CN111007456B - 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 PDFInfo
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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
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 requirement of high-precision position information service for users becomes more and more 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 FDOA measures, using the relationship between the intermediate variable and the Source Location parameter, and performing iterative solution on the basis of the rough estimation to ensure the global optimization and real-time performance of the estimated 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 generally 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 in a three-dimensional scene, when the number of sensors is less than or equal to 4, 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 the time domain joint positioning under the non-line-of-sight environment. For example, COLUCCIA, FASCISTA A, provides adaptive relaxation joint estimation based On likelihood function in "On the hybrid TOA/RSS range estimation in wireless sensor networks", and improves estimation performance by selecting appropriate 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 the advantages of accurate positioning, simple method and less prior information requirement and can combine time domains.
The implementation scheme adopted for solving the technical problems 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 6-9 wireless signal receivers. The specific method comprises the following steps: a wireless signal receiver extracts positioning parameters in the energy domain and the time domain, respectively, from electromagnetic signals transmitted by a signal source, including in-band receptionReceived signal strength P i Time difference of arrival d in time domain j ：
d j ＝||u-s j ||-||u-s 1 ||+β j +n j , (1b)
Wherein i is 1, …, N, j is 2, …, N, 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 ；s i Is the position coordinate of the wireless signal receiver as [ x ] i ,y i ,z i ] T ；r 0 Is a unit distance; p 0 Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m is i Is a logarithmic shadow fading contained in the received signal strength subject to a mean of zero and a variance of
(ii) a gaussian distribution of; n is j Is the measurement noise in the time difference of arrival, obeys mean zero and variance
(ii) a gaussian distribution of; alpha is alpha i Is a non-line-of-sight deviation in the energy domain; beta is a j Is a non-line-of-sight deviation in the time domain; non-line-of-sight deviations exist at defined boundary values, i.e. 0. Ltoreq.alpha i ≤α max 、0≤β j ≤β max 。
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Time domain positioning parameters
Wherein the content of the first and second substances,
is a corrected energy domain measurement value, P i +α max /2；
Is a modified time domain measurement of d j -β max /2；
Is corrected energy domain non-line-of-sight deviation of alpha i -α max /2；
Is a corrected time domain non-line-of-sight deviation of beta j -β max /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 follows 1 (u) initial objective minimization function F in robust least squares operation in time domain 2 (u)：
Wherein
Is made from root of Henan ginsengThe values related to the distance, the positioning parameters, the correction of the non-line-of-sight deviation and the transmission path loss are
ζ i Is a variable related to a positioning parameter and a transmission path loss, is
(4) Determining a maximum minimization objective function
Carrying out robust least square operation on the initial target minimization functions in the formulas (3 a) and (3 b) to respectively obtain the maximum minimization target function F of the energy domain A Maximum minimization objective function F in time domain B The following were used:
(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
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
The absolute value limits of (c) are as follows:
the maximum minimization objective function F in the energy domain represented by the formula (4 a) A Is about
And a monotonous interval equation (5 a), determining the value of the maximized objective function in the energy domain as follows:
wherein
Is composed of
Namely, it is
Is composed of
Namely, it is
Similarly, the value of the maximized objective function in the time domain determined by equations (4 b) and (5 b) is:
wherein
Is composed of
Is composed of
(6) Determining a maximized objective function
Dereferencing the maximized objective function in the energy domain in the step (5)
Maximized objective function value in the time domain
Further relaxed with max { a, b } ≦ a + b, where a > 0, b > 0, resulting in a maximized objective function within the energy domain
Maximizing objective function in time domain
(7) Determining weights and maximum likelihood estimates
Energy domain weighted weights are determined as follows
Time domain weighted weights
d′ i Maximum likelihood estimation of time difference of arrival
(8) Determining a modified minimization objective function
Determining a corrected minimum objective function G (u) according to the following formula, wherein the solving process of the minimum 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:
(9) Determining objective functions for generalized confidence domain sub-problems
The objective function G' (u) of the generalized confidence domain sub-problem obtained by developing the first two molecules in equation (8) is:
wherein the weighting matrix W is represented as:
the matrices A, p in the objective function are:
the matrices D, g in the constraint are:
where I denotes an identity matrix and 0 denotes an all-zero matrix.
