CN113259884B - Indoor positioning base station layout optimization method based on multi-parameter fusion - Google Patents

Indoor positioning base station layout optimization method based on multi-parameter fusion Download PDF

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CN113259884B
CN113259884B CN202110547058.8A CN202110547058A CN113259884B CN 113259884 B CN113259884 B CN 113259884B CN 202110547058 A CN202110547058 A CN 202110547058A CN 113259884 B CN113259884 B CN 113259884B
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CN113259884A (en
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周陬
陈兆
王玫
杨帆
张国立
仇洪冰
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Guilin University of Electronic Technology
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/30—Services specially adapted for particular environments, situations or purposes
    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
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Abstract

The invention discloses an indoor positioning base station layout optimization method based on multi-parameter fusion, which comprises the following steps: (1) inputting a scene size; (2) randomly generating base station coordinates; (3) calculating the performance of the base station array; (4) judging whether the optimization target is reached, if so, turning to the step (5); if not, continuing to search and update the coordinates of the base station, and returning to the step (2); (5) outputting the base station coordinates reaching the optimization target, completing the base station layout optimization mathematical model, and solving the mathematical model by adopting intelligent algorithms such as a firefly algorithm and the like. By adopting the optimization method, the optimized base station layout matrix has obviously reduced positioning error, PDOP and other indexes, meets the optimization target in the multi-target joint optimization framework and achieves the expected effect.

Description

Indoor positioning base station layout optimization method based on multi-parameter fusion
Technical Field
The invention relates to the field of indoor positioning, in particular to an indoor positioning base station layout optimization method based on multi-parameter fusion.
Background
With the development of wireless communication technology, location-based services have become a basic requirement for numerous applications of the internet of things. Currently, Global Navigation Satellite System (GNSS) technology is mature and can provide people with a relatively accurate outdoor location. However, in an indoor environment, satellite signals are severely shielded and weakened by obstacles such as buildings, and it is generally difficult to provide reliable positioning services indoors, so research on indoor positioning services is in progress. The following are common indoor positioning technologies: bluetooth, Wi-Fi, geomagnetism, Pedestrian Dead Reckoning (PDR), sound, Ultra Wide Band (UWB) wireless positioning and the like.
At present, most indoor positioning base station layout schemes roughly select a regular array according to a scene structure by using a design and verification method and analyze positioning accuracy by adopting a relevant criterion. However, only several base station layout arrays are compared, and a method for solving the base station layout optimization is not provided.
The DOP in the satellite navigation field is introduced into indoor positioning, although the DOP can objectively evaluate the layout of base stations according to the angle between the base stations and the labels, the DOP ignores the difference of distances between each base station and each label, and has great limitation in indoor positioning.
A base station layout method based on a Cramal bound (CRB) provides a lower limit for the variance of positioning errors, but adopts a brute force search mode and has overlarge calculation complexity.
Disclosure of Invention
Aiming at the defects pointed out in the prior scheme, the invention provides an indoor positioning base station layout optimization method based on multi-parameter fusion. The goal of base station layout optimization is to reduce errors, improve precision, reduce variance and reduce error fluctuation.
In order to achieve the aim, the indoor positioning base station layout optimization method based on multi-parameter fusion comprises a multi-objective joint optimization framework, a base station layout optimization mathematical model is established according to the mean square error of target use position precision factors PDOP and TDOA and the Clarmer Laue boundary in the optimization framework, and intelligent algorithms such as a firefly algorithm and the like are adopted for solving aiming at the mathematical model.
The multi-target combined optimization framework can continuously search the arrangement positions of the base stations in the base station arrangement region only by inputting the size of a scene until the performance of the base station arrangement matrix meets the set termination condition, namely, the optimization target is reached or the cycle number is reached, and finally the current optimal base station coordinate is output.
The invention discloses an ultra-wideband indoor positioning base station layout optimization method based on multi-parameter fusion, which comprises the following steps:
(1) inputting a scene size;
(2) randomly generating base station coordinates;
(3) calculating the performance of the base station array;
(4) judging whether the optimization target is reached, if so, turning to the step (5); if not, continuing to search and update the coordinates of the base station, and returning to the step (2);
(5) and outputting the base station coordinates reaching the optimization target to complete base station layout optimization.
