CN112748399B - Visible light three-dimensional positioning system and method based on multi-PD receiver - Google Patents
Visible light three-dimensional positioning system and method based on multi-PD receiver Download PDFInfo
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Abstract
The invention discloses a visible light three-dimensional positioning system and a method based on a multi-PD receiver, wherein the system comprises the following steps: an LED light source, a symmetrical structure receiver based on multiple PDs and a processing device; the LED light source is used for sending visible light signals; the receiver comprises a first photoelectric detector which is horizontally arranged and a plurality of second photoelectric detectors which are obliquely arranged, wherein the plurality of second photoelectric detectors are equidistantly distributed around the first photoelectric detector, and the included angles of two adjacent second photoelectric detectors are the same; the photoelectric detector is used for converting the received visible light signals into electric signals; the processing device comprises a signal processing module which is used for solving the three-dimensional coordinate of the receiver based on the received signal intensity of the first photoelectric detector and the received signal intensity of the second photoelectric detector by combining an interior point method. The invention can effectively acquire three-dimensional position information, has high positioning precision, low realization complexity and higher practical value.
Description
Technical Field
The invention relates to the technical field of visible light positioning, in particular to a visible light three-dimensional positioning system and method based on a multi-PD receiver.
Background
In recent years, with the rapid development of information technology, intelligent terminals are becoming increasingly popular, and with the large-scale popularization of smartphones and other wireless devices, the demand of ubiquitous services including indoor positioning is raised. In order to solve the indoor positioning problem, there are some commonly used indoor positioning technologies at present, which mainly include: infrared indoor positioning technology, radio frequency identification (Radio Frequency Identification, RFID) indoor positioning technology, bluetooth indoor positioning technology, wireless local area network (Wireless Local Area Networks, WLAN) indoor positioning technology, zigbee indoor positioning technology, ultra Wide Band (UWB) indoor positioning technology, and the like. Although these techniques can meet the needs of people for daily indoor positioning to some extent, a perfect balance of accuracy and cost is difficult to achieve in practical application. In addition, the indoor positioning technologies have electromagnetic radiation, so that the safety is poor, and the indoor positioning technologies cannot be applied to places where the electromagnetic radiation is strictly limited; at the same time, the scarcity of today's spectrum resources also limits the further widespread use of these technologies.
Visible light positioning technology is widely focused due to the special advantages of high positioning accuracy, no radio frequency interference, low complexity and the like, and is considered as one of the most attractive solutions. Among the many non-imaging positioning technologies based on visible light, mainly include a positioning method based on a single PD receiver and a positioning algorithm based on a multi-PD symmetrical structure receiver; the positioning algorithm based on the receiver with the multi-PD symmetrical structure can realize positioning by utilizing a single LED light source, can be applied to receiving limited positioning scenes of the LED light source, and effectively eliminates positioning errors.
However, the existing non-imaging positioning technology based on visible light mainly obtains two-dimensional positioning information, and in indoor positioning, the high-precision two-dimensional positioning information is required to be obtained, and the vertical height position information is also required to be obtained, namely, the indoor visible light three-dimensional positioning is realized, and the high-precision positioning data acquisition requirement is met. Therefore, there is a need to develop a new non-imaging positioning technology based on visible light to acquire three-dimensional position information.
Disclosure of Invention
The invention provides a visible light three-dimensional positioning system and method based on a multi-PD receiver, which aim to solve the technical problem of indoor three-dimensional positioning.
In order to solve the technical problems, the invention provides the following technical scheme:
in one aspect, the present invention provides a visible light three-dimensional positioning system based on a multi-PD receiver, comprising: an LED light source, a symmetrical structure receiver based on multiple PDs and a processing device; wherein,
the LED light source consists of a single LED lamp and is used for sending visible light signals into the positioning space;
the receiver comprises a first photoelectric detector which is horizontally arranged and a plurality of second photoelectric detectors which are obliquely arranged relative to the first photoelectric detector, wherein the second photoelectric detectors are equidistantly distributed around the first photoelectric detector, and the included angles of two adjacent second photoelectric detectors are the same; the photoelectric detector is used for converting the received visible light signal into an electric signal to obtain the intensity of the received signal;
the processing device comprises a signal processing module, wherein the signal processing module is used for converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method.
