CN104363649B - The WSN node positioning methods of UKF with Prescribed Properties - Google Patents
The WSN node positioning methods of UKF with Prescribed Properties Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
- H04W64/006—Locating users or terminals or network equipment for network management purposes, e.g. mobility management with additional information processing, e.g. for direction or speed determination
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0252—Radio frequency fingerprinting
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W84/00—Network topologies
- H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks
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Abstract
A kind of UKF of Problem with Some Constrained Conditions WSN node positioning methods.First, Maximum Likelihood Estimation Method is combined into progress Primary Location with constraints, be modified using the coordinate pair MLE result of calculations of previous moment in constraints and unknown node adjacent two moment, obtain new initial coordinate values.Secondly, using unknown node coordinate as system state variables, RSSI is observed quantity, sets up the state equation and observational equation of the alignment system based on standard UKF algorithms, is accurately positioned.Compared to traditional node locating algorithm and EKF algorithms, node locating precision is not only increased, and introduces constraint, the robustness and convergence of filtering are enhanced, with very important practical value.
Description
Technical field
It is specifically a kind of carry about the present invention relates to a kind of node self-localization method for wireless sensor network field
The UKF of beam condition WSN node positioning methods.
Background technology
Due to the development of the technologies such as micro electro mechanical system (MEMS) technology, wireless communication technology and Digital Electronic Technique, promote wireless
The generation of sensor network (WSN) and high speed development.Wireless sensor network changes people and oneself as an emerging network
Interactive mode between right boundary, " fourth industrial revolution " of IT field of being known as.1999, the U.S.《Business Weekly》It is miscellaneous
Wireless sensor network is classified as one of 21 century most important 21 technologies by will.2003,《Technology review》By wireless sensing
Device network is classified as first of the ten big emerging technologies for changing the world, the same year《Business Weekly》It is chosen as global following four big high-tech
One of industry.By various abilities and advantage that wireless sensor network possesses, domestic and international many countries have all put into largely
Human and material resources and financial support wireless sensor network research and application.In recent years, China is in National Nature fund, 863
The lasting inputs of many levels such as plan, 973 plans and national science and technology key special subjects, accelerate China's wireless sensor network and grind
Study carefully and using the fast development of each side, research extends from military field to civil area, and industrialization has been done step-by-step.Wirelessly
Sensor network has been widely used in national defense and military, has perceived the fields such as medical treatment, traffic management and space exploration.
Node locating technique can not only effectively improve network as one of important key technology of wireless sensor network
Router efficiency, management whole network can also be realized.And in numerous applications, the location information of network node is further
The premise of research and application and basis, it is achieved that node self-localization has important practical significance.
The conventional classification of node locating algorithm is：Location algorithm based on ranging and the location algorithm without ranging.Need not
The location algorithm of ranging realizes the positioning to unknown node according only to the degree of communication of network, and main method has：Center coordination is calculated
Method, DV-Hop location algorithms, APIT location algorithms, convex programming location algorithm and MDS-MAP location algorithms etc..Determining based on ranging
Position algorithm is mainly made up of ranging, node locating and coordinate modification three phases.The wherein conventional technology of ranging has：RSSI、
Tetra- kinds of TOA, TDOA and AOA；The conventional method of node locating has：Triangulation, trilateration, Maximum Likelihood Estimation Method and
Minimax Estimation method.Because node locating algorithm model has non-linear property, often using nonlinear filtering technique to coordinate
It is modified, conventional has EKF (EKF) and particle filter.And use Taylor series expansion for EKF algorithms
Low order in formula time item approximately replaces the error produced by nonlinear system, not only reduces positioning precision, and it is also possible to
Cause filter divergence.Meanwhile, EKF and its derivative algorithm is inevasible will calculate Jacobian matrix, for non-linear
Often calculated for system complicated and difficult.In order to improve above mentioned problem, one kind that Julier et al. is proposed is based on Unscented transform
UKF nonlinear filtering algorithms, the algorithm need not calculate Jacobian matrix, and filtering estimation has higher precision.Although UKF
Filtering algorithm has very big improvement to some problems that EKF is present, but UKF is also non-linear based on Kalman filtering
Filtering algorithm, causes the precision of algorithm to reduce there are still being influenceed by uncertain factors such as model error, noise and interference
With convergence rate is slack-off etc. asks.Meanwhile, the problem of UKF algorithms have very sensitive to initial value, initial value fluctuation can serious shadow
The performance to filtering algorithm is rung, it could even be possible to causing filter divergence.Given this reason, of the invention to be directed to determining based on UKF
Position algorithm to initial value sensitive issue, it is proposed that a kind of node locating algorithm of Problem with Some Constrained Conditions.