(10) Determining signal source location information
From the sufficiently required optimality condition, the optimal solution of the equation (9) is obtained by a first dichotomy.Determining an optimal solution to a generalized confidence domain problem according to
Where λ is a fixed value obtained by bisection, and the signal source location information is determined by the following equation:
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, m i Is the Gaussian measurement noise of the received signal intensity in the energy domain, and the variance is 1 to 3; n is a radical of an alkyl radical j Is Gaussian measurement noise of arrival time difference in a time domain, and the variance of the Gaussian measurement noise is 1-4; alpha (alpha) ("alpha") i The non-line-of-sight deviation of the measurement parameters in the energy domain is 2-6; beta is a j The non-line-of-sight deviation of the measured parameter in the time domain is 2-6.
In the dichotomy described for determining signal source location information in step (10) of the present invention, λ is determined according to equation (11 a):
λ is a solution of φ (λ) =0, λ ∈ I, where I ranges from
Wherein λ i (D,(WA) T (WA))＝λ i (((WA) T (WA)) -1/2 D((WA) T (WA)) -1/2 ) Is denoted by M -1/2 DM -1/2 The 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.
Figure 4 is a simulated comparison of example 1 with two-step weighted least squares, magnitude squared-weighted least squares, combined self-organization, and cramer plots of localization performance for varying non-line-of-sight deviation maxima.
Figure 5 is a simulated comparison of example 1 with two-step weighted least squares, magnitude squared-weighted least squares, combined self-organization, and cramer plots for localization performance when the number of non-line-of-sight links is varied.
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 domain i Time difference of arrival d in time domain j ：
d j ＝||u-s j ||-||u-s 1 ||+β j +n j , (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers, and is 7; | | × | represents an euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]] T ；s i Is the position coordinate of the wireless signal receiver, is x i ,y i ,z i ] T ；r 0 Is a unit distance; p 0 Is the received signal strength at unit distance; γ is a transmission path loss of a signal, and is 3; m is a unit of i Is 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 is j Is the measurement noise in the arrival time difference, obeys gaussian distribution with a mean value of zero and a variance of 3; alpha is alpha max The maximum value of the non-line-of-sight deviation in the energy domain is 4; beta is a max The maximum value of the non-line-of-sight deviation in the time domain is 4.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Time domain positioning parameters
Wherein the content of the first and second substances,
is a corrected energy domain measurement value of P i +α max /2；
Is a modified time domain measurement value of d j -β max /2；
Is the corrected energy domain non-line-of-sight deviation of alpha i -α max /2；
Is a corrected time domain non-line-of-sight deviation of beta j -β max /2. M of the present embodiment i Variance of 2,n j The 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 follows 1 (u) initial objective minimization function F in robust least squares operation in time domain 2 (u)：
Wherein
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
ζ i Is a variable related to a positioning parameter and a transmission path loss, is
(4) Determining a maximum minimization objective function
Carrying out robust least square operation on the initial target minimization functions in the formulas (3 a) and (3 b) to respectively obtain the maximum minimization target function F of the energy domain A Maximum minimization objective function F in time domain B The following:
(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
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
The absolute value limits of (c) are as follows:
the maximum minimization objective function F in the energy domain represented by the formula (4 a) A Is about
And a monotonous interval equation (5 a), determining the value of the maximized objective function in the energy domain as follows:
wherein
Is composed of
Namely that
Is composed of
Namely that
Similarly, the value of the maximized objective function in the time domain determined by equations (4 b) and (5 b) is:
wherein
Is composed of
Is composed of
α of the present embodiment max Is 4, beta max Is 4.
