Gaussian process space-time modeling and unmanned aerial vehicle flight planning method for signal source tracking

Abstract

The invention discloses a signal source tracking-oriented Gaussian process space-time modeling and unmanned aerial vehicle flight planning method, which comprises the following steps of: firstly, acquiring RSSI (Received Signal Strength Indicator) data of a signal source by a sensor carried by an unmanned aerial vehicle, and recording corresponding position information and timestamps to form a space-time data set; based on the data set, space-time modeling of signal intensity is carried out by using a Gaussian process, the future position of a signal source is predicted, and the challenge of the position change of the signal source in a dynamic environment is overcome. And then, in combination with a designed flight planning algorithm, calculating a target position of the unmanned aerial vehicle at the next moment according to a signal intensity distribution prediction result. The flight planning method is divided into an exploration stage and a tracking stage, and the path of the unmanned aerial vehicle is dynamically optimized by adopting an overall variance reduction (IVR) evaluation function and a likelihood weighting (LW) evaluation function respectively. According to the invention, through spatial-temporal distribution modeling of signal intensity and flight path optimization, accurate tracking of the unmanned aerial vehicle on the mobile signal source is realized, and hardware dependence and realization cost are effectively reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal source tracking research, and particularly relates to a Gaussian process spatio-temporal modeling and UAV flight planning method for signal source tracking, especially applicable to mobile target positioning and tracking applications that rely on signal strength information. Background Art

[0002] Source tracking generally refers to locating the source by sensing the information of the source, or tracking, monitoring, and capturing different types of sources, such as radioactive sources, gas sources, radio frequency sources, sound sources, light sources, etc. Therefore, source tracking has a wide range of applications and can be used in many aspects such as environmental monitoring, public safety, and the military field.

[0003] Traditional source tracking methods mainly include biological search methods, ground robot search methods, and wireless sensor network methods, etc. These methods have their own limitations. For example, biological search methods rely on the sensing ability of organisms and are difficult to apply in dangerous or harsh environments; ground robots are limited by obstacles in complex terrains; while wireless sensor networks require the deployment of a large number of sensors, and there are often problems of high deployment costs and poor flexibility.

[0004] In recent years, with the rapid development of Unmanned Aerial Vehicle (UAV) technology, its application in source tracking has gradually increased. UAVs are flexible, have a large coverage area, and relatively low costs. Therefore, researchers have begun to tend to use UAVs equipped with different sensors for source tracking. For example, Dressel et al. designed a system with a UAV equipped with a directional antenna to track the position of the target source by comparing the changes in the signal strength received by the antenna. However, these methods are mainly used for the positioning and tracking of static sources and do not fully consider the complexity of the source during movement.

[0005] For mobile signal sources with dynamic characteristics (such as Bluetooth devices, Wi-Fi signal sources, etc.), their positions change over time. Application scenarios of mobile signal source tracking include tracking mobile devices, monitoring vehicle pseudo base stations, etc. Currently, there are already some technologies that can obtain relevant information of signal sources, such as Channel State Information (CSI), Angle-of-Arrival (AOA), and Received Signal Strength Indicator (RSSI). Among them, CSI and AOA technologies usually rely on the fusion of multiple sensors or specifically designed hardware devices, which makes the implementation process complex, costly, and not suitable for applications in dynamic environments. And RSSI signals are relatively easier to obtain signal source information, with good versatility and low costs, and thus have been widely used in research.

[0006] In mobile signal source location estimation methods, existing mature technologies are mostly applicable to static source scenarios and rarely consider the real-time changes in the source location. The following are the related works on source tracking problems:

[0007] (1) Fingerprint-based positioning method: It is necessary to construct a fingerprint database containing signal characteristics within the target area, and then use the matching degree between the target point and the fingerprint for location estimation. Although this method is relatively effective in static source scenarios, it is not suitable for real-time tracking of dynamic sources. Ding et al. designed a fingerprint positioning system based on the particle swarm algorithm, which estimates the location by searching for the most matching fingerprint pattern in the database, but this method still relies on database construction and it is difficult to meet the real-time requirement.

[0008] (2) Mathematical and probabilistic methods: Such as grid-based sensor network tracking. Zhou et al. used the least squares method to process the data obtained by sensors to estimate the current location of the signal source and predict its location at the next moment. However, when facing a relatively fast moving speed of the signal source, the accuracy and response time of this method will be limited.

[0009] (3) Multi-sensor fusion method: Lu et al. designed a heterogeneous node target tracking algorithm. By combining data from RFID, cameras, and passive sensors, a performance function of the target is constructed using particle filtering to improve the positioning accuracy. However, this method requires the cooperation of multiple sensors, increasing the complexity and cost of the system, and is not suitable for portable and low-cost application requirements.