The content of the invention
Invention will solve RSSI is influenceed to make that its value distortion is big, cause ranging stage and node by various disturbing factors in environment
The result that positioning stage is obtained has the shortcomings that larger error and fluctuation, introduces constraints in the node locating stage, carries
Go out a kind of positioning precision high, fast convergence rate, the node positioning method of strong robustness.
The UKF of Problem with Some Constrained Conditions of the present invention WSN node positioning methods, its job step is：
Step 1. ranging model has the ranging model in two kinds of theoretical model and empirical model, the present invention to use theoretical model
In logarithm-normal distribution model, using gaussian filtering technology and curve fitting technique to testing the number of acquisition in experimental situation
According to the unknown parameter carried out in processing determination model, RSSI and the relation between are set up.
RSSI is converted to distance value by step 2. using ranging model.Referring to the drawings shown in 2, coordinate is tried to achieve using MLE methods
PMLE, coordinate value is (xMLE,yMLE)；If the coordinate of previous moment is P in unknown node adjacent two moment0, coordinate value is (x0,
y0)；Using R as radius, P0For 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 (x1,y1) and (x2,y2)；Make straight line AP0And BP0, the intersection point with restrained circle is respectively M and N, then fan-shaped
MP0N constitutes a coordinates restriction region, and the coordinate value for obtaining point M and N respectively using formula below is (xM,yM) and (xN,yN)。
In formula：K is the slope value of straight line.
With M, PMLE、N、P04 points are that summit constitutes a quadrangle, try to achieve the center-of-mass coordinate as initial alignment of quadrangle
The coordinate (x', y') of gained.
State variable of the step 3. using the coordinate of unknown node as system, with RSSI value as observation, with ranging mould
Type is observational equation, sets up adaptive UKF filtering systems.
3.1 state equation：
Xk+1=f (Xk)+wk=AXk+wk
In formula：F () is nonlinear function,For state-transition matrix, Xk=[xk,yk]ΤRepresent the kth moment
System mode stochastic variable, wkFor systematic procedure noise, its average is zero, and covariance is Qk。
3.2 observational equation：
Yk,i=h (Xk)+vk=Pr(dk,i)
In formula：H () is nonlinear function,Represent unknown node and i-th of beacon
The distance between node, Pr(dk,i) for the reception RSSI value of i-th beaconing nodes, Pr(d0) it is d0Reception RSSI during=1m
Value, Yk,iIt is the reception RSSI value of beaconing nodes, v for systematic perspective measurementkFor observation noise, covariance is Rk,For path loss
The factor.
Step 4. standard UKF algorithms are realized：
4.1 initialization：
4.2 sampling points are calculated：
4.3 times updated：
4.4 measure renewal：
In formula：λ=α2
(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 that weight is distributed,
L is stochastic variable X dimension,The power system of average and variance statistic characteristic corresponding to respectively i-th sample point
Number.X0For the initial value of system stochastic variable, i.e. step 2) obtained by result, P0For covariance initial value,For the k-1 moment
Sample point set, Yi,k|k-1To convert point set,For a step look-ahead value of stochastic variable,For a step of observed quantity
Look-ahead value, YkMeasured for the systematic perspective at k moment,For a step look-ahead covariance matrix,WithFor association side
Poor matrix, PkFor the covariance matrix value at k moment, KkFor the filtering gain value at k moment,For the stochastic variable at k moment
Estimate, i.e., required node coordinate value.
The advantages of the present invention：
The present invention puts forward a kind of WSN of belt restraining on the basis of logarithm-normal distribution model and standard UKF algorithms
Node locating algorithm.Node locating of the present invention is by initial alignment and is accurately positioned two parts and constitutes, in initial alignment, in tradition
MLE algorithms on the basis of introduce constraint link, improve the result precision of initial alignment, while enhance stability, compared with
Having got well improves the fluctuation of initial alignment coordinate.UKF algorithms are used simultaneously, compared to using only traditional trilateration, three
Angle and MLE methods, and EKF algorithms, not only increase precision, and also add convergence rate, and real-time becomes strong.Cause
This, location algorithm proposed by the invention has more preferable application value.
