CN110286353A - Wireless sensor network target localization method based on RSS-ToA under nlos environment - Google Patents
Wireless sensor network target localization method based on RSS-ToA under nlos environment Download PDFInfo
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- 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
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Abstract
The invention discloses a kind of wireless sensor network target localization methods based on RSS-ToA under nlos environment, first construct the measurement model of the corresponding RSS measured value of anchor node and the measurement model of ToA measured value；Approximate deformation is carried out again after simplifying to two measurement models；According to the approximate deformation expression formula of the simplification measurement model of the approximate deformation expression formula of the simplification measurement model of RSS measured value and ToA measured value, and criterion of least squares is used, obtains non-convex orientation problem；By introducing slack variable and auxiliary variable, non-convex constrained optimization problem is converted by non-convex orientation problem；Using second order cone relaxation method, Second-order cone programming problem is obtained；Second-order cone programming problem is solved using interior point method, obtains the final estimated value of coordinate position of the destination node in reference frame；Advantage is that it takes full advantage of two kinds of metrical informations of received signal strength and arrival time, and can acquire globally optimal solution, substantially increases target location accuracy.
Description
Technical field
The present invention relates to a kind of object localization methods, more particularly, to a kind of nothing based on RSS-ToA under nlos environment
Line sensor network target localization method.
Background technique
Wireless sensor network (Wireless Sensor Networks, WSN) refers to be made of multiple sensor devices
Cordless communication network, a monitoring area is assigned to, for measuring the interested information in certain parts.In recent years,
Wireless sensor network is all widely used in fields such as target following, navigation, emergency service, intelligent transportation.At this
It is most important to target position positioning in a little applications, and some special spaces are such as indoor, underwater, can not use GPS/ Beidou etc.
Satellite positioning needs wireless sensor network to position target.In wireless sensor network, in general, by it is artificial or its
Sensor node known to its means deployed position, sensor node known to these positions are known as anchor node, it is not known in advance that
Self-position needs the sensor node positioned by anchor node to be known as destination node.It is carried out using wireless sensor network
The main thought of target positioning is to utilize the position that destination node is determined with noisy measured value.It is obtained and is believed according to anchor node
The mode of number information is different, wireless sensor network target localization method can be divided into: arrival time (ToA), angle of arrival
(AoA), reaching time-difference (TDOA), received signal strength (RSS) and the associated form between them.
The research of early stage is mainly based upon the object localization method under line of sight conditions, and such methods only considered destination node
It is line communication between anchor node, without any obstruction, but under practical circumstances, such as indoors, anchor node and mesh
Communication between mark node is often blocked by many obstructions, this just will form a kind of non line of sight (NLOS) propagation side
Formula, so as to cause the estimation of the position to destination node, there are biggish errors.Non-market value is as wireless sensor network
How target one of most important error source when positioning, research effectively inhibit non-market value and improve positioning accuracy
Become the hot issue of wireless sensor network target location technology.Slavisa Tomic et al. is in IEEE Wireless
Target is disclosed in Communications Letters (Institute of Electrical and Electric Engineers (IEEE) wirelessly communicates flash report)
Localization in NLOS environments using RSS and TOA measurements is (under nlos environment
Based on RSS and ToA alignment by union Study on Problems), all links are considered as to (LOS) of sighting distance, then apply alternative optimization side
Method, and location estimation and average non-market value estimation are improved in an iterative manner, but this method is difficult to acquire global optimum
Solution, causes target location accuracy poor.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of wireless sensors based on RSS-ToA under nlos environment
Network objectives localization method takes full advantage of two kinds of metrical informations of received signal strength and arrival time, and can acquire complete
Office's optimal solution, to substantially increase target location accuracy.
