CN117715186A - AoA positioning method based on RNDAC-ZNN model - Google Patents
AoA positioning method based on RNDAC-ZNN model Download PDFInfo
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Abstract
The invention discloses an AoA positioning method based on an RNDAC-ZNN model, which comprises the following steps: forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station; constructing an RNDAC-ZNN model based on the original NZNN model; based on the RNDAC-ZNN model, solving the linear equation set to obtain a solution about the target position, the method provided by the application overcomes the defect that the AoA positioning method cannot realize global convergence under the noise interference condition, and greatly improves the accurate solving performance of the model under the noise interference condition.
Description
Technical Field
The invention relates to the technical field of AoA positioning, in particular to an AoA positioning method based on an RNDAC-ZNN model.
Background
Theoretically, positioning can be achieved by obtaining information such as TOA, AOA, and AOD of the signal, which can be obtained by channel state information. Considering sparse features of millimeter wave channels, many millimeter wave positioning algorithms are based on compressed sensing expansion.
Channel noise is one of the unavoidable factors affecting the performance of a communication system, and in order to achieve high-precision positioning, it is desirable to reduce as much as possible its interference to the channel estimation process. In the prior art, the ZNN model is used for eliminating interference, but the model is an initial model or a model with a nonlinear activation function and has less residual information, so that the convergence rate of the model is low and the interference resistance is not strong, and the positioning accuracy of user equipment and a base station is seriously affected.
Disclosure of Invention
Aiming at the prior art, the invention aims to provide an AoA positioning method based on an RNDAC-ZNN model, which mainly solves the technical problems in the background art.
In order to achieve the above object, the technical solution of the embodiment of the present invention is as follows: an AoA positioning method based on an RNDAC-ZNN model, the positioning method comprising:
forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station;
constructing an RNDAC-ZNN model based on the original NZNN model;
solving the linear equation set based on the RNDAC-ZNN model to obtain a solution about the target position.
Optionally, the incident angle of the jth base station is set asThe pitch angle is +.>The position coordinate of the jth base station is +.>Where j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
wherein the method comprises the steps ofIs a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant.
Optionally, the method for converting the coordinate equation into the linear equation set specifically includes:
will beDenoted as->Will->Denoted as->Will beDenoted as->Thus, the linear equation is formed as: />And define its error function as +.>Wherein->Representing the error function of the aforementioned linear equation.
Optionally, the constructed RNDAC-ZNN model is:
wherein,for regulating the coefficient->For the feedback coefficient->Representing an adaptive control function->Representing an adaptive feedback activation function->The element representing time t, < >>Representation->Is a function of the integral of (a).
Optionally, the adaptive control function includes a power bounded adaptive function and an exponent bounded adaptive function.
Optionally, solving the linear equation set based on the RNDAC-ZNN model specifically includes: bringing the expression of the RNDAC-ZNN model into the error function of a system of linear equationsIn (1), obtaining:
wherein the method comprises the steps ofIs->After bringing in the specific values of the coordinates, the first derivative form of (a) is determined with regard to +.>Is about->The solution of (a) is the AoA positioning result.
The invention has the beneficial effects that: the RNDAC-ZNN model-based AoA positioning method provided by the application comprises the steps of 1, using an RNDAC-ZNN model integrating various residual information, remarkably enhancing the convergence performance of the AoA and improving the convergence speed, and under the condition of enough calculation power, the RNDAC has stronger timeliness; 2. the AoA positioning method based on the RNDAC-ZNN model overcomes the defect that the AoA positioning method cannot realize global convergence under the condition of noise interference, and greatly improves the performance of accurately solving the model under the condition of noise interference; 3. compared with the method that some models are converted into non-time-varying or the time-invariant problem is assumed to be solved within a period of time, the method for positioning the AoA based on the RNDAC-ZNN model considers that the environment to be actually solved uses a time-varying equation, so that the influence of environmental parameters and time hysteresis errors in the actual solving process are avoided; 4. the three-dimensional AoA positioning problem is converted into a mathematical linear time-varying matrix decomposition and zero finding problem to be solved, the solving difficulty is reduced, and the positioning accuracy of the proposed model is higher.
Drawings
Fig. 1 is a flow chart of an AoA positioning method based on an RNDAC-ZNN model in an embodiment of the present application;
fig. 2 is a schematic diagram of a 3D-AoA positioning method according to an embodiment of the present application;
FIG. 3 is a graph showing the path comparison between the actual solution and the theoretical solution of RNDAC-ZNN in the embodiment of the present application;
FIG. 4 is a graph comparing error norms of RNDAC-ZNN and OZNN, NTZNN, NZNN in the embodiment of the present application;
FIG. 5 is a real-time position error map of RNDAC-ZNN to resolve AoA positioning in embodiments of the present application;
fig. 6 is a graph of error norms for RNDAC-ZNN to resolve AoA positioning under various noise conditions in an embodiment of the present application.
