CN108871329B - Indoor positioning method and device, electronic equipment and storage medium - Google Patents
Indoor positioning method and device, electronic equipment and storage medium Download PDFInfo
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Abstract
The embodiment of the invention provides an indoor positioning method, an indoor positioning device, electronic equipment and a storage medium, wherein the method comprises the following steps: acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node; obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of an optimization theory; determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm; respectively bringing the values of the position parameters into the convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes. The embodiment of the invention realizes the purpose of obtaining the global optimal solution with stable indoor target position.
Description
Technical Field
The present invention relates to the field of indoor positioning technologies, and in particular, to an indoor positioning method and apparatus, an electronic device, and a storage medium.
Background
Accurate indoor positioning is an important and novel emerging technology that is widely used in commercial, internet of things, public safety, and military applications. However, indoor positioning presents many challenges due to complex signal propagation caused by obstacles like walls, ceilings, moving people, etc. In recent years, various technical solutions have been proposed for Indoor positioning systems, such as infrared, ultrasonic, radio frequency identification, wifi, bluetooth, sensor network, ultra wide band, terrestrial magnetism, visual analysis, pseudolite, etc., each of which utilizes a specific positioning technology or integrates some of them, and they make trade-offs between the performance and complexity of IPS (Indoor positioning systems).
With the increase of the demand of high-precision positioning, positioning based on mixed signals is a good choice, and in the prior art, in the aspect of obtaining the optimal positioning solution, SDR (Semi-fine Relaxation) is widely applied. The SDR is a convex optimization positioning method, and the specific mode is to convert a least square or maximum likelihood estimation nonlinear problem into an equivalent convex optimization problem, then introduce the SDR to convert a joint positioning problem into a low-complexity semi-definite programming problem, and further obtain a global optimal solution of a target position.
However, since SDP is an approximate algorithm that seeks to be effective, the solution found is an approximate global optimal solution, and an accurate lower bound needs to be obtained when solving the positioning problem, the numerical result of the semi-definite programming calculation has a floating point number rounding error, and since the global optimal solution is likely to be an algebraic expression, the calculation result can only be approximately satisfied, that is, only the global optimal solution with an approximate target position can be found, and a stable solution of the target position cannot be found.
Disclosure of Invention
The embodiment of the invention aims to provide an indoor positioning method, an indoor positioning device, electronic equipment and a storage medium, so as to obtain a stable global optimal solution of an indoor target position. The specific technical scheme is as follows:
in order to achieve the above object, an embodiment of the present invention discloses an indoor positioning method, including:
acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node;
obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of an optimization theory;
determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
respectively bringing the values of the position parameters into the convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
Optionally, before the obtaining of the signal propagation delay and angle of the target node, the method further includes:
respectively establishing an equation set of signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node;
the obtaining of the coordinate expression of the target node according to the signal propagation delay and the angle of the target node includes:
and solving each equation group of the non-collinear sensor nodes with the preset number to obtain a coordinate expression of each sensor node corresponding to the target node.
Optionally, after obtaining the coordinate expression of the target node according to the signal propagation delay and the angle of the target node, the method further includes:
squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the abscissa error parameters in each equation set to obtain a first expression;
squaring the ordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the ordinate error parameters in each equation set to obtain a second expression;
and determining an expression obtained by adding the first expression and the second expression as an expression of an error parameter included in the coordinate expression of the target node.
Optionally, before obtaining the convex difference function of the error parameter of the target node with respect to the position parameter according to the analytic equivalence of the lebbeck set of the convex function and the optimality condition of convex maximization and inverse convex optimization related to the optimization theory, the method further includes:
determining a parameter position obtained by transposing the position parameter in the coordinate expression of the target node containing the error value as a first position corresponding to the position parameter of the target node;
the obtaining a convex difference function of the error parameter of the target node with respect to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of an optimization theory includes:
and converting the error parameters included in the coordinate expression of the target node into convex difference functions corresponding to the position parameters and the first position through the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory.
Optionally, the determining, according to an auxiliary problem principle and a sub-gradient algorithm, the value of each position parameter when the partial derivative of the convex difference function is zero includes:
transforming the convex difference function into an objective function capable of solving a partial derivative by using a sub-gradient algorithm through a preset inequality and a preset equality in the auxiliary problem principle; wherein the objective function is a function of a location parameter for the target node in the convex difference function;
and solving the partial derivative of the objective function, and determining the value of the position parameter when the partial derivative of the objective function is zero.