The technical scheme of the invention to solve the technical problem is: a kind of based on RSS-ToA under nlos environment
Wireless sensor network target localization method, it is characterised in that the following steps are included:
Step 1: a two-dimensional Cartesian coordinate system is established in wireless sensor network as reference frame, and is set
There are a destination nodes and N number of anchor for being used to receive metrical information for emission measurement signal in wireless sensor network
Node；Then the coordinate position by destination node in reference frame is denoted as x, by i-th of anchor node in reference frame
Coordinate position be denoted as si, x=(x1,x2), si=(si1,si2)；Wherein, N >=3, i are positive integer, and the initial value of i is 1,1≤i
≤ N, x1Indicate the 1st coordinate components of x, x2Indicate the 2nd coordinate components of x, si1Indicate siThe 1st coordinate components, si2
Indicate siThe 2nd coordinate components；
Step 2: destination node is to each anchor node emission measurement signal, each anchor node in wireless sensor network
Corresponding RSS measured value and ToA measured value are obtained after receiving measuring signal, the corresponding RSS measured value of i-th of anchor node is denoted as
Pi, the corresponding ToA measured value of i-th of anchor node is denoted as di；Then the measurement of the corresponding RSS measured value of each anchor node is constructed
The measurement model of model and ToA measured value, by PiMeasurement model description are as follows:
By diMeasurement model description are as follows: di=| | x-si||+βi+mi；Wherein, d0It indicates in reference frame away from the ginseng of destination node
Examine distance, P0Indicate that distance is d between anchor node and destination node0When measurement power, biIndicate measuring signal when RSS measurement
I-th of anchor node, which is emitted to, from destination node receives non-market value present on transmission path experienced, biIt obeys uniform
Distribution, 0≤bi≤bmax, bmaxIndicate that the maximum non-market value set when RSS measurement, γ indicate measuring signal from destination node
It is emitted to the path loss exponent of the received transmission range of each anchor node, the value range of γ is 2.5~3.5, symbol " | | |
| " it is to ask euclideam norm symbol, niIndicate measuring signal from destination node be emitted to i-th anchor node receive it is experienced
Power loss present on transmission path measures noise, niObey the Gaussian Profile of zero-mean Indicate niFunction
Rate, βiMeasuring signal is emitted in i-th of anchor node reception transmission path experienced from destination node and deposits when expression ToA measurement
Non-market value, βiObedience is uniformly distributed, 0≤βi≤βmax, βmaxIndicate the maximum non-market value set when ToA measurement,
miIndicate that measuring signal is emitted to i-th of anchor node from destination node and receives range loss present on transmission path experienced
Measure noise, miObey the Gaussian Profile of zero-mean Indicate miPower；
Step 3: the measurement model of RSS measured value corresponding to each anchor node and the measurement model difference of ToA measured value
Simplified, by PiSimplification measurement model description are as follows:By diSimplify measurement
Model description are as follows: di=| | x-si||+β+mi；Then it setsAnd | mi| < < 10-4, corresponding to each anchor node
The simplification measurement model approximation deformation of the simplification measurement model and ToA measured value of RSS measured value, by PiSimplification measurement model
Approximation deformation expression formula description are as follows:By diSimplification measurement model approximate deformation expression formula description
Are as follows:Wherein, measuring signal is emitted to all anchor sections from destination node when b expression RSS is measured
Point receives average non-market value present on transmission path experienced, and β indicates when ToA measurement measuring signal from destination node
It is emitted to all anchor nodes and receives average non-market value present on transmission path experienced, symbol " | | " it is to take absolute value
Symbol, symbol " < < " are much smaller than symbol, and symbol " ≈ " is to be approximately equal to symbol, εiIndicate PiNoise component(s), εiObey zero
The Gaussian Profile of valueξiIt is the intermediate variable of introducing with ρ,
Step 4: according toWithAnd it is quasi- using least square
Then, obtain solving the non-convex orientation problem of x, description are as follows:Be essentially ask so thatThe value of x, ρ, β when minimum；
Step 5: slack variable t is introduced in the description of non-convex orientation problem for solving xi、giWith auxiliary variable v, u, h,
And enable | | x | |2=v, | | β | |2=u, | | ρ | |2=h, the non-convex constraint for converting solution x for the non-convex orientation problem for solving x are excellent
Change problem, description are as follows:Constraint condition are as follows: ||x||2=v, | | β | |2=u, | | ρ | |2=h；Wherein,For siTurn
It sets；
Step 6: will be in the description of non-convex constrained optimization problem that solve x using second order cone relaxation method | | x | |2=v
It is loose to be | | x | |2≤v、||β||2=u is loose to be | | β | |2≤u、||ρ||2=h relaxation is | | ρ | |2≤ h obtains solving the two of x
Rank bores planning problem, description are as follows:Constraint condition are as follows: Wherein, symbol " [] " is that matrix indicates symbol；
Step 7: the description for the Second-order cone programming problem for solving x is solved using interior point method, obtains the overall situation of x most
Excellent solution, is denoted as x*, x*The as final estimated value of coordinate position of the destination node in reference frame.
