CN103630874A - Target angle measurement positioning method on basis of convex combinations - Google Patents

Target angle measurement positioning method on basis of convex combinations Download PDF

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CN103630874A
CN103630874A CN201310653551.3A CN201310653551A CN103630874A CN 103630874 A CN103630874 A CN 103630874A CN 201310653551 A CN201310653551 A CN 201310653551A CN 103630874 A CN103630874 A CN 103630874A
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schedule
angle
physical base
virtual reference
target
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齐飞
王昶
石光明
赵亚龙
任京波
林杰
李甫
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Xidian University
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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
    • G01S5/02—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
    • G01S5/04—Position of source determined by a plurality of spaced direction-finders
    • 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
    • G01S5/12—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 by co-ordinating position lines of different shape, e.g. hyperbolic, circular, elliptical or radial

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  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Position Fixing By Use Of Radio Waves (AREA)

Abstract

The invention discloses a target angle measurement positioning method on the basis of convex combinations. The target angle measurement positioning method mainly solves the problem of low positioning precision and positioning efficiency under the condition of errors of measured arrival angles in the prior art. The target angle measurement positioning method includes steps of 1, initializing arrival angle confidence parameters and angle measurement noise coefficients; 2, measuring arrival angles among target positioning points and physical reference points; 3, acquiring feasible regions of the target positioning points and selecting vertexes of the feasible regions as virtual reference points; 4, computing arrival angle matrixes according to coordinates of the virtual reference points and coordinates of the physical reference points; 5, creating the convex combinations of the virtual reference points according to the arrival angle matrixes so as to represent target functions of the target positioning points, and optimally solving the target functions to obtain the optimal combination coefficients; 6, computing coordinates of the target positioning points according to the optimal combination coefficients and the coordinates of the virtual reference points. The target angle measurement positioning method has the advantages that positioning results with high precision and efficiency as compared with the prior art can be acquired according to the measured arrival angles, and the target angle measurement positioning method can be applied to aviation and aerospace positioning.

