CN113794983A - Multi-target indoor positioning method based on nonlinear geometric constraint optimization - Google Patents

Multi-target indoor positioning method based on nonlinear geometric constraint optimization Download PDF

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CN113794983A
CN113794983A CN202110997005.6A CN202110997005A CN113794983A CN 113794983 A CN113794983 A CN 113794983A CN 202110997005 A CN202110997005 A CN 202110997005A CN 113794983 A CN113794983 A CN 113794983A
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positioning
optimization problem
optimization
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geometric constraint
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CN113794983B (en
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俞成浦
夏吟秋
何澄洋
陈杰
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Beijing Institute of Technology BIT
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
    • H04W4/02—Services making use of location information
    • H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
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    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • H—ELECTRICITY
    • 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
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    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
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Abstract

The invention discloses a multi-target indoor positioning method based on nonlinear geometric constraint optimization, which is characterized in that a plurality of labels to be positioned are arranged on the same object to be positioned to obtain accurate prior information about an intelligent agent, and the information is used as the constraint of an optimization problem by means of introduced accurate redundant information, so that the positioning precision of the intelligent agent under the condition of ranging noise of a positioning system is improved.

Description

Multi-target indoor positioning method based on nonlinear geometric constraint optimization
Technical Field
The invention belongs to the technical field of wireless sensor positioning, and particularly relates to a multi-target indoor positioning method based on nonlinear geometric constraint optimization.
Background
The positioning technology is one of important embodiments of intellectualization and one of visual expressions of whether the robot is intelligent, and plays a role which is not negligible in an intelligent robot system, an Internet of things technology and an intelligent industrial system. The quick and accurate positioning is the basis and precondition of an intelligent system, and various intelligent systems can make efficient decisions to complete specific tasks only by mastering the real-time accurate positions of the intelligent systems. Moreover, most intelligent systems are mainly applied to indoor occasions such as home services, factory logistics, business services and the like. Different open outdoor environment, the area is less under the indoor environment, and has structuralized environments such as corridor, passageway, and so on, this has just led to indoor positioning system to have the higher requirement than outdoor location in the aspect of the precision. At present, the most widely used positioning system is a Global Positioning System (GPS), but the positioning accuracy of a common GPS is difficult to meet the requirement of an indoor scene. In addition, the indoor environment has difficulty receiving GPS signals due to physical limitations of the GPS signals. Therefore, high-precision indoor positioning technology for intelligent systems becomes one of the hot problems under current research.
The ultra-wideband signal solves the problems of insensitivity after channel decay and low power spectral density of a transmitted signal in a plurality of radio technologies, and meets the requirements of people on high-speed and short-distance wireless communication. Meanwhile, due to the unique modulation mode and the multiple access technology of the ultra-wideband technology, the UWB signal has a series of advantages of a concealed number, strong anti-multipath effect, strong anti-narrowband interference capability, high transmission rate, large system capacity, strong penetration capability, low power consumption, low system complexity and the like, and can fully utilize frequency spectrum resources, thereby well solving the problem of crowded frequency spectrum resources. Another great advantage of UWB devices is that they have a low average transmit power, and therefore UWB indoor positioning systems do not interfere with other wireless communication systems when operating, which is significant for indoor environments. Through research and characteristic analysis on the ultra-wideband technology, the ultra-wideband technology has irreplaceable advantages compared with other technologies when being used for indoor positioning, and is particularly suitable for indoor high-precision positioning. When UWB technology is used for indoor positioning, a ranging-based positioning algorithm is generally used. Current ranging lateral methods include time of flight signal (TOA) based, time difference of arrival (TDOA) based, angle of arrival location (AOA) based, and received signal strength location (RSS) based.
At present, no matter which positioning-based scheme is adopted, most of the schemes use the position information of an anchor point and the ranging information between the anchor point and a label to calculate the ranging information of the label. However, for co-location of multi-agent systems, this approach can result in much of the known a priori information being lost and wasted. Such as the distance between agents, the height of the agents, and locations where their presence is not possible, etc. If this unutilized accurate information can be added to the positioning process, a higher positioning accuracy and a stronger interference rejection capability can be obtained.
Disclosure of Invention
In view of this, the invention provides a multi-target indoor positioning method based on nonlinear geometric constraint optimization, which can obtain the accurate position of a target according to the geometric structure formed between tags.