(6) Determining a maximized objective function
Taking value of the maximized objective function in the energy domain in the step (5)
Maximized objective function value in the time domain
Further relaxation is performed with max { a, b } ≦ a + b, where a > 0, b > 0, resulting in a maximized objective function in the energy domain
Maximizing objective function in time domain
(7) Determining weights and maximum likelihood estimates
Energy domain weighted weights are determined as follows
Time domain weighted weights
d i ', maximum likelihood estimation of time difference of arrival
(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:
(9) Determining objective functions for generalized confidence domain sub-problems
The first two terms of the numerator in equation (8) are expanded to obtain the objective function G' (u) of the generalized confidence domain subproblem as follows:
wherein the weighting matrix W is represented as:
the matrices A, p in the objective function are:
the matrices D, g in the constraint are:
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
Where λ is a constant value obtained by a dichotomy, λ is determined according to equation (11 a):
λ is the solution of φ (λ) =0, λ ∈ I, where I ranges from:
wherein λ i (D,(WA) T (WA))＝λ i (((WA) T (WA)) -1/2 D((WA) T (WA)) -1/2 ) Is denoted by M -1/2 DM -1/2 The ith characteristic value in descending order, wherein M is (WA) T (WA)。
The signal source location information is determined by:
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
Establishing a positioning model in a non-line-of-sight transmission environment by adopting 6 wireless signal connectionsThe receiver locates the 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 domain i Time difference of arrival d in time domain j ：
d j ＝||u-s j ||-||u-s 1 ||+β j +n j , (1b)
Wherein i is 1, …, N, j is 2, …, N, N is the maximum number of wireless signal receivers and is 6; | | × | represents an euclidean norm; u is the position coordinate of the signal source and is [ x, y, z ]] T ；s i Is the position coordinate of the wireless signal receiver as [ x ] i ,y i ,z i ] T ；r 0 Is a unit distance; p is 0 Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m is i Is logarithmic shadow fading contained in the received signal strength, obeying gaussian distribution with mean value of zero and variance of 1; n is j Is the measurement noise in the arrival time difference, obeys gaussian distribution with mean value of zero and variance of 1; alpha is alpha max The maximum value of the non-line-of-sight deviation in the energy domain is 2; beta is a max The maximum value of the non-line-of-sight deviation in the time domain is 2.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Time domain positioning parameters
Wherein the content of the first and second substances,
is a corrected energy domain measurement value, P i +α max /2；
Is a modified time domain measurement of d j -β max /2；
Is the corrected energy domain non-line-of-sight deviation of alpha i -α max /2；
Is a corrected time domain non-line-of-sight deviation of beta j -β max /2. M of the present embodiment i Variance of 1,n j The 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 threshold value of the non-line-of-sight deviation in the step 1
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
The absolute value limits of (c) are as follows:
the maximum minimization objective function F in the energy domain represented by the formula (4 a) A Is about
And a monotonous interval equation (5 a), determining the value of the maximized objective function in the energy domain as follows:
wherein
Is composed of
Namely, it is
Is composed of
Namely, it is
Similarly, the value of the maximized objective function in the time domain determined by equations (4 b) and (5 b) is:
wherein
Is composed of
Is composed of
α of the present embodiment max Is 2, beta max Is 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 domain i Time difference of arrival d in time domain j ：
d j ＝||u-s j ||-||u-s 1 ||+β j +n j , (1b)
Wherein i is 1, …, N, j is 2, …, N is the maximum number of wireless signal receivers and is 9; | | | represents the euclidean norm; u is the position coordinate of the signal source and is x, y, z] T ；s i Is the position coordinate of the wireless signal receiver as [ x ] i ,y i ,z i ] T ；r 0 Is a unit distance; p is 0 Is the received signal strength at unit distance; γ is a transmission path loss of a signal, and is 3; m is a unit of i Is a receiving messageLogarithmic shadow fading contained in the signal intensity obeys gaussian distribution with a mean value of zero and a variance of 3; n is j Is the measurement noise in the arrival time difference, obeys gaussian distribution with a mean value of zero and a variance of 4; alpha is alpha max The maximum value of the non-line-of-sight deviation in the energy domain is 6; beta is a max The maximum value of the non-line-of-sight deviation in the time domain is 6.
