Aerial positioning method based on inertial navigation

Abstract

The invention provides an aviation positioning method based on inertial navigation, and relates to the technical field of satellite navigation, acceleration data and angular velocity data of an aircraft are collected in real time through an inertial navigation system, and a virtual inertial field is constructed based on the acceleration data and the angular velocity data to represent the dynamic motion trend of the aircraft. Predicting the position and the speed of the aircraft according to the virtual inertial field, comparing the position and the speed with the position and the speed measured by the inertial navigation system, generating error distribution, analyzing a topological structure of the error distribution by using an adaptive topological filter, adaptively adjusting filtering parameters, and correcting accumulated errors of the inertial navigation system, so as to obtain the position and the speed of the aircraft. A virtual inertial field prediction result and a self-adaptive topological filter correction result are fused, real-time position and speed estimation of the aircraft is output, the method can dynamically adapt to a complex flight state, the ATF surpasses limitation of a traditional filter on linear Gaussian error hypothesis through topological data analysis, and the intelligence and accuracy of error correction are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation, and specifically to an aviation positioning method based on inertial navigation. Background Art

[0002] According to an airborne multi-sensor integrated navigation and positioning method, device, equipment and medium disclosed in "CN119354178A" of China, which relates to the technical field of aviation navigation. The method includes: the Beidou navigation system, the altimeter, and the radio navigation system are respectively combined with the inertial navigation system. Each combination outputs observation values through a sub-filter. The observation values output by each sub-filter and the predicted values of the inertial navigation system are fused to output a positioning result, and the data output by the inertial navigation system, the Beidou navigation system, and the altimeter are respectively subjected to fault detection and repair; the observation values output by each sub-filter are respectively subjected to anomaly detection by using state parameter estimation and residual vectors, and the detected abnormal values are repaired by using robust filtering; after the observation values output by each sub-filter are respectively subjected to anomaly detection and repair, new state parameter estimation is calculated, and the dynamic model of the sub-filter is detected for anomalies based on the new state parameter estimation. This solution is beneficial to improving the fault tolerance rate of integrated navigation and positioning.

[0003] According to an aviation navigation network takeoff and landing guidance system error envelope performance evaluation method disclosed in "CN119199912A" of China, which relates to the technical field of satellite navigation, including a single-frequency pseudorange domain error envelope model evaluation method, a dual-frequency pseudorange domain error envelope model evaluation method, and a dual-frequency positioning domain error envelope model evaluation method. The above evaluation methods all include the following steps: Step S1, screening observation data, performing carrier phase smoothing filtering processing and extracting pseudorange single-difference residuals; Step S2, constructing an error envelope model; Step S3, performing error envelope confidence evaluation and error envelope tightness evaluation. The present invention adopts the above-mentioned aviation navigation network takeoff and landing guidance system error envelope performance evaluation method, which is beneficial to the selection of specific error envelope models in integrity evaluation, and can help the integrity monitoring system of the satellite-based precision takeoff and landing guidance system relatively easily obtain a lower protection level and improve the usability of the system.

[0004] The above patent documents and the prior art have the following technical problems when in use: Problem 1: Traditional Inertial Navigation Systems (INS) rely on accelerometer and gyroscope data to calculate position and velocity through integration. However, due to the presence of sensor noise and biases, errors accumulate rapidly over time. Especially in the absence of external auxiliary signals (such as GPS), the error can reach several kilometers after a long flight. The positioning error of traditional INS may exceed 5000 meters, which cannot meet the requirements of high-precision navigation for long-range flight missions. Existing methods usually assume linear motion models or Gaussian error distributions, making it difficult to adapt to complex non-linear flight states, resulting in limited error correction effects and severely restricting the reliability and safety of navigation. Problem 2: In high-dynamic flight scenarios (such as turbulence, high-speed maneuvers, or sharp turns), traditional INS systems often cannot achieve real-time response and highly robust positioning due to computational complexity and the limitation of relying solely on inertial data. The software calculation efficiency of existing methods is low, making it difficult to meet real-time requirements, and lacking the ability to dynamically adapt to environmental changes, which limits their practical application scope. Summary of the Invention

[0005] Technical Problems to be Solved In view of the deficiencies of the prior art, the present invention provides an aviation positioning method based on inertial navigation, which solves the following problems: 1. Aiming at the problem that the error of traditional INS accumulates rapidly without external auxiliary signals and it is difficult to meet the positioning requirements for long flights. 2. Aiming at the problem that existing INS systems lack real-time performance and robustness in high-dynamic environments and are difficult to adapt to extreme flight conditions.

[0006] Technical Solution

[0007] To achieve the above objectives, the present invention is realized through the following technical solutions: An aviation positioning method based on inertial navigation, the aviation positioning method includes the following steps: Sp1: Real-time collect the acceleration data and angular velocity data of the aircraft through an Inertial Navigation System (INSP). Sp2: Based on the acceleration data and angular velocity data, construct a Virtual Inertial Field (VIF) to characterize the dynamic motion trend of the aircraft. Sp3: Predict the position and velocity of the aircraft according to the Virtual Inertial Field (VIF), and compare them with the position and velocity measured by the Inertial Navigation System (INSP) to generate an error distribution. Sp4: Use an Adaptive Topology Filter (ATF) to analyze the topological structure of the error distribution, adaptively adjust the filtering parameters, and correct the cumulative error of the Inertial Navigation System (INSP). Sp5: Fuse the prediction results of the Virtual Inertial Field (VIF) and the correction results of the Adaptive Topology Filter (ATF), and output the real-time position and velocity estimation of the aircraft.

