Meteor trajectory and drop point calculation method based on probability triangulation

Abstract

The invention relates to the technical field of aerolite trajectories and landing point determination. Due to the real-time performance of meteor events, a traditional method is difficult to meet requirements, so that the trajectory prediction effect is not ideal, and in the prior art, probability modeling is not fully utilized to relieve measurement errors and uncertainty, so that the reliability of landing point estimation is low; the invention provides a meteor trajectory and drop point calculation method based on probabilistic triangulation measurement, which comprises the following steps of: capturing the angle data of a meteor in real time by using a plurality of GPS (Global Positioning System) synchronous cameras at different positions, calibrating the angle data through star sky matching, analyzing the uncertainty of the angle data through probabilistic triangulation, modeling and optimizing the motion trajectory of the meteor, and calculating the falling point of the meteor. According to the method, the prediction precision is improved by combining probability estimation according to the simulated trajectory and the landing area, the precision of meteor trajectory prediction is remarkably improved, and an extensible real-time solution is provided for celestial body tracking and recovery operation.

Description

Technical Field

[0001] The present invention relates to the technical field of meteorite trajectories and determination of landing points, and more specifically, to a method for calculating meteor trajectories and landing points based on probability trilateration measurement. Background Art

[0002] Accurate calculation of meteor trajectories and landing points is crucial in astronomical research and space exploration. However, existing technologies have many limitations in data collection, measurement accuracy, and calculation methods, resulting in inaccuracies in trajectory prediction and landing point calculation, thereby affecting the effectiveness of scientific research and meteorite recovery.

[0003] Traditional methods mainly rely on single-camera observations or basic triangulation techniques, but these methods have inherent defects in dealing with environmental noise, measurement error compensation, and tracking of high-speed meteor movements. Single-camera observations have large errors in trajectory calculation due to the lack of depth information, while basic triangulation is affected by pixel resolution differences, misalignment of cameras, and environmental factors (such as light pollution, atmospheric disturbances, etc.), making it difficult to ensure the stability of trajectory calculation. In addition, traditional methods fail to effectively filter background noise, resulting in a decline in data quality and affecting the reliable extraction of meteor trajectories.

[0004] Accurately calculating meteor trajectories and landing points requires high-precision observations from multiple angles to enhance the robustness of triangulation. However, existing methods have deficiencies in multi-camera data fusion, measurement error correction, and dynamic trajectory prediction. Especially in the process of real-time processing of meteor events, traditional algorithms are difficult to meet the requirements of efficient and accurate calculations. In addition, single-camera observations lack depth information, making trajectory calculation highly dependent on limited measurement data and prone to introducing large errors. Even in a multi-camera setup, due to problems such as pixel resolution differences, misalignment of cameras, and atmospheric disturbances, measurement errors are still inevitable, affecting the accuracy of trajectory estimation. At the same time, environmental noise (such as background light sources and weather changes) further reduces the accuracy of observations, and existing methods lack effective noise filtering techniques. In addition, due to the real-time nature of meteor events, the calculation method needs to have efficient data processing capabilities, but traditional methods are difficult to meet this requirement in a high-computation load environment, resulting in unsatisfactory trajectory prediction effects. More importantly, existing technologies fail to fully utilize probability modeling to mitigate measurement errors and uncertainties, resulting in low reliability of landing point estimation. Summary of the Invention

[0005] Aiming at the deficiencies of the existing technology, the purpose of the present invention is to provide a method for calculating meteor trajectories and landing points based on probabilistic triangulation measurements. This invention uses an intelligent camera array to accurately calculate meteor trajectories and landing positions in real time, supplemented by high-fidelity simulations in Unreal Engine, combining probabilistic triangulation with real-time simulations. By adopting a GPS-synchronized intelligent camera array, integrating multi-camera observation data, error compensation, and uncertainty modeling techniques, it optimizes the accuracy of meteor trajectory calculations, uses Unreal Engine for high-fidelity simulations, improves prediction reliability, and enhances the real-time performance of data processing.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A method for calculating meteor trajectories and landing points based on probabilistic triangulation, which uses several GPS-synchronized cameras at different positions to capture the angular data of meteors in real time, calibrates the angular data through star sky matching, analyzes the uncertainty of the angular data by probabilistic triangulation, models and optimizes the movement trajectory of the meteor, and transitions to the dark flight stage for landing prediction. According to the simulated trajectory and landing area, the prediction accuracy is improved by combining probability estimation, specifically including the following steps:

