CN111352065B - High-precision quick positioning method based on TOA mode in non-line-of-sight environment - Google Patents

High-precision quick positioning method based on TOA mode in non-line-of-sight environment Download PDF

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CN111352065B
CN111352065B CN201911034289.8A CN201911034289A CN111352065B CN 111352065 B CN111352065 B CN 111352065B CN 201911034289 A CN201911034289 A CN 201911034289A CN 111352065 B CN111352065 B CN 111352065B
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CN111352065A (en
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何成文
袁运斌
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Institute of Geodesy and Geophysics of CAS
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    • 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/0009—Transmission of position information to remote stations
    • G01S5/0045—Transmission from base station to mobile station
    • 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/0009—Transmission of position information to remote stations
    • G01S5/0072—Transmission between mobile stations, e.g. anti-collision systems
    • 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
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0257—Hybrid positioning
    • G01S5/0268—Hybrid positioning by deriving positions from different combinations of signals or of estimated positions in a single positioning system

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Abstract

A high-precision quick positioning method based on TOA mode under non-line-of-sight environment obtains a basic positioning equation between a mobile station and each base station according to a distance observation value; selecting a basic positioning equation between the corresponding mobile station and the base station when the distance observation value is minimum as a reference equation, and subtracting the basic positioning equation between other mobile stations and the base station from the reference equation to obtain a standard form of least square; constructing an L1 norm expression form, and converting the L1 norm expression form into an L1 norm expression form of additional equation linear constraint; giving an iteration process of solving by an alternating direction method to obtain a positioning solution of the mobile station; substituting the positioning solution into an L1 norm expression to obtain an absolute value residual error, and outputting the positioning solution of the mobile station if the median ratio of the maximum absolute value residual error to the absolute value residual error is greater than a preset value; otherwise, the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as a reference equation. The invention can reduce the influence of non-line-of-sight errors on the positioning precision.

Description

High-precision quick positioning method based on TOA mode in non-line-of-sight environment
Technical Field
The invention belongs to the technical field of wireless positioning, and particularly relates to a high-precision rapid positioning method based on a TOA mode in a non-line-of-sight environment.
Background
Due to the complexity of the environment, after a signal is sent from a sending end, in the process of reaching a receiving end, different degrees of shielding often exist, so that a non-line-of-sight (NLOS) error is introduced. Especially in the field of indoor positioning and 5G positioning, the accuracy and performance of a positioning system can be seriously reduced due to the existence of non-line-of-sight errors, and the most serious result is that the positioning result is diverged, so that the positioning result fails.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the high-precision rapid positioning method based on the TOA mode in the non-line-of-sight environment is provided, and the influence of non-line-of-sight errors on the positioning precision can be reduced.
The technical scheme adopted by the invention for solving the technical problems is as follows: a high-precision quick positioning method based on TOA mode under non-line-of-sight environment is characterized in that: it comprises the following steps:
s1, determining the coordinates of each fixed base station, and receiving the distance observed value between the mobile station and each fixed base station by the mobile station; obtaining a basic positioning equation between the mobile station and each base station according to the distance observation value;
s2, sequencing the distance observation values from small to large, selecting a basic positioning equation between the corresponding mobile station and the base station when the distance observation value is minimum as a reference equation, and subtracting the basic positioning equation between other mobile stations and the base station from the reference equation to obtain a standard form of least square;
s3, constructing an L1 norm expression form, and introducing a new variable in order to apply an alternating direction method, so that the L1 norm expression form is converted into an L1 norm expression form with an additional equation linear constraint;
s4, giving an iterative process of solving by an alternating direction method to the L1 norm expression form of the additional equation linear constraint to obtain a positioning solution of the mobile station;
s5, substituting the positioning solution of the mobile station obtained in the S4 into an L1 norm expression to obtain an absolute value residual error, and if the median ratio of the maximum absolute value residual error to the absolute value residual error is greater than a preset value, outputting the positioning solution of the mobile station;
otherwise, the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the process returns to S2.
