Multi-node mutual positioning method and system in complex environment

By using a linear frequency modulated continuous wave radar system and Doppler frequency shift measurement, combined with DOA estimation, the problem of poor positioning accuracy of multiple nodes in complex environments was solved, achieving high-precision, low-cost inter-node positioning that is adaptable to changing environments.

CN119535343BActive Publication Date: 2025-11-11NANJING UNIV OF SCI & TECH +1
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Patent Information

Application Number
CN202411367743.2
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-09-29
Publication Date
2025-11-11
Estimated Expiration
2044-09-29

AI Technical Summary

Technical Problem

Existing multi-node mutual positioning technology has poor positioning accuracy in complex environments, is easily affected by weather and non-line-of-sight errors, and has high requirements for the accuracy of clock synchronization between nodes, resulting in low flexibility.

Method used

A linear frequency modulated continuous wave radar system is adopted. Distance and velocity are measured by round-trip time of flight (RTOF), and angle is estimated by combining the direction of arrival (DOA) to achieve high-precision positioning between nodes. The nodes are synchronized through ZigBee modules, and signal processing is performed by coarse synchronization and fine synchronization steps.

Benefits of technology

Achieve high-precision inter-node positioning in complex environments. The node system is flexible, can process multi-sensor data, adapts to harsh weather and environments, is low-cost, has simple infrastructure, and is easy to maintain.

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Abstract

This invention discloses a method and system for multi-node mutual positioning in complex environments. Each node can be set as a master node or a slave node. Nodes achieve mutual positioning by transmitting and receiving triangular frequency-modulated continuous wave (FM) signals. When a node operates in master node mode, it synchronizes with the working signals of other slave nodes through coarse and fine synchronization steps. Then, it calculates the distance information of the slave nodes using round-trip time of flight (RTF) and Doppler frequency shift calculations, and estimates the angle information of the slave nodes using the DOA method to complete the positioning of the slave nodes. When a node operates in slave node mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse and fine synchronization steps, and then sends the synchronized signal back to the master node so that the master node can locate the slave node's position. This invention achieves high-precision mutual positioning between multiple nodes by implementing the working principle of FM continuous wave radar between nodes.
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Description

Technical Field

[0001] This invention belongs to the field of autonomous mobile robot mutual positioning systems, specifically a multi-node mutual positioning method and system in complex environments. Background Technology

[0002] With the accelerating pace of industrialization, Autonomous Mobile Robots (AMRs) demonstrate excellent characteristics in high-risk, complex, and repetitive tasks, showing broad application prospects in logistics warehousing, automated transportation systems, and even warfare. Viewing an AMR as multiple mobile node subsystems, if these subsystems can share information and coordinate with each other, the overall system can achieve enhanced functionality. Information collaboration among multiple nodes also significantly increases the platform's operational range and stability, enabling it to reliably and consistently complete tasks in highly time-varying, dynamic, and random environments such as transporting critical supplies, large-scale search and rescue in the field, and complex and ever-changing battlefields. Therefore, researching efficient and easily networkable multi-node mutual localization algorithms is of paramount importance.

[0003] The concept of multi-node mutual localization was proposed as early as the 1960s, with early methods primarily employing GNSS positioning. However, in harsh and complex environments, such as those with numerous trees or other obstructions, GNSS navigation and positioning capabilities become unstable, and it fails to function indoors. Visual or lidar technologies can also achieve localization by scanning surrounding objects to create maps; these systems offer excellent positioning accuracy but are expensive, susceptible to weather and light conditions, and unsuitable for outdoor or indoor environments with smoke, rain, or fog. While Wi-Fi or Bluetooth solutions using RSSI positioning algorithms can achieve low latency and easily combine data from multiple sensors, their positioning accuracy is relatively poor, requiring additional system assistance and exhibiting low flexibility in complex and changing environments. Therefore, autonomous mobile robots employing radar-based multi-node mutual localization technology do not require additional system assistance. Through the coordination of information from various sensors, local node mutual localization can be achieved, and the redundancy of information can be improved through multi-sensor fusion to enhance positioning accuracy and reliability. This allows for accurate and stable mutual localization even in outdoor environments with variable weather or indoor environments filled with smoke.

