CN107820206B - Non-line-of-sight positioning method based on signal intensity - Google Patents

Non-line-of-sight positioning method based on signal intensity Download PDF

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CN107820206B
CN107820206B CN201711126562.0A CN201711126562A CN107820206B CN 107820206 B CN107820206 B CN 107820206B CN 201711126562 A CN201711126562 A CN 201711126562A CN 107820206 B CN107820206 B CN 107820206B
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杨小凤
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Yulin Normal 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
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S11/00—Systems for determining distance or velocity not using reflection or reradiation
    • G01S11/02—Systems for determining distance or velocity not using reflection or reradiation using radio waves
    • G01S11/06—Systems for determining distance or velocity not using reflection or reradiation using radio waves using intensity measurements
    • 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
    • H04W64/003—Locating users or terminals or network equipment for network management purposes, e.g. mobility management locating network equipment

Abstract

The invention discloses a non-line-of-sight positioning method based on signal strength, which comprises the steps of firstly adopting a 3GPP 3D path loss model to calculate the distance between a target to be positioned and at least 3 base stations, then utilizing an observation equation of the distance between the target and the base stations to calculate the least square estimation of a target coordinate to be used as an iteration initial value of a next gradient method, and finally utilizing the gradient method to minimize a target function f of errors between an observed value and a measured value of the distance between the target and each base station to calculate the optimal solution of the target coordinate. The method can effectively improve the positioning accuracy of the positioning system in a complex multipath and non-line-of-sight environment, and is a high-accuracy wireless positioning method.

