CN103487784A - Positioning method based on signal arrival time - Google Patents

Abstract

The invention discloses a positioning method based on signal arrival time. The method includes the steps that first, a nonlinear positioning problem is converted to a multiple integration problem; second, in the process of converting the nonlinear positioning problem to the multiple integration problem, a Gaussian distribution function is constructed according to the position of each base station, the measurement noise variance of signals of each base station and the distance between a terminal to be positioned and each base station in a cellular mobile network environment; third, several samples are randomly drawn from the Gaussian distribution function; fourth, the position of the terminal to be positioned is acquired according to the drawn samples. The method has the advantages that the constructed Gaussian distribution function can improve multiple integral computation efficiency and integral value precision, besides, the accurate position of the terminal to be positioned can be acquired by drawing only a few samples in the process of solving the multiple integration problem, and computation complexity is low.

Description

A kind of localization method based on time of arrival (toa)

Technical field

The present invention relates to a kind of localization method, especially relate to a kind of localization method based on time of arrival (toa).

Background technology

In the research of radar and sonar, terminal positioning is the research topic of classics.Over nearest 30 years, especially, after 911 events, people are more and more higher to the requirement of terminal positioning, thereby make terminal positioning receive increasing concern.The terminal positioning technology all has broad application prospects in fields such as military surveillance, traffic monitoring, industrial or agricultural control, biologic medical, environmental monitoring, rescue and relief work and hazardous location Long-distance Control, therefore studies the localization method tool and is of great significance.Fig. 1 has provided the schematic diagram of a typical orientation problem, terminal to be positioned is by measuring the down-bound pilot frequency signal of different base station, obtain TOA (the Time ofArrival of the down-bound pilot frequency signal of different base station, time of arrival) or TDOA (Time Difference ofArrival, time of arrival is poor), simultaneously in conjunction with the coordinate of each base station, just can calculate the position of terminal to be positioned according to this measurement result.With GPS location, compare, the location in cellular mobile system is fast with its locating speed, cost is low (not needing on mobile terminal to add extra hardware), little power consumption, the indoor advantage such as available, and is widely applied in terminal positioning.

Solve orientation problem although there has been the scholar to propose a variety of methods, due to the non-convexity of orientation problem, orientation problem has a plurality of stable equilibrium states, can't meet the requirement that location high precision int and algorithm are oversimplified simultaneously.In research in early days, usually adopt the linearization technique based on Taylor expansion to solve orientation problem, it is approximate that it carries out the Taylor expansion line linearityization of going forward side by side according to given initial estimation by former location problem, after solving linear solution, carry out Taylor expansion according to this linear solution again, so iteration is until reach last solution, and the method requires that an accurate initial estimation is arranged, otherwise can't converge to the solution that globally optimal solution even obtains, disperses.For the existing problem of the linearization technique based on Taylor expansion, people have proposed spherical interpolation (Spherical Interpolation, SI) method, it carrys out the linearizing non-linear system of equations by introducing an intermediate variable, the intermediate variable of setting is not wanted, but the relation of the position of it and terminal to be positioned is known, the method is based on linear least-squares (Linear Least Squares, LLS) criterion solves system of linear equations, but ignored relation known between intermediate variable above-mentioned and terminal location fully, the position out of true that causes the terminal to be positioned of acquisition.For improving the performance of SI method, people have proposed a kind of two step weighted least-squares (Two-Stage Weighted Least Squares, Two-Stage WLS) method, the method has taken explicitly into account the relation between the position of intermediate variable and terminal to be positioned, thereby can obtain than the better performance of SI method, but the method has threshold effect, when the noise when measuring acquires a certain degree, positioning precision will sharply descend.People attempt adopting the theory of some nonlinear programmings to solve orientation problem in recent years, non-convexity due to orientation problem, people attempt adopting relaxation method that non-protruding problem is relaxed as protruding problem (as positive semidefinite planning), after solving this protruding problem, adopt again some method for subsequent processing to obtain the approximate solution of former location problem, the characteristics of this method are that the precision of position of the terminal to be positioned that obtains is high, but the complexity of its algorithm is far above linearization technique.