The invention provides a multi-target indoor positioning method based on nonlinear geometric constraint optimization, which comprises the following steps:
setting a plurality of labels on a target to be positioned, and converting the positioning problem of the labels into an optimization problem with nonlinear geometric constraint; calculating the initial position of each label, wherein the initial position is used as the initial value of the optimization problem; and solving the optimization problem according to the initial value to obtain the determined position of each label, and positioning the target according to the determined position.
Further, the method also comprises the following formula is adopted to convert the positioning problem of the single label into an optimization problem to be solved:
Figure BDA0003234455790000031
wherein the content of the first and second substances,
Figure BDA0003234455790000035
j is the number of the anchor point, j is more than or equal to 1 and less than or equal to m, and m is the number of the anchor points;
Figure BDA0003234455790000036
i is the number of the labels, n is the number of the labels, and i is more than or equal to 1 and less than or equal to n;
Figure BDA0003234455790000037
the values of (A) are as follows:
Figure BDA0003234455790000032
in the formula (I), the compound is shown in the specification,
Figure BDA0003234455790000038
representing ranging values for the anchor and tag.
Further, the converting the positioning problem of the plurality of labels into the optimization problem with the nonlinear geometric constraint specifically includes the following steps:
when a fixed shape is formed between the plurality of labels, p is given to the labeliAnd plInformation of distance between
Figure BDA0003234455790000039
Wherein l is the number of the label, and l is more than or equal to 1 and less than or equal to n, the optimization problem with the nonlinear geometric constraint is shown as the following formula:
Figure BDA0003234455790000033
Figure BDA0003234455790000034
wherein e is a constant.
Further, the process of calculating the initial position of each tag is calculated by using a least square algorithm.
Further, the process of solving the optimization problem according to the initial values to obtain the determined positions of the labels is to solve by using a sequential quadratic programming algorithm.
Has the advantages that:
1. according to the invention, a plurality of labels to be positioned are arranged on the same object to be positioned, so that accurate prior information about the intelligent agent is obtained, and the information is used as the constraint of an optimization problem by means of introduced accurate redundant information, so that the positioning accuracy of the intelligent agent under the condition of ranging noise of a positioning system is improved.
2. The invention solves by adopting the least square algorithm based on the distance function, respectively calculates the rough positions of the labels under the condition of no constraint, provides relatively accurate initial coordinates for the optimization algorithm, and can improve the convergence speed of the optimization algorithm by the method.
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Fig. 1 is a schematic diagram of an application scenario of a multi-objective indoor positioning method based on nonlinear geometric constraint optimization according to the present invention.
FIG. 2 is a flowchart of a multi-objective indoor positioning method based on nonlinear geometric constraint optimization according to the present invention.
FIG. 3 is a positioning error analysis diagram of an experiment of the nonlinear geometric constraint optimization-based multi-target indoor positioning method under a 20cm ranging error.
FIG. 4 is a positioning error analysis diagram of an experiment of the nonlinear geometric constraint optimization-based multi-target indoor positioning method under different ranging errors of 5-25 cm.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a multi-target indoor positioning method based on nonlinear geometric constraint optimization, which has the core idea that: the method is characterized in that the characteristics of a structure formed by multiple intelligent agents are utilized, the number of labels is increased, accurate prior redundant information is used as nonlinear constraint and is introduced into a positioning algorithm, the positioning problem is abstracted into an optimization problem with nonlinear constraint, and then the optimization problem is solved so as to realize positioning with higher precision and stronger robustness.
The invention provides a multi-target indoor positioning method based on nonlinear geometric constraint optimization, which specifically comprises the following steps:
step 1, converting the positioning problem of a single label into an optimization problem.
Given a finite number of tags to be located, these tags to be located form a fixed-shape structure on a multi-agent systemWherein each tag piAnchor point a capable of being fixed with positionjAnd (6) ranging. The tags do not have communication and ranging capabilities, but the geometric shapes among the tags are used as prior information, namely, the tag p is assumediAnd plInformation of distance between
Figure BDA0003234455790000055
(i, l 1, 2.. n), i 1, 2.. n is known information, and is expressed by using the following formula:
Figure BDA0003234455790000056
in the present invention, it is considered that
Figure BDA0003234455790000057
Is accurate information that no error exists. In addition to this, anchor point coordinates
Figure BDA0003234455790000051
j 1, 2, m is also considered to be calibrated and accurate information. The main source of error is ranging between anchor and tag
Figure BDA0003234455790000058
The distance information is obtained through bilateral two-way flight ranging of UWB signals, and generally, an unequal error of 10-20 cm can be generated under the condition of line of sight.
