CN108871329B - Indoor positioning method and device, electronic equipment and storage medium - Google Patents

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

Indoor positioning method, device, electronic device and storage medium

technical field

The present invention relates to the technical field of indoor positioning, and in particular, to an indoor positioning method, device, electronic device and storage medium.

Background technique

Precise indoor positioning is an important and novel emerging technology widely used in commercial, IoT, public safety, and military applications. However, indoor positioning faces many challenges due to complex signal propagation caused by obstacles such as 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 networks, ultra-wideband, geomagnetic, visual analysis, pseudolites, etc. Each system utilizes specific The positioning technology or integrate some of these technologies, they make a trade-off between the performance and complexity of IPS (Indoor Positioning Systems, indoor positioning systems).

With the increase of high-precision positioning requirements, positioning based on mixed signals is a good choice. In the existing technology, SDR (Semi-Definite Relaxation, semi-definite relaxation method) has been widely used in obtaining the optimal positioning solution. . SDR is a convex optimization localization method. The specific method is to convert the least squares or maximum likelihood estimation nonlinear problem into an equivalent convex optimization problem, and then introduce SDR to convert the joint localization problem into a low-complexity semi-definite programming. problem, and then obtain the global optimal solution of the target position.

However, since SDP is an effective approximation algorithm, the solution obtained is an approximate global optimal solution, and an accurate lower bound needs to be obtained when solving the positioning problem, and the numerical results of the semi-definite programming calculation have floating-point rounding errors. , and because the global optimal solution may be an algebraic formula, the calculation result can only be approximately satisfied, that is, only the approximate global optimal solution of the target position can be obtained, but the stable solution of the target position cannot be obtained.

SUMMARY OF THE INVENTION

The purpose of the embodiments of the present invention is to provide an indoor positioning method, an apparatus, an electronic device and a storage medium, so as to obtain a stable global optimal solution of an indoor target position. The specific technical solutions are as follows:

To achieve the above purpose of the invention, an embodiment of the present invention discloses an indoor positioning method, the method comprising:

Acquire the signal propagation delay and angle of the target node, and obtain the coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes the position parameter of the target node and error parameter;

According to the analytical equivalence of the Lebesgue set of the convex function and the global optimality condition of the optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained;

Determine the value of each position parameter when the partial derivative of the convex difference function is zero according to the principle of the auxiliary problem and the sub-gradient algorithm;

The value of each position parameter is respectively brought into the convex difference function, and the value of the position parameter when the convex difference function value is the smallest is determined as the target value; the coordinate corresponding to the target value is determined as the target The target coordinates of the node.

Optionally, before acquiring the signal propagation delay and angle of the target node, the method further includes:

Establishing equations of the signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node respectively;

Obtaining the coordinate expression of the target node according to the signal propagation delay and angle of the target node, including:

Each equation system of the preset number of non-collinear sensor nodes is solved 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 angle of the target node, the method further includes:

Square each abscissa error parameter in each equation group of the preset number of non-collinear sensor nodes, and add the square of the abscissa error parameter in each equation group to obtain the first expression;

Square each ordinate error parameter in each equation group of the preset number of non-collinear sensor nodes, and add the square of the ordinate error parameter in each equation group to obtain a second expression;

An expression that adds the first expression and the second expression is determined as an expression of the error parameter included in the coordinate expression of the target node.

Optionally, based on the analytical equivalence of the Lebesgue set according to the convex function, and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the error parameter of the target node is obtained with respect to the Before the convex difference function of the position parameter, the method further includes:

The parameter position obtained by transposing the position parameter in the coordinate expression of the target node including the error value is determined as the first position corresponding to the position parameter of the target node;

According to the analytical equivalence of the Lebesgue set of convex functions, and the optimality conditions of convex maximization and inverse convex optimization of optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained ,include:

The error parameters included in the coordinate expression of the target node, the analytical equivalence of the Lebesgue set of convex functions, and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory are converted into the position parameter and the convex difference function corresponding to the first position.

Optionally, determining the value of each position parameter when the partial derivative of the convex difference function is zero according to the principle of the auxiliary problem and the sub-gradient algorithm, including:

Through the preset inequality and preset identity in the auxiliary problem principle, the convex difference function is transformed into an objective function that can use a subgradient algorithm to solve the partial derivative; wherein, the objective function is about the convex difference function. Describe the function of the position parameter of the target node;

A partial derivative is obtained for the objective function, and the value of the position parameter when the partial derivative of the objective function is zero is determined.

