CN108882162B - Indoor positioning method for unknown signal transmitting power - Google Patents

Indoor positioning method for unknown signal transmitting power Download PDF

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CN108882162B
CN108882162B CN201810693757.1A CN201810693757A CN108882162B CN 108882162 B CN108882162 B CN 108882162B CN 201810693757 A CN201810693757 A CN 201810693757A CN 108882162 B CN108882162 B CN 108882162B
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熊文汇
杨超
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University of Electronic Science and Technology of China
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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
    • H04W4/30—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
    • H04W64/006—Locating users or terminals or network equipment for network management purposes, e.g. mobility management with additional information processing, e.g. for direction or speed determination

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Abstract

The invention discloses an indoor positioning method for unknown signal transmitting power, which comprises the following steps: s1, finding the area position of the node to be positioned by using a grid search method; s2, finding out the specific position of the node to be positioned by using a maximum expectation algorithm; the method comprises the following substeps: s21, calculating a conditional probability expectation; s22, maximization L (theta )j) To obtain a new thetaj+1：
Figure DDA0001713148380000011
S23, determining theta obtained in step S22j+1Whether or not to converge, if thetaj+1The algorithm is ended if the convergence is reached; otherwise let θj＝θj+1Returning to step S21. The invention takes the transmitting power as a hidden variable, and the node to be positioned is determined to be the global optimal node under the condition of the change of the transmitting power according to the convergence of the maximum expected algorithm, so that the precision of the node to be positioned can be effectively improved, and the positioning accuracy under the change of the transmitting power is ensured.