Compared with the prior art, the advantages of the present invention are as follows:
1) the method for the present invention takes full advantage of RSS (received signal strength) metrical information and ToA (arrival time) measurement letter
Breath establishes a kind of measurement model for combining RSS metrical information and ToA metrical information, is uniformly distributed in non-market value obedience
In the case where, measured non-market value is replaced using an average non-market value, recycles convex optimization relaxation skill
I.e. non-convex former problem is converted convex problem i.e. Second-order cone programming problem by second order cone relaxation method, has effectively solved original and has asked
Topic, so that the method for the present invention has higher positioning accuracy, and very steady.
2) the method for the present invention is obtained by introducing auxiliary variable in non-convex orientation problem, and using second order cone relaxation method
Second-order cone programming problem, acquires globally optimal solution, and the method for the present invention is enabled relatively accurately to estimate the seat of destination node
Cursor position, relaxation item reduce the influence to positioning performance.
Detailed description of the invention
Fig. 1 is that the overall of the method for the present invention realizes block diagram；
Fig. 2 is to measure the identical item of numerical quantities of the power of noise and the power of range loss measurement noise in power loss
Under part, non line of sight link number is 6, line of sight link is 2, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing
Broad sense feasible zone subinterval method is based on single RSS non line of sight localization method, is based on single ToA non line of sight localization method with function
The situation of change schematic diagram of root-mean-square error when the standard deviation of rate loss measurement noise and range loss measurement noise increases；
Fig. 3 is to measure the identical item of numerical quantities of the power of noise and the power of range loss measurement noise in power loss
Under part, non line of sight link number is 6, line of sight link is 2, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing
Broad sense feasible zone subinterval method, tiring out based on single RSS non line of sight localization method, based on single ToA non line of sight localization method
Distribution function is accumulated with the change curve schematic diagram of evaluated error；
Fig. 4 is 3dB for the standard deviation for measuring noise in power loss and the standard deviation of range loss measurement noise is 3 meters
Under the conditions of, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing broad sense feasible zone subinterval method are based on single RSS
Non line of sight localization method, the root-mean-square error based on single ToA non line of sight localization method with non line of sight link number variation
Curve synoptic diagram；
Fig. 5 is 3dB for the standard deviation for measuring noise in power loss and the standard deviation of range loss measurement noise is 3 meters
Under the conditions of, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing broad sense feasible zone subinterval method are based on single RSS
Non line of sight localization method, the root-mean-square error based on single ToA non line of sight localization method are with maximum non-market value size
Change curve schematic diagram.
Specific embodiment
The present invention will be described in further detail below with reference to the embodiments of the drawings.
A kind of wireless sensor network target localization method based on RSS-ToA under nlos environment proposed by the present invention,
Its totally realize block diagram as shown in Figure 1, itself the following steps are included:
Step 1: a two-dimensional Cartesian coordinate system is established in wireless sensor network as reference frame, and is set
There are a destination nodes and N number of anchor for being used to receive metrical information for emission measurement signal in wireless sensor network
Node；Then the coordinate position by destination node in reference frame is denoted as x, by i-th of anchor node in reference frame
Coordinate position be denoted as si, x=(x1,x2), si=(si1,si2)；Wherein, N >=3 take N=8, i to be positive whole in the present embodiment
Number, the initial value of i are 1,1≤i≤N, x1Indicate the 1st coordinate components of x, x2Indicate the 2nd coordinate components of x, si1Indicate si
The 1st coordinate components, si2Indicate siThe 2nd coordinate components.
