CN108632761B - Indoor positioning method based on particle filter algorithm - Google Patents

Indoor positioning method based on particle filter algorithm Download PDF

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CN108632761B
CN108632761B CN201810361226.2A CN201810361226A CN108632761B CN 108632761 B CN108632761 B CN 108632761B CN 201810361226 A CN201810361226 A CN 201810361226A CN 108632761 B CN108632761 B CN 108632761B
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CN108632761A (en
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廖学文
王梦迪
李乔
田馨元
齐以星
高贞贞
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Xian Jiaotong University
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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
    • H04W4/021—Services related to particular areas, e.g. point of interest [POI] services, venue services or geofences
    • 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
    • H04W4/029—Location-based management or tracking services
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management

Abstract

An indoor positioning method based on a particle filter algorithm is characterized in that pedestrian navigation information, WiFi signal intensity information and a geomagnetic signal three-dimensional sequence in N steps after a user starts to walk are fused, an initial point region is determined through WiFi, initial position coordinates are determined through geomagnetic accurate positioning, and then positioning results of a nearest neighbor matching algorithm based on WiFi, a particle filter algorithm based on WiFi and PDR and a particle filter algorithm based on geomagnetic and PDR are independent and verified with each other, so that positioning is kept tracking, and positioning robustness is improved. The method is suitable for four mobile phone placing modes of flat end, hand throwing, pocket and backpack on the premise of obtaining more accurate pedestrian navigation information (including step counting and pedestrian direction), and has high positioning accuracy.

Description

Indoor positioning method based on particle filter algorithm
Technical Field
The invention relates to the field of indoor positioning and tracking, in particular to an indoor positioning method based on a particle filter algorithm.
Background
With the rapid development of modern mobile communication technology, location based services (lbs) are gaining more and more favor of people, and the realization of low-cost and high-precision indoor positioning algorithm is paid the attention of many researchers. At present, indoor positioning methods based on WiFi, infrared, bluetooth, Ultra Wide Band (UWB), geomagnetism, and inertial sensors have gained wide attention in the research field, but positioning by Ultra Wide Band (UWB) and infrared technologies requires redeployment of equipment, which is expensive.
In recent years, with the rapid development of wireless local area networks (WiFi), WiFi networks are widely deployed in most indoor environments, that is, APs are widely deployed, and smart devices at different locations connect to the local area networks by receiving signals from different APs, that is, the smart devices at different locations receive signals from different APs or receive signals from the same AP but have different signal strength values. Therefore, the received signal strength of the AP can be regarded as a kind of location fingerprint for indoor positioning.
On the other hand, it is inspired by biology that homing pigeons, lobsters and other organisms can use the earth magnetic field to find ways, and researchers find that the earth magnetic field can be used for indoor positioning. In an indoor environment, the geomagnetic field is distorted under the influence of a reinforced concrete structure, an internal pipeline cable, large-scale electromagnetic equipment and the like of a building, so that the indoor geomagnetic field is unevenly distributed, and the geomagnetic field can be regarded as a position fingerprint to carry out indoor positioning.
The indoor positioning technology using the WiFi fingerprint or the geomagnetic fingerprint is suitable for static positioning and cannot play a good role in real-time positioning and tracking. The inertial navigation technology is a completely autonomous navigation positioning method, and measures data of sensors such as an accelerometer, a gyroscope, an electronic compass, a magnetometer and the like integrated by a smart phone are utilized to carry out step detection, step length estimation and course angle estimation, so that a Pedestrian track can be positioned by using a Pedestrian Dead Reckoning (PDR) algorithm. But the PDR algorithm needs to know the exact initial position, which is difficult to obtain in practice; due to the error of the inertial sensor, the positioning accuracy is high in a short time, and a large accumulated error can occur along with the increase of time.
In the existing scheme, dynamic positioning can be realized by utilizing a particle filter algorithm (WiFi-PF) based on WiFi and PDR or a particle filter algorithm (Mag-PF) based on geomagnetism and PDR, so that a continuous user walking track is obtained. However, after long-time positioning and tracking, the WiFi-PF or Mag-PF algorithm is prone to deviation of positioning from the real track of the pedestrian, and positioning and tracking fail. In particular, in the Mag-PF algorithm, since the geomagnetic fingerprint is a three-dimensional vector and has poor spatial uniqueness, once the positioning deviates from the true position, the geomagnetic fingerprint sequence of the particle may still match with the currently observed geomagnetic sequence, thereby estimating the positioning coordinate, and the algorithm itself cannot identify that the positioning has failed. The WiFi fingerprint matching algorithm has the advantages that the positioning results of the front positioning result and the positioning result of the rear positioning result are mutually independent, and the positioning error has a certain range, so that the WiFi-PF, the Mag-PF and the WiFi fingerprint matching algorithm are mutually checked and fused in the positioning of each step by utilizing the independence of the WiFi-PF, the Mag-PF and the WiFi fingerprint matching algorithm, so that the positioning is kept to be correctly tracked.
