CN107786939B

CN107786939B - Indoor positioning model based on Monte Carlo least square method, construction method and application

Info

Publication number: CN107786939B
Application number: CN201710961024.7A
Authority: CN
Inventors: 李玲娜; 石静; 段景; 康芸玮
Original assignee: Southwest Petroleum University
Current assignee: Southwest Petroleum University
Priority date: 2017-10-16
Filing date: 2017-10-16
Publication date: 2020-08-14
Anticipated expiration: 2037-10-16
Also published as: CN107786939A

Abstract

The invention belongs to the technical field of indoor positioning, and discloses an indoor positioning model based on a Monte Carlo least square method, a construction method and application thereof, wherein the indoor positioning model comprises the following steps: a plurality of base stations are arranged indoors and are used for positioning; projecting points in a cuboid where the public area is located by using a Monte Carlo method; by measuring the real radius from the test point to each base station, obtaining a projection point which is related to the real point and is closest to the real point by using a least square method; calculating the ranging mean and the ranging variance of the terminal according to the measured distance from the base station to the terminal; preprocessing the measured distance to obtain an estimated value of the real distance and obtain a correction model of the distance measurement; and correcting by using unbiased estimation, and finding the minimum value of the square difference in all the projection points as the calculated point. The Monte Carlo-based least square method indoor positioning model makes full use of the randomness of Monte Carlo, avoids complex calculation and ensures that the positioning precision in a two-dimensional room is higher.

Description

Indoor positioning model based on Monte Carlo least square method, construction method and application

Technical Field

The invention belongs to the technical field of indoor positioning, and particularly relates to an indoor positioning model based on a Monte Carlo least square method, a construction method and application.

Background

With the rapid development of wireless communication networks and mobile internet, providing Location Based Service (LBS) has become one of the most promising services. In a positioning system, in most cases, a kalman filter method is used to detect a signal, then the received signal is processed, and finally an accurate position is obtained by calculation. In actual positioning, there are generally two cases: 1. line of sight (left in fig. 1), that is, there is no barrier between the base station and the terminal; 2. Non-Line of sight (Non-Line of sight), i.e., there is a block of obstacles between the base station and the terminal. In order to solve the problem under the condition of non-line-of-sight propagation, the positioning method based on the ranging mainly comprises RSSI, TOA, TDOA and the like at present, but some problems exist. With the development of wireless communication technology in China, the research of a positioning system is more and more perfect. The traditional positioning mainly adopts a satellite navigation system, the outdoor accurate positioning effect is better, but the positioning effect is poorer under the conditions of indoor or high-rise standing and more shelters. The RSSI positioning method is that under a certain preset channel attenuation model, the distance between a transmitting node and a receiving node is estimated through the received signal strength obtained by the receiving node at an unknown position, the error of the self attenuated signal is further increased under the non-line-of-sight propagation environment and is difficult to control, and meanwhile, the RSSI is abnormal due to various factors. The TOA is a positioning technology for calculating a physical distance by using propagation delay of a wireless signal between two nodes, and is a measurement method for obtaining a distance between a transmitting point and a receiving point by measuring time for the signal to reach the receiving point from the transmitting point and multiplying the time by a signal propagation speed (generally, an optical speed c). TDOA location is a method of location using time differences. The distance of the signal source is determined by measuring the time of arrival of the signal at the monitoring station. However, the absolute time is generally difficult to measure, and by comparing the time difference of the arrival of the signals at each monitoring station, a hyperbola with the monitoring station as the focus and the distance difference as the major axis can be formed, and the intersection point of the hyperbola is the position of the signals. With the development of wireless communication technology in China, the research of a positioning system is more and more perfect. The traditional positioning mainly adopts a satellite navigation system, the outdoor accurate positioning effect is better, but the positioning effect is poorer under the conditions of indoor or high-rise standing and more shelters. Therefore, positioning methods based on TOA, TDOA, RSSI and other technologies are derived, but in the actual operation process, the calculation time is long. TOA localization disadvantage: positioning based on Time of arrival (TOA) requires Time synchronization of all devices in the system, so higher requirements are put on hardware and power consumption of sensor nodes, the accuracy requirement of indoor three-dimensional positioning of a mobile terminal is considered, the difficulty of Time synchronization accuracy is very high, and especially the synchronization of the mobile terminal is difficult to realize. Meanwhile, under the environment of non line-of-sight path propagation (NLOS), the TOA estimated value is larger than the actual value, so that the positioning accuracy is low and the effect is poor. TDOA location shortcomings: the high hardware requirements, cost and energy consumption of Time Difference of arrival (TDOA) based positioning make this technique challenging for low energy consuming sensor networks. Meanwhile, NLOS also causes the measurement of TDOA to generate errors. RSSI positioning disadvantage: positioning based on Signal Strength (RSSI) is susceptible to indoor environment, and signals are easily reflected if encountering obstacles during propagation. Therefore, the application of the method in indoor positioning is greatly limited, and the project adopting the positioning method needs to carry out a large amount of sampling and repeated updating.

