CN110333481A - A kind of joint positioning method based on distance than round algorithm and Taylor Series Expansion Method - Google Patents
A kind of joint positioning method based on distance than round algorithm and Taylor Series Expansion Method Download PDFInfo
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- CN110333481A CN110333481A CN201910619191.2A CN201910619191A CN110333481A CN 110333481 A CN110333481 A CN 110333481A CN 201910619191 A CN201910619191 A CN 201910619191A CN 110333481 A CN110333481 A CN 110333481A
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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
- G01S5/06—Position of source determined by co-ordinating a plurality of position lines defined by path-difference measurements
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Abstract
The invention discloses a kind of joint positioning methods based on distance than round algorithm and Taylor Series Expansion Method, comprising: step 1. obtains the time difference that signal source reaches each secondary base station and master base station, obtains distance difference according to the formula away from discrete time；Step 2. acquires signal source to the ratio of distances constant of time base station and master base station；Step 3. is established according to ratio of distances constant and tectonic location equation group, and preliminary position location is then obtained by least squares estimate；For step 4. using Primary Location result as the initial value of Taylor series expansion algorithms, iteration obtains more accurate target source locator value；Distance obtains last position estimation value than two groups of locator values that the Taylor series expansion algorithms of round location algorithm and given initial value obtain, weighting processing.The present invention is suitable for the signal source localization method of wireless sensor network, has the characteristics that require low positioning accuracy high monitoring device hardware clock synchronization accuracy, can accurately obtain signal source position.
Description
Technical field
The present invention relates to the signal source field of locating technology of wireless sensor network, and in particular to one kind is based on distance than circle
The joint positioning method of algorithm and Taylor Series Expansion Method.
Background technique
Wireless sensor network is the pass for generating significant impact to the production of human society, life style after internet
Key technology, and carrying out positioning to the signal source in wireless sensor network is one of the hot spot studied at present.Due to wirelessly passing
The distance of monitored signal to target BS can be readily available by ranging technology in sensor network, therefore be based on ranging skill
The localization method of art has obtained extensive research.
In wireless sensor network, the localization method for generalling use ranging technology has: received signal strength indicator
(Received Signal Strength Indication, RSSI), arrival time (Time of Arrival, TOA) reach
Time difference (Time Difference of Arrival, TDOA) and angle of arrival (Angle of Arrival, AOA).But
Each method has the advantages that respective and defect under different conditions and environment, and the localization method based on RSSI is needed according to electricity
The empirical equation that wave is propagated seeks the distance of signal source, therefore when for the environment of empirical formula, the positioning of the algorithm
Error is very big.It is not needing between signal source and base station than the advantage of the algorithm based on TOA based on the location algorithm of TDOA
It is synchronous to carry out clock, it is only necessary to which the synchronization that clock is carried out between each base station uses the clock synchronization requirement ratio of equipment
The algorithm of TOA is low.And based on the location algorithm of AOA due to carry out angle to incoming wave signal by mounted array antenna on base station
Estimation, the requirement for equipment are relatively high.
Due to different location informations, location algorithm is not also identical for the processing capacity of measurement error and various noises,
Become one of the research direction of location algorithm for the research of many algorithms alignment by union in recent years, therefore the present invention has developed one
The new joint positioning method based on distance than circle and Taylor Series Expansion Method of kind.
Summary of the invention
The purpose of the present invention is it is not high for the receiver precision in existing wireless sensor network, in the survey to signal source
Away from there are in the case where large error, individually use distance more more demanding than number of the round location algorithm to base station, and position effect
Fruit is poor, thus proposes a kind of joint positioning method based on Taylor Series Expansion Method, reduces and wants to base station number
It asks and makes its performance close to the Taylor Series Expansion Method of positioning initial value signal source actual position.
The technical solution adopted by the present invention is that:
A kind of joint positioning method based on distance than round algorithm and Taylor Series Expansion Method, specific steps include:
The schematic diagram of step 1. base station is traditional cellular localization 7BS, chooses the center that master base station is cellular localization,
Other base stations are that time base station is located on six vertex of regular hexagon, then obtain signal by broad sense cross-correlation method (GCC)
Source reaches the time difference of each secondary base station and master base station, and the difference of distance is obtained according to the formula away from discrete time；
Step 2. can obtain signal source to each secondary base station and master while executing step 1 by the method for ranging
The distance value of base station, therefore the ratio of distances constant for acquiring signal source to i-th base station and master base station is
Step 3. is according to signal source to the ratio of distances constant of time base station and master base stationEstablish simultaneously tectonic location equation
Group, then obtains preliminary position location by least squares estimate, and the method is distance than round localization method；
Step 4. is using the Primary Location result obtained by distance than round localization method as Taylor series expansion algorithms
Initial value, pass through iteration and obtain more accurate target source locator value；It the ratio between adjusts the distance circle location algorithm and Taylor series exhibition
It opens the position estimation value that algorithm positions respectively and is weighted processing, according to the residual error for indicating TDOA measured value and positioning result difference
Function ResCalculate weighting coefficient Rk, last position estimation value is finally obtained according to weighting processing.