Disclosure of Invention
The invention mainly aims to solve the problem that the existing particle filter algorithm based on WiFi and PDR and the existing particle filter algorithm based on geomagnetic and PDR are easy to fail in positioning and tracking, and aims to provide an indoor positioning method based on the particle filter algorithm.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
an indoor positioning method based on a particle filter algorithm comprises the following steps: determining initial point coordinates by adopting an initial position positioning algorithm, and then realizing positioning by a particle filter algorithm fusing PDR, WiFi and geomagnetism, wherein the specific process is as follows:
step 1: with L0(x0,y0) Respectively initializing particles of a WiFi-PF algorithm and a Mag-PF algorithm for an initial point;
step 2: estimating the walking steps and direction of the user in real time by using a PDR algorithm, and obtaining the positioning coordinate of the corresponding WiFi-PF algorithm for the kth step detected by the PDR algorithm
Figure BDA0001636022080000031
Positioning coordinate of Mag-PF algorithm
Figure BDA0001636022080000032
And positioning coordinates of WiFi-KNN algorithm
Figure BDA0001636022080000033
And step 3: in the kth step, whether positioning tracking fails or not is judged by fusing positioning coordinates of the Mag-PF algorithm and map information;
and 4, step 4: if the positioning tracking of the Mag-PF algorithm fails, the particles are reinitialized by taking the positioning coordinates of the WiFi-PF algorithm as reference, namely the positioning coordinates of the WiFi-PF of the current k step
Figure BDA0001636022080000034
Taking the circle as the center of the circle, drawing a circle by taking R as the radius, randomly generating Num particles in the circle to replace the original particle subset, using the Num particles as the particle subset for carrying out particle filtering by the next Mag-PF algorithm, and then carrying out step 6; if the positioning tracking of the Mag-PF algorithm is judged to be normal, the step 5 is carried out;
and 5: at the k step, the location coordinates are determined
Figure BDA0001636022080000035
And the location coordinates
Figure BDA0001636022080000036
Fusing to obtain the positioning coordinate of the WiFi-PF algorithm and the Mag-PF algorithm after fusing
Figure BDA0001636022080000037
Step 6: the positioning coordinates of the WiFi-PF algorithm are taken as the fused positioning coordinates, namely
Figure BDA0001636022080000038
And 7: calculating positioning coordinates of WiFi-KNN algorithm
Figure BDA0001636022080000039
And fused positioning coordinates
Figure BDA00016360220800000310
The distance between
Figure BDA00016360220800000311
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA00016360220800000312
And fused positioning coordinates
Figure BDA00016360220800000313
Dis of each otherkIf the difference is greater than or equal to the threshold delta, the positioning and tracking of the WiFi-PF algorithm and the Mag-PF algorithm are failed, the particle sets in the WiFi-PF algorithm and the Mag-PF algorithm are respectively processed, and a part of the particle sets distributed at the positions is increased
Figure BDA00016360220800000314
The surrounding random particles, update the set of particles, then the updated particles are active at step k +1, the location coordinates of the current step
Figure BDA00016360220800000315
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA00016360220800000316
And fused positioning coordinates
Figure BDA00016360220800000317
Dis of each otherkLess than the threshold delta, then
Figure BDA00016360220800000318
Location coordinates as current step
Figure BDA00016360220800000319
And 8: if step counting is detected, if k is equal to k +1, jumping to the step 3; otherwise, positioning is finished.
The further improvement of the invention is that the specific initialization process in the step 1) is as follows: with L0(x0,y0) Taking the obtained object as a circle center, drawing a circle by taking R as a radius, and randomly distributing Num particles in the circle as initial particle sets, wherein the initial particles are generated for a WiFi-PF algorithm and a Mag-PF algorithm respectivelyA subset.
The further improvement of the invention is that the specific process for judging whether the positioning tracking fails in the step 3 is as follows:
detecting the positioning coordinate L of the Mag-PF algorithm in 20 steps before the kth stepM-PF(xM-PF,yM-PF) Number of times RI entered inaccessible areaM-PFI.e. the location coordinates L of the Mag-PF algorithmM-PF(xM-PF,yM-PF) Number of times RI for starting re-initialization after entering unreachable areaM-PFAnd comparing the number RI of times that the positioning result of the Mag-PF enters the inaccessible areaM-PFAnd a threshold TM-PFIf RIM-PF>TM-PFIf so, the positioning and tracking of the Mag-PF algorithm fails; otherwise, the positioning tracking of the Mag-PF algorithm is normal.
A further improvement of the present invention is that the specific process of starting the re-initialization is as follows:
① particle initialization, using the positioning coordinate before n steps as the center of circle, R as radius to draw circle, generating Num particles randomly in the circle, wherein the number of steps of the k step leading in the same direction is p, then
Figure BDA0001636022080000041
② state transition, the direction of particle motion is the average direction in n steps, the step length is n times of each step length;
③ observation value, geomagnetic three-dimensional sequence B collected by pedestrian in n stepsnow；
④ weight value updating, namely the geomagnetic three-dimensional sequence B corresponding to the motion trail of the ith particle in n stepsiLinear interpolation is carried out through geomagnetic fingerprints in a database according to the coordinates of the starting point and the end point of the particle motion estimation; calculating the geomagnetic three-dimensional sequence B of the ith particleiAnd the observed value BnowThe distance between DTW is recorded as DiThen the weight of the ith particle is
Figure BDA0001636022080000042
The weights are then normalized, where σD 2Indicating the DTW distanceVariance of the distance;
⑤ resampling, namely performing simple random resampling;
⑥ position estimation the positions of all the particles are averaged to get the positioning coordinates of the k step.
The invention has the further improvement that the specific process of the step 5 is as follows: according to the location coordinates
Figure BDA0001636022080000043
Positioning coordinate with WiFi-KNN algorithm
Figure BDA0001636022080000044
Distance between them
Figure BDA0001636022080000045
Location coordinates
Figure BDA0001636022080000046
And the location coordinates
Figure BDA0001636022080000047
Distance between them
Figure BDA0001636022080000048
Will locate the coordinates
Figure BDA0001636022080000049
And positioning coordinates
Figure BDA0001636022080000051
Weighting to obtain positioning coordinates
Figure BDA0001636022080000052
The weighted weights are respectively
Figure BDA0001636022080000053
Wherein the content of the first and second substances,
Figure BDA0001636022080000054
for locating coordinates
Figure BDA0001636022080000055
The weight of (a) is determined,
Figure BDA0001636022080000056
for locating coordinates
Figure BDA0001636022080000057
Weight of (a), ωkAre parameters.
The invention is further improved in that the parameter omegakThere are two calculation methods:
① reciprocal method:
Figure BDA0001636022080000058
② exponential method:
Figure BDA0001636022080000059
the invention has the further improvement that the positioning coordinate after the positioning coordinate fusion of the WiFi-PF algorithm and the Mag-PF algorithm is
Figure BDA00016360220800000510
Is calculated by the formula
Figure BDA00016360220800000511
The invention has the further improvement that the specific process of determining the initial point coordinate by adopting the initial position positioning algorithm is as follows:
step 1: the method comprises the following steps of (1) after a pedestrian starts to walk, estimating the number of steps of walking and the direction of each step of the pedestrian on accelerometer data, gyroscope data, electronic compass data and magnetometer data of a smart phone through a pedestrian dead reckoning algorithm;
step 2: determining an initial point area by utilizing WiFi, and in N steps of walking, periodically scanning WiFi signals by a WiFi scanning module of the smart phone, so that signal intensity vectors of WiFi are collected for multiple times, averaging the signal intensity vectors of WiFi for multiple times, and obtaining the average WiFi signal within the periodThe number intensity vector is positioned by utilizing a nearest neighbor algorithm to obtain a positioning result
Figure BDA00016360220800000512
The initial point region is then set to locate the result
Figure BDA00016360220800000513
As a center of circle, R0A circle with a radius;
and step 3: the method comprises the steps of accurately positioning by using geomagnetic three-dimensional sequence data and determining the coordinates of an initial point.
