CN104023390A - WSN node positioning method based on combination of PSO and UKF - Google Patents

Abstract

The invention relates to a WSN node positioning method based on combination of PSO and UKF. The PSO is utilized to carry out preliminary positioning, and the acquired coordinate figure is taken as an initial value of the UKF; a state equation and a measurement equation of the positioning system are established, an RSSI value is taken as observed quantity, a coordinate estimate of an unknown node is acquired, and multitime iteration is carried out; a mass center algorithm principle is utilized, and a polygon mass center coordinate is taken as the final estimate coordinate of the unknown node. Compared with a traditional positioning algorithm, the WSN node positioning method has advantages of higher positioning precision, stronger reliability and relatively strong practical value.

Description

WSN node positioning method based on PSO and UKF combination

Technical field

The present invention relates to a kind of node positioning method for wireless sensor network field, specifically a kind of WSN node positioning method based on PSO and UKF combination.

Background technology

Wireless sensor network originates from nineteen seventies the earliest, in recent years, is accompanied by the development of microelectromechanical-systems, wireless communication technology and embedded microprocessor technology, has impelled fast development and the extensive use of the technology of wireless sensor network.Sensor node in network can monitor voluntarily Information Monitoring, self-organizing network, the information of collecting is sent to destination node, can be deployed in the place that some cannot be in for a long time or be difficult to touch.Therefore wireless sensor network has been widely used in the fields such as national defense and military, social safety, environmental monitoring, Medical nursing and Smart Home.Yet in most of application scenarios, the monitoring information that the node in network obtains all will be enclosed corresponding positional information, otherwise the accuracy of this information is doubtful, or even invalid.So the positional information of determining nodes is wireless sensor network research and the basis of applying, and has important practical significance.

There are now many methods and applications to realize the location of node.Node locating technique in wireless sensor network mainly contains: inertial sensor technology, infrared technology, ultrasonic technology and radiotechnics.Node positioning method can be divided into two classes: based on range finding (Range-based) method with based on non-ranging (Range-free) method.Wherein the method based on range finding mainly contains: the measuring-signal method time of advent (TOA), different measuring signal arrival time difference method (TDOA), measuring-signal arrive preset angle configuration (AOA), received signal strength method (RSSI); Non-ranging method is mainly to utilize self network-in-dialing degree to realize location, and main method has: barycenter positioning mode, DV-Hop positioning mode, APIT method, method of convex programming and MDS-MAP method etc.Compare the localization method based on non-ranging, the method based on range finding has higher precision, and based on RSSI range finding location hardware, requires lowly, implements also simply, and practical application is also many, so the present invention adopts RSSI method to realize range finding location.

While only using trilateration, maximum likelihood estimation or maximin method in tradition WSN node locating algorithm, positioning precision is not high, and follow-up normal employing filtering technique further improves node locating precision.Conventional filtering technique is Kalman filtering now.For non linear system, the most frequently used filtering technique is EKF (EKF), but EKF (EKF) and derivative algorithm thereof all will calculate Jacbian matrix, and when being similar to nonlinear function by Taylor expansion, often ignore the higher order term more than second order in Taylor expansion, thereby reduced approximation quality, even can cause filtering divergence.And Unscented kalman filtering (UKF) can well improve the problems referred to above.Because Unscented kalman filtering (UKF) directly adopts real system model, and Posterior Mean and covariance can be accurate to three rank, very high greatly filtering accuracy.Therefore the present invention adopts Unscented kalman filtering (UKF) filtering algorithm as later stage optimized algorithm, simultaneously according to joint density function employing particle group optimizing (PSO) algorithm of the RSSI value of multinode and distance relation, obtain preliminary coordinate estimated value, compare traditional Newton method, Newton iteration method has convergence rate and more accurate optimum results faster.

Summary of the invention

The present invention will solve RSSI and be subject to the large deficiency of impact of transmission environment around, proposes that a kind of precision is high, stability and the real-time WSN node positioning method based on PSO and UKF combination.

WSN node positioning method based on MLE and UKF combination of the present invention, its job step is:

1. according to the residing environment of sensor node, determine the parameter in wireless signal path loss model, the relation curve between matching wireless energy signal attenuation process and distance;

2. according to the relation between a plurality of independent actual ranges and measuring distance, set up the joint probability density function model of error noise, use particle swarm optimization algorithm to try to achieve optimum coordinates value;

Joint probability density function:

$F\left(Z\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f\left(z_i\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{{2\mathrm{\π\σ}}_i^2}}\exp \{-\frac{(z_i-r_i)}{{2\mathrm{\σ}}_i^2}\}$

In formula: z _ibe measuring distance, according to the RSSI value receiving, determine, and r _ifor actual distance, (x _i, y _i) be the coordinate figure of i beaconing nodes, σ _ifor normal distribution mean square deviation.