[0008] Step 1. Acquisition of angular data: Use several cameras synchronized by GPS to detect meteor events in the night sky. The fields of view of the meteor events overlap. Take star sky images of the meteor and record the shooting time. After preprocessing the captured images, verify to ensure the integrity of the images;

[0009] Step 2. Calibration and uncertainty analysis: Match the captured star sky images with the Gaia star catalog to determine the angular position of the meteor relative to the camera; Align the camera coordinate system with the astronomical coordinate system, apply the Gaussian error model, and use Monte Carlo sampling to generate the probability distribution of the observed angles to overcome the uncertainties caused by sensor noise, image distortion, and calibration errors;

[0010] Step 3. Trajectory modeling and prediction: Use physical dynamics and motion equations to model and predict the movement of the meteor, adopt the Runge-Kutta numerical method to solve and predict the movement trajectory of the meteor; Optimize the initial parameters by minimizing the error between the observed trajectory and the predicted trajectory, and iteratively update the meteor state by combining the observation data for observing the meteor state;

[0011] Step 4. Dark flight prediction and landing estimation: After the meteor enters the dark flight phase, the extended Kalman filter continues to predict the meteor's trajectory. The probability simulation method using Monte Carlo sampling is used to model potential trajectories, and kernel density estimation is applied to construct the probability distribution of the landing point. The meteor's motion trajectory and landing probability are visualized in the Unreal Engine to obtain a statistical heat map of the potential landing area, enabling high-precision meteorite recovery and enhancing the effect of trajectory analysis.

[0012] Furthermore, in Step 1, for the starry sky image of the captured meteor, the background subtraction method, i.e., I final = I original - I background , Gaussian filtering, and edge detection techniques are used to isolate the meteor trajectory and star point features; and metadata is recorded, including the geographical location and angle of the camera, lens distortion parameters, and environmental conditions.

[0013] Furthermore, in Step 1, the captured images are verified to check the integrity of the frames, verify the timestamps, and correct or discard sensor artifacts.

[0014] Furthermore, in Step 2, the calibration and uncertainty analysis steps are as follows:

[0015] Step 2.1 Meteor calibration: Determine the angle of the meteor relative to the camera through star chart matching, determine the direction of the camera relative to the celestial coordinate system, and accurately determine the angular position of the meteor relative to the camera.

[0016] Step 2.2 Uncertainty calculation and Monte Carlo sampling: Use the Gaussian error model to quantify the calibration error, and use the Monte Carlo sampling method to generate the probability distribution of potential observation angles.

[0017] Step 2.3 Triangulation to calculate the possible position coordinates of the meteor: According to the probability distribution obtained in Step 2.2 and the principle of triangulation, find the intersection point of the lines of sight of different cameras to determine the possible position coordinates of the meteor.

[0018] Furthermore, in Step 3, it specifically includes the following steps:

[0019] Step 3.1 Establish a dynamic model of the meteor: Predict the state vector X k :

[0020]

[0021] where the position rk: The position of the meteor is represented by the altitude and horizontal coordinates in the Earth reference frame; the velocity v k : The velocity of the meteor describes the motion characteristics of the meteor, including magnitude and direction; the mass m k : The mass of the meteor changes over time during atmospheric ablation; the dynamic model of the meteor state is as follows:

[0022] Position dynamics: The rate of change of the meteor's position is determined by the velocity v

[0023]