Step 2: destination node is to each anchor node emission measurement signal, each anchor node in wireless sensor network
Corresponding RSS (received signal strength) measured value and ToA (arrival time) measured value are obtained after receiving measuring signal, by i-th
The corresponding RSS measured value of anchor node is denoted as Pi, the corresponding ToA measured value of i-th of anchor node is denoted as di；Then each anchor is constructed
The measurement mould of measurement model (model is essentially path loss prediction model) and ToA measured value of the corresponding RSS measured value of node
Type, by PiMeasurement model description are as follows:By diMeasurement model description are as follows: di=
||x-si||+βi+mi；Wherein, d0It indicates in reference frame away from the reference distance of destination node, d0Value according to actual environment
It is manually set, takes d in experiment0It is 1 meter, P0Indicate that distance is d between anchor node and destination node0When measurement power, P0Value
It is manually set according to actual environment, P is taken in experiment0For 20dBm, biIndicate that measuring signal is emitted to from destination node when RSS measurement
I-th of anchor node receives non-market value present on transmission path experienced, biObedience is uniformly distributed, 0≤bi≤bmax,
bmaxIndicate that the maximum non-market value set when RSS measurement, γ indicate that measuring signal is emitted to each anchor node from destination node
The path loss exponent of received transmission range, the value range of γ are 2.5~3.5, such as take γ=3, symbol " | | | | " it is to ask
Euclideam norm symbol, niIndicate that measuring signal is emitted to i-th of anchor node from destination node and receives transmission road experienced
Power loss present on diameter measures noise, niObey the Gaussian Profile of zero-mean Indicate niPower, βi
Indicate that measuring signal is emitted to present on i-th of anchor node reception transmission path experienced from destination node when ToA measurement
Non-market value, βiObedience is uniformly distributed, 0≤βi≤βmax, βmaxIndicate the maximum non-market value set when ToA measurement, miTable
Show that measuring signal is emitted to i-th of anchor node from destination node and receives range loss measurement present on transmission path experienced
Noise, miObey the Gaussian Profile of zero-mean Indicate miPower.
Step 3: the measurement model of RSS measured value corresponding to each anchor node and the measurement model difference of ToA measured value
Simplified, by PiSimplification measurement model description are as follows:By diSimplify measurement
Model description are as follows: di=| | x-si||+β+mi；Then it setsAnd | mi| < < 10-4, i.e. setting ni、miIt is sufficiently small,
The simplification measurement model approximation deformation of the simplification measurement model and ToA measured value of RSS measured value corresponding to each anchor node, will
PiSimplification measurement model approximate deformation expression formula description are as follows:By diSimplification measurement model
Approximation deformation expression formula description are as follows:Wherein, b indicates that measuring signal is from target when RSS measurement
Node is emitted to all anchor nodes and receives average non-market value present on transmission path experienced, when β indicates ToA measurement
Measuring signal is emitted to all anchor nodes from destination node and receives average non-market value present on transmission path experienced,
Due to bi(1≤i≤N) and βi(1≤i≤N) is equally distributed, therefore can is approximately an average non-market value,
B is replaced with b hereini(1≤i≤N), replaces β with βi(1≤i≤N), symbol " | | " it is the symbol that takes absolute value, symbol " <
< " is much smaller than symbol, and symbol " ≈ " is to be approximately equal to symbol, εiIndicate PiNoise component(s), εiObey the Gaussian Profile of zero-meanξiIt is the intermediate variable of introducing with ρ,
Step 4: according toWithAnd it is quasi- using least square
Then, obtain solving the non-convex orientation problem of x, description are as follows:Be essentially ask so thatThe value of x, ρ, β when minimum.
