CN109341682B - Method for improving geomagnetic field positioning accuracy - Google Patents

Method for improving geomagnetic field positioning accuracy Download PDF

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CN109341682B
CN109341682B CN201811337078.7A CN201811337078A CN109341682B CN 109341682 B CN109341682 B CN 109341682B CN 201811337078 A CN201811337078 A CN 201811337078A CN 109341682 B CN109341682 B CN 109341682B
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magnetic field
data
probability
point
confidence
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CN109341682A (en
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张烨
郭艺玲
樊一超
许艇
程康
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/04—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means
    • G01C21/08—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by terrestrial means involving use of the magnetic field of the earth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/005—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 with correlation of navigation data from several sources, e.g. map or contour matching
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/165—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation combined with non-inertial navigation instruments
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/20—Instruments for performing navigational calculations
    • G01C21/206—Instruments for performing navigational calculations specially adapted for indoor navigation

Abstract

A method for improving the positioning accuracy of a geomagnetic field comprises the following steps: step 1, establishing a geomagnetic field fingerprint database based on statistical distribution; step 2, a confidence calculation method for measuring values in each grid of the fingerprint database; step 3, in the positioning stage, the coordinates of the current position are calculated by adopting a path matching method, and the measuring and calculating steps are as follows: and 4, calculating the probability of the possible position of each turning point according to historical path data and the prior probability by adopting a Bayesian classifier in the most key part of the positioning algorithm. The invention establishes a confidence interval fingerprint database of the geomagnetic field by a series of unique methods, and calculates the probability of each possible position by adopting a Bayesian classifier according to the prior probability of historical positioning data in the positioning process.

Description

Method for improving geomagnetic field positioning accuracy
Technical Field
The invention mainly relates to a method for improving the positioning precision of a geomagnetic field, which is characterized in that a confidence interval fingerprint database of the geomagnetic field is established by a series of unique methods, and in the positioning process, the probability of each possible position at present is calculated by adopting a Bayesian classifier according to the prior probability of historical positioning data so as to improve the positioning precision of the geomagnetic field.
Background
Positioning using the earth's magnetic field is one of the many indoor positioning schemes that are currently available, and the main difference between this positioning scheme and the currently popular way of positioning based on multiple rf signal sources is that there is no need to deploy transmitting devices for the positioning signal sources in advance. When the location to be located is uncertain, or the number of the locations to be located is large, so that the location signal source cannot be deployed, the location scheme can be considered to be adopted.
Disclosure of Invention
The present invention overcomes the above-mentioned shortcomings of the prior art and provides a method for improving the positioning accuracy of the geomagnetic field.
The method establishes a perfect geomagnetic field positioning model by combining the confidence coefficient fingerprint database and the path matching method and the naive Bayesian classifier, obtains better positioning precision, and simultaneously proves that the geomagnetic field positioning has higher feasibility and application prospect.
A method for improving the positioning accuracy of a geomagnetic field comprises the following steps:
1. and establishing a geomagnetic field fingerprint database based on statistical distribution.
The earth magnetic field vector can be decomposed generally in three component directions along the coordinate axis: in the geographically due north direction, the due east direction and the direction perpendicular to the horizontal plane, into the due north component, the due east component and the vertical component of the total magnetic field. The projection of the earth's magnetic field on a horizontal plane, called the horizontal component, always points to the north of the earth's geomagnetism. The horizontal component is directed in the direction of the north pole of the compass, commonly referred to as magnetic north; the angle that the horizontal component makes with the true north of geography is called declination. The angle that the earth's magnetic field makes with the horizontal plane is called the declination angle.
In summary, the various parameters of the earth's magnetic field can be labeled as: total magnetic field strength B, north component BθComponent of Zhengdong, BΦPerpendicular component BγHorizontal component BHDeclination D, declination I, as shown in FIG. 2.