Compared with the prior art, the invention has the following advantages:
The present invention than round location algorithm, under identical Simulation Test Environment, can obtain more prior art distance
High positioning accuracy, under any number of base stations, positioning performance of the invention is superior to existing distance than round algorithm.And it solves
The initial-value problem for Taylor Series Expansion Method of having determined, when number of base stations is more, the present invention can reach using true value as initial value
Taylor Series Expansion Method positioning performance, and distance cannot then reach this effect than round location algorithm.
Detailed description of the invention
Fig. 1 is positioning schematic of the distance of the invention provided than round algorithm.
Fig. 2 is the schematic diagram for the co-located method that the present invention provides.
Fig. 3 is the number of base stations that provides of the present invention when being 7, emulation experiment base station present position.
Fig. 4 is the number of base stations that provides of the present invention when being 7, and the error of TDOA measured value in 0-0.8km, calculate by alignment by union
Method changes than the Taylor Series Expansion Method that round location algorithm and initial value are true value with measurement error variance with individual distance
The positioning accuracy comparison diagram of change, and give carat Metro (CRLB) lower bound of unbiased esti-mator.
Fig. 5 is the number of base stations that provides of the present invention when being 6, and the error of TDOA measured value in 0-0.8km, calculate by alignment by union
Method changes than the Taylor Series Expansion Method that round location algorithm and initial value are true value with measurement error variance with individual distance
The positioning accuracy comparison diagram of change, and give carat Metro (CRLB) lower bound of unbiased esti-mator.
Fig. 6 is the number of base stations that provides of the present invention when being 5, and the error of TDOA measured value in 0-0.8km, calculate by alignment by union
Method changes than the Taylor Series Expansion Method that round location algorithm and initial value are true value with measurement error variance with individual distance
The positioning accuracy comparison diagram of change, and give carat Metro (CRLB) lower bound of unbiased esti-mator.
Fig. 7 is the number of base stations that provides of the present invention when being 4, and the error of TDOA measured value in 0-0.8km, calculate by alignment by union
Method and individual distance change than the Taylor Series Expansion Method that round location algorithm and initial value are true value with measurement error
Positioning accuracy comparison diagram, and give carat Metro (CRLB) lower bound of unbiased esti-mator.
Fig. 8 is the number of base stations that provides of the present invention when being 5, alignment by union algorithm and individual distance than round location algorithm and
Initial value is the comparison diagram for the accumulated probability distribution function that the Taylor Series Expansion Method of true value changes with measurement error, and gives
The cumulative distribution function of carat Metro (CRLB) lower bound of unbiased esti-mator is gone out.
Fig. 9 is the number of base stations that provides of the present invention when being 6, alignment by union algorithm and individual distance than round location algorithm and
Initial value is the comparison diagram for the accumulated probability distribution function that the Taylor Series Expansion Method of true value changes with measurement error, and gives
The cumulative distribution function of carat Metro (CRLB) lower bound of unbiased esti-mator is gone out.
Figure 10 is the number of base stations that provides of the present invention when being 7, and alignment by union algorithm and individual distance are than round location algorithm
The comparison diagram of the accumulated probability distribution function changed for the Taylor Series Expansion Method of true value with measurement error with initial value, and
Give the cumulative distribution function of carat Metro (CRLB) lower bound of unbiased esti-mator.
Specific embodiment
Next combined with specific embodiments below invention is further explained, but does not limit the invention to these tools
Body embodiment.One skilled in the art would recognize that present invention encompasses may include in Claims scope
All alternatives, improvement project and equivalent scheme.