To achieve the above purpose of the invention, an embodiment of the present invention further discloses an indoor positioning device, the device comprising:

The expression determination module is used to obtain the signal propagation delay and angle of the target node, and obtain the coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes the Describe the position parameters and error parameters of the target node;

The convex difference function determination module is used to obtain the convex difference function of the error parameter of the target node with respect to the position parameter according to the analytical equivalence of the Lebesgue set of the convex function and the global optimality condition of the optimization theory;

The parameter value determination module is used for determining the value of each position parameter when the partial derivative of the convex difference function is zero according to the principle of the auxiliary problem and the sub-gradient algorithm;

The target coordinate determination module is used to bring the value of each position parameter into the convex difference function respectively, and determine the value of the position parameter when the value of the convex difference function is the smallest as the target value; The coordinates are determined as the target coordinates of the target node.

Optionally, the device further includes:

a set of equations establishing module for respectively establishing a set of equations of the signal propagation delay and angle of a preset number of non-collinear sensor nodes and the target node;

The expression determination module is specifically configured to solve each equation system of the preset number of non-collinear sensor nodes, and obtain a coordinate expression of each sensor node corresponding to the target node.

Optionally, the device further includes:

The first expression determination module is used to square each abscissa error parameter in each equation group of the preset number of non-collinear sensor nodes, and add the square of the abscissa error parameter in each equation group to obtain first expression;

The second expression determination module is used for squaring each ordinate error parameter in each equation group of the preset number of non-collinear sensor nodes, and adding the squares of the ordinate error parameter in each equation group to obtain second expression;

The third expression determination module is configured to determine the expression for adding the first expression and the second expression as an expression of the error parameter included in the coordinate expression of the target node.

Optionally, the device further includes:

a first position determination module, configured to determine the parameter position obtained by transposing the position parameter in the coordinate expression of the target node including the error value as the first position corresponding to the position parameter of the target node;

The convex difference function determination module is specifically used to determine the error parameter included in the coordinate expression of the target node, the analytical equivalence of the Lebesgue set of the convex function, and the convex maximization and inverse convexity related to the optimization theory The optimized optimality condition is converted into a convex difference function corresponding to the position parameter and the first position.

Optionally, the parameter value determination module is specifically configured to transform the convex difference function into an objective function that can solve the partial derivative by using a sub-gradient algorithm by using a preset inequality and a preset identity in the auxiliary problem principle; wherein , the objective function is a function about the position parameter of the target node in the convex difference function; a partial derivative is obtained for the objective function, and the value of the position parameter when the partial derivative of the objective function is zero is determined.

To achieve the above purpose of the invention, an embodiment of the present invention further discloses an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory pass through the communication bus complete communication with each other;

the memory for storing computer programs;

The processor is configured to implement any one of the above indoor positioning methods when executing the program stored in the memory.

In order to achieve the above purpose of the invention, an embodiment of the present invention further discloses a computer-readable storage medium, where a computer program is stored in the computer-readable storage medium, and when the computer program is executed by a processor, the above-mentioned indoor positioning method is realized. any of the methods described.

Embodiments of the present invention also provide a computer program product containing instructions, which, when executed on a computer, cause the computer to execute any one of the above indoor positioning methods.

The indoor positioning method, device, electronic device and storage medium provided by the embodiments of the present invention can achieve a stable global optimal solution for the indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

1 is a flowchart of an indoor positioning method according to an embodiment of the present invention;

2 is a flowchart of a method for processing a convex difference function in an indoor positioning method according to an embodiment of the present invention;

3 is a schematic structural diagram of an indoor positioning device 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 ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

Due to the development of information technology, indoor positioning technology has also been more widely used. With the increasing demand for high-precision positioning, mixed-signal-based positioning is a good choice. Currently, maximum likelihood estimation and nonlinear least squares are the most used methods to obtain the optimal positioning solution. Since the maximum likelihood estimation and the nonlinear least squares method need to use a cost function, the cost function is multimodal, and the maximum likelihood estimation algorithm is a non-convex optimization problem, so it is difficult to ensure global convergence. The semidefinite program relaxation method in convex optimization achieves a balance between nonlinear and linear methods, that is, convex optimization methods have the characteristics of high accuracy and global convergence. Non-convex optimization problems, such as maximum likelihood estimation and nonlinear least squares, can be transformed into a convex second-order cone procedure or a semi-ideal procedure by relaxation methods, which can then be solved by existing solutions.

For example, the existing SDR (Semi-Definite Relaxation, semi-definite relaxation method) is a convex optimization localization method. The specific method is to convert the least squares or maximum likelihood estimation nonlinear problem into an equivalent convex optimization problem, and then introduce SDR to convert the joint localization problem into a low-complexity semidefinite programming problem, and then obtain the global minimum of the target position. optimal solution. However, since SDP is an effective approximation algorithm, the obtained solution is an approximate global optimal solution, and a stable solution for the target position cannot be obtained.