3. make joint probability density function above obtain maximum, can determine the coordinate figure of unknown node; Adopt particle swarm optimization algorithm, the fitness function that the joint probability density function of take is PSO, the speed renewal function of individual in population particle is:

ν(k+1)＝ωv(k)+c ₁λ ₁(pbest-α _i(k))+c ₂λ ₂(gbest-α _i(k))

Wherein, the renewal speed of individual the k time in v (k) expression population, ω is inertial factor, c ₁, c ₂for acceleration factor, λ ₁, λ ₂for obeying [0,1] equally distributed random distribution value, α _i(k) be the positional information of i individual the K time iteration, pbest is colony's optimal location value, and gbest is personal best particle value.

The parameter of regulating the speed in renewal function, chooses suitable change step, and iteration is repeatedly obtained the global optimum of population, coordinate estimated value be ( );

4. with beaconing nodes, get to such an extent that RSSI value and wireless signal path loss model are set up state equation and the observational equation of Unscented kalman filtering system; ( ) as the initial value of Unscented kalman filtering state variable;

(1) state equation: X _k+1=f (X _k, u _k)+w _k=AX _k+ w _k,

Wherein, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$ X _kthe stochastic variable that represents the K time iteration, w _ksystem noise while representing the K time iteration, u _kfor system input variable.

(2) observational equation: Y _k=h (X _k)+v _k=P _r(d _k), reference distance d in wireless signal path loss model ₀=1m;

$\left\{\begin{array}{c}{P}_r\left(d_1\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_1\right)+v\\ P_r\left(d_2\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_2\right)+v\\ \·\\ \·\\ \·\\ P_r\left(d_n\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_n\right)+v\end{array}\right.,$

Wherein, p _r(d _i) be that distance is d _itime receive RSSI value, P _r(d ₀) be d ₀reception RSSI value during=1m, Y _kfor system output variable, v represents observation noise.

5. the UKF in pair location algorithm partly carries out N time iteration, obtains N coordinate estimated value, ( ) represent the coordinate estimated value of the i time iteration Unscented kalman filtering acquisition; Removing wherein coordinate figure and other coordinate has the value of notable difference, adopts barycenter location algorithm, using (M≤N) coordinate of the M after screening as polygonal summit, tries to achieve this polygonal barycenter:

$x=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{x}}_i,y=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{y}}_i$

(x, y) is the coordinate figure of required unknown node.

Advantage of the present invention is: range finding model has stronger environmental suitability, can reduce range error; Adopt particle swarm optimization algorithm and Unscented kalman filtering algorithm simultaneously, compare and use Newton method, Newton iteration method and EKF (EKF), there is convergence rate faster, higher positioning precision.In UKF measurement model, the distance value after RSSI value rather than conversion is directly used in observed quantity, and the error accumulation in the ranging process of avoiding, has improved locating effect.Adopt PSO to carry out pre-determined bit, using the initial value of the coordinate figure obtaining state variable X in UKF, accelerated the convergence rate of UKF, improved positioning precision.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Fig. 2 is energy-distance Curve of the present invention.

Design sketch when Fig. 3 is PSO iteration of the present invention 10 times.

Design sketch when Fig. 4 is PSO iteration of the present invention 100 times.

Fig. 5 is locating effect figure of the present invention.

Embodiment

With reference to accompanying drawing:

WSN node positioning method based on MLE and UKF combination of the present invention, its job step is:

1. according to the residing environment of sensor node, determine the parameter in wireless signal path loss model, the relation curve between matching wireless energy signal attenuation process and distance;

2. according to the relation between a plurality of independent actual ranges and measuring distance, set up the joint probability density function model of error noise, use particle swarm optimization algorithm to try to achieve optimum coordinates value;

Joint probability density function:

$F\left(Z\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f\left(z_i\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{{2\mathrm{\π\σ}}_i^2}}\exp \{-\frac{(z_i-r_i)}{{2\mathrm{\σ}}_i^2}\}$

