CN107271956A - The localization method based on arrival time of unknown initial time in nlos environment - Google Patents

The localization method based on arrival time of unknown initial time in nlos environment Download PDF

Info

Publication number
CN107271956A
CN107271956A CN201710269269.3A CN201710269269A CN107271956A CN 107271956 A CN107271956 A CN 107271956A CN 201710269269 A CN201710269269 A CN 201710269269A CN 107271956 A CN107271956 A CN 107271956A
Authority
CN
China
Prior art keywords
msub
mrow
sensor
msubsup
msup
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201710269269.3A
Other languages
Chinese (zh)
Other versions
CN107271956B (en
Inventor
王刚
高尚超
王伟
李有明
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Ningbo University
Original Assignee
Ningbo University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Ningbo University filed Critical Ningbo University
Priority to CN201710269269.3A priority Critical patent/CN107271956B/en
Publication of CN107271956A publication Critical patent/CN107271956A/en
Application granted granted Critical
Publication of CN107271956B publication Critical patent/CN107271956B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • 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
    • G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
    • 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
    • G01S5/0273—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 using multipath or indirect path propagation signals in position determination

Landscapes

  • Physics & Mathematics (AREA)
  • Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses a kind of localization method based on arrival time of unknown initial time in nlos environment, the model of its signal transmission distance first set up between target source and each sensor；Then the description of measurement noise is obtained according to model；Then according to the description of measurement noise, and using the robust weighted least-squares method under worst case, the orientation problem in unknown signaling launches initial time and there is the environment of non-market value is obtained, then be changed into the orientation problem of non-convex；Afterwards by introducing auxiliary variable, and second order cone relaxation method is used, obtain Second-order cone programming problem；Finally Second-order cone programming problem is solved using interior point method, the final estimate of coordinate position of the target source in reference frame is obtained；Advantage is can be while solve the problems, such as the presence of the unknown signaling transmitting initial time and non-market value existed, so as to improve positioning precision.