[0024] Velocity dynamics: The rate of change of the meteor's velocity is affected by gravity and aerodynamic drag

[0025]

[0026] r represents the position vector of the meteor, v represents the velocity vector, a(r, v) represents the acceleration, g represents the acceleration due to gravity, C d is the drag coefficient, ρ a is the atmospheric density; S represents the cross-sectional area of the meteor, which determines the rate of mass reduction;

[0027] Mass dynamics: Due to the ablation effect, the rate of mass reduction of the meteor:

[0028]

[0029] C h is the ablation coefficient, which represents the material's response to heating; v 3 represents the ablation rate, which is proportional to the cube of the velocity; Step 3.2 Initial parameter optimization: Initial parameter optimization includes obtaining the initial parameters, and applying the trajectory calculation process to calculate the total Euclidean distance between the predicted trajectory and the observed sampling points for each set of parameter combinations, and defining the error function:

[0030]

[0031] where, is the calculated trajectory point, is the actually observed sampling point. The error function measures the deviation between the predicted trajectory and the real observed data. The goal of optimization is to search for the parameter combination in the parameter space that minimizes this error. The particle swarm optimization PSO or genetic algorithm GA is used. The optimization process is as follows:

[0032] Velocity update equation:

[0033]

[0034] Position update equation:

[0035]

[0036] where p iLet \(x^*\) represent the optimal position of the particle, \(G\) represent the global optimal position, and \(w, c_1, c_2, r_1, r_2\) be weight factors. By dynamically adjusting these weight coefficients, the convergence rate is optimized, and after optimization, the optimized \(m_0\), \(r_0\), \(v_0\) and the air resistance coefficient \(c\) are obtained. d , providing high-precision input for subsequent trajectory modeling;

[0037] Step 3.3 Prediction and Update: Optimize the trajectory through the Extended Kalman Filter (EKF), and ensure the precise optimization of the meteor trajectory through noise processing and dynamic adjustment:

[0038] The state vector \(x\) is defined as representing the three-dimensional position, velocity components, and mass of the meteor;

[0039] The prediction step is based on the dynamic model: \(x\) k+1|k \(_{k + 1}\) = \(f(x\) k \(_k\), \(u\) k \(_k\)) + \(w\) k

[0040] where \(x\) k+1|k \(_{k + 1}\) represents the next state predicted based on the model, \(x\) k \(_k\) represents the current state, \(u\) k \(_k\) represents the external input, and \(w\) k is the process noise;

[0041] \(z\) k \(_k\) = \(h(x\) k \(_k\)) + \(v\) k \(z\) k

[0042] where \(z\) k \(_k\) represents the observed value, and \(v\) k is the observation noise;

[0043] Update process:

[0044] State prediction:

[0045] Error covariance prediction:

[0046] Kalman gain calculation:

[0047] State update:

[0048] Error covariance update: \(P\) k|k \(_{k + 1}\) = (\(I - K\) k \(_k\) \(H\) k ) \(P\) k|k―1 .

[0049] Further, in step 4, the landing point probability estimation addresses atmospheric uncertainties through probability modeling. Monte Carlo simulation uses random sampling of initial conditions to generate potential meteor trajectories and landing points. Kernel Density Estimation (KDE) is used to analyze the landing point distribution probability and generate a smooth probability density function to represent the high-probability impact areas:

[0050]

[0051] where n is the number of samples, h is the smoothing parameter, and K is the kernel function; the high landing probability areas are highlighted by overlaying the heatmap and contour lines obtained from the kernel density estimation analysis.

