CN104363649A - UKF (unscented Kalman filter)-based WSN (wireless sensor network) node location method with constraint conditions - Google Patents

Abstract

The invention discloses a UKF (unscented Kalman filter)-based WSN (wireless sensor network) node location method with constraint conditions. The UKF-based WSN node location method includes combining the MLE (maximum likelihood estimation) method and the constraint conditions to primarily locate, and correcting the MLE computation by the aid of the constraint conditions and a front moment of two adjacent moments of an unknown node so as to acquire a novel initial coordinate value; regarding the unknown node coordinate as a system state variable, regarding RSSI (received signal strength indicator) as observed quantity, establishing a state equation and an observation equation of a location system based on the standard UKF algorithm, and performing accurate location. Compared with the traditional node location algorithm and the EKF (extended Kalman filter) algorithm, the UKF-based WSN node location method has the advantages that node location precision is improved, the constraint conditions are introduced so that robustness and convergence of filtering are strengthened, and important practical value is achieved.

Description

The WSN node positioning method of the UKF with Prescribed Properties

Technical field

The present invention relates to a kind of node self-localization method for wireless sensor network field, specifically the WSN node positioning method of a kind of UKF with Prescribed Properties.

Background technology

Due to the development of the technology such as micro electro mechanical system (MEMS) technology, wireless communication technology and Digital Electronic Technique, facilitate generation and the high speed development of wireless sensor network (WSN).Wireless sensor network, as an emerging network, changes the interactive mode between man and nature circle, " fourth industrial revolution " of IT field of being known as.1999, wireless sensor network was classified as one of 21 century most important 21 technology by the Business Week magazine of the U.S..2003, wireless sensor network was classified as first of the ten large emerging technologies in the change world by " technology review ", and the same year, Business Week was chosen as one of following four large high-tech industries in the whole world.The various ability possessed due to wireless sensor network and advantage, domestic and international many countries have all dropped into the investigation and application of a large amount of human and material resources and financial support wireless sensor network.In recent years, the input that China continues at many levels such as National Nature fund, 863 Program, 973 plans and national science and technology key special subjects, accelerate the fast development of China's wireless sensor network investigation and application each side, research is expanded from military field to civil area, and progressively achieves industrialization.Wireless sensor network has now been widely used in the fields such as national defense and military, perception medical treatment, traffic management and space exploration.

Node locating technique, as one of the important key technology of wireless sensor network, not only effectively can improve the router efficiency of network, can also realize managing whole network.And in numerous applications, the locating information of network node is the prerequisite of further investigation and application and basis, has important practical significance so realize node self-localization.

The classification that node locating algorithm is conventional is: based on the location algorithm of range finding and the location algorithm without the need to range finding.Location algorithm without the need to range finding only realizes the location to unknown node according to the degree of communication of network, and main method has: centroid localization algorithm, DV-Hop location algorithm, APIT location algorithm, convex programming location algorithm and MDS-MAP location algorithm etc.Location algorithm based on range finding mainly contains range finding, node locating and coordinate modification three phases composition.Conventional technology of wherein finding range has: RSSI, TOA, TDOA and AOA tetra-kinds; The conventional method of node locating has: triangulation, trilateration, Maximum Likelihood Estimation Method and Minimax Estimation method.Because node locating algorithm model has non-linearity, often adopt nonlinear filtering technique to revise coordinate, conventional has EKF (EKF) and particle filter.And adopt the low order item in taylor series expansion to be similar to the error replacing non linear system to produce for EKF algorithm, not only reduce positioning precision, but also likely cause filter divergence.Meanwhile, EKF and derivative algorithm is inevasible all will calculate Jacobian matrix, for often calculation of complex and difficult non linear system.In order to improve the problems referred to above, a kind of UKF nonlinear filtering algorithm based on Unscented transform that the people such as Julier propose, this algorithm is without the need to calculating Jacobian matrix, and filtering estimates to have higher precision.Although some problems that UKF filtering algorithm exists EKF have had very large improvement, but UKF is also the nonlinear filtering algorithm based on Kalman filtering, still also exists and to cause by the impact of the uncertain factor such as model error, Noise and Interference the precision of algorithm to reduce and convergence rate is slack-off etc. asks.Meanwhile, UKF algorithm exists the highstrung problem of initial value, and initial value fluctuation can badly influence the performance of filtering algorithm, even likely causes filter divergence.Given this reason, the present invention is directed to based on UKF location algorithm to initial value sensitive issue, propose a kind of node locating algorithm of Problem with Some Constrained Conditions.