Firstly, dividing a land to be measured into grids in i rows and j columns, wherein the size of each grid is smaller than the precision requirement of geomagnetic field measurement, and then measuring the geomagnetic field intensity of each grid according to the following formula:
Figure GDA0002635530660000011
wherein
Figure GDA0002635530660000021
Respectively representThe components in the three directions of the earth's magnetic field,
Figure GDA0002635530660000022
representing the total strength of the earth's magnetic field. Due to the fact that the check calculation is carried out,
Figure GDA0002635530660000023
statistically, the distribution is substantially normal, so we can store the distribution characteristics as fingerprint characteristics. The data format of the fingerprint database is therefore:
(μAx,μAy,μAz,σAx,σAy,σAz,xA,yA) (2)
wherein muAx，μAy，μAzRespectively the mean value, sigma, of the magnetic field intensity in three directions after Gaussian filteringAx，σAy，σAzRespectively, the standard deviation, x, of the magnetic field strength in three directionsA，yAAre position coordinates.
2. A confidence calculation method for the measured values located in each grid of the fingerprint database.
When the coincidence degree of the positioning data and the data in the fingerprint database needs to be judged, the confidence degree corresponding to the minimum confidence interval can be calculated, namely:
P(θ1<θ<θ2)＝1-α (3)
there is a set of random variables X (X)1,x2,x3,…,xn) For a set of samples, let X-N (mu, sigma)2) If there is a random interval [ theta ]1,θ2]For a given α (0)<α<1) Satisfying the above formula, the random interval [ theta ] is called1,θ2]Is the confidence interval with a confidence level of theta of 1-alpha, theta1Called confidence lower bound, θ2Called the upper confidence limit and the probability 1-alpha called the confidence level or confidence, the meaning of the confidence interval is that it contains the unknown parameter theta with a probability of 1-alpha.
When the sample capacity is larger than 50, the sample variance S can be used2Estimate σ, make meanIn this case:
Figure GDA0002635530660000024
wherein
Figure GDA0002635530660000025
Is the sample mean, μ is the overall mean, S is the sample standard deviation, and n is the sample volume. For a given confidence 1- α, there is a probability:
Figure GDA0002635530660000026
substituting the formula into the formula can obtain:
Figure GDA0002635530660000027
thus is easily obtained
Figure GDA0002635530660000028
When a confidence interval with a confidence level of 1- α is obtained, and when certain samples can be calculated, a constant expression form of the confidence interval is obtained:
Figure GDA0002635530660000029
3. in the positioning stage, the coordinates of the current position are calculated by adopting a path matching method, and the measuring and calculating steps are as follows:
(1) in the straight-going section, measuring the movement direction and the movement speed through a direction sensor and an acceleration sensor, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(2) acquiring direction data by using an inertial sensor, and judging whether to turn according to whether the angle is changed greatly;
(3) at a turning point, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(4) calculating the length of each straight line segment according to the data of the inertial sensor and the time, and drawing the length into a vector with a direction;
(5) sequentially connecting the vectors to obtain a path track;
(6) obtaining a plurality of possible walking paths through the shape of the track;
(7) combining the walking paths obtained in the last step, calculating confidence coefficient by resolving geomagnetic data of turning points, and obtaining the probability of the turning points of a plurality of paths by adopting a Bayes classifier according to historical path data and prior probability;
the specific method for solving the probability of the turning points of the paths by adopting the Bayesian classifier is as follows:
the basic model of the naive Bayes algorithm is that if an event a1,a2,a3… constitute a complete event group, i.e. these events are independent of each other, and P (a)i)>0, then for any event b, there is the total probability formula:
P(b)＝∑iP(ai)P(b|ai) (8)
if P (b) >0, then there are:
Figure GDA0002635530660000031
in the measurement process, the prior probability refers to the obtained historical data, the posterior probability refers to the probability that the current node is located at a certain position, and when the prior probability P (a ═ a), P (B ═ B) and P (B ═ B | a ═ a) are known, the formula for calculating P (a ═ a | B ═ B) is as follows:
Figure GDA0002635530660000032
in the actual positioning calculation, a set of magnetic field strength data acquired at a certain point epsilon at a certain time is calculated by the following method for calculating the matching probability of the epsilon point and the point (i, j):