[0008] Preferably, the construction of the virtual inertial field (VIF) in the step Sp2 further includes the following steps: Sp2.1: Collect the acceleration and angular velocity within a preset time window to form a dynamic data set ; Sp2.2: Perform non - linear mapping on the data set through a radial basis function (RBF) kernel to generate a virtual inertial field:

[0009] wherein, is the historical position estimate, is the dynamic weight, is the adaptive bandwidth, is the spatial position; Sp2.3: According to the real - time motion characteristics of the aircraft, jointly optimize and . The VIF predicts the next - moment state of the aircraft, the position and angular velocity based on the currently measured acceleration and angular velocity as a reference for INS integration to minimize the deviation between the VIF prediction and the actual motion.

[0010] Preferably, the generation of the error distribution in the step Sp3 specifically includes: Sp3.1: Based on the INS data, obtain the measured position and velocity through homogeneous integral calculation; Sp3.2: Use the VIF to predict the position and velocity at the next moment; Sp3.3: Calculate the error vector and generate an error distribution within the time window.

[0011] Preferably, the adaptive topological filter (ATF) in the step Sp4 further includes the following: Sp4.1: Apply persistent homology analysis to the error distribution to extract topological features, including the number of connected components Betti - 0 and the number of loops Betti - 1; Sp4.2: Adaptively select a filtering strategy according to the topological features. If Betti - 0 is dominant, correct the discrete error through clustering analysis. If Betti - 1 is significant, suppress the periodic error through frequency - domain filtering; Sp4.3: Dynamically adjust the INS state estimation based on the selected strategy to generate the corrected position and velocity.

[0012] Preferably, when fusing the prediction result and the correction result in Sp5, the following further contents are included: Sp5.1: Fuse the position , velocity predicted by VIF with the position and velocity after ATF correction through Kalman filtering; Sp5.2: Update the dynamic weight of VIF according to the fusion result to achieve the closed-loop optimization of prediction and correction.

[0013] Preferably, the joint optimization in the step Sp2.3 further includes introducing the airspeed data of the aircraft as a constraint condition to adjust the VIF bandwidth , and optimize it in real time through the gradient descent method to ensure the prediction accuracy of VIF for high-dynamic flight.

[0014] Preferably, in the step Sp4, it further includes calculating the topological persistence of the error distribution , identifying abnormal error points, and after removing the abnormal points, recalculating the topological features and updating the filtering strategy.

[0015] Preferably, the hardware components of the aviation positioning method include: Inertial Measurement Unit (IMU): including a three-axis accelerometer and a three-axis gyroscope, used to collect the acceleration data of the aircraft in real time and angular velocity data ; Embedded processor: configured with a main frequency of at least 1 GHz and a floating-point operation unit, used to execute the construction of the Virtual Inertial Field (VIF), the calculation of the error distribution, and the real-time operation of the Adaptive Topological Filter (ATF), and the embedded processor realizes the calculation of the Radial Basis Function (RBF) kernel in Sp2 and the extraction of topological features of persistent homology analysis in Sp4 through hardware acceleration algorithms; Storage module: with a capacity of not less than 4 GB, used to store historical motion data within the time window and error distribution , supporting the dynamic update of VIF; Data interface: supporting data transmission with a sampling frequency of at least 100 Hz to ensure the real-time interaction between IMU data and the processor; Auxiliary sensor module: including an airspeed sensor and a magnetic compass, used to collect the airspeed data and direction data of the aircraft, as the constraint condition for the optimization of the VIF bandwidth in Sp2; FPGA Accelerator: Configured with parallel computing units, used to accelerate the topological filtering strategy selection of ATF in Sp4 and the fusion calculation in Sp5, with a processing time not exceeding 5 ms / cycle, and the FPGA accelerator realizes error distribution through hardware description language (HDL). for clustering analysis and frequency domain filtering of; Power Management Unit: Supports at least 10W power consumption and provides stable power supply for IMU, processor, and FPGA.

[0016] Beneficial Effects

[0017] The present invention provides an aviation positioning method based on inertial navigation. It has the following beneficial effects: 1. The present invention optimizes the performance of the inertial navigation system (INS) through the synergistic effect of the virtual inertial field (VIF) and the adaptive topological filter (ATF). The VIF uses the nonlinear mapping of the radial basis function (RBF) kernel and dynamic weight optimization technology to accurately characterize the dynamic motion trend of the aircraft; the ATF is based on topological data analysis (TDA) to intelligently identify and correct error patterns, thus effectively overcoming the problem of the rapid growth of cumulative errors in traditional INS without external auxiliary signals (such as GPS). The nonlinear mapping of the VIF breaks through the dependence of traditional methods on linear motion models and can dynamically adapt to complex flight states. The ATF surpasses the limitations of traditional filters (such as Kalman filter) on the linear Gaussian error assumption through topological data analysis, significantly improving the intelligence and accuracy of error correction. Compared with the errors of traditional INS that can reach several kilometers, this accuracy improvement greatly enhances the navigation reliability and safety during long flights and provides strong technical support for long-range flight missions.