[0052] In summary, the invention has the following beneficial effects:

[0053] The present invention uses a GPS-synchronized intelligent camera array to capture high-precision meteorite data from multiple angles, enhancing the accuracy of triangulation and trajectory calculation. The present invention addresses the uncertainties caused by camera misalignment, sensor errors, and environmental noise through a probabilistic triangulation method; applies Monte Carlo sampling, Gaussian error model, and Extended Kalman Filter to improve the reliability of meteorite position and trajectory prediction. The present invention conducts high-fidelity real-time simulation through the integration of Unreal Engine, clearly visualizes the meteor trajectory and landing area probability, and helps meteor recovery operations by providing detailed statistical heatmaps that represent the confidence intervals of landing area estimation. Probability modeling ensures reliable estimation of meteor paths and landing points even in the case of imperfect data. The present invention significantly improves the accuracy of meteor trajectory prediction and provides a scalable real-time solution for celestial tracking and recovery operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a flowchart of the present invention;

[0055] Figure 2 is a scatter plot of probability distribution. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0056] The present invention will be further described in detail below with reference to the accompanying drawings.

[0057] It should be noted that for the sake of convenience of description, the descriptions of directions in the following text are consistent with the directions of the accompanying drawings themselves, but do not limit the structure of the present invention.

[0058] As Figures 1 to 2As shown, the present invention discloses a method for calculating meteor trajectories and landing points based on probabilistic triangulation. It uses several GPS-synchronized cameras at different positions to capture the angular data of meteors in real time, calibrates the angular data through star sky matching, analyzes the uncertainty of the angular data by probabilistic triangulation, models and optimizes the movement trajectory of the meteor, transitions to the dark flight stage for landing prediction, and improves the prediction accuracy according to the simulated trajectory and landing area combined with probability estimation. The specific steps are as follows:

[0059] Step 1. Acquisition of angular data: Use several cameras synchronized by GPS to detect meteor events in the night sky. The fields of view of the meteor events overlap. Take star sky images of the meteor and record the shooting time. After preprocessing the captured images, verify to ensure the integrity of the images; use the background subtraction method, i.e., I final =I original -I background , Gaussian filtering and edge detection techniques to isolate the meteor trajectory and star point features, which can effectively isolate the meteor trajectory and star point features; and record metadata, including the geographical location and angle of the camera, lens distortion parameters, and environmental conditions; verify the captured images, check the integrity of the frames, verify the timestamps, and correct or discard sensor artifacts.

[0060] The selected high-sensitivity cameras synchronized by GPS are used to detect meteor events in the night sky. The fields of view of the cameras overlap for triangulation. When a meteor event occurs, the cameras capture high-resolution images of the meteor and accurate timestamps. At the same time, through the same camera settings, star sky images are captured before and after the meteor event to align the direction of the camera with the astronomical coordinates. The collected data is preprocessed through techniques such as background subtraction, Gaussian filtering, and edge detection to enhance the image quality and highlight features such as meteor trajectories and star points; record metadata such as camera position, angle, lens distortion parameters, and environmental conditions through the collected data, and verify the data through integrity checks, timestamp verification, and sensor artifact correction to ensure the integrity of the data and prepare for subsequent analysis.

[0061] Step 2. Calibration and uncertainty analysis: Match the captured star sky images with the Gaia star catalog to determine the angular position of the meteor relative to the camera; align the camera coordinate system with the astronomical coordinates; to cope with the uncertainties caused by sensor noise, image distortion, and calibration errors, apply the Gaussian error model and use Monte Carlo sampling to generate the probability distribution of the observed angles, overcoming the uncertainties caused by sensor noise, image distortion, and calibration errors. These angles sampled from multiple cameras are used in the triangulation method to calculate the three-dimensional position of the meteor, and the uncertainty distribution is combined to ensure the robustness of the position estimate. The steps of calibration and uncertainty analysis are as follows:

[0062] Step 2.1 Meteor Calibration: Determine the angle of the meteor relative to the camera through star chart matching, determine the direction of the camera relative to the celestial coordinate system, and accurately determine the angular position of the meteor relative to the camera; Calibrate the camera by aligning the captured starry sky with a celestial catalog (such as Gaia or 2MASS); By matching the stars in the captured image with their known positions in the catalog, the direction of the camera relative to the celestial coordinate system can be determined. In this embodiment, the least squares fitting method is used to calculate the transformation matrix so that the angular measurements of the camera (i.e., the position of the meteor in the field of view) can be represented in right ascension (RA) and declination (Dec), thus matching the coordinates of the celestial catalog. The celestial coordinate system is used to describe the positions of celestial bodies, and the celestial coordinates are used to determine the direction of the camera relative to the sky in order to accurately calculate the angle of the meteor.

