CN113534044B - Millimeter wave indoor positioning method and system - Google Patents

Millimeter wave indoor positioning method and system Download PDF

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CN113534044B
CN113534044B CN202110645632.3A CN202110645632A CN113534044B CN 113534044 B CN113534044 B CN 113534044B CN 202110645632 A CN202110645632 A CN 202110645632A CN 113534044 B CN113534044 B CN 113534044B
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CN113534044A (en
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陈志刚
陈禄
王磊
李文
姬智
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Xian Jiaotong University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0249—Determining position using measurements made by a non-stationary device other than the device whose position is being determined
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0205—Details
    • G01S5/0218—Multipath in signal reception
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
    • 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
    • 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention discloses a millimeter wave indoor positioning method and system, which utilize multipath arrival angle information acquired by random positions of a plurality of terminals to finish estimation of an AP topological structure under the condition that the indoor shape, the size and the like are unknown and the AP position is unknown, then finish estimation of the terminal position and construction of an environment map, and realize millimeter wave indoor positioning. The method has the characteristics of low calculation complexity, full information utilization, high positioning precision and accurate environment map construction.

Description

Millimeter wave indoor positioning method and system
Technical Field
The invention belongs to the technical field of indoor positioning, and particularly relates to a millimeter wave indoor positioning method and system.
Background
The existing WiFi indoor positioning technology is mainly divided into geometric positioning and fingerprint positioning. The traditional WiFi positioning technology based on geometry acquires wireless signals from equipment with WiFi functions, extracts measurement information such as received signal strength, signal arrival time, signal arrival angle and the like from the wireless signals, and then determines a target position by utilizing a geometric relation. Geometric positioning depends on the direct path of the signal, and multipath effects cause separation of the direct paths in the signal to present certain challenges, thereby affecting the positioning accuracy of the system. Traditional WiFi positioning technology based on fingerprint positioning utilizes information such as RSS/CIR and the like acquired by equipment to compare with an offline database, and determines a target position through fingerprint matching. But multipath effects make RSS/CIR fingerprints spatially unstable, resulting in unstable positioning effects.
The millimeter wave technology is used as one of key technologies of 5G mobile communication, can provide more accurate geometric information for indoor positioning, and greatly reduces the influence caused by multipath effect. First, since the millimeter wave system has a very large bandwidth, a higher time resolution can be obtained, so that a more accurate distance estimation value can be obtained. Second, the narrow beam of millimeter waves greatly improves the resolution of the spatial angle, and therefore more accurate angle measurements can be obtained. In addition, the millimeter wave is seriously affected by atmospheric absorption, so that the attenuation speed in the atmosphere is high, the millimeter wave channel is sparse due to the characteristic, the multipath interference is small, and the multipath is easy to distinguish. Finally, due to the high frequency band, the interference sources are few, so that the signal propagation is stable and reliable. The characteristics of millimeter waves enable the multipath resolution of wireless signals to be better, and the positioning potential of higher precision is achieved. However, the improvement of the geometric positioning accuracy of the millimeter waves is severely limited by the requirement of determining or counting information outside the communication generated by the lack of the position information of the virtual mirror image AP, and how to utilize the distinguishable multipath is the biggest problem of geometric positioning of the millimeter waves under the condition that the position of the virtual AP is unknown.
Aiming at the problems, a millimeter wave synchronous indoor positioning and mapping (SLAM) technology based on high-precision multipath signal parameter measurement values is proposed in literature, the millimeter wave SLAM technology can realize high-precision synchronous estimation of an AP position and a terminal position under the condition that an indoor environment is unknown, and a solution is provided for the problems existing in the millimeter wave positioning technology. The existing research on millimeter wave SLAM mainly realizes millimeter wave positioning by searching for geometric relations between APs and between the APs and the terminal and utilizing least square and other methods. However, as the number of APs increases, the time complexity of the search increases exponentially. Most documents adopt corresponding measures to reduce the computational complexity of the algorithm, but the positioning accuracy is limited at the cost of sacrificing the information utilization rate. Therefore, the current study on the SLAM algorithm has a major problem that the low computational complexity and the high information utilization of the algorithm cannot be guaranteed at the same time.
Disclosure of Invention
Aiming at the defects in the prior art, the technical problem to be solved by the invention is to provide the millimeter wave indoor positioning method and the millimeter wave indoor positioning system, and the high-precision single AP indoor positioning and map construction are realized under the condition that the indoor environment is unknown.
