A method, apparatus and medium for measuring a specified time distribution of noise-based positioning

Abstract

The application relates to a specified time distribution positioning method and device under measurement noise and a medium, comprising the following steps: acquiring a to-be-measured target group composed of at least two intelligent agents with known positions and a plurality of intelligent agents with unknown positions, and acquiring a measurement angle with bounded measurement noise in the to-be-measured target group; constructing an angle unbiased estimator, processing the bounded measurement noise based on the constructed angle unbiased estimator, and obtaining an estimated angle value; setting a specified time distribution positioning estimation algorithm, establishing a plurality of triangles with the intelligent agents in the to-be-measured target group as vertices, calculating a relationship coefficient matrix among the vertices of each triangle according to the estimated angle value; and obtaining a positioning result of the intelligent agents with unknown positions according to the estimated angle value and the relationship coefficient matrix through the specified time distribution positioning estimation algorithm. Compared with the prior art, the application has the advantages of being capable of eliminating the influence of measurement noise, high positioning precision and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of multi-agent systems technology, and in particular to a method, apparatus and medium for distributed positioning at a specified time under measurement noise. Background Technology

[0002] Multi-agent systems comprise multiple intelligent individuals that can perceive information from their environment, make decisions based on objectives, and act collaboratively to solve complex tasks. Multi-agent systems possess advantages such as social interaction, autonomy, and fault tolerance, and have a wide range of applications, including rescue, goods transportation, and environmental reconnaissance. Location information is one of the essential foundational pieces of information for multi-agent systems. Therefore, achieving precise positioning within a multi-agent system is a prerequisite for successfully completing various tasks.

[0003] The goal of multi-agent localization is to estimate an agent's position using its own sensory information and communication information with neighboring agents. In localization research, existing algorithms can be categorized into centralized and distributed localization algorithms based on their computational methods. Centralized localization algorithms involve a central agent receiving sensory information from other agents and centrally estimating the position information of all agents. The computational efficiency of centralized localization algorithms decreases as the number of agents increases. Furthermore, if the central agent malfunctions, the entire system will fail. Distributed localization algorithms, on the other hand, do not require a central agent; all agents can concurrently and independently calculate their own positions, improving efficiency and enhancing robustness.

[0004] In many practical applications, high accuracy and timely positioning are crucial, directly impacting the accuracy and timeliness of decision-making. Most positioning algorithms are suited to ideal environments and cannot effectively handle the impact of measurement noise on positioning accuracy. Existing angle-measurement-based positioning estimation algorithms can only guarantee exponential or asymptotic convergence, without controlling the convergence time. Therefore, considering the elimination of measurement noise and achieving accurate positioning within a controllable timeframe in positioning estimation algorithm research has significant theoretical and practical value. Summary of the Invention

[0005] The purpose of this invention is to overcome the defects of the prior art by providing a method, apparatus and medium for distributed positioning at a specified time under measurement noise.

[0006] The objective of this invention can be achieved through the following technical solutions:

[0007] A time-distributed localization method under measurement noise includes the following steps:

[0008] S1: Obtain a target group consisting of agents with at least two known positions and agents with multiple unknown positions, and obtain the measurement angles in the target group containing bounded measurement noise;

[0009] S2: Construct an unbiased angle estimator, process bounded measurement noise based on the constructed unbiased angle estimator, and obtain the estimated angle value;

[0010] S3: Set up a distributed localization estimation algorithm for a specified time, establish multiple triangles with the agents in the target group as vertices, and calculate the relationship coefficient matrix between the vertices of each triangle based on the estimated angle values;

[0011] S4: Using a time-distributed localization estimation algorithm, the localization result of the agent at an unknown location is obtained based on the estimated angle value and the relation coefficient matrix.