Summary of the invention

Invention will solve RSSI to be affected by disturbing factor various in environment and makes its value distortion result that is large, that cause range finding stage and node locating stage to obtain have larger error and the shortcoming of fluctuation, constraints is introduced in the node locating stage, a kind of positioning precision is proposed high, fast convergence rate, the node positioning method of strong robustness.

The WSN node positioning method of the UKF of Problem with Some Constrained Conditions of the present invention, its job step is:

Step 1. model of finding range has theoretical model and empirical model two kinds, range finding model in the present invention adopts the logarithm-normal distribution model in theoretical model, use gaussian filtering technology and curve fitting technique to carry out processing the unknown parameter in Confirming model to the data of testing acquisition in experimental situation, set up the relation between RSSI and distance.

Step 2. uses range finding model that RSSI is converted to distance value.With reference to shown in accompanying drawing 2, MLE method is used to try to achieve coordinate P _mLE, coordinate figure is (x _mLE, y _mLE); If the coordinate of previous moment is P in unknown node adjacent two moment ₀, coordinate figure is (x ₀, y ₀); Take R as radius, P ₀for the center of circle, make a restrained circle; Choose two beaconing nodes maximum in current time RSSI value and be set to A and B, its coordinate is respectively (x ₁, y ₁) and (x ₂, y ₂); Make straight line AP ₀and BP ₀, be respectively M and N with the intersection point of restrained circle, then fan-shaped MP ₀n forms a coordinates restriction region.The coordinate figure using formula below to obtain M and N is respectively (x _m, y _m) and (x _n, y _n).

$\left\{\begin{array}{c}(x-x_0)=k(y-y_0)\\ {(x-x_0)}^2+{(y-y_0)}^2=R^2\end{array}\right.$

In formula: k is the slope value of straight line.

With M, P _mLE, N, P ₀4 form a quadrangle for summit, and the center-of-mass coordinate of trying to achieve quadrangle is the coordinate (x', y') of initial alignment gained.

$x^{\′}=\frac{1}{4}(x_0+x_M+x_{\mathrm{MLE}}+x_N)$

$y^{\′}=\frac{1}{4}(y_0+y_M+y_{\mathrm{MLE}}+y_N)$

Step 3., using the coordinate of unknown node as the state variable of system, by RSSI value as measured value, with model of finding range for observational equation, sets up self adaptation UKF filtering system.

3.1 state equations:

X _k+1＝f(X _k)+w _k＝AX _k+w _k

In formula: f () is nonlinear function, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ For state-transition matrix, X _k=[x _k, y _k] ^Τrepresent the system mode stochastic variable in kth moment, w _kfor systematic procedure noise, its average is zero, and covariance is Q _k.

3.2 observational equations:

Y _k,i＝h(X _k)+v _k＝P _r(d _k,i)

P _r(d _k,i)＝P _r(d ₀)-10·θ·log(d _k,i)+v

In formula: h () is nonlinear function, represent the distance between unknown node and i-th beaconing nodes, P _r(d _k,i) be the reception RSSI value of i-th beaconing nodes, P _r(d ₀) be d ₀reception RSSI value during=1m, Y _kfor the reception RSSI value of systematic perspective measurement and beaconing nodes, v _kfor observation noise, covariance is R _k, θ is path-loss factor.