[0010] In summary, first, currently existing relatively mature methods are only applicable to static source scenarios, that is, they do not consider the mobility of the source. However, in most real applications, the signal source has mobility, and the received signal strength value at the same location will also change over time. In addition, the relationship between signal strength and location cannot be directly obtained, and the sensor can only sense the noisy signal strength value. Second, existing mobile signal source tracking methods mostly rely on complex sensor systems or a large amount of data collection, resulting in high deployment and implementation costs. Especially on resource-constrained micro-unmanned aerial vehicle platforms, these methods are difficult to be effectively applied. Summary of the Invention

[0011] Object of the Invention: The present invention aims to solve the deficiencies of existing dynamic source tracking technologies and provides a Gaussian process spatio-temporal distribution modeling and unmanned aerial vehicle flight planning method for signal source tracking, enabling the unmanned aerial vehicle to achieve real-time positioning and tracking of dynamic signal sources without relying on complex hardware devices.

[0012] Technical Solution: The present invention discloses a Gaussian process spatio-temporal modeling and unmanned aerial vehicle flight planning method for signal source tracking, including the following steps:

[0013] Step 1: The drone uses the sensors it carries to collect the RSSI data of the signal source. The data collection process includes recording the signal strength and its corresponding position information (z1, z2) and timestamp t. The data format of each sampling point is (z1, z2, t, RSSI), and a data set is constructed from it.

[0014] Step 2: Based on the data set in Step 1, use the Gaussian Process to perform spatio-temporal modeling on the signal strength. Specifically, use the spatial position and time information in the collected data set as inputs to predict the signal strength distribution at future times. This modeling method can effectively overcome the challenge of the changing position of the signal source in a dynamic environment and provide an accurate signal source position estimate.

[0015] Step 3: According to the signal source position predicted by the Gaussian process spatio-temporal modeling in Step 2, and then according to the designed flight planning algorithm, calculate the position that the drone needs to reach at the next moment.

[0016] Step 4: Sequentially and cyclically execute Steps 2 and 3, combine the spatio-temporal modeling with the flight planning algorithm to form a dynamically iterative optimization process to complete the tracking task.

[0017] Further explanation, in the data collection part, in Step 1, the signal source intensity value is sensed by the sensors carried by the drone itself. The functional relationship between the signal intensity value observed at a certain position at a certain moment and the position is unknown and can be expressed as:

[0018] y(Z, t) = f(Z, t) + ε

[0019] ε ~ N(0, σ 2 )

[0020] where y(Z, t) is the signal strength measurement value (estimated value) at position Z at time t, f(Z, t) is the true signal strength value at position Z at time t, and ε is Gaussian noise, which follows an independent and identically distributed Gaussian distribution with a mean of 0 and a variance of σ 2 of the Gaussian distribution.

[0021] Further, use the sampling Gaussian process regression method to model the collected RSSI data. Step 2 is specifically as follows:

[0022] Step 2.1: Definition of input vector

[0023] Based on the two-dimensional spatial training data, the time dimension is added, that is, the time information is used as part of the input. The Gaussian process input is represented as x = [z1, z2, t] T ∈R 3, where the first two components refer to the two-dimensional coordinates of the position of the tracking UAV corresponding to time t, the third component refers to time t, and the corresponding signal strength needs to be recorded. These data are used to construct the spatio-temporal distribution model of the signal source;

[0024] Step 2.2: Definition of the mean function

[0025] Based on the signal attenuation model, the form of the mean function is defined as:

[0026] m(x) = a - b * log||(z1, z2) - (x1 + v1Δt, x2 + v2Δt)||,

[0027] where a, b, x1, x2, v1, v2 are all hyperparameters. Among them, a and b are hyperparameters introduced by the signal attenuation model, x1 and x2 are the positions of the signal source at t = 0, that is, the initial positions, z1 and z2 are the current calculation positions, and v1 and v2 are the speeds of the signal source in the horizontal and vertical directions;

[0028] Step 2.3: Definition of the covariance function

[0029] Using the common Gaussian kernel function, the form of the covariance function is defined as:

[0030]

[0031] where σ and l are hyperparameters;

[0032] Step 2.4: Definition of the likelihood function and calculation of hyperparameters

[0033] Based on the Gaussian process assumption, the likelihood function is defined as:

[0034] p(Y|X, ρ, λ) ~ N(U(X, ρ), K(X, λ) + σ 2 I),

[0035] where U(X, ρ) is the mean vector and k(X, λ) is the covariance matrix. The values of the hyperparameters ρ and λ are calculated by maximizing the log-likelihood, and the obtained equivalent formula is:

[0036] ρ, λ = argmin ρ,λ -log(p(Y|X, ρ, λ));

[0037] Step 2.5: Optimization of hyperparameters

[0038] The L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno with Bounds) algorithm is used to optimize the values of the hyperparameters, so that the model can accurately fit the signal strength data and complete the prediction of the Gaussian process regression model;

[0039] Step 2.6: After completing the hyperparameter optimization, based on the mean function and covariance matrix of the Gaussian process model, predict the signal strength distribution at a future time t.