Further, the distances from the second photodetectors to the first photodetectors are equal, the inclination angles of the second photodetectors relative to the first photodetectors are equal, and the side lengths of the first photoelectric detector and the second photodetectors are equal; wherein the coordinates (x r ,y r ,z r ) Coordinates (x r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein->
Wherein Δs represents the horizontal distance from the center of the ith second photodetector to the center of the first photodetector, α represents the tilt angle of the ith second photodetector with respect to the first photodetector, Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located, l represents the side length of the photodetector, β i And the complementary angle of the included angle between the projection of the i-th second photoelectric detector center and the first photoelectric detector center on the horizontal plane where the first photoelectric detector is positioned and the positive direction of the x-axis is represented.
Further, according to the Langbo radiation model, the received signal strength P of the first photodetector r,0 And the i-th received signal strength P of the second photodetector r,i The method comprises the following steps of:
ratio of received signal strength of ith second photodetector to that of the first photodetector RSSR i The method comprises the following steps:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, A represents the physical area of the current photoelectric detector actually receiving the visible light signal, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance of the ith second photodetector from the LED light source.
Further, the signal processing module is specifically configured to:
constructing a square sum function:
taking the square sum function as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved:
and solving the three-dimensional coordinates (x, y, z) to be solved by using an interior point method.
Further, the solving the three-dimensional coordinates (x, y, z) to be solved by using the interior point method comprises the following steps:
defining a domain construction constraint from a given objective function:
wherein->
Constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z); wherein r is a positive parameter;
gradient the barrier function B (x, y, z, r) to obtain equation (7):
introducing Lagrangian multipliersGet the switchEquation for gradient:
wherein,
calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
the initial values of x, y, z and r are selected, and the initial value of λ is obtained from equation (8). And (3) iterating the formula (11) according to the set step length, and when ((x, y, z), lambda) - ((x, y, z) +alpha delta (x, y, z), lambda+alpha delta lambda) to r-0, obtaining the corresponding solution of (x, y, z) as the optimal solution.
Further, the processing device further comprises a position display module, wherein the position display module is used for displaying the three-dimensional coordinates of the receiver solved by the signal processing module.
On the other hand, the invention also provides a visible light three-dimensional positioning method based on the multi-PD receiver, which comprises the following steps:
transmitting visible light signals into the positioning space through the LED light source; wherein the LED light source consists of a single LED lamp;
receiving visible light signals sent by an LED light source through a receiver; the receiver comprises a first photoelectric detector which is horizontally arranged and a plurality of second photoelectric detectors which are obliquely arranged relative to the first photoelectric detector, wherein the second photoelectric detectors are equidistantly distributed around the first photoelectric detector, and the included angles of two adjacent second photoelectric detectors are the same; the photoelectric detector is used for converting the received visible light signal into an electric signal to obtain the intensity of the received signal;
and converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method.
Further, the distances from the second photodetectors to the first photodetectors are equal, the inclination angles of the second photodetectors relative to the first photodetectors are equal, and the side lengths of the first photoelectric detector and the second photodetectors are equal; wherein the coordinates (x r ,y r ,z r ) Coordinates (x r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein->
Wherein Δs represents the horizontal distance from the center of the ith second photodetector to the center of the first photodetector, α represents the tilt angle of the ith second photodetector with respect to the first photodetector, Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located, l represents the side length of the photodetector, β i Representing the ith second photodetector center and the first photodetectorThe projection of the connecting line of the center on the horizontal plane where the first photoelectric detector is located is complementary to the included angle of the positive direction of the x-axis.
