CN103634903A - Noise canceling and positioning method of low-power-consumption small-scale equipment - Google Patents

Noise canceling and positioning method of low-power-consumption small-scale equipment Download PDF

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CN103634903A
CN103634903A CN201310595440.1A CN201310595440A CN103634903A CN 103634903 A CN103634903 A CN 103634903A CN 201310595440 A CN201310595440 A CN 201310595440A CN 103634903 A CN103634903 A CN 103634903A
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bancroft
application region
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CN103634903B (en
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徐兵
齐望东
朱亚松
威力
陈剑
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PLA University of Science and Technology
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Abstract

The invention discloses a noise canceling and positioning method of low-power-consumption small-scale equipment. The method comprises the following steps of measuring to obtain the distance difference between a to-be-positioned node and an anchor node, determining the initial position of the to-be-positioned node by using a Bancroft method, if the Bancroft method cannot be used for resolving or the resolving result is not in a Bancroft method application region, determining the position of the to-be-positioned node by using a Chan method, and regarding the calculating result as a final positioning result. The positioning method disclosed by the invention solves the problem that a morbid region exists in the existing method, creatively and complementarily combines the advantages of the two methods, and is simple in calculation, high in noise canceling capability, high in processing precision and particularly suitable for positioning the low-power-consumption small-scale equipment.

Description

Low-power consumption mini-plant anti-noise localization method
Technical field
The invention belongs to object localization technical field, particularly a kind of low-power consumption mini-plant anti-noise localization method based on range difference.
Background technology
Positional information, as the key foundation information of modern society, is being brought into play the effect becoming more and more important in national economy, science and techniques of defence and daily life.The satellite-based navigation system that the GPS of take is representative has made numerous application obtain conveniently location-based service, but in the systems such as wireless sensor network, mobile Internet, Tactical Internet, satellite-based navigation system is difficult to provide effective location-based service sometimes.For example: in wireless sensor network, for numerous miniature low-power consumption nodes, all to increase GPS receiver still technical all infeasible economically; In mobile Internet, user, normally in city or indoor environment, because gps signal is faint, often can be difficult to play a role because building blocks; In Tactical Internet, satellite based navigational system is probably because being disturbed and cannot use by enemy.At this moment just need to rely on the self align technology of these systems that positional information is provided.Meanwhile, in these systems, distance measuring noises is conventionally larger, to providing exact position service to propose new challenge.
Location technology is divided into two large classes conventionally: the location based on range finding and non-ranging location.Non-ranging location relies on internodal link information to infer node location information, and positioning precision is not high.Position is determined in location based on the range finding generally measurement based on certain range information, and positioning precision is higher conventionally, is therefore more suitable for providing high-precision location-based service.
For the navigation system based on range finding, position fixing process can be divided into range finding and two stages of location compute.
The range finding stage obtains the information such as distance, range difference or azimuth according to certain feature of radio signal (as amplitude, phase place, the time of advent etc.), distance measuring method comprises the range finding time of advent (TOA), the poor range finding time of advent (TDOA), azimuth range finding (AOA), received signal strength range finding (RSSI) and radio interference range finding (RIR) etc.The location compute stage moves according to ranging information the process that certain location algorithm is determined target to be positioned final position.The selection of location compute phase orientation algorithm plays vital effect to final positioning precision.