Description

The localization method based on arrival time of unknown initial time in nlos environment
Technical field
The present invention relates to a kind of object localization method, more particularly, to a kind of base of unknown initial time in nlos environment In the localization method of arrival time.
Background technology
In recent years, wireless sensor network location technology was widely used in numerous areas, can be with convenient quickly Realize location navigation, environmental monitoring, smart home, Industry Control etc. in ground.With the development and the progress of society of technology, high accuracy Location technology shown the prospect of being widely applied in every field.Therefore, to high-precision mesh in wireless sensor network The research of mark localization method is extremely necessary.
At present, realizing the basic skills of target positioning has a lot.The most widely used is to be based on arrival time (Time Of Arrival) Method Of Time Measurement, basic network structure is as shown in Figure 1.The advantage of this method is time measurement system Complexity it is low, the positioning of high-precision target can be achieved.Therefore, when the research of most of object localization methods is all based on reaching Between measurement carry out.
Target be accurately positioned be object localization method design key.However, meeting in the wireless sensor network of reality In the presence of the factor of many influence positioning precisions, there are the asynchronous problem of clock and non line of sight of wireless sensor network the problem of main Error problem, as shown in fig. 1.The so-called asynchronous problem of clock is primarily referred to as the accurate starting of unknown object transmission signal Time, cause transmission time measurement of the signal between target and sensor inaccurate, measurement distance is produced with actual distance Deviation, and then influence positioning precision.So-called non-market value refers to that the transmission of signal is blocked between target and sensor And propagation delay is produced, make time of measuring elongated, produce larger range measurement error, reduce positioning precision.In fact, such as Fruit can not effectively handle unknown signaling transmitting initial time and the presence problem of non-market value, then positioning precision will not be obtained To effectively significantly being lifted.
In order to solve in the localization method based on arrival time simultaneous unknown signaling transmitting initial time and non-regard Presence problem away from error, it is necessary to design a kind of method joint eliminate that clock is asynchronous and non-market value to positioning precision not Profit influence.At present, the method for two kinds of errors of Combined Treatment is less, but individually for unknown initial time and the side of non-market value The research of method is widely.For example, carrying out effective non-market value processing using convex relaxing techniques；Utilize certain methods The unknown initial time of Combined estimator signal transmitting and target location.However, in actual applications, at the same unknown initial time and The presence of non-market value is unusual common scenario, and single Error processing would become hard to be applied in real life, therefore, many The Combined Treatment of error by be a certainty trend.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of localization method based on arrival time, and it can be solved simultaneously The unknown signaling transmitting initial time and the presence problem of non-market value certainly existed, so as to improve positioning precision.
The present invention solve the technical scheme that is used of above-mentioned technical problem for：Unknown initial time in a kind of nlos environment The localization method based on arrival time, it is characterised in that comprise the following steps：
1. a plane coordinate system or space coordinates are set up in wireless sensor network as reference frame；Setting There is a target source for being used for emission measurement signal and N number of sensing for being used to receive measurement signal in wireless sensor network Device, and the clock of the N number of sensor of setting is synchronous, and the clock of target source is asynchronous with the clock of sensor；N number of sensor is existed Coordinate position correspondence in reference frame is designated as s1,…,sN, coordinate position of the target source in reference frame is designated as x； Wherein, N >=3, s1Represent the 1st coordinate position of the sensor in reference frame, sNRepresent n-th sensor with reference to seat Coordinate position in mark system；
2. the signal transmission distance between target source and each sensor is calculated, by between target source and i-th of sensor Signal transmission distance be designated as di, di=c × ti, wherein, 1≤i≤N, c represents the light velocity, tiRepresent that measurement signal is sent out from target source Go out to i-th of sensor and receive the undergone time；