Summary of the invention

Technical matters to be solved by this invention is to provide the localization method based on time of arrival (toa) that a kind of positioning precision is high, computation complexity is low.

The present invention solves the problems of the technologies described above adopted technical scheme: a kind of localization method based on time of arrival (toa) is characterized in that: comprise the following steps:

1. at first in the cellular mobile network environment, set up a plane right-angle coordinate or rectangular coordinate system in space as the reference coordinate system, then suppose in this cellular mobile network environment to exist a terminal to be positioned and N base station, this terminal to be positioned arrives the time of arrival of terminal to be positioned by each base station of signal acquisition that receives N base station, obtain terminal to be positioned to the distance of each base station according to each base station to the time of arrival of terminal to be positioned again, by terminal to be positioned to i base station apart from being designated as z _i, z _i=c ₁t _i, wherein, c ₁for the light velocity, t _ibe the time of arrival of i base station to terminal to be positioned, i=1,2 ..., N, N>=3;

2. according to each base station, the position in reference frame and terminal to be positioned, to the distance of each base station, are constructed a gauss of distribution function, are designated as

wherein,

r=(B ^tq ^-1b) ^-1, B ^tthe transposition that means B, $B=\left[\begin{array}{c}2{(s_2-s_1)}^T\\ \·\\ \·\\ \·\\ 2{(s_N-s_1)}^T\end{array}\right],$ Q=DQ ₁d ^t,

d ^tthe transposition that means D, $c=\left[\begin{array}{c}{\left|\right|s_2\left|\right|}^2-{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\left|\right|}^2-{z_2}^2+{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\left|\right|s_N\left|\right|}^2-{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\left|\right|}^2-{z_N}^2+{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^2\end{array}\right],$ " || || " be Euclid norm, be the measurement noise variance of the signal of the 1st base station, be the measurement noise variance of the signal of the 2nd base station, be the measurement noise variance of the signal of N base station, s ₁be the position of the 1st base station in reference frame, s ₂be the position of the 2nd base station in reference frame, s _nbe the position of N base station in reference frame, z ₁for the distance of 1 base station of terminal to the to be positioned, z ₂for the distance of 2 base stations of terminal to the to be positioned, z _nfor the distance of terminal to be positioned to N base station;

3. at gauss of distribution function

in randomly draw M sample, m sample in M the sample of randomly drawing is designated as to x _m, wherein, m=1,2 ..., M, M>=50;

4. according to M the sample of randomly drawing, obtain the position of terminal to be positioned in reference frame, be designated as

$\hat{x}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m\tilde{w}\left(x_m\right),$ Wherein, $\tilde{w}\left(x_m\right)=\frac{w\left(x_m\right)}{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}w\left(x_m\right)},w\left(x_m\right)=\frac{g\left(x_m\right)}{q\left(x_m\right)},$ $q\left(x_m\right)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^{\frac{n}{2}}{\left|R\right|}^{\frac{1}{2}}}\exp [-\frac{1}{2}{(x_m-\stackrel{\&OverBar;}{x})}^T{R}^{-1}(x_m-\stackrel{\&OverBar;}{x})],$ N means x _mdimension, " | | " means the determinant symbol, exp means the nature radix, mean

transposition,

∫ ... ∫ means n repeated integral symbol, and λ is a constant, x ₁..., x _mmean integration variable, f (x _m)=(z-d _m) ^-1q ₁ ^-1(z-d _m), z=[z ₁, z ₂..., z _n] ^t, d _m=[|| x _m-s ₁||, || x _m-s ₂|| ..., || x _m-s _n||] ^t, " || || " be Euclid norm.