Further, the step (3) of calculating the performance of the base station array, and evaluating the performance of the base station array by using the TDOA mean square error and the krameria bound, includes the steps of:
(3.1) dividing the scene according to grids, wherein the size of each grid is 10cm by 10cm, and the number of the grids is M by N;
(3.2) calculating PDOP, TDOA positioning error and Claritura bound of each grid;
(3.3) calculating the average mean square error (PDOP), the mean square error (TDOA) and the average Cramerlaonian bound of the whole scene;
and (3.4) respectively multiplying the mean square error of the PDOP, the mean square error of the TDOA and the average Claus Laue boundary by weight coefficients and then adding to obtain the performance of the base station array.
Further, calculating PDOP of each grid in the step (3.2), wherein the PDOP is obtained by a horizontal precision factor HDOP and a vertical precision factor VDOP,
Figure BDA0003074042340000021
the HDOP and the VDOP are obtained by an observation matrix H and a weight coefficient matrix Q;
the calculation formula of the observation matrix H is as follows:
Figure BDA0003074042340000022
wherein (x, y, z) is the label coordinate, (x) n ，y n ，z n ) Is the coordinate of the nth base station, r n Is the distance of the tag to the nth base station; the weight coefficient matrix Q is calculated by
Figure BDA0003074042340000023
T represents the transpose of the matrix, q ii Diagonal elements of Q, Q being a 3 × 3 matrix; horizontal precision factor
Figure BDA0003074042340000031
Vertical precision factor
Figure BDA0003074042340000032
Three dimensional position accuracy factor
Figure BDA0003074042340000033
Further, the step (3.2) of calculating the TDOA positioning error of each grid is obtained by deducing the positive correlation between the electromagnetic wave ranging error and the range, wherein the electromagnetic wave ranging error is divided into the ranging error caused by physical measurement and the measurement error caused by multipath effect; the range error caused by the physical measurement can be expressed as follows after linear fitting: gamma ray P，i ＝a+br i +ε i Wherein a is the self-error of the system, b is the influence factor of the distance measurement, a + br i Form a systematic error, ε i As random error, r i Measuring the distance;
the measurement error caused by multipath effect is gamma M，i ＝G log(1+r i ) Wherein G is a parameter of the normalized error, so that the error is normalized and follows Gaussian distribution, therefore, the ranging error equation is gamma i ＝γ P，i +γ M，i ＝a+br i +ε i +G log(1+r i ) (ii) a Since TDOA uses time difference of arrival, i.e., the coordinates of a tag are solved using the difference of distances from the tag to each base station, the difference of observed distances between each base station
Figure BDA0003074042340000034
Comprises the following steps:
Figure BDA0003074042340000035
wherein (r) i -r j ) In order to be the true distance difference,
Figure BDA0003074042340000036
is an error due to a random error epsilon i -ε j Small enough to be negligible;
the formula for TDOA is:
Figure BDA0003074042340000037
the three matrices in the above formula are named with a, theta and b,
wherein
Figure BDA0003074042340000038
θ＝A + b＝(A T A) -1 A T b，A + A pseudo-inverse matrix representing A; (x, y, z) is the label coordinate, (x) n ，y n ，z n ) Is the coordinate of the nth base station, r 1 Distance of the tag to the 1 st base station, r n1 The difference between the distance from the tag to the nth base station and the distance from the tag to the 1 st base station,
Figure BDA0003074042340000041
distance of nth base station to origin of coordinates, K n1 ＝K n -K 1 ；
TDOA calculation is carried out by utilizing observed values, and the formula is changed into
Figure BDA0003074042340000042
Solving the above equation to obtain
Figure BDA0003074042340000043
Then positioning error occurs
Figure BDA0003074042340000044
Further, in step (3.2), the cramer limit CRB of each grid is calculated, and the cramer limit determines a lower limit for the variance of any unbiased estimate, and the formula is:
Figure BDA0003074042340000045
wherein
Figure BDA0003074042340000046