Further, according to the Langbo radiation model, the received signal strength P of the first photodetector r,0 And the i-th received signal strength P of the second photodetector r,i The method comprises the following steps of:
ratio of received signal strength of ith second photodetector to that of the first photodetector RSSR i The method comprises the following steps:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, A represents the physical area of the current photoelectric detector actually receiving the visible light signal, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance of the ith second photodetector from the LED light source.
Further, the solving the three-dimensional coordinate to be solved by using the interior point method comprises the following steps:
constructing a square sum function:
taking the square sum function as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved:
defining a domain construction constraint from a given objective function:
wherein->
Constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z); wherein r is a positive parameter;
gradient the barrier function B (x, y, z, r) to obtain equation (7):
introducing Lagrangian multipliersAn equation for the gradient is derived:
wherein,
calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
the initial values of x, y, z and r are selected, and the initial value of λ is obtained from equation (8). And (3) iterating the formula (11) according to the set step length, and when ((x, y, z), lambda) - ((x, y, z) +alpha delta (x, y, z), lambda+alpha delta lambda) to r-0, obtaining the corresponding solution of (x, y, z) as the optimal solution.
In yet another aspect, the present invention also provides an electronic device including a processor and a memory; wherein the memory stores at least one instruction that is loaded and executed by the processor to implement the above-described method.
In yet another aspect, the present invention also provides a computer readable storage medium having at least one instruction stored therein, the instruction being loaded and executed by a processor to implement the above method.
The technical scheme provided by the invention has the beneficial effects that at least:
the invention converts the acquisition problem of the three-dimensional position coordinates into the optimization problem aiming at the structure of the receiver with the multi-PD symmetrical structure, solves the three-dimensional position information by combining an interior point method, and ensures the optimal positioning error. The invention can effectively acquire three-dimensional position information, has high positioning precision, low realization complexity and higher practical value.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a schematic workflow diagram of a visible light three-dimensional positioning system based on a multi-PD receiver according to an embodiment of the present invention;
fig. 2 is a positioning error diagram of a visible light three-dimensional positioning system based on a multi-PD receiver according to an embodiment of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the embodiments of the present invention will be described in further detail with reference to the accompanying drawings.
First embodiment
As shown in fig. 1, the present embodiment provides a visible light three-dimensional positioning system based on a multi-photodetector PD receiver, including: an LED light source, a symmetrical structure receiver based on multiple PDs and a processing device;
the LED light source is positioned at the center of the transmitting plane and consists of a single LED lamp, and is used for transmitting visible light signals into the positioning space; the visible light signal emitted by the LED light source can cover a positioning plane in a certain area; the position coordinates of the LED light source are (x) t ,y t ,z t )。
The receiver comprises a first photodetector PD arranged horizontally 0 And a plurality of photodetectors PD relative to the first photodetector 0 Second photodetector PD disposed obliquely i (i=1, 2,3, 4), a plurality of the second photodetectors PD i Equally distributed on the first photo detector PD 0 And adjacent two of the second photodetectors PD i The included angles of (2) are the same; the photoelectric detector is used for collecting optical signals, and the I-V conversion circuit is used for converting the optical signals into electric signals to obtain the intensity of received signals;
the processing equipment comprises a signal processing module and a position display module, wherein the signal processing module is used for converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method; the position display module is used for displaying the three-dimensional coordinates of the receiver solved by the signal processing module.
Specifically, in the present embodiment, the second photodetector PD i Is four in number and two adjacent PDs i Is 90. PD 0 Is marked as (x) r ,y r ,z r ) The coordinates are the receiver coordinates which are calculated and which are associated with each of the second photodetectors PD i Coordinates (x) r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein->
Wherein Δs represents a horizontal distance from the center of the ith second photodetector to the center of the first photodetector, and the distances from each second photodetector to the first photodetector are equal; α represents an inclination angle (α∈ (0 °,90 °)) of an ith second photodetector with respect to the first photodetector, and the inclination angles of the second photodetectors with respect to the first photodetector are equal; Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located; l represents the side length of the photoelectric detector, and the side lengths of the first photoelectric detector and each second photoelectric detector are equal; beta i And the complementary angle of the included angle between the projection of the ith second photoelectric detector center and the first photoelectric detector center on the horizontal plane where the first photoelectric detector is positioned and the positive direction of the x-axis is represented.