Location algorithm can be divided into iterative algorithm and closed solution algorithm two classes, and wherein iterative algorithm computation complexity is high, and has the local convergence problem of iteration result, is not suitable for the weak or high application scenarios of requirement of real-time of low-power consumption, computing capability; And closed solution algorithm has explicit solution, computation complexity is low, and there is no the problem of local convergence.In the closed solution location algorithm based on range difference, relatively good two kinds of the most frequently used and performance is that Chan method is [referring to document Chan Y.T., Ho K.C., " A simple and efficient estimator for hyperbolic location " .IEEE Transactions on Signal Processing, vol.42, no.8, pp.1905-1915, August1994] and Bancroft method [referring to document Bancroft S., " An Algebraic Solution of the GPS Equations " .IEEE Transactions on Aerospace and Electronic Systems, vol.AES-21, no.1, pp.56-59, January1985 and Mellen G.II, Pachter M., Raquet J., " Closed-form solution for determining emitter location using time difference of arrival measurements " .IEEE Transactions on Aerospace and Electronic Systems, vol.39, no.3, pp.1056-1058, July2003].First Chan method is regarded the nuisance variable of introducing in linearization procedure and variable to be estimated as independent variable and is carried out first step weighted least-squares and solve, and then utilizes the relation between nuisance variable and variable to be estimated to carry out the precision that second step weighted least-squares further improves positioning result.Bancroft method puts forward for separating GPS equation at first, but its thought equally can be for the positioning calculation based on range difference, first the method is used least square that variable to be estimated is showed by the formula that contains nuisance variable, then utilize the relation between them to form the quadratic equation about nuisance variable, separate quadratic equation and obtain the estimated value of nuisance variable, and then obtain the estimated value of variable to be estimated.
But a little less than above-mentioned closed solution location algorithm anti-noise ability, and research finds that these class methods can exist the ill region of poor performance.As shown in Figure 2 and Figure 3, in ill region, existing closed solution location algorithm often can not reach performance lower bound---CramerRao circle (CRLB, Cramer-Rao Lower Bound), or the noise gate that can reach CRLB is very low, anti-noise ability extremely a little less than, had a strong impact on the precision of positioning result.
Summary of the invention
The object of the present invention is to provide a kind of low-power consumption mini-plant anti-noise localization method, amount of calculation is little, and noise resisting ability is strong, high to the positioning precision of low-power consumption mini-plant.
The technical solution that realizes the object of the invention is: a kind of low-power consumption mini-plant anti-noise localization method, it is characterized in that, and comprise the steps:
10) range difference obtains: obtain node to be positioned to be no less than the range difference of 2 anchor nodes to other with reference to anchor node and node to be positioned;
20) initial position resolves: according to node to be positioned, to the range difference to other anchor node with reference to anchor node and node to be positioned, use Bancroft method to determine node initial position to be positioned;
30) judge whether initial position resolves successful: according to the situation of the quadratic equation solution of Bancroft method, judge that whether initial position resolves successful, as no, goes to (50) step;
40) judge whether node to be positioned is positioned at Bancroft method suitable application region: judge the whether suitable application region in Bancroft method of described node initial position to be positioned, in this way, go to (60) step;
50) use Chan method to determine node location to be positioned;
60) export node location to be positioned.
The present invention compared with prior art, its remarkable advantage: because the technical program makes full use of Chan method and Bancroft method has explicit solution, computation complexity is low, and the advantage that there is no the problem of local convergence, and there is certain complementary feature in both ill regions and non-ill region, overcome the ill regional issue that existing closed solution localization method exists, utilized innovatively the performance advantage of two kinds of methods, noise resisting ability and the positioning precision of closed solution localization method have effectively been improved, amount of calculation is little, noise resisting ability is strong, positioning precision to low-power consumption mini-plant is high.
Below in conjunction with accompanying drawing, the present invention is described in further detail.
Accompanying drawing explanation
Fig. 1 is low-power consumption mini-plant anti-noise localization method flow chart of the present invention.
Fig. 2 is that node to be positioned is p 1=[50,500] ttime MSE-SNR comparison diagram.
Fig. 3 is that node to be positioned is p 2=[1500 ,-200] ttime MSE-SNR comparison diagram.
Fig. 4 is the MSE mean value compare figure of positioning result.
In figure: CRLB is CramerRao circle (CRLB, Cramer-Rao Lower Bound), Chan is for adopting Chan method acquired results, Bancroft is for adopting Bancroft method acquired results, new method is for adopting low-power consumption mini-plant anti-noise localization method acquired results of the present invention, abscissa represents the size (dB) of distance measuring noises, and the longitudinal axis represents positioning result mean square deviation (MSE, Mean Squared Errors).