Is an unbiased estimate of the estimated parameter θ, [ θ ═ θ [ [ θ ] 1 ，θ 2 …θ p ] T Is the vector parameter to be estimated, I (θ) is a p × p snow information matrix (FIM), defined by:
Figure BDA0003074042340000047
where p (x, theta) is the likelihood function, E [.]Referring to the expected value, the Fisher snow information matrix FIM of the noise model is
Figure BDA0003074042340000048
Wherein (x, y, z) is the label coordinate, (x) i ，y i ，z i ) Is the coordinates of the ith base station,
Figure BDA0003074042340000049
is the variance of the noise, d i Is the distance of the tag to the ith base station. The sum of the estimated variances can be obtained
Figure BDA0003074042340000051
Further, the step (3.3) of calculating the average PDOP of the whole scene is
Figure BDA0003074042340000052
Further, the step (3.3) of calculating the TDOA mean square error of the whole scene is
Figure BDA0003074042340000053
Further, the step (3.3) of calculating the average CRB of the whole scene is
Figure BDA0003074042340000054
Further, in the step (3.4), the average PDOP, TDOA mean square error and average CRB are multiplied by weight coefficients respectively and then added to obtain the performance of the base station matrix, and the multi-objective optimization problem is converted into a single-objective optimization problem by using an average weight principle, wherein an optimization objective function is as follows:
Figure BDA0003074042340000055
s.t.x min ＜x n ＜x max ，y min ＜y n ＜y max ，z min ＜z n ＜z max ，n＝1，2，3，4...。
by adopting the optimization method, the optimized coordinates of the base station layout are solved by using intelligent algorithms such as a firefly algorithm and the like, the firefly algorithm simulates information exchange among fireflies, the information exchange is mutually attracted and integrated, the objective function value is used as the brightness of the fireflies, the position is better when the brightness is higher, and other fireflies can be attracted by the fireflies with higher brightness in the solution space and continuously approach the fireflies to search the better position. And taking the optimization objective function value as the brightness of the firefly, wherein the lower the optimization objective function value is, the higher the brightness is, and finally outputting the base station coordinate reaching the optimization objective.
By adopting the indoor positioning base station layout optimization method based on multi-parameter fusion, the optimized base station layout matrix has obviously reduced positioning error, PDOP and other indexes, meets the optimization target in a multi-target combined optimization framework, and achieves the expected effect.
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FIG. 1 is a flow chart of an optimization method of the present invention;
FIG. 2 is a CRB distribution diagram, a PDOP distribution diagram and a positioning error distribution diagram before and after optimization of a simulation experiment by using the optimization method of the present invention;
in fig. 2, (a), (b) and (c) are a CRB profile, a PDOP profile and a positioning error profile of a cubic 8-base-station matrix; (d) and (e) (f) the CRB distribution diagram, the PDOP distribution diagram and the positioning error distribution diagram of the optimized base station array.
Detailed Description
The present invention will be further described with reference to the drawings and simulation experiments, but the present invention is not limited thereto.
Referring to fig. 1, the invention relates to an ultra wide band indoor positioning base station layout optimization method based on multi-parameter fusion, which comprises the following steps:
(1) inputting a scene size;
(2) generating base station coordinates randomly;
(3) calculating the performance of the base station matrix, including calculating errors and calculating variances;
(4) judging whether the optimization target is reached, if not, continuing searching and updating the coordinates of the base station, and returning to the step (2); if yes, turning to the step (5);
(5) and outputting the base station coordinates reaching the optimization target to complete base station layout optimization.
And (3) calculating the performance of the base station array type, wherein the specific steps are calculated according to the method recorded in the invention content.