According to the Lanbo radiation model, the received light power P of the first photodetector can be obtained r,0 And the i-th second photodetector received-light power P r,i The method comprises the following steps of:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, A represents the physical area actually received by the current photoelectric detector, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance of the ith second photodetector from the LED light source.
From the formulas (1), (2) and (3), the ith second photodetector PD can be obtained i With the first photodetector PD 0 Ratio of received signal strength of (2) RSSR i The method comprises the following steps:
based on the above, the process of solving the three-dimensional position coordinates in this embodiment is as follows:
considering the case of m=1, the three-dimensional position coordinates are solved by constructing a sum-of-squares function as in equation (5):
taking the formula (5) as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved, namely:
next, solving the three-dimensional coordinates (x, y, z) to be solved by using an interior point method, wherein the specific steps are as follows:
step one: constructing a constraint as in equation (6) from a given objective function domain:
wherein->
Constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z); where r is a small positive parameter, called penalty factor, and when r goes to 0, B (x, y, z, r) approaches the solution of F (x, y, z).
Step two: gradient the barrier function B (x, y, z, r) to obtain equation (7):
introducing Lagrangian multipliersAn equation for the gradient is derived:
wherein,a is a Jacobian matrix of defined conditions;
step three: calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
step four: the initial values of x, y, z and r are selected, and the initial value of λ is obtained from equation (8). A suitable step size α (α e (0, 1)) is determined and the equation (11) is iterated, and when ((x, y, z), λ) → ((x, y, z) +αΔΔ (x, y, z), λ+αΔλ) to r→0, the corresponding solution of (x, y, z) is the optimal solution.
Next, a simulation experiment is used to verify the positioning effect of the visible light three-dimensional positioning system of the embodiment; in the simulation experiment, the positioning space is 1m multiplied by 1.5m, the coordinates of the LED light source are 0.5,0.5,1.5, the radius l of the receiver is 0.04m, and the PD i Elevation angle α=20°, PD i Azimuth angles of (a) are respectively beta 1 ＝180°,β 2 ＝270°,β 3 ＝0°,β 4 =90°. The definition field of the three-dimensional coordinates (x, y, z) is:x, y, z, r have initial values of 0.1, 1, respectively, step α=0.1; the positioning error result of the simulation experiment is shown in fig. 2. Except that the error of four corners is extremely raised to more than 0.5m, the positioning error of the visible light positioning system in the rest part of the embodiment is within 1 mm. This illustrates that the system of the present embodiment performs well in a positioning scenario, and is suitable for application in a practical environment.
In summary, the visible light three-dimensional positioning system based on the multi-photoelectric detector PD receiver of the embodiment converts the acquisition problem of the three-dimensional position coordinates into an optimization problem, solves the three-dimensional position information by combining an interior point method, and ensures the optimal positioning error. The visible light three-dimensional positioning system based on the PD receiver of the multiple photoelectric detectors can effectively acquire three-dimensional position information, and is high in positioning accuracy, low in implementation complexity and high in practical value.