Compared with prior art, the invention has the advantages that: nonlinear orientation problem is converted to the multiple integral problem, in nonlinear orientation problem, be converted in the process of multiple integral problem, at first construct a gauss of distribution function, then randomly draw a small amount of sample and solve this multiple integral problem in this gauss of distribution function, thereby get the exact position of terminal to be positioned; The structure of gauss of distribution function, can improve the efficiency of calculating multiple integral and the precision of integrated value, thereby improve the precision of the position of the terminal to be positioned got, and reduced the complexity of calculating.

The accompanying drawing explanation

Fig. 1 is typical localizing environment schematic diagram;

Fig. 2 is overview flow chart of the present invention;

Fig. 3 be terminal to be positioned of the present invention while being positioned at (1000,1000) positioning precision with the variation diagram of noise size, wherein, dBm ²=10lg (m ²), m ²(square metre) be σ ²unit, σ means the standard deviation of measurement noise of the signal of base station, σ ²the variance of the measurement noise of the signal of expression base station, MSE means the location square error of terminal to be positioned, for weighing positioning precision;

Fig. 4 be terminal to be positioned of the present invention while being positioned at (5000,6000) positioning precision with the variation diagram of noise size.

Embodiment

Below in conjunction with accompanying drawing, embodiment is described in further detail the present invention.

The present invention proposes a kind of localization method based on time of arrival (toa), Fig. 2 has provided its overall procedure schematic diagram, and it mainly comprises the following steps:

1. at first in the cellular mobile network environment, set up a plane right-angle coordinate or rectangular coordinate system in space as the reference coordinate system, suppose in this cellular mobile network environment to exist a terminal to be positioned and N base station, this terminal to be positioned arrives the time of arrival of terminal to be positioned by each base station of signal acquisition that receives N base station, obtain terminal to be positioned to the distance of each base station according to each base station to the time of arrival of terminal to be positioned again, by terminal to be positioned to i base station apart from being designated as z _i, z _i=c ₁t _i, wherein, c ₁for the light velocity, t _ibe the time of arrival of i base station to terminal to be positioned, i=1,2 ..., N, N>=3.

In this process, obtain the process that i base station signal arrive the needed time of terminal to be positioned as follows: t at a time, the ranging code of a certain structure is sent in i base station under the control of its clock, and (this ranging code is pseudo-random code, reproducible in terminal to be positioned), meanwhile terminal to be positioned copies the identical ranging code of structure (hereinafter to be referred as replica code) under the control of terminal clock to be positioned.The ranging code produced by i base station is through t _iarrive terminal to be positioned after the propagation of time and received by terminal to be positioned.In terminal to be positioned, the replica code produced by i base station carries out related calculation with the base station signal received after a time delay device delay time T, until the peak value of related operation output detected, now measure the delay time T obtained and be (TOA) t time of arrival _i.Obtain terminal to be positioned accurately and arrive the needed time of base station, just need the clock of base station and terminal to be positioned to keep high-precise synchronization.But in practice, due to the skew with respect to system clock of base station and terminal clock to be positioned, cause the time of arrival recorded that error is arranged, this is also the main source that TOA measures noise.

2. according to each base station, the position in reference frame and terminal to be positioned, to the distance of each base station, are constructed a gauss of distribution function, are designated as wherein,

r=(B ^tq ^-1b) ^-1, B ^tthe transposition that means B, $B=\left[\begin{array}{c}2{(s_2-s_1)}^T\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 2{(s_N-s_1)}^T\end{array}\right],$ Q=DQ ₁d ^t,

d ^tthe transposition that means D, $c=\left[\begin{array}{c}{\left|\right|s_2\left|\right|}^2-{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\left|\right|}^2-{z_2}^2+{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\left|\right|s_N\left|\right|}^2-{\left|\right|{\mathrm{<figure-callout\; id="1"\; label="s"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">s</figure-callout>}}_1\left|\right|}^2-{z_N}^2+{{\mathrm{<figure-callout\; id="1"\; label="z"\; filenames="HDA0000377348050000032.png"\; state="\{\{state\}\}">z</figure-callout>}}_1}^2\end{array}\right],$ " || || " be Euclid norm,