According to the method, the S1 adopts a two-dimensional plane positioning scene, and the coordinates of each fixed base station are two-dimensional Cartesian coordinates;
the basic positioning equation between the mobile station and the ith base station is:
Figure GDA0002449580920000021
wherein x and y are respectively the abscissa and ordinate of the mobile station two-dimensional Cartesian coordinate, xi、yiThe abscissa and the ordinate of the ith base station two-dimensional Cartesian coordinate are shown; diIs the distance observed value between the mobile station and the ith base station; etaiAnd εiRespectively represent a mean of 0 and a variance of
Figure GDA0002449580920000022
White gaussian noise ofAnd NLOS error, the magnitude relationship between the two is:
Figure GDA0002449580920000023
i∈φLLOS signal transmission on behalf of the mobile station to the ith base station; i ∈ φNLThe NLOS signal represents the mobile station to the ith base station.
Setting the basic positioning equation between the jth base station and the mobile station as a reference equation according to the method; subtracting the basic positioning equation and the reference equation between other base stations and the mobile station to obtain:
Figure GDA0002449580920000024
in the formula, xj、yjThe abscissa and the ordinate of the jth base station two-dimensional Cartesian coordinate are shown; etajRepresents mean 0 and variance σi 2White gaussian noise of (1);
this is then converted to the standard form of least squares, AX-b ═ E, then
Figure GDA0002449580920000025
X＝[x,y]T,E＝[E1…EN]T (4)
Wherein,
Figure GDA0002449580920000026
wherein A is a design matrix, X is an unknown two-dimensional coordinate vector of the mobile station, b is a least square fitting distance vector, E is a positioning residual vector, and X1-xNIs the abscissa, y, of the 1 st to N th fixed base stations1-yNIs the ordinate of the 1 st to the N fixed base stations, d1-dNAs observed values of the distances between the mobile station and the 1 st to the N-th fixed base stations, EiThe distance difference between the ith base station and the mobile station is obtained according to the positioning result, and N is the total number of the fixed base stations。
According to the method, in S3, the L1 norm expression form is as follows:
min||AX-b||1 (6)
introducing a new variable z so that formula (6) has the latest expression form
Figure GDA0002449580920000031
Wherein s.t. is such that z satisfies the constraint of AX-b;
the S4 specifically includes: converting equation (7) into Lagrange form, there are
Figure GDA0002449580920000032
Wherein L (z, X, w) is a Lagrange expression, w is a Lagrange multiplier, and rho > 0 is a penalty parameter;
for the solution of the formula (8), the formula is iterated by adopting an alternating direction method
Figure GDA0002449580920000033
In the formula, zk+1、Xk+1And wk+1Positioning residual error vector, mobile station coordinate and Lagrange multiplier of the (k + 1) th iteration respectively, wkLagrange multipliers for the kth iteration;
after the formula (9) is processed, the final iteration form is obtained
Figure GDA0002449580920000034
Wherein,
Figure GDA0002449580920000035
s1/rho (y) is a sign operator and represents the operation of soft threshold value operation;
obtaining the positioning solution of the mobile station after iteration K times of convergence
Figure GDA0002449580920000036
According to the method, the S5 specifically comprises the following steps:
solving the position of the mobile station
Figure GDA0002449580920000037
Substituting into equation (6) to obtain the absolute value residual
Figure GDA0002449580920000038
If the following relational expression is satisfied
Figure GDA0002449580920000039
Outputting the location solution of the mobile station
Figure GDA00024495809200000310
Wherein max (E) is the maximum absolute value residual, and mean (E) is the median absolute value residual;
otherwise, the reference equation is incorrectly selected, and the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the step S2 is returned until the formula (12) is satisfied.
According to the scheme, the preset value is 4.
The invention has the beneficial effects that: aiming at the problem that non-line-of-sight errors greatly affect a positioning system with TOA as a positioning mode, under the premise that most of observed values are line-of-sight (LOS) signals and few of the observed values are NLOS signals, namely, the positioning environment is a mixed LOS/NLOS scene and has a certain sparse characteristic, the invention provides an alternate direction method, reduces the influence of the non-line-of-sight errors on the positioning accuracy, and has the advantages of very fast operation time, capability of meeting the requirement of the industrial boundary on the algorithm speed, greatly improved accuracy, relatively stable performance and no divergence.
Drawings
FIG. 1 is a positioning error graph according to an embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following specific examples and figures.