The invention adopts the following technical scheme:
a millimeter wave indoor positioning method comprises the following steps:
s1, acquiring differential arrival angle observation value data of N terminal random positions, and generating sample vectors corresponding to N differential arrival angle observation value vectors;
s2, constructing a differential arrival angle vector generator, inputting M terminal random position coordinates into the constructed differential arrival angle vector generator, and generating M corresponding differential arrival angle vectors;
s3, for all known sample vectors of N differential arrival angle observations in the step S1, sequentially calculating Euclidean distances between each sample vector and M generated vectors in the step S2; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector;
s4, taking N position labels obtained in the step S3 as the input of a differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function, updating an objective function by adopting a gradient descent method, and maximizing expectations of corresponding output generated by the generator by optimizing the AP position parameters;
s5, repeatedly iterating the step S3 and the step S4 until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximized step are optimal, so that the optimal estimation of the AP position coordinate is obtained, and millimeter wave indoor positioning is realized.
Specifically, in step S1, a differential angle of arrival observation vector Σ (ψ (p n ) Is) is:
Figure BDA0003109089120000031
where n=1,..,
Figure BDA0003109089120000032
for the differential angle of arrival between the 1 st AP and the L-th AP, p n Representing the random location of the terminal.
Specifically, in step S2, the differential arrival angle vector is specifically:
Figure BDA0003109089120000033
wherein ,
Figure BDA0003109089120000034
represented at the current generator parameter a 1 ,a 2 ,…,a L Lower terminal position coordinates +.>
Figure BDA0003109089120000035
The corresponding differential angle of arrival generates a vector.
Specifically, in step S3, the current position tag of the sample vector
Figure BDA0003109089120000036
The method comprises the following steps:
Figure BDA0003109089120000037
where n=1,..,
Figure BDA0003109089120000038
for the terminal position, d, of the mth random input generator n,m Representing the euclidean distance between the nth sample vector and the mth generated vector.
Further, euclidean distance d n,m The method comprises the following steps:
Figure BDA0003109089120000041
wherein ,
Figure BDA0003109089120000042
the ith element of the mth generated vector and the nth sample vector are represented, respectively.
Specifically, in step S4, the generation of the desired maximization of the corresponding output by the generator is specifically:
Figure BDA0003109089120000043
wherein ,
Figure BDA0003109089120000044
an observation position estimate representing the current n-th sample vector +.>
Figure BDA0003109089120000045
Generating vector after generator->
Figure BDA0003109089120000046
The probability of the nth sample vector, N is the total number of sample vectors, a l Is the coordinates of the ith AP, L is the total number of APs, ψ (p n ) For angle of arrival vector->
Figure BDA0003109089120000047
Further, the differential angle of arrival vector generator loss function
Figure BDA0003109089120000048
The method comprises the following steps:
Figure BDA0003109089120000049
updating generator parameter a using gradient descent method 1 ,a 2 ,…,a L The following are provided:
Figure BDA00031090891200000410
where l=1, 2, … L, η is the learning rate of the gradient descent method.
Specifically, at the plane position p n The terminal can measure at least 2 independent differential arrival angles, and the corresponding terminal position is estimated by a minimum cost function searching method; and constructing a map based on the estimated terminal position and the AP position determined in the step S5.
Further, according to the estimated real AP 1 With virtual AP 2 The position coordinates of the two points are obtained to obtain a perpendicular bisector of the two points, and the perpendicular bisector is connected with the virtual AP 2 With terminal position estimation
Figure BDA0003109089120000051
Virtual AP 2 And terminal position->
Figure BDA0003109089120000052
An intersection point of the connecting line of (a) and the obtained perpendicular bisector is taken as a reflection point; and generating all reflection points based on the obtained AP position estimation and the terminal position estimation, wherein the collection of the reflection points forms the estimation of the indoor environment, and the map construction is realized.
Another technical scheme of the invention is that the millimeter wave indoor positioning system comprises:
the sample module is used for acquiring differential arrival angle observation value data of N terminal random positions and generating sample vectors corresponding to N differential arrival angle observation value vectors;
the vector module is used for constructing a differential arrival angle vector generator, inputting M terminal random position coordinates into the constructed differential arrival angle vector generator and generating M corresponding differential arrival angle vectors;
the position module is used for sequentially calculating Euclidean distances between each sample vector and M generated vectors in the vector module for all known N differential arrival angle observation value sample vectors in the sample module; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector;
the optimizing module is used for taking N position labels obtained in the position module as the input of the differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function, updating an objective function by adopting a gradient descent method, and maximizing the expectation of corresponding output generated by the generator by optimizing the AP position parameters;
and the positioning module is used for repeatedly iterating the position module and the optimization module until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximization step are optimal, so that the optimal estimation of the AP position coordinate is obtained, and the millimeter wave indoor positioning is realized.