be the measurement noise variance of the signal of the 1st base station,

be the measurement noise variance of the signal of the 2nd base station,

be the measurement noise variance of the signal of N base station, s ₁be the position of the 1st base station in reference frame, s ₂be the position of the 2nd base station in reference frame, s _nbe the position of N base station in reference frame, z ₁for the distance of 1 base station of terminal to the to be positioned, z ₂for the distance of 2 base stations of terminal to the to be positioned, z _nfor the distance of terminal to be positioned to N base station.In the present invention, convert orientation problem to the multiple integral problem, and the structure of gauss of distribution function is exactly in order to solve this multiple integral problem.

3. at gauss of distribution function

in randomly draw M sample, m sample in M the sample of randomly drawing is designated as to x _m, wherein, m=1,2 ..., M, and consider the precision of location and the complexity of computing, get M>=50.

4. according to M the sample of randomly drawing, obtain the position of terminal to be positioned in reference frame, be designated as

$\hat{x}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m\tilde{w}\left(x_m\right),$ Wherein, $\tilde{w}\left(x_m\right)=\frac{w\left(x_m\right)}{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}w\left(x_m\right)},w\left(x_m\right)=\frac{g\left(x_m\right)}{q\left(x_m\right)},$ $q\left(x_m\right)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^{\frac{n}{2}}{\left|R\right|}^{\frac{1}{2}}}\exp [-\frac{1}{2}{(x_m-\stackrel{\&OverBar;}{x})}^T{R}^{-1}(x_m-\stackrel{\&OverBar;}{x})],$ N means x _mdimension, " | | " means the determinant symbol, exp means the nature radix, mean transposition,

∫ ... ∫ means n repeated integral symbol, and λ is a constant, as gets λ=1000, x ₁..., x _nmean integration variable, f (x _m)=(z-d _m) ^-1q ₁ ^-1(z-d _m), z=[z ₁, z ₂..., z _n] ^t, d _m=[|| x _m-s ₁||, || x _m-s ₂|| ..., || x _m-s _n||] ^t, " || || " be Euclid norm.

Below verify feasibility, validity and the positioning performance of localization method of the present invention by emulation.Suppose to settle 5 base stations to be measured, the method for measurement is: plane right-angle coordinate of model, the position of 5 base stations on the plane right-angle coordinate of setting up be followed successively by (0,0), (0,6000),

these 5 base stations form a measured zone.In addition, in measuring process, get M=100, and get λ=1000.CramerRao circle (CRB) is a performance lower bound that is most commonly used at present the evaluating estimated performance, therefore localization method is when weighing positioning precision, introduced CramerRao circle, any positioning performance without inclined to one side localization method all can not be lower than CramerRao circle.

Fig. 3 has provided and has been positioned at (1000 when terminal to be positioned, 1000) positioning precision time, therefrom can find out, when terminal to be positioned is positioned at the measured zone center, in the measurement noise variance change procedure from small to large of the signal of base station, the positioning performance of the localization method that the present invention proposes all approaches CramerRao circle, therefore has very high measuring accuracy.

Fig. 4 has provided and has been positioned at (5000 when terminal to be positioned, 6000) positioning precision time, therefrom can find out, when terminal to be positioned during at the measured zone edge, in the measurement noise variance scope of the signal of whole base station, the positioning performance of method disclosed by the invention only just can be slightly higher than CramerRao circle in the situation that the measurement noise variance of the signal of base station is higher, even therefore for the far field terminal, the localization method that the present invention proposes under larger noise circumstance still can have higher positioning precision.

By simulation result, can be found out, the localization method that the present invention proposes has good positioning performance, can meet well the high-precision demand in location, and the localization method that the present invention proposes only need to just can obtain the exact position of terminal to be positioned by constructing a gauss of distribution function and take out a small amount of sample in this gauss of distribution function, simple to operate and computation complexity is low.