In order to achieve the above object, an embodiment of the present invention further discloses an indoor positioning device, including:
the system comprises an expression determining module, a coordinate calculating module and a coordinate calculating module, wherein the expression determining module is used for acquiring the signal propagation delay and angle of a target node and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, and the coordinate expression comprises a position parameter and an error parameter of the target node;
the convex difference function determining module is used for obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of the optimization theory;
the parameter value determining module is used for determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
a target coordinate determination module, configured to bring the values of the respective position parameters into the convex difference function, and determine the value of the position parameter when the convex difference function value is the minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
Optionally, the apparatus further comprises:
the system comprises an equation set establishing module, a target node establishing module and a data processing module, wherein the equation set establishing module is used for respectively establishing an equation set of signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node;
the expression determining module is specifically configured to solve each equation group of the preset number of non-collinear sensor nodes to obtain a coordinate expression of each sensor node corresponding to the target node.
Optionally, the apparatus further comprises:
the first expression determining module is used for squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the abscissa error parameters in each equation set to obtain a first expression;
the second expression determining module is used for squaring the ordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the ordinate error parameters in each equation set to obtain a second expression;
and a third expression determining module, configured to determine an expression obtained by adding the first expression to the second expression as an expression of an error parameter included in the coordinate expression of the target node.
Optionally, the apparatus further comprises:
a first position determining module, configured to determine a parameter position obtained by transposing the position parameter in the coordinate expression of the target node that includes an error value, as a first position corresponding to the position parameter of the target node;
the convex difference function determining module is specifically configured to convert the error parameter included in the coordinate expression of the target node into a convex difference function corresponding to the position parameter and the first position through analytic equivalence of a lebesge set of the convex function and optimality conditions of convex maximization and inverse convex optimization related to an optimization theory.
Optionally, the parameter value determining module is specifically configured to transform the convex difference function into an objective function capable of solving a partial derivative by using a sub-gradient algorithm, through a preset inequality and a preset equality in the auxiliary problem principle; wherein the objective function is a function of a location parameter for the target node in the convex difference function; and solving the partial derivative of the objective function, and determining the value of the position parameter when the partial derivative of the objective function is zero.
In order to achieve the above object, an embodiment of the present invention further discloses an electronic device, which includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory complete mutual communication through the communication bus;
the memory is used for storing a computer program;
the processor is configured to implement any one of the above-described indoor positioning methods when executing the program stored in the memory.
In order to achieve the above object, an embodiment of the present invention further discloses a computer-readable storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the method of any one of the above indoor positioning methods is implemented.
Embodiments of the present invention also provide a computer program product containing instructions, which when run on a computer, cause the computer to perform any one of the above-mentioned indoor positioning methods.
The indoor positioning method, the indoor positioning device, the electronic equipment and the storage medium can achieve the purpose of obtaining a global optimal solution with stable indoor target positions. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of an indoor positioning method according to an embodiment of the present invention;
FIG. 2 is a flowchart of a convex difference function processing method in an indoor positioning method according to an embodiment of the present invention;
FIG. 3 is a schematic structural diagram of an indoor positioning apparatus according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Due to the development of information technology, indoor positioning technology is also widely applied. With the increase of high-precision positioning requirements, positioning based on mixed signals is a good choice, and in the aspect of obtaining the optimal positioning solution, maximum likelihood estimation and a nonlinear least square method are applied most at present. Since the maximum likelihood estimation and the nonlinear least square method need to use a cost function, the cost function is multi-peak, and the maximum likelihood estimation algorithm is a non-convex optimization problem, it is difficult to ensure that the global convergence is obtained. The semi-fixed program relaxation method in convex optimization balances between a nonlinear method and a linear method, namely the convex optimization method has the characteristics of high accuracy and global convergence. Non-convex optimization problems, such as maximum likelihood estimation and non-linear least squares, can be converted into a convex second order cone program or a semi-ideal program by relaxation methods, and then can be solved by existing solutions.
For example, the existing SDR (Semi-fine Relaxation) is a convex optimization positioning method. The specific method is to convert the least square or maximum likelihood estimation nonlinear problem into an equivalent convex optimization problem, then introduce SDR to convert the joint positioning problem into a low-complexity semi-definite programming problem, and further obtain the global optimal solution of the target position. However, since SDP is an approximation algorithm that seeks efficiency, the solution found is an approximate global optimum solution, and a stable solution for the target position cannot be obtained.
In order to solve the above problems, embodiments of the present invention disclose an indoor positioning method, an indoor positioning device, an electronic device, and a storage medium, so as to obtain a global optimal solution with a stable indoor target position. The specific technical scheme is as follows:
in order to achieve the above object, an embodiment of the present invention discloses an indoor positioning method, as shown in fig. 1. Fig. 1 is a flowchart of an indoor positioning method according to an embodiment of the present invention, including:
s101, obtaining the signal propagation delay and the angle of the target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and the angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node.
Aiming at the problem that a stable global optimal solution cannot be obtained in the indoor positioning method in the prior art, the embodiment of the invention provides a method for solving the stable global optimal solution of indoor fusion positioning of TOA (time of Arrival) and AOA (Angle of Arrival), so that the error of indoor positioning is reduced.