Referring to Fig. 1, a kind of joint positioning method based on distance than round algorithm and Taylor Series Expansion Method of the present embodiment,
Two distances are only gived than round positioning schematic diagram, d0, d1, d2 are respectively distance of the target source to each base station, to obtain
Distance positioned at C1 and C2 is than circle, the two circles intersect at a point, and as target source position, specific steps include:
The center that step 1. chooses positioning is master base station, other base stations are time base station, then obtains signal source and reaches
The time difference of each secondary base station obtains the difference of distance according to the formula away from discrete time；
The step 1 of the present embodiment, the distance R of each base station to target sourceiWith distance difference Ri,1Specific calculating is as follows:
If (x, y) is the position to be estimated of signal source, (xi,yi) be i-th of base station transmitter known location
Away from discrete time (τi,1For TDOA measured value) formula it is as follows:
Wherein Ri,1Signal source is indicated to the distance difference of master base station and time base station, c is radio wave propagation speed,
Step 2. can obtain signal source to time base station and a master while obtaining distance difference by the method for ranging
The position of base station, acquire signal source to i-th base station and master base station ratio of distances constant
Step 3. is according to signal source to the ratio of distances constant of time base station and master base stationIntersected according to the ratio between different distance circle
Method in any carrys out tectonic location equation, and preliminary position location is then obtained by least squares estimate；Ratio of distances constant
Circle localization method is as follows:
Monitoring station B is reached by signal source S (x, y)i(xi, yi), the Euclidean distance formula of i=1,2 ..., N+1 can obtain,
It is available to arrange expansion
If S '=[x, y, x2+y2] it is that unknown vector establishes equation, N number of above-mentioned equation constitutes positional matrix
GS=b (6)
In formula,
Then the least-squares estimation value of S has been obtained:
S=(GTG)-1GTb (8)
Then the position of signal source is S=S [1:2].
With reference to Fig. 2, distance is calculated than the Taylor series expansion of round location algorithm and given initial value in the present embodiment step 4
Two groups of positioning result values that method obtains, then according to the residual error function R for indicating TDOA measured value and positioning result differenceesIt calculates
Weighting coefficient Rk, last position estimation value is finally obtained according to weighting processing.
In order to calculate weighting coefficient, the residual error between positioning result and measured value specifically calculates as follows are as follows:
K kind location algorithm is respectively adopted to same group of TDOA measured value, then the weighting coefficient R of K kind algorithmkCalculating side
Method are as follows:
The final estimated position of signal source are as follows:
As shown in figure 3, benefit MATLAB Programming with Pascal Language is emulated, the distribution form of base station is traditional 7BS, be one just
The structure of hexagon, the master base station including one in center, other base stations are all in the cellular vertex position of regular hexagon.It adopts
Positioning accuracy of the invention is measured with the mean square error between positioning result and true value,
Conclusion:
As seen from Figure 4, base station number be 7 when the present invention than individual distance than round algorithm measurement error variance
Square mean error amount (RMSE) wants low when for 0-0.8km, and the bigger effect of error is more obvious, and is that positioning is initial with true value
The locating effect of the Taylor series expansion algorithms of value is compared to very close, since Taylor series expansion is calculated in actual location
Method can not obtain the positioning initial value in actual signal source, it can be said that bright locating effect of the invention is good.It can be seen by Fig. 5
Out, when base station number is 6, i.e., positioning performance exists than individual distance than round algorithm the present invention in the case that location information is reduced
Small 0.1km or so under mean square error, positioning performance and positioning initial value are the positioning of the Taylor series expansion algorithms of true value
Effect is also very close.In Fig. 6 as can be seen that when number of base stations is 5, when the effect of positioning compared to base station number is 6 and 7
It is more preferable than round localization method than distance, therefore can illustrate that the present invention requires to be lower than distance than circle to the number of base stations for participating in positioning
Algorithm, and positioning performance is better than distance than round location algorithm, closer to the Taylor for true value being positioning initial value
The mean square error of series expansion algorithms.As seen from Figure 7, when locating base station number is 4, locating effect of the invention is still good
In distance than round algorithm.
In addition to the mean square error between positioning result and true value come the performance of measure algorithm, using can more embody algorithm
The Cumulative Distribution Function (CDF) of positioning performance carries out error performance analysis to positioning result.
The comparison changed by Cumulative Distribution Function of the Fig. 8 when base station number is 5 with measurement error, it can be deduced that knot
By: ratio of the present invention is higher than round position success rate based on distance, and especially when measurement error is in 0.6km or less, the present invention has
75% probability positions successfully, and distance than round position success rate 55%, can be seen that by Fig. 9 and Figure 10 Lai when base station
When number reaches 6 and 7 when increasing, cumulative distribution function of the invention is the Taylor grade of true value nearly close to positioning initial value
The Cumulative Distribution Function of number deployment algorithm.
The present invention is suitable for the signal source localization method of wireless sensor network, has synchronous to monitoring device hardware clock
The features such as precision and the number of devices requirement positioned to participation are low, and positioning accuracy is high in large error, can accurately obtain letter
The position in number source.