Embodiment
As shown in Figure 1, low-power consumption mini-plant anti-noise localization method of the present invention, comprises the steps:
10) range difference obtains; Obtain node to be positioned to be no less than the range difference of 2 anchor nodes to other with reference to anchor node and node to be positioned;
This step is prior art.
Apart from difference, can obtain by the mode of TDOA, first between each anchor node, carry out clock synchronous, synchronously by FTSP clock synchronization protocol, complete; Then node emission source signal to be positioned, each anchor node record receives the time t of source signal 1, t 2..., t m(number that wherein M is anchor node); Finally according to the signal reception time of each anchor node, calculate node to be positioned to the range difference of each anchor node and No. 1 anchor node (with reference to anchor node), i.e. r i1=c * (t i-t 1), the propagation velocity that wherein c is source signal.In Cellular Networks, by observation, arrive time difference (OTDOA, Observed Time Difference of Arrival) obtain range difference measured value, each base station keeps clock synchronous, the down-bound pilot frequency signal of moving table measuring different base station to be positioned, obtain the propagation time difference of different base station descending pilot frequency, and then obtain travelling carriage to the range difference of different base station.
Apart from difference also can find range by radio interference (RIR, Radio Interferometric Ranging) obtain, wherein the most basic range cells is two transmitting nodes and two four-tuple that receiving node forms.First carry out clock synchronous, the right approaching sine wave signal of latter two transmitting node tranmitting frequency, two receiving nodes are measured the information such as the amplitude, phase place of received beat signal, phase difference by the measured beat signal of resulting two receiving nodes in a plurality of frequencies just can obtain four internodal distance restraint relations, and this distance restraint relation can be further converted to apart from difference again.
20) initial position resolves: according to node to be positioned, to the range difference to other anchor node with reference to anchor node and node to be positioned, use Bancroft method to determine node initial position to be positioned;
Described use Bancroft method determines that node initial position to be positioned (20) step is specially:
21) separate quadratic equation
(g Tg-1)r 1 2-2g Thr 1+h Th=0
Obtain r 1estimated value;
In formula:
H=(A ta) -1a tb, g=(A ta) -1a tr, wherein A=[x 2-x 1, x 3-x 1..., x m-x 1; y 2-y 1, y 3-y 1..., y m-y 1] t, b=-0.5[r 2, 1 2-|| A 2|| 2+ || A 1|| 2, r 3, 1 2-|| A 3|| 2+ || A 1|| 2..., r m, 1 2-|| A m|| 2+ || A 1|| 2] t, R=[r 2, 1, r 3, 1..., r m, 1] t;
Anchor node is A i=[x i, y i] t, i=1,2 ..., M (number that M is anchor node, M>=3), node to be positioned is p=[x, y] t, r i=|| p – A i|| represent node p to be positioned and anchor node A idistance, r i, jrepresent that node p to be positioned is to anchor node A iand A jrange difference;
22) situation of judgement quadratic equation solution:
Make Δ=(g th) 2-(g tg-1) h th,
221) if g tg-1=0, equation has unique solution r 1=h th/ (2g th);
222) if Δ <0 makes r 1=-1, p=A 1, Bancroft method is resolved end;
223) if Δ=0, equation has unique solution r 1=g th/ (g tg-1);
224) if Δ >0 proceeds as judged:
2241) if (g th-Δ 0.5)/(g tg-1) >0 and (g th+ Δ 0.5)/(g tg-1) <0, equation is correct separates as r 1=(g th-Δ 0.5)/(g tg-1);
2242) if (g th-Δ 0.5)/(g tg-1) <0 and (g th+ Δ 0.5)/(g tg-1) >0, equation is correct separates as r 1=(g th+ Δ 0.5)/(g tg-1);
2243) if (g th-Δ 0.5)/(g tg-1) <0 and (g th+ Δ 0.5)/(g tg-1) <0, makes r 1=-1, p=A 1, Bancroft method is resolved end;
2244) if (g th-Δ 0.5)/(g tg-1) >0 and (g th+ Δ 0.5)/(g tg-1) >0, equation has two efficient solution r 1=(g th-Δ 0.5)/(g tg-1) and r 1=(g th+ Δ 0.5)/(g tg-1), use least square index
Figure BDA0000420109200000051
correct judgment solution,
Wherein
Figure BDA0000420109200000053