The invention provides a high-precision quick positioning method based on a TOA mode in a non-line-of-sight environment, which comprises the following steps:
s1, determining the coordinates of each fixed base station, and receiving the distance observed value between the mobile station and each fixed base station by the mobile station; and obtaining a basic positioning equation between the mobile station and each base station according to the distance observation value.
In the embodiment, a two-dimensional plane positioning scene is adopted, and the coordinates of each fixed base station are two-dimensional Cartesian coordinates and can be expanded to three dimensions according to the invention. If the observed value received by the mobile station is a time signal, the observed value can be converted into a distance observed value by multiplying the propagation velocity.
The basic positioning equation between the mobile station and the ith base station is:
Figure GDA0002449580920000041
wherein x and y are respectively the abscissa and ordinate of the mobile station two-dimensional Cartesian coordinate, xi、yiThe abscissa and the ordinate of the ith base station two-dimensional Cartesian coordinate are shown; diIs the distance observed value between the mobile station and the ith base station; etaiAnd εiRespectively represent a mean of 0 and a variance of
Figure GDA0002449580920000042
The white gaussian noise and the NLOS error have a magnitude relationship of:
Figure GDA0002449580920000043
i∈φLLOS signal transmission on behalf of the mobile station to the ith base station; i ∈ φNLThe NLOS signal represents the mobile station to the ith base station.
S2, the distance observation values are sequenced from small to large, a basic positioning equation between the corresponding mobile station and the base station when the distance observation value is minimum is selected as a reference equation, and the basic positioning equation between other mobile stations and the base station is subtracted from the reference equation to obtain a standard form of least squares.
Setting a basic positioning equation between the jth base station and the mobile station as a reference equation; subtracting the basic positioning equation and the reference equation between other base stations and the mobile station to obtain:
Figure GDA0002449580920000051
in the formula, xj、yjThe abscissa and the ordinate of the jth base station two-dimensional Cartesian coordinate are shown; etajRepresents a mean of 0 and a variance of
Figure GDA0002449580920000052
White gaussian noise of (1);
this is then converted to the standard form of least squares, AX-b ═ E, then
Figure GDA0002449580920000053
X＝[x,y]T,E＝[E1…EN]T (4)
Wherein,
Figure GDA0002449580920000054
wherein A is a design matrix, X is an unknown two-dimensional coordinate vector of the mobile station, b is a least square fitting distance vector, E is a positioning residual vector, and X1-xNIs the abscissa, y, of the 1 st to N th fixed base stations1-yNIs the ordinate of the 1 st to the N fixed base stations, d1-dNBetween the mobile station and the 1 st to the N fixed base stationsA distance observation value of (E)iAnd N is the total number of the fixed base stations for obtaining the distance difference between the ith base station and the mobile station according to the positioning result.
S3, constructing an L1 norm expression form, and introducing a new variable in order to apply an alternating direction method, so that the L1 norm expression form is converted into an L1 norm expression form with an additional equation linear constraint.
Since the mobile station receives signals that are both LOS and NLOS signals, the residual vector E is sparse in general, i.e. the implicit condition of the algorithm is that the number of LOS paths requires a significant excess number of NLOS paths. Therefore, a high-precision positioning result can be obtained through the norm criterion of L1:
min||E||1 (5)
the equivalent forms are:
min||AX-b||1 (6)
since the L1 norm has a non-convex nature, the solution speed is very slow. In order to solve the problem of low speed, the invention adopts an alternating direction method. Introducing a new variable z so that formula (6) has the latest expression form
Figure GDA0002449580920000055
Wherein s.t. is such that z satisfies the constraint of AX-b;
and S4, giving an iterative process of solving by an alternating direction method to the L1 norm expression form of the additional equation linear constraint to obtain a positioning solution of the mobile station.
S4 specifically includes: converting equation (7) into Lagrange form, there are
Figure GDA0002449580920000061
Wherein L (z, X, w) is a Lagrange expression, w is a Lagrange multiplier, and rho > 0 is a penalty parameter;
for the solution of the formula (8), the formula is iterated by adopting an alternating direction method
Figure GDA0002449580920000062
In the formula, zk+1、Xk+1And wk+1Positioning residual error vector, mobile station coordinate and Lagrange multiplier of the (k + 1) th iteration respectively, wkLagrange multipliers for the kth iteration;
after the formula (9) is processed, the final iteration form is obtained
Figure GDA0002449580920000063
Wherein,
Figure GDA0002449580920000064
s1/rho (y) is a sign operator and represents the operation of soft threshold value operation;
obtaining a positioning solution of the mobile station after the iteration K converges
Figure GDA0002449580920000065
S5, substituting the positioning solution of the mobile station obtained in the S4 into an L1 norm expression to obtain an absolute value residual error, and if the median ratio of the maximum absolute value residual error to the absolute value residual error is more than 4, outputting the positioning solution of the mobile station; otherwise, the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the process returns to S2.