3. the signal transmission distance between target source and each sensor is described with model approach, by diModel It is expressed as：di=d0+||x-si||+ei+ni, wherein, d0Represent the signal transmission distance that unknown signaling transmitting initial time is caused Deviation, d0=c × Δ t, d0>=0, Δ t represent the difference of the clock of target source and the clock of sensor, and symbol " | | | | " is asks Euclideam norm symbol, siRepresent coordinate position of i-th of sensor in reference frame, eiRepresent measurement signal from mesh Mark source is issued to i-th of sensor and receives non-market value, n present on undergone pathiRepresent measurement signal from target Source is issued to i-th of sensor and receives measurement noise, n present on undergone pathiObey the Gaussian Profile of zero-mean Represent niPower, 0≤| ni| ＜ ＜ ei≤ρi, symbol " | | " it is take absolute value symbol, ρiRepresent measurement letter Number it is issued to the upper limit that i-th sensor receives non-market value present on undergone path from target source；
4. by di=d0+||x-si||+ei+niIt is changed into di-ei=(d0+||x-si||)+ni；Then to di-ei=(d0+| |x-si||)+niBoth members carry out square, obtainConnect And ignoreInObtain (di-ei)2≈(d0+||x-si| |)2+2ni(d0+||x-si||)；Again by (di-ei)2≈(d0+||x-si||)2+2ni(d0+||x-si| |) be changed into
5. basisAnd using the robust weighted least-squares side under worst case Method, obtains the orientation problem in unknown signaling launches initial time and there is the environment of non-market value, is described as：Then makeWillIt is changed intoThen willIt is changed intoAfterwards in interval [0, ρi] interior determination f (ei) maximum, Work as di≤ρiShi YouWork as di>ρiShi You Finally willWithSubstitute intoIn, the orientation problem of non-convex is obtained,
It is described as：If di≤ρi；
If di>ρi
Wherein, min () is takes minimum value function, and max () is to take max function,
" s.t. " expression " constrained in ... "；
6. auxiliary variable η is introduced in the orientation problem of non-convex1,η2,…,ηi,…ηN, will
If di≤ρiEquivalent description is：
If di>ρi
；Then by f (0), f (ρi),f(di) substitute into
If di≤ρi
And introduce auxiliary variable b1,b2,…bi,…bN, r and y, obtain
If di≤ρi
If di≤ρi；Then relaxed using second order cone
A[x,y,d0,r]T≤f
bi=2d0||x-si||
Method will
If di≤ρi
A[x,y,d0,r]T≤f
bi=2d0||x-si||
In y=| | x | |2It is loose to be | | x | |2≤y、Relaxation isSecond-order cone programming problem is obtained, is described For：
If di≤ρi；
A[x,y,d0,r]T≤f
Wherein, η1,η2,…,ηi,…ηNCorrespondence represent non-convex orientation problem in introduce the 1st auxiliary variable, the 2nd Auxiliary variable ..., i-th auxiliary variable ..., n-th auxiliary variable, b1,b2,…bi,…bNCorrespondence is represented
1st auxiliary variable of middle introducing, the 2nd auxiliary variable ...,If di≤ρi
I auxiliary variable ..., n-th auxiliary variable, r is corresponding with y to be represented
If di≤ρiExtra two auxiliary variables of middle introducing,For siTransposition, For s1Transposition,For sNTransposition, d1Represent between target source and the 1st sensor Signal transmission distance, dNRepresent the signal transmission distance between target source and n-th sensor, [x, y, d0,r]TFor [x, y, d0, r] transposition,
7. Second-order cone programming problem is solved using interior point method, obtains globally optimal solution, be designated as x*, x*As target The final estimate of coordinate position of the source in reference frame.
Described step 6. in constraints A [x, y, d0,r]T≤ f determination process is：Made an uproar according to generally measurement Sound is much smaller than the conclusion of non-market value, obtains di≥d0+||x-si||；Then by di≥d0+||x-si| | it is changed into di-d0≥|| x-si| |, and to di-d0≥||x-si| | both sides carry out a square expansion, obtainThen root According to y=| | x | |2WithWillIt is changed into Finally willIt is described, is described as in the form of vectors：A[x,y,d0,r]T≤ f,
Described step 6. in constraints Determination process be：
6. _ 1, according to the constraints b before relaxationi=2d0||x-si| |, obtained using quadratic sum inequalityThen willIn quadratic term expansion, obtainThen by y=| | x | |2WithSubstitute intoIn, obtain Constraints on clocking errorFurther according to known conditions d0>=0, obtain bi≥0；
6. _ 2, to the constraints b before relaxationi=2d0||x-si| | both members square expansion, obtainThen by y=| | x | |2Substitute into In, obtainThen willRelaxation for it is convex about Beam conditionAgain willSubstitute intoIn, obtain
Compared with prior art, the advantage of the invention is that：
1) the inventive method is during the model for setting up the signal transmission distance between target source and each sensor, Comprehensively consider the error of non-market value and the asynchronous generation of clock, with the presence problem of Combined Treatment non-market value and The nonsynchronous problem of clock of target source, is more nearly practical application.
2) the inventive method is according to measurement noise, and uses the robust weighted least-squares method under worst case, to obtain The orientation problem in unknown signaling launches initial time and there is the environment of non-market value is obtained, then is changed into the positioning of non-convex Problem, carries out robust processing to non-market value, takes full advantage of the upper limit of non-market value to improve positioning performance, even in Under the more harsh conditions of obstructed path, it may have sufficient performance advantage so that the inventive method is more close to reality Using.
3) the inventive method obtains Second-order cone programming problem by introducing auxiliary variable, and using second order cone relaxation method, The rational constraints of clocking error is related to due to being added in Second-order cone programming problem, allow the inventive method compared with For accurately estimation clocking error, influence of the clocking error to positioning performance is reduced, therefore be effectively increased present invention side The robustness for clocking error of method, with stronger antijamming capability.
