CN115226202B - Positioning base station screening method based on maximum mutual information - Google Patents
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- 238000004422 calculation algorithm Methods 0.000 claims abstract description 11
- 238000005259 measurement Methods 0.000 claims description 15
- 239000011159 matrix material Substances 0.000 claims description 8
- 239000013598 vector Substances 0.000 claims description 4
- RGJOEKWQDUBAIZ-IBOSZNHHSA-N CoASH Chemical compound O[C@@H]1[C@H](OP(O)(O)=O)[C@@H](COP(O)(=O)OP(O)(=O)OCC(C)(C)[C@@H](O)C(=O)NCCC(=O)NCCS)O[C@H]1N1C2=NC=NC(N)=C2N=C1 RGJOEKWQDUBAIZ-IBOSZNHHSA-N 0.000 claims 1
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- H—ELECTRICITY
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- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
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- H04W12/12—Detection or prevention of fraud
- H04W12/121—Wireless intrusion detection systems [WIDS]; Wireless intrusion prevention systems [WIPS]
- H04W12/122—Counter-measures against attacks; Protection against rogue devices
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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Abstract
The invention provides a positioning base station screening method based on maximum mutual information, which comprises the steps of gridding the whole positioning service coverage area, selecting 3 base stations from all positioning base stations to perform trilateral positioning calculation, traversing all the selections to obtain user positions under each selection, calculating the probability that the user positions are positioned on a certain grid, and calculating the entropy of the user positions by using the positioning probabilities of all the grids. Removing one of the base stations, traversing all combinations, calculating the user position entropy of the rest base stations, further calculating mutual information, using greedy algorithm, only preserving the base station combination of the maximum mutual information, then repeatedly executing the removing step, the mutual information calculating step and the preserving step until no removing operation with the mutual information larger than 0 exists, wherein the base station combination at the moment is a screening result, performing joint positioning calculation by utilizing all the base stations in the screening result, and obtaining the final user position by utilizing minimum variance unbiased estimation.
Description
[ Field of technology ]
The invention discloses a positioning base station screening method based on maximum mutual information, which is used for eliminating bad positioning base stations and keeping high ranging precision base stations during terminal positioning, and belongs to the technical field of terminal positioning.
[ Background Art ]
Signal Time Of Arrival (TOA) ranging is a widely used positioning technique. The positioning server calculates the distance between different base stations and the user by measuring the time of the reference signals sent by the base stations to reach the user, and estimates the position of the user by using a trilateral positioning algorithm, a least square algorithm and other positioning algorithms according to the measured distance. However, the accuracy of TOA ranging is affected by the degree of time synchronization between the base station and the user, while being sensitive to channel noise, interference, and multipath propagation. Meanwhile, with the vigorous development of base station positioning services, positioning infrastructure is becoming a target of malicious attack, and an attacker can completely distort the ranging information of the base station, so that positioning errors are caused. In a real environment, a screening algorithm capable of rapidly eliminating bad ranging base stations and simultaneously retaining base stations with high ranging accuracy will remarkably improve the accuracy of wireless positioning.
Because the positioning server cannot judge whether the base station ranging is accurate or not, the positioning server can only judge whether the base station ranging participating in positioning is accurate or not by comparing the user position with the actual user position after positioning calculation. However, the trilateral positioning algorithm is used for positioning and resolving, and finally, the scope of the bad base station can only be reduced to three base stations, so that the bad base station can not be accurately removed. Direct rejection of bad ranging base stations and retention of accurate ranging base stations is a great challenge.
The existing screening algorithm uses methods such as compatibility inspection, phantom node filtration, graph rigidity inspection and the like to screen bad ranging base stations, but all the existing screening algorithms have the problems of difficult threshold setting, huge calculation amount and the like, and lack operability in actual scenes. Therefore, how to quickly reject bad ranging base stations and simultaneously reserve accurate ranging base stations under the condition of low calculation amount is a current urgent problem to be solved.