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain localization parameter according to the following formula
Time domain positioning parameters
Wherein the content of the first and second substances,
is a corrected energy domain measurement value, P i +α max /2；
Is a modified time domain measurement of d j -β max /2；
Is the corrected energy domain non-line-of-sight deviation of alpha i -α max /2；
Is a corrected time domain non-line-of-sight deviation of beta j -β max /2. M of the present embodiment i Variance of 3,n j The 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 threshold value of the non-line-of-sight deviation in the step 1
Absolute value limit of (3), corrected time domain non-line-of-sight deviation
The absolute value limits of (c) are as follows:
the maximum minimization of the objective function F in the energy domain represented by equation (4 a) A Is about
And a monotonous interval equation (5 a), determining the value of the maximized objective function in the energy domain as follows:
wherein
Is composed of
Namely, it is
Is composed of
Namely, it is
Similarly, the value of the maximized objective function in the time domain determined by equations (4 b) and (5 b) is:
wherein
Is composed of
Is composed of
α of the present embodiment max Is 6, beta max Is 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 invention, the inventor adopts the robust non-line-of-sight deviation elimination positioning method (RT-GTRS) capable of time domain combination of embodiment 1 of the invention and carries out a comparative simulation experiment with a two-step weighted least square method (TSWLS), an amplitude square-weighted least square method (SR-WLS), a combined self-organizing method (JAH) and a caramello lower bound (CRLB), and the experimental conditions are as follows:
1. simulation conditions
All wireless signal receivers are randomly placed in a BxBxB area in each Monte Carlo simulation, and the source is placed in u = [15,15,15] T (m) the Monte-Keck Luo Fangzhen times is L, and the rest simulation parameters are fixed: p 0 ＝20dBm、γ＝3、r 0 =1m, B =30m, L =10000. The non-line-of-sight transmission error factors (including the received signal strength and the arrival time difference) in each Monte Carlo simulation are randomly and uniformly distributed in 0,bias max ]In (dB, m), wherein bias max Is a non-line-of-sight error factor maximum. The performance index of the method is root mean square error, which is defined as
Wherein
Representing an estimate of the true source position u in the ith monte carlo simulation.
2. Simulation experiment
(1) Simulation experiment 1
Number N of non-line-of-sight channels nlos Is N, the maximum value bias of the non-line-of-sight error factor max Is 6,bias max Signal energy loss in dB, bias, in the energy domain for non-line-of-sight max The 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
Is the number of 3, and the number of the carbon atoms is 3,
in the 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, a JAH curve represents a combined self-organizing method, and a CRLB curve represents a ClarametRo Jie. As can be seen from fig. 2, as the number of wireless signal receivers N increases, the information available for location determination 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. Compared with the JAH method, the method of the embodiment 1 has more obvious positioning performance as N is increased, and compared with the JAH method, the method of the embodiment 1 is easier to reach a limit state and is closer to CRLB.
(2) Simulation experiment 2
The number N of wireless signal receivers is 7, and the number N of non-line-of-sight channels nlos In the case of N, the performance of each method is subject to different measurement errors sigma i The simulation experiment was performed, and the results are shown in fig. 3, the RT-GTRS curve represents the method of example 1, the SR-WLS curve represents the magnitude square-weighted least squares method, the TSWLS curve represents the two-step weighted least squares method, the JAH curve represents the combined self-organizing method, and the CRLB curve represents the clarmero bound. 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 is i The 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 σ i The performance is optimal within the value range of (2). 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
The number N of the wireless signal receivers 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 1 max 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 squares method, the TSWLS curve represents the two-step weighted least squares method, the JAH curve represents the combined self-organizing method, and the CRLB curve represents the variation of the mean square errorRepresenting the cramer-perot boundary. With bias max The 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 offset max And (4) minimizing, wherein 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 1 nlos And observing the change condition of the mean square error. Simulation results as shown in fig. 5, an RT-GTRS curve represents the method of example 1, an SR-WLS curve represents an amplitude square-weighted least squares method, a TSWLS curve represents a two-step weighted least squares method, a JAH curve represents a combined self-organization method, and a CRLB curve represents a cralmelo boundary. 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 domain i Time of arrival in the time domainDifference d j ：
