A medical device positioning system and method based on an artificial neural network

Through the medical device positioning system based on artificial neural network, combined with the RSSI value of the sensor node and the correlation information data of the medical device, the accurate positioning of medical devices in a multi-floor environment of the hospital is achieved, solving the problem of inaccurate positioning in the prior art, and improving positioning accuracy and user experience.

CN115696183BActive Publication Date: 2025-07-01朱瑞銮
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Patent Information

Application Number
CN202211179151.9
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-09-27
Publication Date
2025-07-01
Estimated Expiration
2042-09-27

AI Technical Summary

Technical Problem

The existing medical equipment positioning methods are inaccurate in the multi-floor environment of the hospital, and it is impossible to accurately locate the floor where the medical equipment is located, and it is impossible to accurately locate patients who cannot be affected by radiation.

Method used

Using a medical device positioning system based on artificial neural networks, the RSSI value of sensor nodes is collected in real time, and an information vector matrix is ​​constructed, combined with the correlation information data of the hospital area, buildings, wards, patients and medical equipment, the artificial neural network is trained to achieve accurate positioning of medical equipment.

Benefits of technology

It significantly improves the positioning accuracy and automation level of medical equipment, improves the efficiency and convenience of medical equipment, and enhances the user experience.

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Abstract

A medical device positioning system based on an artificial neural network, comprising a data acquisition module: real-time collecting the RSSI values of N sensor nodes deployed within the positioning area; a module for constructing an information vector matrix, which forms a historical information vector matrix by combining the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI values and time information of the sensor nodes; a training module: training the artificial neural network according to the historical information vector matrix; an identification module, that is, inputting the real-time information vector matrix into the trained artificial neural network for identification; a position output module. The creative artificial neural network of the present invention adopts an improved loss function, adds the time factor of historical data to the weight adjustment process, and adds the correlation information data of the hospital area, building, ward, patient and medical device to the determination of the position of the medical device, greatly increasing the positioning accuracy of the medical device.
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Description

Technical Field

[0001] The present invention relates to the field of device positioning, and particularly to a medical device positioning system and method based on an artificial neural network. Background Art

[0002] Currently, with the development of technology, the types and quantities of medical devices are increasing continuously. Medical devices have become a necessary condition for the normal operation of hospitals, playing an important role in hospitals. How to achieve scientific management of medical devices and give full play to the maximum utilization value of medical devices has become one of the research hotspots. Smart healthcare is also developing rapidly, putting forward new requirements for the refined management of medical devices. Timely positioning of medical devices and quickly obtaining the positions of medical devices play an increasingly important role in ensuring the clinical use of medical devices.

[0003] However, most of the existing medical device positioning methods are absolute positioning. For example, GPS and other methods are used to position medical devices. This method is inaccurate for multi - floor positioning in hospitals and cannot achieve the positioning of the floor where the medical device is located. There is also a method of setting sensors in each ward for positioning, but for patients with requirements such as not being exposed to radiation, accurate positioning cannot be carried out because sensors cannot be installed in the ward. There is also a method of positioning based on deep learning algorithms, but this positioning only considers the device sensor data and does not use patient information and historical ward data, resulting in inaccurate positioning. There is also a method of obtaining positioning based on signal strength, but this method has certain defects. For example, there are no sensors in the ward where the device is located, but the sensor signals in two departments separated by one floor on the same floor are weaker than the signals above the ward where the device is located, resulting in inaccurate positioning. Therefore, achieving accurate positioning of medical devices has become an urgent need. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a medical device positioning system and method based on an artificial neural network. The medical device positioning method and system based on the artificial neural network of the present invention significantly improve the positioning accuracy of medical devices and the level of automated work, greatly improving the use efficiency and convenience of medical devices and enhancing the user experience. A medical device positioning system based on an artificial neural network includes a data acquisition module: real-time collecting the RSSI values of N sensor nodes deployed within the positioning area, where the RSSI value is the signal strength value after the sensor node transmits an electromagnetic wave signal and is received by the medical device; a module for constructing an information vector matrix, which forms a historical information vector matrix by combining the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI value and time information of the sensor node; a training module: training the artificial neural network according to the historical information vector matrix; an identification module; judging the position of the medical device according to the received signal strength value, real-time patient, ward, building, and hospital area data, that is, inputting the real-time information vector matrix into the trained artificial neural network for identification; a position output module: the artificial neural network outputs the position information of the medical device;