[0018] 2. The present invention combines the high-efficiency parallel computing ability of the FPGA accelerator and the environmental adaptability of the auxiliary sensor module. The FPGA accelerates complex algorithms, persistent homology analysis, and filtering strategy selection through hardware optimization to ensure real-time performance, with a processing time not exceeding 5 milliseconds / cycle; the auxiliary sensor dynamically adjusts the VIF parameters to enable the system to quickly adapt to changes in the flight environment. The hardware optimization design of the FPGA accelerator greatly improves the computing efficiency, enabling the system to achieve real-time response in high-dynamic scenarios. The dynamic coupling mechanism between the auxiliary sensor and the VIF breaks through the limitation of relying solely on inertial data, significantly enhancing the system's adaptability to extreme conditions such as turbulence and high-speed maneuvers, and significantly improving the robustness and practicality of the navigation system. This feature is particularly suitable for scenarios with extremely high requirements for stability and reliability in military aviation and commercial aviation. Description of the Drawings

[0019] Figure 1 is the method step diagram of the present invention; Figure 2Hardware structure diagram of the method of the present invention; Figure 3 Graph of the positioning error of the present invention varying with time; Figure 4 Graph comparing the true trajectory and the estimated trajectory of the present invention; Figure 5 Scatter plot of the error distribution of the present invention. Specific implementation manner

[0020] 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. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention. Specific embodiment one: As Figures 1 to 5 shown, a method for aircraft positioning based on inertial navigation, the aircraft positioning method includes the following steps: Sp1: Real-time collect the acceleration data and angular velocity data of the aircraft through an inertial navigation system (INSP). The accelerometer measures the acceleration of the aircraft in three orthogonal directions , and the gyroscope measures the angular velocity around three axes . The data collection frequency is at least 100 Hz to capture the high dynamic motion characteristics of the aircraft and provide basic input data for subsequent virtual inertial field construction and error correction; Sp2: Based on the acceleration data and angular velocity data, construct a virtual inertial field (VIF) to characterize the dynamic motion trend of the aircraft. The construction of the virtual inertial field (VIF) further includes the following steps: Sp2.1: Within a preset time window , collect the acceleration and the angular velocity to form a dynamic data set . The length of the time window is usually several seconds, and the specific length is adjusted according to the motion dynamics of the aircraft; Sp2.2: Perform non-linear mapping on the data set through a radial basis function (RBF) kernel to generate a virtual inertial field:

[0022] wherein, is the historical position estimate; is the dynamic weight, indicating the contribution of each historical data point; is the adaptive bandwidth, controlling the smoothness of the VIF; is the spatial position; Sp2.3: Jointly optimize according to the real-time motion characteristics of the aircraft, such as the change rates of acceleration and angular velocity. and , the optimization method introduces airspeed data (collected by the auxiliary sensor module) as a constraint condition, and uses the gradient descent method to adjust and in real time. The VIF predicts the next moment state of the aircraft, including position and angular velocity , and predicts the position , speed of the aircraft at the next moment as a reference for INS integration, so as to minimize the deviation between the VIF prediction and the actual motion. The joint optimization further includes introducing the airspeed data of the aircraft as a constraint condition to adjust the VIF bandwidth , and optimize in real time through the gradient descent method to ensure the prediction accuracy of the VIF for high-dynamic flight. The VIF provides a prediction of the future state of the aircraft through non-linear modeling and dynamic optimization, making up for the limitations of traditional INS that only relies on integration. Sp3: Predict the position and speed of the aircraft according to the virtual inertial field (VIF), and compare them with the position and speed measured by the inertial navigation system (INSP) to generate an error distribution. The generation of the error distribution specifically includes: Sp3.1: Based on the acceleration and angular velocity collected by INS data, the measured position and speed are obtained through isomorphic integral calculation. The calculation formula is:

[0023] Where: is the velocity vector calculated by INS, which changes with time t and has the unit of m / s; is the initial time, which is the start time of the flight; is the current time point; is the acceleration vector, which changes with time and has the unit of m / s 2 , provided by the IMU; is the time differential, representing the time increment in the integration; is the initial velocity vector, with the unit of m / s, usually input externally or set to zero;

[0024] Where: is the position vector calculated by INS, which changes with time t and has the unit of m; is the initial time; t is the current time point; is the velocity vector, which changes with time The change, with the unit of m / s, is calculated by the above formula; is the time differential; is the initial position vector, with the unit of m, usually input externally or set to zero; Sp3.2: Use VIF to predict the position at the next moment and speed ; Sp3.3: Calculate the error vector , and generate an error distribution within the time window . The error distribution reflects the characteristics of the INS cumulative error and provides input for adaptive filtering; Sp4: Use the adaptive topology filter (ATF) to analyze the topological structure of the error distribution, adaptively adjust the filtering parameters, and correct the cumulative error of the inertial navigation system (INSP). The adaptive topology filter (ATF) further includes the following: Sp4.1: Apply persistent homology analysis to the error distribution , extract topological features, including the number of connected components Betti-0 and the number of loops Betti-1. Among them, the number of connected components (Betti-0) represents the discrete clusters in the error distribution; the number of loops (Betti-1): represents the periodic structure in the error distribution; Sp4.2: Adaptively select a filtering strategy according to the topological features. If Betti-0 dominates (discrete errors are significant), correct the discrete errors through clustering analysis (such as K-means); if Betti-1 is significant (periodic errors are obvious), suppress the periodic errors through frequency domain filtering (such as Fourier transform); Sp4.3: Dynamically adjust the INS state estimation based on the selected strategy, generate the corrected position and speed, calculate the topological persistence of the error distribution , identify abnormal error points. After removing the abnormal points, recalculate the topological features and update the filtering strategy. The ATF intelligently identifies error patterns through topological data analysis (TDA) to achieve targeted correction; Sp5: Fusion the prediction results of the virtual inertial field (VIF) and the correction results of the adaptive topology filter (ATF), and output the real-time position and speed estimation of the aircraft. When fusing the prediction results and the correction results, it further includes the following: Sp5.1: Fusion the position predicted by VIF and the speed with the position and speed corrected by ATF through Kalman filtering: Kalman filter model:

[0025] Measurement update: Combine the VIF prediction and the ATF correction to optimize the state estimation; Sp5.2: Update the dynamic weight of VIF according to the fusion result , realize the closed-loop optimization of prediction and correction, and update the dynamic weight of VIF according to the fusion result :

[0026] Among them, is the error function of the prediction and fusion result, is the learning rate; Through fusion and optimization, ensure that the output position and speed estimation have both prediction accuracy and correction stability.