Description

Indoor positioning method for unknown signal transmitting power
Technical Field
The invention belongs to the technical field of indoor positioning, in particular to an indoor positioning method of unknown signal transmitting power based on signal receiving intensity in the modern indoor positioning processing technology based on signal receiving intensity.
Background
The indoor positioning technology is a method for acquiring coordinate information based on a coordinate system at a certain moment in a specific environment of a person or an object. The traditional positioning algorithm based on the signal receiving strength is realized on the premise that the signal transmitting power is known, so that the positioning error is increased under the condition that the signal transmitting power is changed; meanwhile, the situation of signal transmitting power change can be solved by an expecting Maximum EM (Expectation Maximum EM) indoor positioning algorithm based on the unknown signal transmitting power of the received signal strength, and the positioning error is reduced. The indoor wireless signal propagation model is as follows (1):
in the formula PtRepresenting the signal transmitted power (dBm), PrRepresenting the signal launch power (dBm), d0The euclidean distance between a wireless signal sending end and a reference receiving end is usually 1m, and the euclidean distance is usually 1m in a 2.4GHz frequency band
Figure BDA0001713148360000012
drExpressing the Euclidean distance from a wireless signal sending end to a receiving end, β expressing the loss factor of a signal transmission path, the value is usually determined according to the indoor environment, generally between 1 and 6, N expressing a shading factor, and N to N (0, sigma) being a normal random variable with the mean value of 02) (ii) a The standard deviation sigma is generally related to indoor environment factors and generally ranges from 2 to 10.
Conventional positioning algorithm will PtConsidering a known determination value, the signal transmitting end (x, y) and the signal receiving end (x) can be obtained according to the following equation (2)1,y1) If there are multiple receivers (x)i,yi) Receiving a wireless signal sent by a signal source, a plurality of d can be obtainediThe value, Euclidean distance, is expressed as shown in formula (3).
Figure BDA0001713148360000013
Figure BDA0001713148360000014
Reducing formula (2) to formula (4) and formula (5):
VX＝Q (4)
Figure BDA0001713148360000021
because the wireless signal sending node is a constant known in advance, the matrix is a constant matrix V and Q, X is an unknown vector to be solved, and the coordinate of the wireless signal receiving node is obtained by solving the X, wherein the most common algorithm of the problem is a Least square method (LS); the specific process is described as follows:
the residual value r is defined according to the above formula (4):
r＝Q-VX (6)
the square of the residual is:
Figure BDA0001713148360000022
so far, RSSI-based positioning will translate into the problem of minimizing the f (x) function, which is usually done by deriving f (x) and making it zero, as shown in equation (8) below:
the solution for X can be found as: x ═ VTV)-1VTQ。
In practical application, however, the signal transmission power is not a fixed value, and the service life of the device and the periodic variation of the alternating current affect the signal transmission power, thereby further affecting the positioning performance and causing errors in the positioning result.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide an indoor positioning method of unknown signal transmitting power, which takes the transmitting power as a hidden variable and enables a node to be positioned obtained by calculation under the condition of transmitting power change to be a global optimal node according to the convergence of a maximum expectation algorithm, so that the accuracy of the node to be positioned can be effectively improved, and the positioning accuracy under the condition of transmitting power change can be ensured.
The purpose of the invention is realized by the following technical scheme: an indoor positioning method for unknown signal transmitting power comprises the following steps:
s1, finding the area position of the node to be positioned by using a grid search method; the specific method comprises the following steps: carrying out grid division on an area to be positioned, and dividing the positioning area with the size of L multiplied by M into positioning areas with the length of L
Figure BDA0001713148360000024
A number of disjoint matrix grids;
randomly giving a signal transmission power PtFinding out the best and proper rectangular grid area by the grid searching method, and taking a certain position theta of the area0＝[x0,y0]As an estimated location of the wireless receiving signal node;
s2, finding out the specific position of the node to be positioned by using a maximum expectation algorithm; the method comprises the following substeps:
s21, calculating the expectation of the conditional probability:
Q(Pt)＝f(Pt|Pr,θj) (9)
Figure BDA0001713148360000031
Ptrepresenting the signal transmission power, PrRepresenting the received power of the signal, PiRepresents the received power of the signal at node i, Q (P)t) Representing signal transmission power PtA posterior probability of (theta)jDenotes the coordinate position, θ, of the jth iteration0Denotes the initial position obtained by the grid search method, f (P)i,Pt| θ) represents a joint distribution function, and N represents the total number of nodes;
s22 maximization conditional probability expectation function L (theta )j) To obtain the coordinate position theta of the j +1 th iterationj+1：
Figure BDA0001713148360000032
S23, determining theta obtained in step S22j+1Whether or not to converge, if thetaj+1The algorithm is ended after convergence to obtain the signal node position thetaj+1(ii) a Otherwise let θj+1＝θjReturning to step S21.
Further, the specific implementation method of step S1 is as follows:
assuming that the total number of nodes is N, the received signal vector data observed by the N nodes is represented as P ═ P1,P2,...,PN]，PiRepresenting a received signal vector of the ith node, wherein i is more than or equal to 1 and less than or equal to N;
the likelihood function is obtained from the masking factor obeying a gaussian distribution:
Figure BDA0001713148360000033
where σ denotes a standard deviation, β denotes a loss factor of a signal transmission path, and PtRepresenting the signal transmission power, diRepresenting the Euclidean distance from the position of the wireless signal transmitting node to the position of the wireless signal receiving node moving at the ith time;
Figure BDA0001713148360000034
the vector parameters to be estimated are recorded as [ x, y, P ]t]Converting the likelihood function into a following non-convex function, and solving by a nonlinear least square algorithm;
Figure BDA0001713148360000041
scaling equation (14) by 5 β times yields equation (15):
Figure BDA0001713148360000042
in the formula (15), the reaction mixture is,
the objective function in the formula (15) is a non-convex function, the non-convex function is converted into a convex function, the convex function is solved, and an optimal solution is found; the specific implementation mode is as follows: converting the wireless receiving signal path loss formula into formula (16):
the taylor formula is applied to show the theorem: when x is smaller, ex≈1+lnex(ii) a The above equation is thus converted into the form of equation (17):