Thus, the assumed known information in the present invention is the anchor coordinates ajRanging between tag and anchor point
Figure BDA0003234455790000059
And prior distance information between tags
Figure BDA00032344557900000510
Anchor point ajAnd a label piThe distance between
Figure BDA00032344557900000511
Calculated using the following formula:
Figure BDA00032344557900000512
then, any label
Figure BDA00032344557900000513
The range from all anchor points can be given by equation (3):
Figure BDA0003234455790000052
it is expanded and reduced to formula (4):
Figure BDA0003234455790000053
wherein
Figure BDA00032344557900000514
The value of (a) is shown in formula (5):
Figure BDA0003234455790000054
the rest values are analogized in turn.
At this time, it is found from the above equation that the positioning problem can be described as finding a state value that makes the above equation true in the absence of a ranging error
Figure BDA0003234455790000063
However, certain errors inevitably occur in the actual engineering. Thus, when there is only one tag to be located, then the above problem can be expressed as an optimization problem as follows:
Figure BDA0003234455790000061
step 2, arranging a plurality of labels on the intelligent agent for describing the geometric constraint of the intelligent agent, and then converting the positioning problem of the plurality of labels into an optimization problem with nonlinear geometric constraint;
when multiple tags are under the constraint of a fixed shape, accurate positioning of the multiple tags can be achieved by adding nonlinear constraints among the tags, an optimization problem with nonlinear geometric constraints can be described as follows:
Figure BDA0003234455790000062
wherein i and l both represent the number of the label, and the numeric area is [1, n ]; j 1.. m denotes the anchor point number, and e is a small constant to avoid divergence due to computer-generated rounding errors. It can be seen that the planning problem is an optimization problem in which both the objective function and the constraint condition include nonlinear functions.
And 3, calculating the positions of the labels by using a least square algorithm, and taking the positions as initial values of the optimization problem, so that the calculation amount of the optimization algorithm is reduced, and the calculation speed is increased.
However, solving the optimization problem directly results in a large amount of computation, so the present invention considers that a coarse positioning result is solved as an initial value by using a least square method. The specific scheme is as follows:
for tag piAccording to it and anchor point ajDistance function of
Figure BDA0003234455790000064
The expanded and simplified form of (a), which is written as a matrix form:
Figure BDA0003234455790000071
the above formula may be abbreviated as APi＝GiWherein
Figure BDA0003234455790000074
Euclidean coordinates representing the label pi;
Figure BDA0003234455790000072
i is 1, 2, …, n. The least squares form of this equation is expressed as:
Figure BDA0003234455790000073
the optimal solution can be expressed as:
Pi＝(ATA)-1ATGi (10)
will solve the label p separately1，...，pnCoordinates of (2)
Figure BDA0003234455790000075
And i is 1, 2, …, n is used as an initial value of the optimization algorithm to reduce the calculation amount of the optimization algorithm and improve the overall performance of the algorithm.
And 4, solving the optimization problem of the nonlinear geometric constraint formed in the step 3 by utilizing an SQP algorithm.
At present, a common idea is to combine an objective function with a constraint condition to construct an augmented objective function, and further convert the optimization problem into an unconstrained optimization problem. The SQP (sequential quadratic programming) algorithm is one of the widely accepted schemes for solving the nonlinear constraint optimization problem at present, and the core idea is to convert the optimization problem with complex nonlinear constraints into a quadratic programming problem for solving. The quadratic programming problem refers to an optimization problem that an objective function is a quadratic function and a constraint is a linear function. The above optimization problem can be abbreviated as follows:
min f(X) (11)
s.t.gu(X)≤0(u＝1，2，…，p)
hv(X)＝0(v＝1，2，…，m)
iterating the objective function of the nonlinear constraint optimization problem in k stepsCalculated value XkThe method using taylor expansion is simplified to a quadratic function and the nonlinear constraint function is treated in the same way as a linear function. Let S be X-XkThe above problem can be translated into:
Figure BDA0003234455790000081
Figure BDA0003234455790000082
Figure BDA0003234455790000083
Figure BDA0003234455790000084
Figure BDA0003234455790000085
Figure BDA0003234455790000086
Figure BDA0003234455790000087
Beq＝[h1(Xk)，h2(Xk)，…，hm(Xk)]T
B＝[g1(Xk)，g2(Xk)，…，gm(Xk)]T
further, the optimization problem can be converted into a general form of a quadratic programming problem:
Figure BDA0003234455790000088
s.t.AkS≤-Bk
Figure BDA0003234455790000089
solving the quadratic programming problem, firstly according to the Lagrangian function of the quadratic programming problem:
Figure BDA00032344557900000810
extreme condition of the sum multivariate function
Figure BDA00032344557900000811
The following can be obtained:
Figure BDA00032344557900000812
the unique solution of the equation can be easily solved by using the elimination transformation, and is recorded as [ S ]k+1，λk+1]T. According to the KKT condition, if the multiplier vectors in the solution are not all 0, Sk+1Is the optimal solution of the quadratic programming problem.