[0005] The correlation information data of the hospital area, building, ward, patient and medical device is obtained according to the historical residence time, usage time, usage frequency of the medical device in the hospital area, building, ward, as well as the types of diseases involved in the hospital area, building, ward history, and the disease of the patient and the historical usage frequency and time of the medical device;

[0006] The improved loss function adopted by the artificial neural network is: E = E(p, o) = ∑ k E[p k , o k = ∑ k E[p k , f2(u k )] = ∑ k E[p k , f2(∑ j V tj w jk y j )] = ∑ k E[p k , f2(∑ j V tj w jk f1(u j ))] = ∑ k E[p k , f2(∑ j V tj w jk f1(∑ i v ij x i ))]

[0007] Among them, E represents the energy loss functional, p represents the expected output vector, p k represents the k-th expected output vector, o represents the actual output vector, o k represents the k-th actual output vector, u k represents the net output of the output layer, u j represents the net output of the hidden layer, v ij represents the weight between the i-th input and the j-th extracted feature, w jk represents the weight between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, x i is the input of the input layer, y j is the input of the hidden layer, V tj represents the weight w jk at the weight coefficient value at time t; the smaller the difference between time t and the current time, the larger the weight coefficient value V tj is.

[0008] Preferably, the sensor nodes are arranged in the wards on each floor of the hospital area, and 1-N sensors are arranged on each floor.

[0009] Preferably, the medical device is provided with an intelligent gateway, which is composed of a main board, a wireless board and an interface board. The main board is composed of a main processor system and an FPGA chip; the interface board supports four serial interfaces, including RS232, RS485, RS422 and analog sampling interfaces.

[0010] Preferably, the signal strength value after the medical device receives, and the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

[0011] Preferably, the artificial neural network outputs the location information of the medical device, and further includes transmitting the current location information and historical location information of the medical device to the central monitoring platform, and combining with the GIS map to realize the operation trajectory and real-time location tracking of all medical devices in the hospital area.

[0012] The present invention also includes a medical device positioning method based on an artificial neural network, including step S1: real-time collecting the RSSI values of N sensor nodes deployed in the positioning area, and the RSSI value is the signal strength value after the electromagnetic wave signal emitted by the sensor node is received by the medical device;

[0013] Step S2: constructing an information vector matrix, and forming a historical information vector matrix with the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI value and time information of the sensor node;

[0014] Step S3: training the artificial neural network according to the historical information vector matrix;

[0015] Step S4: Determine the location of the medical device based on the received signal strength value and the real-time data of the patient, ward, building, and hospital area, that is, input the real-time information vector matrix into the trained artificial neural network for recognition;

[0016] Step S5: The artificial neural network outputs the location information of the medical device;

[0017] The correlation information data of the hospital area, building, ward, patient, and medical device is obtained according to the historical residence time, usage time, usage frequency of the medical device in the hospital area, building, and ward, the historical disease types involved in the hospital area, building, and ward, and the historical usage frequency and time of the disease obtained by the patient and the medical device;

[0018] The improved loss function adopted by the artificial neural network is: E = E(p, o) = ∑ k E[p k , o k = ∑ k E[p k , f2(u k )] = ∑ k E[p k , f2(∑ j V tj w jk y j )] = ∑ k E[p k , f2(∑ j V tj w jk f1(u j ))] = ∑ k E[p k , f2(∑ j V tj w jk f1(∑ i v ij x i ))]

[0019] Among them, E represents the energy loss functional, p represents the expected output vector, p k represents the k-th expected output vector, o represents the actual output vector, o k represents the k-th actual output vector, u k represents the net output of the output layer, u j represents the net output of the hidden layer, v ij represents the weight between the i-th input and the j-th extracted feature, w jk represents the weight between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, x iis the input of the input layer, y j is the input of the hidden layer, V tj represents the weight w jk The weight coefficient value at time t. The smaller the difference between time t and the current moment, the larger the weight coefficient value V tj is larger.