[0063] Step 2.2 Uncertainty Calculation and Monte Carlo Sampling: Despite precise calibration, there are still uncertainties in the angular measurements due to factors such as sensor noise, image distortion, and calibration errors. Sensor noise refers to the random fluctuations in measurements introduced by the camera sensor, while image distortion may cause the apparent position of the meteor to shift due to lens defects. Calibration errors occur when the initial alignment between the camera's internal system and the celestial coordinate system is not perfectly accurate. To quantify these uncertainties, Gaussian error models are used to quantify the calibration errors, which assume that the measurement errors follow a normal distribution, where the standard deviation (σ) represents the magnitude of the uncertainty. The Gaussian model provides a statistical representation of the uncertainty in the angular measurements, which can then be used to simulate the possible angular ranges that might be caused by the observed meteor. The Monte Carlo sampling method is used to generate a probability distribution of potential observed angles. The Monte Carlo sampling randomly samples within the uncertainty range to create a reasonable range of angular positions, reflecting the inherent uncertainty in the measurements. Through this probabilistic approach, multiple possible positions are ensured to be considered, thus providing a more robust estimate of the meteor's position.

[0064] Step 2.3 Triangulation to Calculate the Possible Position Coordinates of the Meteor: Based on the probability distribution obtained in Step 2.2 and the principle of triangulation, find the intersection points of the lines of sight of different cameras to determine the possible position coordinates of the meteor. The principle of triangulation is to determine the position of the meteor by finding the intersection points of the lines of sight of different cameras, and these lines of sight are deduced based on their respective angles. This process does not provide a fixed position but generates a series of possible positions, reflecting the uncertainty in the observed angles.

[0065] The final result is a probabilistic position information that takes into account the variability of the measurements, thus providing a more accurate and reliable estimate of the meteor's position and trajectory, especially in cases where the uncertainty is relatively high.

[0066] Step 3. Trajectory Modeling and Prediction: Model and predict the motion of the meteor using physical dynamics and equations of motion, and solve and predict the meteor's motion trajectory using the Runge-Kutta numerical method; optimize the initial parameters by minimizing the error between the observed trajectory and the predicted trajectory, and iteratively update the meteor state in combination with the observation data for observing the meteor state. The observation data includes image data, angular position, motion trajectory, and other relevant measurement data obtained from sensors; specifically, it includes the following steps:

[0067] Step 3.1 Establish the dynamic model of the meteor: The state vector X for predicting the meteor state k :

[0068]

[0069] where the position rk: The position of the meteor is represented by altitude and horizontal coordinates in the Earth reference frame; the velocity v k : The velocity of the meteor describes the motion characteristics of the meteor, including magnitude and direction; the mass m k : The mass of the meteor changes with time during the atmospheric ablation process; the dynamic model of the meteor state is as follows:

[0070] Position dynamics: The motion of the meteor is governed by physical laws. The rate of change of the meteor's position is determined by the velocity v. Predict the meteor's trajectory by iterating through discrete time steps. Based on the position and velocity estimates of the meteor at each time step, form a meteor trajectory prediction.

[0071]

[0072] Velocity dynamics: The rate of change of the meteor's velocity is affected by gravity and aerodynamic drag.