[0040] Step 2.7: Rasterize the plane. At a fixed time t, calculate the signal strength values corresponding to each position after rasterization, and take the position with the maximum mean signal strength value on the plane as the predicted position of the signal source at this time, because the peak position of the signal strength usually indicates the presence of the signal source.

[0041] Step 2.8: After the UAV reaches the next estimated position, collect the signal strength data at this position again. After obtaining new data each time, add the new data to the training set and re - execute the Gaussian process modeling and prediction. The Gaussian process will be continuously updated, and the position of the maximum signal strength predicted according to the Gaussian process model.

[0042] Step 2.9: Repeat Step 2.7 and Step 2.8. According to the prediction results obtained from the established Gaussian process model, the UAV moves towards the area with the maximum signal strength, gradually approaching the signal source position, effectively solving the challenge of the change in the position of the mobile signal source in a dynamic environment and accurately estimating the signal source position.

[0043] Furthermore, the flight plan in Step 3 is divided into an exploration stage and a tracking stage, and the specific steps are as follows:

[0044] Step 3.1: Plane rasterization

[0045] Regard the plane where the UAV and the mobile source are located as a two - dimensional plane, rasterize this two - dimensional plane, discretely select position points on the plane, and each grid point serves as a potential candidate point and reference point.

[0046] Step 3.2: Selection of reference points

[0047] For the selection of reference points, on the two - dimensionally rasterized plane, set reference points evenly at appropriate intervals. The set of reference points is a group of positions on the plane set in advance and is used as a benchmark for evaluating function calculation.

[0048] Step 3.3: Selection of candidate points

[0049] The candidate points are also set in a discrete manner. Since the moving step size of the UAV at each step is determined in advance, the candidate points are selected on an arc with a radius of the UAV's moving step size l. The set of candidate points is the set of optional positions for the UAV's next flight, and the point with the highest benefit needs to be selected as the actual position for the next step through a suitable evaluation function.

[0050] Step 3.4: Filtering of deviated candidate points

[0051] To filter candidate points that deviate from the direction of the signal source, it is first necessary to traverse the set of candidate points. If the angle between a candidate point and the predicted position of the signal source is greater than π / 2, then this candidate point is considered to be too deviated from the direction of the signal source and is deleted from the set of candidate points. This step ensures that the UAV always moves towards the direction of the signal source during the path optimization process;

[0052] Step 3.5: IVR evaluation function in the exploration phase

[0053] In the exploration phase, the UAV tends to explore the entire plane and make an overall estimate of the RSSI distribution on the plane. The IVR (Integrated Variance Reduction) method is used as the candidate point evaluation function. The calculation formula of this evaluation function is as follows:

[0054] a IVR (x) = ∫[σ 2 (x′) - σ 2 (x′; x)]dx′,

[0055] In the formula, x′ is the set reference point, σ 2 (x′) is the variance of the reference point before selecting the candidate point x, and σ 2 (x′; x) is the variance of the reference point after selecting the candidate point. What this method calculates is the change in the predicted variance at the reference point before and after selecting this candidate point. The integral in the formula represents the sum over all discrete reference points. Select the candidate point that maximizes the evaluation function, that is, the candidate point with the highest gain, as the position of the UAV in the next step, that is

[0056]

[0057] Step 3.6: LW evaluation function in the tracking phase

[0058] The UAV executes Step 3.5 multiple times. In order to more accurately find the position of the signal source, that is, the position of the extreme value, the likelihood ratio is added to the evaluation function as the evaluation function in the tracking phase to estimate the area near the extreme value. This method is called the IVR-LW (likelihood-weighted) method, abbreviated as the LW method. Its calculation method is:

[0059] a LW (x) = ∫[σ 2 (x′) - σ 2 (x′; x)]w(x′)dx′,

[0060]

[0061] Among them, w(x′) is used as the sampling weight, called the likelihood ratio, where p x$p(x')$ represents the probability density function at $x'$, $\mu(x')$ represents the predicted mean at $x'$ in the Gaussian process. The likelihood ratio, as a sampling weight, assigns a relevance measure to each candidate point, such that the evaluation function tends to select points with extremely large output values, i.e., points near the extreme values. The function at this stage adds a weight on the basis of maximizing the reduction of the overall variance. Points closer to the extreme values have higher weights, so that the UAV gradually approaches the signal source while exploring the plane;

[0062] Step 3.7: Random exploration initial stage

[0063] At the beginning of the tracking, 3 random explorations are carried out. The random explorations provide initial data for subsequent signal strength modeling and path planning;

[0064] Step 3.8: Enter the path planning in the tracking stage, judge whether the current iteration number index is less than the division threshold th, and then select the evaluation function accordingly;

[0065] Step 3.9: According to the judgment result of Step 3.8, if index < th (in the exploration stage), select the IVR evaluation function, and select the candidate point that maximizes IVR as the position at the next moment; if index >= th (in the tracking stage), select the LW evaluation function, and select the candidate point that maximizes LW as the position at the next moment.