Step 5: slack variable t is introduced in the description of non-convex orientation problem for solving xi、giWith auxiliary variable v, u, h,
And enable | | x | |2=v, | | β | |2=u, | | ρ | |2=h, the non-convex constraint for converting solution x for the non-convex orientation problem for solving x are excellent
Change problem, description are as follows:Constraint condition are as follows: ||x||2=v, | | β | |2=u, | | ρ | |2=h；Wherein,For siTurn
It sets.
Step 6: will be in the description of non-convex constrained optimization problem that solve x using second order cone relaxation method | | x | |2=v
It is loose to be | | x | |2≤v、||β||2=u is loose to be | | β | |2≤u、||ρ||2=h relaxation is | | ρ | |2≤ h obtains solving the two of x
Rank cone planning (SOCP) problem, description are as follows:Constraint condition are as follows: Wherein, symbol " [] " is that matrix indicates symbol.
Step 7: the description for the Second-order cone programming problem for solving x is solved using interior point method, obtains the overall situation of x most
Excellent solution, is denoted as x*, x*The as final estimated value of coordinate position of the destination node in reference frame.
The feasibility, validity and positioning performance of the method for the present invention are verified below by way of emulation experiment.
Assuming that have N=8 anchor node and a destination node in wireless sensor network, all the sensors node (including
Anchor node and destination node) it is all random placement within the scope of 30 × 30 square metres of two-dimensional surface, P is set0=20dBm, γ
=3, d0=1 meter.Assuming that the corresponding power loss measurement noise of all anchor nodes is equal, i.e., Table
Show that measuring signal is emitted to the 1st anchor node from destination node and receives power loss measurement present on transmission path experienced
The power of noise,It indicates that measuring signal is emitted in the 2nd anchor node reception transmission path experienced from destination node to deposit
Power loss measurement noise power,Indicate that measuring signal is emitted to the reception of n-th anchor node from destination node and is passed through
The power of power loss measurement noise, the corresponding range loss of all anchor nodes measure noise present on the transmission path gone through
It is identical, asWherein,Indicate that measuring signal is emitted to the 1st anchor node from destination node and connects
The power of range loss measurement noise present on transmission path experienced is received,Indicate that measuring signal is sent out from destination node
It is mapped to the power that the 2nd anchor node receives range loss measurement noise present on transmission path experienced,Indicate measurement
Signal is emitted to n-th anchor node from destination node and receives range loss measurement noise present on transmission path experienced
Power.
The performance of the method for the present invention is tested with the power of power loss measurement noise and the power of range loss measurement noise
Increased situation of change.
It is identical with the numerical quantities of the power of range loss measurement noise that Fig. 2 gives the power for measuring noise in power loss
Under conditions of, non line of sight link number is 6, line of sight link is 2, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing
Some broad sense feasible zones subinterval method (Target localization in NLOS environments using RSS
And TOA measurements (the target positioning for combining RSS and ToA measurement under nlos environment)), it is existing based on single
RSS non line of sight localization method (RSS-based localization in wireless sensor networks using
Vonvex relaxation:noncooperative and cooperative schemes (is based in wireless sensor network
The objective of RSS positions)), existing be based on single ToA non line of sight localization method (NLOS error mitigation for
TOA-based localization via convex relaxation (the target positioning under nlos environment based on ToA))
The situation of change of root-mean-square error (RMSE) when increasing with the standard deviation of power loss measurement noise and range loss measurement noise.
From figure 2 it can be seen that as power loss measures becoming larger for the standard deviation of noise and range loss measurement noise, various methods
RMSE it is in rising trend, performance is deteriorated；Noise is measured for a variety of different power losses and range loss measurement is made an uproar
The standard deviation of sound, with it is existing based on single RSS non line of sight localization method and it is existing be based on single ToA non line of sight localization method
Compare, the RMSE of the method for the present invention is smaller, therefore sufficiently shows the better performances of the method for the present invention；The RMSE of the method for the present invention
Minimum, positioning performance is best.