[0073]

[0074] r represents the position vector of the meteor, v represents the velocity vector, a(r, v) represents the acceleration, g represents the acceleration due to gravity, and C d is the drag coefficient, ρ a is the atmospheric density; S represents the cross-sectional area of the meteor, which determines the rate of mass reduction;

[0075] Mass dynamics: Due to the ablation effect, the mass of the fireball will continuously decrease. The mass reduction rate of the meteor:

[0076]

[0077] C h is the ablation coefficient, which represents the material's response to heating; v 3Denote the ablation rate, which is proportional to the cube of the velocity; Step 3.2 Initial parameter optimization: Use the method of optimizing the initial parameters of the meteor trajectory prediction to optimize the initial parameters, including obtaining the initial parameters such as mass (m0), velocity (v0) and position (r0), and applying the trajectory calculation process to calculate the meteor trajectory under each set of parameter combinations. To evaluate the quality of each set of parameters, calculate the sum of the Euclidean distances between the predicted trajectory and the observed sampling points, and define the error function:

[0078]

[0079] where, is the calculated trajectory point, is the actually observed sampling point. The error function measures the deviation between the predicted trajectory and the true observed data. The smaller its value, the more accurately the optimized initial parameters can reproduce the meteor's movement trajectory. Therefore, the optimization goal is to search for the parameter combination that minimizes this error in the parameter space to ensure the accuracy and robustness of the trajectory prediction.

[0080] Adopt heuristic optimization techniques such as Particle Swarm Optimization (PSO) or Genetic Algorithm (GA), and the optimization process is as follows:

[0081] Velocity update equation:

[0082]

[0083] Position update equation:

[0084]

[0085] where p i represents the optimal position of the particle, G represents the global optimal position, and w, c1, c2, r1, r2 are weight factors to ensure the global exploration ability of the search. By dynamically adjusting these weight coefficients, the convergence rate is optimized to ensure efficient parameter optimization. The optimized initial parameters are used to improve the accuracy of meteor trajectory modeling and prediction. After optimization, the optimized m0, r0, v0 and air resistance coefficient c d are obtained, providing high-precision input for subsequent trajectory modeling.

[0086] Step 3.3 Prediction and update: In order to optimize the trajectory through the Extended Kalman Filter (EKF), the state of the meteor is iteratively predicted and updated to ensure accuracy in estimating its position, velocity and mass. The EKF method combines the observed data with the system dynamics and noise, optimizes the trajectory through the Extended Kalman Filter EKF, and ensures precise optimization of the meteor trajectory through noise processing and dynamic adjustment:

[0087] The state vector x is defined as Represents the three-dimensional position, velocity components, and mass of a meteor;

[0088] The prediction step is based on a dynamic model: x k+1|k = f(x k , u k ) + w k

[0089] where x k+1|k represents the next state predicted based on the model, x k represents the current state, u k represents the external input, and w k is the process noise;

[0090] z k = h(x k ) + v k z k

[0091] where z k represents the observed value, and v k is the observation noise;

[0092] Update process:

[0093] State prediction:

[0094] Error covariance prediction:

[0095] Kalman gain calculation:

[0096] State update:

[0097] Error covariance update: P k|k = (I - K k H k )P k|k―1 .

[0098] To further optimize the prediction, the Extended Kalman Filter (EKF) is implemented to iteratively update the meteor state by incorporating the observed data. This process enables accurate trajectory modeling and prediction, providing a reliable framework for subsequent meteor motion analysis.

[0099] Step 4. Dark flight prediction and landing estimation: Once the meteor ends its luminous phase and enters the dark flight phase, the Extended Kalman Filter (EKF) continues to predict the meteor's trajectory. During the dark flight phase, the meteor's motion is controlled by air resistance and wind. Given the atmospheric drag and wind, a probabilistic simulation method using Monte Carlo sampling is used to model potential trajectories, and Kernel Density Estimation (KDE) is applied to construct the probability distribution of the landing point; the meteor's motion trajectory and landing probability are visualized in the Unreal Engine to obtain a statistical heat map of the potential landing area, enabling high-precision meteorite recovery and enhancing the effect of trajectory analysis.