[0027] Specific working process and operation logic: The IMU is started, and it collects and in real time. The data is transmitted to the embedded processor through the data interface. The initial position and speed are set by external input or default values; The IMU collects data at a frequency of at least 100Hz. The embedded processor stores the data in the storage module to form a dynamic data set D. The processor extracts 𝐷D from the storage module, calculates VIF through the RBF kernel, and optimizes it in combination with the airspeed data and , predicts and , the processor calculates and based on the INS data, compares the VIF prediction results, generates an error distribution , the processor performs persistent homology analysis on 𝐸E, extracts topological features, selects a filtering strategy according to the features, corrects the INS state estimation, eliminates abnormal points and updates the strategy, uses Kalman filtering to fuse the VIF prediction and ATF correction results, outputs the final p and v, updates the VIF weight, forms a closed-loop optimization, and the system loops through the above steps to output high-precision position and speed estimates in real time. Specific embodiment two: As Figures 1 to 5 shown, according to the content in the above specific embodiment, the following content is further disclosed: Preferably, the hardware composition of the aviation positioning method includes: Inertial measurement unit (IMU): including a three-axis accelerometer and a three-axis gyroscope, used to collect the acceleration data of the aircraft in real time and angular velocity data , By integrating the acceleration, the speed and position changes of the aircraft can be calculated. The data from the triaxial gyroscope is used to track the aircraft's attitude, such as pitch, yaw, and roll. The sampling frequency of the IMU needs to reach at least 100 Hz to ensure capturing fast-changing motion information in high-dynamic flight scenarios and avoid data omission. Aviation-grade IMUs usually require the bias stability of the accelerometer to be better than 0.01 g and the bias stability of the gyroscope to be better than 0.1° / h. This high-precision and low-noise characteristic can significantly reduce the impact of cumulative errors on the positioning accuracy. IMUs are widely used in inertial navigation systems (INS) and are key components for aircraft, drones, missiles, and other aircraft to achieve autonomous positioning; Embedded processor: Configured with a main frequency of at least 1 GHz and a floating-point arithmetic unit, it is used to execute the construction of the virtual inertial field (VIF), the calculation of error distribution, and the real-time operation of the adaptive topology filter (ATF). And the embedded processor realizes the calculation of the radial basis function (RBF) kernel in Sp2 and the extraction of topological features of persistent homology analysis in Sp4 through hardware acceleration algorithms. The main frequency is at least 1 GHz, equipped with a floating-point arithmetic unit, supporting high-performance real-time computing, responsible for executing the construction of the virtual inertial field (VIF), the calculation of error distribution, and the real-time operation of the adaptive topology filter (ATF). It is the computing core of the system. The processor uses the radial basis function (RBF) kernel to perform non-linear mapping on the historical data collected by the IMU to generate the virtual inertial field (VIF). This process involves complex mathematical operations and requires efficient floating-point computing capabilities. The processor compares the INS measurement data with the VIF prediction data, calculates the error vector, and generates the error distribution. This distribution provides a basis for subsequent filtering and optimization. The processor performs persistent homology analysis, extracts topological features from the data, and selects appropriate filtering strategies based on these features to ensure the robustness of the positioning result. To improve the computing efficiency, the processor supports the SIMD (Single Instruction Multiple Data) instruction set or a dedicated coprocessor to optimize the speed of RBF kernel calculation and topological feature extraction. The processor must complete the above tasks within each sampling period (about 10 ms) to ensure the real-time response ability of the system; Storage module: With a capacity of not less than 4 GB, it is used to store historical motion data within the time window and error distribution , supporting the dynamic update of the VIF, with a capacity of not less than 4 GB, supporting high read and write speeds, storing historical motion data within the time window and error distribution providing data support for the dynamic update of the VIF; for historical motion data : including acceleration, angular velocity, and timestamp, used for the construction and update of the VIF; for error distribution : Record the error vector, support the topological analysis and filtering optimization of ATF. The storage module should have a high read-write speed to meet the requirements of real-time data update and fast access. Adopt a circular buffer or sliding window mechanism to ensure the dynamic management of data within the time window, always retain the latest data and overwrite the expired data. According to the system requirements, high-speed flash (such as NAND Flash) can be selected for data persistence, or DRAM for faster access speed. The storage module is used in the aviation system to support real-time data processing and historical data analysis, and is a key link for dynamically adjusting the algorithm. The storage module provides the necessary data basis for VIF and ATF, ensuring that the system can perform adaptive optimization based on historical information; Data interface: Support data transmission with a sampling frequency of at least 100Hz to ensure the real-time interaction between IMU data and the processor. The data interface supports data transmission with a sampling frequency of at least 100Hz to ensure that the data collected by the IMU can be transmitted to the embedded processor in real-time and without loss. Adopt a high-speed serial interface (such as SPI or enhanced I2C) or a parallel interface to achieve low-latency and high-bandwidth data transmission. The interface needs to support a clock synchronization mechanism to ensure the time consistency between IMU data and processor calculations and avoid data offset. In the aviation environment, the data interface needs to have an anti-electromagnetic interference design (such as shielded cables or differential signals) to ensure transmission reliability. The data interface guarantees the efficient communication between hardware components and is the basis for the system to work together; Auxiliary sensor module: Includes an airspeed sensor and a magnetic compass, used to collect the airspeed data and direction data of the aircraft, as the constraint conditions for VIF bandwidth optimization in Sp2. The airspeed sensor measures the speed of the aircraft relative to the air and outputs the airspeed data. These data are used to dynamically adjust the bandwidth of the VIF , to adapt to the motion characteristics at different flight speeds. The magnetic compass measures the magnetic heading of the aircraft and provides direction information to assist in the initialization and directional optimization of the VIF. The auxiliary sensor data is transmitted to the processor through the data interface and fused with the IMU data to further improve the positioning accuracy. The auxiliary sensors provide additional environmental information at different flight stages (such as takeoff, cruise, landing), enhancing the robustness of the system. By providing supplementary data, the auxiliary sensor module optimizes the performance of the VIF and makes the system more adaptable to complex flight conditions; FPGA accelerator: Configured with parallel computing units, used to accelerate the topological filtering strategy selection of ATF in Sp4 and the fusion calculation in Sp5. The processing time does not exceed 5ms / cycle, and the FPGA accelerator realizes the error distribution through a hardware description language (HDL). Clustering analysis and frequency domain filtering. The FPGA accelerator is equipped with parallel computing units, and the processing time does not exceed 5 ms / cycle, accelerating the topological filtering strategy selection and fusion calculation of ATF, improving system performance. The FPGA uses parallel processing units to accelerate the extraction of topological features and error distribution in persistent homology analysis Tasks such as clustering analysis and frequency domain filtering. A dedicated circuit is designed through a hardware description language (such as VHDL or Verilog) to achieve the efficient execution of computationally intensive tasks, ensuring that the processing time is controlled within 5 ms. The FPGA, as a coprocessor, communicates with the embedded processor through a high-speed bus (such as PCIe), receives task instructions, and returns results. The FPGA is commonly used in aviation navigation systems for real-time signal processing and complex algorithm acceleration, significantly improving computational efficiency. The FPGA accelerator reduces the burden on the embedded processor through hardware optimization, ensuring that the system can still maintain real-time performance under high load; Power management unit: Supports at least 10W power consumption, provides stable power supply for the IMU, processor, and FPGA. The power management unit supports at least 10W power consumption, provides stable and reliable power supply for the IMU, embedded processor, and FPGA. Through voltage regulators and filter circuits, it ensures stable power supply voltage, reduces the impact of power noise on the performance of sensors and processors, supports dynamic power consumption adjustment, optimizes energy consumption according to system load, is particularly suitable for battery-powered devices such as drones, and has overcurrent and overvoltage protection mechanisms to ensure the safe operation of the system in abnormal situations.