Simulation experiment binding analysis
From practical application, the simulation experiment sets the scene size to be 14.5m 7.6m 3m, and in order not to influence daily production and life, the base stations can only be arranged along the surrounding walls. Respectively using the traditional cube 8 base station array type and the optimized base station array type obtained by the optimization method of the invention to carry out simulation, wherein the obtained error distribution diagram, PDOP distribution diagram and CRB distribution diagram are shown in figure 2, and in the figure, (a), (b) and (c) are the CRB distribution diagram, PDOP distribution diagram and positioning error distribution diagram of the cube 8 base station array type; (d) and (e) (f) the CRB distribution diagram, the PDOP distribution diagram and the positioning error distribution diagram of the optimized base station array. The dots in the figure represent the base station positions, and the lines in the figure represent the equipotential lines of the values, and the results are shown in table 1. Simulation experiment results show that the optimized base station layout matrix has obviously reduced positioning error, PDOP and other indexes, meets the optimization target in the multi-target joint optimization framework and achieves the expected effect.
TABLE 1 Performance comparison before and after optimization table (simulation)
Figure BDA0003074042340000071
As can be seen from FIG. 2, the equipotential line densities of (d), (e) and (f) are all sparser than those of (a), (b) and (c), which shows that the variation gradients of CRB, PDOP and positioning error of the optimized base station matrix are obviously reduced, and the positioning stability in the whole scene is effectively improved. From the comparison of the CRB distribution diagrams of the base station arrays before and after the optimization in (a) and (d), it can be seen that the maximum CRB value of the optimized base station array is significantly smaller than that of the cubic 8 base station array and is only concentrated in a small region at the top left corner, mainly because this region is not in the region enclosed by the base stations and is far away from the region enclosed by the base stations, while the CRB value of the central region of the cubic 8 base station array is higher, although this region is in the region enclosed by the base stations, the distance between this region and each base station is far, and the positioning stability is reduced. The same problem can also be seen in the comparison of the PDOP profiles of the base station arrays before and after (b) (e) optimization, where the high PDOP area of the cubic 8 base station array is mainly concentrated in the central area, while the high PDOP area of the optimized base station array is concentrated in only a small area in the upper left corner, but the PDOP maximum values of the two base station arrays are not much different. As can be seen from comparison of positioning error distribution diagrams of base station arrays before and after optimization in (c) and (f), the equipotential line density of the cube 8 base station array in the whole area is high, most of the equipotential line density of the optimized base station array is sparse, and is dense only at the right boundary because more base stations are arranged at the right boundary and fewer base stations are arranged at the left boundary, and when a tag is arranged at the right boundary, the difference of distances from the tag to each base station is large, so that the positioning error is increased.

Claims (1)

1. The ultra-wideband indoor positioning base station layout optimization method based on multi-parameter fusion is characterized by comprising the following steps:
(1) inputting a scene size;
(2) randomly generating base station coordinates;
(3) calculating the performance of the base station array;
(4) judging whether the optimization target is reached, if so, turning to the step (5); if not, continuing to search and update the coordinates of the base station, and returning to the step (2);
(5) outputting the base station coordinates reaching the optimization target to complete base station layout optimization;
and (3) calculating the performance of the base station array, and evaluating the performance of the base station array by adopting TDOA mean square error and Cramerlau line, wherein the steps comprise:
(3.1) dividing the scene according to grids, wherein the size of each grid is 10cm by 10cm, and the number of the grids is M by N;
(3.2) calculating PDOP, TDOA positioning error and Claritura bound of each grid;
(3.3) calculating the mean-square error of PDOP and TDOA and the mean Cramer Laue bound of the whole scene;
(3.4) respectively multiplying the mean square error of the PDOP, the mean square error of the TDOA and the average Clausera limit by weight coefficients and then adding to obtain the performance of the base station array;