The TOA positioning technology realizes network positioning, and the sound wave has low cost and low hardware complexity relative to a wireless radio frequency signal, thereby being beneficial to time synchronization of a sender and a receiver. Assuming that the transmitting and receiving nodes are time synchronized and each node contains a transmitter and a receiver, the transmitter transmits an acoustic wave named chirp and at the same time contains the transmission in the acoustic wave to tell the receiver. And after receiving the chirp sound waves, the receiver extracts the sending time from the chirp sound waves, and calculates the distance between the sending node and the receiving node by utilizing a propagation model of the sound waves in the atmosphere. Overall, TOA-based positioning is simple to implement and high in positioning accuracy, but accurate time synchronization is required to be maintained between nodes, which puts high requirements on hardware and power consumption of nodes of a sensor node network.
The AOA positioning technology acquires the angle information of radio wave signals transmitted by a terminal by arranging a directional antenna or an array antenna at more than two position points, and then estimates the position of the terminal by an intersection method. It only needs two antenna arrays to complete the initial positioning of the target. The positioning accuracy of the AOA is greatly influenced by the density, height and topography of the building, and the typical values of the AOA are 360 degrees, 20 degrees and 1 degree in indoor, urban and rural areas respectively. As the distance between the base station and the terminal increases, the positioning accuracy of the AOA gradually decreases. The AOA positioning error is mainly caused by urban multipath propagation and system error, the influence of the system error can be counteracted through pre-correction, the multipath effect in a dense building area is always a difficult problem troubling antenna communication, and an intelligent antenna can reduce the influence of multipath interference to a certain extent, but is not widely applied due to the problems of complexity in implementation and equipment cost. Therefore, the AOA technique, although simple in structure, has not been applied to the urban cellular positioning system.
In this step, first, based on the basic principle of TOA and AOA positioning technologies, the signal propagation delay and angle of the target node are obtained. And then obtaining a coordinate expression of the target node according to the signal propagation delay and the angle of the target node.
Specifically, a plurality of non-collinear sensor nodes can be deployed at will in an observation area, and each sensor node respectively acquires signal propagation delay and angle with the target node. And respectively establishing equation sets according to the signal propagation delay and the angle relation between each sensor node and the target node, and solving each equation set to obtain a coordinate expression of the target node corresponding to each sensor node. Because each sensor node has a time error in the process of detecting the signal propagation with the target node, and has an angle error in the process of detecting the angle with the target node, and further, an equation established by each sensor node and the target node has a time error and an angle error, the coordinate expression of the target node obtained by solving the equation set includes the spatial position of the target node, namely the position parameter of the target node, and includes an error existing in the process of estimating the accurate position of the target node, namely the error parameter of the target node.
And S102, obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of the optimization theory.
The convex function is a real-valued function f defined over a convex subset C (interval) of a certain vector space, and for any two vectors x1, x2 in the convex subset C, there is f ((x1+ x2)/2) ≦ f (x1) + f (x 2))/2.
The Leibegger theorem reveals the theorem on the relationship between almost everywhere convergence and measure-dependent convergence. It asserts that if f (x) (n 1,2, w) and f (x) are almost everywhere finite measurable functions on the measurable set E, and the sequence of functions { person (x) } converges almost everywhere on E to f (x), then { { f, } x } converges on E to f (x) in a measure.
The theory of optimization is a mathematical problem that studies the minimum (or maximum) of a function given a set of constraints. Optimality conditions refer to conditions that must be met for a locally or globally optimal solution to an optimization problem. The optimality condition of the global optimization problem is used as a theoretical basis for data calculation, and one of basic research objects is the global optimal solution of the optimization problem. The global optimality condition is a basic tool to characterize whether a feasible solution is a globally optimal solution.
In this step, the coordinate expression of the target node obtained in step S101 is converted into a convex difference function using the position parameter of the target node as an independent variable and the error parameter of the target node as a dependent variable, according to the convex function property, the lebesge theorem, and the global optimality condition of the optimization theory.
Specifically, a global optimality condition related to a classical optimization theory is obtained through an analysis equivalent set of a Leeberg set of a convex function. And replacing inequality constraints in the non-convex optimization problem by using global optimality conditions, and further obtaining a convex difference function of the error parameters of the target node relative to the position parameters.
S103, determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm.
After the convex difference function of the error parameter of the target node with respect to the position parameter is determined, the value of each position parameter when the partial derivative of the convex difference function is zero is determined according to the auxiliary problem principle and the sub-gradient algorithm in the step.