Figure BDA0001713148360000045
in formula (17) ∈iIs a zero mean Gaussian distribution N (0, (ln10 α σ/5 β)2) Converting it to formula (18):
equation (18) is still a non-convex non-linear function, introducing an auxiliary variable z ═ x2+y2When z is not less than x2+y2When, equation (18) is a convex function;
then, the positioning area is divided into L multiplied by M by length LA number of disjoint matrix grids; randomly giving a range of PtFinding out the rectangular grid region which minimizes the expression (18) by the grid search method, and taking the lower left corner theta of the region0＝[x0,y0]As the location of the wireless receiving signal node.
The invention has the beneficial effects that: according to the invention, the transmitting power is taken as a hidden variable, and the node to be positioned is determined to be the global optimal node under the condition of the change of the transmitting power according to the convergence of the maximum expected algorithm, so that the precision of the node to be positioned can be effectively improved, and the positioning accuracy under the change of the transmitting power is ensured.
Drawings
FIG. 1 is a schematic diagram of an unknown transmit power indoor location of the present invention;
FIG. 2 is a flow chart of an indoor positioning method for unknown signal transmit power according to the present invention;
FIG. 3 is a schematic diagram of objective function values at different positions without Taylor expansion according to the present invention;
FIG. 4 is a schematic diagram of objective function values at different positions during Taylor expansion;
fig. 5 is a comparison graph of cumulative distribution of positioning errors.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
FIG. 1 is a schematic diagram of the indoor location of unknown transmission power of the present invention, in which the processing method of the unknown signal transmission power of the present invention is to treat the signal transmission power as an implicit variable, and the signal transmission power is regarded as a mean value PtVariance is
Figure BDA0001713148360000056
Gaussian variable of (c).
As shown in fig. 2, an indoor positioning method for unknown signal transmission power includes the following steps:
s1, finding the area position of the node to be positioned by using a grid search method; the specific method comprises the following steps: carrying out grid division on an area to be positioned, and dividing the positioning area with the size of L multiplied by M into positioning areas with the length of L
Figure BDA0001713148360000051
A number of disjoint matrix grids;
randomly giving a signal transmission power PtFinding out the best and proper rectangular grid area by the grid searching method, and taking a certain position theta of the area0＝[x0,y0]As an estimated location of the wireless receiving signal node;
the specific implementation method comprises the following steps: assuming that the total number of nodes is N, the received signal vector data observed by the N nodes is represented as P ═ P1,P2,...,PN]，PiRepresenting a received signal vector of the ith node, wherein i is more than or equal to 1 and less than or equal to N;
the likelihood function is obtained from the masking factor obeying a gaussian distribution:
where σ denotes a standard deviation, β denotes a loss factor of a signal transmission path, and PtRepresenting the signal transmission power, diRepresenting the Euclidean distance from the position of the wireless signal transmitting node to the position of the wireless signal receiving node moving at the ith time;
the vector parameters to be estimated are recorded as [ x, y, P ]t]Converting the likelihood function into a following non-convex function, and solving by a nonlinear least square algorithm;
Figure BDA0001713148360000054
scaling equation (21) by 5 β times yields equation (22):
Figure BDA0001713148360000055
in the formula (22), the reaction mixture is,
Figure BDA0001713148360000061
the objective function in equation (22) is a non-convex function, fig. 3 shows the objective function values at different positions, and it can be seen that a plurality of positions in the figure are all local objective function minimum values; algorithms such as a traditional Newton iteration method or a gradient descent method are easy to fall into a local optimal solution, so that the estimation value effect is not good.
Then, converting the solution into a convex function by using a certain relaxation means, solving the convex function, and finding out an optimal solution; the specific implementation mode is as follows: converting the wireless receiving signal path loss formula into an expression (23):
the taylor formula is applied to show the theorem: when x is smaller, ex≈1+lnex(ii) a The above equation is thus converted into the form of equation (24):
Figure BDA0001713148360000063
in the formula (24) ∈iIs a zero mean value of highSi distribution N (0, (ln10 α sigma/5 β)2) Converting it into formula (25):
Figure BDA0001713148360000064
equation (25) is still a non-convex non-linear function, introducing an auxiliary variable z ═ x2+y2When z is not less than x2+y2When, equation (25) is a convex function; it is shown in fig. 4 that the (x, y) values are different to obtain the (25) objective function value, and it can be seen that it is easier to obtain the optimum value than equation (22), because the objective function value curve is smoother for different (x, y) values, and does not fall into the local optimum solution.
Then, the positioning area is divided into L multiplied by M by length L
Figure BDA0001713148360000065
A number of disjoint matrix grids; randomly giving a range of PtFinding out the rectangular grid region with the minimum expression (25) by the grid search method, and taking the lower left corner theta of the region0＝[x0,y0]As the location of the wireless receiving signal node.
S2, finding out the specific position of the node to be positioned by using a maximum expectation algorithm; the method comprises the following substeps:
s21, calculating the expectation of the conditional probability:
Q(Pt)＝f(Pt|Pr,θj) (26)
Ptrepresenting the signal transmission power, PrRepresenting the received power of the signal, PiRepresents the received power of the signal at node i, Q (P)t) Representing signal transmission power PtA posterior probability of (theta)jDenotes the coordinate position, θ, of the jth iteration0Denotes the initial position obtained by the grid search method, f (P)i,PtTheta) represents a joint distribution functionN represents the total number of nodes;
s22 maximization conditional probability expectation function L (theta )j) To obtain the coordinate position theta of the j +1 th iterationj+1：
Figure BDA0001713148360000071
S23, determining theta obtained in step S22j+1Whether or not to converge, if thetaj+1The algorithm is ended after convergence to obtain the signal node position thetaj+1(ii) a Otherwise let θj+1＝θjReturning to step S21.
Fig. 5 is a comparison graph of the maximum expectation algorithm and the cumulative distribution of the positioning errors according to the present invention, (ML is a conventional maximum likelihood algorithm, and is often used as a comparison). It can be seen from the figure that the error of the maximum expectation algorithm adopted by the invention is obviously smaller than that of the traditional algorithm.
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (1)