The invention is further improved in that the specific process of estimating the initial point coordinates in step 3 is as follows:
① within the initial point region determined in step 2, generating NumI samples subject to uniform distribution, the sample positions being set to
{pi＝(xi,yi),i＝1,2,...,NumI}；
② step size d based on the step number N estimated in step 1 for each sample iiAnd average direction of the previous N step directions
Figure BDA0001636022080000068
Move forwards, and the movement track is recorded as liThe ith sample motion formula is
Figure BDA0001636022080000061
Wherein the step length diWith direction of movement thetaiGaussian noise is added, d denotes the step size per step,
Figure BDA0001636022080000062
representing the variance of the N step size Nd,
Figure BDA0001636022080000063
represents the average direction
Figure BDA0001636022080000064
The variance of (a);
for the ith sample, obtaining the motion track l thereofiCorresponding geomagnetic three-dimensional vector sequence MiGeomagnetic three-dimensional vector sequence MiObtaining the geomagnetic data by linear interpolation of geomagnetic fingerprints in a database;
③ the observation value is the geomagnetic three-dimensional vector sequence M collected in the previous N stepsnowThrough MnowCalculating the posterior probability P of the ith sampleiThe posterior probability of the ith sample is calculated as follows: calculating a geomagnetic three-dimensional vector sequence M corresponding to the ith sampleiThe geomagnetic sequence M collected in the previous N stepsnowThe distance between DTW is recorded as DiThen the weight of the ith sample is
Figure BDA0001636022080000065
The posterior probability is the weight normalized value
Figure BDA0001636022080000066
WhereinσD 2A variance representing the DTW distance;
④ selecting K samples with maximum posterior probability, removing abnormal samples according to 3 sigma criterion, and remaining K0Sample { p }j＝(xj,yj),j＝1,2,...,K0}, and finally K0The position coordinates of each sample are subjected to mean value processing, and the coordinates of an initial point are calculated
Figure BDA0001636022080000067
Compared with the prior art, the invention has the following beneficial effects: according to the invention, the independence of the positioning results of a WiFi-based nearest neighbor matching algorithm (WiFi-KNN), a WiFi-and-PDR-based particle filter algorithm (WiFi-PF) and a geomagnetic-and-PDR-based particle filter algorithm (Mag-PF) is utilized for mutual verification, so that the positioning is kept tracking, and the positioning robustness is improved. The key technology of the particle filter algorithm fusing PDR, WiFi and geomagnetism mainly comprises the following steps: the method comprises a WiFi-PF and Mag-PF positioning result fusion strategy, a particle filter algorithm positioning failure self-detection strategy based on geomagnetism and PDR, a WiFi-KNN auxiliary judgment positioning failure strategy, a particle re-initialization strategy and a Mag-PF re-initialization strategy. The system is suitable for four mobile phone placing modes of flat end, throwing hands, pocket and backpack on the premise of obtaining more accurate pedestrian navigation information (including step counting and pedestrian direction), and has high positioning accuracy. The method utilizes the independence of a particle filter algorithm based on WiFi and PDR, a particle filter algorithm based on geomagnetic WiFi and PDR and a fingerprint matching algorithm based on WiFi in positioning to check each other, so that the positioning is kept tracking, and the positioning robustness is improved.
Drawings
FIG. 1 is a flow chart of an accurate initial position location algorithm;
FIG. 2 is a flowchart of a particle filter algorithm that integrates PDR, WiFi and geomagnetism;
FIG. 3 is a plan view of a test environment.
Detailed Description
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, all the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings obtained without creative efforts for those skilled in the art belong to the protection scope of the present invention.
The WiFi-PF algorithm is a particle filter algorithm based on WiFi and PDR, the Mag-PF algorithm is a particle filter algorithm based on geomagnetism and PDR, the fingerprint matching algorithm based on WiFi uses a nearest neighbor matching algorithm based on WiFi, the WiFi-KNN algorithm is a nearest neighbor matching algorithm based on WiFi, the PDR algorithm is a pedestrian dead reckoning algorithm, and the KNN algorithm is a nearest neighbor algorithm.