Brief description of the drawings
Fig. 1 is flow chart of the present invention.
Fig. 2 is constraint principles figure of the invention.
Fig. 3 is the node locating Error Graph that constraints is not used.
Fig. 4 is the node locating Error Graph using constraints.
Embodiment
Referring to the drawings：
The UKF of Problem with Some Constrained Conditions of the present invention WSN node positioning methods, its job step is：
Step 1. ranging model has the ranging model in two kinds of theoretical model and empirical model, the present invention to use theoretical model
In logarithm-normal distribution model, using gaussian filtering technology and curve fitting technique to testing the number of acquisition in experimental situation
According to the unknown parameter carried out in processing determination model, RSSI and the relation between are set up.
RSSI is converted to distance value by step 2. using ranging model.Referring to the drawings shown in 2, coordinate is tried to achieve using MLE methods
PMLE, coordinate value is (xMLE,yMLE)；If the coordinate of previous moment is P in unknown node adjacent two moment0, coordinate value is (x0,
y0)；Using R as radius, P0For 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 (x1,y1) and (x2,y2)；Make straight line AP0And BP0, the intersection point with restrained circle is respectively M and N, then fan-shaped
MP0N constitutes a coordinates restriction region, and the coordinate value for obtaining point M and N respectively using formula below is (xM,yM) and (xN,yN)。
In formula：K is the inverse of the slope value of straight line.
With M, PMLE、N、P04 points are that summit constitutes a quadrangle, try to achieve the center-of-mass coordinate as initial alignment of quadrangle
The coordinate (x', y') of gained.
State variable of the step 3. using the coordinate of unknown node as system, with RSSI value as observation, with ranging mould
Type is observational equation, sets up adaptive UKF filtering systems.
3.1 state equation：
Xk+1=f (Xk)+wk=AXk+wk
In formula：F () is nonlinear function,For state-transition matrix, Xk=[xk,yk]ΤRepresent the kth moment
System mode stochastic variable, wkFor systematic procedure noise, its average is zero, and covariance is Qk。
3.2 observational equation：
Yk,i=h (Xk)+vk=Pr(dk,i)
In formula：H () is nonlinear function,Represent unknown node and i-th of beacon
The distance between node, Pr(dk,i) for the reception RSSI value of i-th beaconing nodes, Pr(d0) it is d0Reception RSSI during=1m
Value, Yk,iIt is the reception RSSI value of beaconing nodes, v for systematic perspective measurementkFor observation noise, covariance is Rk,For path loss
The factor.
Step 4. standard UKF algorithms are realized：
4.1 initialization：
4.2 sampling points are calculated：
4.3 times updated：
4.4 measure renewal：
In formula：λ=α2
(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 that weight is distributed,
L is stochastic variable X dimension,The power system of average and variance statistic characteristic corresponding to respectively i-th sample point
Number.X0For the initial value of system stochastic variable, i.e. step 2) obtained by result, P0For covariance initial value,For the k-1 moment
Sample point set, Yi,k|k-1To convert point set,For a step look-ahead value of stochastic variable,For a step of observed quantity
Look-ahead value, YkMeasured for the systematic perspective at k moment,For a step look-ahead covariance matrix,WithFor association side
Poor matrix, PkFor the covariance matrix value at k moment, KkFor the filtering gain value at k moment,For the stochastic variable at k moment
Estimate, i.e., required node coordinate value.
For example, referring to accompanying drawing 1：
It is determined that after localization method, proposing the technical solution adopted for the present invention to solve the technical problems：
1. building experiment porch in Experimental Area, actual experiment test is carried out, is obtained under multigroup different known distances
RSSI value, the RSSI data to acquisition carry out gaussian filtering process on MATLAB platforms, it is determined that apart from corresponding optimization
RSSI relations afterwards, using least square fitting RSSI- distance Curves, determine the unknown parameter in ranging model, are joined
Numerical value isPr(d0)=- 41.
2. arrange 3 beaconing nodes one 30 meters × 20 meters of rectangular area edges.Beaconing nodes coordinate is respectively：
(30,0), (14,20), (0,8), while 1 unknown node of arrangement at random in region, carries out node locating experiment.