Compared with the prior art, the invention has at least the following beneficial effects:
according to the millimeter wave indoor positioning method, the AP estimation problem is modeled as the parameter estimation problem containing the hidden variable, and the simulation result verifies the superiority of the result of the method by combining the parameter estimation problem with the expectation maximization algorithm. In the maximizing step, optimization is used for replacing optimization, least square searching is avoided, and algorithm complexity is greatly reduced. The generator adopts a strict geometric relation structure, and compared with the prior literature for reducing the computational complexity and relaxing geometric relation constraint, the generator has the advantages of more sufficient information utilization and higher positioning precision.
Further, the differential arrival angle observation value vector in step S1 includes all independent differential arrival angles observed at any position, and is all angle information that can be provided by the millimeter wave communication system, so that the advantage of this arrangement is that known information is fully utilized.
Further, in step S2, the form of the generated vector of the generator is consistent with the form of the true differential arrival angle vector, so that the euclidean distance is conveniently calculated in the expected step, and vector matching is performed.
Further, in step S3, the generated vector most similar to the sample vector is matched by calculating the euclidean distance, and the corresponding terminal position of the generated vector is used as the position label of the sample vector, which is the optimal terminal position estimation obtained under the current AP position parameter estimation value.
Further, euclidean distance is used to measure similarity between vectors, with smaller euclidean distances being more similar between vectors.
Further, in step S4, by optimizing parameters of the generator, the expectation of the generator for generating the corresponding output is maximized, so as to obtain the optimal AP position estimate under the current terminal position estimate.
Further, the basis for the differential angle of arrival vector generator loss function setting is that the error between the generator generated vector and the corresponding sample vector is minimized at the current AP position estimate.
Further, the present invention does not require known indoor environment information, so that an environment map can be constructed based on the obtained AP and terminal position estimates in the case where the indoor environment is unknown.
Furthermore, the method constructs the environment map by searching the signal reflection points, and the method is simple and effective by only utilizing the obtained AP and terminal position estimation. The basis of the method of finding the signal reflection point is that the millimeter wave signal has a propagation characteristic of approximately optics, so that the virtual AP can be regarded as a mirror image of the real AP with respect to the reflection surface.
In conclusion, the method has the characteristics of low calculation complexity, full information utilization, high positioning precision and accurate environment map construction.
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
Drawings
FIG. 1 is a millimeter wave SLAM system model diagram;
FIG. 2 is a schematic block diagram of AP topology estimation based on a expectation maximization algorithm in the present invention;
FIG. 3 is a schematic view of an environmental map construction;
FIG. 4 is a schematic diagram of a simulation environment of the present invention;
FIG. 5 is a graph of terminal positioning accumulated error distribution;
FIG. 6 is a graph of the results of environmental map construction under different noise conditions, wherein (a) is 1 °, (b) is 2 °, (c) is 5 °;
fig. 7 is a view of the results of the environment map construction under the number of samples, wherein (a) is 100, (b) is 200, and (c) is 500.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be understood that the terms "comprises" and "comprising," when used in this specification and the appended claims, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in this specification and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in the present specification and the appended claims refers to any and all possible combinations of one or more of the associated listed items, and includes such combinations.
Various structural schematic diagrams according to the disclosed embodiments of the present invention are shown in the accompanying drawings. The figures are not drawn to scale, wherein certain details are exaggerated for clarity of presentation and may have been omitted. The shapes of the various regions, layers and their relative sizes, positional relationships shown in the drawings are merely exemplary, may in practice deviate due to manufacturing tolerances or technical limitations, and one skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions as actually required.
Referring to fig. 1, in the millimeter wave indoor positioning method of the present invention, only 1 millimeter wave AP needs to be deployed in an indoor space with unknown shape and size, and a mirror image (virtual AP) about a wall generated by a real AP is used to simulate the real AP, i.e. a primary reflection path generated by the real AP is regarded as a direct path generated by the virtual AP. The function completed by the invention can be described as that under the condition that the indoor shape, the size and the like are unknown and the AP position is unknown, the multipath arrival angle information acquired by the random positions of a plurality of terminals is utilized to firstly complete the estimation of the AP topological structure, and then the estimation of the terminal position and the construction of an environment map are completed.