Second embodiment
The embodiment provides a visible light three-dimensional positioning method based on a multi-photoelectric detector PD receiver, which comprises the following steps:
transmitting visible light signals into the positioning space through the LED light source; the LED light source is positioned at the center of the transmitting plane and consists of a single LED lamp, and visible light signals emitted by the LED light source can cover a positioning plane in a certain area; the position coordinates of the LED light source are (x) t ,y t ,z t )。
Receiving visible light signals sent by an LED light source through a receiver; wherein the receiver comprises a first photodetector PD arranged horizontally 0 And a plurality of photodetectors PD relative to the first photodetector 0 Second photodetector PD disposed obliquely i (i=1, 2,3, 4), a plurality of the second photodetectors PD i Equally distributed on the first photo detector PD 0 And adjacent two of the second photodetectors PD i The included angles of (2) are the same; the photoelectric detector is used for collecting optical signals, and the I-V conversion circuit is used for converting the optical signals into electric signals to obtain the intensity of received signals.
And converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method.
Specifically, in the present embodiment, the second photodetector PD i Is four in number and two adjacent PDs i Is 90. PD 0 Is marked as (x) r ,y r ,z r ) The coordinates are the receiver coordinates which are calculated and which are associated with each of the second photodetectors PD i Coordinates (x) r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein->
Wherein Δs represents a horizontal distance from the center of the ith second photodetector to the center of the first photodetector, and the distances from each second photodetector to the first photodetector are equal; α represents an inclination angle (α∈ (0 °,90 °)) of an ith second photodetector with respect to the first photodetector, and the inclination angles of the second photodetectors with respect to the first photodetector are equal; Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located; l represents the side length of the photoelectric detector, and the side lengths of the first photoelectric detector and each second photoelectric detector are equal; beta i And the complementary angle of the included angle between the projection of the ith second photoelectric detector center and the first photoelectric detector center on the horizontal plane where the first photoelectric detector is positioned and the positive direction of the x-axis is represented.
According to the Lanbo radiation model, the received light power P of the first photodetector can be obtained r,0 And the i-th second photodetector received-light power P r,i The method comprises the following steps of:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, A represents the physical area actually received by the current photoelectric detector, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance of the ith second photodetector from the LED light source.
From the formulas (1), (2) and (3), the ith second photodetector PD can be obtained i With the first photodetector PD 0 Ratio of received signal strength of (2) RSSR i The method comprises the following steps:
based on the above, the process of solving the three-dimensional position coordinates in this embodiment is as follows:
solving the three-dimensional position coordinates by constructing a square sum function as shown in formula (5):
taking the formula (5) as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved, namely:
next, solving the three-dimensional coordinates (x, y, z) to be solved by using an interior point method, wherein the specific steps are as follows:
step one: constructing a constraint as in equation (6) from a given objective function domain:
wherein->
Constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z); where r is a small positive parameter, called penalty factor, and when r goes to 0, B (x, y, z, r) approaches the solution of F (x, y, z).
Step two: gradient the barrier function B (x, y, z, r) to obtain equation (7):
and introducing a Lagrangian multiplier g (i) lambda i =r (i e { x, y, z }) gets the information about the gradientEquation (8) of (2):
wherein,a is a Jacobian matrix of defined conditions; />
Step three: calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
step four: the initial values of x, y, z and r are selected, and the initial value of λ is obtained from equation (8). A suitable step size α (α e (0, 1)) is determined and the equation (11) is iterated, and when ((x, y, z), λ) → ((x, y, z) +αΔΔ (x, y, z), λ+αΔλ) to r→0, the corresponding solution of (x, y, z) is the optimal solution.
In summary, the visible light three-dimensional positioning method based on the multi-photoelectric detector PD receiver of the embodiment converts the acquisition problem of the three-dimensional position coordinates into an optimization problem, solves the three-dimensional position information by combining an interior point method, and ensures the optimal positioning error. The visible light three-dimensional positioning method based on the PD receiver of the multi-photoelectric detector can effectively acquire three-dimensional position information, and is high in positioning accuracy, low in implementation complexity and high in practical value.
Third embodiment
The embodiment provides an electronic device, which comprises a processor and a memory; wherein the memory has stored therein at least one instruction that is loaded and executed by the processor to implement the method of the second embodiment.
