CN114205749A - Ultra-wideband iterative positioning algorithm and device suitable for through-wall scene - Google Patents

Ultra-wideband iterative positioning algorithm and device suitable for through-wall scene Download PDF

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CN114205749A
CN114205749A CN202111520329.7A CN202111520329A CN114205749A CN 114205749 A CN114205749 A CN 114205749A CN 202111520329 A CN202111520329 A CN 202111520329A CN 114205749 A CN114205749 A CN 114205749A
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董梦瑶
刘一鸣
王霞
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Southwest Jiaotong University
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    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H04W4/02—Services making use of location information
    • H04W4/021—Services related to particular areas, e.g. point of interest [POI] services, venue services or geofences
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    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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    • H04W4/33—Services specially adapted for particular environments, situations or purposes for indoor environments, e.g. buildings
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Abstract

The invention discloses an ultra-wideband iterative positioning algorithm suitable for a through-wall scene, which comprises the following steps: s1: estimating the initial position of the UWB tag by using a least square method based on at least 3 through-wall ranging values; s2: calculating a ranging error of each through-wall ranging value based on the initial position of the step S1 and each base station position, and correcting each through-wall ranging value; s3: based on each corrected through-wall distance measurement value, re-estimating the position of the UWB tag by using a least square method; s4: whether a stopping condition is reached is judged, and the current UWB tag estimation position is output after the stopping condition is reached, so that high-precision wall-through positioning is realized, and the method is used for overcoming the problem that the distance measurement error under the condition that a wall body is shielded is difficult to calculate when the distance measurement precision is improved in the indoor positioning and distance measurement process of the existing ultra-wideband technology.

Description

Ultra-wideband iterative positioning algorithm and device suitable for through-wall scene
Technical Field
The invention relates to the field of wireless electromagnetic wave propagation and indoor positioning, in particular to an ultra-wideband iterative positioning algorithm and device suitable for a through-wall scene.
Background
With the development of social economy and the continuous improvement of life quality of people, how to improve the distance measurement precision is an urgent problem to be solved in the practical application of various distance measurement technologies such as asset tracking, robot service, site inspection, autonomous navigation and environment-assisted life. Global Positioning Satellites (GPS) or beidou navigation systems are commonly used in outdoor environments to obtain precise location information of located objects. However, these high precision positioning systems fail in indoor environments because the signals propagate indoors and are susceptible to interference from various complex environments, resulting in low signal-to-noise ratios (SNRs) and multipath propagation effects. Accordingly, various indoor positioning technologies have been continuously developed to solve the indoor positioning problem, including Wi-Fi, bluetooth, RFID, Zigbee, and ultra wideband methods. Among them, the ultra-wideband technology is widely regarded and adopted because of its good spatial resolution and resistance to multipath errors.
However, the applicant finds that the existing ultra-wideband positioning technology has a large positioning error under the condition of wall penetration, and although the error can be effectively reduced by adopting a wall penetration error model algorithm, the wall penetration error model can only adapt to the condition that the positions of the UWB tag and the UWB base station are known. In the positioning scenario, although the position of the UWB base station is known, the position of the UWB tag is constantly changing and unknown. Therefore, the UWB through-wall ranging error in this case cannot be calculated.
Therefore, it is very important for the indoor positioning technology to research a positioning accuracy improving method of the ultra-wideband positioning technology under the wall-through condition.
Disclosure of Invention
The invention aims to provide an ultra-wideband iterative positioning algorithm and an ultra-wideband iterative positioning device suitable for a through-wall scene, which are used for overcoming the problem that the existing ultra-wideband technology is difficult to calculate the distance measurement error under the condition that a wall body is blocked when the distance measurement precision is improved in the indoor positioning and distance measurement process.