It is identical with the numerical quantities of the power of range loss measurement noise that Fig. 3 gives the power for measuring noise in power loss
Under conditions of, non line of sight link number is 6, line of sight link is 2, bmax=6dB, βmaxAt=6 meters, the method for the present invention and existing
Some broad sense feasible zones subinterval method, it is existing based on single RSS non line of sight localization method, it is existing based on single ToA it is non-
The cumulative distribution function (cumulative distribution function, CDF) of sighting distance localization method is with evaluated error
Change curve.As can be known from Fig. 3, within the scope of evaluated error, the method for the present invention all has preferable performance.Specifically, when
When evaluated error is 4 meters, the cumulative distribution function of the method for the present invention can achieve 90%, and other three kinds of methods are not up to
90%；When evaluated error is 6 meters, the cumulative distribution function of the method for the present invention can achieve 99%, existing broad sense feasible zone
Subinterval method reaches 97%, existing based on single RSS non line of sight localization method and existing fixed based on single ToA non line of sight
The performance of position method is poor, and cumulative distribution function is respectively 81% and 78%, thus under the same assumed condition of evaluated error, this
For inventive method compared with other methods, positioning performance is best.
Fig. 4 give power loss measurement noise standard deviation be 3dB and range loss measurement noise standard deviation be 3
Under conditions of rice, bmax=6dB, βmaxIt is the method for the present invention and existing broad sense feasible zone subinterval method, existing at=6 meters
Based on single RSS non line of sight localization method, it is existing based on the root-mean-square error (RMSE) of single ToA non line of sight localization method with
The change curve of non line of sight link (i.e. obstructed path) number.Figure 4, it is seen that with non line of sight link number
Increase, the method for the present invention and existing broad sense feasible zone subinterval method are positioned relative to existing based on single RSS non line of sight
Method and the existing RMSE based on single ToA non line of sight localization method are smaller, all show good non-market value suppression
Ability processed, and the method for the present invention, with the increase of non line of sight link number, RMSE performance change amplitude is smaller, and relative to
Other several method RMSE are minimum, it can be seen that it inhibits the ability of non-market value best.
Fig. 5 give power loss measurement noise standard deviation be 3dB and range loss measurement noise standard deviation be 3
Under conditions of rice, bmax=6dB, βmaxIt is the method for the present invention and existing broad sense feasible zone subinterval method, existing at=6 meters
Based on single RSS non line of sight localization method, it is existing based on the root-mean-square error (RMSE) of single ToA non line of sight localization method with
The change curve of maximum non-market value size.From figure 5 it can be seen that with the increase of maximum non-market value, this hair
Bright method and existing broad sense feasible zone subinterval method are relative to existing based on single RSS non line of sight localization method and existing
The RMSE performance based on single ToA non line of sight localization method have a distinct increment；In addition, the RMSE of the method for the present invention is minimum, it is non-
Sighting distance error rejection is better than other methods, it is sufficient to illustrate that the method for the present invention has enough advantages in terms of positioning accuracy.
Can be seen that the method for the present invention from above-mentioned simulation result has good positioning performance under nlos environment,
And can preferably inhibit non-market value, very well satisfy the high-precision demand of positioning.