[ Invention ]
The invention relates to a positioning method based on maximum mutual information, which can rapidly remove bad ranging base stations and reserve high ranging precision base stations. Removing one of the base stations, traversing all combinations, calculating the user position entropy of the rest base stations, further calculating mutual information, using greedy algorithm, only preserving the base station combination of the maximum mutual information, then repeatedly executing the removing step, the mutual information calculating step and the preserving step until no removing operation with the mutual information larger than 0 exists, wherein the base station combination at the moment is a screening result, performing joint positioning calculation by utilizing all the base stations in the screening result, and obtaining the final user position by utilizing minimum variance unbiased estimation. The method is realized by the following steps:
Step one, establishing a gridding model of a positioning service coverage area. The method specifically comprises the following steps: the location service coverage area is considered as a rectangle and a rectangular coordinate system is established, with length a and width b, and four vertex coordinates of the rectangular coordinate system are (0, 0), (a, 0), (0, b), (a, b), respectively. The grid is rectangular, the length of the grid is a m, and the calculation formula is as follows: a m＝a/na, wherein n a is an integer, and as a number of average segments, the value is [ a/epsilon ], wherein epsilon is the positioning precision. The width is b m, and the calculation formula is: b m＝b/nb, wherein n b is an integer, and the value of the average number of segments is [ b/. Epsilon ]. The location service coverage area is equally divided into n a×nb rectangular grids.
And step two, selecting base stations participating in positioning calculation. The method specifically comprises the following steps: the set of base stations is m= { s 1,s2,···,sp },Where s i is the coordinate of the base station with index i, s p is the coordinate of the base station with index p, np is the number of elements of the base station set M, and x i、yi is the abscissa and ordinate of the ith base station, respectively. The corresponding set of measurement distances is d= { D 1,d2,…,dp }, where D i is the measurement distance of the base station with index i. 3 base stations are selected from the set M, and the base stations are shared/>A combination of species, wherein one of the combinations is designated as/>I 1,i2,i3 is the index of the base station in the combination, and the corresponding measurement distance set is/>The corresponding coordinates are respectively,/>
And thirdly, carrying out user position calculation according to the base station combination. The method specifically comprises the following steps: resolved user positionWhere x t、yt is the abscissa and ordinate, respectively, of the resolved user position. Calculating user position/>, using a trilateral algorithm, using a minimum variance unbiased estimateThe formula is/>Wherein the method comprises the steps ofMatrix H is the observation matrix, H T represents the transpose of matrix H,/>For observing vectors
And step four, calculating entropy of the user position according to all the calculated user positions. The method specifically comprises the following steps: the positioning probability p j of each grid is calculated by the formulaWhere n j is the number of user positions falling in the j-th grid. Entropy HS of the user position is calculated according to the positioning probabilities of all grids, and the formula is/>
And fifthly, eliminating elements in the base station set according to the principle of maximum mutual information. The specific envelope is as follows: removing one element in the base station set M, and sharingAnd (5) seed selection. Generating a new base station set M * and a corresponding measured distance set D * after each selection, executing the second, third and fourth steps to obtain entropy HS * of the user position of the new base station set M *, calculating mutual information I (M; M *), wherein the formula is I (M; M *)＝HS-HS*. The set with the maximum and positive mutual information in all the generated new sets is reserved as/>And corresponding measurement distance set/>Circularly executing the step five until all the generated mutual information of the new sets is negative, stopping the operation, reserving the set before executing the removal operation, and recording as/>At this time set/>The base station with bad ranging is not contained and the base station with accurate ranging is reserved.
And step six, calculating the user position according to the optimal base station set. Specifically, a base station set is providedB 1,b2,bg are indexes of base stations in the set, and the corresponding coordinates are respectivelyG is the element number of the set, and the corresponding measurement distance set isIs the best set of base stations. Due to the base station set/>The base station does not contain bad ranging base stations and keeps accurate ranging, so the base station set/>, is utilizedThe user position obtained by the joint positioning of all base stations is the most accurate, and the final user position/>, is calculated by the minimum variance unbiased estimationX best is the abscissa of the end user position, y best is the ordinate of the end user, and the calculation formula is
Wherein/> H best is the observation matrix using best base station set positioning,/>The observation vectors are located for the set of best base stations to use.
The invention has the advantages that: the method for screening the positioning base stations based on the maximum mutual information can rapidly remove the bad positioning base stations from all positioning base station sets in a short time, simultaneously reserve the base stations with high ranging accuracy, eliminate the interference of the ranging results of the bad base stations on positioning calculation, effectively improve the positioning accuracy of the user position, and meanwhile, has small calculated amount, does not need to manually set parameters, has low requirement on the computing capability of a positioning server and has strong operability of actual scenes. In addition, the invention can exclude the positioning base station which is attacked maliciously and can effectively enhance the safety of positioning service.
