=[-50 ,-100], X₄=[50,100], X₅ =[50 ,-100], X₆=[100,0].

We will carry out M by MATLAB to the location algorithm proposed_cThe test of=1000 Monte Carlo simulations, and with Some location algorithms contrast.We mainly use position root-mean-square error (RMSE) present invention proposes algorithm and has Algorithm carries out comparative evaluation.The expression formula of RMSE is as follows:

$RMSE=\sqrt{E\[{(x-x_0)}^2+{(y-y_0)}^2\]}$

Wherein (x is y) by calculated tag coordinate, (x₀,y₀) it is the true coordinate of label.

Below in conjunction with technical scheme process in detail:

1. angle parameter is converted into range information

Present invention contemplates that two dimension WSNs, including N number of reference mode and a destination node to be positioned, N number of Reference mode is expressed as X₁,X₂,...,X_N, destination node to be positioned is expressed as X, and supposes all reference nodes in WSNs Non line of sight is there is not between point and destination node.If recording destination node X and reference mode X_iBetween direction of arrival degree For θ_i, then trigonometric function relation can be utilized to calculate destination node X and reference node by structure as schemed the triangle of (2) Point X_iBetween range information d_i。

D calculated as below can be obtained according to the angular relationship in figure (2)_iRelational expression:

$d_i=\frac{1}{N-1}\underset{j=1,j\≠i}{\overset{N}{\Σ}}\left|\frac{sin({\mathrm{\θ}}_i-{\mathrm{\θ}}_j)}{sin({\mathrm{\θ}}_j-{\mathrm{\α}}_{ij})}\right|L_{ij}$

In formula, θ_iAnd θ_jIt is respectively reference mode X_iAnd X_jMeasure the direction of arrival obtained, L_ijFor reference mode X_iAnd X_j Between the length of line, α_ijFor line and the angle of axis of abscissas.

2. the maximal possibility estimation of destination node

Assume the range noise n recorded_iFor Gaussian noise, then based on the range information d obtained in previous step_i, by pushing away Lead and can obtain following maximal possibility estimation optimization problem:

$X=\underset{X}{min}\underset{i=1}{\overset{N}{\Σ}}{f}_i$

f_i=(d_i-r_i)²

$r_i={||X-X_i||}_2=\sqrt{{(x-x_i)}^2+{(y-y_i)}^2}$

Wherein, r_iFor destination node X to reference mode X_iActual range, r_i=| | X-X_i||₂, d_i=r_i+n_i=| | X-X_i| |₂+n_i, i=1,2 ..., N,I=1,2 ..., N.

3. the convex optimization problem of Semidefinite Programming

By introducing redundant variables y_s=X^TMLE optimization problem can be converted into constrained optimization problems by X, then by application Constrained optimization problems can be converted into the convex optimization of Semidefinite Programming by semidefinite decoding (SDR) technology and minimax criterion further Problem is as follows:

$\underset{X,y_s}{min}\mathrm{\θ}$

$s.t.-\mathrm{\θ}\≤d_i^2-(X_i^T{X}_i-2X_i^{T}X-y_s)\≤\mathrm{\θ}$

I=1,2 ..., N

$\left[\begin{array}{cc}I& X\\ X^T& y_s\end{array}\right]\≥0.$

Above formula can solve, by using SeDuMi to carry out, Semidefinite Programming (SDP) the convex optimization obtaining measuring based on AOA The optimal solution of problem, thus complete the location to destination node, wherein, SeDuMi is a kind of being integrated in MATLAB tool kit The method solving Semidefinite Programming.

In order to verify that this method positioning performance is better than existing algorithm intuitively, Fig. 3 depicts this method and existing Two kinds of methods of Stansfield, PLS are along with angular surveying noise bias σ²Change curve, be provided with reference mode number N=6, destination node coordinate is X=[0,25]^T(within being positioned at the convex set of reference mode composition).It can be seen that no matter It is noise bias σ²Big or little, the algorithm positioning performance in the present invention is substantially better than other two kinds of algorithms, and positioning precision is high.

The invention have the advantages that

(1) present invention is by being converted into range information by the angle information between destination node and reference mode, can reduce The impact on positioning performance of the internodal time synchronization problem；

(2) present invention solves by former maximum likelihood optimization problem is converted into the convex optimization problem of Semidefinite Programming, can To obtain the globally optimal solution of optimization problem, thus improve the positioning precision to destination node.

Claims (1)

1. a two dimensional wireless sensor network Semidefinite Programming localization method based on AOA, including following step:

1) it is located in wireless sensor network and between reference mode and destination node to be positioned, there is not shelter, do not exist Non line-of-sight communication, sets up xy rectangular coordinate system, measures each direction of arrival；

2) direction of arrival is converted into internodal range information, calculates destination node X and reference mode X_iBetween distance Information d_i；

3) by wireless sensor network target node locating problem being converted into the mathematical optimization problem of maximal possibility estimation MLE Solving, provide the object function optimized for subsequent step, object function is:

$\tilde{X}=\underset{X}{min}\underset{i=1}{\overset{N}{\Σ}}{f}_i$

f_i=(d_i-r_i)²

In formula,For the estimated value of destination node, r_iFor destination node X to reference mode X_iActual range.

4) on the basis of the fresh target function that the 3rd step obtains, by introducing redundant variables y_s=X^TX is by maximal possibility estimation The mathematical optimization problem of MLE is converted into constrained optimization problems, wherein, and X^TThe transposition of representing matrix X；

5) by application minimax criterion and semidefinite decoding SDR method, the constrained optimization problems obtained is further converted to The convex optimization problem of Semidefinite Programming SDP, by using integrated SeDuMi method in Matlab tool kit to try to achieve Semidefinite Programming SDP The optimal solution of convex optimization problem, thus complete the location to destination node.