calculating PDOP of each grid according to the step (3.2), wherein the PDOP is obtained by a horizontal precision factor HDOP and a vertical precision factor VDOP,
Figure FDA0003752209530000011
the HDOP and the VDOP are obtained by an observation matrix H and a weight coefficient matrix Q;
the calculation formula of the observation matrix H is as follows:
Figure FDA0003752209530000012
wherein (x, y, z) is the label coordinate, (x) n ,y n ,z n ) Is the coordinate of the nth base station, r n Is the distance of the tag to the nth base station;
the weight coefficient matrix Q is calculated by
Figure FDA0003752209530000021
T represents the transpose of the matrix, q ii Diagonal elements of Q, Q being a 3 × 3 matrix;
horizontal precision factor
Figure FDA0003752209530000022
Vertical precision factor
Figure FDA0003752209530000023
Three dimensional position accuracy factor
Figure FDA0003752209530000024
Calculating the TDOA positioning error of each grid in the step (3.2), wherein the TDOA positioning error is obtained by deducing the positive correlation between the electromagnetic wave ranging error and the range, and the electromagnetic wave ranging error is divided into the ranging error caused by physical measurement and the measurement error caused by multipath effect; the range error due to the physical measurement can be expressed as: gamma ray P,i ＝a+br i +ε i Wherein a is the self-error of the system, b is the influence factor of the distance measurement, a + br i Form a systematic error, ε i As random error, r i Measuring the distance;
the measurement error caused by multipath effect is gamma M,i ＝Glog(1+r i ) Wherein G is a parameter of the normalized error, so that the error is normalized and follows Gaussian distribution, therefore, the ranging error equation is gamma i ＝γ P,i +γ M,i ＝a+br i +ε i +Glog(1+r i )；
Since TDOA uses time difference of arrival, i.e., the coordinates of a tag are solved using the difference of distances from the tag to each base station, the difference of observed distances between each base station
Figure FDA0003752209530000025
Comprises the following steps:
Figure FDA0003752209530000026
wherein (r) i -r j ) In order to be the true distance difference,
Figure FDA0003752209530000027
is an error due to a random error epsilon i -ε j Small enough to be ignored;
the formula for TDOA is:
Figure FDA0003752209530000031
the three matrices in the above formula are named with a, theta and b,
wherein
Figure FDA0003752209530000032
θ＝A + b＝(A T A) -1 A T b，A + A pseudo-inverse matrix representing a; (x, y, z) is the label coordinate, (x) n ,y n ,z n ) Is the coordinate of the nth base station, r 1 Is the distance of the tag to the 1 st base station, r n1 The difference between the distance from the tag to the nth base station and the distance from the tag to the 1 st base station,
Figure FDA0003752209530000033
is the square of the distance from the nth base station to the origin of coordinates, K n1 ＝K n -K 1 ；
TDOA calculation is carried out by utilizing observed values, and the formula is changed into
Figure FDA0003752209530000034
Solving the above equation to obtain
Figure FDA0003752209530000035
Then positioning error occurs
Figure FDA0003752209530000036
Step (3.2) the Clarithrome bound CRB of each grid is calculated, the Clarithrome bound determines a lower limit for the variance of any unbiased estimate, and the formula is as follows:
Figure FDA0003752209530000037
wherein
Figure FDA0003752209530000038
Is an unbiased estimate of the estimation parameter theta ═ theta [ [ theta ] ] 1 ,θ 2 …θ p ] T Is the vector parameter to be estimated, and I (θ) is the p × p Fisher information matrix FIM, defined by the following equation:
Figure FDA0003752209530000039
where p (x, theta) is the likelihood function, E.]Referring to the expected value, the Fisher snow information matrix FIM of the noise model is
Figure FDA0003752209530000041
Wherein (x, y, z) is the label coordinate, (x) i ,y i ,z i ) Is the coordinates of the ith base station,
Figure FDA0003752209530000042
is the variance of the noise, d i The sum of the estimated variances for the tag's distance to the ith base station
Figure FDA0003752209530000043
Figure FDA0003752209530000044
Step (3.3) calculating the average PDOP of the whole scene as
Figure FDA0003752209530000045
Step (3.3) said calculating the TDOA mean square error of the entire scene as
Figure FDA0003752209530000046
Step (3.3) calculating the average Cramal circle CRB of the whole scene as
Figure FDA0003752209530000047
And (3.4) respectively multiplying the mean square error of the PDOP, the mean square error of the TDOA and the mean CRB by weight coefficients and then adding the result to obtain the performance of the base station array, wherein the average weight principle is adopted to convert the multi-objective optimization problem into the single-objective optimization problem, and the optimization objective function is as follows:
Figure FDA0003752209530000048
s.t.x min <x n <x max ,y min <y n <y max ,z min <z n <z max ,n＝1,2,3,4…。
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