In summary, the problems of the prior art are as follows: the existing indoor positioning method has the defects of long calculation time and long positioning time.

Disclosure of Invention

Aiming at the problems in the prior art, the invention provides an indoor positioning model based on a Monte Carlo least square method, a construction method and application.

The invention is realized in such a way that an indoor positioning model based on a Monte Carlo least square method obtains the distance from a terminal to a base station through the time from the base station to the TOA of the terminal, so that the distance can be used as a radius, a plurality of balls are taken by taking the base station as a circle center, the position of the terminal is in the common part of the balls, a plurality of points positioned in the common part are generated through the Monte Carlo method, the point with the minimum distance error from each base station is searched, namely the position of the terminal, and the TOA time is processed to ensure that the result is more real. The indoor positioning model based on the Monte Carlo least square method is as follows:

another object of the present invention is to provide a method for constructing an indoor positioning model based on monte carlo least squares, the method comprising the following steps:

step one, a plurality of base stations are arranged indoors, positioning is carried out through the base stations, and the time from each base station to a positioning terminal can be detected through a receiver and a conversion device; obtaining the distance from each base station to a positioning terminal; selecting a certain coordinate system, projecting the spatial position of each base station, and positioning an unknown terminal by using the position information of the three base stations;

secondly, projecting points in a cuboid where the public area is located by using a Monte Carlo method, wherein one point is always closest to the actual position under the condition that the projected points are enough according to the thought of the Monte Carlo; only the points in the region are left for subsequent judgment through screening;

thirdly, measuring the real radius between the test point and each base station by customs, solving the distance between the test point and each base station by using the time from each base station to the positioning terminal, and solving a projection point which is closest to the relevant real point by using a least square method;

step four, calculating the distance measurement mean value and the distance measurement variance of the terminal according to the measurement distance from the base station to the terminal; preprocessing the measured distance to obtain an estimated value of the real distance and obtain a correction model of the distance measurement;

and fifthly, correcting all the points left in the public area after screening by using unbiased estimation, correspondingly making difference and square between the selected points and the distances from the Monte Carlo projection points to each base station, then summing to obtain the corresponding sum of squared distance errors, searching the minimum value of the squared differences in all the projection points as a solved point, and estimating the point for the actually solved reference position.

Further, in the step one: there are j base stations (B)₁,B₂...B_j) Detecting the time TOA (TOA) from each base station to the positioning terminal through the receiver and the conversion device₁,TOA₂...TOA_j) Using the formula:

R＝TOA×C(C＝3×10⁸m/s)；

obtaining the distance from each base station to the positioning terminal as R₁,R₂...R_j。

Selecting a certain coordinate system, projecting the spatial position of each base station, taking the position of each base station in the coordinate space as the center of a sphere, taking the distance corresponding to the terminal as the radius, and making j base station spheres, wherein the TOA value is real, no error influence exists, and the terminal is required to be positioned at the intersection point of all the base station spheres; the base station coordinates are (X)_j,Y_j,Z_j) The unknown terminal coordinate is (x, y, z) and is represented by the formula

Therefore, an unknown terminal can be positioned by using the position information of the three base stations.

Further, in the third step: assuming that there are n energy points in the feasible region, the true radius r from the ith possible end store to each base station is measured_ij(i 1,2.. n, j 1,2.. m), and the distance R from the ith possible terminal store to each base station, which is solved by TOA_ij(i 1,2.. n, j 1,2.. m), and solving a corresponding correction function;

in the formula (x)_i,y_i,z_i) Coordinates representing the ith possible point M; (X)_j,Y_j,Z_j) Representing the coordinates of the base station S.

The real distances from the ith possible terminal point to the m base stations and the measured distances satisfy the following linear relation:

in the formula: r is_ijIndicating the correction distance from the ith possible terminal point to the jth base station;

R_ijindicating the measured distance from the ith terminal to the jth base station.