S5 specifically includes:
solving the position of the mobile station
Figure GDA0002449580920000066
Substituting into equation (6) to obtain the absolute value residual
Figure GDA0002449580920000067
Since the hybrid LOS/NLOS scene is sparse, its residual vector is also sparse. If the following relational expression is satisfied
Figure GDA0002449580920000071
The selected reference equation is correct and the positioning solution of the mobile station is output
Figure GDA0002449580920000072
Wherein max (E) is the maximum absolute residual, and mean (E) is the median of the absolute residuals; otherwise, the reference equation is incorrectly selected, and the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the step S2 is returned until the formula (12) is satisfied.
4 in the formula (12) is an empirical value, and can be other preset values.
In this embodiment, 6 fixed base stations are selected, and the coordinates are s1(0,0),s2(10,0),s3(10,10),s4(0,10),s5(15,5) and s6(-5,5), 6 base stations form a hexagon. Of which 5 are LOS base stations and 1 is an NLOS base station. EtaiObeying a mean of 0 and a variance of
Figure GDA0002449580920000073
The error range of the NLOS is set to be evenly distributed from 8 × max (η) to 15 × max (η). The mobile station positions were randomly generated within the hexagon, with a monte carlo simulation number of 400 per noise. The experimental results are shown in FIG. 1. As can be seen from FIG. 1, when the white Gaussian noise variance is 0.01, the system positioning error is 0.0175 m; when the Gaussian noise is 0.1, the positioning error is 0.16 m; when the white gaussian noise variance is 0.6, the system positioning error is 1 m.
The experimental conditions of table 1 were substantially identical to those of fig. 1, except that white gaussian noise was set to 0.1, resulting in a mean run time of the program of 0.002s after 400 experiments in monte carlo simulation.
TABLE 1 alternate direction method average calculation schedule
Method Iterative alternation method
Average calculation time (unit: second) 0.002
The possible application field of the method is the field of wireless positioning, including but not limited to the field of indoor positioning and 5G positioning; the method is suitable for the sparse LOS/NLOS coexisting environment, and has the advantages of being high in operation speed, simple in calculation and high in iteration precision due to the combination of the L1 norm criterion and the iteration solution idea. And has important reference value and significance for industrial popularization and market application.
The above embodiments are only used for illustrating the design idea and features of the present invention, and the purpose of the present invention is to enable those skilled in the art to understand the content of the present invention and implement the present invention accordingly, and the protection scope of the present invention is not limited to the above embodiments. Therefore, all equivalent changes and modifications made in accordance with the principles and concepts disclosed herein are intended to be included within the scope of the present invention.

Claims (6)

1. A high-precision quick positioning method based on TOA mode under non-line-of-sight environment is characterized in that: it comprises the following steps:
s1, determining the coordinates of each fixed base station, and receiving the distance observed value between the mobile station and each fixed base station by the mobile station; obtaining a basic positioning equation between the mobile station and each base station according to the distance observation value;
s2, sequencing the distance observation values from small to large, selecting a basic positioning equation between the corresponding mobile station and the base station when the distance observation value is minimum as a reference equation, and subtracting the basic positioning equation between other mobile stations and the base station from the reference equation to obtain a standard form of least square;
s3, constructing an L1 norm expression form, and introducing a new variable in order to apply an alternating direction method, so that the L1 norm expression form is converted into an L1 norm expression form with an additional equation linear constraint;
s4, giving an iterative process of solving by an alternating direction method to the L1 norm expression form of the additional equation linear constraint to obtain a positioning solution of the mobile station;
s5, substituting the positioning solution of the mobile station obtained in the S4 into an L1 norm expression to obtain an absolute value residual error, and if the median ratio of the maximum absolute value residual error to the absolute value residual error is greater than a preset value, outputting the positioning solution of the mobile station;
otherwise, the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the process returns to S2.