Step 4. standard UKF algorithm realization:

4.1 initialization:

$\left\{\begin{array}{c}{\hat{X}}_0=E\left[X_0\right]\\ P_0=E\left[(X_0-{\hat{X}}_0){(X_0-{\hat{X}}_0)}^T\right]\end{array}\right.$

4.2 sampling points calculate:

$\left\{\begin{array}{cc}{\mathrm{\χ}}_{k-1}^{\left(0\right)}={\hat{X}}_{k-1}& \\ {\mathrm{\χ}}_{k-1}^{\left(i\right)}={\hat{X}}_{k-1}+\sqrt{(L+\mathrm{\λ})}{\left(\sqrt{P_{k-1}}\right)}_{\left(i\right)}& i=\mathrm{1,2},...,L\\ {\mathrm{\χ}}_{k-1}^{\left(i\right)}={\hat{X}}_{k-1}-\sqrt{(L+\mathrm{\λ})}{\left(\sqrt{P_{k-1}}\right)}_{(i-L)}& i=L+1,L+2,...,2L\end{array}\right.$

4.3 times upgraded:

${\mathrm{\χ}}_{k|k-1}^x=f\left({\mathrm{\χ}}_{k-1}^x\right)$

${\hat{X}}_{k|k-1}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(m\right)}{\mathrm{\χ}}_{i,k|k-1}^x$

${\hat{P}}_{k|k-1}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(c\right)}{[{\mathrm{\χ}}_{i,k|k-1}^x-{\hat{X}}_{k|k-1}][{\mathrm{\χ}}_{i,k|k-1}^x-{\hat{X}}_{k|k-1}]}^T+Q_{k-1}$

4.4 measure renewal:

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1}$

${\hat{X}}_k={\hat{X}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1})$

$P_k={\hat{P}}_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T$

In formula: ${\mathrm{\ω}}_0^m=\frac{\mathrm{\λ}}{(L+\mathrm{\λ})},{\mathrm{\ω}}_0^c=\frac{\mathrm{\λ}}{(L+\mathrm{\λ})}+(L-{\mathrm{\α}}^2+\mathrm{\β}),{\mathrm{\ω}}_i^m={\mathrm{\ω}}_i^c=\frac{\mathrm{\λ}}{2(L+\mathrm{\λ})},$ I=1,2 ...., 2L, α are normal number, and β represents the distributed intelligence of sample point, and κ is the parameter of weight distribution, and L is the dimension of stochastic variable X, be respectively the weight coefficient of average corresponding to i-th sample point and variance statistic characteristic.X ₀for the initial value of system stochastic variable, i.e. the result of step 2 gained, P ₀for covariance initial value, for the sample point set in k-1 moment, for conversion point set, for a step look-ahead value of stochastic variable, for a step look-ahead value of observed quantity, Y _kfor the systematic perspective in k moment is measured, be a step look-ahead covariance matrix, with for covariance matrix, P _kfor the covariance matrix value in k moment, K _kfor the filter gain value in k moment, for the stochastic variable estimated value in k moment, i.e. required node coordinate value.

Advantage of the present invention and beneficial effect:

The present invention, on the basis of logarithm-normal distribution model and standard UKF algorithm, puts forward a kind of WSN node locating algorithm of belt restraining.Node locating of the present invention is made up of initial alignment and accurate location two parts, in initial alignment, the basis of traditional MLE algorithm introduces constraint link, improve the result precision of initial alignment, enhance stability, the better fluctuation improving initial alignment coordinate simultaneously.Adopt UKF algorithm simultaneously, compare and only use traditional trilateration, triangulation and MLE method, and EKF algorithm, not only increase precision, but also add convergence rate, real-time grow.Therefore, location algorithm proposed by the invention has better using value.

Accompanying drawing explanation

Fig. 1 is flow chart of the present invention.

Fig. 2 is constraint principles figure of the present invention.

Fig. 3 is the node locating Error Graph not using constraints.

Fig. 4 is the node locating Error Graph using constraints.