In formula: z _ibe measuring distance, according to the RSSI value receiving, determine, and r _ifor actual distance, (x _i, y _i) be the coordinate figure of i beaconing nodes;

3. make joint probability density function above obtain maximum, can determine the coordinate figure of unknown node; Adopt particle swarm optimization algorithm, the fitness function that the joint probability density function of take is PSO, the speed renewal function of individual in population particle is:

ν(k+1)＝ωv(k)+c ₁λ ₁(pbest-α _i(k))+c ₂λ ₂(gbest-α _i(k))

The parameter of regulating the speed in renewal function, chooses suitable change step, and iteration is repeatedly obtained the global optimum of population, coordinate estimated value be ( );

4. with beaconing nodes, get to such an extent that RSSI value and wireless signal path loss model are set up state equation and the observational equation of Unscented kalman filtering system; ( ) as the initial value of Unscented kalman filtering state variable;

(1) state equation: X _k+1=f (X _k, u _k)+w _k=AX _k+ w _k,

Wherein, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

(2) observational equation: Y _k=h (X _k)+v _k=P _r(d _k), reference distance d in wireless signal path loss model ₀=1m;

$\left\{\begin{array}{c}{P}_r\left(d_1\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_1\right)+v\\ P_r\left(d_2\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_2\right)+v\\ \·\\ \·\\ \·\\ P_r\left(d_n\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_n\right)+v\end{array}\right.,$ Wherein, $d_i=\sqrt{{(x-x_i)}^2-{(y-y_i)}^2}$

5. the UKF in pair location algorithm partly carries out N time iteration, obtains N coordinate estimated value, ( ) represent the coordinate estimated value of the i time iteration Unscented kalman filtering acquisition; Removing wherein coordinate figure and other coordinate has the value of notable difference, adopts barycenter location algorithm, using (M≤N) coordinate of the M after screening as polygonal summit, tries to achieve this polygonal barycenter:

$x=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{x}}_i,y=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{y}}_i$

(x, y) is the coordinate figure of required unknown node.

With reference to accompanying drawing 1:

After determining localization method, the technical solution adopted for the present invention to solve the technical problems is proposed:

1. we are at 10 beaconing nodes of indoor layout of one 30 meters * 20 meters.Beaconing nodes coordinate is: (4,0), (12,0), (22,0), (30,4), (30,12), (28,20), (18,20), (8,20), (0,18), (0,18).

2. unify the transmitting power of each node, in above-mentioned environment, repeatedly test, according to the RSSI value obtaining and known distance value, on MATLAB, adopt least square method to carry out curve fitting, as shown in Figure 3, determine the parameter in path loss range finding model, path loss factor values is 2.41.

3. 15 unknown node of random arrangement in locating area, are converted to corresponding distance value by the RSSI value obtaining according to path loss model, according to joint probability density function and particle cluster algorithm, try to achieve unknown node Primary Location coordinate figure.Formula is as follows:

Joint probability density function:

$F\left(Z\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f\left(z_i\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{{2\mathrm{\π\σ}}_i^2}}\exp \{-\frac{(z_i-r_i)}{{2\mathrm{\σ}}_i^2}\}$

Particle swarm optimization algorithm: the fitness function that the joint probability density function of take is PSO, the speed renewal function of individual in population particle is,

ν(k+1)＝ωv(k)+c ₁λ ₁(pbest-α _i(k))+c ₂λ ₂(gbest-α _i(k))

In formula: z _ibe measuring distance, according to the RSSI value receiving, determine, and r _ifor actual distance, (x _i, y _i) be the coordinate figure of i beaconing nodes.The parameter of regulating the speed in renewal function, chooses suitable change step, and iteration is repeatedly obtained the global optimum of population, coordinate estimated value be ( ).

3. coordinate figure PSO optimized algorithm being obtained and receive RSSI value respectively as initial value and the observed quantity of Unscented kalman filtering, set up state equation and the measurement equation of navigation system.According to Unscented kalman filtering Solving Equations, obtain the coordinate figure that quantity of state X is unknown node.

(1) state equation: X _k+1=f (X _k, u _k)+w _k=AX _k+ w _k,

Wherein, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right].$

(2) observational equation: Y _k=h (X _k)+v _k=P _r(d _k),

$\left\{\begin{array}{c}{P}_r\left(d_{k,1}\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_{k,1}\right)+v_k\\ P_r\left(d_{k,2}\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_{k,2}\right)+v_k\\ \·\\ \·\\ \·\\ P_r\left(d_{k,n}\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_{k,n}\right)+v_k\end{array}\right.$

4. by the coordinate figure of Unscented kalman filtering iteration N time, remove and wherein have the value of notable difference point with other coordinate, adopt barycenter location algorithm, using the individual coordinate of M (M≤N) after screening as polygonal summit, try to achieve this polygonal barycenter, formula is as follows:

(x, y) is the coordinate figure of required unknown node.