2. The high-precision rapid positioning method according to claim 1, characterized in that: the S1 adopts a two-dimensional plane positioning scene, and the coordinates of each fixed base station are two-dimensional Cartesian coordinates;
the basic positioning equation between the mobile station and the ith base station is:
Figure FDA0003349112810000011
wherein x and y are respectively the abscissa and ordinate of the mobile station two-dimensional Cartesian coordinate, xi、yiThe abscissa and the ordinate of the ith base station two-dimensional Cartesian coordinate are shown; diIs the distance observed value between the mobile station and the ith base station; etaiAnd εiRespectively represent a mean of 0 and a variance of
Figure FDA0003349112810000012
The white gaussian noise and the NLOS error have a magnitude relationship of:
Figure FDA0003349112810000013
i∈φLLOS signal transmission on behalf of the mobile station to the ith base station; i ∈ φNLThe NLOS signal represents the mobile station to the ith base station.
3. The high-precision rapid positioning method according to claim 2, characterized in that: setting a basic positioning equation between the jth base station and the mobile station as a reference equation; subtracting the basic positioning equation and the reference equation between other base stations and the mobile station to obtain:
Figure FDA0003349112810000021
in the formula, xj、yjThe abscissa and the ordinate of the jth base station two-dimensional Cartesian coordinate are shown; etajRepresents a mean of 0 and a variance of
Figure FDA0003349112810000022
White gaussian noise of (1);
this is then converted to the standard form of least squares, AX-b ═ E, then
Figure FDA0003349112810000023
X＝[x,y]T,E＝[E1 …EN]T (4)
Wherein,
Figure FDA0003349112810000024
wherein A is a design matrix, X is an unknown two-dimensional coordinate vector of the mobile station, b is a least square fitting distance vector, E is a positioning residual vector, and X1-xNIs the abscissa, y, of the 1 st to N th fixed base stations1-yNIs 1 to NOrdinate of a fixed base station, d1-dNAs observed values of the distances between the mobile station and the 1 st to the N-th fixed base stations, EiAnd N is the total number of the fixed base stations for obtaining the distance difference between the ith base station and the mobile station according to the positioning result.
4. A high precision fast positioning method according to claim 3, characterized in that: in S3, the L1 norm expression form is:
min||AX-b||1 (6)
introducing a new variable z so that formula (6) has the latest expression form
Figure FDA0003349112810000025
Wherein s.t. is such that z satisfies the constraint of AX-b;
the S4 specifically includes: converting equation (7) into Lagrange form, there are
Figure FDA0003349112810000026
Wherein L (z, X, w) is a Lagrange expression, w is a Lagrange multiplier, and rho > 0 is a penalty parameter;
for the solution of the formula (8), the formula is iterated by adopting an alternating direction method
Figure FDA0003349112810000031
In the formula, zk+1、Xk+1And wk+1Positioning residual error vector, mobile station coordinate and Lagrange multiplier of the (k + 1) th iteration respectively, wkLagrange multipliers for the kth iteration;
after the formula (9) is processed, the final iteration form is obtained
Figure FDA0003349112810000032
Wherein,
Figure FDA0003349112810000033
S1/ρ(y) is a sign operator, characterizing the soft threshold operation;
obtaining the positioning solution of the mobile station after iteration K times of convergence
Figure FDA0003349112810000034
5. The high-precision rapid positioning method according to claim 4, characterized in that: the S5 specifically includes:
solving the position of the mobile station
Figure FDA0003349112810000035
Substituting into equation (6) to obtain the absolute value residual
Figure FDA0003349112810000036
If the following relational expression is satisfied
Figure FDA0003349112810000037
Outputting the location solution of the mobile station
Figure FDA0003349112810000038
Wherein max (E) is the maximum absolute value residual, and mean (E) is the median absolute value residual;
otherwise, the reference equation is incorrectly selected, and the basic positioning equation between the mobile station and the base station corresponding to the next distance observation value is used as the reference equation, and the step S2 is returned until the formula (12) is satisfied.
6. The high-precision rapid positioning method according to claim 1, characterized in that: the preset value is 4.
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