In order to solve the above problem, the embodiments of the present invention disclose an indoor positioning method, device, electronic device and storage medium, so as to obtain a stable global optimal solution of the indoor target position. The specific technical solutions are as follows:

To achieve the above purpose of the invention, an embodiment of the present invention discloses an indoor positioning method, as shown in FIG. 1 . 1 is a flowchart of an indoor positioning method according to an embodiment of the present invention, including:

S101: Acquire the signal propagation delay and angle of the target node, and obtain a coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes a position parameter and an error parameter of the target node.

In view of the problem that a stable global optimal solution cannot be obtained in the indoor positioning method of the prior art, an embodiment of the present invention proposes a solution for indoor fusion of TOA (time of arrival, time of arrival) and AOA (Angle of Arrival, angle of arrival). The method of positioning the stable global optimal solution reduces the error of indoor positioning.

TOA positioning technology realizes network positioning. Compared with wireless radio frequency signals, sound waves have low cost and low hardware complexity, which is beneficial to the time synchronization of sender and receiver. Assuming that the sending node and the receiving node are time-synchronized and each node contains a transmitter and a receiver, the transmitter emits a sound wave named chirp, and the time of transmission is also included in the sound wave to tell the receiver. When the receiver receives the chirp sound wave, the sending time is extracted from it, and the distance between the sending node and the receiving node is calculated using the propagation model of the sound wave in the atmosphere. On the whole, TOA-based positioning is simple to implement and has high positioning accuracy, but requires precise time synchronization between nodes, which puts forward higher requirements on the hardware and power consumption of nodes in the sensor node network.

AOA positioning technology obtains the angle information of the radio wave signal emitted by the terminal by setting up directional antennas or array antennas at more than two position points, and then estimates the position of the terminal through the intersection method. It only needs to use two antenna arrays to complete the initial positioning of the target. The density of buildings, height and topography have a great influence on the positioning accuracy of AOA. In indoor, urban and rural areas, the typical values of AOA are 360 degrees, 20 degrees and 1 degree respectively. As the distance between the base station and the terminal increases, the positioning accuracy of AOA gradually decreases. AOA positioning error is mainly caused by urban multipath propagation and system error. The influence of system error can be offset by pre-correction. However, multipath effect in densely built areas has always been a problem that plagues antenna communication. To reduce the influence of multipath interference, it has not been widely used due to the complexity of implementation and equipment cost. Therefore, although the AOA technology has a simple structure, it has not been applied in the urban cellular positioning system.

In this step, first, based on the basic principles of TOA and AOA positioning technology, the signal propagation delay and angle of the target node are obtained. Then, the coordinate expression of the target node is obtained according to the signal propagation delay and angle of the target node.

Specifically, multiple non-collinear sensor nodes can be arbitrarily deployed in the observation area, and each sensor node obtains the signal propagation delay and angle with the target node respectively. Equations are established respectively for the signal propagation delay and angle relationship between each sensor node and the target node, and the equations are solved to obtain the coordinate expression of the target node corresponding to each sensor node. Because each sensor node has a time error when detecting the signal propagation with the target node, and there is an angle error when detecting the angle with the target node, and then the equation established by each sensor node and the target node has a time error and angle error, so the coordinate expression of the target node obtained by solving the equation system includes the spatial position of the target node, which is the position parameter of the target node, and the error existing in the process of estimating the accurate position of the target node, that is, is the error parameter of the target node.

S102 , according to the analytical equivalence of the Lebesgue set of the convex function and the global optimality condition of the optimization theory, obtain the convex difference function of the error parameter of the target node with respect to the position parameter.

A convex function is a real-valued function f defined on a convex subset C (interval) of a certain vector space, and for any two vectors x1 and x2 in the convex subset C, there is f((x1+x2)/2 )≤(f(x1)+f(x2))/2.

Lebesgue's theorem reveals the relationship between convergence almost everywhere and convergence in measure. It asserts: if f(x)(n=1,2,w) and f(x) are measurable functions that are finite almost everywhere on the measurable set E, and the function sequence {person(x)} is almost everywhere on E converges to f(x), then {{f.,}x} converges to f(x) by measure on E.

Optimization theory is a mathematical problem that studies the minimum (or maximum) value of a function under a given set of constraints. The optimality condition refers to the condition that must be satisfied by the local or global optimal solution of the optimization problem. The optimality condition of the global optimization problem is the theoretical basis of the data calculation, and one of the 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 global optimal solution.