Determining initial point coordinates by adopting an initial position positioning algorithm, and then realizing positioning by a particle filter algorithm fusing PDR, WiFi and geomagnetism, wherein the specific process is as follows:
the method adopts an accurate initial position positioning algorithm to determine the initial point coordinates, and specifically comprises the following steps:
step 1: estimating the number of steps and the direction of each step of walking of the travelers for accelerometer data, gyroscope data, electronic compass data and magnetometer data of the smart phone by a pedestrian dead reckoning algorithm (PDR algorithm) after the pedestrians start walking for N steps;
step 2: determining an initial point area by utilizing WiFi, periodically scanning WiFi signals by a WiFi scanning module of the smart phone within N steps of walking of a pedestrian, acquiring signal intensity vectors of WiFi for multiple times, carrying out mean value processing on the signal intensity vectors of WiFi for multiple times to obtain a WiFi average signal intensity vector within the period of time, positioning by utilizing a nearest neighbor algorithm (KNN algorithm), and obtaining a positioning result
Figure BDA0001636022080000081
The initial point region is then set to locate the result
Figure BDA0001636022080000082
As a center of circle, R0A circle with a radius;
and step 3: the method comprises the following steps of accurately positioning by using geomagnetic three-dimensional sequence data, and determining an initial point coordinate, wherein the principle is that the posterior probability of a sample is estimated through an observed value by using a maximum posterior estimation criterion, so that the initial point coordinate is estimated, and the specific process is as follows:
① in the initial point region determined in step 2, generating NumI samples subject to uniform distribution, the sample positions being set to { p }i＝(xi,yi),i＝1,2,...,NumI}；
② step size d based on the step number N estimated in step 1 for each sample iiAnd average direction of the previous N step directions
Figure BDA0001636022080000083
Move forwards, and the movement track is recorded as liThe ith sample motion formula is
Figure BDA0001636022080000084
Wherein the step length diWith direction of movement thetaiGaussian noise is added, d denotes the step size per step,
Figure BDA0001636022080000085
representing the variance of the N step size Nd,
Figure BDA0001636022080000086
represents the average direction
Figure BDA0001636022080000087
The variance of (a);
③ for the ith sample, its motion trail l is obtainediCorresponding geomagnetic three-dimensional vector sequence MiGeomagnetic three-dimensional vector sequence MiObtaining the geomagnetic data by linear interpolation of geomagnetic fingerprints in a database; the observation value is a geomagnetic three-dimensional vector sequence M acquired in the previous N stepsnowThrough MnowCalculating the posterior probability P of the ith sampleiThe posterior probability of the ith sample is calculated as follows: calculating a geomagnetic three-dimensional vector sequence M corresponding to the ith sampleiThe geomagnetic sequence M collected in the previous N stepsnowThe distance between DTW is recorded as DiThen the weight of the ith sample is
Figure BDA0001636022080000088
The posterior probability is the weight normalized value
Figure BDA0001636022080000089
WhereinσD 2A variance representing the DTW distance;
④ selecting K samples with maximum posterior probability, removing abnormal samples according to 3 sigma criterion, and remaining K0Sample { p }j＝(xj,yj),j＝1,2,...,K0}, and finally K0The position coordinates of each sample are subjected to mean value processing, and the coordinates of an initial point are calculated
Figure BDA0001636022080000091
Positioning is realized by a particle filter algorithm fusing navigation information, WiFi and geomagnetism, and the specific process is as follows:
step 1: with L0(x0,y0) Respectively carrying out particle initialization based on a particle filter algorithm (WiFi-PF algorithm) based on WiFi and PDR and a particle filter algorithm (Mag-PF algorithm) based on geomagnetism and PDR for an initial point, wherein the specific process of the initialization is L0(x0,y0) Taking the obtained object as a circle center, drawing a circle by taking R as a radius, and randomly distributing Num particles in the circle as initial particle sets, wherein the initial particle sets are generated for a WiFi-PF algorithm and a Mag-PF algorithm;
step 2: the PDR algorithm is utilized to estimate the walking steps and the direction of the user in real time, and for the kth step detected by the PDR algorithm, the positioning coordinate of the corresponding WiFi-PF algorithm can be obtained
Figure BDA0001636022080000092
Positioning coordinate of Mag-PF algorithm
Figure BDA0001636022080000093
And WiFi-KNN positioning coordinates
Figure BDA0001636022080000094
And step 3: and k, judging whether the positioning tracking fails by fusing positioning coordinates based on geomagnetism and a particle filter algorithm (Mag-PF algorithm) of the PDR and map information, wherein the specific process is as follows:
detecting the positioning coordinate L of the Mag-PF algorithm in 20 steps before the kth stepM-PF(xM-PF,yM-PF) Number of times RI entered inaccessible areaM-PFI.e. the location coordinates L of the Mag-PF algorithmM-PF(xM-PF,yM-PF) Number of times RI for starting re-initialization after entering unreachable areaM-PFAnd comparing the RI times of the positioning result of the Mag-PF algorithm entering the inaccessible areaM-PFAnd a threshold TM-PFIf RIM-PF>TM-PFIf so, the positioning and tracking of the Mag-PF algorithm fails; otherwise, the positioning tracking of the Mag-PF algorithm is normal;
and 4, step 4: if the positioning tracking of the Mag-PF algorithm fails, thenReinitializing the particles by taking the positioning coordinates of the WiFi-PF algorithm as reference, namely the positioning coordinates of the WiFi-PF algorithm in the current k step
Figure BDA0001636022080000095
Taking the circle as the center of the circle, drawing a circle by taking R as the radius, randomly generating Num particles in the circle to replace the original particle subset, using the Num particles as the particle subset for carrying out particle filtering by the next Mag-PF algorithm, and then carrying out step 6; if the positioning tracking of the Mag-PF algorithm is judged to be normal, the step 5 is carried out;
and 5: at the k step, the location coordinates are determined
Figure BDA0001636022080000096
And the location coordinates
Figure BDA0001636022080000097
Carrying out fusion: according to the location coordinates
Figure BDA0001636022080000101
Positioning coordinate with WiFi-KNN algorithm
Figure BDA0001636022080000102
Distance between them
Figure BDA0001636022080000103
Location coordinates
Figure BDA0001636022080000104
And the location coordinates
Figure BDA0001636022080000105
Distance between them
Figure BDA0001636022080000106
Will locate the coordinates
Figure BDA0001636022080000107
And positioning coordinates
Figure BDA0001636022080000108
Weighting to obtain positioning coordinates
Figure BDA0001636022080000109
The weighted weights are respectively
Figure BDA00016360220800001010
Wherein the content of the first and second substances,
Figure BDA00016360220800001011
for locating coordinates
Figure BDA00016360220800001012
The weight of (a) is determined,
Figure BDA00016360220800001013
for locating coordinates
Figure BDA00016360220800001014
The weight of (c);
parameter omegakThere are two calculation methods:
① reciprocal method:
Figure BDA00016360220800001015
② exponential method:
Figure BDA00016360220800001016
then, the positioning coordinate after the positioning coordinates of the WiFi-PF algorithm and the Mag-PF algorithm are fused is as
Figure BDA00016360220800001017
Is calculated by the formula
Figure BDA00016360220800001018
Step 6: the positioning coordinates of the WiFi-PF algorithm are taken as fused positioning coordinates, i.e.