[0066] Step 3.11: Repeat Step 3.8 and Step 3.9. On the basis of Step 2, continuously collect signal strength data, update the Gaussian process spatio-temporal model and optimize the path until the signal strength is detected to exceed the threshold twice in a row, which indicates that the UAV has completed the tracking task of the signal source.

[0067] Furthermore, the signal strength is collected and processed in real time through the NINA module of the AI-Deck expansion board carried on the UAV. Specifically, the AI-Deck expansion board at the signal source end is set to the AP (Access Point) mode and continuously broadcasts Wi-Fi signals; the AI-Deck expansion board on the tracking UAV is configured to the Station mode, and the NINA module is controlled by writing ESP32 firmware code to obtain RSSI (Received Signal Strength Indication) data from the signal source in a scanning manner.

[0068] The present invention enables the UAV to efficiently track a moving signal source in a dynamic environment and complete the real-time positioning task of the signal source by constructing a spatio-temporal distribution model of the signal source based on the Gaussian process and combining a path planning algorithm based on an evaluation function.

[0069] Compared with the prior art, the present invention adopts the above technical solutions and has the following technical innovations:

[0070] 1. Innovation in spatio-temporal modeling: The present invention introduces the time dimension into the input of the Gaussian process, forming a method for modeling the spatio-temporal distribution of signal sources. Traditional signal source localization methods usually estimate the static position of signal sources only based on spatial positions, and it is difficult to cope with the mobility of signal sources in a dynamic environment. By taking time as an input dimension of the Gaussian process model, the present invention enables the model to update the spatio-temporal distribution prediction of signal sources in real time and dynamically adjust the estimated position of signal sources.

[0071] 2. Intelligence in path planning: To improve the tracking efficiency of unmanned aerial vehicles (UAVs), the present invention proposes a path optimization algorithm that combines the IVR and LW evaluation functions, enabling UAVs to adaptively perform path planning during the exploration and tracking phases, thereby achieving more efficient tracking. Exploration phase: In the initial stage of tracking, since the UAV has not yet grasped the approximate position of the signal source, it is necessary to collect signal data within a large range to obtain the global distribution information of signal strength. For this purpose, the present invention introduces the IVR evaluation function in the exploration phase. By calculating the reduction in the prediction variance of signal strength for candidate positions, it selects the flight path with the maximum information gain. The use of the IVR evaluation function ensures that the UAV can quickly converge to the approximate position of the signal source in the initial stage, improving the efficiency of signal source tracking. Tracking phase: After approaching the signal source, the UAV switches to the tracking phase and further focuses on the high-signal-strength area of the signal source. The present invention adopts the LW evaluation function. By weighted evaluation of candidate positions near the signal source, the UAV preferentially selects points near high signal strength value areas when choosing flight paths. This weighting method further improves the accuracy of path planning, enabling the UAV to find the signal source position more quickly and accurately. The LW evaluation function can guide the UAV to accurately track near the signal source, avoiding unnecessary path deviations, thus significantly reducing flight time and resource consumption.

[0072] 3. Simplification of hardware requirements: The present invention can achieve precise tracking of dynamic signal sources only based on RSSI (Received Signal Strength Indication) data without relying on complex hardware devices, reducing the implementation cost. Traditional methods for tracking dynamic signal sources usually rely on multi-sensor fusion or high-cost hardware devices (such as AOA sensors, CSI antennas, etc.) to obtain accurate signal source position information. However, the deployment and maintenance costs of these complex devices are relatively high, and it is difficult to implement on resource-constrained UAV platforms.

[0073] In summary, the present invention significantly improves the tracking efficiency and positioning accuracy of dynamic signal sources by introducing spatio-temporal modeling, intelligent path planning, and low-cost hardware design. Compared with the prior art, the present invention realizes real-time, efficient, and precise tracking of dynamic signal sources without increasing the hardware complexity, and has broad application potential and technical value. Description of the Drawings

[0074] Figure 1 It is a flowchart of the overall method of the present invention.

[0075] Figure 2 It is a schematic diagram of the selection of candidate points and reference points in the present invention.

[0076] Figure 3 It is the signal strength distribution map on the plane calculated by the Gaussian process at different times of the unmanned aerial vehicle in the embodiment of the present invention.

[0077] Figure 4 It is the flight process diagram of the source tracking of the unmanned aerial vehicle in the embodiment of the present invention. Detailed implementation manners

[0078] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention.