The principle of the problem is explained by taking the minimization as an example. Assuming that the function J1(x) is differentiable, the function J2(x) is not necessarily differentiable, and the minimum value is solved for the original problem J1(x) + J2(x), if an auxiliary problem ming (x) + J2(x) is constructed, and x is present so that G '(x) ═ J1' (x) is established, the original problem can be converted into solving the auxiliary problem, x is the solution of the original problem, and G (x) is called as an auxiliary function. The construction aid function is of the form g (x) ═ K (x) +< J '(x) -K' (x), x >, where K (x) is a kernel function; <, > represents the product of numbers.
The algorithm of the sub-gradient type is simply called derivation, and the one-dimensional sub-gradient is called a sub-derivative, and the sub-gradient of the function at a point can be found by finding the sub-derivative of the function at each component of the point.
According to the auxiliary problem principle and the sub-gradient algorithm principle, a convex difference function of the error parameters of the target node in S102 with respect to the position parameters is solved, and the value of each position parameter is obtained when the partial derivative is zero.
S104, respectively bringing the values of the position parameters into a convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
And after the value of each position parameter is obtained when the partial derivative of the convex difference function is zero, bringing the value of each position parameter back to the convex difference function, and obtaining the value of the convex difference function corresponding to the value of each position parameter. The smallest value among all the convex difference function values is selected and determined as the target value of the convex difference function value. And further determining a coordinate expression of the target node position corresponding to the target value, and obtaining the accurate coordinate position of the target node through the coordinate expression.
The indoor positioning method provided by the embodiment of the invention can realize obtaining of a global optimal solution with stable indoor target position. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
Optionally, in an embodiment of the indoor positioning method in the embodiment of the present invention, before acquiring the signal propagation delay and angle of the target node, the method further includes:
step one, respectively establishing an equation set of signal propagation delay and angle of a preset number of non-collinear sensor nodes and a target node.
The embodiment of the invention provides an implementation method for determining a coordinate expression of an indoor target node to be positioned. This step is an implementation of establishing an equation set for the signal propagation delay and angle of the target position detected by each sensor node.
In this step, considering the measurement of the target node position in two-dimensional space using hybrid TOA/AOA, L non-collinear sensor nodes are arbitrarily deployed first in the observation area, and the coordinates of the sensor nodes can be expressed as xi＝[xi,yi]T,(xi∈R2) 1.., L, wherein xiAbscissa, y, representing the ith sensor nodeiIndicating the ordinate of the i-th sensor node. The coordinates of the target node may be expressed as u ═ x, y]T,(u∈R2)。
Assuming that all sensor node clocks are ideally synchronized, all sensor nodes can receive the signal from the target node, and each sensor node can measure the signal transmitted from the target nodeTOA and AOA, let tiRepresenting the signal propagation delay, θ, from the target node to the i-th sensor nodeiRepresenting the angle from the target node to the ith sensor node, the target node and the ith sensor node may establish the following equation set:
wherein c represents the signal propagation speed; | l | represents the euclidean norm, when the signal leaves the target node, the local time of the ith sensor node is 0; x is the number ofiAn abscissa representing an ith sensor node; y isiRepresents the ordinate of the ith node; u represents the coordinates of the target node; x represents the abscissa of the target node; y represents the ordinate of the target node; e.g. of the typetiRepresenting a signal propagation delay error from the target node to the ith sensor node; e.g. of the typeθiRepresenting the angle measurement error from the target node to the ith sensor node.
In the above manner, a system of equations for each sensor node and the target node is established. The specific process is similar to the real-time steps described above, and is not described here again.
Obtaining a coordinate expression of the target node according to the signal propagation delay and the angle of the target node, wherein the coordinate expression comprises the following steps:
and step two, solving each equation group of the non-collinear sensor nodes with the preset number to obtain a coordinate expression of each sensor node corresponding to the target node.
After the equation sets of each sensor node and the target node are obtained, the equation sets are respectively solved, and then the coordinate expression of each sensor node about the target node is obtained.
For example, according to the equation set established by the ith sensor node and the target node in the step one, the following coordinate expression of the target node can be obtained:
wherein the content of the first and second substances,
representing the abscissa of the target node obtained by an equation set established by the ith sensor node and the target node;
expressing a vertical coordinate of a target node obtained by an equation set established by the ith sensor node and the target node; x is the number ofiAn abscissa representing an ith sensor node; y isiDenotes the ordinate, θ, of the i-th sensor nodeiRepresenting the angle of the ith sensor node and the target node; e.g. of the typexiError representing the abscissa of the ith sensor node; e.g. of the typeyiError of ordinate representing ith sensor node, which is summed with e in step oneti、eθiIs a non-linear functional relationship.
Therefore, the embodiment of the invention can obtain the coordinate expression of the target node through the sensor nodes, further obtain the expression of the target node through the equation relation between each sensor node and the target node, realize the positioning of the target node through a plurality of sensor nodes, and further ensure that the coordinate position of the target node is accurately obtained in the later period.