here, the event H is actually "a certain point in the training example set is (i, j)", and the attribute D is that the magnetic field data in three directions in the training example set are approximately equal to the magnetic field data in three directions at the point ∈. Since the magnetic field data conforms to a normal distribution, approximately equal between the two data means that the magnitude of the intensity in a certain direction at the e point is less than a certain confidence level xi, and the magnitude of xi is set to be 5% of the standard deviation of the direction data corresponding to the matched point, i.e., xi is 0.05 σ. Applying a Bayesian classifier formula to obtain:
Figure GDA0002635530660000041
wherein xε、yε、zεThe magnetic field strength in three directions measured at the point epsilon, and x, y, z are the magnetic field strength in three directions measured at the points in the training example set. Because the magnetic field intensity in any point and three directions are independent of each other, | xε-x|，|yε-y|，|zε-z | independently of each other, there are:
P(|xε-x|<ξx,|yε-y|<ξy,|zε-z|<ξz)＝P(|xε-x|<ξx)×P(|yε-y|<ξy)×P(|zε-z|<ξz) (12)
and:
Figure GDA0002635530660000042
therefore, the matching probability of the epsilon point and the point (i, j) can be obtained, and then the matching probability of the epsilon point and other points is calculated to obtain the point with the maximum matching probability, namely the position where the epsilon point is most likely to be located. And then measuring the magnetic field data measured on all the nodes in the whole measuring area, carrying out average value filtering, and positioning the obtained data characteristics according to the method for processing the epsilon point to obtain the positioning result of each node.
(8) And matching the most probable path by comparing the probability values of the paths at the turning points, thereby obtaining the positioning position.
The invention has the advantages that:
from the perspective of geomagnetic field positioning, the invention does not need to arrange a transmitting device of a positioning signal source in advance, and can achieve efficient utilization in scenes with certain characteristics. Compared with the traditional positioning method, the probability of each possible position is calculated by adopting the Bayesian classifier, so that the positioning error can be greatly reduced, and the accuracy of geomagnetic field positioning can be improved.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
fig. 2 is a schematic diagram of the component parameters in each direction of the earth magnetic field.
Note: description of the variables in FIG. 2, B denotes the total intensity of the magnetic field, BθRepresenting the north component of the magnetic field strength, BΦRepresenting the positive east component of the magnetic field strength, BγRepresenting the vertical component of the magnetic field strength, BHRepresents the horizontal component of the magnetic field strength, D represents the declination, and I represents the declination.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
A method for improving the positioning accuracy of a geomagnetic field comprises the following steps:
1. and establishing a geomagnetic field fingerprint database based on statistical distribution.
The earth magnetic field vector can be decomposed generally in three component directions along the coordinate axis: in the geographically due north direction, the due east direction and the direction perpendicular to the horizontal plane, into the due north component, the due east component and the vertical component of the total magnetic field. The projection of the earth's magnetic field on a horizontal plane, called the horizontal component, always points to the north of the earth's geomagnetism. The horizontal component is directed in the direction of the north pole of the compass, commonly referred to as magnetic north; the angle that the horizontal component makes with the true north of geography is called declination. The angle that the earth's magnetic field makes with the horizontal plane is called the declination angle.
In summary, the followingTo mark the various parameters of the earth's magnetic field as: total magnetic field strength B, north component BθComponent of Zhengdong, BΦPerpendicular component BγHorizontal component BHDeclination D, declination I, as shown in FIG. 2.
Firstly, dividing a land to be measured into grids in i rows and j columns, wherein the size of each grid is smaller than the precision requirement of geomagnetic field measurement, and then measuring the geomagnetic field intensity of each grid according to the following formula:
Figure GDA0002635530660000051
wherein
Figure GDA0002635530660000052
Respectively representing components in three directions of the earth's magnetic field,
Figure GDA0002635530660000053
representing the total strength of the earth's magnetic field. Due to the fact that the check calculation is carried out,
Figure GDA0002635530660000054
statistically, the distribution is substantially normal, so we can store the distribution characteristics as fingerprint characteristics. The data format of the fingerprint database is therefore:
(μAx,μAy,μAz,σAx,σAy,σAz,xA,yA) (2)
wherein muAx，μAy，μAzRespectively the mean value, sigma, of the magnetic field intensity in three directions after Gaussian filteringAx，σAy，σAzRespectively, the standard deviation, x, of the magnetic field strength in three directionsA，yAAre position coordinates.