Claims (1)
1. a kind of wireless sensor network target localization method based on RSS-ToA under nlos environment, it is characterised in that including
Following steps:
Step 1: a two-dimensional Cartesian coordinate system is established in wireless sensor network as reference frame, and is set in nothing
There are a destination nodes and N number of anchor section for being used to receive metrical information for emission measurement signal in line sensor network
Point；Then the coordinate position by destination node in reference frame is denoted as x, by i-th of anchor node in reference frame
Coordinate position is denoted as si, x=(x1,x2), si=(si1,si2)；Wherein, N >=3, i are positive integer, and the initial value of i is 1,1≤i≤
N, x1Indicate the 1st coordinate components of x, x2Indicate the 2nd coordinate components of x, si1Indicate siThe 1st coordinate components, si2Table
Show siThe 2nd coordinate components；
Step 2: destination node is received to each anchor node emission measurement signal, each anchor node in wireless sensor network
Corresponding RSS measured value and ToA measured value are obtained after measuring signal, and the corresponding RSS measured value of i-th of anchor node is denoted as Pi,
The corresponding ToA measured value of i-th of anchor node is denoted as di；Then the measurement mould of the corresponding RSS measured value of each anchor node is constructed
The measurement model of type and ToA measured value, by PiMeasurement model description are as follows:By di
Measurement model description are as follows: di=| | x-si||+βi+mi；Wherein, d0Indicate reference in reference frame away from destination node away from
From P0Indicate that distance is d between anchor node and destination node0When measurement power, biIndicate that measuring signal is from mesh when RSS measurement
Mark node is emitted to i-th of anchor node and receives non-market value present on transmission path experienced, biObedience is uniformly distributed,
0≤bi≤bmax, bmaxIndicate that the maximum non-market value set when RSS measurement, γ indicate that measuring signal emits from destination node
To the path loss exponent of the received transmission range of each anchor node, the value range of γ is 2.5~3.5, symbol " | | | | " be
Ask euclideam norm symbol, niIndicate that measuring signal is emitted to i-th of anchor node from destination node and receives transmission experienced
Power loss present on path measures noise, niObey the Gaussian Profile of zero-mean Indicate niPower,
βiMeasuring signal is emitted to i-th of anchor node and receives in transmission path experienced and exists from destination node when expression ToA measurement
Non-market value, βiObedience is uniformly distributed, 0≤βi≤βmax, βmaxIndicate the maximum non-market value set when ToA measurement, mi
Indicate that measuring signal is emitted to i-th of anchor node from destination node and receives range loss survey present on transmission path experienced
Measure noise, miObey the Gaussian Profile of zero-mean Indicate miPower；
Step 3: the measurement model of RSS measured value corresponding to each anchor node and the measurement model of ToA measured value carry out respectively
Simplify, by PiSimplification measurement model description are as follows:By diSimplification measurement model
Description are as follows: di=| | x-si||+β+mi；Then it setsAnd | mi| < < 10-4, RSS corresponding to each anchor node
The simplification measurement model approximation deformation of the simplification measurement model and ToA measured value of measured value, by PiSimplification measurement model it is close
Like deformation expression formula description are as follows:By diSimplification measurement model approximate deformation expression formula description
Are as follows:Wherein, measuring signal is emitted to all anchor sections from destination node when b expression RSS is measured
Point receives average non-market value present on transmission path experienced, and β indicates when ToA measurement measuring signal from destination node
It is emitted to all anchor nodes and receives average non-market value present on transmission path experienced, symbol " | | " it is to take absolutely
It is worth symbol, symbol " < < " is much smaller than symbol, and symbol " ≈ " is to be approximately equal to symbol, εiIndicate PiNoise component(s), εiObey zero
The Gaussian Profile of mean valueξiIt is the intermediate variable of introducing with ρ,
Step 4: according toWithAnd criterion of least squares is used, it obtains
To the non-convex orientation problem for solving x, description are as follows:
Be essentially ask so thatThe value of x, ρ, β when minimum；
Step 5: slack variable t is introduced in the description of non-convex orientation problem for solving xi、giWith auxiliary variable v, u, h, and enable |
|x||2=v, | | β2=u, | | ρ | |2=h converts the non-convex orientation problem for solving x to the non-convex constrained optimization problem for solving x,
Description are as follows:Constraint condition are as follows: ||x||2=v, | | β | |2=u, | | ρ | |2=h；Wherein,For siTurn
It sets；
Step 6: will be in the description of non-convex constrained optimization problem that solve x using second order cone relaxation method | | x | |2=v is loose
For | | x | |2≤v、||β||2=u is loose to be | | β | |2≤u、||ρ||2=h relaxation is | | ρ | |2≤ h obtains the second order cone for solving x
Planning problem, description are as follows:Constraint condition are as follows: Wherein, symbol " [] " is that matrix indicates symbol；
Step 7: solving the description for the Second-order cone programming problem for solving x using interior point method, obtain the globally optimal solution of x,
It is denoted as x*, x*The as final estimated value of coordinate position of the destination node in reference frame.
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