[ Description of the drawings ]
Fig. 1 is a general flow chart of a positioning base station screening method based on maximum mutual information according to the present invention.
FIG. 2 is a graph comparing the positioning results of the present invention in a simulation environment with those based on a compatibility detection method and a phantom node screening method.
[ Detailed description ] of the invention
The number np=12 of positioning base stations, the length of the coverage area of the positioning service is a=30m, the width is b=30m, the true position of the user is (15, 15), the element of the base station set M is { s 1,s2,…,s12 }, wherein,
s1＝(28.239,7.3232),s2＝(28.7133，15.3247)，
s3＝(16.9374,29.8115),s4＝(23.1295，9.4141)，
s5＝(1.7362,1.3222),s6＝(24.3883，12.3622)，
s7＝(11.5249,15.6938),s8＝(26.7645，12.1776)，
s9＝(18.1317,2.8441),s10＝(10.0794，4.3453)，
s11＝(7.3464,11.3691),s12＝(8.1096，6.4680)，
The corresponding measurement distance set d= { D 1,d2,…,d12 }, wherein d1＝26.3736,d2＝16.1149,d3＝22.6058,d4＝13.0337,d5＝31.0185,d6＝10.0429,d7＝7.3034,d8＝12.6174,d9＝10.2943,d10＝14.5982,d11＝11.3671,d12＝9.4733, positioning accuracy epsilon=5m, the detailed description of the specific embodiment of the invention is given as an example, and the overall flow of the method is shown in fig. 1.
Step one, establishing a positioning service coverage area gridding model. Based on the positioning accuracy epsilon=5m, a m＝5,na＝6,bm＝5,nb =6 is calculated, and the positioning service coverage area is equally divided into 36 rectangles.
Selecting base stations participating in positioning calculation, and calculating the user position of each combination. Optionally 3 base stations from set M, co-Seed combination, taking one of the combinations { s 1,s3,s5 } as an example,
s1＝(28.239,7.3232),s3＝(16.9374，29.8115)，
S 5 = (1.7362,1.3222), the corresponding measurement distance combination is { d 1,d3,d5 }.
And thirdly, carrying out user position calculation on each combination. Taking one of the combinations { s 1,s3,s5 } as an example, the correspondingAccording to the formula/>Calculated/>The user position is solved for by the combination s 1,s3,s5. The above-described positioning solutions are performed for all combinations.
And step four, calculating entropy of the user position according to all the calculated user positions. The positioning probability p j of each grid is calculated by the formulaWhere n j is the number of user positions falling in the j-th grid. Entropy HS of the user position is calculated according to the positioning probabilities of all grids, and the formula is/>Hs= 7.4181 bits in this example.
And fifthly, eliminating elements in the base station set according to the principle of maximum mutual information. Removing one element in the base station set M, and sharingAnd (5) seed selection. Generating a new base station set M * and a corresponding measurement distance set D * after each selection, executing the steps II, III and IV to obtain entropy HS * of the user position of the new base station set M *, calculating mutual information I (M; M *), wherein the formula is I (M; M *)＝HS-HS*. For example, eliminating s 1 in the base station set M, generating a new base station set M *＝{s2,s3,...,s12, and the distance set D *＝{d2,d3,...,d12 }, executing the steps II, III and IV to obtain entropy HS * = 6.8820 of the user position of the new base station set M *, calculating mutual information I (M; M *) = 7.4181-6.8820 = 0.5361bit, and reserving the set with the largest mutual information and positive number in all generated new sets as/>And corresponding measurement distance set/>Circularly executing the step four until all the generated mutual information of the new sets is negative, stopping the operation, reserving the set before executing the removal operation, and recording as/>At this time set/>The base station with bad ranging is not contained and the base station with accurate ranging is reserved.