Description

Non-line-of-sight positioning method based on signal intensity
Technical Field
The invention relates to the technical field of wireless positioning, in particular to a non-line-of-sight positioning method based on signal intensity.
Background
In practical communication environments, the line-of-sight path between the transmitter and the receiver is blocked by obstacles, and the signal propagation path is usually a non-line-of-sight path, i.e. the signal takes a longer path to reach the receiver, thereby affecting the measurement value of the positioning algorithm. The common positioning method based on the time of arrival (TOA) and the angle of arrival (DOA) of the signal is greatly influenced by non-line-of-sight signals, and the positioning accuracy is low. The Received Signal Strength (RSS) measurement is generally very accurate regardless of whether the signal propagation path is out of line of sight. Therefore, the target can be accurately positioned by adopting the positioning method based on the RSS. The basic principle is as follows: and (3) calculating distance measurement values between the target and at least 3 base stations by using the path loss model, wherein the target is positioned at the intersection point of at least 3 circles taking the base stations as the circle centers and taking the distance measurement values as the radiuses as long as the path loss model is reasonably selected and the base stations are not on the same straight line. If the RSS estimate is accurate, the intersection of the circles is unique. However, the distance measurement inevitably has errors, so that each circle cannot be intersected at a single point, which is also a key problem of the positioning method based on the RSS.
Disclosure of Invention
The invention aims to provide a non-line-of-sight positioning method based on signal intensity, which can effectively improve positioning accuracy, aiming at the technical problem of low positioning accuracy of target coordinates in the prior art.
The technical scheme of the invention is as follows: a non-line-of-sight positioning method based on signal strength comprises the following steps:
(1) calculation using a path loss modelObtaining the distance d between the target and the corresponding base stationiWherein i is more than or equal to 1 and less than or equal to n, n is the number of base stations, and n is more than or equal to 3;
(2) obtaining a least squares estimate of the target coordinates (initial solution of the target coordinates) using a set of observation equations for the distance between the target and the base station;
(3) and (3) establishing a minimized objective function f by utilizing errors between the distance observed values and the measured values of the target and each base station, taking least square estimation in the step (2) as an iteration starting point, and solving the optimal solution of the target coordinate by using a gradient method.
As a further improvement, in step (1), the path loss model adopts a 3GPP 3D model, and the calculation formula is as follows:
Figure BDA0001468459430000021
wherein W is street width, 5m<W<50m, h is the average height of the building, 5m<h<50m,hBS10m for base station antenna height<hBS<150m，diFor the distance from the ith base station antenna to the target receiving antenna, fcIs the signal frequency;
calculating the path loss PL from PL ═ RSP-RSRP + G, substituting the above equation to calculate diWherein, RSP is signal transmitting power, RSRP is signal receiving power, and G is antenna gain.
Further, in step (2), the set of observation equations of the distances between the target and the plurality of base stations is as follows:
Figure BDA0001468459430000022
wherein the base station coordinate is (x)i,yi) The initial solution of the target coordinates is (x)0,y0)，viIs noise;
in the above equation, the 1 st equation is subtracted from each of the 2 nd equations to obtain the following equation:
Figure BDA0001468459430000023
the matrix form of the above formula is as follows:
AP0+V＝B；
wherein
Figure BDA0001468459430000031
Figure BDA0001468459430000032
P0V is the initial solution of the target coordinate, and is the noise;
to obtain P0The least squares estimate of (c) is as follows:
Figure BDA0001468459430000033
further, in the step (3), let
Figure BDA0001468459430000034
P is the optimal solution of the target coordinate, and the minimized objective function is as follows:
Figure BDA0001468459430000035
wherein, PkSpecifically calculating a kth iteration value of the target coordinate by using a gradient method, wherein the kth iteration value comprises the following steps:
(3.1) let the number of iterations k equal to 0, from P0At first, the tolerance error is 0<ε<1；
(3.2) calculation of
Figure BDA0001468459430000036
If | gk‖<E, then P is outputkFinal positioning result for target coordinate, wherein gkIs the gradient vector of the objective function, i.e. the steepest descent direction;
(3.3) if | gk‖>E, then k is k +1, by the iterative formula Pk+1＝Pk-cgkAnd (4) obtaining a (k + 1) th iteration value, and turning to the step (3.2), wherein c is a search step length.
Advantageous effects
Compared with the prior art, the invention has the advantages that:
1. calculating the distances between the target and the base stations through a path loss model, obtaining the least square estimation of the target coordinate according to an observation equation set of the distances between the target and the base stations, and finally solving the optimal solution of the target coordinate by using a gradient method, so that the positioning precision of the target coordinate can be effectively improved, and the calculation speed is high;
2. the 3GPP 3D path loss model is adopted to calculate the distance between the target and the base station, which is most suitable for 4G frequency band signals and can simulate outdoor non-line-of-sight propagation conditions;
3. solving an initial solution of the target coordinate by using a least square method, providing an iteration initial value for a next gradient method, and accelerating the convergence speed of the algorithm;
4. the optimal solution of the target coordinate is obtained by a gradient method, the calculation speed is high, and the precision is high.
Drawings
FIG. 1 is a flow chart of gradient calculation in the present invention.
Detailed Description
The invention will be further described with reference to specific embodiments shown in the drawings.
Referring to fig. 1, a non-line-of-sight positioning method based on signal intensity includes the steps of:
(1) calculating the distance d between the target and the corresponding base station by adopting a path loss modeliWherein i is more than or equal to 1 and less than or equal to n, n is the number of base stations, and n is more than or equal to 3;
(2) the target coordinate and the base station coordinate refer to the positions of the target and the base station on an X axis and a Y axis in a rectangular coordinate system, and the least square estimation (the initial solution of the target coordinate) of the target coordinate is obtained by using an observation equation set of the distance between the target and the base station;
(3) establishing a minimized objective function f by using errors between the distance observed values and the measured values of the target and each base station, taking least square estimation in the step (2) as an iteration starting point, and solving the optimal solution of the target coordinate by using a gradient method;
the distance between the target and the base stations is calculated through the path loss model, the least square estimation of the target coordinate is obtained according to the observation equation set of the distance between the target and the base stations, and finally the optimal solution of the target coordinate is obtained through a gradient method, so that the positioning precision of the target coordinate can be effectively improved, and the calculation speed is high.
In step (1), the path loss model adopts a 3GPP 3D model, and the calculation formula is as follows:
Figure BDA0001468459430000041
Figure BDA0001468459430000051
wherein W is street width, 5m<W<50m, h is the average height of the building, 5m<h<50m,hBS10m for base station antenna height<hBS<150m，diFor the distance from the ith base station antenna to the target receiving antenna, fcIs the signal frequency;
calculating the path loss PL from PL ═ RSP-RSRP + G, substituting the above equation to calculate diWherein, RSP is signal transmitting power, RSRP is signal receiving power, and G is antenna gain; the 3GPP 3D path loss model is adopted to calculate the distance between the target and the base station, which is most suitable for 4G frequency band signals and can simulate outdoor non-line-of-sight propagation conditions.
In step (2), the set of observation equations for the distances between the target and the plurality of base stations is as follows:
Figure BDA0001468459430000052
wherein the base station coordinate is (x)i,yi) The initial solution of the target coordinates is (x)0,y0)，viIs noise;
in the above equation, the 1 st equation is subtracted from each of the 2 nd equations to obtain the following equation:
Figure BDA0001468459430000053
the matrix form of the above formula is as follows:
AP0+V＝B；
wherein
Figure BDA0001468459430000054
Figure BDA0001468459430000055
P0V is the initial solution of the target coordinate, and is the noise;
to obtain P0The least squares estimate of (c) is as follows:
Figure BDA0001468459430000061
and solving the least square estimation of the target coordinate by using a least square method, providing an iteration initial value for a next gradient method, and accelerating the convergence speed of the algorithm.
In step (3), let
Figure BDA0001468459430000062
P is the optimal solution of the target coordinate, and the minimized objective function is as follows:
Figure BDA0001468459430000063
wherein, PkSpecifically calculating a kth iteration value of the target coordinate by using a gradient method, wherein the kth iteration value comprises the following steps:
(3.1) let the number of iterations k equal to 0, from P0At first, the tolerance error is 0<ε<1；
(3.2) calculation of
Figure BDA0001468459430000064
If | gk‖<E, then P is outputkFinal positioning result for target coordinate, wherein gkIs the gradient vector of the objective function, i.e. the steepest descent direction;
(3.3) if‖gk‖>E, then k is k +1, by the iterative formula Pk+1＝Pk-cgkObtaining a (k + 1) th iteration value, and turning to the step (3.2), wherein c is a search step length;
the optimal solution of the target coordinate is obtained by a gradient method, the calculation speed is high, and the precision is high.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that those skilled in the art can make various changes and modifications without departing from the structure of the invention, which will not affect the effect of the invention and the practicability of the patent.