Optionally, in an embodiment of the indoor positioning method in the embodiment of the present invention, after obtaining the coordinate expression of the target node according to the signal propagation delay and the angle of the target node, the method further includes:
step A, squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the abscissa error parameters in each equation set to obtain a first expression.
The embodiment of the invention relates to an implementation method for determining an error parameter expression in a coordinate expression of a target node. In the step, a first expression corresponding to the abscissa error parameter in the error expressions is determined.
Specifically, the error parameter square of the abscissa in the coordinate expression of the sensor node corresponding to the target node is used to obtain a first expression.
For example, the first expression may be expressed as
Wherein e isxiRepresenting the abscissa error of the ith sensor node; x is the number ofiAn abscissa representing an ith sensor node; diRepresenting the distance between the ith sensor node and the target node; thetaiThe angle of the ith sensor node to the target node is shown, and x represents an unknown abscissa of the target node.
According to the method, the first expression of each sensor node corresponding to the target node is obtained.
And step B, squaring the vertical coordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the vertical coordinate error parameters in each equation set to obtain a second expression.
In the step, a second expression corresponding to the ordinate error parameter in the error expression is determined.
Specifically, the error parameter square of the ordinate in the coordinate expression of the sensor node corresponding to the target node is obtained to obtain a second expression.
For example, the second expression can be expressed as
Wherein e isyiRepresenting the ordinate error of the ith sensor node; y isiRepresents the ordinate of the ith sensor node; diRepresenting the distance between the ith sensor node and the target node; thetaiRepresenting the angle of the ith sensor node and the target node; y represents the ordinate unknown to the target node.
And obtaining a second expression of each sensor node corresponding to the target node according to the mode.
And step C, determining an expression obtained by adding the first expression and the second expression as an expression of the error parameter included in the coordinate expression of the target node.
After the first expression and the second expression of the target node corresponding to each sensor node are obtained, the first expression and the second expression are added to obtain the expression of the error parameter included in the coordinate expression of the target node.
For example, the first expression and the second expression of the target node corresponding to the sensor node are added to obtain an expression of the error parameter of the target node corresponding to the sensor node, that is:
according to the method, the expression of the error parameter of each sensor node is obtained, and then the expressions of the error parameters of each sensor node are added to obtain the expression of the error parameter included in the coordinate expression of the target node in the embodiment of the invention.
Therefore, the error parameter expressions of the target expressions corresponding to all the sensor nodes can be determined through the embodiment of the invention, and the convex difference function of the error parameters can be conveniently obtained through the error parameter expressions in the later period.
Optionally, in an embodiment of the indoor positioning method provided in the embodiment of the present invention, before obtaining a convex difference function of an error parameter of a target node with respect to a position parameter according to analytic equivalence of a lebbeck set of a convex function and optimality conditions of convex maximization and inverse convex optimization related to an optimization theory, the method further includes:
and determining a parameter position obtained by transposing the position parameter in the coordinate expression of the target node containing the error value as a first position corresponding to the position parameter of the target node.
The embodiment of the invention relates to an implementation method of a convex difference function of error parameters of a determined target node relative to position parameters.
In this step, the parameter position obtained by transposing the position parameter can be determined as the first position, thereby ensuring that the convex difference function determined in the following step is related to the position parameter of the target node.
Specifically, the position parameter in the coordinate expression of the target node including the error value may be transposed by using a transposition operation, so as to obtain a first position corresponding to the position parameter of the target node.
For example, the position corresponding to the position parameter is represented by u ═ x, y]Then the first position can be represented as
Obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of an optimization theory, wherein the convex difference function comprises the following steps:
and converting the error parameters included in the coordinate expression of the target node into convex difference functions corresponding to the position parameters and the first position through the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory.
The above expression of the error parameter included in the coordinate expression of the target node
After the determination, the expression of the error parameters of all sensor nodes can be expressed as:
subject to y＝Aξ
wherein the content of the first and second substances,
the above-mentioned y ═ a ζ is a typical non-convex optimization problem, and only an approximate global optimal solution can be obtained by using least square or sum-convex relaxation, but a stable global optimal solution cannot be obtained. In order to obtain a stable global optimal solution, the above formula y ═ a ζ is transformed into a convex difference function corresponding to the position parameter and the first position of the embodiment of the present invention, using the analytic equivalence of the lebbeck set and the global optimality condition of the optimization theory:
wherein the content of the first and second substances,
u∈{(x,y)|x,y∈Rn}。
therefore, the convex difference function of the error parameter of the target node relative to the position parameter is obtained through the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of the optimization theory, and the stable global optimal solution of the indoor target position is obtained conveniently in the later period through the convex optimization characteristic of the convex difference function.