Brief description of the drawings
Fig. 1 is that the localizing environment based on arrival time (TOA) shows under conditions of unknown initial time in nlos environment It is intended to；
Fig. 2 is the overall procedure block diagram of the inventive method；
Fig. 3 is for the inventive method in the case where obstructed path is more and existing robust positive semidefinite relaxation method and now The coordinate estimate of some robust second order cone relaxation methods becomes with the root-mean-square error of coordinate actual value with measurement noise is increased Change figure；
Fig. 4 is for the inventive method in the case where obstructed path is less and existing robust positive semidefinite relaxation method and now The coordinate estimate of some robust second order cone relaxation methods becomes with the root-mean-square error of coordinate actual value with measurement noise is increased Change figure；
Fig. 5 is the inventive method and existing robust positive semidefinite relaxation method and existing robust second order cone relaxation method Coordinate estimate and the root-mean-square error of coordinate actual value are with the increased number of variation diagram of obstructed path.
Embodiment
The present invention is described in further detail below in conjunction with accompanying drawing embodiment.
The localization method based on arrival time of unknown initial time in a kind of nlos environment proposed by the present invention, its is total Body FB(flow block) is as shown in Fig. 2 it comprises the following steps：
1. a plane coordinate system or space coordinates are set up in wireless sensor network as reference frame；Setting There is a target source for being used for emission measurement signal and N number of sensing for being used to receive measurement signal in wireless sensor network Device, and the clock of the N number of sensor of setting is synchronous, and the clock of target source is asynchronous with the clock of sensor；N number of sensor is existed Coordinate position correspondence in reference frame is designated as s1,…,sN, coordinate position of the target source in reference frame is designated as x； Wherein, N >=3, take N=8, s in the present embodiment1Represent the 1st coordinate position of the sensor in reference frame, sNRepresent Coordinate position of the n-th sensor in reference frame.
2. the signal transmission distance between target source and each sensor is calculated, by between target source and i-th of sensor Signal transmission distance be designated as di, di=c × ti, wherein, 1≤i≤N, c represents the light velocity, tiRepresent that measurement signal is sent out from target source Go out to i-th of sensor and receive the undergone time.
3. the signal transmission distance between target source and each sensor is described with model approach, by diModel It is expressed as：di=d0+||x-si||+ei+ni, wherein, d0Represent the signal transmission distance that unknown signaling transmitting initial time is caused Deviation, d0=c × Δ t, d0>=0, Δ t represent the difference of the clock of target source and the clock of sensor, and symbol " | | | | " is asks Europe A few Reed norm signs, siRepresent coordinate position of i-th of sensor in reference frame, eiRepresent measurement signal from target Source is issued to i-th of sensor and receives non-market value, n present on undergone pathiRepresent measurement signal from target source It is issued to i-th of sensor and receives measurement noise, n present on undergone pathiObey the Gaussian Profile of zero-mean Represent niPower, generally, 0≤| ni| ＜ ＜ ei≤ρi, symbol " | | " it is take absolute value symbol, ρi Represent that measurement signal is issued to i-th of sensor from target source and receives the upper of non-market value present on undergone path Limit, ρiValue carry out target positioning before be measured, ρiFor constant.
4. by di=d0+||x-si||+ei+niIt is changed into di-ei=(d0+||x-si||)+ni；Then to di-ei=(d0+| |x-si||)+niBoth members carry out square, obtainConnect And ignoreInObtain (di-ei)2≈(d0+||x-si| |)2+2ni(d0+||x-si||)；Again by (di-ei)2≈(d0+||x-si||)2+2ni(d0+||x-si| |) be changed into
5. basisAnd using the robust weighted least-squares side under worst case Method, obtains the orientation problem in unknown signaling launches initial time and there is the environment of non-market value, is described as：Then makeWillIt is changed intoBecause f (ei) begin It is positive number eventually, therefore then willIt is changed intoAfterwards in area Between [0, ρi] interior determination f (ei) maximum, work as di≤ρiShi YouWork as di >ρiShi YouFinally willWithSubstitute intoIn, the orientation problem of non-convex is obtained, is retouched State for：
If di≤ρi；
If di>ρi
Wherein, min () is takes minimum value function, and max () is to take max function,
" s.t. " expression " constrained in ... ".
6. auxiliary variable η is introduced in the orientation problem of non-convex1,η2,…,ηi,…ηN, will
If di≤ρiEquivalent description is：
If di>ρi
Then by f (0), f (ρi),f(di) substitute into
If di≤ρi
And introduce auxiliary variable b1,b2,…bi,…bN, r and y, obtainIf di≤ρi
If di≤ρi；Then relaxed using second order cone
A[x,y,d0,r]T≤f
bi=2d0||x-si||
Method will
If di≤ρi
A[x,y,d0,r]T≤f
bi=2d0||x-si||
In y=| | x | |2It is loose to be | | x | |2≤y、Relaxation isSecond-order cone programming problem is obtained, is described For：