The next search direction S with its best solution as the original problemk+1And performing constrained one-dimensional search of the original constrained problem objective function in the direction to obtain an approximate solution X of the original constrained problemk+1. By repeating the process, the optimal solution of the original problem can be obtained.
Example 1:
in the embodiment, the nonlinear geometric constraint optimization-based multi-target indoor positioning method provided by the invention is adopted to realize the positioning of a group of unmanned mobile platforms in formation in an intelligent parking lot, and the application scene is shown in fig. 1.
UWB tags are typically provided on each platform separately to determine the unmanned vehicle location. However, in the actual positioning process, due to errors in the ranging process, the positioning result may be inaccurate. Therefore, adding distance information between different agents in a multi-agent formation to a positioning algorithm as redundant information is a viable solution. In addition, more accurate positioning results can be obtained by taking the accurate distance and the height between the labels as prior information. In this embodiment, a multi-objective indoor positioning method based on nonlinear geometric constraint optimization is specifically disclosed. As shown in fig. 2, the positioning method includes:
first, setting a given anchor position as (unit: m):
a1(0，0，1)、a2(10，0，1)、a3(10，10，1)、a4(0，10，2)
we consider the values of these given anchor coordinates to be true values. Assuming that the size of the topology formed by the four unmanned mobile platforms is 0.5m × 0.5m, four tags are respectively arranged on each unmanned vehicle, and the distance between them is (unit: m):
Figure BDA0003234455790000091
Figure BDA0003234455790000092
in addition to this, the height of the unmanned platform can also be obtained in advance, i.e. the height of the tag is (unit: m):
h1＝0.3、h2＝0.3、h3＝0.3、h4＝0.3
the accurate distance information can be used as redundant information in the algorithm, and the accuracy of the positioning algorithm can be improved by adding the information into the positioning algorithm. For arbitrary labels
Figure BDA0003234455790000095
It and any anchor point
Figure BDA0003234455790000093
The distance between
Figure BDA0003234455790000096
Can be described as:
Figure BDA0003234455790000094
a total of 16 pairs of ranging information are available, and the above equation is expanded and simplified to yield:
Figure BDA0003234455790000101
wherein
Figure BDA0003234455790000107
Can be expressed as:
Figure BDA0003234455790000102
since the part with errors is introduced when ranging the UWB anchor point and the tag, i.e.
Figure BDA0003234455790000108
Not the exact distance information, so the positioning problem can be described as an optimization problem, finding the appropriate tag location coordinates
Figure BDA0003234455790000109
The following loss function is minimized:
Figure BDA0003234455790000103
because there are four labels to be positioned, the accurate distance information between the labels is introduced as nonlinear constraint, and the height information is introduced as linear constraint, the optimization problem can be described as the following form:
Figure BDA0003234455790000104
Figure BDA00032344557900001010
Figure BDA00032344557900001011
excessive equality constraints may cause the optimization problem to diverge due to computer generated rounding errors, so consideration is given to converting part of the constraints of the optimization problem into inequality constraints as follows:
Figure BDA0003234455790000105
Figure BDA0003234455790000106
Figure BDA00032344557900001012
the problem can now be abbreviated and expressed as:
min f(X)
s.t.gu(X)≤0(u＝1，2，…，6)
hv(X)＝0(v＝1，2，3，4)
before solving the optimization problem, the initial positioning value is solved first. Solving the optimization problem directly results in a large amount of computation, so the invention considers that a rough positioning result is solved as an initial value by using a least square method. The specific scheme is as follows:
for tag p1、p2、p3、p4According to it and anchor point a1、a2、a3、a4Distance function of
Figure BDA0003234455790000114
i, j is an expanded and simplified form of 1, 2, 3, 4, which is written in matrix form as:
Figure BDA0003234455790000111
the above formula may be abbreviated as APi＝GiWherein
Figure BDA0003234455790000115
Representing a label piEuclidean coordinates of (a);
Figure BDA0003234455790000116
i is 1, 2, 3, 4. The least squares form of this equation can be expressed as:
Figure BDA0003234455790000112
Figure BDA0003234455790000113
the optimal solution can be expressed as:
Pi＝(ATA)-1ATGi
respectively solve the label p1，...，p4Coordinates of (2)
Figure BDA0003234455790000117
And i is 1, 2, 3 and 4 as an initial value of the optimization algorithm, so that the calculation amount of the optimization algorithm is reduced, and the overall performance of the algorithm is improved.