Referring to fig. 2, a large number of unlabeled differential angle-of-arrival observations vectors at random locations are known, and with the AP location fixed, there is a definite geometric relationship between the differential angle-of-arrival observations vector and the terminal location. However, since the position tag corresponding to the differential arrival angle observation value vector is unknown, the AP position cannot be calculated directly by using the geometric relationship. The method is a parameter estimation problem under the typical data missing condition, the missing data is a terminal position label corresponding to each differential arrival angle observation value vector, and the parameter to be estimated is AP position coordinates. The EM algorithm is influenced by the missing idea, and the effectiveness of the EM algorithm is proved to be proved in order to solve the parameter estimation problem under the condition of data missing. The invention thus employs a expectation maximization algorithm to achieve an estimation of the AP geometry:
and constructing an arrival angle vector generator according to the geometrical relationship between the differential arrival angle observation value vector and the terminal position. The input of the generator is the random position coordinates of the terminal, the output is the differential arrival angle observation value vector, and the AP coordinates are parameters to be adjusted in the vector generator. Knowing a large number of sample vectors of label-free differential arrival angle observations at random positions, searching a current best matching position label for the sample vectors in a desired step, and updating AP position parameters based on the sample vectors and a corresponding position label optimization generator in a maximizing step. Repeating the expected step and the maximizing step until convergence; the parameters of the generator are now the estimated AP position.
The invention discloses a millimeter wave indoor positioning method, which comprises the following steps:
s1, acquiring differential arrival angle observation value data of random positions of N terminals, and generating N sample vectors corresponding to the formula (1);
acquiring multipath arrival angle information theta of multiple terminal positions in indoor environment l (p n ) Calculating differential arrival angle between any two APs
Figure BDA0003109089120000091
Obtaining a database containing N differential arrival angle observation value vectors;
wherein ,pn Representation terminalEnd random position, l=1, 2, 3.
Position p n The differential angle of arrival observation vector at is expressed as:
Figure BDA0003109089120000101
where n=1,..,
Figure BDA0003109089120000102
is the differential angle of arrival between the 1 st AP and the L-th AP.
S2, constructing a differential arrival angle vector generator, and inputting M terminal random position coordinates into the constructed differential arrival angle vector generator to generate M corresponding differential arrival angle vectors shown in formula (4);
by utilizing the analysis geometric property, the positions of the two parts are not difficult to obtain
Figure BDA0003109089120000103
Is located at->
Figure BDA0003109089120000104
Differential angle of arrival between target terminals +.>
Figure BDA0003109089120000105
Satisfy the following requirements
Figure BDA0003109089120000106
Thus, a combination of arbitrary AP positions corresponding to arbitrary plane random positions is generated
Figure BDA0003109089120000107
Is defined by the differential angle of arrival vector data:
Figure BDA0003109089120000108
wherein ,
Figure BDA0003109089120000109
represented at the current generator parameter a 1 ,a 2 ,…,a L Lower terminal position coordinates +.>
Figure BDA00031090891200001010
The corresponding differential angle of arrival generates a vector.
S3, for all known sample vectors of N differential arrival angle observations in the step S1, sequentially calculating Euclidean distances between each sample vector and M generated vectors in the step S2, wherein the Euclidean distances are shown as a formula (5); taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label (or position estimation) of the sample vector, as shown in the formula (6);
randomly selecting M terminal position coordinates
Figure BDA00031090891200001011
As inputs to the differential angle of arrival vector generator, corresponding M differential angle of arrival observation vector outputs are obtained:
Figure BDA0003109089120000111
where m=1,..m. For all known N differential angle-of-arrival observation sample vectors, the euclidean distance between each sample vector and M generated vectors is calculated in turn:
Figure BDA0003109089120000112
wherein ,dn,m Representing the Euclidean distance between the nth sample vector and the mth generated vector;
Figure BDA0003109089120000113
Ξ i (ψ(p n ) Respectively representing the mth generated vector and the nth sampleThe i-th element of the vector.