The invention is realized by the following technical scheme:
an ultra-wideband iterative positioning algorithm suitable for a through-wall scene comprises the following steps:
s1: estimating the initial position of the UWB tag by using a least square method based on at least 3 through-wall ranging values;
the UWB base station and UWB label of 1 continuous removal position, use the bilateral range finding method of UWB technique to carry out real-time range finding constantly between UWB base station and the UWB label in 3 at least fixed positions. However, if there is a wall occlusion between the UWB base station and the UWB tag, the ranging value at this time is inaccurate, including an error of the wall occlusion. In the first step of the method, the position of the UWB tag is directly calculated by using a least square method without considering wall shielding errors, and the specific method is as follows:
coordinates of three UWB base stations are A1, A2 and A3 respectively, and distances of the UWB tags measured by the three UWB base stations are D respectively1，D2And D3And coordinates (X, Y) of the UWB tag are to be measured. Calculating an observation value equation of each UWB base station by adopting the formula (3):
Figure BDA0003408433500000021
wherein v isiIs the error term of the ith base station, XiIs the abscissa value, Y, of the ith base station in spaceiIs the longitudinal coordinate value of the ith base station in space, X and Y are the coordinates to be measured of UWB tag, DiIs the distance value from the UWB tag measured by the ith base station.
Taylor expansion is carried out on the formula (3) to obtain a first-order term (power reduction), and a first-order equation is obtained:
Figure BDA0003408433500000022
wherein (X)0，Y0)TAnd (delta)x，δy)TRespectively, an approximation and a correction of the coordinates of the UWB tag.
Equation (4) is simplified to:
V＝AX+L (5)
wherein the content of the first and second substances,
Figure BDA0003408433500000023
X＝(δx，δy)T。
solving the unknowns using least squares adjustment according to:
X＝-(ATA)-1(ATL) (6)
obtaining a corrected coordinate (delta) of the UWB tagx，δy)T。
S2: calculating a ranging error of each through-wall ranging value based on the initial position of the step S1 and each base station position, and correcting each through-wall ranging value;
s3: based on each corrected through-wall distance measurement value, re-estimating the position of the UWB tag by using a least square method;
and (3) correcting each through-wall distance measurement value according to the formula (7):
Figure BDA0003408433500000024
wherein the content of the first and second substances,
Figure BDA0003408433500000025
is the m-th corrected through-wall distance measurement value,
Figure BDA0003408433500000026
is the m-th through-wall distance measurement value, emIs the range error value calculated according to step S2.
S4: judging whether a stopping condition is reached or not, and outputting the current UWB tag estimation position after the stopping condition is reached so as to realize high-precision wall-through positioning; the method is used for solving the problem that the existing ultra-wideband technology is difficult to calculate the ranging error under the condition that the wall body is shielded when the ranging precision is improved in the indoor positioning ranging process.
Further, estimating the position of the UWB tag using the least square method in step S1 includes a preliminary estimated position of the wall occlusion error. Based on the initial position, the through-wall distance measurement error of the current position of the base station and the label can be solved, an initial value is provided for the next iteration of the algorithm, the effect of eliminating the through-wall positioning error is finally achieved by the algorithm, if the initial position does not exist, the through-wall distance measurement error model cannot be applied to calculate the through-wall distance measurement error, and then the subsequent steps cannot be carried out.
Further, step S2 includes the following sub-steps:
s21: when only one wall and normal incidence between UWB basic station and UWB label, adopt (1) formula calculation range finding error:
Figure BDA0003408433500000031
where e is the distance measurement error, w is the wall thickness, εrThe relative dielectric constant of the wall body, and theta is an included angle between a connection line of the UWB base station and the UWB tag and the wall body. The formula provides a distance measurement error for formula (7), and finally the algorithm achieves the effect of eliminating the through-wall positioning error.
Further, step S2 includes the following sub-steps:
s22: when a wall exists between the UWB base station and the UWB tag and the wall is not vertically incident, the distance measurement error is calculated by adopting the formula (2):
Figure BDA0003408433500000032
where e is the distance measurement error, w is the wall thickness, εrIs the relative dielectric constant of the wall, beta is the angle of refraction, dABIs the linear distance between the UWB base station and the point of incidence, dCDIs the linear distance between the point of departure and the UWB tag, dADIs the straight-line distance between the UWB base station and the UWB tag. The formula provides a distance measurement error for formula (7), and finally the algorithm achieves the effect of eliminating the through-wall positioning error.
Further, two stop conditions are included:
the first condition is that the Euclidean distance between the location of the kth position and the location of the (k-1) th position is less than 1 cm;
the second condition is when the loop iteration condition is greater than 5 times.