To sum up, the result is taken as the initial value of the optimization problem, namely:
Figure BDA0003234455790000118
solving the optimization problem by using SQP algorithm, and setting the objective function of the nonlinear constraint optimization problem at XkThe process is simplified to a quadratic function using taylor expansion and the nonlinear constraint function is treated in the same way as a linear function. Let S be X-XkThe above problem can be translated into:
Figure BDA0003234455790000121
Figure BDA0003234455790000122
Figure BDA0003234455790000123
get
Figure BDA0003234455790000124
Figure BDA0003234455790000125
Figure BDA0003234455790000126
Figure BDA0003234455790000127
Beq＝[h1(Xk)，h2(Xk)，…，hm(Xk)]T
B＝[g1(Xk)，g2(Xk)，…，gm(Xk)]T
Further, the optimization problem can be converted into a general form of a quadratic programming problem,
Figure BDA0003234455790000128
s.t.AkS≤-Bk
Figure BDA0003234455790000129
solving the quadratic programming problem, firstly, according to the Lagrange function of the quadratic programming problem
Figure BDA00032344557900001210
Extreme condition of the sum multivariate function
Figure BDA00032344557900001211
The following can be obtained:
Figure BDA00032344557900001212
the unique solution of the equation can be easily solved by using the elimination transformation, and is recorded as [ S ]k+1，λk+1]T. According to the K-T condition, if the multiplier vectors in the solution are not all 0, Sk+1Optimal solution S for quadratic programming problem*。
Solve it optimally S*Next search direction S as original problemkAnd performing constrained one-dimensional search of the original constrained problem objective function in the direction to obtain an approximate solution X of the original constrained problemk+1. By repeating the process, the optimal solution of the original problem can be obtained.
Based on the positioning method, the accuracy degree of the multi-target indoor positioning method based on nonlinear geometric constraint optimization is verified as follows:
the real coordinates of the node to be positioned selected in this example are as follows (unit: m):
p1，r(2，2，0.3)、p2，r(2.5，2，0.3)、p3，r(2.5，2.5，0.3)、p4，r(2，2.5，0.3)
directly using coordinates of the true position of the tag
Figure BDA0003234455790000132
And the location coordinates
Figure BDA0003234455790000133
The distance therebetween represents the absolute error of the distance E:
Figure BDA0003234455790000131
the numerical example carries out a plurality of groups of experiments, and the effectiveness of the method provided by the invention in an actual scene is observed by setting an error with a standard deviation of 20cm in a distance measurement stage.
Fig. 3 is a comparison of the error of the positioning result of the method proposed in this example using a common least squares algorithm with a standard deviation of the range error of 20 cm. It can be seen that, under the condition that the distance measurement errors are the same, the positioning error generated by the optimal positioning method based on the geometric non-linear constraint provided by the example is smaller than the positioning error generated by the least square method, which indicates that the overall performance of the scheme provided by the invention is better than that of the least square method.
FIG. 4 shows the comparison of the final positioning error of the method of the present invention with the positioning error of the least square algorithm under the same ranging error, respectively, in the range of 5-25 cm. It can be seen that the least square method positioning error increases significantly with the increase of the ranging error; although the positioning error fluctuates along with the increase of the error, the method is still smaller than the positioning error generated by the least square method in general. The multi-objective indoor positioning method based on nonlinear geometric constraint optimization adopted by the embodiment has stronger immunity and robustness.
Simulation can show that compared with a common positioning scheme in the market, the nonlinear geometric constraint optimization-based multi-target indoor positioning method provided by the embodiment can realize positioning effects with higher precision and stronger robustness by increasing the number of labels under the constraint of the geometric shape of an intelligent agent; meanwhile, the shape of the intelligent agent can be described through the topology formed by the plurality of tags, so that the intelligent agent can be accurately controlled and decision can be made in a complex environment.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A multi-objective indoor positioning method based on nonlinear geometric constraint optimization is characterized by comprising the following steps:
setting a plurality of labels on a target to be positioned, and converting the positioning problem of the labels into an optimization problem with nonlinear geometric constraint; calculating the initial position of each label, wherein the initial position is used as the initial value of the optimization problem; and solving the optimization problem according to the initial value to obtain the determined position of each label, and positioning the target according to the determined position.