3. it is distance value that RSSI is converted by ranging model, Maximum Likelihood Estimation Method is used to obtain coordinate (xMLE,yMLE),
Point M and point N coordinate (x are tried to achieve further according to Restricted operator principleM,yM) and (xN,yN), try to achieve the node after Restricted operator
Initial alignment coordinate (x', y').
4. setting up the state equation and observational equation of the node positioning system based on UKF algorithms, RSSI conducts are directly used
The observed quantity Y of observational equationk, parameter L=2, α=0.01, κ=0, β=2, Q in UKF equations are setk=diag ([0.4,
0.4]), Rk=diag ([0.01,0.01,0.01]), performs standard UKF equations, you can obtain state estimationAnd covariance
Pk.By without using constraints and using constraints location algorithm iteration 100 times, obtained node are distinguished on MATLAB
Positioning Error Simulation effect difference is as shown in Figure 3 and Figure 4.Contrast is it can be found that not only smart using the location algorithm of constraints
It is significantly improved on degree, and the fluctuation of position error has decrease largely, further illustrates this hair
The bright good performance having.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Scope is not construed as being only limitted to the concrete form that embodiment is stated, protection scope of the present invention is also and in art technology
Personnel according to present inventive concept it is conceivable that equivalent technologies mean.
Claims (1)
1. a kind of UKF of Problem with Some Constrained Conditions WSN node positioning methods, UKF is Unscented kalman filtering, and WSN is wireless sensing
Device network, its job step is：
1) ranging model has two kinds of theoretical model and empirical model, and ranging model uses logarithm-normal distribution in theoretical model
The data that acquisition is tested in experimental situation are carried out processing using gaussian filtering technology and curve fitting technique and determine model by model
In unknown parameter, set up the signal intensity received and indicate RSSI and the relation between；
2) RSSI is converted into distance value using ranging model；Coordinate P is tried to achieve using Maximum-likelihood estimation MLE methodsMLE, coordinate value
For (xMLE,yMLE)；If the coordinate of previous moment is P in unknown node adjacent two moment0, coordinate value is (x0,y0)；Using R as half
Footpath, P0For 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
Respectively (x1,y1) and (x2,y2)；Make straight line AP0And BP0, the intersection point with restrained circle is respectively M and N, then sector MP0N constitutes one
Individual coordinates restriction region；The coordinate value for obtaining point M and N respectively using formula below is (xM,yM) and (xN,yN)；
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In formula：K is the slope value of straight line；
With M, PMLE、N、P04 points are that summit constitutes a quadrangle, and the center-of-mass coordinate for trying to achieve quadrangle is obtained by initial alignment
Coordinate (x', y')；
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3) using the coordinate of unknown node as the state variable of system, with RSSI value as observation, using ranging model as observation
Equation, sets up adaptive UKF filtering systems；
3.1) state equation：
Xk+1=f (Xk)+wk=AXk+wk
In formula：F () is nonlinear function,For state-transition matrix, Xk=[xk,yk]ΤRepresent that kth moment is
System state stochastic variable, wkFor systematic procedure noise, its average is zero, and covariance is Qk；
3.2) observational equation：
Yk,i=h (Xk)+vk=Pr(dk,i)
Pr(dk,i)=Pr(d0)-10·θ·log(dk,i)+vk
In formula：H () is nonlinear function,Represent unknown node and i-th beaconing nodes it
Between distance, Pr(dk,i) for the reception RSSI value of i-th beaconing nodes, Pr(d0) it is d0Reception RSSI value during=1m, Yk,iFor
Systematic perspective measurement is the reception RSSI value of beaconing nodes, vkFor observation noise, covariance is Rk, θ is path-loss factor；
4) standard UKF algorithms are realized：
4.1) initialize：
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4.2) sampling point is calculated：
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<mo>)</mo>
</mrow>
</msub>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mi>L</mi>
<mo>+</mo>
<mn>1</mn>
<mo>,</mo>
<mi>L</mi>
<mo>+</mo>
<mn>2</mn>
<mo>,</mo>
<mn>...</mn>
<mo>,</mo>
<mn>2</mn>
<mi>L</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
4.3) time updates：
<mrow>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>L</mi>
</mrow>
</munderover>
<msubsup>
<mi>&omega;</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>)</mo>
</mrow>
</msubsup>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