Next, the expectation and variance are respectively determined for them:

in the formula: e (r)_ij)、E(R_ij) Represents the mathematical expectation of R, R;

D(r_ij)、D(R_ij) The variance of R and R is shown.

Further, a modified model of the distance measurement:

the minimum of the squared differences among all projection points is the sought point:

the Monte Carlo-based least square method indoor positioning model makes full use of the randomness of Monte Carlo and avoids complex calculation, so that the positioning precision in a three-dimensional room is higher, and the error is within 1 m.

Drawings

Fig. 1 is a flowchart of a construction method of an indoor positioning model based on a monte carlo least square method according to an embodiment of the present invention.

Fig. 2 is a schematic diagram of a base station ball provided by an embodiment of the present invention.

Fig. 3 is a pictorial view of two base station balls provided by the practice of the present invention.

Fig. 4 is a pictorial view of a plurality of base station balls provided in the practice of the invention.

Fig. 5 is a plan view of a plurality of base station balls provided by the practice of the present invention.

Fig. 6 is a diagram of the common area for all base station balls provided by the practice of the present invention.

Fig. 7 is a monte carlo projection point diagram provided by an implementation of the present invention.

FIG. 8 is a screen-retained dot map provided by the practice of the present invention.

FIG. 9 is a graph of a calibration relationship provided by the practice of the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

The following detailed description of the principles of the invention is provided in connection with the accompanying drawings.

The indoor positioning model based on the Monte Carlo least square method provided by the embodiment of the invention is as follows:

as shown in fig. 1, a method for constructing an indoor positioning model based on a monte carlo least square method according to an embodiment of the present invention includes the following steps:

s101: a plurality of base stations are arranged indoors, positioning is carried out through the base stations, and the time from each base station to a positioning terminal can be detected through a receiver and a conversion device; obtaining the distance from each base station to a positioning terminal; selecting a certain coordinate system, projecting the spatial position of each base station, and positioning an unknown terminal by using the position information of the three base stations;

s102: utilizing a Monte Carlo method to project points in a cuboid where the public area is located, and always enabling one point to be closest to the actual position under the condition that the projected points are enough according to the thought of the Monte Carlo; only the points in the region are left for subsequent judgment through screening;

s103: the method comprises the steps that the real radius between a test point and each base station is measured in a clearance mode, the distance between the test point and each base station is obtained by means of time from each base station to a positioning terminal, and then a projection point which is closest to the relevant real point is obtained by means of a least square method;

s104: calculating the ranging mean and the ranging variance of the terminal according to the measured distance from the base station to the terminal; preprocessing the measured distance to obtain an estimated value of the real distance and obtain a correction model of the distance measurement;

s105: and correcting all the points left in the public area after screening by using unbiased estimation, correspondingly making difference and square between the point and the distance from the Monte Carlo projection point to each base station, and then summing to obtain the corresponding sum of squared distance errors, searching the minimum value of the squared differences in all the projection points as the solved point, and estimating the point for the actually solved reference position.

The application of the principles of the present invention will now be described in further detail with reference to the accompanying drawings.

1 Monte Carlo method and least squares method

1.1 Monte Carlo method idea

The basic idea of monte carlo is to estimate the probability of a random event with the frequency of the occurrence of the event or obtain some digital features of the random variable as the solution to the problem by some "experimental" method when the problem to be solved is the probability of the occurrence of the random event or the expected value of the random variable. Generally, the Monte Carlo method solves various problems in mathematics by constructing random numbers that meet certain rules. For those problems that it is difficult to obtain an analytical solution due to too complicated calculation or that there is no analytical solution at all, the monte carlo method is an effective method for finding a numerical solution. The most common application of the general Monte Carlo method in mathematics is Monte Carlo integration.

1.2 least squares idea

Least squares (also known as the least squares method) is a mathematical optimization technique. It finds the best functional match of the data by minimizing the sum of the squares of the errors. Unknown data can be easily obtained by the least square method, and the sum of squares of errors between these obtained data and actual data is minimized. The least squares method can also be used for curve fitting. Other optimization problems may also be expressed in a least squares method by minimizing energy or maximizing entropy.