expression is according to the range difference calculating after the estimated value of position that solves of quadratic equation, and the position of node to be positioned is according to p=h-gr 1calculate,
Figure BDA0000420109200000054
represent range difference measured value, with the residual sum of squares (RSS) minimum of measured value be correct solution;
23) separate quadratic equation and obtain r 1estimated value after, by its substitution formula p=h-gr 1, obtain the non-weighted estimation p of node location to be positioned u:
By p ucalculate node to be positioned to the distance r of each anchor node Ai i,
Make h=(A twA) -1a twb, g=(A twA) -1a twR, wherein the definition of A, b, R is the same, W=(DQD) -1, D=diag{r 2, r 3..., r m, Q=I m-1+ 1, separate quadratic equation (g tg-1) r 1 2-2g thr 1+ h th=0 just can obtain r 1estimated value, the solution of quadratic equation can run into several situations with (22) step, and adopts same processing mode
24) obtaining r 1estimated value after, by its substitution formula p=h-gr 1just obtain the weighted estimation p of node location to be positioned w:
25) calculate p urange difference and p to each anchor node wto the range difference of each anchor node, then according to least square index
Figure BDA0000420109200000052
at p uand p wthe conduct node initial position to be positioned p of middle selection residual error minimum.
30) judge whether initial position resolves successful: according to the situation of the quadratic equation solution of Bancroft method, judge that whether initial position resolves successful, as no, goes to (50) step;
Describedly judge that initial position resolves whether success (30) step and is specially:
If quadratic equation solution r 1=-1, initial position resolve unsuccessful, otherwise success.
40) judge whether node to be positioned is positioned at Bancroft method suitable application region: judge the whether suitable application region in Bancroft method of described node initial position to be positioned, in this way, go to (60) step;
Area to be targeted is divided into two parts: anchor node perimeter and anchor node interior zone, used respectively Chan method and Bancroft method to resolve.
Described judge described node initial position to be positioned whether a kind of method of suitable application region (40) step in Bancroft method be specially:
41) get the barycenter C of anchor node,
Figure BDA0000420109200000061
42) for all adjacent anchor node A that form direction in accordance with polygon iand A j, carry out whether in Bancroft side
The suitable application region judgement of method;
Described for all adjacent anchor node A iand A j, carry out the whether judgement of the suitable application region in Bancroft method (42) step and be specially:
421) get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is line segment A ia jthe point P of 1/2nd length;
422) judgement is by node p to be positioned and barycenter C substitution A ia jwhether linear equation is positive and negative identical;
423) if different, the node to be positioned suitable application region in Bancroft method not;
424) if identical, judgement is by node to be positioned and barycenter C point substitution PA i, PA jwhether linear equation is positive and negative all identical;
425) if different, the node to be positioned suitable application region in Bancroft method not.
43) if still there is not the not suitable application region in Bancroft method of node to be positioned after finishing for all adjacent anchor node judgements, node to be positioned is in Bancroft method suitable application region.
Describedly judging whether node initial position to be positioned is positioned at Bancroft method suitable application region (40) step, can also be to comprise:
61) judge the triangle inside whether node p to be positioned forms at any three anchor nodes, if at least one triangle is inner therein, node p to be positioned is in Bancroft method suitable application region, and judgement finishes; Otherwise, proceed following steps;
Judge node p to be positioned whether the method in triangle inside comprise area determining method, utilize vector cross product determining method, some homonymy determining method and oriented area determining method.