Figure BDA00016360220800001019
Step (ii) of7: calculating positioning coordinates of WiFi-KNN
Figure BDA00016360220800001020
With fused particle filter location coordinates
Figure BDA00016360220800001021
The distance between
Figure BDA00016360220800001022
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA00016360220800001023
With fused particle filter location coordinates
Figure BDA00016360220800001024
Dis of each otherkIf the difference is greater than or equal to the threshold delta, the positioning and tracking of the WiFi-PF algorithm and the Mag-PF algorithm are failed, the particle sets in the WiFi-PF algorithm and the Mag-PF algorithm are respectively processed, and a part of the particle sets distributed at the positions is increased
Figure BDA00016360220800001025
The surrounding random particles, update the set of particles, then the updated particles are active at step k +1, and the location coordinates of the current step
Figure BDA00016360220800001026
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA00016360220800001027
With fused particle filter location coordinates
Figure BDA00016360220800001028
Dis of each otherkIf the threshold is less than delta, then the control unit
Figure BDA00016360220800001029
Location coordinates as current step
Figure BDA00016360220800001030
And 8: if step counting is detected, if k is equal to k +1, jumping to the step 3; otherwise, positioning is finished.
Wherein, the specific process of starting reinitialization in the Mag-PF algorithm in step 3: when the positioning coordinate of the Mag-PF algorithm in the kth step reaches an inaccessible area, the method is reinitialized according to historical positioning information, and comprises the following specific steps:
① particle initialization, using the positioning coordinate before n steps as the center of circle, R as radius to draw circle, generating Num particles randomly in the circle, wherein the number of steps of the k step leading in the same direction is p, then
Figure BDA0001636022080000111
② state transition, the direction of particle motion is the average direction in n steps, the step length is n times of each step length;
③ observation value, geomagnetic three-dimensional sequence B collected by pedestrian in n stepsnow；
④ weight value updating, namely the geomagnetic three-dimensional sequence B corresponding to the motion trail of the ith particle in n stepsiLinear interpolation can be carried out through geomagnetic fingerprints in a database according to the coordinates of the starting point and the end point of particle motion estimation; calculating the geomagnetic three-dimensional sequence B of the ith particleiAnd the observed value BnowThe distance between DTW is recorded as DiThen the weight of the ith particle is
Figure BDA0001636022080000112
The weights are then normalized, where σD 2A variance representing the DTW distance;
⑤ resampling, namely performing simple random resampling;
⑥ position estimation the positions of all the particles are averaged to get the positioning coordinates of the k step.
The technical scheme in the embodiment of the invention is clearly and completely described below by combining the attached drawings of the invention:
the test environment is an open office, the size of the test environment is 52m × 60m, a specific test environment plan is shown in fig. 3, and the experimental test mobile phone is a gorgeous magic mobile phone.
In the off-line stage, WiFi fingerprints are statically acquired at fixed anchor points for 1min, the anchor point distance is 3m, a plurality of WiFi signal intensity vectors acquired at each anchor point are subjected to mean value processing, and then anchor point coordinates and corresponding WiFi signal intensity mean value vectors are uploaded to a database; the geomagnetic fingerprint adopts a continuous walking acquisition mode, walking routes need to cover all reachable areas without overlapping, then the acquired geomagnetic sequences are subjected to discretization treatment, and a geomagnetic fingerprint database with anchor points at intervals of 0.5m is generated, namely each anchor point corresponds to a three-dimensional geomagnetic vector.
In the online stage, pedestrians walk in the test environment by holding the mobile phone, the walking distance is about 280m, and the positioning process is as follows:
the method adopts an accurate initial position positioning algorithm to determine the initial point coordinates, and specifically comprises the following steps:
as shown in fig. 1, an algorithm flowchart for performing initial point positioning at an online stage includes the following specific steps, in fig. 1:
step 1: n steps after the pedestrian starts walking, the number of steps and the direction of each step of walking of the pedestrian are estimated from accelerometer data, gyroscope data and magnetometer data of the smartphone by a pedestrian dead reckoning algorithm (PDR algorithm), and N is 5 in the embodiment.
Step 2: determining an initial point area by utilizing WiFi, periodically scanning WiFi signals by a WiFi scanning module of the smart phone within N steps of walking of a pedestrian, acquiring signal intensity vectors of WiFi for multiple times, carrying out mean value processing on the signal intensity vectors of WiFi for multiple times to obtain WiFi average signal intensity vectors within the period of time, and positioning by utilizing a nearest neighbor algorithm (KNN) to obtain a positioning result
Figure BDA0001636022080000121
The initial point region is then set to locate the result
Figure BDA0001636022080000122
As a center of circle, R0Is a circle of radius.
And step 3: the method comprises the following steps of accurately positioning by using geomagnetic three-dimensional sequence data, estimating posterior probability of a sample by using a maximum posterior estimation criterion through an observed value so as to estimate an initial point coordinate, wherein the specific process comprises the following steps:
in the initial point positioning area determined in step 2, NumI samples which are subject to uniform distribution are generated, and the positions of the samples are set to be { pi＝(xi,yi),i＝1,2,...,NumI}；
① step size d based on the step number N estimated in step 1 for each sample iiAnd average direction of the previous N step directions
Figure BDA0001636022080000123
The motion track is recorded as the motion formula of the ith sample
Figure BDA0001636022080000124
Wherein the step length diWith direction of movement thetaiGaussian noise is added, d denotes the step size per step,
Figure BDA0001636022080000125
representing the variance of the N step size Nd,
Figure BDA0001636022080000126
represents the average direction
Figure BDA0001636022080000127
The variance of (a);
for the ith sample, obtaining the motion track l thereofiCorresponding geomagnetic three-dimensional vector sequence MiGeomagnetic three-dimensional vector sequence MiObtaining the geomagnetic data by linear interpolation of geomagnetic fingerprints in a database;
② the observation value is the geomagnetic three-dimensional vector sequence M collected in the previous N stepsnowThrough MnowCalculating the posterior probability P of the ith sampleiThe posterior probability of the ith sample is calculated as follows: calculating the corresponding of the ith sampleGeomagnetic three-dimensional vector sequence MiThe geomagnetic sequence M collected in the previous N stepsnowThe distance between DTW is recorded as DiThen the weight of the ith sample is