[0079] As Figure 1 shown, a Gaussian process spatio-temporal modeling and unmanned aerial vehicle flight planning method for signal source tracking disclosed in the embodiment of the present invention mainly includes the following steps:

[0080] Step 1: Use the NINA module of the AI-Deck expansion board carried on the unmanned aerial vehicle to simulate the signal source to obtain the signal strength value. Set the AI-Deck expansion board carried on the unmanned aerial vehicle to Station mode, write experimental code to modify the ESP32 firmware and obtain RSSI information through scanning, and set the AI-Deck expansion board used by the signal source to AP mode;

[0081] Step 2: According to the configuration in Step 1, the NINA module (set to Station mode) of the unmanned aerial vehicle continuously scans the WiFi signal source of the signal source (configured as AP mode) to obtain the signal strength RSSI value. Each piece of data collected will be accompanied by the position information and time of the current unmanned aerial vehicle, in the format of (z1, z2, t, RSSI). The collected data set will provide input for modeling the spatio-temporal distribution of the signal strength;

[0082] Step 3: According to the data set collected in Step 2, use the Gaussian Process to perform spatio-temporal modeling on the signal strength, and estimate the position of the signal source according to the extreme value of the prediction result;

[0083] In the said Step 3, establishing the Gaussian process spatio-temporal distribution modeling specifically includes the following steps:

[0084] First, regard the space where a single unmanned aerial vehicle and the mobile source are located as a two-dimensional plane, rasterize the two-dimensional plane, and the signal strength value corresponding to each position after rasterization at each moment can be calculated;

[0085] Step 3.1: Based on the RSSI dataset preliminarily collected in Step 2, the system defines the mean function and covariance function of the signal strength;

[0086] Step 3.2: Define the mean function according to the signal attenuation model as

[0087] m(x) = a - b * log ||(z1, z2) - (x1 + v1Δt, x2 + v2Δt)||,

[0088] where a, b, x1, x2, v1, v2 are all hyperparameters, where a and b are hyperparameters introduced by the signal attenuation model, x1 and x2 are the positions of the signal source at t = 0, i.e., the initial positions, and z1, z2 are the current calculation positions;

[0089] Step 3.3: The covariance function adopts the Gaussian kernel function and is defined as follows:

[0090]

[0091] where σ and l are hyperparameters;

[0092] Step 3.4: Definition of the likelihood function and calculation of hyperparameters

[0093] Based on the Gaussian process assumption, the likelihood function is defined as:

[0094] p(Y|X, ρ, λ) ~ N(U(X, ρ), K(X, λ) + σ 2 I),

[0095] where U(X, ρ) is the mean vector and K(X, λ) is the covariance matrix. Calculate the values of hyperparameters ρ and λ by maximizing the log-likelihood, and the obtained equivalent formula is:

[0096] ρ, λ = argmin ρ,λ -log(p(Y|X, ρ, λ));

[0097] Step 3.5: Optimize hyperparameters

[0098] Use the L-BFGS-B (Limited-memory Broyden-Fletcher-Goldfarb-Shanno with Bounds) algorithm to optimize the values of hyperparameters, so that the model can accurately fit the signal strength data and complete the prediction of the Gaussian process regression model;

[0099] Step 3.6: After completing the hyperparameter optimization, the system uses the Gaussian process for spatio-temporal modeling to model and predict the signal strength data in the spatial and temporal dimensions;

[0100] Step 4: According to the signal source position predicted by the Gaussian process spatio-temporal modeling in Step 3, design a flight planning algorithm to calculate the position that the UAV will reach at the next moment;

[0101] The flight planning algorithm designed in Step 4 specifically includes the following steps:

[0102] In order to achieve efficient tracking of dynamic signal sources, after two-dimensional plane rasterization, reference points and candidate points need to be selected, as Figure 2 shown, and the specific explanation is as follows: The reference points are evenly distributed on the two-dimensional plane at a fixed interval. Each reference point represents a fixed spatial position and is used as a benchmark for calculating the evaluation function; The candidate points are selected on an arc with the UAV's moving step length l as the radius. The central angle between every two candidate points is θ. In the present invention, θ = π / 6 is set, and 12 candidate points are selected at each step. At the same time, in order to ensure that the UAV will not always fly in the opposite direction of the signal source during the exploration stage, the candidate points deviating from the signal source direction are filtered out, that is, the candidate points are only selected on the semi-circular arc in the direction of the signal source;

[0103] Step 4.1: For the Gaussian process spatio-temporal distribution model established for the signal source in Step 3, in the initial stage, the UAV conducts random flights to collect RSSI data at different positions to help the Gaussian process make a preliminary estimate of the signal strength in the entire space and provide a basis for the subsequent flight path optimization;

[0104] Step 4.2: The system checks whether the current iteration number index is less than the set threshold th;