In this step, the coordinate expression of the target node obtained in the above step S101 is converted into the position parameter of the target node as the independent variable through the above-mentioned convex function properties, Lebesgue's theorem and the global optimality condition of the optimization theory. , a convex difference function with the error parameter of the target node as the dependent variable.

Specifically, firstly, the global optimality conditions related to classical optimization theory are obtained through the analytical equivalence set of the Lebesgue set of convex functions. The inequality constraints in the non-convex optimization problem are replaced with global optimality conditions, and then the convex difference function of the error parameters of the target node with respect to the position parameters is obtained.

S103 , according to the auxiliary problem principle and the sub-gradient algorithm, determine the value of each position parameter when the partial derivative of the convex difference function is zero.

After determining the convex difference function of the error parameter of the target node with respect to the position parameter, in this step, according to the principle of the auxiliary problem and the sub-gradient algorithm, determine the value of each position parameter when the partial derivative of the convex difference function is zero.

Taking the minimum value as an example, the principle of the auxiliary problem is explained. Assuming that the function J1(x) is differentiable, and the function J2(x) is not necessarily differentiable, for the original problem J1(x)+J2(x) to find the minimum value, if an auxiliary problem can be constructed: minG(x)+εJ2( x), and there is x* such that G'(x*)=εJ1'(x*) holds, then the original problem can be transformed into an auxiliary problem, x* is the solution of the original problem, and G(x) is called the auxiliary function . The auxiliary function is constructed in the form of G(x)=K(x)+<εJ′(x)-K′(x), x>, where K(x) is the kernel function; <,> represents the quantity product.

The sub-gradient algorithm is simply called derivative, and the one-dimensional sub-gradient is called the sub-derivative. By calculating the sub-derivative of each component of the function at the point, the sub-gradient of the function at the point can be obtained.

According to the above-mentioned auxiliary problem principle and the sub-gradient algorithm principle, the convex difference function of the error parameter of the target node with respect to the position parameter in S102 is solved, and the value of each position parameter when the partial derivative is zero.

S104, the value of each position parameter is respectively brought into the convex difference function, and the value of the position parameter when the convex difference function value is the smallest is determined as the target value; the coordinate corresponding to the target value is determined as the target coordinate of the target node.

After obtaining the value of each position parameter when the partial derivative of the convex difference function is zero, the value of each position parameter is brought back to the convex difference function, and the value of the convex difference function corresponding to the value of each position parameter is obtained. The smallest value is selected among all the convex difference function values, and this value is determined as the target value of the convex difference function value. Then, the coordinate expression of the target value corresponding to the position of the target node can be determined, and the precise coordinate position of the target node can be obtained through the coordinate expression.

The indoor positioning method provided by the embodiment of the present invention can achieve a stable global optimal solution for the indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

Optionally, in an embodiment of the indoor positioning method according to the embodiment of the present invention, before acquiring the signal propagation delay and angle of the target node, the method further includes:

In step 1, a set of equations of signal propagation delay and angle of a preset number of non-collinear sensor nodes and target nodes are respectively established.

The embodiment of the present invention is an implementation method for determining a coordinate expression of a target node to be located indoors. This step is an embodiment of establishing a system of equations for the signal propagation delay and angle of the target position detected by each sensor node.

In this step, consider using hybrid TOA/AOA to measure the position of target nodes in two-dimensional space, firstly deploy L non-collinear sensor nodes in the observation area, the coordinates of the sensor nodes can be expressed as x _i =[x _i ,y _i ] ^T , ( _xi ∈ R ² ), i=1,...,L, where x _i represents the abscissa of the ith sensor node, and y _i represents the ordinate of the ith sensor node. The coordinates of the target node can be expressed as u=[x,y] ^T , (u∈R ² ).

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 TOA and AOA of the signal transmitted from the target node, let t _i represent the slave The signal propagation delay from the target node to the ith sensor node, θ _i represents the angle from the target node to the ith sensor node, then the target node and the ith sensor node can establish the following equations:

Among them, c represents the signal propagation speed; ||·| represents the Euclidean norm, when the signal leaves the target node, the local time of the ith sensor node is 0; x _i represents the abscissa of the ith sensor node; y _i represents the ordinate of the ith node; u represents the coordinate of the target node; x represents the abscissa of the target node; y represents the ordinate of the target node; e _ti represents the signal propagation delay from the target node to the ith sensor node. time error; e _θi represents the angle measurement error from the target node to the ith sensor node.

In the above-mentioned manner, a system of equations for each sensor node and the target node is established. The specific process is similar to the above-mentioned real-time steps, and will not be repeated here.

According to the signal propagation delay and angle of the target node, the coordinate expression of the target node is obtained, including:

In step 2, each equation system of a preset number of non-collinear sensor nodes is solved to obtain a coordinate expression of each sensor node corresponding to the target node.