The electronic device may vary considerably in configuration or performance and may include one or more processors (central processing units, CPU) and one or more memories having at least one instruction stored therein that is loaded by the processors and performs the methods described above.
Fourth embodiment
The present embodiment provides a computer-readable storage medium having stored therein at least one instruction that is loaded and executed by a processor to implement the above-described method. The computer readable storage medium may be, among other things, ROM, random access memory, CD-ROM, magnetic tape, floppy disk, optical data storage device, etc. The instructions stored therein may be loaded by a processor in the terminal and perform the method of the second embodiment.
Furthermore, it should be noted that the present invention can be provided as a method, an apparatus, or a computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the invention may take the form of a computer program product on one or more computer-usable storage media having computer-usable program code embodied therein.
Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. 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, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, 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.
It is further noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article or terminal device comprising the element.
It is finally pointed out that the above description of the preferred embodiments of the invention, it being understood that although preferred embodiments of the invention have been described, it will be obvious to those skilled in the art that, once the basic inventive concepts of the invention are known, several modifications and adaptations can be made without departing from the principles of the invention, and these modifications and adaptations are intended to be within the scope of the invention. It is therefore intended that the following claims be interpreted as including the preferred embodiment and all such alterations and modifications as fall within the scope of the embodiments of the invention.
Claims (3)
1. A multi-PD receiver-based visible light three-dimensional positioning system, the system comprising: an LED light source, a symmetrical structure receiver based on multiple PDs and a processing device; wherein,
the LED light source consists of a single LED lamp and is used for sending visible light signals into the positioning space;
the receiver comprises a first photoelectric detector which is horizontally arranged and a plurality of second photoelectric detectors which are obliquely arranged relative to the first photoelectric detector, wherein the second photoelectric detectors are equidistantly distributed around the first photoelectric detector, and the included angles of two adjacent second photoelectric detectors are the same; the photoelectric detector is used for converting the received visible light signal into an electric signal to obtain the intensity of the received signal;
the processing equipment comprises a signal processing module, wherein the signal processing module is used for converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method;
the distance from each second photoelectric detector to the first photoelectric detector is equal, the inclination angles of each second photoelectric detector relative to the first photoelectric detector are equal, and the side lengths of the first photoelectric detector and each second photoelectric detector are equal; wherein the coordinates (x r ,y r ,z r ) Coordinates (x r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein Δs represents the horizontal distance from the center of the ith second photodetector to the center of the first photodetector, α represents the tilt angle of the ith second photodetector with respect to the first photodetector, Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located, l represents the side length of the photodetector, β i The complementary angle of the included angle between the projection of the ith second photoelectric detector center and the line of the first photoelectric detector center on the horizontal plane where the first photoelectric detector is positioned and the positive direction of the x-axis is represented;
according to the Langbo radiation model, the received signal strength P of the first photodetector r,0 And the i-th received signal strength P of the second photodetector r,i The method comprises the following steps of:
ratio of received signal strength of ith second photodetector to that of the first photodetector RSSR i The method comprises the following steps:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, S represents the physical area of the current photoelectric detector actually receiving the visible light signal, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance from the ith second photodetector to the LED light source; x is x t ，y t ，z t Representing the position coordinate value of the LED light source;
the signal processing module is specifically configured to:
constructing a square sum function:
taking the square sum function as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved:
solving the three-dimensional coordinates (x, y, z) to be solved by using an interior point method;
the method for solving the three-dimensional coordinates (x, y, z) to be solved by using the interior point method comprises the following steps:
defining a domain construction constraint from a given objective function:
constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z); wherein r is a positive parameter;
gradient the barrier function B (x, y, z, r) to obtain equation (7):
introducing Lagrangian multipliersAn equation for the gradient is derived:
wherein,
calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
selecting initial values of x, y, z and r, and obtaining an initial value of lambda according to a formula (8); and (3) iterating the formula (11) according to the set step length, and when ((x, y, z), lambda) - ((x, y, z) +alpha delta x, y, z), lambda+alpha 4 lambda to r-0, obtaining the corresponding solution of (x, y, z) as the optimal solution.