[0004] Currently, the main multi-node mutual positioning methods used in radar systems include Angle of Arrival (AOA) positioning, Received Signal Strength Indication (RSSI) positioning, Time of Arrival (TOA) positioning, and Time Difference of Arrival (TDOA) positioning. Among these, AOA positioning is simple in concept and requires little data, but its accuracy is relatively poor. RSSI positioning is low-cost and requires low power, but factors such as signal reflection, non-line-of-sight errors, and antenna gain can significantly affect its accuracy. TOA or TDOA techniques can achieve high-precision positioning, but they require precise clock offsets between the mutual positioning nodes and cannot measure angles. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for multi-node mutual positioning in complex environments. The nodes are connected by a radar system, which uses linear frequency modulated continuous wave to measure distance and velocity using round-trip time of flight (RTOF). Multiple antennas are added to use the direction of arrival (DOA) estimation method for angle measurement, thereby achieving high-precision and reliable positioning between multiple nodes. It also has good working performance in complex environments. Furthermore, the node subsystem using the radar system has the advantages of flexibility and the ability to process multi-sensor data.

[0006] The technical solution to achieve the purpose of this invention is as follows: a multi-node mutual positioning method in a complex environment, wherein each node includes a transmit link, a receive link, a transmit and receive antenna, a ZigBee module and a signal processing module; each node can be set as a master node or a slave node, and the nodes achieve mutual positioning function by transmitting and receiving triangular wave frequency modulated continuous wave signal waveforms;

[0007] When a node operates in master node mode, it synchronizes with the working signals of other slave nodes through coarse and fine synchronization steps, and then locates the slave node using the working principle of frequency-modulated continuous wave radar. When a node operates in slave node mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse and fine synchronization steps, and then sends the synchronized signal to the master node so that the master node can locate the slave node's position. The positioning method includes the following steps:

[0008] Step S1: Set up a master node in the node network and set the other nodes as slave nodes; use the ZigBee module of each node to make each node work on the same time base to achieve coarse time synchronization between multiple nodes.

[0009] Step S2: After coarse synchronization, the master node sends the signal to be synchronized to the slave node. The slave node processes the received signal to obtain the time and frequency offset between the nodes, and then adjusts the transmitted signal of the slave node to make the transmitted signal of the slave node precisely synchronized with the local oscillator signal in the master node.

[0010] Step S3: After fine synchronization, the master node receives the transmitted signal from the slave node, processes the received signal to obtain the distance, speed and angle information of the slave node in order to locate the slave node.

[0011] A multi-node mutual positioning system for complex environments is provided to implement the above method. The system includes multiple nodes, each of which includes a transmit link, a receive link, a transmit and receive antenna, a ZigBee module, and a signal processing module. Each node is set as a master node or a slave node, and the nodes achieve mutual positioning by transmitting and receiving triangular wave frequency-modulated continuous wave signal waveforms.

[0012] When a node operates in master node mode, it synchronizes with the working signals of other slave nodes through coarse and fine synchronization steps, and then locates the slave node using the working principle of frequency-modulated continuous wave radar. When a node operates in slave node mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse and fine synchronization steps, and then sends the synchronized signal to the master node so that the master node can locate the slave node's position.

[0013] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described above.

[0014] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the above-described method.

[0015] A computer program product includes a computer program that, when executed by a processor, implements the above-described method.

[0016] Compared with existing technologies, the significant advantages of this invention are: each node has both receiving and transmitting systems, enabling it to locate other nodes and be located by other nodes. The mutual positioning method between nodes is equivalent to the operation of a secondary radar system, ensuring that the power of signals received by each node from other nodes is significantly greater than the power of other noise, thus achieving high-precision wireless local positioning. Each node operates within the 1GHz to 100GHz wireless local positioning system range. Within this wavelength range, the effects of rain, fog, and dust are minimal, resulting in good performance even in harsh working environments such as agriculture, mining, and waste management. Attached Figure Description

[0017] Figure 1This diagram illustrates an application scenario of the multi-node mutual positioning method in a complex environment according to the present invention.

[0018] Figure 2 This is a hardware implementation block diagram of a multi-node mutual positioning method in a complex environment according to the present invention.