After obtaining the equation sets of each sensor node and the target node above, solve the equation sets respectively, and then obtain the coordinate expression of each sensor node with respect to the target node.

For example, according to the equation system established by the ith sensor node and the target node established in the above step 1, the following coordinate expressions of the target node can be obtained:

表示第i个传感器节点与目标节点建立的方程组得到的目标节点的横坐标；

表示第i个传感器节点与目标节点建立的方程组得到的目标节点的纵坐标；x_i表示第i个传感器节点的横坐标；y_i表示第i个传感器节点的纵坐标，θ_i表示第i个传感器节点与目标节点的角度；e_xi表示第i个传感器节点的横坐标的误差；e_yi表示第i个传感器节点的纵坐标的误差，其和步骤一中的e_ti、e_θi是非线性函数关系。in,

represents the abscissa of the target node obtained from the equation system established by the ith sensor node and the target node;

Represents the ordinate of the target node obtained from the equation system established by the ith sensor node and the target node; x _i represents the abscissa of the ith sensor node; y _i represents the ordinate of the ith sensor node, θ _i represents the ith sensor node The angle between each sensor node and the target node; e _xi represents the error of the abscissa of the ith sensor node; e _yi represents the error of the ordinate of the ith sensor node, and e _ti and e _θi in step 1 are nonlinear Functional relationship.

It can be seen that through the embodiment of the present invention, the coordinate expression of the target node can be obtained through the sensor nodes, and then the expression of the target node can be obtained through the equation relationship between each sensor node and the target node, so as to realize the positioning of the target node through multiple sensor nodes, This ensures that the coordinate position of the target node can be accurately obtained later.

Optionally, in an embodiment of the indoor positioning method according to the embodiment of the present invention, after obtaining the coordinate expression of the target node according to the signal propagation delay and angle of the target node, the method further includes:

Step A: Square each abscissa error parameter in each equation group of a preset number of non-collinear sensor nodes, and add the squares of the abscissa error parameter in each equation group to obtain a first expression.

The embodiment of the present invention is an implementation method for determining the error parameter expression in the coordinate expression of the target node. In this step, the first expression corresponding to the abscissa error parameter in the error expression is determined.

Specifically, the first expression is obtained by squaring the error parameter of the abscissa in the coordinate expression of the sensor node corresponding to the target node.

For example, the first expression can be expressed as

Among them, e _xi represents the abscissa error of the ith sensor node; _xi represents the abscissa of the ith sensor node; d _i represents the distance between the ith sensor node and the target node; θ _i represents the ith sensor node and the target The angle of the node, x represents the unknown abscissa of the target node.

According to the above method, the first expression of each sensor node corresponding to the target node is obtained.

Step B: Square each ordinate error parameter in each equation group of a preset number of non-collinear sensor nodes, and add the squares of the ordinate error parameter in each equation group to obtain a second expression.

In this step, the second expression corresponding to the ordinate error parameter in the error expression is determined.

Specifically, the second expression is obtained by squaring the error parameter of the ordinate in the coordinate expression of the sensor node corresponding to the target node.

For example, the second expression can be expressed as

Among them, e _yi represents the ordinate error of the ith sensor node; y _i represents the ordinate of the ith sensor node; d _i represents the distance between the ith sensor node and the target node; θ _i represents the ith sensor node and the target The angle of the node; y represents the unknown ordinate of the target node.

According to the above method, the second expression of each sensor node corresponding to the target node is obtained.

In step C, the expression obtained by adding the first expression and the second expression is determined as the expression of the error parameter included in the coordinate expression of the target node.

After obtaining the first expression and the second expression of the target node corresponding to each sensor node, 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. Mode.

For example, add the first expression and the second expression of the sensor node corresponding to the target node to obtain the expression of the error parameter of the sensor node corresponding to the target node, which is:

According to the above method, the expression of the error parameter of each sensor node is obtained, and then the expression of the error parameter of each sensor node is added to obtain the expression of the error parameter included in the coordinate expression of the target node in the embodiment of the present invention .

It can be seen that the embodiment of the present invention can realize the determination of the error parameter expressions corresponding to the target expressions of all sensor nodes, thereby facilitating the later use of the error parameter expressions to obtain the convex difference function of the error parameters.

Optionally, in an embodiment of the indoor positioning method provided by the embodiment of the present invention, in accordance with the analytical equivalence of the Lebesgue set of convex functions, and the optimization theory related to convex maximization and inverse convex optimization. Before obtaining the convex difference function of the error parameter of the target node with respect to the position parameter, the method further includes:

The parameter position obtained by transposing the position parameter in the coordinate expression of the target node including the error value is determined as the first position corresponding to the position parameter of the target node.

The embodiment of the present invention is an implementation method for determining the convex difference function of the error parameter of the target node with respect to the position parameter.

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 steps is related to the position parameter of the target node.

Specifically, a transposition operation can be used to transpose the position parameter in the coordinate expression of the target node including the error value to obtain the first position corresponding to the position parameter of the target node.

For example, the position corresponding to the position parameter is expressed as u=[x,y], then the first position can be expressed as

According to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization of optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, including:

Convert the error parameter included in the coordinate expression of the target node, the analytical equivalence of the Lebesgue set through the convex function, and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory into position parameters and The convex difference function corresponding to the first position.

确定后，所有传感器节点的误差参数的表达式可以被表示为：The above expression of the error parameter included in the coordinate expression of the target node

After being determined, the expression of the error parameters of all sensor nodes can be expressed as:

subject to y=Aξ

in,

The above y=Aζ is a typical non-convex optimization problem. Only approximate global optimal solution can be obtained by using least squares or sum convex relaxation, but a stable global optimal solution cannot be obtained. In order to obtain a stable global optimal solution, using the analytical equivalence of the Lebesgue set and the global optimality condition of the optimization theory, the above formula y=Aζ is transformed into the position parameters and the first The convex difference function corresponding to the position:

u∈{(x,y)|x,y∈Rⁿ}。in,

u∈{(x,y)|x, ^y∈Rn }.

It can be seen that through the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of the convex maximization and inverse convex optimization of the optimization theory, the convex difference of the error parameter of the target node with respect to the position parameter is obtained through the embodiment of the present invention function, and then it is convenient to obtain the global optimal solution with stable indoor target position through the convex optimization characteristics of the convex difference function in the later stage.

Optionally, in an embodiment of the indoor positioning method provided by the embodiment of the present invention, the value of each position parameter when the partial derivative of the convex difference function is zero is determined according to the principle of the auxiliary problem and the sub-gradient algorithm, as shown in the figure. 2 shown. 2 is a flowchart of a method for processing a convex difference function in an indoor positioning method according to an embodiment of the present invention, including:

S201 , transform the convex difference function into an objective function capable of solving partial derivatives by using a sub-gradient type algorithm by using preset inequalities and preset identities in the auxiliary problem principle; wherein, the objective function is a position parameter about the target node in the convex difference function The function.

The embodiment of the present invention is an implementation method for determining the value of each position parameter when the partial derivative of the convex difference function is zero. This step is to determine the objective function of transforming the convex difference function into an objective function that can use the subgradient algorithm to solve the partial derivative.

The principle of the auxiliary problem is: Assuming that the function J1(x) is differentiable, the function J2(x) is not necessarily differentiable. For the original problem J1(x)+J2(x) to find the minimum value, if an auxiliary problem can be constructed: minG (x)+εJ2(x), and there is x* such that G'(x*)=εJ1'(x*) holds, then the original problem can be transformed into an auxiliary problem, x* is the solution of the original problem, G( x) is called an auxiliary function. The auxiliary function is constructed in the form of G(x)=K(x)+<εJ′(x)-K′(x), x>, where K(x) is the kernel function; <,> represents the quantity product.

Specifically, there are identities in the auxiliary problem principle

in,

At this time, the error parameter of the above target node can be related to the convex difference function of the position parameter:

Converted to an objective function capable of solving partial derivatives using a subgradient-type algorithm:

在坐标为Θ＝[x₀,y₀]^T，

为常数。Among them, it is assumed that the coordinate Θ=[x ₀ , y ₀ ] ^T is the solution of the above formula, and at the same time

At coordinates Θ=[x ₀ , y ₀ ] ^T ,

is a constant.

Therefore, for each pair (ξ, φ) ∈ IR ⁿ × IR, Λ(ξ) = Ξ(t, θ) = φ

其中，

表示点ξ的次微分。Then there are inequalities:

in,

represents the sub-derivative of the point ξ.

S202, a partial derivative is obtained for the objective function, and the value of the position parameter when the partial derivative of the objective function is zero is determined.

After obtaining the objective function that can solve the partial derivative by using the sub-gradient algorithm, the partial derivative of the objective function is obtained, and the value of the position parameter when the partial derivative of the objective function is zero is determined.

Specifically, solve the value of the position parameter corresponding to when the partial derivative of the objective function is zero in the following formula:

是函数

在点ξ处的次微分，N(ξ；S)是在点ξ对S的正常的锥。in,

is a function

Subdifferential at point ξ, N(ξ; S) is the normal cone of S at point ξ.

After obtaining the value of the position parameter when the partial derivative of the objective function in the above formula is zero, the value of each position parameter is respectively brought into the convex difference function of the error parameter with respect to the position parameter, and the corresponding value of the convex difference function is the smallest. The value of the position parameter is determined as the target value. Then, the coordinate expression of the target value corresponding to the position of the target node can be determined, and the precise coordinate position of the target node can be obtained through the coordinate expression.

It can be seen that the partial derivative of the objective function is obtained by the embodiment of the present invention, and the value of the position parameter when the partial derivative of the objective function is zero is determined, and then the value of the position parameter when the partial derivative is zero is brought back to the convex difference function, the convex difference The coordinate of the expression corresponding to the minimum function value is determined as the coordinate of the target node, so as to achieve a stable global optimal solution for the indoor target position.

To achieve the above purpose of the invention, an embodiment of the present invention further discloses an indoor positioning device, as shown in FIG. 3 . 3 is a schematic structural diagram of an indoor positioning device according to an embodiment of the invention, the device includes:

The expression determination module 301 obtains the coordinate expression of the target node from the angle, wherein the coordinate expression includes the position parameter and the error parameter of the target node;

The convex difference function determination module 302 is used to obtain the convex difference function of the error parameter of the target node with respect to the position parameter according to the analytical equivalence of the Lebesgue set of the convex function and the global optimality condition of the optimization theory;

The parameter value determination module 303 is used for determining the value of each position parameter when the partial derivative of the convex difference function is zero according to the principle of the auxiliary problem and the sub-gradient algorithm;

The target coordinate determination module 304 is used to respectively bring the value of each position parameter into the convex difference function, and determine the value of the position parameter when the convex difference function value is the smallest as the target value; the coordinates corresponding to the target value are determined as the target node. target coordinates.

The indoor positioning device provided by the embodiment of the present invention can achieve a stable global optimal solution for the indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

Optionally, in an embodiment of the indoor positioning device according to the embodiment of the present invention, the device further includes:

The equation system establishment module is used to establish the equation system of the signal propagation delay and angle of the preset number of non-collinear sensor nodes and the target node respectively;

The expression determination module is specifically used to solve each equation system of a preset number of non-collinear sensor nodes, and obtain the coordinate expression of each sensor node corresponding to the target node.

Optionally, in an embodiment of the indoor positioning device according to the embodiment of the present invention, the device further includes:

The first expression determination module is used to square each abscissa error parameter in each equation group of a preset number of non-collinear sensor nodes, and add the squares of the abscissa error parameters in each equation group to obtain the first expression;

The second expression determination module is used for squaring each ordinate error parameter in each equation group of a preset number of non-collinear sensor nodes, and adding the squares of the ordinate error parameter in each equation group to obtain the second expression;

The third expression determination module is configured to determine the expression for 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 device according to the embodiment of the present invention, the device further includes:

The first position determination module is used to determine the parameter position obtained by transposing the position parameter in the coordinate expression of the target node including the error value as the first position corresponding to the position parameter of the target node;

The convex difference function determination module 302 is specifically used to determine the error parameter included in the coordinate expression of the target node, the analytical equivalence of the Lebesgue set of the convex function, and the optimization theory related to convex maximization and inverse convex optimization. The optimality condition is converted into a convex difference function with respect to the position parameters and the corresponding first position.

Optionally, in an embodiment of the indoor positioning device according to the embodiment of the present invention, the parameter value determination module 303 is specifically configured to transform the convex difference function into a value capable of Use subgradient algorithm to solve the objective function of partial derivative; wherein, the objective function is a function of the position parameter of the target node in the convex difference function; find the partial derivative of the objective function, and determine the position parameter when the partial derivative of the objective function is zero value.

To achieve the above purpose of the invention, an embodiment of the present invention further discloses an electronic device, as shown in FIG. 4 . 4 is a schematic structural diagram of an electronic device according to an embodiment of the present invention, including a processor 401 , a communication interface 402 , a memory 403 and a communication bus 404 , wherein the processor 401 , the communication interface 402 , and the memory 403 communicate with each other through the communication bus 404 Communication;

a memory 403 for storing computer programs;

When the processor 401 is used to execute the program stored in the memory 403, the following method steps are implemented:

Obtain the signal propagation delay and angle of the target node, and obtain the coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes the position parameter and the error parameter of the target node;

According to the analytical equivalence of the Lebesgue set of convex functions, and the optimal conditions of convex maximization and inverse convex optimization of optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained;

According to the principle of auxiliary problem and sub-gradient algorithm, determine the value of each position parameter when the partial derivative of the convex difference function is zero;

The value of each position parameter is brought into the convex difference function respectively, and the value of the position parameter when the value of the convex difference function is the smallest is determined as the target value; the coordinate corresponding to the target value is determined as the target coordinate of the target node.