Embodiment

With reference to accompanying drawing:

The WSN node positioning method of the UKF of Problem with Some Constrained Conditions of the present invention, its job step is:

Step 1. model of finding range has theoretical model and empirical model two kinds, range finding model in the present invention adopts the logarithm-normal distribution model in theoretical model, use gaussian filtering technology and curve fitting technique to carry out processing the unknown parameter in Confirming model to the data of testing acquisition in experimental situation, set up the relation between RSSI and distance.

Step 2. uses range finding model that RSSI is converted to distance value.With reference to shown in accompanying drawing 2, MLE method is used to try to achieve coordinate P _mLE, coordinate figure is (x _mLE, y _mLE); If the coordinate of previous moment is P in unknown node adjacent two moment ₀, coordinate figure is (x ₀, y ₀); Take R as radius, P ₀for the center of circle, make a restrained circle; Choose two beaconing nodes maximum in current time RSSI value and be set to A and B, its coordinate is respectively (x ₁, y ₁) and (x ₂, y ₂); Make straight line AP ₀and BP ₀, be respectively M and N with the intersection point of restrained circle, then fan-shaped MP ₀n forms a coordinates restriction region.The coordinate figure using formula below to obtain M and N is respectively (x _m, y _m) and (x _n, y _n).

$\left\{\begin{array}{c}(x-x_0)=k(y-y_0)\\ {(x-x_0)}^2+{(y-y_0)}^2=R^2\end{array}\right.$

In formula: k is the slope value of straight line.

With M, P _mLE, N, P ₀4 form a quadrangle for summit, and the center-of-mass coordinate of trying to achieve quadrangle is the coordinate (x', y') of initial alignment gained.

$x^{\′}=\frac{1}{4}(x_0+x_M+x_{\mathrm{MLE}}+x_N)$

$y^{\′}=\frac{1}{4}(y_0+y_M+y_{\mathrm{MLE}}+y_N)$

Step 3., using the coordinate of unknown node as the state variable of system, by RSSI value as measured value, with model of finding range for observational equation, sets up self adaptation UKF filtering system.

3.1 state equations:

X _k+1＝f(X _k)+w _k＝AX _k+w _k

In formula: f () is nonlinear function, $A=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$ For state-transition matrix, X _k=[x _k, y _k] ^Τrepresent the system mode stochastic variable in kth moment, w _kfor systematic procedure noise, its average is zero, and covariance is Q _k.

3.2 observational equations:

Y _k,i＝h(X _k)+v _k＝P _r(d _k,i)

P _r(d _k,i)＝P _r(d ₀)-10·θ·log(d _k,i)+v

In formula: h () is nonlinear function, represent the distance between unknown node and i-th beaconing nodes, P _r(d _k,i) be the reception RSSI value of i-th beaconing nodes, P _r(d ₀) be d ₀reception RSSI value during=1m, Y _kfor the reception RSSI value of systematic perspective measurement and beaconing nodes, v _kfor observation noise, covariance is R _k, θ is path-loss factor.

Step 4. standard UKF algorithm realization:

4.1 initialization:

$\left\{\begin{array}{c}{\hat{X}}_0=E\left[X_0\right]\\ P_0=E\left[(X_0-{\hat{X}}_0){(X_0-{\hat{X}}_0)}^T\right]\end{array}\right.$

4.2 sampling points calculate:

$\left\{\begin{array}{cc}{\mathrm{\χ}}_{k-1}^{\left(0\right)}={\hat{X}}_{k-1}& \\ {\mathrm{\χ}}_{k-1}^{\left(i\right)}={\hat{X}}_{k-1}+\sqrt{(L+\mathrm{\λ})}{\left(\sqrt{P_{k-1}}\right)}_{\left(i\right)}& i=\mathrm{1,2},...,L\\ {\mathrm{\χ}}_{k-1}^{\left(i\right)}={\hat{X}}_{k-1}-\sqrt{(L+\mathrm{\λ})}{\left(\sqrt{P_{k-1}}\right)}_{(i-L)}& i=L+1,L+2,...,2L\end{array}\right.$