Description

Target angle finding position fixing method based on convex combination
Technical field
The invention belongs to wireless communication technology field, relate in particular to a kind of angle finding position fixing method, for target being carried out to high precision and high-level efficiency location.
Background technology
At wireless communication technology field, nowadays location technology and relevant value-added service have become study hotspot, and wherein the location technology based on wireless measurement highlights important using value in fields such as mobile communication, mobile Internet, Aero-Space.
The main thought of location technology is the distance between measurement target anchor point and known physical reference point, according to space geometry relation, set up target equation and restriction relation, again in conjunction with the coordinate information of known physical reference point, obtain the actual coordinate of target localization point, in this process, can choose two-way time that signal propagates or direction of arrival of signal angle as measure information.But in reality, due to the noise existing in the transmitting procedure of signal in various degree, cause target localization point and the physical base information measurement value between on schedule can have corresponding error.In order to reduce the impact of noise on positioning result, conventionally can choose as far as possible many physical bases on schedule around at target localization point, to obtain more distance measurement information, and then target localization point coordinate is made more accurately and being estimated.
The patented claim that Novatek Technology Co proposes " radio communication localization method " (application number: 201210013775.3, publication number: CN103207382A), a kind of radio communication localization method is disclosed, although the distance weighting method that the method adopts is than the Taylor series method of known technology, computation complexity and precision have more excellent performance.But the deficiency that the method still exists is, to having relatively high expectations of additional information, larger on the impact of positioning result when the measurement reliability of additional constraint is not high.In addition, the method can not reach the inhibition completely to distance measuring noises, when ranging information noise is larger, causes positioning precision to decline to a great extent.
Summary of the invention
The object of the invention is to the deficiency for above-mentioned prior art, proposed a kind of target angle finding position fixing method based on convex combination, to improve degree of accuracy and the location efficiency of location.
Realizing basic ideas of the present invention is, detects physical base around target localization point on schedule, by physical base, puts letter parameter acquiring target location to be positioned feasible zone with angle on schedule, and using the summit of feasible zone as virtual reference point.Virtual reference point by structure, is expressed as target localization point the convex combination of virtual reference point.Utilize space constraint relation and optimization method in the hope of this convex combination coefficient, to utilize convex combination coefficient and virtual reference point coordinate can calculate the actual coordinate of target localization point.Because virtual reference point is to be obtained by mathematical computations by physical base on schedule, do not have the noise in measuring process, so virtual reference point and the physical base angle calculation value between is on schedule accurate, improved the precision of location.
Technical scheme of the present invention comprises the steps:
(1) initiation parameter: user is according to actual location environment, that sets the angle of arrival puts letter parameter beta and angle measurement noise figure τ;
(2) communication measurement: the arrival angle θ that measurement target anchor point and physical base communicate on schedule, and the number of statistical physics reference point, record physical base coordinate a on schedule;
(3) judge whether to meet location condition: if physical base on schedule number be more than or equal to physical base coordinate dimension on schedule, execution step (4), otherwise, finish location;
(4) angle of arrival θ between on schedule according to coordinate a on schedule of physical base and the target localization point of measuring and physical base, in conjunction with initiation parameter β and τ, calculate the feasible zone of target localization point, and using the summit of feasible zone as virtual reference point, obtain collection and the V of virtual reference point coordinate value;
(5), according to virtual reference point and physical base coordinate figure on schedule, build and arrive angle matrix Φ:
Φ＝[φ ij] p×q，φ ij＝φ(a i,v j)
Wherein p represents physical base number on schedule, and q represents the number of virtual reference point, φ ijrepresent that i physical base is on schedule to the arrival angle of j virtual reference point, a irepresent i the physical base coordinate figure of correspondence on schedule, v jrepresent that j virtual reference put corresponding coordinate figure, φ () represents the computing function of the angle of arrival between virtual reference point and physical base are on schedule;
(6) press the optimum convex combination coefficient of following formula Optimization Solution:
w * = arg min w | | Φw - θ | | 2 2 , s . t . | | w | | 1 = 1 w ≥ 0 ,
Wherein, w *represent to represent the optimum convex combination coefficient in target localization point coordinate with virtual reference point coordinate,
Figure BDA0000430085620000022
represent objective function
Figure BDA0000430085620000023
variable in optimizing process is combination coefficient w,