2. A confidence calculation method for the measured values located in each grid of the fingerprint database.
When the coincidence degree of the positioning data and the data in the fingerprint database needs to be judged, the confidence degree corresponding to the minimum confidence interval can be calculated, namely:
P(θ1<θ<θ2)＝1-α (3)
there is a set of random variables X (X)1,x2,x3,…,xn) For a set of samples, let X-N (mu, sigma)2) If there is a random interval [ theta ]1,θ2]For a given α (0)<α<1) Satisfying the above formula, the random interval [ theta ] is called1,θ2]Is the confidence interval with a confidence level of theta of 1-alpha, theta1Called confidence lower bound, θ2Called the upper confidence limit and the probability 1-alpha called the confidence level or confidence, the meaning of the confidence interval is that it contains the unknown parameter theta with a probability of 1-alpha.
When the sample capacity is larger than 50, the sample variance S can be used2Estimate σ, perform confidence interval calculation of the mean, here:
Figure GDA0002635530660000061
wherein
Figure GDA0002635530660000062
Is the sample mean, μ is the overall mean, S is the sample standard deviation, and n is the sample volume. For a given confidence 1- α, there is a probability:
Figure GDA0002635530660000063
substituting the formula into the formula can obtain:
Figure GDA0002635530660000064
thus is easily obtained
Figure GDA0002635530660000065
When a confidence interval with a confidence level of 1-alpha is obtained for mu, thisIf certain samples can be calculated, a constant expression form of a confidence interval is obtained:
Figure GDA0002635530660000066
3. in the positioning stage, the coordinates of the current position are calculated by adopting a path matching method, and the measuring and calculating steps are as follows:
(1) in the straight-going section, measuring the movement direction and the movement speed through a direction sensor and an acceleration sensor, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(2) acquiring direction data by using an inertial sensor, and judging whether to turn according to whether the angle is changed greatly;
(3) at a turning point, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(4) calculating the length of each straight line segment according to the data of the inertial sensor and the time, and drawing the length into a vector with a direction;
(5) sequentially connecting the vectors to obtain a path track;
(6) obtaining a plurality of possible walking paths through the shape of the track;
(7) combining the walking paths obtained in the last step, calculating confidence coefficient by resolving geomagnetic data of turning points, and obtaining the probability of the turning points of a plurality of paths by adopting a Bayes classifier according to historical path data and prior probability;
the specific method for solving the probability of the turning points of the paths by adopting the Bayesian classifier is as follows:
the basic model of the naive Bayes algorithm is that if an event a1,a2,a3… constitute a complete event group, i.e. these events are independent of each other, and P (a)i)>0, then for any event b, there is the total probability formula:
P(b)＝∑iP(ai)P(b|ai) (8)
if P (b) >0, then there are:
Figure GDA0002635530660000071
in the measurement process, the prior probability refers to the obtained historical data, the posterior probability refers to the probability that the current node is located at a certain position, and when the prior probability P (a ═ a), P (B ═ B) and P (B ═ B | a ═ a) are known, the formula for calculating P (a ═ a | B ═ B) is as follows:
Figure GDA0002635530660000072
in the actual positioning calculation, a set of magnetic field strength data acquired at a certain point epsilon at a certain time is calculated by the following method for calculating the matching probability of the epsilon point and the point (i, j):
here, the event H is actually "a certain point in the training example set is (i, j)", and the attribute D is that the magnetic field data in three directions in the training example set are approximately equal to the magnetic field data in three directions at the point ∈. Since the magnetic field data conforms to a normal distribution, approximately equal between the two data means that the magnitude of the intensity in a certain direction at the e point is less than a certain confidence level xi, and the magnitude of xi is set to be 5% of the standard deviation of the direction data corresponding to the matched point, i.e., xi is 0.05 σ. Applying a Bayesian classifier formula to obtain:
Figure GDA0002635530660000073
wherein xε、yε、zεThe magnetic field strength in three directions measured at the point epsilon, and x, y, z are the magnetic field strength in three directions measured at the points in the training example set. Because the magnetic field intensity in any point and three directions are independent of each other, | xε-x|，|yε-y|，|zε-z | independently of each other, there are:
P(|xε-x|<ξx,|yε-y|<ξy,|zε-z|<ξz)＝P(|xε-x|<ξx)×P(|yε-y|<ξy)×P(|zε-z|<ξz) (12)
and:
Figure GDA0002635530660000074
Figure GDA0002635530660000081
therefore, the matching probability of the epsilon point and the point (i, j) can be obtained, and then the matching probability of the epsilon point and other points is calculated to obtain the point with the maximum matching probability, namely the position where the epsilon point is most likely to be located. And then measuring the magnetic field data measured on all the nodes in the whole measuring area, carrying out average value filtering, and positioning the obtained data characteristics according to the method for processing the epsilon point to obtain the positioning result of each node.