And step six, calculating the user position according to the optimal base station set. In this example, the resulting set of best base stationsWherein ,s7＝(11.5249,15.6938),s8＝(26.7645,12.1776),s9＝(18.1317,2.8441),s12＝(8.1096,6.4680), corresponds to the set of measurement distances/>Utilizing a set of base stations/>The joint positioning is carried out on all base stations in the network, the calculation process is that,Calculated according to the formulaThe results are shown in fig. 2, and meanwhile, fig. 2 shows the results of a screening method based on compatibility and a screening method based on phantom nodes, wherein the error of the method is 3.6992m, the error of the screening method based on compatibility is 7.0117m, and the error of the screening method based on phantom nodes is 7.82m.
Claims (5)
1. A positioning base station screening method based on maximum mutual information is characterized by comprising the following steps:
Step one, establishing a gridding model of a positioning service coverage area;
selecting base stations participating in positioning calculation;
step three, user position calculation is carried out according to the base station combination;
Step four, calculating entropy of the user position according to all the calculated user positions;
fifthly, removing elements in the base station set according to the principle of maximum mutual information;
step six, calculating the user position according to the optimal base station set;
In the fourth step, specifically, the method includes: the positioning probability p j of each grid is calculated by the formula Where n j is the number of user positions falling in the jth grid; entropy HS of the user position is calculated according to the positioning probabilities of all grids, and the formula is/>
In the fifth step, the method specifically includes: removing one element in the base station set M, and sharingSeed selection; for each selected new base station set M * and corresponding measured distance set D *, performing the second, third and fourth steps to obtain entropy HS * of user position of new base station set M *, calculating mutual information I (M; M *), wherein the formula is I (M; M *)＝HS-HS* keeps the largest and positive number of the mutual information in all the generated new sets as/>And corresponding measurement distance set/>Circularly executing the step five until all the generated mutual information of the new sets is negative, stopping the operation, reserving the set before executing the removal operation, and recording as/>At this time set/>The base station does not contain bad ranging base stations and reserves accurate ranging base stations;
In the sixth step, the method specifically includes providing a base station set B 1,b2,bg is the index of the base station in the set, and the corresponding coordinates are/>G is the element number of the set, and the corresponding measurement distance set is/> Is the best base station set; due to the base station set/>The base station does not contain bad ranging base stations and keeps accurate ranging, so the base station set/>, is utilizedThe user position obtained by the joint positioning of all base stations is the most accurate, and the final user position is calculated by the minimum variance unbiased estimationX best is the abscissa of the end user position, y best is the ordinate of the end user, and the calculation formula is:
Wherein,
H best is the observation matrix located using the best set of base stations,The observation vectors are located for the set of best base stations to use.
2. The positioning base station screening method based on maximum mutual information as claimed in claim 1, wherein: in the first step, specifically, the method includes: the location service coverage area is considered as a rectangle and a rectangular coordinate system is established, the length is a, the width is b, and four vertex coordinates are (0, 0), (a, 0), (0, b), (a, b) respectively; the grid is rectangular, the length is a m, and the calculation formula is: a m＝a/na, wherein n a is an integer, and the value of the integer is [ a/epsilon ] as an average segment number, and s is positioning precision; the width is b m, and the calculation formula is: b m＝b/nb, wherein n b is an integer, and the value of the average segment number is [ b/epsilon ]; the location service coverage area is equally divided into n a×nb rectangular grids.
3. The positioning base station screening method based on maximum mutual information as claimed in claim 1, wherein: in the second step, specifically, the method includes: the set of base stations is m= { s 1,s2,…,sp },X i∈[0,a],yi epsilon [0, b ], wherein s i is the coordinate of the base station with index i, s p is the coordinate of the base station with index p, and np is the element number of the base station set M; x i、yi is the abscissa and the ordinate of the ith base station, respectively; the corresponding set of measurement distances is d= { D 1,d2,…,dp }, where D i is the measurement distance of the base station with index i.
4. A positioning base station screening method based on maximum mutual information according to claim 3, wherein: optionally 3 base stations from set M, co-A seed combination, one of which is set asRespectively index the base stations in the combination, and the corresponding measurement distance set isThe corresponding coordinates are/>, respectively
5. The positioning base station screening method based on maximum mutual information according to claim 4, wherein: in the third step, specifically, the method includes: resolved user positionWherein x t、yi is the abscissa and ordinate of the resolved user position, respectively; calculating user position/>, using a trilateral algorithm, using a minimum variance unbiased estimateThe formula isWherein,Matrix H is the observation matrix, H T represents the transpose of matrix H,/>Is an observation vector.
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