[0020] Preferably, the sensor nodes are arranged in the wards on each floor of the hospital area, and 1 - N sensors are arranged on each floor.

[0021] Preferably, the medical device is provided with an intelligent gateway, which is composed of a main board, a wireless board and an interface board. The main board is composed of a main processor system and an FPGA chip; the interface board supports four serial interfaces, including RS232, RS485, RS422 and an analog sampling interface.

[0022] Preferably, the signal strength value after the medical device receives the signal, and the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

[0023] Preferably, the artificial neural network outputs the position information of the medical device, and also includes transmitting the current position information and historical position information of the medical device to the central monitoring platform, and combining with the GIS map to realize the operation trajectory and real-time position tracking of all medical devices in the hospital area.

[0024] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0025] It solves the problem of low positioning accuracy in the traditional technology. The creative artificial neural network of the present application adopts an improved loss function, adding the time factor of historical data to the weight adjustment process, that is, the closer to the current moment, the larger the weight, which greatly enhances the calculation accuracy. By adding V tj which represents the weight W jk the weight coefficient value at time t to the loss function, the smaller the difference between time t and the current moment, the larger the weight coefficient value V tj is larger, realizing the updated accuracy of the artificial neural network; and by constructing an information vector matrix module, adding the correlation information data of the hospital area, building, ward, patient and medical device to the judgment of the position of the medical device, greatly increasing the positioning accuracy of the medical device; and by forming a historical information vector matrix from the RSSI value corresponding to the sensor node and the time information, realizing the accurate positioning of the medical device.

[0026] In addition, the correlation information data of the hospital area, building, ward, patient and medical device is obtained based on the historical residence time, usage time, usage frequency of the medical device in the hospital area, building, ward, the historical disease types involved in the hospital area, building, ward, and the historical usage frequency and time of the disease obtained by the patient and the medical device, which greatly improves the positioning accuracy of the medical device. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 is a diagram of a medical device positioning method based on an artificial neural network according to the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0028] Those skilled in the art understand that, as described in the background art, most of the existing medical device positioning methods in the traditional technology are absolute positioning. For example, GPS or other methods are used to position medical devices. This method is inaccurate for positioning in multi-story hospitals and cannot achieve the positioning of the floor where the medical device is located. There is also a method of setting sensors in each ward for positioning, but for patients with requirements such as not being able to be irradiated, accurate positioning cannot be achieved because sensors cannot be installed in the ward. There is also a method of positioning according to deep learning algorithms, but this positioning only considers the device sensor data and does not use the patient's information and the historical data of the ward, resulting in inaccurate positioning. There is also a method of obtaining positioning by signal strength, but this method has certain defects. For example, there is no sensor in the ward where the device is located, but the sensor signals of two departments separated by one floor on the same floor are weaker than the signals of the ward upstairs where the device is located, resulting in inaccurate positioning. Therefore, achieving accurate positioning of medical devices has become an urgent need. To make the above objects, features and beneficial effects of the present invention more obvious and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0029] Embodiment 1:

[0030] Figure 1 A diagram of the medical device positioning method based on an artificial neural network according to the present application is shown. In some embodiments, it includes step S1: real-time collecting the RSSI values of N sensor nodes deployed in the positioning area, where the RSSI value is the signal strength value after the electromagnetic wave signal emitted by the sensor node is received by the medical device;

[0031] Step S2: constructing an information vector matrix, and forming a historical information vector matrix with the correlation information data of the hospital area, building, ward, patient and medical device, as well as the RSSI value corresponding to the sensor node and the time information;

[0032] Step S3: training the artificial neural network according to the historical information vector matrix;

[0033] Step S4: Determine the location of the medical device based on the received signal strength value and the real-time data of the patient, ward, building, and campus, that is, input the real-time information vector matrix into the trained artificial neural network for recognition;

[0034] Step S5: The artificial neural network outputs the location information of the medical device;

[0035] The correlation information data of the campus, building, ward, patient, and medical device is obtained based on the historical residence time, usage time, usage frequency of the medical device in the campus, building, and ward, the historical disease types involved in the campus, building, and ward, and the historical usage frequency and time of the disease obtained by the patient and the medical device;

[0036] The improved loss function adopted by the artificial neural network is: E = E(p, o) = ∑ k E[p k , o k = ∑ k E[p k , f2(u k )] = ∑ k E[p k , f2(∑ j V tj w jk y j )] = ∑ k E[p k , f2(∑ j V tj w jk f1(u j ))] = ∑ k E[p k , f2(∑ j V tj w jk f1(∑ i v ij x i ))]

[0037] Among them, E represents the energy loss functional, p represents the expected output vector, p k represents the k-th expected output vector, o represents the actual output vector, o k represents the k-th actual output vector, u k represents the net output of the output layer, u j represents the net output of the hidden layer, v ij represents the weight between the i-th input and the j-th extracted feature, w jk represents the weight between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, x i is the input of the input layer, y jis the input to the hidden layer, V tj represents the weight W jk At time t, the weight coefficient value. The smaller the difference between time t and the current time, the larger the weight coefficient value V tj is.

[0038] In some embodiments, the sensor nodes are arranged in the wards on each floor of the hospital area, and 1 - N sensors are arranged on each floor.

[0039] In some embodiments, the medical device is provided with an intelligent gateway, which is composed of a main board, a wireless board and an interface board. The main board is composed of a main processor system and an FPGA chip; the interface board supports four serial interfaces, including RS232, RS485, RS422 and an analog sampling interface.

[0040] In some embodiments, the received signal strength value of the medical device, wherein the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

[0041] In some embodiments, the artificial neural network outputs the location information of the medical device, and further includes transmitting the current location information and historical location information of the medical device to the central monitoring platform, and combining with the GIS map to realize the operation trajectory and real-time location tracking of all medical devices in the hospital area.

[0042] Embodiment 2

[0043] The present invention further includes a medical device positioning system based on an artificial neural network, including a data acquisition module: collecting the RSSI values of N sensor nodes deployed in the positioning area in real time. The RSSI value is the signal strength value received by the medical device after the sensor node emits an electromagnetic wave signal; a module for constructing an information vector matrix, which forms a historical information vector matrix by combining the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI value and time information of the sensor node; a training module: training the artificial neural network according to the historical information vector matrix; an identification module; judging the location of the medical device according to the received signal strength value, real-time patient, ward, building, hospital area data, that is, inputting the real-time information vector matrix into the trained artificial neural network for identification; a location output module: the artificial neural network outputs the location information of the medical device;

[0044] The correlation information data of the hospital area, building, ward, patient and medical device is obtained according to the historical residence time, usage time, usage times of the medical device in the hospital area, building, ward, as well as the historical disease types involved in the hospital area, building, ward, and the disease obtained by the patient and the historical usage times and time of the medical device;

[0045] The improved loss function adopted by the artificial neural network is: E = E(p, o) = ∑k E[p k ,o k =∑ k E[p k ,f2(u k )]=∑ k E[p k ,f2(∑ j V tj w jk y j )]=∑ k E[p k ,f2(∑ j V tj w jk f1(u j ))]=∑ k E[p k ,f2(∑ j V tj w jk f1(∑ i v ij x i ))]

[0046] Among them, E represents the energy loss functional, p represents the expected output vector, p k represents the k-th expected output vector, o represents the actual output vector, o k represents the k-th actual output vector, u k represents the net output of the output layer, u j represents the net output of the hidden layer, v ij represents the weight value between the i-th input and the j-th extracted feature, w jk represents the weight value between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, x i is the input of the input layer, y j is the input of the hidden layer, V tj represents the weight coefficient value of the weight w jk at time t; the smaller the difference between time t and the current moment, the larger the weight coefficient value V tj is.

[0047] In some embodiments, the sensor nodes are arranged in the wards on each floor of the hospital area, and 1-N sensors are arranged on each floor.

[0048] In some embodiments, the medical device is provided with an intelligent gateway, which is composed of a main board, a wireless board and an interface board. The main board is composed of a main processor system and an FPGA chip; the interface board supports four serial interfaces, including RS232, RS485, RS422 and an analog sampling interface.

[0049] In some embodiments, the signal strength value after the medical device is received, wherein the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

[0050] In some embodiments, the artificial neural network outputs the location information of the medical device, and further includes transmitting the current location information and historical location information of the medical device to the central monitoring platform, and combining with the GIS map to realize the operation trajectory and real-time location tracking of all medical devices in the hospital area.

[0051] A medical device positioning method and system based on an artificial neural network according to the present invention solves the problem of low positioning accuracy in the traditional technology. The creative artificial neural network of the present application adopts an improved loss function, and adds the time factor of historical data to the weight adjustment process, that is, the closer to the current time, the greater the weight, which greatly enhances the calculation accuracy. By adding the weight coefficient value V tj representing the weight w jk at time t to the loss function, the smaller the difference between time t and the current time, the greater the weight coefficient value V tj is, realizing the updated accuracy of the artificial neural network; and by constructing an information vector matrix module, adding the correlation information data of the hospital area, building, ward, patient and medical device to the judgment of the location of the medical device, greatly increasing the positioning accuracy of the medical device; and by forming a historical information vector matrix from the RSSI value and time information corresponding to the sensor node, the accurate positioning of the medical device is realized.

[0052] In addition, the correlation information data of the hospital area, building, ward, patient and medical device is obtained according to the historical residence time, usage time, usage times of the medical device in the hospital area, building, ward, as well as the historical disease types involved in the hospital area, building, ward, and the diseases of the patient and the historical usage times and time of the medical device, greatly improving the positioning accuracy of the medical device.

[0053] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects.

[0054] Although the present invention is disclosed as above, the present invention is not limited thereto. Any person skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention should be subject to the scope defined by the claims.

Claims

1. A medical device positioning system based on an artificial neural network, characterized in that, It includes a data acquisition module: It collects the RSSI values of N sensor nodes deployed inside the positioning area in real time. The RSSI value is the signal strength value after the electromagnetic wave signal emitted by the sensor node is received by the medical device. An information vector matrix construction module, which forms a historical information vector matrix by combining the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI value and time information of the sensor node; A training module: It trains the artificial neural network according to the historical information vector matrix; An identification module; It determines the location of the medical device according to the received signal strength value, real-time patient, ward, building, and hospital area data, that is, it inputs the real-time information vector matrix into the trained artificial neural network for identification. A location output module: The artificial neural network outputs the location information of the medical device. The correlation information data of the hospital area, building, ward, patient and medical device is obtained according to the historical retention time, usage time, usage times of the medical device in the hospital area, building, ward, as well as the historical disease types involved in the hospital area, building, ward, and the historical usage times and time of the disease obtained by the patient and the medical device. The improved loss function adopted by the artificial neural network is: E = E(p,o) = ∑kE[pk,ok] = ∑kE[pk,f2(uk)] = ∑kE[pk,f2(∑jVtjwjkyj)] = ∑kE[pk,f2(∑jVtjwjkf1(uj))] = ∑kE[pk,f2(∑jVtjwjkf1(∑ivijxi))] Where, E represents the energy loss functional, p represents the expected output vector, pk represents the k-th expected output vector, o represents the actual output vector, ok represents the k-th actual output vector, uk represents the net output of the output layer, uj represents the net output of the hidden layer, vij represents the weight value between the i-th input and the j-th extracted feature, wjk represents the weight value between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, xi is the input of the input layer, yj is the input of the hidden layer, Vtj represents the weight coefficient value of the weight wjk at time t; The smaller the difference between time t and the current moment, the larger the weight coefficient value Vtj. The sensor nodes are set in the wards on each floor of the hospital area, and 1 - N sensors are set on each floor. The medical device is equipped with an intelligent gateway, which consists of a main board, a wireless board and an interface board. The main board consists of a main processor system and an FPGA chip; The interface board supports four serial interfaces, including RS232, RS485, RS422 and analog sampling interfaces.

2. The medical device positioning system based on an artificial neural network according to claim 1, wherein The signal strength value received by the medical device, where the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

3. The medical device positioning system based on an artificial neural network according to claim 1, characterized in that, The artificial neural network outputs the location information of the medical device, and it also includes transmitting the current location information and historical location information of the medical device to the central monitoring platform to realize the operation trajectory and real-time location tracking of all medical devices in the hospital area in combination with the GIS map.

4. A medical device positioning method based on an artificial neural network, characterized in that, It includes step S1: Collect the RSSI values of N sensor nodes deployed inside the positioning area in real time. The RSSI value is the signal strength value after the electromagnetic wave signal emitted by the sensor node is received by the medical device; step S2: Construct an information vector matrix, and form a historical information vector matrix with the correlation information data of the hospital area, building, ward, patient and medical device, as well as the corresponding RSSI value and time information of the sensor node; step S3: Train the artificial neural network according to the historical information vector matrix; step S4: Judge the position of the medical device according to the received signal strength value, real-time patient, ward, building, and hospital area data, that is, input the real-time information vector matrix into the trained artificial neural network for recognition; step S5: The artificial neural network outputs the medical device position information; The correlation information data of the hospital area, building, ward, patient and medical device is obtained according to the historical residence time, usage time, usage times of the medical device in the hospital area, building, ward, as well as the historical disease types involved in the hospital area, building, ward, and the historical usage times and time of the disease obtained by the patient and the medical device; The improved loss function adopted by the artificial neural network is: E = E(p,o) = ∑kE[pk,ok] = ∑kE[pk,f2(uk)] = ∑kE[pk,f2(∑jVtjwjkyj)] = ∑kE[pk,f2(∑jVtjwjkf1(uj))] = ∑kE[pk,f2(∑jVtjwjkf1(Σivijxi))] where E represents the energy loss functional, p represents the expected output vector, pk represents the k-th expected output vector, o represents the actual output vector, ok represents the k-th actual output vector, uk represents the net output of the output layer, uj represents the net output of the hidden layer, vij represents the weight value between the i-th input and the j-th extracted feature, wjk represents the weight value between the j-th extracted feature and the k-th output, f1 and f2 are the first activation function and the second activation function respectively, xi is the input of the input layer, yj is the input of the hidden layer, Vtj represents the weight coefficient value of the weight wjk at time t; the smaller the difference between time t and the current moment, the larger the weight coefficient value Vtj; The sensor nodes are set in the wards on each floor of the hospital area, and 1 - N sensors are set on each floor; The medical device is provided with an intelligent gateway, which consists of a main board, a wireless board and an interface board. The main board consists of a main processor system and an FPGA chip; the interface board supports four serial interfaces, including RS232, RS485, RS422 and analog sampling interfaces.

5. The medical device positioning method based on an artificial neural network according to claim 4, wherein For the signal strength value received by the medical device, the received signal strength value is transmitted using the wireless NB-IOT communication protocol.

6. A method for positioning a medical device based on an artificial neural network according to claim 4, wherein When the artificial neural network outputs the medical device position information, it also includes transmitting the current position information and historical position information of the medical device to the central monitoring platform, and combining with the GIS map to realize the operation trajectory and real-time position tracking of all medical devices in the hospital area.

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