62) get the barycenter C of anchor node,
Figure BDA0000420109200000062
63) for all adjacent anchor node A that form direction in accordance with polygon iand A j, get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is the some P of l length, wherein 0≤l≤50*A ia j; If node p to be positioned is positioned at triangle PA ia jinside, node to be positioned is in Bancroft method suitable application region, judgement finishes;
64) if all there is not the above-mentioned condition that judgement is stopped, node to be positioned is not positioned at Bancroft method suitable application region.
Describedly judging whether node initial position to be positioned is positioned at Bancroft method suitable application region (40) step, can be also to comprise:
(71) judge whether node p to be positioned is positioned at the polygonal inside being comprised of all anchor nodes, if so, node p to be positioned is in Bancroft method suitable application region, and judgement finishes, otherwise ,-proceed following steps;
Judge node p to be positioned whether the method in polygon inside comprise that horizontal/vertical intersects diagnostic method, multiplication cross diagnostic method, angle and diagnostic method, the oriented area determining method of counting.
72) get the barycenter C of anchor node,
Figure BDA0000420109200000071
73) for all adjacent anchor node A that form direction in accordance with polygon iand A j, get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is the some P of l length, wherein 0≤l≤50*A ia j; If node p to be positioned is positioned at triangle PA ia jinside, node to be positioned is in Bancroft method suitable application region, judgement finishes;
74) if all there is not the above-mentioned condition that judgement is stopped, node to be positioned is not positioned at Bancroft method suitable application region.
50) use Chan method to determine node location to be positioned;
If node to be positioned is positioned at Chan method suitable application region, or use Bancroft method to occur situation about can not successfully resolve, use Chan method to resolve.
Described use Chan method determines that node location to be positioned (50) step is specially:
51) node location to be positioned is worth p according to a preliminary estimate efor
p e=(G 1 TQ -1G 1) -1G 1 TQ -1h 1，
Wherein: Q=I m-1+ 1, G 1=[x 2-x 1, x 3-x 1..., x m-x 1; y 2-y 1, y 3-y 1..., y m-y 1; r 21, r 3, 1..., r m, 1] t, p e=[x, y, r 1] t, h 1=-0.5[r 2, 1 2-|| A 2|| 2+ || A 1|| 2, r 3, 1 2-|| A 3|| 2+ || A 1|| 2..., r m, 1 2-|| A m|| 2+ || A 1|| 2] t;
52) utilize node location to be positioned to be worth according to a preliminary estimate p ecalculate node p to be positioned to each anchor node A idistance r i;
53) node location estimated value to be positioned
p e=( G1 TW 1G 1) -1G 1 TW 1h 1，
Wherein: W 1=(DQD) -1, D=diag{r 2, r 3..., r m;
54) node location reference value to be positioned
p a=(G 2 TW 2G 2) -1G 2 TW 2h 2，
Wherein: G 2=[1,0; 0,1; 1,1; ], p a=[(x-x 1) 2; (y-y 1) 2], h 2=[(p e(1)-x 1) 2; (p e(2)-y 1) 2; (p e(3)) 2], W 2=(D ' (G 1 tw 1g 1) -1d ') -1, D '=diag{x – x 1, y – y 1, r 1;
Thereby, utilize r 1and the restriction relation between x, y further improves the precision of estimation.
55) node location determined value to be positioned
p=p a 0.5⊙sgn(p e(1,2)-A 1)+A 1，
Wherein: sgn () is sign function;
Thereby utilize node location estimated value p to be positioned eget rid of ambiguous solution.
If p under strong noise ain element there is the situation of negative value,
p=p e(1,2)。
60) export node location to be positioned.
To display, export the position coordinates of node to be positioned;
Because the technical program makes full use of Chan method and Bancroft method has advantages of explicit solution, computation complexity is low and there is no local convergence problem, and there is certain complementary feature in both ill regions and non-ill region, overcome the ill regional issue that existing closed solution localization method exists, effectively improved the precision of noise resisting ability and the positioning result of closed solution localization method.