And if the two conditions are met, the iterative positioning algorithm is stopped. When the tag position calculated by the positioning algorithm is very close to the real position of the tag (e.g. less than 1 cm), the result of running the positioning algorithm again will be similar to the previous result, so that it is not necessary to iterate again, which is the first stop condition. In order to prevent the number of iterations from being too large, which leads to a reduction in the calculation speed, the patent defines the maximum number of iterations as 5. When the number of iterations is greater than 5, the positioning algorithm stops the iterations, which is the second stop condition. Based on the two stopping conditions, the through-wall iterative positioning algorithm provided by the patent has the iteration stopping conditions, and finally the through-wall iterative positioning algorithm achieves the effect of eliminating through-wall positioning errors.
Further, the following components are also included: the device comprises a preliminary estimation component, a ranging error correction component, a position re-estimation component, a condition judgment component and an output estimation position component, wherein the preliminary estimation component is used for estimating the initial position of the UWB tag, the ranging error correction component is used for calculating the ranging error of each through-wall ranging value through the initial position of the UWB tag and each base station position, and corrects each through-wall ranging value: a re-estimate location component for re-estimating the UWB tag location with each modified through-wall ranging value; the condition judging component is used for judging whether a stopping condition is reached or not; the output estimated position component is used for outputting the current estimated position of the UWB tag after reaching the stop condition. The positioning device comprising the components can eliminate the negative influence of wall shielding on ultra-wideband positioning, so that the positioning precision of the ultra-wideband positioning system can reach the level when no wall is shielded.
Compared with the prior art, the invention has the following advantages and beneficial effects:
according to the scheme, the UWB tag initial position is estimated through a least square method, the ranging error of each through-wall ranging value is calculated by the UWB initial position and each base station position, each through-wall ranging value is corrected, based on each through-wall ranging value after correction, the UWB tag position is re-estimated through the least square method, whether a stop condition is reached is judged, and the current UWB tag estimation position is output after the stop condition is reached, so that high-precision through-wall positioning is achieved, and the problem that the ranging error under the condition that a wall body is shielded in the indoor positioning ranging process in the existing ultra-wideband technology is difficult to calculate is solved.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is a flow chart of the algorithm calculation of the present invention;
FIG. 2 is a schematic illustration of a UWB through-wall positioning;
FIG. 3 is a diagram of a first simulation scenario of the present invention;
FIG. 4 is a diagram of a second simulation scenario of the present invention;
FIG. 5 is a schematic diagram of a third simulation scenario of the present invention;
FIG. 6 is a graph of the cumulative error distribution for different algorithms (including the algorithm of the present invention) in locating scene 1;
FIG. 7 is a graph of the cumulative error distribution for different algorithms (including the algorithm of the present invention) in localization scenario 2;
fig. 8 is a graph of the cumulative error distribution in localization scenario 3 for different algorithms, including the algorithm of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not meant to limit the present invention.
Example 1:
as shown in fig. 1, the present invention comprises the steps of:
s1: estimating the initial position of the UWB tag by using a least square method based on at least 3 through-wall ranging values;
the UWB base station and UWB label of 1 continuous removal position, use the bilateral range finding method of UWB technique to carry out real-time range finding constantly between UWB base station and the UWB label in 3 at least fixed positions. However, if there is a wall occlusion between the UWB base station and the UWB tag, the ranging value at this time is inaccurate, including an error of the wall occlusion. In the first step of the method, the position of the UWB tag is directly calculated by using a least square method without considering wall shielding errors, and the specific method is as follows:
coordinates of three UWB base stations are A1, A2 and A3 respectively, and distances of the UWB tags measured by the three UWB base stations are D respectively1，D2And D3And coordinates (X, Y) of the UWB tag are to be measured. Calculating an observation value equation of each UWB base station by adopting the formula (3):
Figure BDA0003408433500000051
wherein v isiIs the error term of the ith base station, XiIs the abscissa value, Y, of the ith base station in spaceiIs the longitudinal coordinate value of the ith base station in space, X and Y are the coordinates to be measured of UWB tag, DiIs the distance value from the UWB tag measured by the ith base station.
Taylor expansion is carried out on the formula (3) to obtain a first-order term (power reduction), and a first-order equation is obtained:
Figure BDA0003408433500000052
wherein (X)0，Y0)TAnd (delta)x，δy)TRespectively, an approximation and a correction of the coordinates of the UWB tag.