2 creation of model

2.1 TOA correction not made.

A plurality of base stations are arranged indoors, and positioning is carried out through the base stations. Setting a total of j base stations (B)₁,B₂...B_j) Through the receiver and the conversion device, the time TOA (TimeOfArrival) from each base station to the positioning terminal can be detected₁,TOA₂...TOA_j) Using the formula:

R＝TOA×C(C＝3×10⁸m/s)；

the distance from each base station to the positioning terminal can be obtained to be R₁,R₂...R_jNamely, the following relationship is satisfied (table 1):

table 1 base station and terminal mapping chart

Selecting a certain coordinate system, projecting the spatial position of each base station, taking the position of each base station in the coordinate space as the sphere center, taking the distance corresponding to the terminal as the radius, and making j base station spheres, wherein if the TOA value is real and no error influence exists, the terminal should be at the intersection point position of all base station spheres. Let the base station coordinate be (X)_j,Y_j,Z_j) Let the unknown terminal coordinate be (x, y, z), and use the above formula

Therefore, the unknown terminal can be positioned by utilizing the position information of the three base stations.

However, in practice, due to diffraction, reflection, etc., the true propagation time from the base station to the terminal increases, and the calculated radius increases, so that the terminal should be in the common range of all base station circles:

when there is only one base station sphere, the unknown terminal is within the range of the base station sphere, as shown in fig. 2.

When there are two base station balls, the unknown terminal is in the common range where the two base station balls intersect, as shown in fig. 3.

When there are multiple base station balls, the unknown terminal is in their common range, as shown in fig. 4, which can be seen more intuitively from the plane, and the terminal should be in the red circle range to draw its common area.

When there are multiple base station balls, the unknown terminal is in their common range, as shown in fig. 5, which can be more visually seen from the plane, as shown in fig. 6, the terminal should be in the red circle range, as shown in fig. 7, to draw its common area.

By using the Monte Carlo method to project the point in the rectangular solid where the public area is located, as shown in FIG. 7, according to the Monte Carlo idea, under the condition that the projected points are enough, one point is always closest to the actual position. By screening, only the points within the region are left for subsequent determination, as shown in fig. 8.

2.2TOA correction

For the TOA error problem, under different conditions, there are different errors, i.e. the true TOA value and the detected TOA value satisfy different relationships. With respect to such problems. The gateway measures the true radius r between the ith possible end point and each base station_ij(i 1,2.. n, j 1,2.. m), and the distance R from the ith possible terminal store to each base station, which is solved by TOA_ij(i 1,2.. n, j 1,2.. m), the relationship between the two can be found, and the corresponding correction function can be solved. Under the test condition, the two are in a linear relation, and a better correction function can be obtained by an unbiased estimation method as shown in FIG. 9. And finally, solving the projection point which is closest to the real point by using a least square method.

It can be seen from fig. 9 that there is a linear relationship between the true distance and the measured distance, and thisThe method has universality, so that the linear relation is considered to be used for preprocessing the measured data, so that the influence of the measurement error and the NLOS error on the positioning precision of the terminal can be directly reduced, and the specific influence mode and the influence degree of the error are not considered. It can be seen that the error type and size do not need to be determined in advance, and the method has good adaptability. The key point is how to determine the specific linear relationship, i.e. coefficients a, b, for example, one of the terminals, assuming that there are m base stations S_jN feasible points M of which the Monte Carnot throwing point falls in the region_iThe estimation methods of a and b will be described.

Table 2 base station and terminal mapping table

Distance:

The following linear relationship is satisfied between the real distances from the ith possible terminal point to the m base stations and the measured distances:

Next, the expectation and variance are respectively determined for them:

D(r_ij)、D(R_ij) The variance of R and R is shown.

Table 3 base station and terminal mapping chart

According to m measuring distances from m base stations to the ith terminal, calculating the distance measuring average value E (r) of the terminal_ij) And the distance measurement variance D (r)_ij) The same method for calculating the ranging mean and the ranging variance of the other terminals includes:

therefore, the values of e (r) and d (r) can be calculated according to the measured distance from the terminal to each base station. Meanwhile, each randomly generated feasible solution is an estimated value of the real position, so the values of E (r) and D (r) can be calculated according to the distance from the feasible solution to each base station. By substituting E (r), E (R), D (r), D (R) and D (R) into the equation:

after a and b are obtained, the measured distance can be preprocessed to obtain an estimated value of the real distance, and a distance measurement correction model is obtained:

for all points remaining in the common area after screening (assuming that there are n points), correction is performed one by one using unbiased estimation. From the above, the corrected distance of TOA can be obtained

Namely, it is

The distance r between the Monte Carlo projection point and each base station_ij(i 1,2.. n, j 1,2.. m), performing difference and square operations, and summing, so as to obtain the sum of squared distance errors corresponding to n points, and finding the minimum value of the squared differences in all projection points as the found point, that is:

and finally, the LS corresponds to the minimum point, namely the reference position estimation point obtained actually.