The present invention can carry out by emulation the validity of verification method.The anchor node coordinate using during emulation is A 1=[0,0] t, A 2=[600 ,-100] t, A 3=[1225,50] t, A 4=[1300,1350] t, A 5=[650,1550] t, A 6=[150,1200] t.
Fig. 2 represents that working as node to be positioned is p 1=[50,500] ttime positioning result MSE-SNR figure.
Fig. 3 represents that working as node to be positioned is p 2=[1500 ,-200] ttime positioning result MSE-SNR figure, in figure, abscissa represents the size (10dB～25dB) of distance measuring noises, the longitudinal axis represents the size of positioning result mean square deviation (MSE, Mean Squared Errors).
Fig. 4 represents that the working range when navigation system is [500,1700;-500,1700], take 10 * 10 under the time-10dB～25dB noise of getting anchor point in working range of interval the MSE average of positioning result.
From simulation result, can find out: Chan method is of serious failure when p1 position, only can when be less than when noise-5dB, just can reach CRLB, and new method still can reach CRLB when noise size is 25dB, comparing Chan method has improved 30dB; When p2 position, Bancroft method is of serious failure, even-10dB noise still can not reach CRLB when big or small, and new method can reach CRLB equally when 25dB noise size.As can be seen from Figure 4, the MSE average of Bancroft method is very poor, and far away higher than CRLB, the ill region that illustration method exists is a lot, has had a strong impact on the overall performance of method; Although and Chan method can reach CRLB under low noise, when noise increases, the MSE of positioning result can be higher than CRLB; Meanwhile, new method can be closer to CRLB than two kinds of methods before, under best-case MSE average can than Chan method low 4.1dB(be MSE average be Chan method 38.91%), the performance boost of comparing Bancroft method is larger.
Simulation result shows, in p1 position, than Chan method, noise gate brought up to 25dB from-5dB, in p2 position, than Bancroft method, noise gate brought up to 25dB from-10dB; Under best-case, MSE average can be reduced to 38.91% of Chan method, and the performance boost of comparing Bancroft method is larger.The technical program significantly improves noise resisting ability and the positioning precision of method in the situation that having low computation complexity.

Claims (8)

1. a low-power consumption mini-plant anti-noise localization method, is characterized in that, comprises the steps:
10) range difference obtains: obtain node to be positioned to be no less than the range difference of 2 anchor nodes to other with reference to anchor node and node to be positioned;
20) initial position resolves: according to node to be positioned, to the range difference to other anchor node with reference to anchor node and node to be positioned, use Bancroft method to determine node initial position to be positioned;
30) judge whether initial position resolves successful: according to the situation of the quadratic equation solution of Bancroft method, judge that whether initial position resolves successful, as no, goes to (50) step;
40) judge whether node to be positioned is positioned at Bancroft method suitable application region: judge the whether suitable application region in Bancroft method of described node initial position to be positioned, in this way, go to (60) step;
50) use Chan method to determine node location to be positioned;
60) export node location to be positioned.