Calculating all known sample vectors of the differential arrival angle observation values to obtain a generated vector with the minimum Euclidean distance, and taking the terminal position coordinates corresponding to the generated vector as the current position label of the sample vector:
Figure BDA0003109089120000114
wherein ,
Figure BDA0003109089120000115
representing the current position tag of the nth sample vector, i.e. the current position estimate of the nth sample vector.
S4, taking N position labels obtained in the step S3 as the input of a differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function as shown in a formula (8), and updating an objective function by adopting a gradient descent method as shown in a formula (9), so that the expectation of the generator for generating corresponding output is maximized;
the N differential arrival angle observation value sample vectors obtained in the step E and N position labels corresponding to the N differential arrival angle observation value sample vectors are respectively used as the output and the input of an arrival angle vector generator, and the expectation of the generator for generating corresponding output is maximized by optimizing AP position parameters:
Figure BDA0003109089120000121
wherein
Figure BDA0003109089120000122
An observation position estimate representing the current n-th sample vector +.>
Figure BDA0003109089120000123
Generating vector after generator->
Figure BDA0003109089120000124
The probability of the nth sample vector.
The least square method is a method for solving the problem of the equation (6) stably and effectively, and the error between the generator output vector and the sample vector is minimized by searching the AP coordinate space. But the time complexity of the least squares method grows exponentially as the search dimension increases. In the case of multiple AP position coordinates to be estimated, the least squares method obviously cannot meet our requirement of low computational complexity. In consideration of the effectiveness of the gradient descent method in parameter optimization, the optimization is used to replace the optimization, the gradient descent method is used to update the AP position parameters, and although the current optimal generator is not obtained in each maximizing step, the AP position estimation is optimized towards the direction of error reduction, and more importantly, the calculation complexity is greatly reduced. The differential angle of arrival vector generator loss function is constructed from the sample vector sum generator generation vector as follows:
Figure BDA0003109089120000125
generator parameter optimization is then achieved by minimizing the objective function described above, updating the generator parameter a using a gradient descent method 1 ,a 2 ,…,a L (i.e., each AP location coordinate) is as follows:
Figure BDA0003109089120000126
where l=1, 2, … L, η is the learning rate of the gradient descent method.
And S5, repeatedly iterating the step S3 and the step S4 until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximized step are optimal, and the optimal estimation of the AP position coordinate is obtained.
S6, estimating a target position;
assuming to be located at the plane position p n Capable of measuring not less than 2 independent differences toThe angle of arrival is recorded as the set of the observable differential angles of arrival
Figure BDA0003109089120000131
The analytical geometry of the cosine function is used to obtain:
Figure BDA0003109089120000132
thus, the plane position is estimated by minimizing the following cost function search method.
Figure BDA0003109089120000133
S7, building an environment map.
Based on the terminal position estimated in the step S6 and the AP position determined in the step S5, map construction is realized, specifically:
referring to fig. 3, the true AP is estimated from 1 With virtual AP 2 The position coordinates of (a) are obtained, and a perpendicular bisector (a straight line where the reflecting surface is located) of two points is connected to the virtual AP 2 With terminal position estimation
Figure BDA0003109089120000134
Virtual AP 2 And terminal position->
Figure BDA0003109089120000135
The intersection point of the connecting line of (C) and the obtained perpendicular bisector is the reflection point. Based on the obtained AP position estimate and the terminal position estimate, all reflection points are generated according to the above steps, and the set of reflection points constitutes an estimate of the indoor environment. />
In still another embodiment of the present invention, a millimeter wave indoor positioning system is provided, which can be used to implement the millimeter wave indoor positioning method described above, and specifically, the millimeter wave indoor positioning system includes a sample module, a vector module, a location module, an optimization module, and a positioning module.
The sample module acquires differential arrival angle observation value data of N terminal random positions and generates sample vectors corresponding to N differential arrival angle observation value vectors;
the vector module is used for constructing a differential arrival angle vector generator, inputting M terminal random position coordinates into the constructed differential arrival angle vector generator and generating M corresponding differential arrival angle vectors;
the position module is used for sequentially calculating Euclidean distances between each sample vector and M generated vectors in the vector module for all known N differential arrival angle observation value sample vectors in the sample module; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector;
the optimizing module is used for taking N position labels obtained in the position module as the input of the differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function, updating an objective function by adopting a gradient descent method, and maximizing the expectation of corresponding output generated by the generator by optimizing the AP position parameters;
and the positioning module is used for repeatedly iterating the position module and the optimization module until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximization step are optimal, so that the optimal estimation of the AP position coordinate is obtained, and the millimeter wave indoor positioning is realized.