1. An indoor positioning method of unknown signal transmitting power is characterized by comprising the following steps:
s1, finding the area position of the node to be positioned by using a grid search method; the specific method comprises the following steps: carrying out grid division on an area to be positioned, and dividing the positioning area with the size of L multiplied by M into positioning areas with the length of L
Figure FDA0002301939820000011
A number of disjoint matrix grids;
randomly giving a signal transmission power PtFinding out the best and proper rectangular grid area by the grid searching method and taking the best and proper rectangular grid areaA certain position theta of the region0＝[x0,y0]As an estimated location of the wireless receiving signal node;
the specific implementation method comprises the following steps:
assuming that the total number of nodes is N, the received signal vector data observed by the N nodes is represented as P ═ P1,P2,...,PN]，PiRepresenting the signal receiving power of a node i, wherein i is more than or equal to 1 and less than or equal to N;
the likelihood function is obtained from the masking factor obeying a gaussian distribution:
Figure FDA0002301939820000012
where σ denotes a standard deviation, β denotes a loss factor of a signal transmission path, and PtRepresenting the signal transmission power, dmRepresenting the Euclidean distance from the position of the wireless signal transmitting node to the position of the wireless signal receiving node moving at the mth time;
the vector parameters to be estimated are recorded as [ x, y, P ]t]Converting the likelihood function into a following non-convex function, and solving by a nonlinear least square algorithm;
Figure FDA0002301939820000013
scaling equation (5) by 5 β times yields equation (6):
Figure FDA0002301939820000014
in the formula (6), the reaction mixture is,
Figure FDA0002301939820000015
the target function in the formula (6) is a non-convex function, the non-convex function is converted into a convex function, the convex function is solved, and an optimal solution is found; the specific implementation mode is as follows: converting the wireless receiving signal path loss formula into an expression (7):
Figure FDA0002301939820000016
the taylor formula is applied to show the theorem: when x is smaller, ex≈1+lnex(ii) a The above equation is thus converted into the form of equation (8):
in the formula (8) ∈iIs a zero mean Gaussian distribution N (0, (ln10 α σ/5 β)2) Converting it into formula (9):
Figure FDA0002301939820000021
equation (9) is still a non-convex non-linear function, introducing an auxiliary variable z ═ x2+y2When z is not less than x2+y2When, equation (9) is a convex function;
then, the positioning area is divided into L multiplied by M by length L
Figure FDA0002301939820000022
A number of disjoint matrix grids; randomly giving a range of PtFinding out the rectangular grid region with the minimum expression (9) by the grid search method, and taking the lower left corner theta of the region0＝[x0,y0]As the location of the wireless receiving signal node;
s2, finding out the specific position of the node to be positioned by using a maximum expectation algorithm; the method comprises the following substeps:
s21, calculating the expectation of the conditional probability:
Q(Pt)＝f(Pt|Pr,θj) (1)
Ptrepresenting signal transmission power，PrRepresenting the received power of the signal, PiRepresents the received power of the signal at node i, Q (P)t) Representing signal transmission power PtA posterior probability of (theta)jDenotes the coordinate position, θ, of the jth iteration0Denotes the initial position obtained by the grid search method, f (P)i,Pt| θ) represents a joint distribution function, and N represents the total number of nodes;
s22 maximization conditional probability expectation function L (theta )j) To obtain the coordinate position theta of the j +1 th iterationj+1：
Figure FDA0002301939820000024
S23, determining theta obtained in step S22j+1Whether or not to converge, if thetaj+1The algorithm is ended after convergence to obtain the signal node position thetaj+1(ii) a Otherwise let θj+1＝θjReturning to step S21.
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CN104185270A (en) * 2013-05-28 2014-12-03 中国电信股份有限公司 Indoor positioning method, system and positioning platform
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