[0105] Step 4.3: If index < th, enter the exploration stage, select the IVR (Integrated Variance Reduction) evaluation function to perform a more comprehensive scan of the entire space. The purpose of using the IVR evaluation function is to calculate the variance reduction amount of the candidate points, and select the point with the largest variance reduction as the next target position of the UAV. The specific form of the IVR evaluation function is as follows:

[0106] a IVR (x) = ∫[σ 2 (x′) - σ 2 (x′; x)]dx′,

[0107] where x′ is the set reference point, σ 2 (x′) is the variance of the reference point before selecting the candidate point x, and σ 2 (x′; x) is the variance of the reference point after selecting the candidate point. What this method calculates is the change in the predicted variance at the reference point before and after selecting this candidate point. The integral in the formula represents the sum over all discrete reference points;

[0108] Step 4.4: If index ≥ th, enter the tracking phase, select the LW (Likelihood-Weighted) evaluation function, focus on the area near the signal source to accurately locate the signal source. The LW evaluation function is different from the IVR evaluation function and incorporates the likelihood ratio weight. The specific form of the LW evaluation function is as follows:

[0109] a LW (x) = ∫[σ 2 (x′) - σ 2 (x′; x)]w(x′)dx′,

[0110]

[0111] where w(x′) is used as the sampling weight, called the likelihood ratio. Here, p x (x′) represents the probability density function at x′, and μ(x′) represents the predicted mean at x′ in the Gaussian process. The likelihood ratio, as a sampling weight, assigns a correlation measure to each candidate point, making the evaluation function tend to select points with extremely large output values, that is, points near the extreme values. The function in this stage adds a weight on the basis of minimizing the overall variance the most. Points closer to the extreme values have higher weights, so that the UAV gradually approaches the signal source while exploring the plane;

[0112] Through the selection of the evaluation function in stages, optimize the path planning of the UAV, enabling it to conduct extensive searches in the early stage and focus on accurate positioning in the target area in the later stage;

[0113] Step 5: Sequentially and cyclically execute Steps 2, 3, and 4, combine the spatio-temporal modeling with the flight planning algorithm to form a dynamically iterative optimization process, and complete the tracking task;

[0114] In the above Step 5, it is necessary to sequentially and cyclically execute Steps 2, 3, and 4. According to the next position of the flight plan calculated in Step 4, the new data collected at the new position is added to the dataset, gradually updating the Gaussian process model to improve the accuracy of the signal source position estimation. If the RSSI value collected by the UAV exceeds the set threshold after two consecutive movements, it is determined that the UAV is close enough to the signal source, the source search is successful, and the algorithm terminates. Otherwise, the iteration count is incremented by 1, and it returns to Step 4.2.

[0115] Figure 3It shows the distribution diagrams of signal intensity on a plane calculated by the Gaussian process at different times, which can better illustrate the effectiveness of the Gaussian process spatio-temporal modeling method implemented in the present invention. In the first diagram at t = 28.1 s, the signal intensity distribution is relatively flat and no significant peak is formed, indicating that the drone is still in the initial signal acquisition stage and has not approached the signal source yet. As data is collected and the amount of training data increases, the RSSI distribution predicted by the Gaussian process is relatively smooth and has obvious peaks. For example, in the second diagram at t = 55.4 s, the signal intensity distribution begins to form significant peaks, and the drone gradually approaches the signal source position, and the model prediction accuracy is significantly improved. In the third diagram at t = 79.6 s, the peak in the signal intensity distribution is significantly enhanced, indicating that the drone is very close to the signal source position, and the model can accurately predict the specific position of the signal source.

[0116] Figure 4 It shows the flight process of the drone from takeoff to completing the source tracking task after deploying the source tracking method of the present invention. First, the drone needs to be initialized and the corresponding modes are configured. The tracking drone is in the Station mode and the signal source drone is in the AP mode. During the tracking experiment, the signal source moves in a uniform straight line. The tracking drone first flies randomly 3 times, and then explores the entire plane according to the flight planning algorithm, making a relatively accurate modeling of the signal intensity distribution on the plane. After setting the threshold, it starts to fly towards the signal source. Figure 4 It shows the actual flight trajectories at different time points, demonstrating the process from random exploration to gradually locking the signal source. Figure 4 (a) At time t = 5 s, the drone flies randomly to collect initial signal data, providing a basis for subsequent signal intensity distribution modeling. Figure 4 (b) At time t = 30 s, the drone is in the exploration stage, searching more targeted, and the flight path gradually heads towards the signal source direction. Figure 4 (c) At time t = 60 s, the drone transitions from the exploration stage to the tracking stage and starts to move clearly towards the signal source through the path planning algorithm. Figure 4 (d) At time t = 80 s, the tracking drone reaches directly above the signal source position, indicating that the signal intensity reaches the preset tracking threshold, and the drone completes the tracking task. During the entire experimental process, the tracking drone moved a total of 24 steps and took 80 s.