d j ＝||u-s j ||-||u-s 1 ||+β j +n j , (1b)
Wherein i is 1, …, N, j is 2, …, N, 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 ；s i Is the position coordinate of the wireless signal receiver as [ x ] i ,y i ,z i ] T ；r 0 Is a unit distance; p is 0 Is the received signal strength per unit distance; γ is a transmission path loss of a signal, and is 3; m is i Is a logarithmic shadow fading contained in the received signal strength, subject to a mean of zero and a variance of
(ii) a gaussian distribution of; n is j Is the measurement noise in the time difference of arrival, obeys mean zero and variance
(ii) a gaussian distribution of; alpha is alpha i Is a non-line-of-sight deviation in the energy domain; beta is a j Is a non-line-of-sight deviation in the time domain; non-line-of-sight deviations exist at defined boundary values, i.e. 0. Ltoreq.alpha i ≤α max 、0≤β j ≤β max ；
(2) Determining modified energy domain and time domain positioning parameters
Determining the corrected energy domain location parameter according to
Time domain positioning parameters
Wherein the content of the first and second substances,
is a corrected energy domain measurement value, P i +α max /2；
Is a modified time domain measurement of d j -β max /2；
Is the corrected energy domain non-line-of-sight deviation of alpha i -α max /2；
Is a corrected time domain non-line-of-sight deviation of beta j -β max /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 follows 1 (u) initial objective minimization function F in robust least squares operation in time domain 2 (u)：
Wherein
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
ζ i Is a variable related to a positioning parameter and a transmission path loss, is
(4) Determining a maximum minimization objective function
Carrying out robust least square operation on the initial target minimization functions in the formulas (3 a) and (3 b) to respectively obtain the maximum minimization target function F of the energy domain A Maximum minimization objective function F in time domain B The following:
(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
Absolute value limit of (1), corrected time domain non-line-of-sight deviation
The absolute value limits of (c) are as follows:
the maximum minimization of the objective function F in the energy domain represented by equation (4 a) A Is about
And a monotonous interval equation (5 a), determining the value of the maximized objective function in the energy domain as follows:
wherein
Is composed of
Namely, it is
Is composed of
Namely that
Similarly, the value of the maximized objective function in the time domain determined by equations (4 b) and (5 b) is:
wherein
Is composed of
Is composed of
(6) Determining a maximized objective function
Dereferencing the maximized objective function in the energy domain in the step (5)
Maximized objective function value in the time domain
Further relaxed with max { a, b } ≦ a + b, where a > 0, b > 0, resulting in a maximized objective function within the energy domain
Maximizing objective function in time domain
(7) Determining weights and maximum likelihood estimates
Energy domain weighted weights are determined as follows
Time domain weighted weights
d′ i Maximum likelihood estimation of time difference of arrival
(8) Determining a modified minimization objective function
Determining a corrected minimum objective function G (u) according to the following formula, wherein the solving process of the minimum 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:
(9) Determining objective functions for generalized confidence domain sub-problems
The first two terms of the numerator in equation (8) are expanded to obtain the objective function G' (u) of the generalized confidence domain subproblem as follows:
wherein the weighting matrix W is represented as:
the matrices A, p in the objective function are:
the matrices D, g in the constraint are:
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
Where λ is a fixed value obtained by bisection, and the signal source location information is determined by the following equation:
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, m i Is the Gaussian measurement noise of the received signal intensity in the energy domain, and the variance is 1 to 3; n is j Is Gaussian measurement noise of arrival time difference in a time domain, and the variance of the Gaussian measurement noise is 1-4; alpha (alpha) ("alpha") i The non-line-of-sight deviation of the measurement parameters in the energy domain is 2-6; beta is a j The non-line-of-sight deviation of the measured parameter in the time domain is 2-6.
3. The robust non-line-of-sight offset cancellation localization method of claim 1, capable of temporal union, characterized in that: determining signal source location information in step (10) in said dichotomy λ is determined according to equation (11 a):
λ is the solution of φ (λ) =0, λ ∈ I, where I ranges from:
wherein λ i (D,(WA) T (WA))＝λ i (((WA) T (WA)) -1/2 D((WA) T (WA)) -1/2 ) Is denoted by M -1/2 DM -1/2 The ith characteristic value in descending order, wherein M is (WA) T (WA)。
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