[0029] Working mechanism: After the IMU collects raw data, it is transmitted to the embedded processor through the data interface. The processor uses historical data in the storage module to construct the VIF and optimizes parameters in combination with auxiliary sensor data. The FPGA accelerator is responsible for the complex calculations of ATF to ensure real-time performance. The power management unit provides support for all components. Through the efficient parallel computing of the FPGA accelerator and the environmental adaptability of the auxiliary sensor module, this hardware composition not only meets the real-time requirements but also significantly improves the computational power and positioning accuracy of the system, and is particularly suitable for high-dynamic flight scenarios. Specific Embodiment Three: Such as Figures 1 to 5 shown, based on the content in the above specific embodiments, the following content is further disclosed: To further verify the feasibility and technical features of the technical solution of this application, experiments are designed to compare the positioning accuracy of this method with that of the standard INS and the traditional INS + dynamic model, verify the distinguishing features of the core technology of this application, and enhance credibility. The specific experiments include the following content: Simulated flight scenario: Tools and data: Use the open-source flight simulator JSBSim to generate real flight paths, covering straight flight, turning (shallow turn and sharp turn), climbing, descending, and turbulence scenarios, simulating actual aviation tasks.

[0031] Data generation: The simulator outputs real position, velocity, attitude data, and IMU data (acceleration and angular velocity), and different noise levels (such as Gaussian white noise with standard deviations of 0.01g and 0.1° / s respectively) are added to test the adaptability of the system to sensor quality; Flight duration: Each group of experiments runs for 10 hours to simulate long - duration flight conditions; The system is implemented as follows: Standard INS: Based on IMU data, the position and velocity are calculated by numerical integration without any error correction mechanism, reflecting the drift characteristics of traditional INS:

[0032] Where: is the velocity vector calculated by INS, which changes with time t and has the unit of m / s; is the initial time, which is the start time of the flight; is the current time point; is the acceleration vector, which changes with time and has the unit of m / s 2 , provided by the IMU; is the time differential, representing the time increment in the integration; is the initial velocity vector, with the unit of m / s, usually input externally or set to zero;