In yet another embodiment of the present invention, a terminal device is provided, the terminal device including a processor and a memory, the memory for storing a computer program, the computer program including program instructions, the processor for executing the program instructions stored by the computer storage medium. The processor may be a central processing unit (Central Processing Unit, CPU), but may also be other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), off-the-shelf Programmable gate arrays (FPGAs) or other Programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc., which are the computational core and control core of the terminal adapted to implement one or more instructions, in particular adapted to load and execute one or more instructions to implement a corresponding method flow or a corresponding function; the processor in the embodiment of the invention can be used for the operation of the millimeter wave indoor positioning method, and comprises the following steps:
acquiring differential arrival angle observation value data of N terminal random positions, and generating sample vectors corresponding to N differential arrival angle observation value vectors; constructing a differential arrival angle vector generator, and inputting M terminal random position coordinates into the constructed differential arrival angle vector generator to generate M corresponding differential arrival angle vectors; for all known sample vectors of N differential arrival angle observations, sequentially calculating Euclidean distances between each sample vector and M generated vectors; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector; n position labels are used as the input of a differential arrival angle vector generator, AP position parameters are optimized, errors between output vectors corresponding to the generator and sample vectors are minimized, a differential arrival angle vector generator loss function is constructed, a gradient descent method is adopted to update an objective function, and the AP position parameters are optimized to maximize expectations of the generator for generating corresponding outputs; and iterating repeatedly until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximized step reach the optimal value, so as to obtain the optimal estimation of the AP position coordinate and realize millimeter wave indoor positioning.
In a further embodiment of the present invention, the present invention also provides a storage medium, in particular, a computer readable storage medium (Memory), which is a Memory device in a terminal device, for storing programs and data. It will be appreciated that the computer readable storage medium herein may include both a built-in storage medium in the terminal device and an extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space storing an operating system of the terminal. Also stored in the memory space are one or more instructions, which may be one or more computer programs (including program code), adapted to be loaded and executed by the processor. The computer readable storage medium herein may be a high-speed RAM memory or a non-volatile memory (non-volatile memory), such as at least one magnetic disk memory.
One or more instructions stored in a computer-readable storage medium may be loaded and executed by a processor to implement the corresponding steps of the millimeter wave indoor positioning method in the above-described embodiments; one or more instructions in a computer-readable storage medium are loaded by a processor and perform the steps of:
acquiring differential arrival angle observation value data of N terminal random positions, and generating sample vectors corresponding to N differential arrival angle observation value vectors; constructing a differential arrival angle vector generator, and inputting M terminal random position coordinates into the constructed differential arrival angle vector generator to generate M corresponding differential arrival angle vectors; for all known sample vectors of N differential arrival angle observations, sequentially calculating Euclidean distances between each sample vector and M generated vectors; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector; n position labels are used as the input of a differential arrival angle vector generator, AP position parameters are optimized, errors between output vectors corresponding to the generator and sample vectors are minimized, a differential arrival angle vector generator loss function is constructed, a gradient descent method is adopted to update an objective function, and the AP position parameters are optimized to maximize expectations of the generator for generating corresponding outputs; and iterating repeatedly until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximized step reach the optimal value, so as to obtain the optimal estimation of the AP position coordinate and realize millimeter wave indoor positioning.
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 4, a simulation scenario is simulated. In a two-dimensional environment (the invention can be generalized to a three-dimensional scene) of 10m×8m, a millimeter wave AP is deployed, 4 reflection walls are arranged in the environment, corresponding to 4 virtual APs formed by primary reflection, and the coordinates of each AP are (2, 2), (-2, 2), (2, -2), (2, 14), (18, 2) respectively. The multipath arrival angle measurement of the current position is acquired at any time, assuming the user moves in it. The noise of the multipath arrival angle measurement is assumed to be Gaussian noise, and the standard deviation of the noise is set to be 1 degree, 2 degrees and 5 degrees respectively.