If di≤ρi；
A[x,y,d0,r]T≤f
Wherein, η1,η2,…,ηi,…ηNCorrespondence represent non-convex orientation problem in introduce the 1st auxiliary variable, the 2nd Auxiliary variable ..., i-th auxiliary variable ..., n-th auxiliary variable, b1,b2,…bi,…bNCorrespondence is represented
1st auxiliary variable of middle introducing, the 2nd auxiliary variable ...,If di≤ρi
I auxiliary variable ..., n-th auxiliary variable, r is corresponding with y to be represented If di≤ρiExtra two auxiliary variables of middle introducing,For siTransposition, For s1Transposition,For sNTransposition, d1Represent the signal transmission distance between target source and the 1st sensor, dNRepresent mesh Signal transmission distance between mark source and n-th sensor, [x, y, d0,r]TFor [x, y, d0, r] transposition,
In this particular embodiment, step 6. in constraints A [x, y, d0,r]T≤ f determination process is：According to one As in the case of measurement noise be much smaller than non-market value conclusion, obtain di≥d0+||x-si||；Then by di≥d0+||x-si| | it is changed into di-d0≥||x-si| |, and to di-d0≥||x-si| | both sides carry out a square expansion, obtainThen according to y=| | x | |2WithWill It is changed intoFinally willIn the form of vectors It is described, is described as：A[x,y,d0,r]T≤ f,
In this particular embodiment, step 6. in constraints
Determination process be：
6. _ 1, according to the constraints b before relaxationi=2d0||x-si| |, it can be seen that relaxed it is difficult to which this non-convex is constrained For convex constraint, but can be using corresponding conversion, therefore can be obtained using quadratic sum inequality Then willIn quadratic term expansion, obtainThen will Y=| | x | |2WithSubstitute intoIn, obtain the constraints on clocking errorFurther according to known conditions d0>=0, obtain bi≥0。
6. _ 2, to the constraints b before relaxationi=2d0||x-si| | both members square expansion, obtainThen by y=| | x | |2Substitute into In, obtainDue to constraintsRight and wrong Convex, therefore then willRelaxation is convex constraintsAgain willSubstitute intoIn, obtain
7. Second-order cone programming problem is solved using interior point method, obtains globally optimal solution, be designated as x*, x*As target The final estimate of coordinate position of the source in reference frame.
To verify the feasibility and validity of the inventive method, l-G simulation test is carried out to the inventive method.
Assuming that there is N=8 sensor, 10 × 10m centered on origin (0,0) is evenly distributed on2Square edge On, the position of target source is in 15 × 15m2Region in randomly choose.Assuming that power (the side of the measurement noise of all the sensors Difference) it is identical, beThe identical upper bound of non-market value is ρ1=ρ2=...=ρN=ρ.
The performance of test the inventive method is in the case of different obstructed path numbers with the increased of measurement noise Situation of change.Fig. 3 is given in it there is the environment of non line of sight, under conditions of unknown initial time, the number of obstructed path For 6 when, the positioning of the inventive method and existing robust positive semidefinite relaxation method and existing robust second order cone relaxation method The situation of change that performance increases with measurement noise；Fig. 4 is given in it there is the environment of non line of sight, the condition of unknown initial time Under, when the number of obstructed path is 2, the inventive method and existing robust positive semidefinite relaxation method and existing robust two The situation of change that the positioning performance of rank cone relaxation method increases with measurement noise.No matter non-regard is can be seen that from Fig. 3 and Fig. 4 Away from path it is more or less when, the performance of the inventive method is all the time better than existing robust positive semidefinite relaxation method and existing Robust second order cone relaxation method, it is sufficient to illustrate that the inventive method has enough advantages in terms of positioning precision.
The performance of the inventive method is tested with the situation of change of the number of obstructed path.Fig. 5, which gives, has non-regard Away from environment in, under conditions of unknown initial time, the standard deviation sigma of measurement noise is randomly choosed in interval [0.2,1], this hair The positioning performance of bright method and existing robust positive semidefinite relaxation method and existing robust second order cone relaxation method is with non line of sight The situation of change of the number in path.From figure 5 it can be seen that the performance of the inventive method is better than existing robust positive semidefinite all the time Relaxation method and existing robust second order cone relaxation method, it is sufficient to illustrate that the inventive method has in terms of positioning precision enough excellent Gesture.
In analogous diagram 3, Fig. 4 and Fig. 5, " robust positive semidefinite relaxation method " represents in time synchronized and there is non line of sight mistake On the premise of difference, the algorithm of the positive semidefinite relaxation based on maximum likelihood；" robust second order cone relaxation method " is represented in time synchronized With it there is non-market value on the premise of, the robust second order cone relaxed algorithm based on least square；The inventive method be when Clock is asynchronous and there is the method under conditions of non-market value.