[0033] Where: is the position vector calculated by INS, which changes with time t and has the unit of m; is the initial time; t is the current time point; is the velocity vector, which changes with time and has the unit of m / s, calculated by the above formula; is the time differential; is the initial position vector, with the unit of m, usually input externally or set to zero; Traditional INS + dynamic model: Kalman filter is used in combination with a predefined aircraft dynamic model (such as assuming constant acceleration or a simple dynamics calculated based on thrust and drag) for error correction. The dynamic model depends on aircraft parameters (such as mass, thrust), performs well in low - dynamic scenarios, but may fail in high - dynamic scenarios due to inaccurate models. The Kalman filter update formula (simplified to two steps: prediction and update): Prediction:

[0034] Where: The state prediction vector at the current time k (including position and velocity), based on the previous - moment estimation; is the state transition matrix, which describes the system dynamics (such as the constant acceleration model); is the state estimation vector at the previous moment ; is the control input matrix, which maps the control quantity to the state; is the control input vector (such as thrust), and the unit depends on the model; Update:

[0035] is the state estimation vector at the current moment k, which fuses prediction and measurement; is the Kalman gain matrix, which balances the weights of prediction and measurement; is the measurement vector (here it is the INS integration result); is the measurement matrix, which maps the state to the measurement space; is the predicted state vector; Depends on the dynamic model accuracy and is limited by the nonlinear error in high-dynamic scenarios.

[0036] The method of this application: VIF construction: Using historical IMU data, generate a virtual inertial field through the RBF kernel to predict the position and velocity at the next moment;

[0037] Among them: : The virtual inertial field function, which changes with the position and time and has a unit of dimensionless field value; The summation symbol, which accumulates over historical data points; The dynamic weight of the th historical data point, dimensionless, and is adjusted by the optimization algorithm; is the exponential function, with the base of the natural logarithm ; is the Euclidean distance between the current position x and the historical position in meters; 2 is a constant, the scaling factor in the denominator; It is the square of the adaptive bandwidth, with the unit of , which is the influence range of the control field; ATF correction: Apply persistent homology analysis to the error distribution to extract topological features (Betti-0 and Betti-1), and adaptively select filtering strategies (such as clustering analysis or frequency-domain filtering); Error distribution:

[0038] Among them:

[0039] Among them: is the error distribution set, representing the error vectors at multiple time points; is the set symbol, containing error vectors ; is the error vector, which changes with time ; is the position vector measured by INS, with the unit of m; is the position vector predicted by VIF, with the unit of m; is the velocity vector measured by INS, with the unit of m / s; is the velocity vector predicted by VIF, with the unit of m / s; Fuse the VIF prediction and ATF correction results through Kalman filtering, output the final estimate, which depends on external signals or predefined models, is data-driven, and adapts to high-dynamic scenarios.

[0040] Operation and comparison: In each group of flight scenarios, run three systems, record the position error (Euclidean distance) and velocity error (vector difference), and calculate through the root mean square error (RMSE):

[0041] Among them: is the root mean square error, a statistical index to measure the positioning accuracy, with the unit of m; is the average factor, is the total number of time steps; is the summation symbol, summing over all time steps from 1 to accumulating; To estimate the position vector, over time varying, with the unit of m; is the true position vector, over time varying, with the unit of m.

[0042] The error growth curve over time, focusing on the performance after 10 hours, the error performance in specific segments (such as high - dynamic turns), to verify the contributions of VIF and ATF.

[0043] The results are analyzed as follows: Standard INS: The error grows quadratically over time and may reach more than 5000 meters after 10 hours due to the lack of a correction mechanism; Traditional INS + dynamic model: The error is small in low - dynamic scenarios (100 - 500 meters), and may reach 1000 meters in high - dynamic scenarios due to inaccurate models; The method of this application: Through VIF prediction and ATF correction, the positioning error is controlled within 15 meters during 10 - hour flight, significantly better than other methods.

[0044] The comparison table of key indicators is as follows:

[0045] This application does not rely on external signals or predefined dynamic models. VIF learns the motion trend through data - driven, and ATF intelligently corrects errors through topological analysis, different from the limitations of traditional methods. In high - dynamic scenarios, this application has stronger robustness, reflecting the synergistic effect of VIF and ATF.

[0046] This experiment simulates flight scenarios to quantitatively compare the positioning accuracy of the method of this application with existing systems, and verifies the effectiveness of its core technologies (VIF and ATF). The results are expected to show the high precision and robustness of this application without external auxiliary signals, which is particularly suitable for navigation tasks in military aviation and extreme environments. The experimental design considers different noise levels and dynamic conditions to ensure the wide applicability and statistical significance of the results. Specific Embodiment 4: As Figures 1 to 5 shown, based on the content in the above - mentioned specific embodiments, the following content is further disclosed: To further verify the feasibility of this application, the following are cases of this application in practical applications, specifically as follows: Case 1: Long - distance flight navigation in military covert reconnaissance missions: During a military stealth reconnaissance mission, an unmanned reconnaissance aircraft needs to perform a 12-hour flight mission in hostile airspace. The mission requires the aircraft to maintain high-precision positioning without GPS signal support to ensure the geographical marking accuracy of reconnaissance data. Due to the deployment of strong electromagnetic interference by the enemy, the traditional INS system shows rapid error accumulation in the simulation test, reaching several kilometers after 8 hours, which cannot meet the mission requirements. After implementing the technical solution of this application, the system first collects the acceleration and angular velocity data of the aircraft in real time at a frequency of 100Hz through the inertial measurement unit (IMU). These data are received by the embedded processor and stored in a storage module with a capacity of 4GB. The processor uses these data to construct a virtual inertial field (VIF), performs non-linear mapping on the historical motion data through a radial basis function (RBF) kernel, and generates a dynamic field to predict the position and velocity trend of the aircraft. At the same time, the auxiliary data provided by the airspeed sensor and the magnetic compass are used to optimize the bandwidth and weight of the VIF to ensure that the prediction adapts to the high-speed cruising state of the reconnaissance aircraft. Then, the system compares the VIF prediction results with the position and velocity calculated by INS integration to generate an error distribution, which is then taken over by the adaptive topology filter (ATF) for analysis. The ATF uses persistent homology analysis to extract the topological features of the error distribution, discovers significant periodic components (high Betti-1 values) in the errors, and then suppresses these periodic errors through frequency domain filtering while removing outliers to improve the correction accuracy. The FPGA accelerator plays a key role in this process, completing the topological analysis and filtering strategy selection within 5 milliseconds through parallel computing units to ensure real-time performance. Finally, the Kalman filter fuses the VIF prediction and the ATF correction results to output real-time position and velocity estimates, and the entire process is stably powered by the power management unit. The actual flight data shows that the positioning error is always controlled within 18 meters during the 12-hour mission, far better than the 6000-meter error of the traditional INS, successfully completing the reconnaissance mission and ensuring the geographical accuracy of the data and the secrecy of the mission.