The communication bus 404 mentioned in the above electronic device may be a peripheral component interconnect standard (Peripheral Component Interconnect, PCI) bus or an Extended Industry Standard Architecture (Extended Industry Standard Architecture, EISA) bus or the like. The communication bus 404 can be divided into an address bus, a data bus, a control bus, and the like. For ease of presentation, only one thick line is used in the figure, but it 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-mentioned electronic device and other devices.

The memory 403 may include random access memory (Random Access Memory, RAM), or may include non-volatile memory (Non-Volatile Memory, NVM), such as at least one disk storage. Optionally, the memory may also be at least one storage device located away from the aforementioned processor 401 .

The above-mentioned processor 401 may be a general-purpose processor, including a central processing unit (Central Processing Unit, CPU), a network processor (Network Processor, NP), etc.; may also be a digital signal processor (Digital Signal Processing, DSP), an application-specific integrated circuit (Application Specific Integrated Circuit, ASIC), Field-Programmable Gate Array (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

An electronic device provided by an embodiment of the present invention can achieve a stable global optimal solution for an indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

To achieve the above purpose of the invention, an embodiment of the present invention also discloses a computer-readable storage medium, where a computer program is stored in the computer-readable storage medium, and when the computer program is executed by a processor, the following method steps are implemented:

Obtain the signal propagation delay and angle of the target node, and obtain the coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes the position parameter and the error parameter of the target node;

According to the analytical equivalence of the Lebesgue set of convex functions, and the optimal conditions of convex maximization and inverse convex optimization of optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained;

According to the principle of auxiliary problem and sub-gradient algorithm, determine the value of each position parameter when the partial derivative of the convex difference function is zero;

The value of each position parameter is brought into the convex difference function respectively, and the value of the position parameter when the value of the convex difference function is the smallest is determined as the target value; the coordinate corresponding to the target value is determined as the target coordinate of the target node.

A computer-readable storage medium provided by an embodiment of the present invention can achieve a stable global optimal solution for an indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

Embodiments of the present invention also provide a computer program product containing instructions, which, when running on a computer, cause the computer to execute the following method steps:

Obtain the signal propagation delay and angle of the target node, and obtain the coordinate expression of the target node according to the signal propagation delay and angle of the target node, wherein the coordinate expression includes the position parameter and the error parameter of the target node;

According to the analytical equivalence of the Lebesgue set of convex functions, and the optimal conditions of convex maximization and inverse convex optimization of optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained;

According to the principle of auxiliary problem and sub-gradient algorithm, determine the value of each position parameter when the partial derivative of the convex difference function is zero;

The value of each position parameter is brought into the convex difference function respectively, and the value of the position parameter when the value of the convex difference function is the smallest is determined as the target value; the coordinate corresponding to the target value is determined as the target coordinate of the target node.

A computer program product including instructions provided by an embodiment of the present invention can achieve a stable global optimal solution for an indoor target position. Specifically, according to the signal propagation delay and angle of the target node detected by a preset number of non-collinear sensor nodes, a coordinate expression of the target node is obtained, and the coordinate expression includes a position parameter and an error parameter of the target node. Then, according to the analytical equivalence of the Lebesgue set of convex functions and the optimality conditions of convex maximization and inverse convex optimization related to optimization theory, the convex difference function of the error parameter of the target node with respect to the position parameter is obtained, that is, by The error parameter is converted into a convex difference function, and the auxiliary problem principle and sub-gradient algorithm are used under the convex difference function to determine the value of each position parameter corresponding to the zero partial derivative of the convex difference function. By bringing the value of each position parameter corresponding to zero partial derivative into the convex difference function, the value of the position parameter corresponding to the minimum value of the convex difference function is determined, that is, the minimum error value. Finally, the coordinate corresponding to the smallest error value is determined as the target coordinate of the target node, so as to obtain a stable global optimal solution for the indoor target position.

It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass a non-exclusive inclusion such that a process, method, article or device that includes a list of elements includes not only those elements, but also includes not explicitly listed or other elements inherent to such a process, method, article or apparatus. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in the process, method, article, or device that includes the element.

Each embodiment in this specification is described in a related manner, and the same and similar parts between the various embodiments may be referred to each other, and each embodiment focuses on the differences from other embodiments. Especially, for the embodiments of the apparatus, electronic equipment and storage medium, since they are basically similar to the method embodiments, the description is relatively simple, and reference may be made to some descriptions of the method embodiments for related parts.

The above are only preferred embodiments of the present invention, and are not intended to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention are included in 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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