(8) And matching the most probable path by comparing the probability values of the paths at the turning points, thereby obtaining the positioning position.
The embodiments described in this specification are merely illustrative of implementations of the inventive concept and the scope of the present invention should not be considered limited to the specific forms set forth in the embodiments but rather by the equivalents thereof as may occur to those skilled in the art upon consideration of the present inventive concept.

Claims (1)

1. A method for improving the positioning accuracy of a geomagnetic field comprises the following steps:
step 1, establishing a geomagnetic field fingerprint database based on statistical distribution;
the earth magnetic field vector is resolved in three component directions of the coordinate axes: decomposing the magnetic field into a north component, an east component and a vertical component of the total magnetic field in a geographical north direction, a geographical east direction and a direction vertical to the horizontal plane; the projection of the earth's magnetic field on the horizontal plane, called the horizontal component, always points to the north of the earth's geomagnetism; the horizontal component is directed in the direction of the north pole of the compass, commonly referred to as magnetic north; the angle formed by the horizontal component and the north direction of geography is called magnetic declination; the angle formed by the earth magnetic field and the horizontal plane is called the magnetic dip angle;
in summary, the various parameters of the earth's magnetic field can be labeled as: total magnetic field strength B, north component BθComponent of Zhengdong, BΦPerpendicular component BγHorizontal component BHDeclination D and declination I;
firstly, dividing a land to be measured into grids in i rows and j columns, wherein the size of each grid is smaller than the precision requirement of geomagnetic field measurement, and then measuring the geomagnetic field intensity of each grid according to the following formula:
Figure FDA0002836684320000011
wherein
Figure FDA0002836684320000012
Respectively representing components of the earth magnetic field in the true north, the true east and the vertical directions,
Figure FDA0002836684320000013
represents the total strength of the earth's magnetic field; due to the fact that the check calculation is carried out,
Figure FDA0002836684320000014
the distribution is basically consistent with normal distribution in statistics, so that the distribution characteristics can be stored as fingerprint characteristics; the data format of the fingerprint database is therefore:
(μAx,μAy,μAz,σAx,σAy,σAz,xA,yA) (2)
wherein muAx，μAy，μAzRespectively the mean value, sigma, of the magnetic field intensity in three directions after Gaussian filteringAx，σAy，σAzRespectively the standard deviation of the magnetic field intensity in three directions，xA，yAIs a position coordinate;
step 2, a confidence calculation method for measuring values in each grid of the fingerprint database;
when the coincidence degree of the positioning data and the data in the fingerprint database needs to be judged, the confidence degree corresponding to the minimum confidence interval can be calculated, namely:
P(θ1＜θ＜θ2)＝1-α (3)
there is a set of random variables X (X)1,x2,x3,…,xn) For a set of samples, let X-N (mu, sigma)2) If there is a random interval [ theta ]1,θ2]If 0 < alpha < 1 for a given alpha, and the above formula is satisfied, the random interval [ theta ] is called1,θ2]Is the confidence interval with a confidence level of theta of 1-alpha, theta1Called confidence lower bound, θ2Called upper confidence limit, probability 1- α called confidence level or confidence, the meaning of the confidence interval is that it contains the unknown parameter θ with a probability of 1- α;
when the sample capacity is larger than 50, the sample variance S can be used2Estimate σ, perform confidence interval calculation of the mean, here:
Figure FDA0002836684320000021
wherein
Figure FDA0002836684320000022
Is the sample mean, mu is the overall mean, S is the sample standard deviation, and n is the sample capacity; for a given confidence 1- α, there is a probability:
Figure FDA0002836684320000023
substituting the formula into the formula can obtain:
Figure FDA0002836684320000024
thus is easily obtained
Figure FDA0002836684320000025