[0048] Case 2: High-latitude navigation during polar scientific research flights: During a polar scientific research mission, a scientific research aircraft needs to fly for 10 hours in the Arctic region to collect ice thickness and climate data. Due to geomagnetic anomalies and aurora interference in high-latitude regions, the GPS signal is frequently interrupted. The traditional INS + dynamic model method shows an error exceeding 500 meters after 6 hours in simulation, unable to meet the high-precision positioning requirements of scientific research data. After adopting the method of this application, the system collects the acceleration and angular velocity data of the aircraft through the IMU, and the data flows through the data interface to the embedded processor. The processor constructs the VIF using the historical data in the storage module, generates a continuous field through the RBF kernel, and dynamically adjusts the bandwidth and weight in combination with the airspeed sensor data to predict the movement trend of the aircraft under polar low-temperature and turbulent conditions. Due to frequent turbulence during polar flight, the error distribution between the VIF prediction result and the INS measurement result presents a complex pattern. The ATF then intervenes, uses topological data analysis to identify the discrete clusters (high Betti-0 value) and periodic structures (high Betti-1 value) in the error. For the discrete clusters, the ATF corrects the instantaneous error through cluster analysis; for the periodic structures, it suppresses the long-term drift through frequency-domain filtering. The FPGA accelerator completes these calculations in less than 5 milliseconds, ensuring the real-time response ability of the system in turbulence. In the fusion stage, the Kalman filter integrates the VIF prediction and the ATF correction results, and updates the VIF weight through closed-loop optimization to make the system adapt to the dynamic changes of the polar environment. The entire system is stably powered by the power management unit to ensure continuous operation under low-temperature conditions. Finally, the positioning error during the 10-hour flight is controlled within 15 meters. Compared with the 500-meter error of the traditional method, the spatial resolution of the scientific research data is significantly improved, ensuring the scientific value of the mission.

[0049] Case 3: High-dynamic logistics distribution of commercial freight drones: In a high-dynamic logistics delivery mission of a commercial cargo drone, the drone needs to perform a 6-hour cargo transportation in an urban environment. The flight route involves frequent takeoffs and landings, sharp turns, and high-altitude turbulence. In a high-dynamic scenario, the error of the traditional INS system increases rapidly and reaches 800 meters after 4 hours, threatening the safety of the delivery. After implementing the method of this application, the drone collects acceleration and angular velocity data at a frequency of 100Hz through the IMU, and the data is received and stored by the embedded processor. The processor uses this data to construct the VIF, generates a dynamic field through the RBF kernel, and combines the airspeed sensor and magnetic compass data to optimize the prediction model, accurately capturing the movement trend of the drone during sharp turns and turbulence. After the error distribution is generated, the ATF analyzes its topological structure and finds that the error in the high-dynamic scenario presents a mixed characteristic of discrete clusters and periodicity. The ATF then adaptively selects a strategy combining clustering analysis and frequency-domain filtering to correct instantaneous and long-term errors. The FPGA accelerator supports the real-time processing of the ATF through parallel computing, ensuring that complex calculations are completed within 5 milliseconds to meet the rapid response requirements of the drone. The Kalman filter fuses the VIF prediction and ATF correction results, outputs high-precision position and velocity estimates, and dynamically adjusts the VIF parameters through closed-loop optimization to make the system adapt to the changing conditions of the urban environment. The power management unit provides stable power supply for all components to ensure the continuous operation of the drone under high load. In the actual mission, the flight positioning error within 6 hours is kept within 12 meters, far better than the 800-meter error of the traditional INS, ensuring the accuracy and safety of the cargo delivery and improving the logistics efficiency.

[0050] In three cases, the VIF accurately predicts the movement trend of the aircraft in different scenarios (stealth cruise, polar turbulence, urban high-dynamics) through data-driven non-linear mapping, overcoming the dependence of the traditional INS on external signals or predefined models. The ATF uses topological data analysis to identify complex error patterns and adaptively selects a filtering strategy to effectively suppress the error accumulation under long-term flight and high-dynamic conditions, demonstrating its intelligence and robustness. The FPGA accelerator and auxiliary sensor module ensure the real-time response and environmental adaptability of the system in high-dynamic scenarios, significantly improving the performance in practical applications. The cases show that the positioning error during long-term flight is controlled within 12 - 18 meters, far exceeding the error of hundreds to thousands of meters of traditional methods. Under conditions such as turbulence and sharp turns, the system operates stably, meeting the needs of military, scientific research, and commercial applications.