Claims (2)

1. A non-line-of-sight positioning method based on signal strength comprises the following steps:
(1) calculating the distance d between the target and the corresponding base station by adopting a path loss modeliWherein i is more than or equal to 1 and less than or equal to n, n is the number of base stations, and n is more than or equal to 3;
(2) obtaining a least squares estimate of the target coordinates (initial solution of the target coordinates) using a set of observation equations for the distance between the target and the base station;
(3) establishing a minimized objective function f by using errors between the distance observed values and the measured values of the target and each base station, taking least square estimation in the step (2) as an iteration starting point, and solving the optimal solution of the target coordinate by using a gradient method;
in step (2), the set of observation equations for the distances between the target and the plurality of base stations is as follows:
Figure FDA0002355258170000011
wherein the base station coordinate is (x)i,yi) The initial solution of the target coordinates is (x)0,y0)，viIs noise;
in the above equation, the 1 st equation is subtracted from each of the 2 nd equations to obtain the following equation:
Figure FDA0002355258170000012
the matrix form of the above formula is as follows:
AP0+V＝B；
wherein
Figure FDA0002355258170000013
Figure FDA0002355258170000014
P0Is the initial value of the target coordinate, and V is noise;
to obtain P0The least squares estimate of (c) is as follows:
Figure FDA0002355258170000021
in step (3), let
Figure FDA0002355258170000022
P is the optimal solution of the target coordinate, and the minimized objective function is as follows:
Figure FDA0002355258170000023
wherein, PkSpecifically calculating a kth iteration value of the target coordinate by using a gradient method, wherein the kth iteration value comprises the following steps:
(3.1) let the number of iterations k equal to 0, from P0At first, the tolerance error is 0<ε<1；
(3.2) calculation of
Figure FDA0002355258170000024
If | gk‖<E, then P is outputkFinal positioning result for target coordinate, wherein gkIs the gradient vector of the objective function, i.e. the steepest descent direction;
(3.3) if | gk‖>E, then k is k +1, by the iterative formula Pk+1＝Pk-cgkAnd (4) obtaining a (k + 1) th iteration value, and turning to the step (3.2), wherein c is a search step length.
2. The signal strength-based non-line-of-sight positioning method according to claim 1, wherein in step (1), the path loss model is a 3GPP 3D model calculated as follows:
Figure FDA0002355258170000025
wherein W is street width, 5m<W<50m, h is the average height of the building, 5m<h<50m,hBS10m for base station antenna height<hBS<150m，diFor the distance from the ith base station antenna to the target receiving antenna, fcIs the signal frequency;
calculating the path loss PL from PL ═ RSP-RSRP + G, substituting the above equation to calculate diWherein, RSP is signal transmitting power, RSRP is signal receiving power, and G is antenna gain.
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CN111257827B (en) * 2020-01-16 2023-07-14 玉林师范学院 High-precision non-line-of-sight tracking and positioning method
CN112462325A (en) * 2020-11-11 2021-03-09 清华大学 Spatial positioning method and device and storage medium
CN112800983B (en) * 2021-02-01 2024-03-08 玉林师范学院 Random forest-based non-line-of-sight signal identification method
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