Figure BDA0001636022080000131
The posterior probability is the weight normalized value
Figure BDA0001636022080000132
WhereinσD 2A variance representing the DTW distance;
③ selecting K samples with maximum posterior probability, removing abnormal samples according to 3 sigma criterion, and remaining K0Sample { p }j＝(xj,yj),j＝1,2,...,K0}, and finally K0The position coordinates of each sample are subjected to mean value processing, and the coordinates of an initial point are calculated
Figure BDA0001636022080000133
Positioning is realized by a particle filter algorithm fusing navigation information, WiFi and geomagnetism, and the method specifically comprises the following steps:
as shown in fig. 2, which is a flow chart of the fusion algorithm in the online phase, in fig. 2:
step 1: with L0(x0,y0) Respectively carrying out particle initialization based on a particle filter algorithm (WiFi-PF algorithm) based on WiFi and PDR and a particle filter algorithm (Mag-PF algorithm) based on geomagnetism and PDR for an initial point, wherein the specific process of the initialization is L0(x0,y0) Taking the obtained object as a circle center, drawing a circle by taking R as a radius, and randomly distributing Num particles in the circle as initial particle sets, wherein the initial particle sets are generated for a WiFi-PF algorithm and a Mag-PF algorithm;
step 2: the PDR algorithm is utilized to estimate the walking steps and the direction of the user in real time, and for the kth step detected by the PDR algorithm, the positioning coordinate of the corresponding WiFi-PF algorithm can be obtained
Figure BDA0001636022080000134
Positioning coordinate of Mag-PF algorithm
Figure BDA0001636022080000135
And WiFi-KNN positioning coordinates
Figure BDA0001636022080000136
And step 3: for the k step, the positioning coordinates estimated by the Mag-PF algorithm
Figure BDA0001636022080000137
And judging whether the current frame is in the inaccessible area, if so, starting reinitialization, and recording the reinitialization steps. The re-initialization is performed using the history information. Wherein, the unreachable area is the non-grid area in fig. 3. The reinitialization process is as follows:
① particle initialization, using the positioning coordinate before n steps as the center of circle, R as radius to draw circle, generating Num particles randomly in the circle, wherein the number of steps of the k step leading in the same direction is p, then
Figure BDA0001636022080000138
Wherein R is the radius of particle initialization at the beginning of positioning;
② state transition, the direction of particle motion is the average direction in n steps, the step length is n times of each step length;
③ observed value, namely geomagnetic three-dimensional sequence B acquired by the intelligent mobile phone in n steps by the pedestriannow；
④ weight value updating, namely the geomagnetic three-dimensional sequence B corresponding to the motion trail of the ith particle in n stepsiGeomagnetic three-dimensional sequence BiLinear interpolation can be carried out through geomagnetic fingerprints in a database according to the coordinates of the starting point and the end point of the particle motion track; calculating the geomagnetic three-dimensional sequence B of the ith particleiAnd the observed value BnowThe distance between DTW is recorded as DiThen the weight of the ith particle is
Figure BDA0001636022080000141
The weights are then normalized, where σD 2A variance representing the DTW distance;
⑤ resampling, namely simply and randomly resampling according to the position coordinates and the weight of the particle set;
⑥ position estimation the position of all particles is averaged to get the location coordinates of step k.
And 4, step 4: and k, performing self-detection of Mag-PF algorithm positioning failure on the positioning coordinates of a geomagnetic-based particle filter algorithm (Mag-PF algorithm) by fusing map information:
detecting the positioning coordinate L of the Mag-PF algorithm in 20 steps before the kth stepM-PF(xM-PF,yM-PF) Number of times of entering inaccessible area, i.e. location coordinate L of Mag-PF algorithmM-PF(xM-PF,yM-PF) Number of times RI for starting re-initialization after entering unreachable areaM-PFAnd comparing the RI times of the positioning result of the Mag-PF algorithm entering the inaccessible areaM-PFAnd a threshold TM-PFIf RIM-PF>TM-PFIf so, the positioning and tracking of the Mag-PF algorithm fails; otherwise, the positioning tracking of the Mag-PF algorithm is normal; wherein the threshold TM-PF＝5。
And 5: if the positioning tracking of the Mag-PF algorithm fails, the particles are reinitialized by taking the positioning coordinates of the WiFi-PF algorithm as reference, namely the positioning coordinates of the WiFi-PF algorithm in the current k step
Figure BDA0001636022080000142
Taking the circle as the center of the circle, drawing a circle by taking R as the radius, randomly generating Num particles in the circle to replace the original particle subset, using the Num particles as the particle subset for carrying out particle filtering by the next Mag-PF algorithm, and then carrying out step 7; if the positioning tracking of the Mag-PF algorithm is judged to be normal, performing step 6;
step 6: step k, the Mag-PF algorithm does not detect the failure of particle tracking, and the positioning coordinates are obtained
Figure BDA0001636022080000143
And the location coordinates
Figure BDA0001636022080000144
Carrying out fusion: according to the positioningCoordinates of the object
Figure BDA0001636022080000145
And positioning coordinates
Figure BDA0001636022080000146
Positioning coordinate with WiFi-KNN algorithm
Figure BDA0001636022080000147
Distance between them
Figure BDA0001636022080000148
And
Figure BDA0001636022080000149
will locate the coordinates
Figure BDA0001636022080000151
And positioning coordinates
Figure BDA0001636022080000152
Weighting to obtain positioning coordinates
Figure BDA0001636022080000153
The weighted weights are respectively
Figure BDA0001636022080000154
Wherein the content of the first and second substances,
Figure BDA0001636022080000155
for locating coordinates
Figure BDA0001636022080000156
The weight of (a) is determined,
Figure BDA0001636022080000157
for locating coordinates
Figure BDA0001636022080000158
The weight of (c); parameter omegakThere are two calculation methods:
① reciprocal method:
Figure BDA0001636022080000159
② exponential method:
Figure BDA00016360220800001510
wherein the location coordinates
Figure BDA00016360220800001511
Positioning coordinate with WiFi-KNN algorithm
Figure BDA00016360220800001512
The distance between the two is calculated by the formula
Figure BDA00016360220800001513
Location coordinates
Figure BDA00016360220800001514
And the location coordinates
Figure BDA00016360220800001515
The distance between the two is calculated by the formula
Figure BDA00016360220800001516
Then, the positioning coordinate after the positioning results of the WiFi-PF algorithm and the Mag-PF algorithm are fused is
Figure BDA00016360220800001517
Is calculated by the formula
Figure BDA00016360220800001518
If the Mag-PF algorithm detects that the particle tracking fails, the positioning coordinate of the WiFi-PF algorithm is used as a fused positioning coordinate, namely
Figure BDA00016360220800001519
In the embodiment, the WiFi-PF algorithm and the Mag-PF algorithm are weighted by an index method.