[0100] Landing point probability estimation solves the atmospheric uncertainty through probabilistic modeling. Monte Carlo simulation uses random sampling of initial conditions, such as wind speed and air density, to generate potential meteor trajectories and landing points. Kernel Density Estimation (KDE) is used to analyze the probability distribution of the landing points, generating a smooth probability density function to represent the high-likelihood impact area:

[0101]

[0102] where n is the number of samples, h is the smoothing parameter, and K is the kernel function; by superimposing the heat map and contour lines obtained from the kernel density estimation analysis, the high landing probability areas are highlighted.

[0103] The predicted trajectories and landing areas are visualized in the Unreal Engine, combining the atmospheric model and terrain data to create a realistic representation of the meteor's descent. By superimposing the heat map and contour lines obtained from the kernel density estimation analysis, the high landing probability areas are highlighted. This interactive visualization supports parameter sensitivity testing and improves the accuracy of the prediction.

[0104] The above are only the preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions falling within the concept of the present invention belong to the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, several improvements and refinements made without departing from the principle of the present invention should also be regarded as within the protection scope of the present invention.

Claims

1. A method for calculating meteor trajectories and landing points based on probabilistic triangulation, characterized in that Use GPS-synchronized cameras at several different positions to capture the angular data of meteors in real time, calibrate the angular data through star field matching, analyze the uncertainty of the angular data by probability triangulation, model and optimize the motion trajectory of the meteors, transition to the dark flight stage for landing prediction, and improve the prediction accuracy according to the simulated trajectory and landing area combined with probability estimation. The specific steps are as follows: Step 1. Acquisition of angular data: Use several cameras synchronized by GPS to detect meteor events in the night sky. There is an overlap in the field of view of meteor events. Take starry sky images of the meteors and record the shooting time. After preprocessing the captured images, verify them to ensure the integrity of the images; Step 2. Calibration and uncertainty analysis: Match the captured starry sky images with the Gaia star catalog to determine the angular position of the meteors relative to the cameras; Align the camera coordinate system with the astronomical coordinates, apply the Gaussian error model, and use Monte Carlo sampling to generate the probability distribution of the observed angles to overcome the uncertainties caused by sensor noise, image distortion, and calibration errors; Step 3. Trajectory modeling and prediction: Use physical dynamics and motion equations to model and predict the motion of the meteors, and use the Runge-Kutta numerical method to solve and predict the motion trajectory of the meteors; Optimize the initial parameters by minimizing the error between the observed trajectory and the predicted trajectory, and iteratively update the meteor state by combining the observation data for observing the meteor state; Step 4. Dark flight prediction and landing estimation: After the meteor enters the dark flight stage, the extended Kalman filter continues to predict the trajectory of the meteor. Use the probability simulation method of Monte Carlo sampling to model the potential trajectories, and apply kernel density estimation to construct the probability distribution of the landing points; The motion trajectory and landing probability of the meteors are visualized in the Unreal Engine to obtain the statistical heat map of the potential landing area, which can achieve high-precision meteorite recovery and enhance the effect of trajectory analysis.

2. The method for calculating meteor trajectories and landing points based on probabilistic triangulation according to claim 1, wherein, In the said step 1, the background subtraction method, i.e., I final = I original - I background , Gaussian filtering, and edge detection techniques are used to isolate the meteor trajectory and star point features; and metadata is recorded, where the metadata includes the geographical location and angle of the camera, lens distortion parameters, and environmental conditions.

3. The method for calculating meteor trajectories and landing points based on probabilistic triangulation according to claim 1, wherein In the said Step 1, verify the captured images, check the integrity of the frames, verify the timestamps, and correct or discard sensor artifacts.