</mrow>
<mrow>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>L</mi>
</mrow>
</munderover>
<msubsup>
<mi>&omega;</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>&lsqb;</mo>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>+</mo>
<msub>
<mi>Q</mi>
<mrow>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
<mrow>
<msub>
<mi>Y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<mi>h</mi>
<mrow>
<mo>(</mo>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mover>
<mi>Y</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>L</mi>
</mrow>
</munderover>
<msubsup>
<mi>&omega;</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>m</mi>
<mo>)</mo>
</mrow>
</msubsup>
<msub>
<mi>Y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
</mrow>
4.4) measure and update：
<mrow>
<msub>
<mi>P</mi>
<mrow>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>L</mi>
</mrow>
</munderover>
<msubsup>
<mi>&omega;</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>&lsqb;</mo>
<msub>
<mi>Y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>Y</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>Y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>Y</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mi>T</mi>
</msup>
<mo>+</mo>
<msub>
<mi>R</mi>
<mi>k</mi>
</msub>
</mrow>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<mo>=</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mrow>
<mn>2</mn>
<mi>L</mi>
</mrow>
</munderover>
<msubsup>
<mi>&omega;</mi>
<mi>i</mi>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mo>)</mo>
</mrow>
</msubsup>
<mo>&lsqb;</mo>
<msubsup>
<mi>&chi;</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
<mi>x</mi>
</msubsup>
<mo>-</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
<msup>
<mrow>
<mo>&lsqb;</mo>
<msub>
<mi>Y</mi>
<mrow>
<mi>i</mi>
<mo>,</mo>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>Y</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>&rsqb;</mo>
</mrow>
<mi>T</mi>
</msup>
</mrow>
<mrow>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mi>P</mi>
<mrow>
<msub>
<mi>x</mi>
<mi>k</mi>
</msub>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>P</mi>
<mrow>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
<mrow>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msubsup>
</mrow>
<mrow>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>X</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>+</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<mrow>
<mo>(</mo>
<msub>
<mi>Y</mi>
<mi>k</mi>
</msub>
<mo>-</mo>
<msub>
<mover>
<mi>Y</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<msub>
<mi>P</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<msub>
<mover>
<mi>P</mi>
<mo>^</mo>
</mover>
<mrow>
<mi>k</mi>
<mo>|</mo>
<mi>k</mi>
<mo>-</mo>
<mn>1</mn>
</mrow>
</msub>
<mo>-</mo>
<msub>
<mi>K</mi>
<mi>k</mi>
</msub>
<msub>
<mi>P</mi>
<mrow>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
<msub>
<mi>y</mi>
<mi>k</mi>
</msub>
</mrow>
</msub>
<msubsup>
<mi>K</mi>
<mi>k</mi>
<mi>T</mi>
</msubsup>
</mrow>
In formula：λ=α2(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 that weight is distributed, and L is
Stochastic variable X dimension,The weight coefficient of average and variance statistic characteristic corresponding to respectively i-th sample point；
X0For the initial value of system stochastic variable, i.e. step 2) obtained by result, P0For covariance initial value,For the k-1 moment
Sample point set, Yi,k|k-1To convert point set,For a step look-ahead value of stochastic variable,Carried for a step of observed quantity
Preceding predicted value, YkMeasured for the systematic perspective at k moment,For a step look-ahead covariance matrix,WithFor covariance
Matrix, PkFor the covariance matrix value at k moment, KkFor the filtering gain value at k moment,Stochastic variable for the k moment is estimated
Evaluation, i.e., required node coordinate value.
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| CN105163385B (en) * | 2015-08-25 | 2019-01-29 | 华南理工大学 | A kind of localization method based on fan-shaped overlapping region clustering |
| CN106226732B (en) * | 2016-07-08 | 2018-11-16 | 西安电子科技大学 | The indoor wireless positioning and tracing method filtered based on TOF and iteration without mark |
| CN106507313B (en) * | 2016-12-30 | 2019-10-11 | 上海真灼科技股份有限公司 | A kind of method for tracking and positioning and system based on RSSI detection |
| CN106707235B (en) * | 2017-03-08 | 2019-07-02 | 南京信息工程大学 | A kind of indoor distance-measuring and positioning method based on improved Unscented kalman filtering |
| CN111356072B (en) * | 2018-12-21 | 2020-12-11 | 珠海格力电器股份有限公司 | Position estimation method and device for indoor positioning and readable storage medium |
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