2. The method of claim 1, further comprising solving the positioning problem of the single label by converting it into an optimization problem using the following formula:
Figure FDA0003234455780000011
wherein the content of the first and second substances,
Figure FDA0003234455780000012
j is the number of the anchor point, j is more than or equal to 1 and less than or equal to m, and m is the number of the anchor points;
Figure FDA0003234455780000013
i is the number of the labels, n is the number of the labels, and i is more than or equal to 1 and less than or equal to n;
Figure FDA0003234455780000018
the values of (A) are as follows:
Figure FDA0003234455780000014
in the formula (I), the compound is shown in the specification,
Figure FDA0003234455780000019
representing ranging values for the anchor and tag.
3. The method according to claim 2, wherein the converting of the positioning problem of the plurality of labels into the optimization problem with the non-linear geometric constraint comprises the following steps:
when a fixed shape is formed between the plurality of labels, p is given to the labeliAnd plInformation of distance between
Figure FDA0003234455780000017
Wherein l is the number of the label, and l is more than or equal to 1 and less than or equal to n, the optimization problem with the nonlinear geometric constraint is shown as the following formula:
Figure FDA0003234455780000015
Figure FDA0003234455780000016
wherein e is a constant.
4. The method of claim 1, wherein the calculating of the initial position of each tag is performed using a least squares algorithm.
5. The method of claim 1, wherein solving the optimization problem based on the initial values to obtain the determined locations of the tags is performed using a sequential quadratic programming algorithm.
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Publication number Priority date Publication date Assignee Title
CN114828214A (en) * 2022-05-17 2022-07-29 上海船舶运输科学研究所有限公司 Information fusion maritime search and rescue wireless sensor network positioning method
CN115022800A (en) * 2022-05-27 2022-09-06 国网江苏省电力有限公司电力科学研究院 Self-adaptive positioning method and system for indoor personnel of transformer substation

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103716879A (en) * 2013-12-26 2014-04-09 北京交通大学 Novel wireless positioning method by adopting distance geometry under NLOS environment
CN108489495A (en) * 2018-03-29 2018-09-04 东南大学 A kind of RFID tag indoor orientation method and equipment based on SVR and PSO
CN111126520A (en) * 2019-11-28 2020-05-08 清研讯科（北京）科技有限公司 Positioning method and device, storage medium and electronic device
CN111880144A (en) * 2020-07-29 2020-11-03 广东博智林机器人有限公司 Positioning method, device, equipment and storage medium
US20210055370A1 (en) * 2019-08-21 2021-02-25 University Of Washington Position determination systems and methods utilizing error of multiple candidate positions
WO2021065196A1 (en) * 2019-10-03 2021-04-08 Mitsubishi Electric Corporation Method and system for trajectory optimization for nonlinear robotic systems with geometric constraints

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103716879A (en) * 2013-12-26 2014-04-09 北京交通大学 Novel wireless positioning method by adopting distance geometry under NLOS environment
CN108489495A (en) * 2018-03-29 2018-09-04 东南大学 A kind of RFID tag indoor orientation method and equipment based on SVR and PSO
US20210055370A1 (en) * 2019-08-21 2021-02-25 University Of Washington Position determination systems and methods utilizing error of multiple candidate positions
WO2021065196A1 (en) * 2019-10-03 2021-04-08 Mitsubishi Electric Corporation Method and system for trajectory optimization for nonlinear robotic systems with geometric constraints
CN111126520A (en) * 2019-11-28 2020-05-08 清研讯科（北京）科技有限公司 Positioning method and device, storage medium and electronic device
CN111880144A (en) * 2020-07-29 2020-11-03 广东博智林机器人有限公司 Positioning method, device, equipment and storage medium

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114828214A (en) * 2022-05-17 2022-07-29 上海船舶运输科学研究所有限公司 Information fusion maritime search and rescue wireless sensor network positioning method
CN115022800A (en) * 2022-05-27 2022-09-06 国网江苏省电力有限公司电力科学研究院 Self-adaptive positioning method and system for indoor personnel of transformer substation
CN115022800B (en) * 2022-05-27 2024-02-20 国网江苏省电力有限公司电力科学研究院 Self-adaptive positioning method and system for indoor personnel of transformer substation

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