Claims (3)

1. the localization method based on arrival time of unknown initial time in a kind of nlos environment, it is characterised in that including following Step：
1. a plane coordinate system or space coordinates are set up in wireless sensor network as reference frame；Setting is wireless There is a target source for being used for emission measurement signal and N number of sensor for being used to receive measurement signal in sensor network, and The clock for setting N number of sensor is synchronous, and the clock of target source is asynchronous with the clock of sensor；By N number of sensor in reference Coordinate position correspondence in coordinate system is designated as s1,…,sN, coordinate position of the target source in reference frame is designated as x；Wherein, N >=3, s1Represent the 1st coordinate position of the sensor in reference frame, sNRepresent n-th sensor in reference frame Coordinate position；
2. the signal transmission distance between target source and each sensor is calculated, by the letter between target source and i-th of sensor Number transmission range is designated as di, di=c × ti, wherein, 1≤i≤N, c represents the light velocity, tiRepresent that measurement signal is issued to from target source I-th of sensor receives the undergone time；
3. the signal transmission distance between target source and each sensor is described with model approach, by diModel represent For：di=d0+||x-si||+ei+ni, wherein, d0The signal transmission distance deviation that unknown signaling transmitting initial time is caused is represented, d0=c × Δ t, d0>=0, Δ t represent the difference of the clock of target source and the clock of sensor, symbol " | | | | " in asking Europe several Moral norm sign, siRepresent coordinate position of i-th of sensor in reference frame, eiRepresent that measurement signal is sent out from target source Go out to i-th of sensor and receive non-market value, n present on undergone pathiRepresent that measurement signal is sent from target source Measurement noise, n present on undergone path are received to i-th of sensoriObey the Gaussian Profile of zero-mean Represent niPower, 0≤| ni| ＜ ＜ ei≤ρi, symbol " | | " it is take absolute value symbol, ρiRepresent measurement signal from target Source is issued to the upper limit that i-th of sensor receives non-market value present on undergone path；
4. by di=d0+||x-si||+ei+niIt is changed into di-ei=(d0+||x-si||)+ni；Then to di-ei=(d0+||x-si ||)+niBoth members carry out square, obtain
Then ignore
InObtain
(di-ei)2≈(d0+||x-si||)2+2ni(d0+||x-si||)；Again will
(di-ei)2≈(d0+||x-si||)2+2ni(d0+||x-si| |) be changed into
5. basisAnd using the robust weighted least-squares method under worst case, obtain Orientation problem in launching initial time in unknown signaling and there is the environment of non-market value, is described as：
Then make WillIt is changed intoThen willIt is changed intoAfterwards in interval [0, ρi] interior determination f (ei) maximum, Work as di≤ρiShi YouWork as di>ρiShi You Finally willWithSubstitute intoIn, the orientation problem of non-convex is obtained, is described as：
Wherein, min () is takes minimum value function, and max () is to take max function,
<mrow> <mi>f</mi> <mrow> <mo>(</mo> <mn>0</mn> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>|</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> </mfrac> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>|</mo> <mo>-</mo> <msup> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>|</mo> </mrow> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> </mfrac> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>x</mi> <mo>-</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> <mo>)</mo> </mrow> <mo>,</mo> </mrow>
" s.t. " expression " constrained in ... "；
6. auxiliary variable η is introduced in the orientation problem of non-convex1,η2,…,ηi,…ηN, will
Equivalent description is：
Then by f (0), f (ρi),f(di) substitute into
And introduce auxiliary variable b1,b2,…bi,…bN, r and y, obtainThen using second order cone relaxation side Method will
<mrow> <munder> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> <mrow> <mi>x</mi> <mo>,</mo> <msub> <mi>d</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>y</mi> <mo>,</mo> <mi>r</mi> <mo>,</mo> <mo>{</mo> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>}</mo> </mrow> </munder> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> </mrow>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mi>r</mi> <mo>-</mo> <mi>y</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>s</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>x</mi> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>r</mi> <mo>+</mo> <mi>y</mi> <mo>-</mo> <mn>2</mn> <msubsup> <mi>s</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>x</mi> <mo>+</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <mn>4</mn> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mrow> <mfrac> <msup> <mrow> <mo>(</mo> <msubsup> <mi>&amp;rho;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mn>2</mn> <msub> <mi>d</mi> <mi>i</mi> </msub> <msub> <mi>&amp;rho;</mi> <mi>i</mi> </msub> <mo>+</mo> <msubsup> <mi>d</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mi>r</mi> <mo>-</mo> <mi>y</mi> <mo>+</mo> <mn>2</mn> <msubsup> <mi>s</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>x</mi> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mi>r</mi> <mo>+</mo> <mi>y</mi> <mo>-</mo> <mn>2</mn> <msubsup> <mi>s</mi> <mi>i</mi> <mi>T</mi> </msubsup> <mi>x</mi> <mo>+</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>i</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>+</mo> <msub> <mi>b</mi> <mi>i</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <mn>4</mn> <msubsup> <mi>&amp;sigma;</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>&amp;eta;</mi> <mi>i</mi> </msub> </mrow> 3
If di≤ρi
A [x, y, d0, r]T≤f
Y=| | x | |2,
bi=2d0||x-si||
In y=| | x | |2It is loose to be | | x | |2≤y、Relaxation isSecond-order cone programming problem is obtained, is described as：
Wherein, η1,η2,…,ηi,…ηNCorrespondence represents the 1st auxiliary variable, the 2nd auxiliary introduced in the orientation problem of non-convex Variable ..., i-th auxiliary variable ..., n-th auxiliary variable, b1,b2,…bi,…bNCorrespondence is represented
1st auxiliary variable of middle introducing, the 2nd auxiliary variable ..., i-th Auxiliary variable ..., n-th auxiliary variable, r is corresponding with y represent in the volume 4 that introduces Outer two auxiliary variables, the transposition for being si, the transposition for being s1, the transposition for being sN, d1 The signal transmission distance between target source and the 1st sensor is represented, dN represents the signal between target source and n-th sensor Transmission range, [x, y, d0, r] T is the transposition of [x, y, d0, r], <mrow> <mi>f</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mn>1</mn> <mn>2</mn> </msubsup> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>d</mi> <mi>N</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>N</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>;</mo> </mrow>
7. Second-order cone programming problem is solved using interior point method, obtains globally optimal solution, be designated as x*, x* is that target source exists The final estimate of coordinate position in reference frame.
2. the localization method based on arrival time of unknown initial time in nlos environment according to claim 1, it is special Levy constraints A [x, y, the d in being described step 6.0,r]T≤ f determination process is：Made an uproar according to generally measurement Sound is much smaller than the conclusion of non-market value, obtains di≥d0+||x-si||；Then by di≥d0+||x-si| | it is changed into di-d0≥|| x-si| |, and to di-d0≥||x-si| | both sides carry out a square expansion, obtainThen root According to y=| | x | |2WithWillIt is changed intoMost Afterwards willIt is described, is described as in the form of vectors：A[x,y,d0,r]T≤ f,
3. the localization method based on arrival time of unknown initial time in nlos environment according to claim 1 or 2, It is characterized in that described step 6. in constraints Determination process be：
6. _ 1, according to the constraints b before relaxationi=2d0||x-si| |, obtained using quadratic sum inequalityThen willIn quadratic term expansion, obtainThen by y=| | x | |2WithSubstitute intoIn, obtain To the constraints on clocking errorFurther according to known conditions d0>=0, obtain bi≥0；
6. _ 2, to the constraints b before relaxationi=2d0||x-si| | both members square expansion, obtainThen by y=| | x | |2Substitute into In, obtainThen willRelaxation for it is convex about Beam conditionAgain willSubstitute intoIn, obtain
CN201710269269.3A 2017-04-24 2017-04-24 The localization method based on arrival time of unknown initial time in nlos environment Active CN107271956B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201710269269.3A CN107271956B (en) 2017-04-24 2017-04-24 The localization method based on arrival time of unknown initial time in nlos environment