2. low-power consumption mini-plant anti-noise localization method according to claim 1, is characterized in that, described initial position resolves (20) step and comprises:
21) separate quadratic equation
(g Tg-1)r 1 2-2g Thr 1+h Th=0
Obtain r 1estimated value;
In formula:
H=(A ta) -1a tb, g=(A ta) -1a tr, wherein A=[x 2-x 1, x 3-x 1..., x m-x 1; y 2-y 1, y 3-y 1..., y m-y 1] t, b=-0.5[r 2, 1 2-|| A 2|| 2+ || A 1|| 2, r 3, 1 2-|| A 3|| 2+ || A 1|| 2..., r m, 1 2-|| A m|| 2+ || A 1|| 2] t, R=[r 2, 1, r 3, 1..., r m, 1] t;
Anchor node is A i=[x i, y i] t, i=1,2 ..., M (number that M is anchor node, M>=3), node to be positioned is p=[x, y] t, r i=|| p – A i|| represent node p to be positioned and anchor node A idistance, r i, jrepresent that node p to be positioned is to anchor node A iand A jrange difference;
22) situation of judgement quadratic equation solution:
Make Δ=(g th) 2-(g tg-1) h th,
221) if g tg-1=0, equation has unique solution r 1=h th/ (2g th);
222) if Δ <0 makes r 1=-1, p=A 1, Bancroft method is resolved end;
223) if Δ=0, equation has unique solution r 1=g th/ (g tg-1);
224) if Δ >0 proceeds as judged:
2241) if (g th-Δ 0.5)/(g tg-1) >0 and (g th+ Δ 0.5)/(g tg-1) <0, equation is correct separates as r 1=(g th-Δ 0.5)/(g tg-1);
2242) if (g th-Δ 0.5)/(g tg-1) <0 and (g th+ Δ 0.5)/(g tg-1) >0, equation is correct separates as r 1=(g th+ Δ 0.5)/(g tg-1);
2243) if (g th-Δ 0.5)/(g tg-1) <0 and (g th+ Δ 0.5)/(g tg-1) <0, makes r 1=-1, p=A 1, Bancroft method is resolved end;
2244) if (g th-Δ 0.5)/(g tg-1) >0 and (g th+ Δ 0.5)/(g tg-1) >0, equation has two efficient solution r 1=(g th-Δ 0.5)/(g tg-1) and r 1=(g th+ Δ 0.5)/(g tg-1), use least square index
Figure FDA0000420109190000021
correct judgment solution,
R wherein
Figure FDA0000420109190000023
expression is according to the range difference calculating after the estimated value of position that solves of quadratic equation, and the position of node to be positioned is according to p=h-gr 1calculate,
Figure FDA0000420109190000024
represent range difference measured value, with the residual sum of squares (RSS) minimum of measured value be correct solution;
23) separate quadratic equation and obtain r 1estimated value after, by its substitution formula p=h-gr 1, obtain the non-weighted estimation p of node location to be positioned u:
By p ucalculate node to be positioned to each anchor node A idistance r i,
Make h=(A twA) -1a twb, g=(A twA) -1a twR, wherein the definition of A, b, R is the same, W=(DQD) -1, D=diag{r 2, r 3..., r m, Q=I m-1+ 1,
Separate quadratic equation (g tg-1) r 1 2-2g thr 1+ h th=0 obtains r 1estimated value, the solution of quadratic equation can run into several situations with (22) step, and adopts same processing mode;
24) obtaining r 1estimated value after, by its substitution formula p=h-gr 1just obtain the weighted estimation p of node location to be positioned w:
25) calculate p urange difference and p to each anchor node wto the range difference of each anchor node, then according to least square index
Figure FDA0000420109190000022
at p uand p wthe conduct node initial position to be positioned p of middle selection residual error minimum.
3. low-power consumption mini-plant anti-noise localization method according to claim 2, is characterized in that: describedly judge initial position resolves whether success (30) step is specially:
If quadratic equation solution r 1=-1, initial position resolve unsuccessful, otherwise success.
4. low-power consumption mini-plant anti-noise localization method according to claim 2, is characterized in that, describedly judges whether node initial position to be positioned is positioned at Bancroft method suitable application region (40) step and comprises:
41) get the barycenter C of anchor node,
Figure FDA0000420109190000031
42) for all adjacent anchor node A that form direction in accordance with polygon iand A j, carry out the whether judgement of the suitable application region in Bancroft method;
43) if still there is not the not suitable application region in Bancroft method of node to be positioned after finishing for all adjacent anchor node judgements, node to be positioned is in Bancroft method suitable application region.
5. low-power consumption mini-plant anti-noise localization method according to claim 4, it is characterized in that, described for all adjacent anchor node Ai and Aj that form direction in accordance with polygon, carry out whether suitable application region judgement (42) step in Bancroft method and comprise:
421) get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is the some P of l length, wherein 0≤l≤50*A ia j;
422) judgement is by node p to be positioned and barycenter C substitution A ia jwhether linear equation is positive and negative identical;
423) if different, the node to be positioned suitable application region in Bancroft method not;
424) if identical, judgement is by node to be positioned and barycenter C point substitution PA i, PA jwhether linear equation is positive and negative all identical;
425) if different, the node to be positioned suitable application region in Bancroft method not.