Result is presented in Fig. 5, and figure hollow core circle represents the true coordinate value of nodes of locations, and solid dot is the estimated value of the unknown node coordinate that obtains by this invention.

Content described in this specification embodiment is only enumerating the way of realization of inventive concept; protection scope of the present invention should not be regarded as only limiting to the concrete form that embodiment states, protection scope of the present invention also and in those skilled in the art, according to the present invention, conceive the equivalent technologies means that can expect.

Claims (1)

1. the WSN node positioning method based on MLE and UKF combination, its job step is:

Step 1., according to the residing environment of sensor node, is determined the parameter in wireless signal path loss model, the relation curve between matching wireless energy signal attenuation process and distance;

Step 2. is set up the joint probability density function model of error noise according to the relation between a plurality of independent actual ranges and measuring distance, use particle swarm optimization algorithm to try to achieve optimum coordinates value;

Joint probability density function:

$F\left(Z\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}f\left(z_i\right|(x,y))=\underset{i=1}{\overset{n}{\mathrm{\Π}}}\frac{1}{\sqrt{{2\mathrm{\π\σ}}_i^2}}\exp \{-\frac{(z_i-r_i)}{{2\mathrm{\σ}}_i^2}\}$

In formula: z _ibe measuring distance, according to the RSSI value receiving, determine, and r _ifor actual distance, σ _ifor normal distribution mean square deviation.(x _i, y _i) be the coordinate figure of i beaconing nodes;

Step 3. makes joint probability density function above obtain maximum, can determine the coordinate figure of unknown node; Adopt particle swarm optimization algorithm, the fitness function that the joint probability density function of take is PSO, the speed renewal function of individual in population particle is:

ν(k+1)＝ωv(k)+c ₁λ ₁(pbest-α _i(k))+c ₂λ ₂(gbest-α _i(k))

Wherein, the renewal speed of individual the k time in v (k) expression population, ω is inertial factor, c ₁, c ₂for acceleration factor, λ ₁, λ ₂for obeying [0,1] equally distributed random distribution value, α _i(k) be the positional information of i individual the K time iteration, pbest is colony's optimal location value, and gbest is personal best particle value;

The parameter of regulating the speed in renewal function, chooses suitable change step, and iteration is repeatedly obtained the global optimum of population, coordinate estimated value be ( );

Step 4. gets to such an extent that RSSI value and wireless signal path loss model are set up state equation and the observational equation of Unscented kalman filtering system with beaconing nodes; ( ) as the initial value of Unscented kalman filtering state variable;

(1) state equation: X _k+1=f (X _k, u _k)+w _k=AX _k+ w _k,

Wherein, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],$ X _kthe stochastic variable that represents the K time iteration, w _ksystem noise while representing the K time iteration, u _kfor system input variable.

(2) observational equation: Y _k=h (X _k)+v _k=P _r(d _k), reference distance d in wireless signal path loss model ₀=1m;

$\left\{\begin{array}{c}{P}_r\left(d_1\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_1\right)+v\\ P_r\left(d_2\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_2\right)+v\\ \·\\ \·\\ \·\\ P_r\left(d_n\right)=P_r\left(d_0\right)-10\·n\·\log \left(d_n\right)+v\end{array}\right.,$

Wherein, p _r(d _i) be that distance is d _itime receive RSSI value, P _r(d ₀) be d ₀reception RSSI value during=1m, Y _kfor system output variable, v represents observation noise;

UKF in step 5. pair location algorithm partly carries out N time iteration, obtains N coordinate estimated value, ( ) represent the coordinate estimated value of the i time iteration Unscented kalman filtering acquisition; Removing wherein coordinate figure and other coordinate has the value of notable difference, adopts barycenter location algorithm, using (M≤N) coordinate of the M after screening as polygonal summit, tries to achieve this polygonal barycenter:

$x=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{x}}_i,y=\frac{1}{M}\underset{i=0}{\overset{M}{\mathrm{\Σ}}}{\hat{y}}_i$

(x, y) is the coordinate figure of required unknown node.