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201710269269.3A CN107271956B (en) 2017-04-24 2017-04-24 The localization method based on arrival time of unknown initial time in nlos environment

Publications (2)

Publication Number Publication Date
CN107271956A true CN107271956A (en) 2017-10-20
CN107271956B CN107271956B (en) 2019-07-09

Family

ID=60073987

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201710269269.3A Active CN107271956B (en) 2017-04-24 2017-04-24 The localization method based on arrival time of unknown initial time in nlos environment

Country Status (1)

Country Link
CN (1) CN107271956B (en)

Cited By (13)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108200547A (en) * 2017-11-30 2018-06-22 宁波大学 Rigid body localization method based on measurement distance
CN108872934A (en) * 2018-04-19 2018-11-23 南京邮电大学 A kind of indoor 3-D positioning method inhibited based on non-market value
CN108896959A (en) * 2018-08-02 2018-11-27 南京理工大学 A kind of mobile communication positioning method based on time of arrival (toa)
CN109061563A (en) * 2018-09-25 2018-12-21 宁波大学 Localization method based on fractional programming in a kind of nonsynchronous network
CN109597028A (en) * 2018-11-05 2019-04-09 宁波大学 Robust positioning method based on arrival time under the conditions of a kind of mixing sighting distance non line of sight
CN109597023A (en) * 2018-12-10 2019-04-09 中国人民解放军陆军工程大学 Semi-definite programming positioning method based on NLOS error elimination
CN110221245A (en) * 2019-05-28 2019-09-10 宁波大学 The robust TDOA localization method of Combined estimator target position and non-market value
CN110221244A (en) * 2019-05-24 2019-09-10 宁波大学 Based on the robust positioning method of reaching time-difference under the conditions of non line of sight
CN110658492A (en) * 2019-10-10 2020-01-07 重庆邮电大学 Iteration method for optimizing positions of indoor target and scatterer
CN110673088A (en) * 2019-08-23 2020-01-10 宁波大学 Target positioning method based on arrival time in mixed line-of-sight and non-line-of-sight environment
CN110888111A (en) * 2019-11-08 2020-03-17 宁波大学 Robust non-line-of-sight target self-positioning method based on TOA in asynchronous network
CN111007456A (en) * 2019-12-09 2020-04-14 西安邮电大学 Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination
CN111505575A (en) * 2020-03-23 2020-08-07 宁波大学 Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20020094736A (en) * 2001-06-13 2002-12-18 주식회사 케이티 Method of correction NOLS error for wireless positioning system
CN105334495A (en) * 2015-11-04 2016-02-17 宁波大学 Non-line-of-sight stable positioning method based on signal arrival time in wireless network
CN105425206A (en) * 2015-11-04 2016-03-23 宁波大学 Steady least square positioning method in nonsynchronous wireless network
CN105607039A (en) * 2016-01-27 2016-05-25 宁波大学 Robust least square positioning method based on arrival time difference in non line of sight (NLOS) environment
WO2016179202A1 (en) * 2015-05-07 2016-11-10 Alcatel Lucent Method and apparatus for determining non-line of sight bias estimation

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
KR20020094736A (en) * 2001-06-13 2002-12-18 주식회사 케이티 Method of correction NOLS error for wireless positioning system
WO2016179202A1 (en) * 2015-05-07 2016-11-10 Alcatel Lucent Method and apparatus for determining non-line of sight bias estimation
CN105334495A (en) * 2015-11-04 2016-02-17 宁波大学 Non-line-of-sight stable positioning method based on signal arrival time in wireless network
CN105425206A (en) * 2015-11-04 2016-03-23 宁波大学 Steady least square positioning method in nonsynchronous wireless network
CN105607039A (en) * 2016-01-27 2016-05-25 宁波大学 Robust least square positioning method based on arrival time difference in non line of sight (NLOS) environment