6. low-power consumption mini-plant anti-noise localization method according to claim 2, is characterized in that: describedly judge whether node initial position to be positioned is positioned at Bancroft method suitable application region (40) step and comprises:
61) judge the triangle inside whether node p to be positioned forms at any three anchor nodes, if at least one triangle is inner therein, node p to be positioned is in Bancroft method suitable application region, and judgement finishes; Otherwise, proceed following steps;
62) get the barycenter C of anchor node,
Figure FDA0000420109190000032
63) for all adjacent anchor node A that form direction in accordance with polygon iand A j, get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is the some P of l length, wherein 0≤l≤50*A ia j; If node p to be positioned is positioned at triangle PA ia jinside, node to be positioned is in Bancroft method suitable application region, judgement finishes;
64) if all there is not the above-mentioned condition that judgement is stopped, node to be positioned is not positioned at Bancroft method suitable application region.
7. low-power consumption mini-plant anti-noise localization method according to claim 2, is characterized in that, describedly judges whether node initial position to be positioned is positioned at Bancroft method suitable application region (40) step and comprises:
(71) judge whether node p to be positioned is positioned at the polygonal inside being comprised of all anchor nodes, if so, node p to be positioned is in Bancroft method suitable application region, and judgement finishes, otherwise ,-proceed following steps;
72) get the barycenter C of anchor node,
Figure FDA0000420109190000041
73) for all adjacent anchor node A that form direction in accordance with polygon iand A j, get anchor node A i, A jmid point M, from C, to a M, do extended line, getting distance on extended line is the some P of l length, wherein 0≤l≤50*A ia j; If node p to be positioned is positioned at triangle PA ia jinside, node to be positioned is in Bancroft method suitable application region, judgement finishes;
74) if all there is not the above-mentioned condition that judgement is stopped, node to be positioned is not positioned at Bancroft method suitable application region.
8. low-power consumption mini-plant anti-noise localization method according to claim 1, is characterized in that, described use Chan method determines that node location to be positioned (50) step comprises:
51) node location to be positioned is worth p according to a preliminary estimate efor
p e=(G 1 TQ -1G 1) -1G 1 TQ -1h 1，
Wherein: Q=I m-1+ 1, G 1=[x 2-x 1, x 3-x 1..., x m-x 1; y 2-y 1, y 3-y 1..., y m-y 1; r 21, r 3, 1..., r m, 1] t, p e=[x, y, r 1] t, h 1=-0.5[r 2, 1 2-|| A 2|| 2+ || A 1|| 2, r 3, 1 2-|| A 3|| 2+ || A 1|| 2..., r m, 1 2-|| A m|| 2+ || A 1|| 2] t;
52) utilize node location to be positioned to be worth according to a preliminary estimate p ecalculate node p to be positioned to each anchor node A idistance r i;
53) node location estimated value to be positioned
p e=(G 1 TW 1G 1) -1G 1 TW 1h 1，
Wherein: W 1=(DQD) -1, D=diag{r 2, r 3..., r m;
54) node location reference value to be positioned
p a=(G 2 TW 2G 2) -1G 2 TW 2h 2，
Wherein: G 2=[1,0; 0,1; 1,1; ], p a=[(x-x 1) 2; (y-y 1) 2], h 2=[(p e(1)-x 1) 2; (p e(2)-y 1) 2; (p e(3)) 2], W 2=(D ' (G 1 tw 1g 1) -1d ') -1, D '=diag{x – x 1, y – y 1, r 1;
55) node location determined value to be positioned
p=p a 0.5⊙sgn(p e(1,2)-A 1)+A 1，
Wherein: sgn () is sign function;
If at p ain element there is the situation of negative value, p=p e(1,2).
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