[0117] In the specific implementation of the present invention, the drone first flies randomly to collect signal strength (RSSI) data and form an initial Gaussian process model. As data accumulates continuously, the drone uses the Gaussian process model to predict the signal source position and adjusts the flight path according to the prediction results.

[0118] In the exploration stage, the drone selects the flight path by the variance change of the signal strength and gradually reduces the distance from the signal source. In the tracking stage, the drone uses a likelihood-weighted evaluation function to precisely track the area near the signal strength peak until it reaches the signal source location. Through the synergistic effect of the dynamic modeling of the signal strength and the path planning algorithm, the drone realizes the efficient positioning and tracking of the dynamic signal source.

[0119] The present invention also proposes a signal strength value acquisition module, which collects and processes the signal strength in real time through the NINA module of the AI-Deck expansion board carried on the drone. Specifically, the AI-Deck expansion board at the signal source end is set to the AP (Access Point) mode and continuously broadcasts Wi-Fi signals; the AI-Deck expansion board on the tracking drone is configured to the Station mode, and the NINA module is controlled by writing ESP32 firmware code to obtain RSSI (Received Signal Strength Indication) data from the signal source in a scanning manner.

[0120] Although the embodiments of the present invention are shown and described above, it can be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those of ordinary skill in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention. Any other corresponding changes and variations made according to the technical concept of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A Gaussian process spatiotemporal modeling and UAV flight planning method for signal source tracking, characterized in that: The following steps are involved: Step 1: The drone uses its own sensors to collect RSSI data of the signal source. The data collection process includes recording the signal strength and its corresponding location information (z1, z2) and timestamp t. The data format of each sampling point is (z1, z2, t, RSSI), which is constructed into a data set. Step 2: Based on the data set in step 1, the signal strength is modeled in space and time using the Gaussian process. Specifically, the signal strength distribution at future moments is predicted based on the spatial position and time information in the collected data set as input, providing an accurate estimate of the signal source location. Step 3: Based on the signal source position predicted by the Gaussian process spatiotemporal modeling in step 2, calculate the position that the drone will reach at the next moment according to the designed flight planning algorithm; Step 4: Execute steps 2 and 3 in a loop, combining spatiotemporal modeling with the flight planning algorithm to form a dynamic iterative optimization process to complete the tracking task.

2. The Gaussian process spatiotemporal modeling and UAV flight planning method for signal source tracking according to claim 1 is characterized in that: During the data collection process of step 1, the signal source strength value is sensed by the sensor carried by the drone itself. The functional relationship between the signal strength value observed at a certain time and a certain position and the position is unknown, which can be expressed as: y(Z,t)=f(Z,t)+ε ε~N(0,σ 2 ) Where y(Z,t) is the signal strength measurement value at position Z at time t, i.e., the estimated value; f(Z,t) is the true signal strength value at position Z at time t; ε is Gaussian noise, which follows an independent and identically distributed distribution with a mean of 0 and a variance of σ 2 Gaussian distribution.

3. The Gaussian process spatiotemporal modeling and UAV flight planning method for signal source tracking according to claim 2 is characterized in that: The step 2 adopts the Gaussian process regression method to model the collected RSSI data, specifically: Step 2.1: Input vector definition The time dimension is added to the spatial two-dimensional training data, that is, the time information is taken as part of the input. The Gaussian process input is represented as x = [z1, z2, t] T ∈R 3 , where the first two components refer to the two-dimensional coordinates of the position of the tracking drone corresponding to time t, and the third component refers to time t. At the same time, the corresponding signal strength needs to be recorded. These data are used to construct the spatiotemporal distribution model of the signal source; Step 2.2: Mean function definition Based on the signal attenuation model, the mean function is defined as: m(x)=ab*log||(z1,z2)-(x1+v1Δt,x2+v2Δt)||, Among them, a, b, x1, x2, v1, v2 are all hyperparameters, where a and b are hyperparameters introduced by the signal attenuation model, x1 and x2 are the positions of the signal source at time t = 0, i.e., the initial positions, z1 and z2 are the current calculated positions, and v1 and v2 are the speeds of the signal source in the horizontal and vertical directions; Step 2.3: Covariance function definition Using the commonly used Gaussian kernel function, the covariance function is defined as: Where σ,l are hyper parameters; Step 2.4: Likelihood function definition and calculation of hyperparameters Based on the Gaussian process assumption, the likelihood function is defined as: p(Y|X,ρ,λ)~N(U(X,ρ),K(X,λ)+σ 2 I), Where U(X,ρ) is the mean vector, K(X,λ) is the covariance matrix, and the values ​​of hyperparameters ρ and λ are calculated by maximizing the logarithm of the likelihood. The equivalent formula is: p,λ=argmin ρ,λ -log(p(Y|X,ρ,λ)); Step 2.5: Optimize Hyperparameters The L-BFGS-B algorithm is used to optimize the values ​​of hyperparameters so that the model can accurately fit the signal intensity data and complete the prediction of the Gaussian process regression model; Step 2.6: After completing the hyperparameter optimization, predict the signal strength distribution at a certain time t in the future based on the mean function and covariance matrix of the Gaussian process model; Step 2.7: Rasterize the plane, and at a fixed time t, calculate the signal strength value of each position after rasterization at the corresponding time, and take the position with the largest mean signal strength value on the plane as the predicted position of the signal source at that time; Step 2.8: After the UAV reaches the next estimated position, collect the signal strength data at this position again. After obtaining new data each time, add the new data to the training set, and re - execute Gaussian process modeling and prediction. The Gaussian process will be continuously updated, and the position of the maximum signal strength is predicted according to the Gaussian process model; Step 2.9: Repeat Step 2.7 and Step 2.