Referring to fig. 5, first, the positioning performance and the lower boundary of the positioning error of the EM algorithm and the GAN and the jace algorithms are compared under the same conditions. The cumulative error distribution curves of the EM algorithm and GAN, jace algorithm positioning errors and the cladoceram bound are shown in fig. 5. Wherein the number of samples is set to 500 and the noise standard deviation is set to 2. It can be seen from the figure that the EM algorithm has higher positioning accuracy than the GAN and JADE algorithms under the same conditions. This is because the JADE algorithm does not search the AP coordinate plane and the terminal coordinate plane simultaneously, but searches the AP coordinate plane and the terminal coordinate plane iteratively and sequentially, respectively, in order to reduce the computational complexity, and in each iteration process, all the known information is not fully utilized, and the positioning accuracy is limited. The GAN algorithm fully utilizes the information, but requires more samples to fully mine the distribution feature, and the current sample setting limits its positioning accuracy. The EM algorithm continuously searches for a more suitable label for the sample vector in the repeated iteration of the expected step and the maximized step, and the more random positions are input into the generator, so that the position label of the sample vector is more accurate, and the higher the AP position estimation accuracy is. There is still a certain gap between the EM algorithm accuracy and the lower bound of claimepirone, because in order to reduce the time complexity of the algorithm, the number of samples is limited, the number of samples is insufficient to fill the whole simulation space, the information amount is limited, and in addition, the random position number is limited, so that the position label accuracy of the sample vector is limited, and the AP estimation accuracy is affected.
Referring to fig. 6, the number of samples is set to 500, and fig. 6 (a), 6 (b) and 6 (c) respectively represent the map construction results when the standard deviation of noise is 1 °,2 ° and 5 °. It can be seen from the figure that the smaller the noise standard deviation, the higher the accuracy of the map construction, and the closer to the real environment. This is because the smaller the noise, the more accurate the multipath arrival angle observation, and the higher the accuracy of the AP coordinate estimation and the terminal position coordinate estimation, and thus the more accurate the environment map construction.
Referring to fig. 7, the noise standard deviation is set to 2 °, and fig. 7 (a), 7 (b) and 7 (c) represent the map construction results when the number of samples is 100, 200 and 500, respectively. It can be seen from the figure that the larger the number of samples, the higher the accuracy of the map construction, and the closer to the real environment. This is because the greater the number of samples, the higher the accuracy of the AP coordinate estimation and the terminal position coordinate estimation, and thus the more accurate the environment map construction.
In summary, according to the millimeter wave indoor positioning method and system provided by the invention, the AP position parameters are updated by adopting the gradient descent method in the maximization step, and the AP position estimation is optimized towards the direction of error reduction although the current optimal generator is not obtained in each maximization step, so that more importantly, the calculation complexity is greatly reduced; by skillfully combining the millimeter wave SLAM with the expected maximization algorithm, least square search is avoided, and known information is fully utilized while the calculation complexity is low; the known information is fully utilized, the AP positioning precision is high, the terminal positioning precision is high, and the environment map is accurately constructed.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above is only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by this, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. The millimeter wave indoor positioning method is characterized by comprising the following steps of:
s1, acquiring differential arrival angle observation value data of N terminal random positions, and generating sample vectors corresponding to N differential arrival angle observation value vectors;
s2, constructing a differential arrival angle vector generator, inputting M terminal random position coordinates into the constructed differential arrival angle vector generator, and generating M corresponding differential arrival angle vectors;
s3, for all known sample vectors of N differential arrival angle observations in the step S1, sequentially calculating Euclidean distances between each sample vector and M generated vectors in the step S2; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector;
s4, taking N position labels obtained in the step S3 as the input of a differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function, updating an objective function by adopting a gradient descent method, and maximizing expectations of corresponding output generated by the generator by optimizing the AP position parameters;
s5, repeatedly iterating the step S3 and the step S4 until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximized step are optimal, so that the optimal estimation of the AP position coordinate is obtained, and millimeter wave indoor positioning is realized.
2. The method according to claim 1, characterized in that in step S1 the differential angle of arrival observations vector Σ (ψ (p n ) Is) is:
Figure FDA0004169366880000011
where n=1,..,
Figure FDA0004169366880000012
for the differential angle of arrival between the 1 st AP and the L-th AP, p n Representing the random location of the terminal.
3. The method according to claim 1, wherein in step S2, the differential angle of arrival vector is specifically:
Figure FDA0004169366880000021
wherein ,
Figure FDA0004169366880000022
represents the mth terminal position->
Figure FDA0004169366880000023
Corresponding differential angle of arrival generation vector, +.>
Figure FDA0004169366880000024
For the differential angle of arrival between the 1 st AP and the L-th AP, m=1.