Claims (4)
1. a kind of joint positioning method based on distance than round algorithm and Taylor Series Expansion Method, it is characterized in that as follows
It carries out:
The center that step 1. chooses cellular localization is master base station, and six vertex of the regular hexagon of cellular localization are time base
It stands, then obtains the time difference that signal source reaches each secondary base station, signal source is obtained to master according to the formula away from discrete time
The distance difference of base station and time base station；
Step 2. while obtaining distance difference, acquire signal source to i-th base station and master base station ratio of distances constant
Step 3. is according to signal source to the ratio of distances constant of time base station and master base station, and ratio of distances constant circle localization method tectonic location
Then equation obtains preliminary position location by least square method；
Step 4. is using preliminary position location as the initial value of Taylor series expansion algorithms, circle location algorithm of the ratio between adjusting the distance
The position estimation value positioned respectively with Taylor series expansion algorithms is weighted processing, obtains last position estimation value.
2. a kind of alignment by union side based on distance than round algorithm and Taylor Series Expansion Method according to claim 1
Method, it is characterised in that: in step 1, the specific calculating of the distance difference of signal source to master base station and i-th base station is as follows:
The distance of each base station to target source is Ri
If (x, y) is the position to be estimated of signal source, (xi,yi) be i-th of base station transmitter known location；
Formula away from discrete time is as follows:
Wherein Ri,1Signal source is indicated to the distance difference of master base station and time base station, c is radio wave propagation speed, τi,1For TDOA measurement
Value.
3. a kind of alignment by union side based on distance than round algorithm and Taylor Series Expansion Method according to claim 2
Method, it is characterised in that: in step 3, the method construct positioning equation that the ratio between different distance circle intersects at a point, specially
Monitoring station B is reached by signal source S (x, y)i(xi, yi), the Euclidean distance formula of i=1,2 ..., N+1 can obtain,
It is available to arrange expansion
If S '=[x, y, x2+y2] it is that unknown vector establishes equation, N number of above-mentioned equation constitutes positional matrix
GS=b (5)
In formula,
Then the least-squares estimation value of S has been obtained:
S=(GTG)-1GTb (7)
The then Primary Location position S=S [1:2] of signal source.
4. a kind of combining than round algorithm and Taylor Series Expansion Method based on distance according to claim 1-3
Localization method, it is characterised in that: the detailed process of processing is weighted in step 4 are as follows:
Define the residual error between positioning result and measured value are as follows:
riFor target source to the distance measure of i base station,For the vector of positioning result, NBSFor the base for participating in positioning
It stands number；
K kind location algorithm is respectively adopted to same group of TDOA measured value, then the weighting coefficient R of K kind location algorithmkCalculating side
Method are as follows:
For the positioning result of kth kind algorithm, the final estimated position of signal sourceAre as follows:
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111148219A (en) * | 2019-12-23 | 2020-05-12 | 杭州电子科技大学 | Distance ratio circle positioning method based on TOA/AOA |
| CN111414578A (en) * | 2020-03-18 | 2020-07-14 | 电子科技大学 | Wireless propagation model based on Taylor expansion |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102026370A (en) * | 2010-12-21 | 2011-04-20 | 西安电子科技大学 | Time difference on arrival (TDOA) locating method based on circumferentially distributed monitoring nodes |
| CN104080165A (en) * | 2014-06-05 | 2014-10-01 | 杭州电子科技大学 | Indoor wireless sensor network positioning method based on TDOA |
| CN109283490A (en) * | 2018-11-14 | 2019-01-29 | 东南大学 | The UWB localization method of Taylor series expansion based on mixing least square method |
-
2019
- 2019-07-10 CN CN201910619191.2A patent/CN110333481A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102026370A (en) * | 2010-12-21 | 2011-04-20 | 西安电子科技大学 | Time difference on arrival (TDOA) locating method based on circumferentially distributed monitoring nodes |
| CN104080165A (en) * | 2014-06-05 | 2014-10-01 | 杭州电子科技大学 | Indoor wireless sensor network positioning method based on TDOA |
| CN109283490A (en) * | 2018-11-14 | 2019-01-29 | 东南大学 | The UWB localization method of Taylor series expansion based on mixing least square method |
Non-Patent Citations (2)
| Title |
|---|
| 刘恩华 等: ""基于Chan和Taylor的改进定位算法在智慧农业中的应用研究"", 《中国农机化学报》 * |
| 耿友林 等: ""基于卡尔曼滤波的接收信号强度指示差值定位算法"", 《电子与信息学报》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111148219A (en) * | 2019-12-23 | 2020-05-12 | 杭州电子科技大学 | Distance ratio circle positioning method based on TOA/AOA |
| CN111414578A (en) * | 2020-03-18 | 2020-07-14 | 电子科技大学 | Wireless propagation model based on Taylor expansion |
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Application publication date: 20191015 |