And 7: calculating positioning coordinates of WiFi-KNN algorithm
Figure BDA00016360220800001520
With fused particle filter location coordinates
Figure BDA00016360220800001521
The distance between
Figure BDA00016360220800001522
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA00016360220800001523
With fused particle filter location coordinates
Figure BDA00016360220800001524
Dis of each otherkIf the difference is larger than or equal to the threshold delta, the positioning of the WiFi-PF algorithm and the Mag-PF algorithm fails. Therefore, the operation of updating the particle set is needed, the particle swarm of the WiFi-PF algorithm and the Mag-PF algorithm are respectively processed, and a part of the particle swarm is added and distributed on the coordinates
Figure BDA0001636022080000161
The surrounding random particles update the particle set, so that the updated particles play a role in the (k + 1) th step, and the positioning coordinate of the current step is the positioning coordinate weighted by the WiFi-PF algorithm and the Mag-PF algorithm
Figure BDA0001636022080000162
If the positioning coordinates of the WiFi-KNN algorithm
Figure BDA0001636022080000163
With fused particle filter location coordinates
Figure BDA0001636022080000164
Dis of each otherkIs less than the thresholdDelta, then directly handle
Figure BDA0001636022080000165
Location coordinates as current step
Figure BDA0001636022080000166
And 8: if step counting is detected, if k is equal to k +1, jumping to the step 3; otherwise, positioning is finished.
The positioning result of this embodiment is shown in table 1, where table 1 shows the percentage of positioning accuracy improvement of the average positioning error and Hybrid-PF of the WiFi-knn (WiFi) algorithm, the Mag-PF algorithm, the WiFi-PF algorithm, and the fusion positioning algorithm (Hybrid-PF) compared with the other three algorithms:
name of algorithm WiFi-KNN Mag-PF WiFi-PF Hybrid-PF
Mean positioning error (m) 2.86 2.79 3.54 2.41
Positioning accuracy improvement (%) 15.73 13.62 31.92 -
As can be seen from table 1, the positioning method of the present invention is highly accurate.

Claims (9)

1. An indoor positioning method based on a particle filter algorithm is characterized by comprising the following steps: determining initial point coordinates by adopting an initial position positioning algorithm, and then realizing positioning by a particle filter algorithm fusing PDR, WiFi and geomagnetism, wherein the specific process is as follows:
step 1: with L0(x0,y0) Respectively initializing particles of a WiFi-PF algorithm and a Mag-PF algorithm for an initial point;
step 2: estimating the walking steps and direction of the user in real time by using a PDR algorithm, and obtaining the positioning coordinate of the corresponding WiFi-PF algorithm for the kth step detected by the PDR algorithm
Figure FDA0002261529290000011
Positioning coordinate of Mag-PF algorithm
Figure FDA0002261529290000012
And positioning coordinates of WiFi-KNN algorithm
Figure FDA0002261529290000013
And step 3: in the kth step, whether positioning tracking fails or not is judged by fusing positioning coordinates of the Mag-PF algorithm and map information;
and 4, step 4: if the positioning tracking of the Mag-PF algorithm fails, the particles are reinitialized by taking the positioning coordinates of the WiFi-PF algorithm as reference, namely the positioning coordinates of the WiFi-PF of the current k step
Figure FDA0002261529290000014
Taking R as the radius to draw a circle as the center of the circle, randomly generating Num particles in the circle to replace the original particle subset, using the Num particles as the particle set for carrying out particle filtering by the next Mag-PF algorithm,then step 6 is carried out; if the positioning tracking of the Mag-PF algorithm is judged to be normal, the step 5 is carried out;
and 5: at the k step, the location coordinates are determined
Figure FDA0002261529290000015
And the location coordinates
Figure FDA0002261529290000016
Fusing to obtain the positioning coordinate of the WiFi-PF algorithm and the Mag-PF algorithm after fusing
Figure FDA0002261529290000017
Then, step 7 is carried out;
step 6: the positioning coordinates of the WiFi-PF algorithm are taken as the fused positioning coordinates, namely
Figure FDA0002261529290000018
And 7: calculating positioning coordinates of WiFi-KNN algorithm
Figure FDA0002261529290000019
And fused positioning coordinates
Figure FDA00022615292900000110
The distance between
Figure FDA00022615292900000111
If the positioning coordinates of the WiFi-KNN algorithm
Figure FDA00022615292900000112
And fused positioning coordinates
Figure FDA00022615292900000113
Dis of each otherkIf the difference is greater than or equal to the threshold delta, the positioning and tracking of the WiFi-PF algorithm and the Mag-PF algorithm are failed, and the particle sets in the WiFi-PF algorithm and the Mag-PF algorithm are respectively processedIncreasing a portion distributed at a location
Figure FDA0002261529290000021
The surrounding random particles, update the set of particles, then the updated particles are active at step k +1, the location coordinates of the current step
Figure FDA0002261529290000022
If the positioning coordinates of the WiFi-KNN algorithm
Figure FDA0002261529290000023
And fused positioning coordinates
Figure FDA0002261529290000024
Dis of each otherkLess than the threshold delta, then
Figure FDA0002261529290000025
Location coordinates as current step
Figure FDA0002261529290000026
And 8: if step counting is detected, if k is equal to k +1, jumping to the step 3; otherwise, positioning is finished.
2. The indoor positioning method based on the particle filter algorithm according to claim 1, wherein the specific initialization process in the step 1 is as follows: with L0(x0,y0) And as a circle center, drawing a circle by taking R as a radius, and randomly distributing Num particles in the circle as initial particle sets, wherein the initial particle sets are generated for the WiFi-PF algorithm and the Mag-PF algorithm.
3. The indoor positioning method based on the particle filter algorithm as claimed in claim 1, wherein the specific process of determining whether the positioning tracking fails in step 3 is as follows:
detecting the positioning of the Mag-PF algorithm within 20 steps before the k stepCoordinate LM-PF(xM-PF,yM-PF) Number of times RI entered inaccessible areaM-PFI.e. the location coordinates L of the Mag-PF algorithmM-PF(xM-PF,yM-PF) Number of times RI for starting re-initialization after entering unreachable areaM-PFAnd comparing the number RI of times that the positioning result of the Mag-PF enters the inaccessible areaM-PFAnd a threshold TM-PFIf RIM-PF>TM-PFIf so, the positioning and tracking of the Mag-PF algorithm fails; otherwise, the positioning tracking of the Mag-PF algorithm is normal.