[0051] It should be noted that, in this document, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, such that a process, method, article or device comprising a series of elements not only includes those elements but also includes other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising a reference structure" does not exclude the presence of additional identical elements in the process, method, article or device comprising the element.

[0052] Although the embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the present invention, and the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An aviation positioning method based on inertial navigation, characterized in that: The aviation positioning method comprises the following steps: Sp1: collects aircraft acceleration and angular velocity data in real time through the inertial navigation system (INSP); Sp2: constructing a virtual inertial field (VIF) based on the acceleration data and angular velocity data to characterize the dynamic motion trend of the aircraft; Sp3: predicting the position and velocity of the aircraft based on the virtual inertial field (VIF), and comparing them with the position and velocity measured by the inertial navigation system (INSP) to generate an error distribution; Sp4: Use the adaptive topology filter (ATF) to analyze the topological structure of the error distribution, adaptively adjust the filter parameters, and correct the accumulated error of the inertial navigation system (INSP); Sp5: Fuse the virtual inertial field (VIF) prediction results with the adaptive topology filter (ATF) correction results to output the real-time position and velocity estimation of the aircraft.

2. The aviation positioning method based on inertial navigation according to claim 1, characterized in that: The construction of the virtual inertial field (VIF) in step Sp2 further includes the following steps: Sp2.1: Collect acceleration within the preset time window and angular velocity , forming a dynamic data set ; Sp2.2: Validating the Dataset Using the Radial Basis Function (RBF) Perform nonlinear mapping to generate a virtual inertia field: ； in, is the historical position estimate, is the dynamic weight, is the adaptive bandwidth, is the spatial position; Sp2.3: Joint optimization based on the real-time motion characteristics of the aircraft and , VIF is based on the currently measured acceleration and angular velocity , predict the next state and position of the aircraft ,speed , serves as a reference for INS integration to minimize the deviation between the VIF prediction and the actual motion.

3. The aviation positioning method based on inertial navigation according to claim 1, characterized in that: The generation of the error distribution in step Sp3 specifically includes: Sp3.1: Based on INS data, the measurement position is obtained by isomorphic integral calculation and speed ; Sp3.2: Using VIF to predict the next moment's position and speed ; Sp3.3: Calculate the error vector , and generates an error distribution within the time window .

4. The aviation positioning method based on inertial navigation according to claim 1, characterized in that: The adaptive topology filter (ATF) in step Sp4 further includes the following contents: Sp4.1: Error distribution Apply persistent homology analysis to extract topological features, including the number of connected components Betti-0 and the number of rings Betti-1; Sp4.2: Adaptively select the filtering strategy based on the topological characteristics. If Betti-0 is dominant, the discrete error is corrected by cluster analysis. If Betti-1 is significant, the periodic error is suppressed by frequency domain filtering. Sp4.3: Dynamically adjust INS state estimates based on the selected strategy to generate corrected position and velocity.

5. The aviation positioning method based on inertial navigation according to claim 1, characterized in that: The fusion prediction result and correction result in the Sp5 further include the following contents: Sp5.1: Fusion of VIF predicted positions via Kalman filtering ,speed Position and velocity after correction with ATF; Sp5.2: Update the dynamic weight of VIF according to the fusion result to achieve closed-loop optimization of prediction and correction.

6. The aviation positioning method based on inertial navigation according to claim 2, characterized in that: The joint optimization in step Sp2.3 further includes introducing the aircraft's airspeed data as a constraint to adjust the VIF bandwidth , real-time optimization through gradient descent , ensuring VIF’s prediction accuracy for highly dynamic flights.

7. The aviation positioning method based on inertial navigation according to claim 4, characterized in that: The step Sp4 further includes calculating the error distribution The topological persistence is used to identify abnormal error points. After removing the abnormal points, the topological features are recalculated and the filtering strategy is updated.

8. An aviation positioning method based on inertial navigation according to any one of claims 1 to 7, characterized in that: The hardware components of the aviation positioning method include: Inertial Measurement Unit (IMU): includes a three-axis accelerometer and a three-axis gyroscope, which is used to collect the aircraft's acceleration data in real time and angular velocity data ; Embedded processor: Equipped with at least 1GHz main frequency and floating-point unit, used to perform the construction of virtual inertial field (VIF), error distribution calculation and real-time operation of adaptive topology filter (ATF). The embedded processor realizes the calculation of radial basis function (RBF) kernel in Sp2 and the topological feature extraction of persistent homology analysis in Sp4 through hardware acceleration algorithm. Storage module: The capacity is not less than 4GB, used to store historical motion data within the time window and error distribution , support dynamic update of VIF; Data interface: supports data transmission with a sampling frequency of at least 100 Hz to ensure real-time interaction between IMU data and the processor; Auxiliary sensor module: includes airspeed sensor and magnetic compass, used to collect aircraft airspeed data and direction data, as the VIF bandwidth in Sp2 Optimization constraints; FPGA accelerator: Equipped with parallel computing units, it is used to accelerate the topological filtering strategy selection of ATF in Sp4 and the fusion calculation in Sp5. The processing time does not exceed 5ms / cycle, and the FPGA accelerator implements error distribution through hardware description language (HDL) Cluster analysis and frequency domain filtering; Power management unit: supports at least 10W power consumption and provides stable power supply for IMU, processor and FPGA.

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