When a confidence interval with a confidence level of 1- α is obtained, and when certain samples can be calculated, a constant expression form of the confidence interval is obtained:
Figure FDA0002836684320000026
step 3, in the positioning stage, the coordinates of the current position are calculated by adopting a path matching method, and the measuring and calculating steps are as follows:
(1) in the straight-going section, measuring the movement direction and the movement speed through a direction sensor and an acceleration sensor, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(2) acquiring direction data by using an inertial sensor, and judging whether to turn according to whether the angle is changed greatly;
(3) at a turning point, calling a geomagnetic sensor, and measuring 10 groups of geomagnetic intensity data;
(4) calculating the length of each straight line segment according to the data of the inertial sensor and the time, and drawing the length into a vector with a direction;
(5) sequentially connecting the vectors to obtain a path track;
(6) obtaining a plurality of possible walking paths through the shape of the track;
(7) combining the walking paths obtained in the last step, calculating confidence coefficient by resolving geomagnetic data of turning points, and obtaining the probability of the turning points of a plurality of paths by adopting a Bayes classifier according to historical path data and prior probability;
the specific method for solving the probability of the turning points of the paths by adopting the Bayesian classifier is as follows:
the basic model of the naive Bayes algorithm is that if an event a1,a2,a3… constitute a complete event group, i.e. these events are independent of each other, and P (a)i)>0, then for any event b, there is the total probability formula:
P(b)＝∑iP(ai)P(b|ai) (8)
if P (b) >0, then there are:
Figure FDA0002836684320000031
in the measurement process, the prior probability refers to the obtained historical data, the posterior probability refers to the probability that the current node is located at a certain position, and when the prior probability P (a ═ a), P (B ═ B) and P (B ═ B | a ═ a) are known, the formula for calculating P (a ═ a | B ═ B) is as follows:
Figure FDA0002836684320000032
in the actual positioning calculation, a set of magnetic field strength data acquired at a certain point epsilon at a certain time is calculated by the following method for calculating the matching probability of the epsilon point and the point (i, j):
here, a certain point in the training example set is (i, j), and the magnetic field data in three directions in the training example set are respectively approximately equal to the magnetic field data in three directions at the e point; since the magnetic field data conforms to a normal distribution, the two data are approximately equal to each other in the sense that the difference between the intensity of an epsilon point in a certain direction and the matched point data is less than a certain confidence coefficient xi, and the size of xi is set to be 5% of the standard deviation of the direction data corresponding to the matched point, namely xi is 0.05 sigma; applying a Bayesian classifier formula to obtain:
Figure FDA0002836684320000033
wherein xε、yε、zεThe magnetic field strength in three directions measured at the epsilon point is divided into x, y and zThe other is the magnetic field strength in three directions measured by points in the training example set; because the magnetic field intensity in any point and three directions are independent of each other, | xε-x|，|yε-y|，|zε-z | independently of each other, there are:
P(|xε-x|＜ξx,|yε-y|＜ξy,|zε-z|＜ξz)＝P(|xε-x|＜ξx)×P(|yε-y|＜ξy)×P(|zε-z|＜ξz) (12)
and:
Figure FDA0002836684320000034
therefore, the matching probability of the epsilon point and the point (i, j) can be obtained, and then the matching probability of the epsilon point and other points is calculated to obtain the point with the maximum matching probability, namely the position where the epsilon point is most likely to be located; measuring magnetic field data measured on all nodes in the whole measuring area, carrying out average value filtering, and positioning the obtained data characteristics according to an epsilon point processing method to obtain a positioning result of each node;
(8) and matching the most probable path by comparing the probability values of the paths at the turning points, thereby obtaining the positioning position.
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