Cited By (20)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108200547A (en) * 2017-11-30 2018-06-22 宁波大学 Rigid body localization method based on measurement distance
CN108200547B (en) * 2017-11-30 2020-07-14 宁波大学 Rigid body positioning method based on measured distance
CN108872934A (en) * 2018-04-19 2018-11-23 南京邮电大学 A kind of indoor 3-D positioning method inhibited based on non-market value
CN108872934B (en) * 2018-04-19 2022-05-17 南京邮电大学 Indoor three-dimensional positioning method based on non-line-of-sight error suppression
CN108896959A (en) * 2018-08-02 2018-11-27 南京理工大学 A kind of mobile communication positioning method based on time of arrival (toa)
CN109061563A (en) * 2018-09-25 2018-12-21 宁波大学 Localization method based on fractional programming in a kind of nonsynchronous network
CN109597028A (en) * 2018-11-05 2019-04-09 宁波大学 Robust positioning method based on arrival time under the conditions of a kind of mixing sighting distance non line of sight
CN109597028B (en) * 2018-11-05 2022-11-29 宁波大学 Robust positioning method based on arrival time under mixed-line-of-sight and non-line-of-sight conditions
CN109597023A (en) * 2018-12-10 2019-04-09 中国人民解放军陆军工程大学 Semi-definite programming positioning method based on NLOS error elimination
CN110221244A (en) * 2019-05-24 2019-09-10 宁波大学 Based on the robust positioning method of reaching time-difference under the conditions of non line of sight
CN110221245A (en) * 2019-05-28 2019-09-10 宁波大学 The robust TDOA localization method of Combined estimator target position and non-market value
CN110221245B (en) * 2019-05-28 2022-04-19 宁波大学 Robust TDOA (time difference of arrival) positioning method for jointly estimating target position and non-line-of-sight error
CN110673088A (en) * 2019-08-23 2020-01-10 宁波大学 Target positioning method based on arrival time in mixed line-of-sight and non-line-of-sight environment
CN110673088B (en) * 2019-08-23 2021-06-15 宁波大学 Target positioning method based on arrival time in mixed line-of-sight and non-line-of-sight environment
CN110658492A (en) * 2019-10-10 2020-01-07 重庆邮电大学 Iteration method for optimizing positions of indoor target and scatterer
CN110888111A (en) * 2019-11-08 2020-03-17 宁波大学 Robust non-line-of-sight target self-positioning method based on TOA in asynchronous network
CN111007456B (en) * 2019-12-09 2022-11-22 西安邮电大学 Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination
CN111007456A (en) * 2019-12-09 2020-04-14 西安邮电大学 Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination
CN111505575B (en) * 2020-03-23 2022-02-11 宁波大学 Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model
CN111505575A (en) * 2020-03-23 2020-08-07 宁波大学 Sensor selection method aiming at TDOA (time difference of arrival) location based on conversion TOA (time of arrival) model

Also Published As

Publication number Publication date
CN107271956B (en) 2019-07-09

Similar Documents

Publication Publication Date Title
CN107271956A (en) The localization method based on arrival time of unknown initial time in nlos environment
CN105607039B (en) Robust least squares localization method based on reaching time-difference under nlos environment
CA2819661C (en) Correction of pressure signals measured during supersonic wind tunnel testing
CN109597028B (en) Robust positioning method based on arrival time under mixed-line-of-sight and non-line-of-sight conditions
CN110221244B (en) Robust positioning method based on arrival time difference under non-line-of-sight condition
CN106842121B (en) Robust position location method based on reaching time-difference in sighting distance and non line of sight hybird environment
CN108668358B (en) Arrival time-based cooperative positioning method applied to wireless sensor network
AU2011202367B2 (en) Method and apparatus for passive determination of target data
CN110275139B (en) Ultra-short baseline positioning system and method based on rotary primitive multiplexing
CN104296607B (en) Laser fuze closes feedback test device and test system and method for testing
CN105698886A (en) Gas flow detection method based on ultrasonic detection technique
CN109975745A (en) Localization method is unified in a kind of nearly far field based on reaching time-difference
CN105425206A (en) Steady least square positioning method in nonsynchronous wireless network
CN110554364A (en) system and method for testing radar signal pulse arrival time measurement accuracy
CN107356523A (en) Feedback force modification method is tested in real-time hybrid analog-digital simulation based on the estimation of discrete tangent rigidity
US7952523B2 (en) Method and apparatus for passively locating radar emissions from rotating transmitters
CN110673088B (en) Target positioning method based on arrival time in mixed line-of-sight and non-line-of-sight environment
CN110221245B (en) Robust TDOA (time difference of arrival) positioning method for jointly estimating target position and non-line-of-sight error
CN108828509B (en) Multi-platform multi-radiation source bearing relation judgment method
KR101850394B1 (en) Scenario based RF threat generation method and equipment
CN115685108A (en) Pulse pseudo code system fuze body target simulation system and method thereof
CN104655151B (en) The design method in swing type infrared earth sensor electric excitation source
CN108646719B (en) Weak fault detection method and system
CN109740204B (en) Method for rapidly detecting weak sinusoidal signal based on duffing oscillator reverse phase change
CN108169634B (en) Method for accurately obtaining partial discharge ultrahigh frequency signal time difference

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant