Low-altitude electromagnetic surveying and mapping air-ground collaborative integrated system

Through the integrated system of low-altitude electromagnetic surveying and mapping, the problems of incomplete data and poor real-time performance in low-altitude electromagnetic environment surveying and mapping are solved, and the rapid and accurate cognition and dynamic update of spectrum situations are achieved, and spectrum management and decision-making of low-altitude intelligent networking are supported.

CN120294409APending Publication Date: 2025-07-11NANJING UNIV
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
CN202510544363.X
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-04-28
Publication Date
2025-07-11

AI Technical Summary

Technical Problem

The existing technology has problems such as incomplete data, poor real-time performance, insufficient spectrum cognition, large bandwidth resource consumption, and low frequency decision-making timeliness in low-altitude electromagnetic environment surveying and mapping, which seriously restricts the development of low-altitude intelligent networking.

Method used

The integrated system of air-ground collaborative systems for low-altitude electromagnetic surveying and mapping is adopted to realize the recognition of air-ground collaborative electromagnetic spectrum through the collaborative work of the drone platform, ground control center and cloud data processing unit. Combined with machine learning and data mining technology, efficient data processing and dynamic mapping and update of spectrum maps are carried out.

Benefits of technology

It realizes efficient management and decision-making support for low-altitude electromagnetic spectrum space, providing fast and accurate cognition of spectrum situations and dynamic update capabilities.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN120294409A_ABST
    Figure CN120294409A_ABST
Patent Text Reader

Abstract

The invention discloses a low-altitude electromagnetic surveying and mapping air-ground collaborative integrated system, which aims at the requirements of high calculation load and strong real-time performance of low-altitude electromagnetic surveying and mapping, and comprises an unmanned aerial vehicle platform carrying observation equipment, an unmanned aerial vehicle, a data acquisition control module, software radio equipment USRP, a positioning module and a communication module, the acquisition module is responsible for acquiring electromagnetic data in a low-altitude area; the ground control center is used for processing the data transmitted back by the unmanned aerial vehicle through the communication module and determining the position and the frequency band of the next observation of the unmanned aerial vehicle according to the processing result; and the cloud data processing unit performs complex data analysis and processing, is responsible for constructing a frequency spectrum knowledge graph, and realizes deep cognition of the frequency spectrum situation through technologies such as machine learning and data mining. According to the method, space electromagnetic spectrum cognition, efficient data processing under a cloud edge-end architecture and dynamic drawing and updating of a spectrum map can be realized through air-ground cooperation, and powerful support is provided for management and decision-making of an electromagnetic spectrum space.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of radar signal processing, and specifically to a low-altitude electromagnetic mapping air-ground collaborative integrated system. Background Art

[0002] In recent years, with the development of the low-altitude economy, the low-altitude intelligent network has emerged as the times require. Among them, the number of low-altitude aircraft has shown an explosive growth, resulting in an explosive growth of wireless data transmission services. To meet the urgent needs such as spectrum security control and efficient sharing in the low-altitude intelligent network, it is necessary to quickly and accurately recognize the complex low-altitude electromagnetic spectrum environment, construct a spectrum situation map for spectrum decision-making for low-altitude aircraft networking, and formulate agile and adaptable frequency usage decisions considering the characteristics of rapid movement of low-altitude intelligent network nodes, diverse mission scenarios, and relatively limited resources.

[0003] In the prior art, low-altitude electromagnetic environment mapping usually relies on ground monitoring stations and sensors carried by unmanned aerial vehicles (UAVs) for data collection. However, these methods have problems such as incomplete data and poor real-time performance when dealing with complex electromagnetic environments. Moreover, spectrum cognition usually adopts a two-layer processing paradigm in the cloud, but there are problems such as high consumption of bandwidth resources, insufficient situation targeting, and low timeliness of frequency usage decisions, which seriously restrict the spectrum cognition of the low-altitude intelligent network and become a bottleneck in the development of the low-altitude intelligent network. Summary of the Invention

[0004] Object of the Invention: To provide a low-altitude electromagnetic mapping air-ground collaborative integrated system, which aims to meet the requirements of high computing load and strong real-time performance in low-altitude electromagnetic mapping, and realizes air-ground collaboration for spatial electromagnetic spectrum cognition, efficient data processing under the cloud-edge-end architecture, and dynamic drawing and updating of the spectrum map.

[0005] To solve the above technical problems, the present invention provides the following technical solutions:

[0006] A low-altitude electromagnetic mapping air-ground collaborative integrated system, the system includes:

[0007] A UAV platform equipped with observation equipment, responsible for collecting electromagnetic data in the low-altitude area;

[0008] A ground control center, used to process the data transmitted back by the UAV through the communication module, and determine the position and frequency band of the next observation of the UAV according to the processing results;

[0009] A cloud data processing unit, which performs complex data analysis and processing, is responsible for constructing a spectrum knowledge graph, and realizes in-depth cognition of the spectrum situation through machine learning and data mining technologies.

[0010] Preferably, the UAV platform equipped with observation equipment includes: a data acquisition module and a UAV part;

[0011] The data acquisition module is used to collect electromagnetic data in the low-altitude area, perform simple data processing, and then transmit the data to the ground control center and conduct the next observation according to the frequency band and bandwidth data transmitted by the ground control center.

[0012] The UAV part is used to transmit GPS / IMU data to the ground control center, wait for instructions from the ground control center, and reach the corresponding observation position according to the instructions for the next observation.

[0013] Preferably, the data acquisition module includes: a software-defined radio device USRP B210 and a Raspberry Pi 5 development board;

[0014] The software-defined radio device USRP B210 is used to collect wide-band signals;

[0015] The Raspberry Pi 5 development board serves as the main control unit of the data acquisition module, responsible for controlling signal acquisition and data processing, and conducting preliminary processing and analysis based on the electromagnetic data transmitted by the USRP to control the USRP for continuous signal acquisition.

[0016] Preferably, the UAV part includes: a high-precision GPS / IMU module and a flight control system;

[0017] In the high-precision GPS / IMU module, GPS provides accurate geographical location information for the UAV, including longitude, latitude, and altitude; IMU is used to measure the acceleration and angular velocity of the UAV to determine the pitch angle, roll angle, and yaw angle of the UAV, that is, the three-dimensional attitude of the UAV.

[0018] The flight control system obtains flight data through sensors, then calculates the corresponding control instructions to achieve the takeoff, hover, flight, and landing actions of the UAV, transmits the sensor data to the ground control center, waits for instructions from the ground control center, and reaches the corresponding observation position according to the instructions for the next observation.

[0019] Preferably, the ground control center includes: a communication module and a high-performance PC;

[0020] The communication module is used to establish a communication network to achieve wireless communication with the UAV observation platform;

[0021] Before performing tasks, the high-performance PC plans the flight path of the UAV according to the acquisition requirements, determines the area where signals need to be collected, monitors the status of the UAV and the data acquisition situation to dynamically adjust the flight path of the UAV, and further processes the electromagnetic signals and then transmits them to the cloud;

[0022] The high-performance PC is connected to the wireless router through its network interface, and is used to receive the data transmitted back by the UAV observation platform, and remotely control and task plan the UAV, including transmitting the transmission frequency band and bandwidth data to the data acquisition module for the next observation, and transmitting the flight path data to the UAV part to reach the corresponding observation position for the next observation.

[0023] Preferably, before executing the task, the high-performance PC plans the flight path of the UAV according to the acquisition requirements, including:

[0024] Before the UAV executes the task, it needs to first model the target area, and then formulate the optimal path according to the acquisition requirements. It adopts Spiral path planning and moves gradually inwards or outwards along a spiral line. According to the formula:

[0025] r(θ) = a + bθ;

[0026] Where, r represents the radius from the current position to the center, θ represents the current angle turned, a represents the starting radius, and b represents the control pitch;

[0027] During the flight, it receives sensor and signal data in real time to dynamically update the path. Through the direction adjustment based on the electromagnetic signal gradient, if the signal intensity suddenly changes or a new hot spot area appears, the flight direction is adjusted to the gradient ascending direction. According to the formula:

[0028] Where, v new represents the updated movement direction, v current represents the current flight speed or direction vector, γ represents the step size coefficient, represents the signal intensity gradient.

[0029] Preferably, the cloud data processing unit includes: a data storage unit, a data preprocessing unit, and a data analysis unit;

[0030] The data storage unit adopts a distributed storage technology, which can automatically compress and back up the data, and supports the efficient storage of massive data;

[0031] The data preprocessing unit preprocesses the uploaded raw electromagnetic data, including data cleaning, format conversion, and noise removal operations to improve the data quality;

[0032] The data analysis unit uses advanced electromagnetic data processing algorithms. For the preprocessed data, it combines the data-driven method that depends on the actually collected spectrum data and processes the data through statistical analysis and machine learning techniques, and the model-driven method that depends on the prior knowledge of the spectrum data generation process and describes the physical and statistical characteristics of the data by establishing a mathematical model to generate an electromagnetic spectrum map.

[0033] Preferably, the data-driven and model-driven methods of the cloud data processing unit include:

[0034] Assume that the electromagnetic propagation model and the transmitter power are known. Then, use the transmitter position estimation method to solve the transmitter power and position based on the free channel propagation model, and deduce the complete spectrum situation according to the estimation results and the propagation model. The formula of the free channel propagation model is as follows:

[0035]

[0036] where P R (d) represents the power received at a distance d, P T represents the transmit power, G T represents the transmit gain, G R represents the receive gain, λ represents the signal wavelength, and d represents the distance between the transmitter and the receiver;

[0037] The data-driven completion algorithm directly estimates the spectrum data in the unknown area by leveraging the existing spectrum data and uses the spatial interpolation algorithm based on autoregression. The autoregressive model predicts the spectrum data in the vacant area, and the completion formula is:

[0038]

[0039] where represents the spectrum data of the entire area to be completed, a r represents the weight coefficient, represents the observed spectrum data at the position P′ z±r and represents the difference between the model prediction value and the actual observed value.

[0040] Compared with the prior art, the beneficial effects achieved by the present invention are:

[0041] Through the collaborative work among the drone platform equipped with observation devices, the ground control center, and the cloud data processing unit, the present invention can achieve air-ground collaboration for spatial electromagnetic spectrum cognition, efficient data processing under the cloud-edge-end architecture, and dynamic mapping and updating of the spectrum map, providing strong support for the management and decision-making of the electromagnetic spectrum space. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention and do not constitute a limitation to the present invention. In the drawings:

[0043] Figure 1 is the architecture diagram of the low-altitude electromagnetic mapping air-ground collaborative integration system of the present invention;

[0044] Figure 2 Schematic diagram of the low-altitude electromagnetic mapping air-ground collaborative integration system of the present invention;

[0045] Figure 3 To draw the spatial intensity spectrogram of the signal acquisition area. Specific implementation manners

[0046] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0047] Please refer to Figures 1 - 3 , the present invention provides a technical solution:

[0048] Embodiment 1: As Figure 1 shown, the present invention provides a low-altitude electromagnetic mapping air-ground collaborative integration system, including a drone platform carrying observation equipment, which consists of a drone, a data acquisition and control module, a software radio device USRP, a positioning module, and a communication module, and is responsible for collecting electromagnetic data in the low-altitude area;

[0049] The ground control center processes the data transmitted back by the drone through the communication module, and determines the position and frequency band of the next observation of the drone according to the processing result;

[0050] The cloud data processing unit performs complex data analysis and processing, is responsible for constructing a spectrum knowledge graph, and realizes in-depth cognition of the spectrum situation through technologies such as machine learning and data mining.

[0051] Through the collaborative work of the above modules, the present invention can achieve air-ground collaboration for spatial electromagnetic spectrum cognition, efficient data processing under the cloud-edge-end architecture, and dynamic drawing and updating of the spectrum map, providing strong support for the management and decision-making of the electromagnetic spectrum space.

[0052] Among them, the drone platform carrying the observation equipment includes a data acquisition module and a drone part;

[0053] The data acquisition module is responsible for collecting electromagnetic data in the low-altitude area, performing simple data processing, then transmitting the data to the ground control center, and performing the next observation according to the frequency band and bandwidth data transmitted by the ground control center;

[0054] The drone part transmits the GPS / IMU data to the ground control center, waits for the ground control center to issue an instruction, and reaches the corresponding observation position according to the instruction for the next observation.

[0055] Among them, the data acquisition module of the unmanned aerial vehicle (UAV) platform carrying the observation equipment is specifically as follows:

[0056] A software-defined radio device USRP B210, which is used to collect wideband signals;

[0057] A Raspberry Pi 5 development board, serving as the main control unit of the data acquisition module, responsible for controlling signal acquisition and data processing, and performing preliminary processing and analysis based on the electromagnetic data transmitted by the USRP to control the USRP to perform continuous signal acquisition.

[0058] Among them, the UAV part of the UAV platform carrying the observation equipment is specifically as follows:

[0059] A high-precision GPS / IMU module. The GPS provides accurate geographical location information for the UAV, including longitude, latitude, and altitude. The IMU can measure the acceleration and angular velocity of the UAV, thereby determining the pitch angle, roll angle, and yaw angle of the UAV, that is, the three-dimensional attitude of the UAV.

[0060] A flight control system, which obtains flight data through sensors (GPS / IMU), then calculates corresponding control commands to achieve actions such as takeoff, hover, flight, and landing of the UAV, and transmits the sensor data to the ground control center, waits for instructions from the ground control center, and reaches the corresponding observation position according to the instructions for the next observation.

[0061] Among them, the ground control center is specifically as follows:

[0062] A communication module, which is used to establish a communication network to achieve wireless communication with the UAV observation platform;

[0063] A high-performance PC, which plans the flight path of the UAV according to the acquisition requirements before performing the task, determines the area where signals need to be collected, monitors the status of the UAV and the data acquisition situation to dynamically adjust the flight path of the UAV, and further processes the electromagnetic signals and then transmits them to the cloud.

[0064] The high-performance PC is connected to a wireless router through its network interface, and is used to receive the data transmitted back by the UAV observation platform, and perform remote control and task planning for the UAV, including transmitting frequency band and bandwidth data to the data acquisition module for the next observation, and transmitting flight path data to the UAV part to reach the corresponding observation position for the next observation.

[0065] Among them, the planning and adjustment of the analysis path of the ground control center for the UAV are specifically as follows:

[0066] Before the UAV executes a mission, it needs to first model the target area, then formulate the optimal path according to the collection requirements, adopt Spiral path planning, and move gradually inwards or outwards along a spiral. The mathematical representation of the spiral path is as follows:

[0067] r(θ) = a + bθ;

[0068] Where r represents the radius from the current position to the center, θ represents the current angle turned, a represents the starting radius, and b represents the control pitch;

[0069] During the flight, it receives sensor and signal data in real time to dynamically update the path. It mainly adjusts the direction based on the electromagnetic signal gradient. If the signal intensity changes suddenly or a new hot spot area appears, the flight direction is adjusted to the gradient ascending direction. The formula is as follows:

[0070]

[0071] Where, v new represents the updated movement direction, v current represents the current flight speed or direction vector, γ represents the step size coefficient, represents the signal intensity gradient.

[0072] Wherein, the cloud data processing unit is specifically as follows:

[0073] Data storage unit, adopting distributed storage technology, can automatically compress and backup data, and supports the efficient storage of massive data;

[0074] Data preprocessing unit, preprocesses the uploaded raw electromagnetic data, including operations such as data cleaning, format conversion, and noise removal, to improve data quality;

[0075] Data analysis unit, using advanced electromagnetic data processing algorithms, combines the data-driven method that processes the preprocessed data depending on the actually collected spectrum data through statistical analysis and machine learning techniques and the model-driven method that depends on the prior knowledge of the spectrum data generation process to describe the physical and statistical characteristics of the data by establishing a mathematical model, and generates an electromagnetic spectrum map.

[0076] The cloud data processing unit is responsible for deeply analyzing and processing the data from the ground control center, constructing a spectrum knowledge graph, and realizing a deep understanding of the spectrum situation.

[0077] Wherein, the data-driven and model-driven methods of the cloud data processing unit are specifically as follows:

[0078] The model-driven type mainly assumes that the electromagnetic propagation model and the transmitter power are known. Using the Location of the Transmitter Estimation (LIvE) method, the transmitter power and location are solved based on the free channel propagation model, and then the complete spectrum situation is deduced according to the estimation results and the propagation model. The formula of the free channel propagation model is as follows:

[0079]

[0080] where P R (d) represents the power received at a distance d, P T represents the transmit power, G T represents the transmit gain, G R represents the receive gain, λ represents the signal wavelength, and d represents the distance between the transmitter and the receiver;

[0081] The data-driven type of completion algorithm directly uses the existing spectrum data to estimate the spectrum data in the unknown area, and uses the spatial interpolation algorithm based on autoregression. The autoregressive model completes the spectrum data in the vacant area through prediction, and the completion formula is:

[0082]

[0083] where represents the spectrum data of the entire area to be completed, a r represents the weight coefficient, represents the observed spectrum data at the position P′ z±r , and represents the difference between the model prediction value and the actual observed value.

[0084] On the campus, a drone platform equipped with observation equipment is used to collect data on the 5G communication frequency point (2.52495 GHz). The system schematic diagram is as Figure 2 shown. The drone platform equipped with observation equipment flies at low altitude on the campus to collect electromagnetic signals, and can also obtain the interference range of the interference source based on the preliminary processing of the collected electromagnetic signals, so that the flight path will not enter the interference source range again, making the obtained electromagnetic data more accurate. At the same time, the GPS / IMU data is transmitted to the ground control center, and waits for the ground control center to issue an instruction, and arrives at the corresponding observation position according to the instruction for the next observation. The collected electromagnetic signal data is preliminarily processed by the Raspberry Pi and then transmitted back to the ground control center. The ground control center further processes the electromagnetic signal data and then transmits it to the cloud. The cloud data processing unit uses the data-driven and model-driven electromagnetic data processing algorithms to Figure 3 generate an electromagnetic spectrum map for the signal acquisition area in the box, and the circle is the location of the observed base station.

[0085] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. An integrated low-altitude electromagnetic mapping air-ground cooperation system, characterized in that: The system includes: A drone platform carrying observation equipment, which is responsible for collecting electromagnetic data in the low-altitude area; A ground control center, which is used to process the data transmitted back by the drone through the communication module, and determine the position and frequency band of the next observation of the drone according to the processing results; A cloud data processing unit, which conducts complex data analysis and processing, is responsible for constructing a spectrum knowledge graph, and realizes in-depth cognition of the spectrum situation through machine learning and data mining technologies.

2. The integrated low-altitude electromagnetic mapping air-ground cooperation system according to claim 1, characterized in that The drone platform carrying the observation equipment includes: a data acquisition module and a drone part; The data acquisition module is used to collect electromagnetic data in the low-altitude area, perform simple data processing, and then transmit the data to the ground control center and conduct the next observation according to the frequency band and bandwidth data transmitted by the ground control center; The drone part is used to transmit GPS / IMU data to the ground control center, wait for instructions from the ground control center, and reach the corresponding observation position according to the instructions for the next observation.

3. The integrated air-ground collaborative system for low-altitude electromagnetic mapping according to claim 2, characterized in that The data acquisition module includes: a software-defined radio device USRP B210 and a Raspberry Pi 5 development board; The software-defined radio device USRP B210 is used to collect wide-band signals; The Raspberry Pi 5 development board serves as the main control unit of the data acquisition module, is responsible for controlling signal acquisition and data processing, and conducts preliminary processing and analysis according to the electromagnetic data transmitted by the USRP to control the USRP to perform continuous signal acquisition.

4. The integrated air-ground collaborative system for low-altitude electromagnetic mapping according to claim 2, characterized in that, The drone part includes: a high-precision GPS / IMU module and a flight control system; In the high-precision GPS / IMU module, GPS provides accurate geographical location information for the drone, including longitude, latitude, and altitude; IMU is used to measure the acceleration and angular velocity of the drone, so as to determine the pitch angle, roll angle, and yaw angle of the drone, that is, the three-dimensional attitude of the drone; The flight control system obtains flight data through sensors, then calculates corresponding control commands to realize the takeoff, hover, flight, and landing actions of the drone, transmits the sensor data to the ground control center, waits for instructions from the ground control center, and reaches the corresponding observation position according to the instructions for the next observation.

5. An integrated low-altitude electromagnetic mapping air-ground cooperation system according to claim 1, characterized in that The ground control center includes: a communication module and a high-performance PC; The communication module is used to establish a communication network to achieve wireless communication with the drone observation platform; Before executing the task, the high-performance PC plans the flight path of the drone according to the acquisition requirements, determines the area where signals need to be collected, monitors the state of the drone and the data acquisition situation to dynamically adjust the flight path of the drone, and further processes the electromagnetic signals and then transmits them to the cloud; The high-performance PC is connected to a wireless router through its network interface, is used to receive the data transmitted back by the drone observation platform, and conducts remote control and task planning for the drone, including transmitting frequency band and bandwidth data to the data acquisition module for the next observation, and transmitting flight path data to the drone part to reach the corresponding observation position for the next observation.

6. The integrated low-altitude electromagnetic mapping air-ground cooperation system according to claim 5, wherein Before executing the task, the high-performance PC plans the flight path of the drone according to the acquisition requirements, including: Before performing tasks, the drone needs to first model the target area, then formulate the optimal path according to the acquisition requirements, adopt Spiral path planning, and move gradually inwards or outwards along a spiral line. According to the formula: r(θ) = a + bθ; where r represents the radius from the current position to the center, θ represents the current rotation angle, a represents the starting radius, and b represents the control pitch; During flight, sensor and signal data are received in real time to dynamically update the path. Through direction adjustment based on the electromagnetic signal gradient, if the signal intensity suddenly changes or a new hot spot area appears, the flight direction is adjusted to the gradient ascending direction, according to the formula: Among them, v new represents the updated movement direction, v current represents the current flight speed or direction vector, γ represents the step size coefficient, represents the signal strength gradient.

7. An integrated low-altitude electromagnetic mapping air-ground collaborative system according to claim 1, characterized in that, The cloud data processing unit includes: a data storage unit, a data preprocessing unit, and a data analysis unit; The data storage unit adopts distributed storage technology, can automatically compress and back up data, and supports the efficient storage of massive data; The data preprocessing unit preprocesses the uploaded raw electromagnetic data, including data cleaning, format conversion, and noise removal operations to improve data quality; The data analysis unit uses advanced electromagnetic data processing algorithms to process the preprocessed data using a data-driven method that depends on the actually collected spectrum data and a model-driven method that depends on the prior knowledge of the spectrum data generation process. By establishing a mathematical model to describe the physical and statistical characteristics of the data, an electromagnetic spectrum map is generated.

8. The integrated air-ground collaborative system for low-altitude electromagnetic mapping according to claim 7, characterized in that The data-driven and model-driven methods of the cloud data processing unit include: Assuming that the electromagnetic propagation model and the transmitter power are known, the transmitter position estimation method is used to solve the transmitter power and position based on the free channel propagation model, and then the complete spectrum situation is deduced according to the estimation results and the propagation model; The formula of the free channel propagation model is as follows: Among them, P R (d) represents the power received at a distance d, P T represents the transmit power, G T represents the transmit gain, G R represents the receive gain, λ represents the signal wavelength, and d represents the distance between the transmit point and the receive point; The data-driven completion algorithm directly estimates the spectrum data of the unknown area by leveraging the existing spectrum data and uses a spatial interpolation algorithm based on autoregression. The autoregressive model predicts the spectrum data of the vacant area to complete the spectrum data. The completion formula is: Among them, represents the spectral data of the global area to be supplemented, a r represents the weight coefficient, represents at position P′ z±r the observed spectral data at the location, represents the difference between the model prediction value and the actual observed value.