[0012] Furthermore, the expression for the measurement angle, which includes bounded measurement noise, is:

[0013]

[0014] In the formula, α represents the measured angle value containing measurement noise. kij (t) represents the actual angle value, Δα kij (t) represents the measurement noise, and t is the sampling time. Let Δα be a set of intelligent agents. kij (t) is bounded and independently and identically distributed along the time axis.

[0015] Furthermore, the estimated angle value is:

[0016]

[0017]

[0018] In the formula, This represents the estimated angle value.

[0019] Furthermore, the time-specified distributed positioning estimation algorithm is calculated using a time-varying scaling function, the expression of which is:

[0020]

[0021] In the formula, μ(t) represents the time-varying scaling function, T represents the specified time, and s > 0 is a parameter selected by the user.

[0022] Furthermore, the calculation expression for the time-specified distributed positioning estimation algorithm is as follows:

[0023]

[0024] c, d > 0

[0025]

[0026] In the formula, Represents the relative positional relationships between agents at unknown locations. This represents the relative positional relationship between an agent at an unknown location and an agent at a known location. p represents the estimated position of an agent at an unknown location. a This represents the actual position of an agent whose location is known. The derivative of μ(t), for The derivative of .

[0027] Furthermore, the relative positional relationships between agents in unknown locations. The relative positional relationship between an agent in an unknown location and an agent in a known location. The calculation method is as follows:

[0028] Assume the environment contains n = n a +n f There are n intelligent agents, where n are intelligent agents. a n represents the number of agents with known locations. f Let m represent the number of agents whose positions are unknown. Construct a total of m triangles with each agent as a vertex, ensuring that each agent appears in at least one triangle. Let each of the three angles represent an estimated angle in a triangle, and then we obtain the relation coefficient matrix corresponding to that triangle. The calculation expression is:

[0029]

[0030]

[0031]

[0032] In the formula, I2 is a two-dimensional rotation matrix, and I2 is a 2×2 identity matrix;

[0033] By combining the relation coefficient matrices of the various triangles, we obtain:

[0034]

[0035] Among them, matrix Each column of the matrix represents an agent. Each row represents a triangle, and 0 represents a 2×2 zero matrix. The part related to the agent with known location The part related to agents in unknown locations The relative positional relationships between agents at unknown locations are calculated. The relative positional relationship between an agent in an unknown location and an agent in a known location.

[0036]

[0037]

[0038] A second aspect of the present invention is a time-distributed positioning device under measurement noise, comprising a memory, a processor, and a program stored in the memory, wherein the processor executes the program to implement any of the time-distributed positioning methods under measurement noise as described above.

[0039] A third aspect of the invention is a storage medium having a program stored thereon, which, when executed, implements any of the above-described distributed positioning methods under measurement noise at a specified time.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] 1) This invention uses an unbiased angle estimator to weight angles collected at different times that contain bounded measurement noise, gradually eliminating the influence of noise on the angle measurement results and the influence of measurement noise on the positioning results, thus obtaining the estimated angle values ​​at each time point. Based on the estimated angle values, a positional relationship matrix is ​​established between agents with known positions, agents with unknown coordinates, and agents with known coordinates. Using a distributed positioning algorithm, the positioning results of agents with unknown coordinates are calculated through the positional relationship matrix, enabling high-precision positioning results to be obtained even when subjected to measurement noise interference.

[0042] 2) Based on angle measurement, this invention can obtain the precise position information of the intelligent agent within a specified time through a time-varying scaling function, resulting in high positioning efficiency. Attached Figure Description

[0043] Figure 1 This is a flowchart of the method of the present invention;

[0044] Figure 2 This is an angle measurement diagram of the intelligent agent in the embodiment;

[0045] Figure 3 This is a convergence trajectory diagram of the estimated location in the embodiment;

[0046] Figure 4 This is a position estimation error curve diagram from the embodiment. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0048] Example 1

[0049] like Figure 1 As shown, the present invention is a time-distributed positioning method under measurement noise, comprising the following steps:

[0050] S1: Obtain a target group consisting of agents with at least two known positions and agents with multiple unknown positions, and obtain the measurement angles in the target group containing bounded measurement noise;

[0051] In this embodiment, the agents with known locations are numbered 1 and 2, and the agents with unknown locations are numbered 3, 4, 5, 6, 7, and 8.

[0052] The expression for the measurement angle including bounded measurement noise is:

[0053]

[0054] In the formula, α represents the measured angle value containing measurement noise. kij (t) represents the actual angle value, Δα kij (t) represents the measurement noise, and t is the sampling time. Let Δα be a set of intelligent agents. kij (t) is bounded and independently and identically distributed along the time axis.

[0055] S2: Construct an unbiased angle estimator, process bounded measurement noise based on the constructed unbiased angle estimator, and obtain the estimated angle value;

[0056]

[0057]

[0058] In the formula, This represents the estimated angle value.

[0059] By using an unbiased angle estimator, angles collected at different times that contain bounded measurement noise are weighted to gradually eliminate the influence of noise on the angle measurement results.

[0060] S3: Set up a distributed localization estimation algorithm for a specified time, establish multiple triangles with the agents in the target group as vertices, and calculate the relationship coefficient matrix between the vertices of each triangle based on the estimated angle values;

[0061] The time-varying distributed positioning estimation algorithm is calculated using a time-varying scaling function, the expression of which is:

[0062]

[0063] In the formula, μ(t) represents the time-varying scaling function, T represents the specified time, and s > 0 is a parameter selected by the user;

[0064] The calculation expression for the time-specified distributed positioning estimation algorithm is as follows:

[0065]

[0066]

[0067] In the formula, Represents the relative positional relationships between agents at unknown locations. This represents the relative positional relationship between an agent at an unknown location and an agent at a known location. p represents the estimated position of an agent at an unknown location. a This represents the actual position of an agent whose location is known. The derivative of μ(t) for The derivative of .

[0068] Adjusting the positioning coefficient using a time-varying scale function Improve positioning accuracy and efficiency within a specified time.

[0069] The environment contains n=n a +n f There are n intelligent agents, where n are intelligent agents. a n represents the number of agents with known locations. f Let m represent the number of agents whose positions are unknown. A total of m triangles are constructed with the agents as vertices, and each agent must appear in at least one triangle. For example... Figure 2 The diagram illustrates the measurement of the angles of a triangle in an intelligent agent. Let each of the three angles represent an estimated angle in a triangle, and then we obtain the relation coefficient matrix corresponding to that triangle. The calculation expression is:

[0070]

[0071]

[0072]

[0073] In the formula, I2 is a two-dimensional rotation matrix, and I2 is a 2×2 identity matrix;

[0074] By combining the relation coefficient matrices of the various triangles, we obtain:

[0075]

[0076] For the matrix Each column of the matrix represents an agent, and each row represents a triangle. Taking a triangle formed by points i, j, and k as an example, the values ​​in the i, j, and k columns of this row are the relation coefficients. The remaining columns correspond to a 2×2 zero matrix.

[0077] matrix The part related to the agent with known location The part related to agents in unknown locations Taking this embodiment as an example, The relative positional relationships between agents at unknown locations are calculated. The relative positional relationship between an agent in an unknown location and an agent in a known location.

[0078]

[0079]

[0080] At each moment, the relative positional relationships between agents at the unknown locations can be calculated. The relative positional relationship between an agent in an unknown location and an agent in a known location.

[0081] S4: Using a time-distributed localization estimation algorithm, the localization result of the agent at an unknown location is obtained based on the estimated angle value and the relation coefficient matrix.

[0082] Using the distributed positioning algorithm proposed in this embodiment, the following results are obtained: Figure 3 The diagram shows the convergence trajectory of the estimated positions of six agents at unknown locations. Asterisks represent the actual positions of the agents at unknown locations, circles represent the initial estimated positions, agents labeled 1-2 represent agents at known positions, and agents labeled 3-8 represent agents at unknown positions. The diagram shows that the estimated positions eventually converge to the actual positions. Figure 4 As shown in the figure, the convergence curve of the position estimation error is displayed. It can be seen from the figure that at a specified time T = 60s, the error converges to an acceptable zero neighborhood. Simulation results verify the effectiveness of the time-based distributed positioning algorithm based on angle measurement under measurement noise conditions proposed in this invention.

[0083] The program code used to implement the methods of the present invention can be written in any combination of one or more programming languages. This program code can be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code can be executed entirely on the machine, partially on the machine, as a standalone software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0084] In the context of this invention, a machine-readable medium storing the method of the invention can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. The machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can include, but are not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0085] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A distributed positioning method for a specified time under measurement noise, characterized in that, Includes the following steps: S1: Obtain a target group consisting of agents with at least two known positions and agents with multiple unknown positions, and obtain the measurement angles in the target group containing bounded measurement noise; S2: Construct an unbiased angle estimator, process bounded measurement noise based on the constructed unbiased angle estimator, and obtain the estimated angle value; S3: Set up a distributed localization estimation algorithm for a specified time, establish multiple triangles with the agents in the target group as vertices, and calculate the relationship coefficient matrix between the vertices of each triangle based on the estimated angle values; S4: Using a time-distributed localization estimation algorithm, the localization result of the agent at an unknown location is obtained based on the estimated angle value and the relation coefficient matrix; The specified time distributed positioning estimation algorithm is calculated using a time-varying scaling function, the expression of which is: In the formula, Represents the time-varying scaling function. Indicates a specified time. These are parameters selected by the user; Sampling time; The calculation expression for the specified time distributed positioning estimation algorithm is as follows: In the formula, Represents the relative positional relationships between agents at unknown locations. This represents the relative positional relationship between an agent at an unknown location and an agent at a known location. This represents the estimated position of an agent at an unknown location. This represents the actual position of an agent whose location is known. for The derivative of for The derivative; The relative positional relationship between the agents at the unknown location The relative positional relationship between an agent in an unknown location and an agent in a known location. The calculation method is as follows: Assuming the environment contains There are 1 intelligent agents, among which This represents the number of agents at known locations. This represents the number of agents whose positions are unknown, and a total number of agents are established with each agent as a vertex. There are three triangles, and each agent must appear in at least one of them. , , Let each of the three angles represent an estimated angle in a triangle, and then we obtain the relation coefficient matrix corresponding to that triangle. , , The calculation expression is: In the formula, It is a two-dimensional rotation matrix. for identity matrix; By combining the relation coefficient matrices of the various triangles, we obtain: Among them, matrix Each column of the matrix represents an agent. Each row represents a triangle, and 0 represents The zero matrix, matrix The part related to the agent with known location The part related to agents in unknown locations The relative positional relationships between agents at unknown locations are calculated. The relative positional relationship between an agent in an unknown location and an agent in a known location. : 。 2. The time-distributed positioning method under measurement noise according to claim 1, characterized in that, The expression for the measurement angle containing bounded measurement noise is: In the formula, This indicates the measured angle value containing measurement noise. This is the actual angle value. To measure noise, , A collection of intelligent agents, Bounded and independently and identically distributed along the time axis.

3. The time-distributed positioning method under measurement noise according to claim 2, characterized in that, The estimated angle value is: In the formula, This represents the estimated angle value.

4. A time-distributed positioning device for measuring noise, comprising a memory, a processor, and a program stored in the memory, characterized in that, When the processor executes the program, it implements a time-distributed positioning method under measurement noise as described in any one of claims 1-3.

5. A storage medium having a program stored thereon, characterized in that, When the program is executed, it implements a time-distributed positioning method under measurement noise as described in any one of claims 1-3.

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