Claims (1)

1. the localization method based on time of arrival (toa) is characterized in that: comprise the following steps:

1. at first in the cellular mobile network environment, set up a plane right-angle coordinate or rectangular coordinate system in space as the reference coordinate system, then suppose in this cellular mobile network environment to exist a terminal to be positioned and N base station, this terminal to be positioned arrives the time of arrival of terminal to be positioned by each base station of signal acquisition that receives N base station, obtain terminal to be positioned to the distance of each base station according to each base station to the time of arrival of terminal to be positioned again, by terminal to be positioned to i base station apart from being designated as z _i, z _i=c ₁t _i, wherein, c ₁for the light velocity, t _ibe the time of arrival of i base station to terminal to be positioned, i=1,2 ..., N, N>=3;

2. according to each base station, the position in reference frame and terminal to be positioned, to the distance of each base station, are constructed a gauss of distribution function, are designated as wherein, r:(B ^tq ^-1b) ^-1, B ^tthe transposition that means B, $B=\left[\begin{array}{c}2{(s_2-s_1)}^T\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ 2{(s_N-s_1)}^T\end{array}\right],$ Q=DQ ₁d ^t,

d ^tthe transposition that means D, $c=\left[\begin{array}{c}{\left|\right|s_2\left|\right|}^2-{\left|\right|s_1\left|\right|}^2-{z_2}^2+{z_1}^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\left|\right|s_N\left|\right|}^2-{\left|\right|s_1\left|\right|}^2-{{z_N}^2}^{}{+z_1}^2\end{array}\right],$ " || || " be Euclid norm,

be the measurement noise variance of the signal of the 1st base station,

be the measurement noise variance of the signal of the 2nd base station, be the measurement noise variance of the signal of N base station, s ₁be the position of the 1st base station in reference frame, s ₂be the position of the 2nd base station in reference frame, s _nbe the position of N base station in reference frame, z ₁for the distance of 1 base station of terminal to the to be positioned, z ₂for the distance of 2 base stations of terminal to the to be positioned, z _nfor the distance of terminal to be positioned to N base station;

3. at gauss of distribution function

in randomly draw M sample, m sample in M the sample of randomly drawing is designated as to x _m, wherein, m=1,2 ..., M, M>=50;

4. according to M the sample of randomly drawing, obtain the position of terminal to be positioned in reference frame, be designated as

$\hat{x}=\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}{x}_m\tilde{w}\left(x_m\right),$ Wherein, $\tilde{w}\left(x_m\right)=\frac{w\left(x_m\right)}{\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}w\left(x_m\right)},w\left(x_m\right)=\frac{g\left(x_m\right)}{q\left(x_m\right)},$ $q\left(x_m\right)=\frac{1}{{\left(2\mathrm{\&pi;}\right)}^{\frac{n}{2}}{\left|R\right|}^{\frac{1}{2}}}\exp [-\frac{1}{2}{(x_m-\stackrel{\&OverBar;}{x})}^T{R}^{-1}(x_m-\stackrel{\&OverBar;}{x})],$ N means x _mdimension, " | | ' ' mean the determinant symbol, exp means the nature radix,

mean transposition, $g\left(x_m\right)=\frac{\exp [-\mathrm{\&lambda;f}\left(x_m\right)]}{\&Integral;\&CenterDot;\&CenterDot;\&CenterDot;\&Integral;\exp [-\mathrm{\&lambda;f}\left(x_m\right)]{\mathrm{dx}}_1...{\mathrm{dx}}_n},$ ∫ ... ∫ means n repeated integral symbol, and λ is a constant, x ₁..., x _nmean integration variable, f (x _m)=(z-d _m) ^-1q ₁ ^-1(z-d _m), z=[z ₁, z ₂..., z _n] ^t, d _m=[|| x _m-s ₁||, || x _m-s ₂|| ..., || x _m-s _n||] ^t, " || || " be Euclid norm.

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