8. According to the prediction results obtained from the established Gaussian process model, the UAV moves towards the area with the maximum signal strength, gradually approaching the signal source position, and accurately estimates the signal source position.

4. The Gaussian process spatiotemporal modeling and UAV flight planning method for signal source tracking according to claim 3 is characterized in that: The flight planning in Step 3 is divided into an exploration stage and a tracking stage. The specific steps are as follows: Step 3.1: Planar gridification Regard the plane where the UAV and the mobile source are located as a two - dimensional plane, gridify this two - dimensional plane, discretely select position points on the plane, and each grid point serves as a potential candidate point and reference point; Step 3.2: Selection of reference points On the two - dimensionally gridified plane, set reference points uniformly. The reference point set is a group of positions on the plane set in advance, which is used as a benchmark for evaluation function calculation; Step 3.3: Selection of candidate points Set in a discrete manner. Since the movement step size of the UAV at each step is determined in advance, candidate points are selected on an arc with the movement step size l of the UAV as the radius. The candidate point set is the set of optional positions for the UAV's next flight, and the point with the highest benefit is selected as the actual position for the next step; Step 3.4: Filtering of candidate points deviating from the path Filter candidate points deviating from the signal source direction. First, traverse the candidate point set. If the angle between a candidate point and the predicted position of the signal source is greater than π / 2, it is considered that this candidate point is too deviated from the signal source direction and is deleted from the candidate point set. This step ensures that the UAV always moves towards the signal source direction during the path optimization process; Step 3.5: IVR evaluation function in the exploration stage In the exploration stage, the UAV tends to explore the entire plane and make an overall estimate of the RSSI distribution on the plane. The IVR method is used as the candidate point evaluation function. The calculation formula of this evaluation function is as follows: a IVR (x)=∫[σ 2 (x′)-σ 2 (x′;x)]dx′, Where x′ is the reference point, σ 2 (x′) is the variance of the reference point before selecting the candidate point x, σ 2 (x′; x) is the variance of the reference point after the candidate point is selected. This method calculates the change in the prediction variance of the reference point before and after the candidate point is selected. The integral in the formula represents the sum of all discrete reference points. The candidate point that maximizes the evaluation function, that is, the candidate point with the highest benefit, is selected as the next UAV position, that is, Step 3.6: LW evaluation function in the tracking stage The UAV executes Step 3.5 multiple times. In order to further accurately find the position of the signal source, that is, the extreme value position, a likelihood ratio is added to the evaluation function as the evaluation function in the tracking stage to estimate the area near the extreme value. The calculation method is: a LW (x)=∫[σ 2 (x′)-σ 2 (x′;x)]w(x′)dx′, Among them, w(x′) is the sampling weight, called the likelihood ratio, where p x (x′) represents the probability density function at x′, μ(x′) represents the predicted mean at x′ in the Gaussian process, and the likelihood ratio is used as a sampling weight to assign a correlation measure to each candidate point, so that the evaluation function tends to select points with abnormally large output values, that is, points near the extreme value. The function of this stage adds a weight on the basis of reducing the overall variance the most. Points closer to the extreme value have higher weights. The drone gradually approaches the signal source while exploring the plane; Step 3.7: Random exploration initial stage At the beginning of tracking, conduct 3 random explorations. Random exploration provides initial data for subsequent signal strength modeling and path planning; Step 3.8: Enter the path planning in the tracking stage, judge whether the current iteration number index is less than the division threshold th, and then select the evaluation function accordingly; Step 3.9: According to the judgment result of Step 3.8, if index < th, that is, in the exploration stage, select the IVR evaluation function, and select the candidate point that maximizes IVR as the position at the next moment; if index >= th, that is, in the tracking stage, select the LW evaluation function, and select the candidate point that maximizes LW as the position at the next moment; Step 3.11: Repeat steps 3.8 and 3.

9. Based on step 2, continuously collect signal strength data, update the Gaussian process spatiotemporal model, and optimize the path until the signal strength is detected to exceed the threshold twice in a row, indicating that the UAV has completed the task of tracking the signal source.

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