4.3 times upgraded:

${\mathrm{\χ}}_{k|k-1}^x=f\left({\mathrm{\χ}}_{k-1}^x\right)$

${\hat{X}}_{k|k-1}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(m\right)}{\mathrm{\χ}}_{i,k|k-1}^x$

${\hat{P}}_{k|k-1}=\underset{i=0}{\overset{2L}{\mathrm{\Σ}}}{\mathrm{\ω}}_i^{\left(c\right)}{[{\mathrm{\χ}}_{i,k|k-1}^x-{\hat{X}}_{k|k-1}][{\mathrm{\χ}}_{i,k|k-1}^x-{\hat{X}}_{k|k-1}]}^T+Q_{k-1}$

4.4 measure renewal:

$K_k=P_{x_k{y}_k}{P}_{y_k{y}_k}^{-1}$

${\hat{X}}_k={\hat{X}}_{k|k-1}+K_k(Y_k-{\hat{Y}}_{k|k-1})$

$P_k={\hat{P}}_{k|k-1}-K_k{P}_{y_k{y}_k}{K}_k^T$

In formula: ${\mathrm{\ω}}_0^m=\frac{\mathrm{\λ}}{(L+\mathrm{\λ})},{\mathrm{\ω}}_0^c=\frac{\mathrm{\λ}}{(L+\mathrm{\λ})}+(L-{\mathrm{\α}}^2+\mathrm{\β}),{\mathrm{\ω}}_i^m={\mathrm{\ω}}_i^c=\frac{\mathrm{\λ}}{2(L+\mathrm{\λ})},$ I=1,2 ...., 2L, α are normal number, and β represents the distributed intelligence of sample point, and κ is the parameter of weight distribution, and L is the dimension of stochastic variable X, be respectively the weight coefficient of average corresponding to i-th sample point and variance statistic characteristic.X ₀for the initial value of system stochastic variable, i.e. the result of step 2 gained, P ₀for covariance initial value, for the sample point set in k-1 moment, for conversion point set, for a step look-ahead value of stochastic variable, for a step look-ahead value of observed quantity, Y _kfor the systematic perspective in k moment is measured, be a step look-ahead covariance matrix, with for covariance matrix, P _kfor the covariance matrix value in k moment, K _kfor the filter gain value in k moment, for the stochastic variable estimated value in k moment, i.e. required node coordinate value.

For example, referring to accompanying drawing 1:

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

1. in Experimental Area, build experiment porch, carry out actual experiment test, obtain the RSSI value under the different known distance of many groups, on MATLAB platform, gaussian filtering process is carried out to the RSSI data obtained, determine the RSSI relation after the optimization that distance is corresponding with it, adopt least square fitting RSSI-distance Curve, determine the unknown parameter of finding range in model, acquisition parameter value is θ=2.2, P _r(d ₀)=-41.

2. arrange 3 beaconing nodes the rectangular area edge of 30 meters × 20 meters.Beaconing nodes coordinate is respectively: (30,0), (14,20), (0,8), and random arrangement 1 unknown node in region, carries out node locating experiment simultaneously.

3. RSSI is converted as distance value through range finding model, use Maximum Likelihood Estimation Method to obtain coordinate (x _mLE, y _mLE), then try to achieve a M according to Restricted operator principle and put the coordinate (x of N _m, y _m) and (x _n, y _n), try to achieve node initial alignment coordinate (x', y') after Restricted operator.

$x^{\′}=\frac{1}{4}(x_0+x_M+x_{\mathrm{MLE}}+x_N),y^{\′}=\frac{1}{4}(y_0+y_M+y_{\mathrm{MLE}}+y_N)$

4. set up the state equation based on the node positioning system of UKF algorithm and observational equation, directly adopt RSSI as the observed quantity Y of observational equation _k, parameter L=2, α=0.01, κ=0, β=2, Q in UKF equation are set _k=diag ([0.4,0.4]), R _k=diag ([0.01,0.01,0.01]), operative norm UKF equation, can obtain state estimation with covariance P _k.The constraints do not used and use constraints location algorithm are distinguished iteration 100 times on MATLAB, and the node locating error simulated effect obtained respectively as shown in Figure 3 and Figure 4.Contrast can find, use the location algorithm of constraints not only precision to be significantly improved, and the fluctuation of position error has had weakening to a great extent, further illustrates the good performance that the present invention has.