Detailed Description
The technical scheme of the invention is further elaborated below by referring to the drawings in the specification and the specific embodiments. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used herein 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. In the following description, reference is made to the expression "some embodiments" which describe a subset of all possible embodiments, but it should be understood that "some embodiments" may be the same subset or a different subset of all possible embodiments and may be combined with each other without conflict.
In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that the invention may be practiced without one or more of these details. In other instances, well-known features have not been described in detail in order to avoid obscuring the invention.
It should be understood that the present invention may be embodied in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. And the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, 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. As used herein, the term "and/or" includes any and all combinations of the associated listed items.
It will be further understood that when an element is referred to as being "fixed to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present. The terms "vertical," "horizontal," "inner," "outer," "left," "right," and the like are used herein for illustrative purposes only and are not meant to be the only embodiment.
In order to provide a thorough understanding of the present invention, detailed structures will be presented in the following description in order to illustrate the technical solutions presented by the present invention. Alternative embodiments of the invention are described in detail below, however, the invention may have other implementations in addition to these detailed descriptions.
Referring to fig. 1 in combination, the present application provides an AoA positioning method based on an RNDAC-ZNN model, where the positioning method includes:
s1, forming a linear equation set about a coordinate equation based on position coordinates of an ith base station to a jth base station;
s2, constructing an RNDAC-ZNN model based on an original NZNN model;
and S3, solving the linear equation set based on the RNDAC-ZNN model to obtain a solution about the target position.
Specifically, the incident angle of the jth base station is set asThe pitch angle is +.>The position coordinate of the jth base station is +.>Where j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
wherein the method comprises the steps ofIs a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant.
Further, the method for converting the coordinate equation into the linear equation set specifically includes:
will beDenoted as->Will->Denoted as->Will beDenoted as->Thus, the linear equation is formed as: />And define its error function as +.>Wherein->Representing the error function of the aforementioned linear equation.
Specifically, the constructed RNDAC-ZNN model is as follows:
wherein,for regulating the coefficient->For the feedback coefficient->Representing an adaptive control function->Representing an adaptive feedback activation function->The element representing time t, < >>Representation->Is a function of the integral of (a).
In some embodiments of the present application, the constructed RNDAC-ZNN model can be used to solve LR decomposition problems and QR decomposition problems in practical applications, where LR decomposition can be applied to image watermarking, finite difference and finite element methods, recursive segmentation algorithms, and so on, many problems in engineering can be solved by converting into LR decomposition, which shows superior decomposition characteristics and reduces many calculation amounts, such as parallel operation research. QR decomposition can be applied to pseudo-inverse computation of matrices, least squares fitting, and is applied in real life to adaptive beamformers for ultrasound imaging.
For example, when solving the LR decomposition problem, the RNDAC-ZNN model is deformed into the form of the RNDAC-LZNN model, and the evolution formula is as follows:
order theThe following equation can be obtained:
vectorization is performed on the above results in:
order theRNDAC-LZNN is given as:
the noise model is as follows:
when the RNDAC-ZNN model solves the problem of QR solution, the RNDAC-LZNN model is deformed into an RNDAC-LZNN form, and an evolution formula is as follows:
order theThe following equation can be obtained: />
Vectorization is performed on the above results in:
converting the above formula into a matrix form, the RNDAC-QZNN model can be changed into:
the noise model is as follows:
further, the adaptive control function includes a power bounded adaptive function and an exponent bounded adaptive function.
Wherein the power bounded adaptive function is expressed as:
the expression of the exponential bounded adaptive function is:
in both cases, where i, j=1, 2,..n, whereAnd->Is a positive parameter defining an upper bound and a lower bound, controlling the behavior of the function within the bounds. Parameter->Is adjusted to limit the residual error of the solution system and to enhance its robustness. Parameter->And->Is used forSuper parameter for controlling convergence speed
Specifically, for the linear equation:it->，/>，QR decomposition->The method comprises the following steps:
wherein,is an orthogonal matrix->Is an upper triangular matrix, which is composed of orthogonal moment
The array properties are:
wherein the method comprises the steps ofRepresents the upper triangular matrix, 0 represents the zero matrix, < ->Representing the rank of B.
Order theThe method can obtain:
based on the solving process of the general solution, the expression of the RNDAC-ZNN model is brought into an error function of a linear equation setIn (1), obtaining:
wherein the method comprises the steps ofIs->In the form of the first derivative of the brought coordinatesAfter specific values, the relation +.>Is about->The solution of (a) is the AoA positioning result.
In order to verify the effect of the present invention, the present application further provides a process of designing and executing a verification experiment, such as fig. 2, which shows a solid model of the AoA positioning method.
For experimental needs, the OZNN model is given:
，
NTZNN model:
，
N-Acf activated NZNN:
,
wherein the N-Acf activation function is:
and (3) experimental parameter design:,/>，/>，/>and the initial states of the models are randomly generated.