2. The multi-PD-based receiver-based three-dimensional positioning system of claim 1, wherein the processing apparatus further comprises a location display module for displaying the three-dimensional coordinates of the receiver solved by the signal processing module.
3. The visible light three-dimensional positioning method based on the multi-PD receiver is characterized by comprising the following steps of:
transmitting visible light signals into the positioning space through the LED light source; wherein the LED light source consists of a single LED lamp;
receiving visible light signals sent by an LED light source through a receiver; the receiver comprises a first photoelectric detector which is horizontally arranged and a plurality of second photoelectric detectors which are obliquely arranged relative to the first photoelectric detector, wherein the second photoelectric detectors are equidistantly distributed around the first photoelectric detector, and the included angles of two adjacent second photoelectric detectors are the same; the photoelectric detector is used for converting the received visible light signal into an electric signal to obtain the intensity of the received signal;
converting the acquisition problem of the three-dimensional position coordinates into an optimization problem, and solving the three-dimensional coordinates of the receiver based on the received signal strength of the first photoelectric detector and the received signal strength of the second photoelectric detector by combining an interior point method;
the distance from each second photoelectric detector to the first photoelectric detector is equal, the inclination angles of each second photoelectric detector relative to the first photoelectric detector are equal, and the side lengths of the first photoelectric detector and each second photoelectric detector are equal; wherein the coordinates (x r ,y r ,z r ) Coordinates (x r,i ,y r,i ,z r,i ) The relation of (2) is:
wherein Δs represents the horizontal distance from the center of the ith second photodetector to the center of the first photodetector, α represents the tilt angle of the ith second photodetector with respect to the first photodetector, Δh represents the vertical distance from the center of the ith second photodetector to the horizontal plane in which the first photodetector is located, l represents the side length of the photodetector, β i The complementary angle of the included angle between the projection of the ith second photoelectric detector center and the line of the first photoelectric detector center on the horizontal plane where the first photoelectric detector is positioned and the positive direction of the x-axis is represented;
according to the Langbo radiation model, the received signal strength P of the first photodetector r,0 And the i-th received signal strength P of the second photodetector r,i The method comprises the following steps of:
ratio of received signal strength of ith second photodetector to that of the first photodetector RSSR i The method comprises the following steps:
wherein P is t Representing the emitting power of the LED light source, m represents the Langbo radiation coefficient, S represents the physical area of the current photoelectric detector actually receiving the visible light signal, and d r Represents the distance from the first photodetector to the LED light source, d i Representing the distance from the ith second photodetector to the LED light source; x is x t ，y t ，z t Representing the position coordinate value of the LED light source;
the method for solving the three-dimensional coordinate to be solved by utilizing the interior point method comprises the following steps:
constructing a square sum function:
taking the square sum function as an objective function, and setting a definition domain of a three-dimensional coordinate (x, y, z) to be solved:
defining a domain construction constraint from a given objective function:
constructing a function C (x, y, z) = - (ln (g (x)) +ln (g (y)) +ln (g (z))) using the constraint conditions, and defining an obstacle function B (x, y, z, r) =f (x, y, z) +rc (x, y, z (; where r is a positive parameter;
gradient the barrier function B (x, y, z, r) to obtain equation (7):
introducing Lagrangian multipliersAn equation for the gradient is derived:
wherein,
calculate the black plug matrix W of F (x, y, z), and the diagonal matrix B of λ:
the Newton iteration method is used for obtaining:
wherein,
selecting initial values of x, y, z and r, and obtaining an initial value of lambda according to a formula (8); and (3) iterating the formula (11) according to the set step length, and when ((x, y, z), lambda) - ((x, y, z) +alpha delta (x, y, z (, lambda+alpha delta lambda) to r-0), obtaining the corresponding solution of (x, y, z) as the optimal solution.
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