4. The indoor positioning method based on the particle filter algorithm as claimed in claim 3, wherein the specific process of starting the reinitialization is as follows:
① particle initialization, using the positioning coordinate before n steps as the center of circle, R as radius to draw circle, generating Num particles randomly in the circle, wherein the number of steps of the k step leading in the same direction is p, then
Figure FDA0002261529290000027
② state transition, the direction of particle motion is the average direction in n steps, the step length is n times of each step length;
③ observation value, geomagnetic three-dimensional sequence B collected by pedestrian in n stepsnow；
④ weight value updating, namely the geomagnetic three-dimensional sequence B corresponding to the motion trail of the ith particle in n stepsiLinear interpolation is carried out through geomagnetic fingerprints in a database according to the coordinates of the starting point and the end point of the particle motion estimation; calculating the geomagnetic three-dimensional sequence B of the ith particleiAnd the observed value BnowThe distance between DTW is recorded as DiThen the weight of the ith particle is
Figure FDA0002261529290000031
The weights are then normalized, where σD 2A variance representing the DTW distance;
⑤ resampling, namely performing simple random resampling;
⑥ position estimation the positions of all the particles are averaged to get the positioning coordinates of the k step.
5. The indoor positioning method based on the particle filter algorithm as claimed in claim 1, wherein the specific process of step 5 is as follows: according to the location coordinates
Figure FDA0002261529290000032
Positioning coordinate with WiFi-KNN algorithm
Figure FDA0002261529290000033
Distance between them
Figure FDA0002261529290000034
Location coordinates
Figure FDA0002261529290000035
And the location coordinates
Figure FDA0002261529290000036
Distance between them
Figure FDA0002261529290000037
Will locate the coordinates
Figure FDA0002261529290000038
And positioning coordinates
Figure FDA0002261529290000039
Weighting to obtain positioning coordinates
Figure FDA00022615292900000310
The weighted weights are respectively
Figure FDA00022615292900000311
Wherein the content of the first and second substances,
Figure FDA00022615292900000312
for locating coordinates
Figure FDA00022615292900000313
The weight of (a) is determined,
Figure FDA00022615292900000314
for locating coordinates
Figure FDA00022615292900000315
Weight of (a), ωkAre parameters.
6. The indoor positioning method based on particle filter algorithm as claimed in claim 5, wherein the parameter ω iskThere are two calculation methods:
① reciprocal method:
Figure FDA00022615292900000316
② exponential method:
Figure FDA00022615292900000317
7. the indoor positioning method based on the particle filter algorithm as claimed in claim 5, wherein the positioning coordinate after the fusion of the positioning coordinates of the WiFi-PF algorithm and the Mag-PF algorithm is as follows
Figure FDA00022615292900000318
Is calculated by the formula
Figure FDA00022615292900000319
8. The indoor positioning method based on the particle filter algorithm as claimed in claim 1, wherein the specific process of determining the initial point coordinate by using the initial position positioning algorithm is as follows:
step 1: the method comprises the following steps of (1) after a pedestrian starts to walk, estimating the number of steps of walking and the direction of each step of the pedestrian on accelerometer data, gyroscope data, electronic compass data and magnetometer data of a smart phone through a pedestrian dead reckoning algorithm;
step 2: determining an initial point area by utilizing WiFi, periodically scanning WiFi signals by a WiFi scanning module of the smart phone within N steps of walking of a pedestrian, acquiring signal intensity vectors of WiFi for multiple times, carrying out mean value processing on the signal intensity vectors of WiFi for multiple times to obtain WiFi average signal intensity vectors within the period of time, positioning by utilizing a nearest neighbor algorithm to obtain a positioning result
Figure FDA0002261529290000041
The initial point region is then set to locate the result
Figure FDA0002261529290000042
As a center of circle, R0A circle with a radius;
and step 3: the method comprises the steps of accurately positioning by using geomagnetic three-dimensional sequence data and determining the coordinates of an initial point.
9. The indoor positioning method based on particle filter algorithm as claimed in claim 8, wherein the specific process of estimating the initial point coordinates in step 3 is as follows:
① in the initial point region determined in step 2, generating NumI samples subject to uniform distribution, the sample positions being set to { p }i＝(xi,yi),i＝1,2,...,NumI}；
② step size d based on the step number N estimated in step 1 for each sample iiAnd average direction of the previous N step directions
Figure FDA0002261529290000048
Move forward, the movement locus is recordedliThe ith sample motion formula is
Figure FDA0002261529290000043
Wherein the step length diWith direction of movement thetaiGaussian noise is added, d denotes the step size per step,
Figure FDA0002261529290000044
representing the variance of the N step size Nd,
Figure FDA0002261529290000045
represents the average direction
Figure FDA0002261529290000046
The variance of (a);
for the ith sample, obtaining the motion track l thereofiCorresponding geomagnetic three-dimensional vector sequence MiGeomagnetic three-dimensional vector sequence MiObtaining the geomagnetic data by linear interpolation of geomagnetic fingerprints in a database;
③ the observation value is the geomagnetic three-dimensional vector sequence M collected in the previous N stepsnowThrough MnowCalculating the posterior probability P of the ith sampleiThe posterior probability of the ith sample is calculated as follows: calculating a geomagnetic three-dimensional vector sequence M corresponding to the ith sampleiThe geomagnetic sequence M collected in the previous N stepsnowThe distance between DTW is recorded as DiThen the weight of the ith sample is
Figure FDA0002261529290000047
The posterior probability is the weight normalized value
Figure FDA0002261529290000051
WhereinσD 2A variance representing the DTW distance;
④ selecting K samples with maximum posterior probability, removing abnormal samples according to 3 sigma criterion, and remaining K0Sample { p }j＝(xj,yj),j＝1,2,...,K0}, and finally K0The position coordinates of each sample are subjected to mean value processing, and the coordinates of an initial point are calculated
Figure FDA0002261529290000052
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