Alternatively, in an embodiment of the indoor positioning method provided in the embodiment of the present invention, the values of the position parameters when the partial derivative of the convex difference function is zero are determined according to an auxiliary problem principle and a sub-gradient algorithm, as shown in fig. 2. Fig. 2 is a flowchart of a convex difference function processing method in an indoor positioning method according to an embodiment of the present invention, where the method includes:
s201, transforming the convex difference function into an objective function capable of solving a partial derivative by using a sub-gradient algorithm through a preset inequality and a preset equality in the auxiliary problem principle; wherein the objective function is a function of a location parameter of the target node in the convex difference function.
The embodiment of the invention provides an implementation method for determining values of position parameters when a partial derivative of a convex difference function is zero. The step is to determine the transformation of the convex difference function into an objective function capable of solving the partial derivative by using a sub-gradient algorithm.
The principle of the auxiliary problem is as follows: assuming that the function J1(x) is differentiable, the function J2(x) is not necessarily differentiable, and the minimum value is solved for the original problem J1(x) + J2(x), if an auxiliary problem ming (x) + J2(x) is constructed, and x is present so that G '(x) ═ J1' (x) is established, the original problem can be converted into solving the auxiliary problem, x is the solution of the original problem, and G (x) is called as an auxiliary function. The construction aid function is of the form g (x) ═ K (x) +< J '(x) -K' (x), x >, where K (x) is a kernel function; <, > represents the product of numbers.
Specifically, there is an identity in the principle of the problem of assistance
Wherein the content of the first and second substances,
at this time, the convex difference function of the error parameter of the target node with respect to the position parameter may be:
conversion to an objective function capable of solving partial derivatives using a sub-gradient type algorithm:
wherein, the coordinate Θ is assumed to be [ x ═ x0,y0]TIs a solution of the above formula while
In the coordinate theta ═ x0,y0]T，
Is a constant.
Thus, each pair (ξ, φ) ∈ IRn×IR,Λ(ξ)＝Ξ(t,θ)＝φ
There is an inequality:
wherein the content of the first and second substances,
representing the sub-differential of point ξ.
S202, solving the partial derivative of the objective function, and determining the value of the position parameter when the partial derivative of the objective function is zero.
After the objective function capable of solving the partial derivative by using the sub-gradient algorithm is obtained, the partial derivative of the objective function is solved, and the value of the position parameter when the partial derivative of the objective function is zero is determined.
Specifically, the value of the position parameter corresponding to when the partial derivative of the objective function is zero in the following formula is solved:
wherein the content of the first and second substances,
is a function of
The second derivative at point ξ, N (ξ; S), is the normal cone of points ξ vs S.
And after the value of the position parameter when the partial derivative of the objective function is zero in the formula is obtained, the value of each position parameter is respectively brought into a convex difference function of the error parameter relative to the position parameter, and the value of the corresponding position parameter when the convex difference function value is minimum is determined as the target value. And further determining a coordinate expression of the target node position corresponding to the target value, and obtaining the accurate coordinate position of the target node through the coordinate expression.
Therefore, the embodiment of the invention calculates the partial derivative of the target function, determines the value of the position parameter when the partial derivative of the target function is zero, further brings the value of the position parameter when the partial derivative is zero back to the convex difference function, and determines the corresponding expression coordinate when the convex difference function value is minimum as the coordinate of the target node, thereby realizing the purpose of obtaining the stable global optimal solution of the indoor target position.
In order to achieve the above object, an indoor positioning device is further disclosed in the embodiments of the present invention, as shown in fig. 3. Fig. 3 is a schematic structural diagram of an indoor positioning device according to an embodiment of the present invention, where the device includes:
the expression determining module 301 obtains a coordinate expression of the target node from the angle, where the coordinate expression includes a position parameter and an error parameter of the target node;
a convex difference function determining module 302, configured to obtain a convex difference function of the error parameter of the target node with respect to the position parameter according to the analytic equivalence of the lebbeck set of the convex function and the global optimality condition of the optimization theory;
a parameter value determining module 303, configured to determine, according to an auxiliary problem principle and a sub-gradient algorithm, a value of each position parameter when a partial derivative of the convex difference function is zero;
a target coordinate determination module 304, configured to bring the values of the position parameters into the convex difference functions, and determine the value of the position parameter when the convex difference function value is the minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
The indoor positioning device provided by the embodiment of the invention can realize the purpose of obtaining the global optimal solution with stable indoor target position. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
Optionally, in an embodiment of the indoor positioning apparatus in the embodiment of the present invention, the apparatus further includes:
the system comprises an equation set establishing module, a data processing module and a data processing module, wherein the equation set establishing module is used for respectively establishing equation sets of signal propagation delay and angle of a preset number of non-collinear sensor nodes and target nodes;
and the expression determining module is specifically used for solving each equation group of the non-collinear sensor nodes with the preset number to obtain a coordinate expression of each sensor node corresponding to the target node.