[0019] Figure 3 This is a flowchart of a multi-node mutual positioning method in a complex environment according to the present invention. Detailed Implementation

[0020] This invention proposes a multi-node mutual positioning method in complex environments. Each node in this method includes a transmit link, a receive link, a transmit / receive antenna, a ZigBee module, and a signal processing module. Each node operates in a triangular wave frequency-modulated continuous wave (FM-CLL) mode and has both receive and transmit capabilities. Each node can be configured as either a master or slave node. Mutual positioning is achieved between nodes by transmitting and receiving triangular wave FM-CLL signals. When a node operates in master mode, it synchronizes with the working signals of other slave nodes through coarse and fine synchronization steps. Then, it calculates the distance information of the slave nodes using the round-trip time of flight (RTOF), calculates the distance information of the slave nodes using Doppler frequency shift, and estimates the angle information of the slave nodes using the DOA method to complete the positioning of the slave nodes. When a node operates in slave mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse and fine synchronization steps, and then sends the synchronized signal to the master node so that the master node can locate the slave node's position.

[0021] Preferably, a time reference is first established using a ZigBee module for the multiple nodes requiring mutual positioning, avoiding unknown time differences when multiple nodes initiate mutual positioning, i.e., the aforementioned coarse synchronization. Then, precise synchronization is performed between the master and slave nodes that have established the time reference. The slave node performs frequency mixing on the received master node signal to obtain an intermediate frequency (IF) signal, and then performs FFT on the IF signal to obtain the IF values ​​of the upper and lower sweep frequencies. The time and frequency offset between nodes can be calculated using formulas. Then, based on the obtained time and frequency offsets, the operating frequency and time of the slave node's local oscillator signal are adjusted to achieve precise synchronization between the slave and master node's operating signals. In step S3, a triangular wave frequency-modulated continuous wave method is used to measure the relative position, velocity, and angle between the nodes to achieve master node positioning of the slave node. After achieving precise synchronization between nodes, the master node switches from transmit mode to receive mode, and the slave nodes switch from receive mode to transmit mode. The master node can then begin locating other slave nodes. Upon receiving signals from slave nodes, the master node calculates the round-trip time of flight (RTF) to obtain the distance information. The node's velocity information can be obtained through the Doppler shift of the intermediate frequency (IF) signal. A master node with multiple receiving antennas can obtain the node's angle information via DOA (Depth of Angle). Each node can operate in master node mode to locate other nodes, or in slave node mode to be located by the master node, thus enabling mutual location among multiple nodes.

[0022] Preferably, step S2 is required to perform fine synchronization of the signals between the master and slave nodes. This is because different nodes operate under different system clock crystal oscillators, and the operating signals of the master and slave nodes will have time and frequency offsets. After receiving the synchronization signal from the master node, the slave node obtains the intermediate frequency (IF) signal through mixing, performs FFT operation and peak search to detect the IF signal frequency value f1 of the up-sweep frequency and the IF signal frequency value f2 of the down-sweep frequency. The correspondence between the two IF signal frequency values ​​f1, f2 and the time and frequency offsets Δt and Δf between the nodes is as follows:

[0023] f1=Δf+Δf a -μΔt

[0024] f2=Δf+Δf a +μΔt

[0025] in The specific formula for calculating time and frequency offset can be derived from the formula:

[0026]

[0027] Where T is the sweep period, B is the sweep bandwidth, and Δf a It is a known frequency offset of the local oscillator signal from the slave node relative to the master node, in order to prevent the intermediate frequency signal of the up-and-down frequency sweep signal from having a negative frequency.

[0028] Preferably, after precise synchronization, the slave node can be located using a triangular wave frequency-modulated continuous wave method. At this time, the slave node's operating signal is only delayed by the signal propagation time t compared to the master node's local oscillator signal. d Therefore, after the node transmits the synchronized signal to the master node, the master node can calculate the distance information between the nodes using the round-trip time of flight (RTOF) through signal processing. The synchronization signal received by the master node has a 2t difference from the initial transmitted signal. d The delay is such that the master node performs FFT operation and peak search on the obtained intermediate frequency signal to detect the intermediate frequency signal frequency value f of the up-sweep and down-sweep frequencies. up f dn With time 2t of RTOF d The specific relationship is as follows:

[0029]

[0030] The formula for obtaining the specific distance information between the master node and the slave node is as follows:

[0031]

[0032] Where c is the speed of light, and the distance information of the node can be obtained through the frequency value f. up or f dn get.

[0033] Furthermore, the spectrum between master and slave nodes with relative velocities will contain a Doppler frequency shift f. D Then the intermediate frequency signal values ​​f obtained by the master node for the up-sweep and down-sweep frequencies are... up f dn With time 2t of RTOF d The specific relationship becomes:

[0034]

[0035] Therefore, the specific formula by which the master node can calculate the distance and speed information of the slave nodes is as follows:

[0036]

[0037] Where f l This is the starting frequency for the node's frequency sweep.

[0038] For a master node with multiple receiving antennas, the angle of the slave node relative to the master node can be measured using the DOA (Direct Occurrence of Angles) method. Different DOA methods are used for different antenna arrays, including Bartlett Beamforming, Capon Beamforming, and MUSIC Beamforming. The master node can obtain the specific angle information of the slave node by performing beamforming estimation on the received signal. Each node can operate in master node mode to locate other nodes, or it can operate in slave node mode to be located by the master node, thus achieving mutual positioning among multiple nodes.

[0039] This invention achieves high-precision mutual positioning between multiple nodes by implementing the working principle of frequency-modulated continuous wave radar between nodes. It overcomes the shortcomings of existing multi-node mutual positioning technologies, such as susceptibility to environmental weather, poor positioning accuracy, susceptibility to non-line-of-sight errors and antenna gain factors, high requirements for the synchronization accuracy of clock units between nodes, and low flexibility of the positioning node subsystem.

[0040] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0041] Combination Figure 1 The paper introduces a multi-node mutual positioning scenario diagram in which the method is applied, and one node is set as the master node to locate the positions of the other three slave nodes in the center position.

[0042] In a further embodiment, combined with Figure 2This paper introduces the specific hardware references used to implement this method. First, one transmitting antenna 1 and eight receiving antennas 3 are required. The transmitting component of each node includes an RF module 8 for controlling the specific parameters of the transmitted signal and a signal modulation module 2 for generating the RF signal. The receiving component includes a mixer 4 for mixing the received signal and the local oscillator signal to obtain an intermediate frequency (IF) signal, a low-pass filter 5 for filtering out high-frequency signals, and an IF amplifier 6 for amplifying the processed signal. Both the receiving and transmitting channels require a switching switch 7 controlled by a ZYNQ chip 10. The IF signal is then acquired by an eight-channel ADC chip 9 after passing through the IF amplifier 6. The acquired data undergoes FFT operations in the ZYNQ chip 10 and is stored in DDR RAM 13 for further processing. The ZYNQ chip performs peak detection by reading the FFT data results and performs synchronization in step S2 and positioning in step S3 by controlling the RF module 8 and the transmit / receive switching switch 7. The Zigbee module 11 controls each node system to operate under the same time base. Simultaneously, the hardware circuit also requires a power supply module 14 to provide a crystal oscillator 12 for clocking the system, which in turn provides a stable power supply for the circuit.

[0043] In a further embodiment, combined with Figure 3 The specific implementation process of the multi-node mutual positioning method is as follows: Two or more nodes that need to be positioned define a time reference through a ZigBee module to achieve coarse synchronization between master and slave nodes. Then, the master node sends a frequency sweep signal to the slave node to initiate the synchronization step. After receiving the signal, the slave node performs the following: 1. AD acquisition and FFT operation on the intermediate frequency signals of the upper and lower frequency sweeps; 2. Peak detection on 2×8 signal spectra; 3. Calculation of the average time and frequency offset according to the formula to achieve precise synchronization with the master node signal. The above signal processing is performed within a predefined signal processing time. After the predefined signal processing time is reached, the slave node sends a synchronization signal to the master node. After receiving the signal, the master node performs the following: 1. AD acquisition and FFT operation on the intermediate frequency signals of the upper and lower frequency sweeps; 2. Peak detection on 2×8 signal spectra; 3. Calculation of the distance and velocity information of the slave node according to the formula; 4. Estimation of the angle information of the slave node based on the phase in the 8 spectra to achieve the purpose of locating the slave node position.

[0044] This invention achieves high-precision mutual positioning between multiple nodes in complex environments by requiring only one synchronization and measurement positioning operation between multiple nodes operating under a linear frequency modulation system. The infrastructure is simple, low-cost, and easy to maintain. This method offers advantages such as fast detection speed, long detection distance, immunity to weather conditions, and strong environmental adaptability.

[0045] The present invention will be further described in detail below with reference to specific embodiments.

[0046] Example

[0047] Multiple nodes using this method have the same structural composition; each node includes a transmitting component, a receiving component, and a digital signal processing module; the transmitting component includes a transmitting antenna for radiating transmitted signals, an RF module and a signal modulation module for configuring transmitted signal parameters, and a transmitting switch for turning the transmitted signal on or off; the receiving component includes a receiving antenna for receiving signals transmitted by another positioning unit, a mixer for mixing the received signals to obtain an intermediate frequency (IF) signal, a filter and an amplifier for filtering out unwanted signals and amplifying the IF signal, respectively, and a receiving switch for turning the received signal on or off; the digital signal processing module includes a ZigBee module for coarse synchronization, a crystal oscillator module for providing clock reference signals to the chip and RF module, a RAM module for storing and reading data, and a power supply module for power management of the entire node; the digital signal processing module is also connected to the RF module to regulate the RF module, perform precise synchronization of the two positioning systems, condition and process the IF signal, and control the node's transmitting and receiving state transitions.

[0048] In this embodiment, all nodes employ a frequency-modulated continuous wave (FMCV) system. This method includes multiple nodes. During positioning, the master node sends information to other slave nodes to be positioned, performing step S1 (coarse synchronization). After establishing a working time reference between nodes, the master node sends a modulated signal to be synchronized to the slave nodes, performing step S2 (fine synchronization). Upon receiving the signal, the slave node processes it to obtain its time and frequency offset relative to the master node. The slave node adjusts its own transmitted signal. After a predefined signal processing time, the slave node sends a precisely synchronized signal to the master node. Upon receiving the signal, the master node performs step S3 (positioning), using the RTOF method for distance positioning, the Doppler frequency shift method for velocity estimation, and the DOA method for angle estimation. These three steps achieve master-to-slave positioning, allowing each node to act as a master node and acquire the position information of other nodes, enabling multi-node mutual positioning.

[0049] In this embodiment, the transmitting and receiving antennas use patch antennas with identical structures. The patch antenna element has a total length of 6cm, operates at a center frequency of 24GHz, has a bandwidth of 250MHz, and a frequency sweep of 1ms. The AD sampling rate is 8MHz, and the maximum measurable distance range is 2.4km.

[0050] In summary, the present invention provides a multi-node mutual positioning method in complex environments, which overcomes the shortcomings of existing multi-node mutual positioning technologies, such as susceptibility to environmental and weather conditions, poor positioning accuracy, susceptibility to non-line-of-sight errors and antenna gain factors, high requirements for the synchronization accuracy of clock units between nodes, and low flexibility of the positioning node subsystem.

[0051] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto.

[0052] Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this invention should be included within the protection scope of this invention.

[0053] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

[0054] It should be understood that the modules, units, components, etc., included in the device of one embodiment of the present invention can be adaptively changed to be placed in a device different from that embodiment. Different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A method for multi-node mutual positioning in complex environments, characterized in that, Each node includes a transmit link, a receive link, a transmit and receive antenna, a ZigBee module, and a signal processing module; each node can be set as a master node or a slave node, and nodes can achieve mutual positioning by transmitting and receiving triangular wave frequency modulated continuous wave signal waveforms; When a node operates in master node mode, it synchronizes with the working signals of other slave nodes through coarse and fine synchronization steps, and then locates the slave node using the working principle of frequency-modulated continuous wave radar. When a node operates in slave node mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse and fine synchronization steps, and then sends the synchronized signal to the master node so that the master node can locate the slave node's position. The positioning method includes the following steps: Step S1: Set up a master node in the node network and set the other nodes as slave nodes; use the ZigBee module of each node to make each node work on the same time base to achieve coarse time synchronization between multiple nodes. Step S2: After coarse synchronization, the master node sends the signal to be synchronized to the slave node. The slave node processes the received signal to obtain the time and frequency offset between the nodes, and then adjusts the transmitted signal of the slave node to make the transmitted signal of the slave node precisely synchronized with the local oscillator signal in the master node. After coarsely synchronizing the time base between nodes, precise synchronization of the working signals between master and slave nodes is required. After receiving the synchronization signal from the master node, the slave node obtains the intermediate frequency (IF) signal through mixing, performs FFT operations and peak search to detect the IF signal frequency values ​​f1 (upward sweep) and f2 (downward sweep). The corresponding relationships between the two IF signal frequencies f1 and f2 and the time Δt and frequency offset Δf between the nodes are as follows: f1=Δf+Δf a -μΔt f2=Δf+Δf a +μΔt in The specific formula for calculating time and frequency offset is derived from the formula: Where T is the sweep period, B is the sweep bandwidth, and Δf a It is the known frequency offset of the slave node's local oscillator signal relative to the master node; after obtaining the time Δt and frequency offset Δf, the slave node adjusts the frequency and time of its own local oscillator signal to achieve precise synchronization between the slave node and the master node's working signals; Step S3: After fine synchronization, the master node receives the transmitted signal from the slave node, processes the received signal to obtain the distance, speed and angle information of the slave node in order to locate the slave node.

2. The multi-node mutual positioning method according to claim 1, characterized in that, After precise synchronization, the master node switches from transmit mode to receive mode, allowing it to begin locating other slave nodes. The slave nodes then switch from receive mode to transmit mode; at this point, the slave node's signal is only delayed by a propagation time t compared to the master node's local oscillator signal. d Therefore, the slave node transmits the synchronized signal to the master node, which can then calculate the distance between the nodes using the round-trip time of the signal through signal processing. The synchronization signal received by the master node has a 2t difference from the initially transmitted signal. d The delay is such that the master node performs FFT operation and peak search on the obtained intermediate frequency signal to detect the intermediate frequency signal frequency value f of the up-sweep and down-sweep frequencies. up f dn With time 2t of RTOF d The specific relationship is as follows: The formula for obtaining the specific distance information from the master node to the slave node is: Where c is the speed of light, and the distance information of the node is obtained through the frequency value f. up or f dn get.

3. The multi-node mutual positioning method according to claim 2, characterized in that, For intermediate frequency signals between master and slave nodes with relative speeds, there will be a Doppler frequency shift f. D Then the intermediate frequency signal values ​​f obtained by the master node for the up-sweep and down-sweep frequencies are... up f dn With time 2t of RTOF d The specific relationship becomes: The specific formulas for the distance and velocity information of the slave node relative to the master node are as follows: Where f l This is the starting frequency for the node's frequency sweep.

4. The multi-node mutual positioning method according to claim 3, characterized in that, For a master node with multiple receiving antennas, the angle of the slave node relative to the master node is measured by the DOA method. The master node can obtain the specific angle information of the slave node by performing beamforming estimation on the obtained signal. Each node can operate in master node mode to locate other nodes, or operate in slave node mode to be located by the master node, so as to realize mutual positioning of multiple nodes.

5. A multi-node mutual positioning system in a complex environment, characterized in that, To implement the method described in any one of claims 1 to 4, the system includes multiple nodes, each node including a transmit link, a receive link, a transmit and receive antenna, a ZigBee module, and a signal processing module; each node is configured as a master node or a slave node, and the nodes achieve mutual positioning function by transmitting and receiving triangular wave frequency modulated continuous wave signal waveforms; When a node operates in master node mode, it synchronizes with the working signals of other slave nodes through coarse synchronization and fine synchronization steps, and then locates the slave node through the working principle of frequency-modulated continuous wave radar. When a node operates in slave node mode, it waits for the synchronization signal sent by the master node, synchronizes with the master node's signal through coarse synchronization and fine synchronization steps, and then sends the synchronized signal to the master node so that the master node can locate the slave node's position.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps of the method as described in any one of claims 1-4.

8. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-4.

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