Equation (4) is simplified to:
V＝AX+L (5)
wherein the content of the first and second substances,
Figure BDA0003408433500000053
X＝(δx，δy)T。
solving the unknowns using least squares adjustment according to:
X＝-(ATA)-1(ATL) (6)
obtaining a corrected coordinate (delta) of the UWB tagx，δy)T。
S2: calculating a ranging error of each through-wall ranging value based on the initial position of the step S1 and each base station position, and correcting each through-wall ranging value;
the step S2 further includes the following sub-steps:
s21: when only one wall and normal incidence between UWB basic station and UWB label, adopt (1) formula calculation range finding error:
Figure BDA0003408433500000061
where e is the distance measurement error, w is the wall thickness, εrThe relative dielectric constant of the wall body, and theta is an included angle between a connection line of the UWB base station and the UWB tag and the wall body.
The step S2 further includes the following sub-steps:
s22: when a wall exists between the UWB base station and the UWB tag and the wall is not vertically incident, the distance measurement error is calculated by adopting the formula (2):
Figure BDA0003408433500000062
where e is the distance measurement error, w is the wall thickness, εrIs the relative dielectric constant of the wall, beta is the angle of refraction, dABIs the linear distance between the UWB base station and the point of incidence, dCDIs the linear distance between the point of departure and the UWB tag, dADIs the straight-line distance between the UWB base station and the UWB tag.
S3: based on each corrected through-wall distance measurement value, re-estimating the position of the UWB tag by using a least square method;
and (3) correcting each through-wall distance measurement value according to the formula (7):
Figure BDA0003408433500000063
wherein the content of the first and second substances,
Figure BDA0003408433500000064
is the m-th corrected through-wall distance measurement value，
Figure BDA0003408433500000065
Is the m-th through-wall distance measurement value, emIs the range error value calculated according to step S2.
S4: judging whether a stopping condition is reached or not, and outputting the current UWB tag estimation position after the stopping condition is reached so as to realize high-precision wall-through positioning; estimating the position of the UWB tag using the least squares method in step S1 includes a preliminary estimated position of the wall occlusion error. Two stop conditions are included: the first condition is that the Euclidean distance between the location of the kth position and the location of the (k-1) th position is less than 1 cm; the second condition is when the loop iteration condition is greater than 5 times.
Example 2:
example 2 is based on example 1:
as shown in fig. 2, in a common UWB indoor positioning system, there are often at least 3 UWB base stations at fixed positions and 1 UWB tag at a constantly moving position. And the UWB base station and the UWB tag continuously carry out real-time ranging by using a bilateral ranging method of a UWB technology. However, if there is a wall occlusion between the UWB base station and the UWB tag, the ranging value at this time is inaccurate, including an error of the wall occlusion.
As shown in fig. 3, 4 and 5, the present invention considers three scenarios: scene 1, scene 2 and scene 3 represent common wall occlusion cases in indoor positioning. There are three ultra-wideband base stations of known location and one ultra-wideband mobile tag in each scene. The size of each room is 7 by 6 square meters, according to the uniform distribution of each wall
Figure BDA0003408433500000072
And
Figure BDA0003408433500000073
the wall thickness and the relative dielectric constant of the wall are randomly generated, which is the real range of the wall thickness and the relative dielectric constant of the wall. Table 1 gives the simulation configuration.
TABLE 1 simulation configuration parameters
Figure BDA0003408433500000071
Here, the inventors evaluated the positioning performance using the positioning error. And respectively adopting the algorithm of the invention, the original trilateral localization algorithm, the through-wall error model 1 algorithm, the through-wall error model 2 algorithm, the through-wall error model 3 algorithm and the reference measurement algorithm to carry out comparison experiments in the same scene 1, scene 2 and scene 3, and the following need to be explained: the complexity of scenes 1 to 3 gradually increases.
The statistical data of the positioning errors are shown in table 2, and fig. 6, fig. 7 and fig. 8 are respectively error accumulation distribution graphs of different algorithms in three positioning scenes. As can be seen from table 2 and fig. 6, fig. 7 and fig. 8, the mean, standard deviation and RMSE of the proposed algorithm are minimal compared to other methods. The performance of the algorithm provided by the invention in the scene 1 is obviously superior to that of the trilateration algorithm and the model 1 algorithm, and is slightly superior to that of the model 2 algorithm. For the scene 2 and the scene 3, the method provided by the invention has obvious advantages compared with the trilateration algorithm, the model 1 algorithm and the model 2 algorithm. The RMSE of the trilateration algorithm was 73.10cm, 153.99cm, and 152.39cm for scene 1, scene 2, and scene 3, respectively. The RMSE of the proposed algorithm in each scene is significantly reduced to 21.79cm, 25.83cm and 29.40cm, respectively, close to the baseline algorithm. Experimental results show that the method is effective in improving the positioning performance under the non-line-of-sight condition.