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 being only limitted to the concrete form that embodiment is stated, protection scope of the present invention also and conceive the equivalent technologies means that can expect according to the present invention in those skilled in the art.

Claims (1)

1. the WSN node positioning method of the UKF of Problem with Some Constrained Conditions, its job step is:

1) model of finding range has theoretical model and empirical model two kinds, range finding model adopts the logarithm-normal distribution model in theoretical model, use gaussian filtering technology and curve fitting technique to carry out processing the unknown parameter in Confirming model to the data of testing acquisition in experimental situation, set up the relation between RSSI and distance;

2) use range finding model that RSSI is converted to distance value; MLE method is used to try to achieve coordinate P _mLE, coordinate figure is (x _mLE, y _mLE); If the coordinate of previous moment is P in unknown node adjacent two moment ₀, coordinate figure is (x ₀, y ₀); Take R as radius, P ₀for the center of circle, make a restrained circle; Choose two beaconing nodes maximum in current time RSSI value and be set to A and B, its coordinate is respectively (x ₁, y ₁) and (x ₂, y ₂); Make straight line AP ₀and BP ₀, be respectively M and N with the intersection point of restrained circle, then fan-shaped MP ₀n forms a coordinates restriction region; The coordinate figure using formula below to obtain M and N is respectively (x _m, y _m) and (x _n, y _n);

In formula: k is the slope value of straight line;

With M, P _mLE, N, P ₀4 form a quadrangle for summit, and the center-of-mass coordinate of trying to achieve quadrangle is the coordinate (x', y') of initial alignment gained;

3) using the coordinate of unknown node as the state variable of system, by RSSI value as measured value, with model of finding range for observational equation, self adaptation UKF filtering system is set up;

3.1) state equation:

X _k+1＝f(X _k)+w _k＝AX _k+w _k

In formula: f () is nonlinear function, for state-transition matrix, X _k=[x _k, y _k] ^Τrepresent the system mode stochastic variable in kth moment, w _kfor systematic procedure noise, its average is zero, and covariance is Q _k.

3.2) observational equation:

Y _k,i＝h(X _k)+v _k＝P _r(d _k,i)

In formula: h () is nonlinear function, represent the distance between unknown node and i-th beaconing nodes, P _r(d _k,i) be the reception RSSI value of i-th beaconing nodes, P _r(d ₀) be d ₀reception RSSI value during=1m, Y _kfor the reception RSSI value of systematic perspective measurement and beaconing nodes, v _kfor observation noise, covariance is R _k, for path-loss factor.

4) standard UKF algorithm realization:

4.1) initialization:

4.2) sampling point calculates:

4.3) time upgrades:

4.4) renewal is measured:

In formula: λ=α ²(L-κ)-L, i=1,2 ...., 2L, α are normal number, and β represents the distributed intelligence of sample point, and κ is the parameter of weight distribution, and L is the dimension of stochastic variable X, be respectively the weight coefficient of average corresponding to i-th sample point and variance statistic characteristic; X ₀for the initial value of system stochastic variable, i.e. the result of step 2 gained, P ₀for covariance initial value, for the sample point set in k-1 moment, Y _k|k-1for conversion point set, for a step look-ahead value of stochastic variable, for a step look-ahead value of observed quantity, Y _kfor the systematic perspective in k moment is measured, be a step look-ahead covariance matrix, with for covariance matrix, P _kfor the covariance matrix value in k moment, K _kfor the filter gain value in k moment, for the stochastic variable estimated value in k moment, i.e. required node coordinate value.