Figure BDA0000430085620000024
represent 2 norms square, Φ represents that virtual reference puts physical base angle of arrival matrix on schedule, w represents that the use virtual reference point coordinate in restriction range represents the convex combination coefficient of target localization point, and θ represents that target localization puts the arrival angle vector that physical base is measured on schedule, θ=[θ 1..., θ i..., θ p] t, its i element θ irepresent that target localization is o'clock to i physical base arrival angle measurement on schedule, p represents physical base number on schedule, and s.t. represents the restriction range of combination coefficient w, || || 1represent 1 norm, w>=0 represents that all elements in w is all greater than 0;
(7) according to optimum convex combination coefficient w *calculate the coordinate figure of target localization point:
x *＝Vw *，
Wherein, x *the optimal estimation coordinate figure that represents target localization point, V represents virtual reference point coordinate matrix, V=[v l..., v j..., v q], v jthe column vector that expression consists of j virtual reference point coordinate value, q represents virtual reference point number.
The present invention compared with prior art tool has the following advantages:
The first, the present invention only uses Angle Information in to the process of target localization, and localizing objects is required simply, and metrical information is few, and positioning precision is high, and speed is fast.
The second, the present invention is by building virtual reference point, optimize virtual reference point and physical base on schedule between the convex combination coefficient of angle, approach target localization point and the physical base angle measurement between on schedule, effectively raise the precision of location.
The 3rd, the present invention by site undetermined and physical base the measurement between on schedule put letter angle, obtain the feasible zone of target localization point, and select the summit of feasible zone as virtual reference point, utilize virtual reference point to carry out convex combination strategy to target localization point, avoid target localization point to carry out the local convergence of coordinate while solving, and effectively accelerated to solve speed, improved location efficiency.
Accompanying drawing explanation
Fig. 1 is target localization process flow diagram of the present invention;
Fig. 2 is the schematic diagram that the present invention intends generating target localization point feasible zone;
Fig. 3 is one group of positioning result of the present invention;
Fig. 4 is the contrast schematic diagram of the present invention and additive method positioning precision and positioning time.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described.
With reference to accompanying drawing 1, the concrete implementation step of technical scheme of the present invention is as follows:
Step 1. initiation parameter.
User can be in conjunction with actual conditions, and initialization arrives angle and puts letter parameter beta and these two parameters of angle measurement noise figure τ:
According to situations such as whether localizing environment block, the angle of arrival is put letter parameter beta and is conventionally taken as 0～10, and in embodiments of the invention, β is made as 4; Noise figure τ is definite according to real sensor parameter and extraneous localizing environment, and this example is got τ≤0.25.
Step 2. communication measurement.
Communication measurement measurement device target localization point by positioning system and the physical base arrival angle θ between on schedule, the number p of statistical physics reference point, records physical base coordinate a on schedule.This physical base is telstar, base station or other benchmark beacon that coordinate is known on schedule.
Step 3. judges whether to meet location condition.
When the target on two dimensional surface positions, physical base on schedule number p must meet can location condition p >=2; When the target in three dimensions positions, physical base on schedule number p must meet can location condition p >=3.When physical base can not position target when number p does not meet location condition on schedule, finish position fixing process.In an embodiment of the present invention, emulation the process according to Angle Information, target being positioned in two-dimensional space.
Step 4., according to the angle of arrival θ of physical base a and measurement on schedule, is obtained the feasible zone of target localization point, and is chosen virtual reference point.
4a) take each physical base is summit on schedule, and target localization point and the physical base line between on schedule of take is axis, with axis both sides, departs from θ ithe ray of ± β τ angle is limit, generates wedge shape subspace corresponding to physics reference point:
Ω i＝{x|-βτ≤φ(x,a i)-θ i≤βτ},
Wherein, Ω isatisfy condition-β τ≤φ (x, a i)-θ i≤ β τ have a some x to form a space, φ (x, a i) be an x to physical base a on schedule ithe angle of arrival, θ irepresent target localization point and i physical base a on schedule itake measurement of an angle, τ is angle measurement noise figure, β is that the angle of arrival is put letter parameter, i=1 wherein, 2 ..., p;
4b) calculate the common factor of all wedge shapes subspace, obtain the feasible zone H of target localization point:
H = ∩ i = 1 p Ω i ;
The summit of 4c) choosing feasible zone is as virtual reference point.
Because the feasible zone of target localization point in the present invention is a convex set, the convex combination on convex set summit can represent its inside institute a little, therefore the coordinate that can be target localization point by the apex coordinate linear expression of feasible zone, so the summit that this step is directly chosen target localization point feasible zone is as virtual reference point.
In accompanying drawing 2, provided and utilized two physical bases to obtain the exemplary plot of feasible zone, a in figure on schedule 1, a 2represent that respectively two physical bases ，Tu2Zhong shadow region, position H (x) is on schedule a 1, a 2the common factor of corresponding two wedge shape subspaces, is the feasible zone of target localization point x.
Step 5. builds physics reference point to the angle of arrival matrix Φ of virtual reference point.
5a) according to p physical base on schedule with the coordinate figure of q virtual reference point, respectively computational physics reference point a iwith virtual reference point v jbetween arrival angle: φ ij=φ (a i, v j), i=1,2 ..., p, j=1,2 ..., q;
5b) to the angle of arrival φ calculating ijby subscript order, arrange, obtain angle of arrival matrix: Φ=[φ ij] p * q.
Step 6. solves the optimum convex combination coefficient w that represents target localization point coordinate with virtual reference point coordinate *.
Utilize convex optimized algorithm to solve following formula and can obtain optimum convex combination coefficient w *:
w * = arg min w | | Φw - θ | | 2 2 , s . t . | | w | | 1 = 1 w ≥ 0 ,
Wherein, Φ represents that virtual reference puts physical base arrival angle matrix on schedule, and w represents to represent with virtual reference point coordinate the convex combination coefficient of target localization point coordinate, and θ represents that target localization puts the angle of arrival vector that physical base is measured on schedule, θ=[θ 1..., θ i..., θ p] t, its i element θ irepresent that target localization is o'clock to i physical base arrival angle measurement on schedule, p represents the physical base that detects number on schedule;
The optimum convex combination coefficient w that step 7. utilization obtains *, the optimum coordinates estimated value x of calculating target localization point *.
x *＝Vw *，
Wherein, V represents virtual reference point coordinate matrix, V=[v 1..., v j..., v q], v jthe column vector that expression consists of j virtual reference point coordinate, q represents the virtual reference point number obtaining.
Below in conjunction with emulation experiment, locating effect of the present invention is further described.
1. simulated conditions
Simulated running system of the present invention is Intel (R) Core (TM) i7-2600CPU650@3.40GHz, 32-bit Windows operating system, simulation software adopts MATLAB(R2012b).Simulation parameter arranges as follows:
2. emulation content and interpretation of result
Emulation 1, establish physical base on schedule with site undetermined all in [0,1] * [0,1] random generation in rectangular area, the noise figure unification in angle measurement process is set as τ=0.05, and the angle of arrival is put letter parameter beta=4, utilize localization method of the present invention to carry out angle finding position fixing, result is as Fig. 3.In Fig. 3, be designated little triangle be physical base on schedule, little square is the estimated position that utilizes the anchor point that site undetermined and physical base obtain with the Angle Information of error on schedule, small circle is the actual position in site undetermined.
As seen from Figure 3, the distance between estimated position and actual position is Δ d=0.0168, and locating consuming time is 6.1ms.
Emulation 2, if physical base on schedule with site undetermined all [0,1] * [0,1] random generation in rectangular area, physical base is number p=10 on schedule, and the angle of arrival is put the unification of letter parameter beta and is set as β=4, different noise figure τ with the inventive method and existing weighted least-squares localization method and based on the lax localization method of positive semidefinite do respectively 1000 times independently repeat experiment, position the contrast of precision and location efficiency, its result as shown in Figure 4.Positioning precision in Fig. 4 is described by following index,
RMSD = 1 K Σ k = 1 K | | x k * - x k | | 2 2
Wherein, RMSD represents positioning error index,
Figure BDA0000430085620000062
the estimated value that represents point coordinate to be positioned in the k time experiment, x kthe actual value that represents point coordinate to be positioned in the k time experiment, K=1000.
The curve that is labeled as fork in Fig. 4 is the positioning result of localization method of the present invention, the curve WLS that is labeled as rhombus is that the people such as P.Kulakowski are at article " Angle-of-arrival localization based on antenna arrays for wireless sensor networks, " (Computers and Electrical Engineering, vol.36, no.6, pp.1181 – 1186, 2010) disclosed weighted least-squares localization method in, the curve S DP that is labeled as little rectangle is that the people such as F.K.Chan are at article " A flexible semi-definite programming approach for source localization problems, " (Digital Signal Process., vol.23, no.2, pp.601 – 609, 2013) disclosed based on the lax localization method of positive semidefinite in.
As seen from Figure 4, increase along with angle measurement noise figure τ, overall positioning error is also increasing, but under same angle measurement noise figure τ, positioning error of the present invention is all less than weighted least-squares localization method and the positioning error based on the lax localization method of positive semidefinite that current positioning precision is higher, and the average positioning time of the technology of the present invention is 11.7ms, and average location based on the lax localization method of positive semidefinite consuming time be 168.2ms.
To sum up, localization method of the present invention not only positioning precision is high, and location efficiency is also higher, can meet the requirement of real-time.

Claims (4)

1. the target angle finding position fixing method based on convex combination, comprises the steps:
(1) initiation parameter: user is according to actual location environment, that sets the angle of arrival puts letter parameter beta and angle measurement noise figure τ;
(2) communication measurement: the arrival angle θ that measurement target anchor point and physical base communicate on schedule, and the number of statistical physics reference point, record physical base coordinate a on schedule;
(3) judge whether to meet location condition: if physical base on schedule number be more than or equal to physical base coordinate dimension on schedule, execution step (4), otherwise, finish location;
(4) angle of arrival θ between on schedule according to coordinate a on schedule of physical base and the target localization point of measuring and physical base, in conjunction with initiation parameter β and τ, calculate the feasible zone of target localization point, and using the summit of feasible zone as virtual reference point, obtain collection and the V of virtual reference point coordinate value;
(5), according to virtual reference point and physical base coordinate figure on schedule, build and arrive angle matrix Φ:
Φ＝[φ ij] p×q，φ ij＝φ(a i,v j)
Wherein p represents physical base number on schedule, and q represents the number of virtual reference point, φ ijrepresent that i physical base is on schedule to the arrival angle of j virtual reference point, a irepresent i the physical base coordinate figure of correspondence on schedule, v jrepresent that j virtual reference put corresponding coordinate figure, φ () represents the computing function of the angle of arrival between virtual reference point and physical base are on schedule;
(6) press the optimum convex combination coefficient of following formula Optimization Solution:
w * = arg min w | | Φw - θ | | 2 2 , s . t . | | w | | 1 = 1 w ≥ 0 ,
Wherein, w *represent to represent the optimum convex combination coefficient in target localization point coordinate with virtual reference point coordinate,
Figure FDA0000430085610000012
represent objective function
Figure FDA0000430085610000013
variable in optimizing process is combination coefficient w,
Figure FDA0000430085610000014
represent 2 norms square, Φ represents that virtual reference puts physical base angle of arrival matrix on schedule, w represents that the use virtual reference point coordinate in restriction range represents the convex combination coefficient of target localization point, and θ represents that target localization puts the arrival angle vector that physical base is measured on schedule, θ=[θ 1..., θ i..., θ p] t, its i element θ irepresent that target localization is o'clock to i physical base arrival angle measurement on schedule, p represents physical base number on schedule, and s.t. represents the restriction range of combination coefficient w, || || 1represent 1 norm, w>=0 represents that all elements in w is all greater than 0;
(7) according to optimum convex combination coefficient w *calculate the coordinate figure of target localization point:
x *＝Vw *，
Wherein, x *the optimal estimation coordinate figure that represents target localization point, V represents virtual reference point coordinate matrix, V=[v 1..., v j..., v q], v jthe column vector that expression consists of j virtual reference point coordinate value, q represents virtual reference point number.
2. the angle finding position fixing method based on convex combination according to claim 1, is characterized in that, the scope that the angle of arrival described in step (1) is put letter parameter beta is 0～10, and the scope of angle measurement noise τ is 0～0.25.
3. the angle finding position fixing method based on convex combination according to claim 1, is characterized in that, the physical base described in step (2) on schedule, the satellite that expression state is known, communication base station or other benchmark beacons.
4. the angle finding position fixing method based on convex combination according to claim 1, is characterized in that, the feasible zone of the calculating target localization point described in step (4) comprises following two steps:
4a) take respectively each physical base is summit on schedule, calculates its corresponding subspace Ω i={ x|| φ (x, a i)-θ i|≤β τ }, wherein, θ irepresent target localization point and i physical base a on schedule itake measurement of an angle, τ is angle measurement noise figure, β is that the angle of arrival is put letter parameter, subspace Ω iscope by angle, be θ itwo rays of ± β τ are definite, and p physical base symbiosis on schedule becomes p sub spaces;
4b). calculate the common factor of p sub spaces, be the feasible zone of target localization point.
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Application publication date: 20140312