4. The method for calculating meteor trajectories and landing points based on probabilistic triangulation according to claim 1, wherein In the said Step 2, the calibration and uncertainty analysis steps are as follows: Step 2.1 Meteor calibration: Determine the angle of the meteor relative to the camera through star chart matching, determine the direction of the camera relative to the celestial coordinate system, and accurately determine the angular position of the meteor relative to the camera; Step 2.2 Uncertainty calculation and Monte Carlo sampling: Use the Gaussian error model to quantify the calibration error, and use the Monte Carlo sampling method to generate the probability distribution of potential observation angles; Step 2.3 Triangulation to calculate the possible position coordinates of the meteor: According to the probability distribution obtained in Step 2.2 and the principle of triangulation, find the intersection points of the lines of sight of different cameras to determine the possible position coordinates of the meteor.

5. The method for calculating meteor trajectories and landing points based on probabilistic triangulation according to claim 1, wherein In the said Step 3, it specifically includes the following steps: Step 3.1 Establish a dynamic model of the meteor: Predict the state vector X of the meteor state k : where the position rk: the position of the meteor is represented by altitude and horizontal coordinates in the Earth reference frame; the velocity v k : the velocity of the meteor describes the motion characteristics of the meteor, including magnitude and direction; the mass m k : the mass of the meteor changes with time during atmospheric ablation; the dynamic model of the meteor state is as follows: Position dynamics: The rate of change of the meteor's position is determined by the velocity v Velocity dynamics: The rate of change of the meteor's velocity is affected by gravity and aerodynamic drag r represents the position vector of the meteor, v represents the velocity vector, a(r, v) represents the acceleration, g represents the acceleration due to gravity, C d is the drag coefficient, ρ a is the atmospheric density; S represents the cross-sectional area of the meteor, which determines the rate of mass reduction; Mass dynamics: Due to the ablation effect, the rate of decrease of the meteor's mass: C h is the ablation coefficient, representing the material's response to heating; v 3 represents the ablation rate and is proportional to the cube of the velocity; Step 3.2 Initial parameter optimization: Initial parameter optimization includes obtaining initial parameters, and applying the trajectory calculation process to calculate the sum of the Euclidean distances between the predicted trajectories of meteor trajectories and the observed sampling points under each set of parameter combinations, and defining an error function: Among them, is the calculated trajectory point, is the actually observed sampling point. The error function measures the deviation between the predicted trajectory and the true observed data. The optimization objective is to search for the parameter combination in the parameter space that minimizes this error. The particle swarm optimization (PSO) or genetic algorithm (GA) is adopted. The optimization process is as follows: Velocity update equation: Position update equation: where p i represents the optimal position of the particle, G represents the global optimal position, w, c1, c2, r1, r2 are weight factors, and by dynamically adjusting these weight coefficients, the convergence rate is optimized. After optimization, the optimized m0, r0, v0 and air resistance coefficient c d are obtained, providing high-precision input for subsequent trajectory modeling; Step 3.3 Prediction and update: Optimize the trajectory through the Extended Kalman Filter (EKF), and ensure the precise optimization of the meteor trajectory through noise processing and dynamic adjustment: The state vector x is defined as representing the three-dimensional position, velocity components, and mass of the meteoroid; The prediction step is based on the dynamic model: x k+1|k = f(x k , u k ) + w k where x k+1|k represents the next state predicted based on the model, x k represents the current state, u k represents the external input, w k is the process noise; z k = h(x k ) + v k z k where z k represents the observed value, and v k is the observation noise; Update process: State prediction: Error covariance prediction: Kalman gain calculation: Status update: Error covariance update: P k|k = (I - K k H k ) P k|k―1 .

6. The method for calculating meteor trajectories and landing points based on probabilistic triangulation according to claim 1, characterized in that In step 4, the landing point probability estimation solves the atmospheric uncertainty through probability modeling. The Monte Carlo simulation uses random sampling of the initial conditions to generate potential meteor trajectories and landing points, and uses Kernel Density Estimation (KDE) to analyze the landing point distribution probability and generate a smooth probability density function to represent the high-probability impact area: Where n is the number of samples, h is the smoothing parameter, and K is the kernel function; By overlaying the heatmap and contour lines obtained from the kernel density estimation analysis, the high landing probability areas are highlighted.

Images