Optionally, in an embodiment of the indoor positioning apparatus in the embodiment of the present invention, the apparatus further includes:
the first expression determining module is used for squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the abscissa error parameters in each equation set to obtain a first expression;
the second expression determining module is used for squaring the ordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the ordinate error parameters in each equation set to obtain a second expression;
and the third expression determining module is used for determining the expression obtained by adding the first expression and the second expression as the expression of the error parameter included in the coordinate expression of the target node.
Optionally, in an embodiment of the indoor positioning apparatus in the embodiment of the present invention, the apparatus further includes:
the first position determining module is used for determining a parameter position obtained by transposing the position parameter in the coordinate expression of the target node containing the error value as a first position corresponding to the position parameter of the target node;
the convex difference function determining module 302 is specifically configured to convert the error parameter included in the coordinate expression of the target node into a convex difference function corresponding to the position parameter and the first position through the analytic equivalence of the lebbeck set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory.
Optionally, in an embodiment of the indoor positioning device in the embodiment of the present invention, the parameter value determining module 303 is specifically configured to transform the convex difference function into an objective function capable of solving a partial derivative by using a sub-gradient algorithm through a preset inequality and a preset equality in the auxiliary problem principle; wherein the target function is a function of the position parameters of the target nodes in the convex difference function; and solving the partial derivative of the objective function, and determining the value of the position parameter when the partial derivative of the objective function is zero.
In order to achieve the above object, an embodiment of the present invention further discloses an electronic device, as shown in fig. 4. Fig. 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, which includes a processor 401, a communication interface 402, a memory 403, and a communication bus 404, where the processor 401, the communication interface 402, and the memory 403 complete communication with each other through the communication bus 404;
a memory 403 for storing a computer program;
the processor 401, when executing the program stored in the memory 403, implements the following method steps:
acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node;
obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of an optimization theory;
determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
respectively bringing the value of each position parameter into a convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
The communication bus 404 mentioned in the above electronic device may be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The communication bus 404 may be divided into an address bus, a data bus, a control bus, and the like. For ease of illustration, only one thick line is shown, but this does not mean that there is only one bus or one type of bus.
The communication interface 402 is used for communication between the above-described electronic apparatus and other apparatuses.
The Memory 403 may include a Random Access Memory (RAM) or a Non-Volatile Memory (NVM), such as at least one disk Memory. Alternatively, the memory may be at least one memory device located remotely from the processor 401.
The Processor 401 may be a general-purpose Processor, including a Central Processing Unit (CPU), a Network Processor (NP), and the like; but also Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field Programmable Gate Arrays (FPGAs) or other Programmable logic devices, discrete Gate or transistor logic devices, discrete hardware components.
The electronic equipment provided by the embodiment of the invention can realize obtaining of the global optimal solution with stable indoor target position. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
In order to achieve the above object, an embodiment of the present invention further discloses a computer-readable storage medium, in which a computer program is stored, and when the computer program is executed by a processor, the following method steps are implemented:
acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node;
obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of an optimization theory;
determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
respectively bringing the value of each position parameter into a convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
The computer-readable storage medium provided by the embodiment of the invention can realize obtaining of a stable global optimal solution of an indoor target position. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
Embodiments of the present invention also provide a computer program product comprising instructions which, when run on a computer, cause the computer to perform the following method steps:
acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node;
obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization of an optimization theory;
determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
respectively bringing the value of each position parameter into a convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; and determining the coordinates corresponding to the target values as target coordinates of the target nodes.
The computer program product containing the instructions provided by the embodiment of the invention can realize obtaining a stable global optimal solution of an indoor target position. Specifically, a coordinate expression of the target node is obtained according to the signal propagation delay and the angle of the target node detected by the non-collinear sensor nodes of the preset number, wherein the coordinate expression comprises a position parameter and an error parameter of the target node. And then according to the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory, obtaining a convex difference function of the error parameter of the target node relative to the position parameter, namely converting the error parameter into the convex difference function, and determining the value of each position parameter corresponding to the convex difference function with the partial derivative being zero by using an auxiliary problem principle and a sub-gradient algorithm under the convex difference function. And substituting the value of each position parameter corresponding to the partial derivative of zero into the convex difference function, and further determining the value of the position parameter corresponding to the minimum value of the convex difference function, namely the minimum error value. And finally, determining the coordinate corresponding to the minimum error value as the target coordinate of the target node, and realizing obtaining a stable global optimal solution of the indoor target position.
It is noted that, herein, relational terms such as first and second, and the like may be 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. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus 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 apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
All the embodiments in the present specification are described in a related manner, and the same and similar parts among the embodiments may be referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, as for the device, the electronic apparatus and the storage medium embodiments, since they are substantially similar to the method embodiments, the description is relatively simple, and the relevant points can be referred to the partial description of the method embodiments.
The above description is only for the preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention shall fall within the protection scope of the present invention.