3.3 model building

Through the above analysis, the final model can be obtained as follows:

through the steps, the terminal coordinates are calculated through the TOC value obtained through simulation, and are compared with the terminal coordinates obtained through simulation, as shown in the table 4:

TABLE 4 comparison table of real terminal coordinates and calculated terminal coordinates

The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.

Claims

1. A construction method based on a Monte Carlo least square method indoor positioning model is characterized in that the Monte Carlo least square method indoor positioning model constructed by the construction method based on the Monte Carlo least square method indoor positioning model is as follows:

wherein:

a coefficient of linear fit

b coefficient of linear fit

Speed of C light

D variance

E mathematical expectation

LS_iSum of squares of differences in distances between the ith possible terminal point and all base stations

R_ijDistance between ith possible terminal point and jth base station solved by TOA

The distance between the ith possible terminal point and the jth base station obtained after the correction processing

r_ijThe real distance between the ith possible terminal point and the jth base station

(X_j,Y_j,Z_j) Location of jth base station

(x_i,y_i,z_i) The location of the ith possible end point;

the construction method comprises the following steps:

step one, a plurality of base stations are arranged indoors, positioning is carried out through the base stations, and the time from each base station to a positioning terminal can be detected through a receiver and a conversion device; obtaining the distance from each base station to a positioning terminal; selecting a certain coordinate system, projecting the spatial position of each base station, and positioning a positioning terminal by using the position information of the three base stations;

secondly, taking the position of each base station in the coordinate space as a sphere center, taking the distance corresponding to the terminal as a radius to make a base station circle, utilizing Monte Carlo to project points in a cuboid where the public area of all the base station circles is located, and always enabling one point to be closest to the actual position under the condition that the projected points are enough according to the thought of Monte Carlo; only the points in the region are left for subsequent judgment through screening;

step three, by measuring the real radius between the test point and each base station, the distance between the test point and each base station is solved by using the time from each base station to the positioning terminal, and then the projection point closest to the related real point is obtained by using the least square method;

step four, calculating the distance measurement mean value and the distance measurement variance of the terminal according to the measurement distance from the base station to the positioning terminal; preprocessing the measured distance to obtain an estimated value of the real distance, and further obtain a correction model of distance measurement;

and fifthly, correcting all the points left in the public area after screening by using unbiased estimation, correspondingly differentiating and squaring the distances between the corrected points and the Monte Carlo projection points and each base station, then summing to obtain the corresponding sum of squared distance errors, searching the minimum value of the squared differences in all the projection points as the solved point, and estimating the point for the actually solved reference position.

2. The method for constructing the indoor positioning model based on the Monte Carlo least square method as claimed in claim 1, wherein in the first step: there are j base stations (B)₁,B₂...B_j) Detecting the time of arrival (TOA) of each base station to the positioning terminal by means of the receiver and the translation means₁,TOA₂...TOA_j) Using the formula:

R＝TOA×C(C＝3×10⁸m/s)；

obtaining the distance from each base station to the positioning terminal as R₁,R₂...R_j；

Selecting a certain coordinate system, projecting the spatial position of each base station, taking the position of the coordinate space of each base station as the center of sphere and the distance from the corresponding terminal asThe radius can be used as j base station balls, the TOA value is real, no error influence exists, and the terminal is required to be positioned at the intersection point of all the base station balls; the base station coordinates are (X)_j,Y_j,Z_j) The unknown terminal coordinate is (x, y, z), and the formula can be obtained

And an unknown terminal can be positioned by utilizing the position information of the three base stations.

3. The method for constructing the indoor positioning model based on the Monte Carlo least square method as claimed in claim 1, wherein in the third step: assuming that there are n possible points in the common area, by measuring the true distance r between the ith possible end point and the jth base station_ijWhere i 1,2.. n, j 1,2.. m, the distance R from the ith possible terminal point to the jth base station, which is solved using TOA_ijWherein i is 1,2.. n, j is 1,2.. m, and solving a corresponding correction function;

in the formula (x)_i,y_i,z_i) Coordinates representing the ith possible point M; (X)_j,Y_j,Z_j) Indicating the location of the jth base station;

R_ijindicating the measurement distance from the ith terminal to the jth base station;

next, the expectation and variance are respectively determined for them:

D(r_ij)、D(R_ij) The variance of R and R is shown.

4. The method of claim 1 for constructing the indoor positioning model based on the monte carlo least squares method, wherein the distance measurement modification model is: