CN111007456A - Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination - Google Patents

Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination Download PDF

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CN111007456A
CN111007456A CN201911251857.XA CN201911251857A CN111007456A CN 111007456 A CN111007456 A CN 111007456A CN 201911251857 A CN201911251857 A CN 201911251857A CN 111007456 A CN111007456 A CN 111007456A
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determining
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time domain
positioning
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CN111007456B (en
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万鹏武
王军选
闫千里
卢光跃
周继军
王颖
王瑾
黄琼丹
陈煜飞
姚媛媛
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Xian University of Posts and Telecommunications
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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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

Abstract

A robust non-line-of-sight deviation elimination positioning method capable of achieving time-domain combination comprises the steps of extracting positioning parameters in an energy domain and a time domain, determining corrected energy domain and time domain positioning parameters, determining an initial target minimization function, determining a maximum minimization target function, determining the value of a maximum maximization target function, determining a minimization target function, determining weight and maximum likelihood estimation, determining a corrected minimization target function, determining a target function of a generalized confidence domain subproblem, and determining signal source position information. Through simulation experiments, compared with the existing amplitude square-weighted least square method, two-step weighted least square method and combined self-organizing method, the method has the advantages of accurate positioning, simplicity, less prior information requirement and the like, and can be used for signal source positioning in the technical field of communication.

Description

Robust non-line-of-sight deviation elimination positioning method capable of realizing time domain combination
Technical Field
The invention belongs to the technical field of communication, and relates to a passive positioning technology of a radiation source of a wireless signal.
Background
With the rapid development of emerging technologies such as 5G and industrial Internet of things, the demand of high-precision location information service for users becomes increasingly important. At present, the positioning service based on the global satellite navigation system basically meets the requirement of outdoor positioning, and the same high-precision position service cannot be provided for environments with small scene size and complex actual conditions, such as indoor or equipment coverage blind areas and the like. Therefore, the passive information source positioning technology based on the sensor network is an important research direction for the indoor positioning problem due to the advantages of strong concealment, small equipment, high positioning accuracy and the like. The current wireless communication environment is increasingly complex, and the positioning technology only depending on single domain information is difficult to meet the requirements of high-precision information source positioning, such as an energy domain, a time domain, a frequency domain, a space domain and the like. Therefore, the students began to research the multi-domain information fusion positioning mechanism. The method has obvious advantages in the aspects of improving the adaptability of the positioning system to the signal types, reducing the requirement on the number of receiving stations, improving the positioning accuracy and the like. For example, in the process of locating a moving object, a time-frequency domain fusion method is generally adopted. Yu H, HUANG G, GAO J et al, in An effective Constrained weighted least Squares method for Moving Source Location Using TDOA and FDOAMeasurements, Using the relationship between the intermediate variable and the Source Location parameter, iterate solution on the basis of the rough estimation to ensure the global optimum and real-time of the estimation value. Compared with a two-step weighted least square method, the method can still reach the lower boundary of Cramer Rao when the measurement noise is large.
In an indoor environment, obstacles between a source and a sensor enable electromagnetic waves to have common reflection and multipath effects in the transmission process, so that the propagation process is usually non-line-of-sight. In this case, the non-line-of-sight error will cause a serious deterioration in positioning performance. How to effectively inhibit the influence of the positioning performance is an urgent problem to be solved in indoor positioning. One common approach is to identify the link environment between the source and the sensor and discard the positioning parameters containing non-line-of-sight information, taking into account only the line-of-sight situation. The method loses a large amount of positioning information and has certain false alarm and false alarm probabilities in the identification process. In addition, it is limited by the quantitative relationship between the number of sensors and the positioning dimension, such as when the number of sensors is less than or equal to 4 in a three-dimensional scene, the information contained in any link is indispensable. Another approach is to use different bias elimination methods to suppress the influence of non-line-of-sight environment on the positioning result under the assumption that the prior information is known.
At present, a method of combining the arrival time of the received signal strength is mostly adopted for time domain joint positioning in a non-line-of-sight environment. Like COLUCCIA, FASCISTA A proposes adaptive relaxation joint estimation based On likelihood function in the On the hybrid TOA/RSS range estimation in wireless sensor networks, and improves estimation performance by selecting proper deviation and variance. The limitation of this method is that it is not suitable for passive positioning of the source, i.e. blind positioning, and requires strict clock synchronization between the source and the node to be implemented. And iterative operation involved in the solving process cannot ensure the convergence of the solution and improves the calculation complexity to a certain extent.
Disclosure of Invention
The technical problem to be solved by the invention is to overcome the defects of the prior art and provide a robust non-line-of-sight deviation elimination positioning method which has accurate positioning, simple method and less prior information requirement and can realize time-domain combination
The implementation scheme adopted for solving the technical problems comprises the following steps:
(1) extracting location parameters in energy and time domains
Establishing non-line-of-sight transmissionsThe positioning model under the environment adopts 6-9 wireless signal receivers to position a signal source. The specific method comprises the following steps: a wireless signal receiver extracts positioning parameters in an energy domain and a time domain respectively from electromagnetic signals transmitted by a signal source, including received signal strength P in the energy domainiTime difference of arrival d in time domainj：
Figure BDA0002309267710000021
dj＝||u-sj||-||u-s1||+βj+nj, (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers and is 6-9; | | | represents the euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]]T；siIs the position coordinate of the wireless signal receiver as [ x ]i,yi,zi]T；r0Is a unit distance; p0Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m isiIs a logarithmic shadow fading contained in the received signal strength subject to a mean of zero and a variance of
Figure BDA0002309267710000022
(ii) a gaussian distribution of; n isjIs the measurement noise in the time difference of arrival, obeys mean zero and variance
Figure BDA0002309267710000023
αiIs a non-line-of-sight deviation in the time domain βjIs the non-line-of-sight deviation in the energy domain, the non-line-of-sight deviation has a definite boundary value, namely 0 is less than or equal to αi≤αmax、0≤βj≤βmax。
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Figure BDA0002309267710000024
Time domain positioning parameters
Figure BDA0002309267710000025
Figure BDA0002309267710000026
Figure BDA0002309267710000027
Wherein the content of the first and second substances,
Figure BDA0002309267710000028
is a corrected energy domain measurement value, Pi+αmax/2；
Figure BDA0002309267710000029
Is a modified time domain measurement of dj-βmax/2；
Figure BDA00023092677100000210
α is the corrected energy domain non-line-of-sight deviationi-αmax/2；
Figure BDA00023092677100000211
Is the corrected time domain non line of sight deviation, βj-βmax/2。
(3) Determining an initial objective minimization function
Determining an initial objective minimization function F in robust least squares operation in the energy domain as follows1(u) initial objective minimization function F in robust least squares operation in time domain2(u)：
Figure BDA0002309267710000031
Figure BDA0002309267710000032
Wherein
Figure BDA0002309267710000033
Is a value related to the reference distance, the positioning parameter, the corrected non-line-of-sight deviation and the transmission path loss, and is
Figure BDA0002309267710000034
ζiIs a variable related to a positioning parameter and a transmission path loss, is
Figure BDA0002309267710000035
(4) Determining a maximum minimization objective function
Carrying out robust least square operation on the initial target minimization functions in the formulas (3a) and (3b) to respectively obtain the maximum minimization target function F of the energy domainAMaximum minimization objective function F in time domainBAs follows
Figure BDA0002309267710000036
Figure BDA0002309267710000037
(5) Determining a value of a maximized objective function
Determining the corrected energy domain non-line-of-sight deviation according to the limit value of the non-line-of-sight deviation in the step 1
Figure BDA0002309267710000038
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
Figure BDA0002309267710000039
The absolute value limits of (c) are as follows:
Figure BDA00023092677100000310
Figure BDA00023092677100000311
the maximum minimization of the objective function F in the energy domain represented by equation (4a)AIs about
Figure BDA00023092677100000312
And a monotonous interval equation (5a), the value of the maximized objective function in the energy domain can be determined as
Figure BDA00023092677100000313
Wherein
Figure BDA00023092677100000314
Is composed of
Figure BDA00023092677100000315
Namely, it is
Figure BDA00023092677100000316
Figure BDA00023092677100000317
Is composed of
Figure BDA00023092677100000318
Namely, it is
Figure BDA00023092677100000319
Similarly, the maximized objective function in the time domain is determined by equations (4a) and (4b) as
Figure BDA0002309267710000041
Wherein
Figure BDA0002309267710000042
Is composed of
Figure BDA0002309267710000043
Figure BDA0002309267710000044
Is composed of
Figure BDA0002309267710000045
(6) Determining a minimization objective function
Taking value of the maximized objective function in the energy domain in the step (5)
Figure BDA0002309267710000046
Maximized objective function value in the time domain
Figure BDA0002309267710000047
Further relaxation with max { a, b } ≦ a + b, where a > 0, b > 0, yields a minimized objective function for the energy domain
Figure BDA0002309267710000048
Minimizing an objective function in the time domain
Figure BDA0002309267710000049
Figure BDA00023092677100000410
Figure BDA00023092677100000411
(7) Determining weights and maximum likelihood estimates
Energy domain weighted weights are determined as follows
Figure BDA00023092677100000412
Time domain weighted weights
Figure BDA00023092677100000413
Maximum likelihood estimate P of received signal strengthi', maximum likelihood estimation of time difference of arrival
Figure BDA00023092677100000414
Figure BDA00023092677100000415
Figure BDA00023092677100000416
Figure BDA00023092677100000417
Figure BDA00023092677100000418
(8) Determining a modified minimization objective function
The modified minimization objective function g (u) is determined as follows. The solving process of the minimized objective function is a positioning process for simultaneously minimizing the energy domain, the non-line-of-sight deviation in the time domain and the measurement noise.
Figure BDA00023092677100000419
(9) Determining objective functions for generalized confidence domain sub-problems
The objective function G' (u) for obtaining the generalized confidence domain subproblem by developing the numerator of equation (8) is:
Figure BDA0002309267710000051
wherein the weighting matrix W is represented as
Figure BDA0002309267710000052
Figure BDA0002309267710000053
Figure BDA0002309267710000054
The matrices A, p in the objective function are respectively
Figure BDA0002309267710000055
Figure BDA0002309267710000056
Figure BDA0002309267710000057
Figure BDA0002309267710000058
Figure BDA0002309267710000059
The matrices D, g in the constraints are respectively
Figure BDA00023092677100000510
Figure BDA00023092677100000511
Where I denotes an identity matrix and 0 denotes an all-zero matrix.
(10) Determining signal source location information
The optimal solution of the equation (9) is obtained by the first dichotomy from the optimality condition required for the equation. Determining an optimal solution to the generalized confidence domain problem according to
Figure BDA0002309267710000061
Figure BDA0002309267710000062
Where λ is a constant value obtained by bisection, the signal source position information can be determined by
Figure BDA0002309267710000063
The positional information of the signal source is obtained from equation (10 b).
In the step (1) of extracting the positioning parameters in the energy domain and the time domain of the invention, miThe Gaussian measurement noise is the received signal strength in an energy domain, and the variance of the Gaussian measurement noise is 1-3; n isjIs Gaussian measurement noise of arrival time difference in time domain, the variance of which is 1-4, αiThe non-line-of-sight deviation of the measurement parameters in the energy domain is 2-6, βjThe non-line-of-sight deviation of the measurement parameters in the time domain is 2-6.
In the bisection method described in the step (10) of determining the source position information of the signal of the present invention, λ is determined according to equation (11 a):
Figure BDA0002309267710000064
λ is the solution of φ (λ) ═ 0, λ ∈ I, where I ranges from
Figure BDA0002309267710000065
Wherein λi(D,(WA)T(WA))＝λi(((WA)T(WA))-1/2D((WA)T(WA))-1/2) Denotes M-1/2DM-1/2The ith characteristic value in descending order, wherein M is (WA)T(WA)。
In the non-line-of-sight transmission, the information of each domain is fully utilized to improve the passive positioning performance of the information source in the non-line-of-sight environment; only the prior information of the maximum value of the non-line-of-sight deviation is needed, and the robust relaxation operation is adopted to perform high-precision positioning on the target; in the operation process, only one iteration is needed, the target is accurately positioned, and compared with other multi-domain combined positioning methods, the calculation complexity is reduced. The method has the advantages of accurate positioning, simple method, less prior information requirement and the like, and can be used for signal source positioning in the technical field of communication.
Drawings
FIG. 1 is a flowchart of example 1 of the present invention.
Fig. 2 is a simulation comparison curve of the two-step weighted least square method, the amplitude square-weighted least square method, the combined self-organization method and the positioning performance of the cramer-circle when the number of the wireless signal receivers changes in the embodiment 1.
FIG. 3 is a comparison graph of the two-step weighted least squares, magnitude squared-weighted least squares, combined self-organization, and Cramer-Lo plot simulation for localization performance in measuring noise variations for example 1.
FIG. 4 is a comparison graph of the two-step weighted least squares, magnitude squared-weighted least squares, combined self-organization, and simulated location performance of Clarithrome boundary for non-line-of-sight maximum variation in example 1.
FIG. 5 is a comparison graph of the two-step weighted least squares, magnitude squared-weighted least squares, combined self-organization, and simulated location performance of the Cramer-Rao plot for varying numbers of non-line-of-sight links in example 1.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, but the present invention is not limited to the examples described below.
Example 1
In fig. 1, the robust non-line-of-sight offset cancellation positioning method capable of time-domain combination of this embodiment is composed of the following steps:
(1) extracting location parameters in energy and time domains
And establishing a positioning model in a non-line-of-sight transmission environment, and positioning the signal source by adopting 7 wireless signal receivers. The specific method comprises the following steps: a wireless signal receiver extracts positioning parameters in an energy domain and a time domain respectively from electromagnetic signals transmitted by a signal source, including received signal strength P in the energy domainiTime difference of arrival d in time domainj：
Figure BDA0002309267710000071
dj＝||u-sj||-||u-s1||+βj+nj, (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers, and is 7; | | | represents the euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]]T；siIs the position coordinate of the wireless signal receiver as [ x ]i,yi,zi]T；r0Is a unit distance; p0Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m isiIs logarithmic shadow fading contained in the received signal strength, obeying a gaussian distribution with a mean value of zero and a variance of 2; n isjIs the measurement noise in the arrival time difference, obeys a Gaussian distribution with a mean of zero and a variance of 3 αmaxIs the maximum value of the non-line-of-sight deviation in the time domain, 4; βmaxThe maximum value of the non-line-of-sight deviation in the energy domain is 4.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Figure BDA0002309267710000072
Time domain positioning parameters
Figure BDA0002309267710000073
Figure BDA0002309267710000074
Figure BDA0002309267710000075
Wherein the content of the first and second substances,
Figure BDA0002309267710000076
is a corrected energy domain measurement value of Pi+αmax/2；
Figure BDA0002309267710000077
Is a modified time domain measurement of dj-βmax/2；
Figure BDA0002309267710000078
α is the corrected energy domain non-line-of-sight deviationi-αmax/2；
Figure BDA0002309267710000079
Is the corrected time domain non line of sight deviation, βj-βmax/2. M of the present embodimentiVariance of 2, njThe variance is 3.
(3) Determining an initial objective minimization function
Determining an initial objective minimization function F in robust least squares operation in the energy domain as follows1(u) initial objective minimization function F in robust least squares operation in time domain2(u)：
Figure BDA0002309267710000081
Figure BDA0002309267710000082
Wherein
Figure BDA0002309267710000083
Is a value related to the reference distance, the positioning parameter, the corrected non-line-of-sight deviation and the transmission path loss, and is
Figure BDA0002309267710000084
ζiIs a variable related to a positioning parameter and a transmission path loss, is
Figure BDA0002309267710000085
(4) Determining a maximum minimization objective function
Robust least squares for the initial objective minimization function in equations (3a), (3b)Operation of obtaining the maximum minimum objective function F of the energy domain respectivelyAMaximum minimization objective function F in time domainBAs follows
Figure BDA0002309267710000086
Figure BDA0002309267710000087
(5) Determining a value of a maximized objective function
Determining the corrected energy domain non-line-of-sight deviation according to the limit value of the non-line-of-sight deviation in the step 1
Figure BDA0002309267710000088
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
Figure BDA0002309267710000089
The absolute value limits of (c) are as follows:
Figure BDA00023092677100000810
Figure BDA00023092677100000811
the maximum minimization of the objective function F in the energy domain represented by equation (4a)AIs about
Figure BDA00023092677100000812
And a monotonous interval equation (5a), the value of the maximized objective function in the energy domain can be determined as
Figure BDA00023092677100000813
Wherein
Figure BDA00023092677100000814
Is composed of
Figure BDA00023092677100000815
Namely, it is
Figure BDA00023092677100000816
Figure BDA00023092677100000817
Is composed of
Figure BDA00023092677100000818
Namely, it is
Figure BDA00023092677100000819
Similarly, the maximized objective function in the time domain is determined by equations (4a) and (4b) as
Figure BDA00023092677100000820
Wherein
Figure BDA00023092677100000821
Is composed of
Figure BDA00023092677100000822
Figure BDA00023092677100000823
Is composed of
Figure BDA00023092677100000824
α of the embodimentmaxIs 4, βmaxIs 4.
(6) Determining a minimized objective function
Taking value of the maximized objective function in the energy domain in the step (5)
Figure BDA0002309267710000091
Maximized objective function value in the time domain
Figure BDA0002309267710000092
Further loosening by using max (a, b) less than or equal to a + bRelaxation, where a > 0, b > 0, yields a minimized objective function of the energy domain
Figure BDA0002309267710000093
Minimizing an objective function in the time domain
Figure BDA0002309267710000094
Figure BDA0002309267710000095
Figure BDA0002309267710000096
(7) Determining weights and maximum likelihood estimates
Energy domain weighted weights are determined as follows
Figure BDA0002309267710000097
Time domain weighted weights
Figure BDA0002309267710000098
Maximum likelihood estimate P of received signal strengthi', maximum likelihood estimation of time difference of arrival
Figure BDA0002309267710000099
Figure BDA00023092677100000910
Figure BDA00023092677100000911
Figure BDA00023092677100000912
Figure BDA00023092677100000913
(8) Determining a modified minimization objective function
The modified minimization objective function g (u) is determined as follows. The solving process of the minimized objective function is a positioning process for simultaneously minimizing the energy domain, the non-line-of-sight deviation in the time domain and the measurement noise.
Figure BDA00023092677100000914
(9) Determining objective functions for generalized confidence domain sub-problems
The objective function G' (u) for obtaining the generalized confidence domain subproblem by developing the numerator of equation (8) is:
Figure BDA00023092677100000915
wherein the weighting matrix W is represented as
Figure BDA00023092677100000916
Figure BDA00023092677100000917
Figure BDA0002309267710000101
The matrices A, p in the objective function are respectively
Figure BDA0002309267710000102
Figure BDA0002309267710000103
Figure BDA0002309267710000104
Figure BDA0002309267710000105
Figure BDA0002309267710000106
The matrices D, g in the constraints are respectively
Figure BDA0002309267710000107
Figure BDA0002309267710000108
Where I denotes an identity matrix and 0 denotes an all-zero matrix.
(10) Determining signal source location information
The optimal solution of the formula (9) is obtained by a first dichotomy from the fully necessary optimality condition, and the optimal solution of the generalized confidence domain problem is determined according to the formula
Figure BDA0002309267710000109
Figure BDA00023092677100001010
Where λ is a constant value obtained by bisection, λ is determined according to equation (11 a):
Figure BDA00023092677100001011
λ is the solution of Φ (λ) ═ 0, λ ∈ I, where I ranges from:
Figure BDA0002309267710000111
wherein λi(D,(WA)T(WA))＝λi(((WA)T(WA))-1/2D((WA)T(WA))-1/2) Denotes M-1/2DM-1/2In descending orderThe ith characteristic value, wherein M is (WA)T(WA)。
The signal source position information can be determined by
Figure BDA0002309267710000112
The positional information of the signal source is obtained from equation (10 b).
Example 2
The robust non-line-of-sight deviation elimination positioning method capable of time-domain combination in the embodiment comprises the following steps:
(1) extracting location parameters in energy and time domains
And establishing a positioning model in a non-line-of-sight transmission environment, and positioning the signal source by adopting 6 wireless signal receivers. The specific method comprises the following steps: a wireless signal receiver extracts positioning parameters in an energy domain and a time domain respectively from electromagnetic signals transmitted by a signal source, including received signal strength P in the energy domainiTime difference of arrival d in time domainj：
Figure BDA0002309267710000113
dj＝||u-sj||-||u-s1||+βj+nj, (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers, 6; | | | represents the euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]]T；siIs the position coordinate of the wireless signal receiver as [ x ]i,yi,zi]T；r0Is a unit distance; p0Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m isiIs logarithmic shadow fading contained in the received signal strength, obeying gaussian distribution with mean value of zero and variance of 1; n isjIs the measurement noise in the arrival time difference, obeys a Gaussian distribution with a mean of zero and a variance of 1 αmaxMaximum value of non-line-of-sight deviation in time domain, 2; βmaxThe maximum value of the non-line-of-sight deviation in the energy domain is 2.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Figure BDA0002309267710000114
Time domain positioning parameters
Figure BDA0002309267710000115
Figure BDA0002309267710000116
Figure BDA0002309267710000117
Wherein the content of the first and second substances,
Figure BDA0002309267710000118
is a corrected energy domain measurement value, Pi+αmax/2；
Figure BDA0002309267710000119
Is a modified time domain measurement of dj-βmax/2；
Figure BDA00023092677100001110
α is the corrected energy domain non-line-of-sight deviationi-αmax/2；
Figure BDA00023092677100001111
Is the corrected time domain non line of sight deviation, βj-βmax/2. M of the present embodimentiVariance of 1, njThe variance is 1.
(3) Determining an initial objective minimization function
This procedure is the same as in example 1.
(4) Determining a maximum minimization objective function
This procedure is the same as in example 1.
(5) Determining a value of a maximized objective function
Determining the corrected energy domain non-line-of-sight deviation according to the limit value of the non-line-of-sight deviation in the step 1
Figure BDA0002309267710000121
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
Figure BDA0002309267710000122
The absolute value limits of (c) are as follows:
Figure BDA0002309267710000123
Figure BDA0002309267710000124
the maximum minimization of the objective function F in the energy domain represented by equation (4a)AIs about
Figure BDA0002309267710000125
And a monotonous interval equation (5a), the value of the maximized objective function in the energy domain can be determined as
Figure BDA0002309267710000126
Wherein
Figure BDA0002309267710000127
Is composed of
Figure BDA0002309267710000128
Namely, it is
Figure BDA0002309267710000129
Figure BDA00023092677100001210
Is composed of
Figure BDA00023092677100001211
Namely, it is
Figure BDA00023092677100001212
Similarly, the maximized objective function in the time domain is determined by equations (4a) and (4b) as
Figure BDA00023092677100001213
Wherein
Figure BDA00023092677100001214
Is composed of
Figure BDA00023092677100001215
Figure BDA00023092677100001216
Is composed of
Figure BDA00023092677100001217
α of the embodimentmaxIs 2, βmaxIs 2.
The other steps are the same as the embodiment 1, and the position information of the signal source is finally obtained.
Example 3
The robust non-line-of-sight deviation elimination positioning method capable of time-domain combination in the embodiment comprises the following steps:
(1) extracting location parameters in energy and time domains
And establishing a positioning model in a non-line-of-sight transmission environment, and positioning the signal source by adopting 9 wireless signal receivers. The specific method comprises the following steps: a wireless signal receiver extracts positioning parameters in an energy domain and a time domain respectively from electromagnetic signals transmitted by a signal source, including received signal strength P in the energy domainiTime difference of arrival d in time domainj：
Figure BDA00023092677100001218
dj＝||u-sj||-||u-s1||+βj+nj, (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers, 9; | | | represents the euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]]T；siIs the position coordinate of the wireless signal receiver as [ x ]i,yi,zi]T；r0Is a unit distance; p0Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m isiIs logarithmic shadow fading contained in the received signal strength, obeying a gaussian distribution with a mean value of zero and a variance of 3; n isjIs the measurement noise in the arrival time difference, obeys a Gaussian distribution with a mean of zero and a variance of 4 αmaxMaximum value of non-line-of-sight deviation in time domain, 6; βmaxThe maximum value of the non-line-of-sight deviation in the energy domain is 6.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Figure BDA0002309267710000131
Time domain positioning parameters
Figure BDA0002309267710000132
Figure BDA0002309267710000133
Figure BDA0002309267710000134
Wherein the content of the first and second substances,
Figure BDA0002309267710000135
is a corrected energy domain measurement value, Pi+αmax/2；
Figure BDA0002309267710000136
Is a modified time domain measurement of dj-βmax/2；
Figure BDA0002309267710000137
α is the corrected energy domain non-line-of-sight deviationi-αmax/2；
Figure BDA0002309267710000138
Is the corrected time domain non line of sight deviation, βj-βmax/2. M of the present embodimentiVariance of 3, njThe variance is 4.
(3) Determining an initial objective minimization function
This procedure is the same as in example 1.
(4) Determining a maximum minimization objective function
This procedure is the same as in example 1.
(5) Determining a value of a maximized objective function
Determining the corrected energy domain non-line-of-sight deviation according to the limit value of the non-line-of-sight deviation in the step 1
Figure BDA0002309267710000139
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
Figure BDA00023092677100001310
The absolute value limits of (c) are as follows:
Figure BDA00023092677100001311
Figure BDA00023092677100001312
the maximum minimization of the objective function F in the energy domain represented by equation (4a)AIs about
Figure BDA00023092677100001313
And a monotonous interval equation (5a), the value of the maximized objective function in the energy domain can be determined as
Figure BDA00023092677100001314
Wherein
Figure BDA00023092677100001315
Is composed of
Figure BDA00023092677100001316
Namely, it is
Figure BDA00023092677100001317
Figure BDA00023092677100001318
Is composed of
Figure BDA00023092677100001319
Namely, it is
Figure BDA00023092677100001320
Similarly, the maximized objective function in the time domain is determined by equations (4a) and (4b) as
Figure BDA00023092677100001321
Wherein
Figure BDA0002309267710000141
Is composed of
Figure BDA0002309267710000142
Figure BDA0002309267710000143
Is composed of
Figure BDA0002309267710000144
α of the embodimentmaxIs 6, βmaxIs 6.
The other steps are the same as the embodiment 1, and the position information of the signal source is finally obtained.
Simulation experiment
In order to verify the beneficial effects of the present invention, the inventor conducted comparative simulation experiments using the robust non-line-of-sight deviation elimination positioning method (RT-GTRS) capable of time-domain combination of embodiment 1 of the present invention, and the two-step weighted least square method (TSWLS), the amplitude square-weighted least square method (SR-WLS), the combined self-organizing method (JAH), and the cramer-circle lower bound (CRLB), and the experimental conditions were as follows:
1. simulation conditions
All wireless signal receivers are randomly placed within the bxbxb area in each monte carlo simulation, and the source is placed at u ═ 15,15]T(m), the Monte Carlo simulation frequency is L, and the rest simulation parameters are fixed: p0＝20dBm、γ＝3、r01m, 30m and 10000L. In each Monte Carlo simulation, non-line-of-sight transmission error factors (including received signal strength and arrival time difference) are randomly and uniformly distributed in [0, biasmax]In (dB, m), wherein biasmaxIs a non-line-of-sight error factor maximum. The performance index of the method is root mean square error, which is defined as
Figure BDA0002309267710000145
Wherein
Figure BDA0002309267710000146
Representing an estimate of the true source position u in the ith monte carlo simulation.
2. Simulation experiment
(1) Simulation experiment 1
Number of non-line-of-sight channels NnlosIs N, maximum value bias of non-line-of-sight error factormaxIs 6, biasmaxSignal energy loss in dB, bias, in the energy domain for non-line-of-sightmaxThe difference in arrival time in the time domain for non-line-of-sight causes is in m. The standard deviation of two kinds of measurement noise is respectively
Figure BDA0002309267710000147
Is the number of 3, and the number of the carbon atoms is 3,
Figure BDA0002309267710000148
in case of 4, the performance of each method is simulated under the condition of different numbers of wireless signal receivers N, and the simulation result is shown in fig. 2, an RT-GTRS curve represents the method of the embodiment 1, an SR-WLS curve represents an amplitude square-weighted least square method, a TSWLS curve represents a two-step weighted least square method, an JAH curve represents a combined self-organization method, and a CRLB curve represents a Cramer-Rao bound. As can be seen from fig. 2, as the number N of wireless signal receivers increases, the information available for positioning increases, and the performance of all methods improves. When N is increased to 9, the information available in the network is sufficient and the positioning performance of the various methods hardly changes any more. The method of example 1 performed optimally over all ranges of values of N. The method of example 1 has more remarkable localization property as N increases compared to the JAH method, and the method of example 1 is easier to reach the limit state, closer to CRLB, compared to the JAH method.
(2) Simulation experiment 2
The number N of wireless signal receivers is 7, and the number N of non-line-of-sight channelsnlosIn the case of N, the performance of each method is subject to different measurement errors sigmaiThe following simulation experiment was performed, and the results are shown in fig. 3, RT-GTRS curve represents the method of example 1, SR-WLS curve represents amplitude square-weighted least squares method, TSWLS curve represents two-step weighted least squares method, JAH curve represents combined self-organization method, and CRLB curve represents cramer-circle. To determine the effect of noise power on positioning errors, a non-line-of-sight offset is set to a fixed value of 3. When sigma isiThe performance of all the methods worsened with increasing, and the method of example 1 performed better with smaller measurement errors compared to the SR-WLS method, and the difference between the two methods gradually decreased with increasing measurement errors, but it can still be seen that the method of example 1 performed at all σiThe performance is optimal within the value range of (A). The most obvious difference between the method of example 1 and the TSWLS and JAH methods is that less prior knowledge about non-line-of-sight is required (only the maximum value of non-line-of-sight deviation is determined), and better positioning performance can be obtained.
(3) Simulation experiment 3
Wireless signal receiverThe number N is 7, and the maximum value bias of the non-line-of-sight error is changed when the other conditions are the same as those in experiment 1maxObserving the variation of the mean square error, the simulation result is shown in fig. 4, the RT-GTRS curve represents the method of example 1, the SR-WLS curve represents the magnitude square-weighted least square method, the TSWLS curve represents the two-step weighted least square method, the JAH curve represents the combined self-organization method, and the CRLB curve represents the clarmero bound. With biasmaxThe positioning accuracy of the method of example 1 and the SR-WLS method suffers from a small amplitude of attenuation. The method of example 1 is based on the addition of bias to the same non-line-of-sight offsetmaxThe minimization is carried out, and the attenuation amplitude of the performance is slightly smaller than that of the SR-WLS method only considering noise factors. The performance of the TSWLS and JAH methods is fixed given the non-line-of-sight transmission error and noise power.
(4) Simulation experiment 4
The number N of the wireless signal receivers is 7, and the number N of the non-line-of-sight links is changed when the other conditions are the same as those in experiment 1nlosAnd observing the change condition of the mean square error. Simulation results as shown in fig. 5, RT-GTRS curve represents the method of example 1, SR-WLS curve represents amplitude square-weighted least squares, TSWLS curve represents two-step weighted least squares, JAH curve represents combined self-organization, and CRLB curve represents cramer-circle. All methods are robust to line-of-sight/non-line-of-sight links. The robustness of the method of embodiment 1 is predictable and also justifies the approximate operation.
3. Simulation experiment results
By combining the simulation results and analysis, the effectiveness, reliability and robustness of the method are verified by comparing the performances of different positioning methods, and the positioning accuracy can be improved by using the positioning method in a non-line-of-sight environment.

Claims (3)

1. A robust non-line-of-sight deviation elimination positioning method capable of time domain combination is characterized by comprising the following steps:
(1) extracting location parameters in energy and time domains
Establishing a positioning model in a non-line-of-sight transmission environment, and positioning a signal source by adopting 6-9 wireless signal receivers, wherein the specific method comprises the following steps:
a wireless signal receiver extracts positioning parameters in an energy domain and a time domain respectively from electromagnetic signals transmitted by a signal source, including received signal strength P in the energy domainiTime difference of arrival d in time domainj：
Figure FDA0002309267700000011
dj＝||u-sj||-||u-s1||+βj+nj, (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers and is 6-9; | | | represents the euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]]T；siIs the position coordinate of the wireless signal receiver as [ x ]i,yi,zi]T；r0Is a unit distance; p0Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m isiIs a logarithmic shadow fading contained in the received signal strength subject to a mean of zero and a variance of
Figure FDA0002309267700000012
(ii) a gaussian distribution of; n isjIs the measurement noise in the time difference of arrival, obeys mean zero and variance
Figure FDA0002309267700000013
αiIs a non-line-of-sight deviation in the time domain βjIs the non-line-of-sight deviation in the energy domain, the non-line-of-sight deviation has a definite boundary value, namely 0 is less than or equal to αi≤αmax、0≤βj≤βmax；
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Figure FDA0002309267700000014
Time domain positioning parameters
Figure FDA0002309267700000015
Figure FDA0002309267700000016
Figure FDA0002309267700000017
Wherein the content of the first and second substances,
Figure FDA0002309267700000018
is a corrected energy domain measurement value, Pi+αmax/2；
Figure FDA0002309267700000019
Is a modified time domain measurement of dj-βmax/2；
Figure FDA00023092677000000110
α is the corrected energy domain non-line-of-sight deviationi-αmax/2；
Figure FDA00023092677000000111
Is the corrected time domain non line of sight deviation, βj-βmax/2；
(3) Determining an initial objective minimization function
Determining an initial objective minimization function F in robust least squares operation in the energy domain as follows1(u) initial objective minimization function F in robust least squares operation in time domain2(u)：
Figure FDA00023092677000000112
Figure FDA0002309267700000021
Wherein
Figure FDA0002309267700000022
Is a value related to the reference distance, the positioning parameter, the corrected non-line-of-sight deviation and the transmission path loss, and is
Figure FDA0002309267700000023
ζiIs a variable related to a positioning parameter and a transmission path loss, is
Figure FDA0002309267700000024
(4) Determining a maximum minimization objective function
Carrying out robust least square operation on the initial target minimization functions in the formulas (3a) and (3b) to respectively obtain the maximum minimization target function F of the energy domainAMaximum minimization objective function F in time domainBThe following were used:
Figure FDA0002309267700000025
Figure FDA0002309267700000026
(5) determining a value of a maximized objective function
Determining the corrected energy domain non-line-of-sight deviation according to the limit value of the non-line-of-sight deviation in the step 1
Figure FDA0002309267700000027
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
Figure FDA0002309267700000028
The absolute value limits of (c) are as follows:
Figure FDA0002309267700000029
Figure FDA00023092677000000210
the maximum minimization of the objective function F in the energy domain represented by equation (4a)AIs about
Figure FDA00023092677000000221
And a monotonous interval equation (5a), the value of the maximized objective function in the energy domain can be determined as
Figure FDA00023092677000000211
Wherein
Figure FDA00023092677000000222
Is composed of
Figure FDA00023092677000000223
Namely, it is
Figure FDA00023092677000000212
Figure FDA00023092677000000224
Is composed of
Figure FDA00023092677000000225
Namely, it is
Figure FDA00023092677000000213
Similarly, the maximized objective function in the time domain is determined by equations (4a) and (4b) as
Figure FDA00023092677000000214
Wherein
Figure FDA00023092677000000215
Is composed of
Figure FDA00023092677000000216
Figure FDA00023092677000000217
Is composed of
Figure FDA00023092677000000218
(6) Determining a minimization objective function
Taking value of the maximized objective function in the energy domain in the step (5)
Figure FDA00023092677000000219
Maximized objective function value in the time domain
Figure FDA00023092677000000220
Further relaxation with max { a, b } ≦ a + b, where a > 0, b > 0, yields a minimized objective function for the energy domain
Figure FDA0002309267700000031
Minimizing an objective function in the time domain
Figure FDA0002309267700000032
Figure FDA0002309267700000033
Figure FDA0002309267700000034
(7) Determining weights and maximum likelihood estimates
Is as followsEnergy-dependent domain weighted weights
Figure FDA00023092677000000314
Time domain weighted weights
Figure FDA00023092677000000315
Maximum likelihood estimate P of received signal strengthi', maximum likelihood estimation of time difference of arrival
Figure FDA00023092677000000316
Figure FDA0002309267700000035
Figure FDA0002309267700000036
Figure FDA0002309267700000037
Figure FDA0002309267700000038
(8) Determining a modified minimization objective function
The modified minimization objective function g (u) is determined as follows. The solving process of the minimized objective function is a positioning process for simultaneously minimizing the energy domain, the non-line-of-sight deviation in the time domain and the measurement noise:
Figure FDA0002309267700000039
(9) determining objective functions for generalized confidence domain sub-problems
The objective function G' (u) for obtaining the generalized confidence domain subproblem by developing the numerator of equation (8) is:
Figure FDA00023092677000000310
wherein the weighting matrix W is represented as
Figure FDA00023092677000000311
Figure FDA00023092677000000312
Figure FDA00023092677000000313
The matrices A, p in the objective function are respectively
Figure FDA0002309267700000041
Figure FDA0002309267700000042
Figure FDA0002309267700000043
Figure FDA0002309267700000044
Figure FDA0002309267700000045
The matrices D, g in the constraints are respectively
Figure FDA0002309267700000046
Figure FDA0002309267700000047
Wherein I represents an identity matrix and 0 represents an all-zero matrix;
(10) determining signal source location information
The optimal solution of the formula (9) is obtained by a first dichotomy from the fully necessary optimality condition, and the optimal solution of the generalized confidence domain problem is determined according to the formula
Figure FDA0002309267700000048
Figure FDA0002309267700000049
Where λ is a constant value obtained by bisection, the signal source position information can be determined by
Figure FDA00023092677000000410
The positional information of the signal source is obtained from equation (10 b).
2. The robust non-line-of-sight offset cancellation localization method of time-domain combinable of claim 1, wherein: in the step (1) of extracting the positioning parameters in the energy domain and the time domain, miThe Gaussian measurement noise is the received signal strength in an energy domain, and the variance of the Gaussian measurement noise is 1-3; n isjIs Gaussian measurement noise of arrival time difference in time domain, the variance of which is 1-4, αiThe non-line-of-sight deviation of the measurement parameters in the energy domain is 2-6, βjThe non-line-of-sight deviation of the measurement parameters in the time domain is 2-6.
3. The robust non-line-of-sight offset cancellation localization method of time-domain combinable of claim 1, wherein: determining λ according to equation (11a) in the dichotomy in the step of determining signal source position information (10):
Figure FDA0002309267700000051
λ is the solution of φ (λ) ═ 0, λ ∈ I, where I ranges from
Figure FDA0002309267700000052
Wherein λi(D,(WA)T(WA))＝λi(((WA)T(WA))-1/2D((WA)T(WA))-1/2) Denotes M-1/2DM-1/2The ith characteristic value in descending order, wherein M is (WA)T(WA)。
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