Wherein the activation function of RNDAC-ZNN is designed
Power bounded adaptive function:
exponential bounded adaptive function:
in this experimental example, the moving path of the moving object is:
the number of base stations in the computer simulation experiment was set to 2. Their locations wereAndthe path solved by the RNDAC-ZNN model in the AoA positioning in figure 3 indicates that the actual path and the path track are almost completely unified, and the fitting degree is extremely high. In FIG. 4, the steady state error convergence of RNDAC is most accurate with respect to the OZNN, NTZNN, NZNN error, and in FIG. 5, it is indicated that the solving position of RNDAC-ZNN has a real-time steady state error of +.>On the order of magnitude of (2).
Experiments under noise conditions were designed for the integrity of the experiments and the robustness of the performance model. Wherein the constant noise is [5; 5] (the variation range of the bounded random noise is [ -2,2]; the linear time-varying noise is t, t and t. FIG. 6 shows the steady-state norms of the RNDAC-ZNN under various noise conditions, which shows that the RNDAC-ZNN has strong noise immunity under the influence of noise, and the solving process under the influence of environment has almost no influence on the RNDAC-ZNN, so that the strong robustness of the RNDAC-ZNN model to AoA solving is proved, the AoA positioning method based on the RNDAC-ZNN model has high convergence rate, and the CPU solving time is approximately equal to 0.1s convergence. Under the condition of enough calculation force, RNDAC timeliness is stronger.
The foregoing is merely illustrative embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think about variations or substitutions within the technical scope of the present invention, and the invention should be covered. The scope of the invention is to be determined by the appended claims.
Claims (6)
1. An AoA positioning method based on an RNDAC-ZNN model, wherein the positioning method comprises the following steps:
forming a linear equation set about the coordinate equation based on the position coordinates of the i base station to the j base station;
constructing an RNDAC-ZNN model based on the original NZNN model;
solving the linear equation set based on the RNDAC-ZNN model to obtain a solution about the target position.
2. The method for positioning AoA based on RNDAC-ZNN model as claimed in claim 1, wherein the incidence angle of the jth base station is set asThe pitch angle is +.>The position coordinate of the jth base station is +.>Where j belongs to 1,2, 3..n, n is a constant, and the coordinate equation thus formed is:
wherein the method comprises the steps ofIs a calculation parameter related to the distance from the base station to the origin of the virtual three-dimensional coordinate system, wherein the value of n is constant, t is a time value,/for the base station>Indicating the angle of incidence of the nth base station, +.>、/>、/>Representing the position coordinates.
3. The method for positioning an AoA based on an RNDAC-ZNN model according to claim 2, wherein the transforming the coordinate equation into a system of linear equations comprises:
will beDenoted as->Will->Denoted as->Will beDenoted as->Thus, the linear equation is formed as: />And define its error function as +.>Wherein->Representing the error function of the aforementioned linear equation.
4. The AoA positioning method based on the RNDAC-ZNN model according to claim 3, wherein the constructed RNDAC-ZNN model is:
wherein,for regulating the coefficient->For the feedback coefficient->Representing an adaptive control function->Representing an adaptive feedback activation function->The element representing time t, < >>Representation->Integration of->Representing the error function of the model.
5. The method of claim 4, wherein the adaptive control function comprises a power-bounded adaptive function and an exponential-bounded adaptive function.
6. The method for positioning an AoA based on an RNDAC-ZNN model according to claim 5, wherein solving the system of linear equations based on the RNDAC-ZNN model specifically comprises: bringing the expression of the RNDAC-ZNN model into the error function of a system of linear equationsIn (1), obtaining:
wherein the method comprises the steps ofIs->After bringing in the specific values of the coordinates, the first derivative form of (a) is determined with regard to +.>In relation to the solution of (1)The solution of (a) is the AoA positioning result.
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| US11658752B1 (en) * | 2022-01-21 | 2023-05-23 | Qinghai Normal University | Node positioning method for underwater wireless sensor network (UWSN) based on zeroing neural dynamics (ZND) |
| CN116383574A (en) * | 2023-03-23 | 2023-07-04 | 哈尔滨工业大学 | Humanoid upper limb robot inverse kinematics solving method based on high-order differentiator |
| CN116702828A (en) * | 2023-03-02 | 2023-09-05 | 广东技术师范大学 | Adaptive gradient neuromechanical optimization method and application thereof in AOA (automated optical analysis) positioning |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107391445A (en) * | 2017-07-19 | 2017-11-24 | 曲阜师范大学 | A kind of neural computation model for solution matrix equation group |
| US11658752B1 (en) * | 2022-01-21 | 2023-05-23 | Qinghai Normal University | Node positioning method for underwater wireless sensor network (UWSN) based on zeroing neural dynamics (ZND) |
| CN116702828A (en) * | 2023-03-02 | 2023-09-05 | 广东技术师范大学 | Adaptive gradient neuromechanical optimization method and application thereof in AOA (automated optical analysis) positioning |
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