Claims (9)
1. An indoor positioning method, characterized in that the method comprises:
acquiring signal propagation delay and angle of a target node, and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression comprises a position parameter and an error parameter of the target node;
determining a parameter position obtained by transposing the position parameter in the coordinate expression of the target node containing the error value as a first position corresponding to the position parameter of the target node;
obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of an optimization theory;
determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
respectively bringing the values of the position parameters into the convex difference function, and determining the value of the position parameter when the convex difference function value is minimum as a target value; determining the coordinates corresponding to the target values as target coordinates of the target nodes;
the obtaining a convex difference function of the error parameter of the target node with respect to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition includes:
and converting the error parameters included in the coordinate expression of the target node into convex difference functions corresponding to the position parameters and the first position through the analytic equivalence of the Leeberg set of the convex function and the optimality conditions of convex maximization and inverse convex optimization related to the optimization theory.
2. The method of claim 1, wherein prior to said obtaining signal propagation delay and angle for the target node, the method further comprises:
respectively establishing an equation set of signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node;
the obtaining of the coordinate expression of the target node according to the signal propagation delay and the angle of the target node includes:
and solving each equation group of the non-collinear sensor nodes with the preset number to obtain a coordinate expression of each sensor node corresponding to the target node.
3. The method of claim 2, wherein after obtaining the coordinate expression of the target node according to the signal propagation delay and the angle of the target node, the method further comprises:
squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the abscissa error parameters in each equation set to obtain a first expression;
squaring the ordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number, and adding the squares of the ordinate error parameters in each equation set to obtain a second expression;
and determining an expression obtained by adding the first expression and the second expression as an expression of an error parameter included in the coordinate expression of the target node.
4. The method of claim 1, wherein determining the value of each position parameter when the partial derivative of the convex difference function is zero according to a secondary problem principle and a sub-gradient type algorithm comprises:
transforming the convex difference function into an objective function capable of solving a partial derivative by using a sub-gradient algorithm through a preset inequality and a preset equality in the auxiliary problem principle; wherein the objective function is a function of a location parameter for the target node in the convex difference function;
and solving the partial derivative of the objective function, and determining the value of the position parameter when the partial derivative of the objective function is zero.
5. An indoor positioning device, the device comprising:
the system comprises an expression determining module, a coordinate calculating module and a coordinate calculating module, wherein the expression determining module is used for acquiring the signal propagation delay and angle of a target node and obtaining a coordinate expression of the target node according to the signal propagation delay and angle of the target node, and the coordinate expression comprises a position parameter and an error parameter of the target node;
the first position determining module is used for determining a parameter position obtained by transposing the position parameter in the coordinate expression of the target node containing the error value as a first position corresponding to the position parameter of the target node;
the convex difference function determining module is used for obtaining a convex difference function of the error parameter of the target node relative to the position parameter according to the analytic equivalence of the Leeberg set of the convex function and the global optimality condition of the optimization theory;
the parameter value determining module is used for determining the value of each position parameter when the partial derivative of the convex difference function is zero according to an auxiliary problem principle and a sub-gradient algorithm;
a target coordinate determination module, configured to bring the values of the respective position parameters into the convex difference function, and determine the value of the position parameter when the convex difference function value is the minimum as a target value; determining the coordinates corresponding to the target values as target coordinates of the target nodes;
the convex difference function determining module is specifically configured to convert an error parameter included in the coordinate expression of the target node into a convex difference function corresponding to the position parameter and the first position through an analytic equivalence of a Leeberg set of the convex function and optimality conditions of convex maximization and inverse convex optimization related to an optimization theory.
6. The apparatus of claim 5, further comprising:
the system comprises an equation set establishing module, a target node establishing module and a data processing module, wherein the equation set establishing module is used for respectively establishing an equation set of signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node;
the expression determining module is specifically configured to solve each equation group of the preset number of non-collinear sensor nodes to obtain a coordinate expression of each sensor node corresponding to the target node.
7. The apparatus of claim 6, further comprising:
the first expression determining module is used for squaring each abscissa error parameter in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the abscissa error parameters in each equation set to obtain a first expression;
the second expression determining module is used for squaring the ordinate error parameters in each equation set of the non-collinear sensor nodes with the preset number and adding the squares of the ordinate error parameters in each equation set to obtain a second expression;
and a third expression determining module, configured to determine an expression obtained by adding the first expression to the second expression as an expression of an error parameter included in the coordinate expression of the target node.
8. An electronic device, comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory complete communication with each other through the communication bus;
the memory is used for storing a computer program;
the processor, when executing the program stored in the memory, implementing the method steps of any of claims 1-4.
9. A computer-readable storage medium, characterized in that a computer program is stored in the computer-readable storage medium, which computer program, when being executed by a processor, carries out the method steps of any one of claims 1 to 4.
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