TABLE 2 statistical results of positioning errors
Figure BDA0003408433500000081
Furthermore, in terms of computational complexity, the present invention uses time consumption to evaluate the computational complexity of different algorithms. It is noted that due to the different positions of UWB tags, the time consumption of each position estimation may be different even for the same algorithm. Thus, the present invention compares the average time consumption of different algorithms for all study locations. The average time consumption for the trilateration algorithm, model 1 and model 2 algorithms are all 0.001s, whereas the average time consumption for the algorithm herein is 0.003 s. Although the algorithm proposed by the present invention is more complex than other algorithms, the time consumption is acceptable. To improve the computational efficiency, the algorithm of model 3 can be used in a scene that only wears one wall, because the proposed algorithm of the present invention has similar localization performance to the model 3 algorithm, and the time complexity of model 3 is slightly less than the algorithm of the present invention.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (6)

1. An ultra-wideband iterative positioning algorithm suitable for a through-wall scene is characterized by comprising the following steps:
s1: estimating the initial position of the UWB tag by using a least square method based on at least 3 through-wall ranging values;
s2: calculating a ranging error of each through-wall ranging value based on the initial position of the step S1 and each base station position, and correcting each through-wall ranging value;
s3: based on each corrected through-wall distance measurement value, re-estimating the position of the UWB tag by using a least square method;
s4: and judging whether a stopping condition is reached or not, and outputting the current UWB tag estimation position after the stopping condition is reached so as to realize high-precision wall-through positioning.
2. The ultra-wideband iterative location algorithm for through-wall scenes as claimed in claim 1, wherein the estimation of the position of the UWB tag in step S1 using the least square method comprises a preliminary estimation of the position of the wall occlusion error.
3. The ultra-wideband iterative location algorithm for through-wall scenes as claimed in claim 1, further comprising the following sub-steps in step S2:
s21: when only one wall and normal incidence between UWB basic station and UWB label, adopt (1) formula calculation range finding error:
Figure FDA0003408433490000011
where e is the distance measurement error, w is the wall thickness, εrThe relative dielectric constant of the wall body, and theta is an included angle between a connection line of the UWB base station and the UWB tag and the wall body.
4. The ultra-wideband iterative location algorithm for through-wall scenes as claimed in claim 1, further comprising the following sub-steps in step S2:
s22: when a wall exists between the UWB base station and the UWB tag and the wall is not vertically incident, the distance measurement error is calculated by adopting the formula (2):
Figure FDA0003408433490000012
where e is the distance measurement error, w is the wall thickness, εrIs the relative dielectric constant of the wall, beta is the angle of refraction, dABIs the linear distance between the UWB base station and the point of incidence, dCDIs the linear distance between the point of departure and the UWB tag, dADIs the straight-line distance between the UWB base station and the UWB tag.
5. The ultra-wideband iterative location algorithm for through-wall scenes as claimed in claim 1, wherein two stop conditions are included:
the first condition is that the Euclidean distance between the location of the kth position and the location of the (k-1) th position is less than 1 cm;
the second condition is when the loop iteration condition is greater than 5 times.
6. The device for the ultra-wideband iterative positioning algorithm of the through-wall scene according to any one of the claims 1 to 5, characterized by comprising the following components: the device comprises a preliminary estimation component, a ranging error correction component, a position re-estimation component, a condition judgment component and an output estimation position component, wherein the preliminary estimation component is used for estimating the initial position of the UWB tag, the ranging error correction component is used for calculating the ranging error of each through-wall ranging value through the initial position of the UWB tag and each base station position, and corrects each through-wall ranging value: a re-estimate location component for re-estimating the UWB tag location with each modified through-wall ranging value; the condition judging component is used for judging whether a stopping condition is reached or not; the output estimated position component is used for outputting the current estimated position of the UWB tag after reaching the stop condition.
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