4. The method according to claim 1, wherein in step S3, the sample vector is currently position-tagged
Figure FDA0004169366880000025
The method comprises the following steps:
Figure FDA0004169366880000026
where n=1,..,
Figure FDA0004169366880000027
for the mth terminal positionD is set to n,m The euclidean distance between the nth sample vector and the mth generated vector, m=1.
5. The method according to claim 4, wherein the Euclidean distance d n,m The method comprises the following steps:
Figure FDA0004169366880000028
wherein ,
Figure FDA0004169366880000029
Ξ i (ψ(p n ) An mth element representing an mth generated vector and a differential angle of arrival observation vector, respectively.
6. The method according to claim 1, characterized in that in step S4 the desired maximization of the generator generation of the corresponding output is in particular:
Figure FDA00041693668800000210
wherein ,
Figure FDA00041693668800000211
a position tag representing the current sample vector +.>
Figure FDA00041693668800000212
Generating vector after generator->
Figure FDA00041693668800000213
The probability of the nth sample vector, N is the total number of sample vectors, a l Is the coordinates of the ith AP, L is the total number of APs, ψ (p n ) For angle of arrival vector->
Figure FDA00041693668800000214
Is the differential angle of arrival between the 1 st AP and the L-th AP.
7. The method of claim 6, wherein the differential angle of arrival vector generator loss function
Figure FDA00041693668800000215
The method comprises the following steps:
Figure FDA0004169366880000031
updating current generator parameter a using gradient descent method 1 ,a 2 ,…,a L The following are provided:
Figure FDA0004169366880000032
wherein, l=1, 2, … L, eta is the learning rate of the gradient descent method,
Figure FDA0004169366880000033
Ξ i (ψ(p n ) I-th element of the mth generated vector and the differential angle of arrival observation vector, m=1.
8. A method according to claim 1, characterized in that it is located at a terminal random position p n The terminal can measure at least 2 independent differential arrival angles, and the corresponding terminal position is estimated by a minimum cost function searching method; and constructing a map based on the estimated terminal position and the AP position determined in the step S5.
9. The method of claim 8, wherein the true AP is based on an estimate 1 With virtual AP 2 The position coordinates of the two points are obtained to obtain a perpendicular bisector of the two points, and the perpendicular bisector is connected with the virtual AP 2 Position tag with sample vector current
Figure FDA0004169366880000034
Virtual AP 2 And sample vector current position tag +.>
Figure FDA0004169366880000035
An intersection point of the connecting line of (a) and the obtained perpendicular bisector is taken as a reflection point; and generating all reflection points based on the obtained AP position estimation and the terminal position estimation, wherein the collection of the reflection points forms the estimation of the indoor environment, and the map construction is realized.
10. A millimeter wave indoor positioning system, comprising:
the sample module is used for acquiring differential arrival angle observation value data of N terminal random positions and generating sample vectors corresponding to N differential arrival angle observation value vectors;
the vector module is used for constructing a differential arrival angle vector generator, inputting M terminal random position coordinates into the constructed differential arrival angle vector generator and generating M corresponding differential arrival angle vectors;
the position module is used for sequentially calculating Euclidean distances between each sample vector and M generated vectors in the vector module for all known N differential arrival angle observation value sample vectors in the sample module; taking the terminal position coordinate corresponding to the generated vector with the minimum Euclidean distance of the sample vector as the current position label of the sample vector;
the optimizing module is used for taking N position labels obtained in the position module as the input of the differential arrival angle vector generator, optimizing AP position parameters, minimizing errors between output vectors corresponding to the generator and sample vectors, constructing a differential arrival angle vector generator loss function, updating an objective function by adopting a gradient descent method, and maximizing the expectation of corresponding output generated by the generator by optimizing the AP position parameters;
and the positioning module is used for repeatedly iterating the position module and the optimization module until convergence, wherein the label estimated value of each sample vector in the expected step and the estimated value of the AP position coordinate in the maximization step are optimal, so that the optimal estimation of the AP position coordinate is obtained, and the millimeter wave indoor positioning is realized.
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Citations (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102395192A (en) * 2011-03-15 2012-03-28 苏州摩多物联科技有限公司 Method and device for locating wireless sensor terminal

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* Cited by examiner, † Cited by third party
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US11963150B2 (en) * 2018-11-01 2024-04-16 Qualcomm Incorporated Positioning enhancements for locating a mobile device in a wireless network
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN102395192A (en) * 2011-03-15 2012-03-28 苏州摩多物联科技有限公司 Method and device for locating wireless sensor terminal

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