An aviation positioning method based on inertial navigation

Abstract

The present invention provides an aviation positioning method based on inertial navigation, which relates to the field of satellite navigation technology. The method collects acceleration data and angular velocity data of an aircraft in real time through an inertial navigation system. Based on the acceleration data and angular velocity data, a virtual inertial field is constructed to characterize the dynamic motion trend of the aircraft. The position and velocity of the aircraft are predicted based on the virtual inertial field and compared with the position and velocity measured by the inertial navigation system to generate an error distribution. The topological structure of the error distribution is analyzed using an adaptive topological filter, and the filter parameters are adaptively adjusted to correct the accumulated error of the inertial navigation system. The virtual inertial field prediction result and the adaptive topological filter correction result are integrated to output the real-time position and velocity estimation of the aircraft. The method can dynamically adapt to complex flight conditions. The ATF surpasses the limitation of traditional filters on the linear Gaussian error assumption through topological data analysis, significantly improving the intelligence and accuracy of error correction.

Description

Technical Field

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

[0002] According to Chinese publication number "CN119354178A," an airborne multi-sensor integrated navigation and positioning method, device, equipment, and medium are disclosed, relating to the field of aviation navigation technology. The method includes: combining a Beidou navigation system, an altimeter, and a radio navigation system with an inertial navigation system. Each combination outputs observations through subfilters. The observations output by each subfilter are fused with the predicted values ​​of the inertial navigation system to output a positioning result. Fault detection and repair are performed on the data output by the inertial navigation system, Beidou navigation system, and altimeter. The observations output by each subfilter are individually tested for anomalies using state parameter estimates and residual vectors, and detected anomalies are repaired using an anti-error filtering method. After the observations output by each subfilter are individually tested for anomalies and repaired, new state parameter estimates are calculated, and anomaly detection is performed on the subfilter's dynamic model based on the new state parameter estimates. This solution is beneficial for improving the fault tolerance of integrated navigation and positioning.

[0003] According to a method for evaluating the error envelope performance of an aviation navigation network take-off and landing guidance system disclosed in China with the publication number "CN119199912A", it relates to the field of satellite navigation technology, 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 method for evaluating the error envelope performance of an aviation navigation network take-off and landing guidance system, which is beneficial to the selection of a specific error envelope model in integrity evaluation, and can help the satellite-based precision take-off and landing guidance system integrity monitoring system to relatively easily obtain a lower protection level, thereby improving the availability of the system.

[0004] The above patent documents and prior art have the following technical problems when used:

[0005] Problem 1: Traditional inertial navigation systems (INS) rely on accelerometer and gyroscope data to calculate position and velocity through integration. However, due to sensor noise and bias, errors accumulate rapidly over time. Especially without external auxiliary signals (such as GPS), errors can reach several kilometers after long-term flight. The positioning error of traditional INS may exceed 5,000 meters, which cannot meet the high-precision navigation requirements of long-range flight missions. Existing methods generally assume linear motion models or Gaussian error distributions, which are difficult to adapt to complex nonlinear flight conditions. This results in limited error correction effectiveness and severely restricts navigation reliability and safety.

[0006] Problem two: Traditional INS systems often cannot achieve real-time response and highly robust positioning in highly dynamic flight scenarios (such as turbulence, high-speed maneuvers, or sharp turns) due to computational complexity and the limitation of relying solely on inertial data. The software computational efficiency of existing methods is low, making it difficult to meet real-time requirements, and they lack the ability to dynamically adapt to environmental changes, limiting their practical application scope. Summary of the Invention

[0007] Technical problems solved

[0008] In view of the shortcomings of the existing technology, the present invention provides an aviation positioning method based on inertial navigation, which solves the following problems:

[0009] 1. The traditional INS has a problem that the error accumulation increases rapidly when there is no external auxiliary signal, making it difficult to meet the positioning requirements of long-term flight;

[0010] 2. The existing INS system lacks real-time performance and robustness in highly dynamic environments and is difficult to adapt to extreme flight conditions.

[0011] Technical Solution

[0012] To achieve the above objectives, the present invention is implemented through the following technical solutions: an aviation positioning method based on inertial navigation, the aviation positioning method comprising the following steps:

[0013] Sp1: Real-time acquisition of aircraft acceleration and angular velocity data through the inertial navigation system (INS);

[0014] Sp2: Based on the acceleration data and angular velocity data, a virtual inertial field (VIF) is constructed to characterize the dynamic motion trend of the aircraft;

[0015] Sp3: Predicting the aircraft's position and velocity based on the virtual inertial field (VIF) and comparing them with the position and velocity measured by the inertial navigation system (INS) to generate an error distribution;

[0016] 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 (INS);

[0017] 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.

[0018] Preferably, the construction of the virtual inertial field (VIF) in step Sp2 further includes the following steps:

[0019] Sp2.1: Collect acceleration within the preset time window and angular velocity , forming a dynamic data set ;

[0020] Sp2.2: Validating the Dataset Using Radial Basis Function (RBF) Perform nonlinear mapping to generate a virtual inertia field:

[0021]

[0022] in, is the historical position estimate, is the dynamic weight, is the adaptive bandwidth, is the spatial position;

[0023] 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 moment state and position of the aircraft ,speed , serves as a reference for INS integration to minimize the deviation between VIF prediction and actual motion.

[0024] Preferably, the generation of the error distribution in step Sp3 specifically includes:

[0025] Sp3.1: Based on INS data, obtain the measured position by isomorphic integral calculation and speed ;

[0026] Sp3.2: Using VIF to predict the next moment's position and speed ;

[0027] Sp3.3: Calculate the error vector , and generate the error distribution within the time window .

[0028] Preferably, the adaptive topology filter (ATF) in step Sp4 further includes the following contents:

[0029] 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;

[0030] Sp4.2: Adaptively selects filtering strategies based on topological features. If Betti-0 is dominant, cluster analysis is used to correct discrete errors. If Betti-1 is significant, frequency domain filtering is used to suppress periodic errors.

[0031] Sp4.3: Dynamically adjust the INS state estimate based on the selected strategy to generate corrected position and velocity.

[0032] Preferably, the fusion prediction result and correction result in Sp5 further include the following contents:

[0033] Sp5.1: Fusion of VIF predicted positions via Kalman filtering ,speed Position and velocity after correction with ATF;

[0034] Sp5.2: Update the dynamic weight of VIF based on the fusion result , achieving closed-loop optimization of prediction and correction.

[0035] Preferably, the joint optimization in step Sp2.3 further includes introducing the aircraft's airspeed data as a constraint condition to adjust the VIF bandwidth , real-time optimization through gradient descent method , ensuring VIF’s prediction accuracy for highly dynamic flights.

[0036] Preferably, the step Sp4 further includes calculating the error distribution The topological persistence is determined, abnormal error points are identified, and after removing the abnormal points, the topological features are recalculated and the filtering strategy is updated.

[0037] Preferably, the hardware components of the aerial positioning method include:

[0038] Inertial Measurement Unit (IMU): includes a three-axis accelerometer and a three-axis gyroscope, used to collect aircraft acceleration data in real time and angular velocity data ;

[0039] Embedded processor: Equipped with a main frequency of at least 1GHz and a floating-point arithmetic unit, it is used to perform the construction of the virtual inertial field (VIF), error distribution calculation, and real-time operation of the adaptive topology filter (ATF). The embedded processor uses hardware acceleration algorithms to implement the calculation of the radial basis function (RBF) kernel in Sp2 and the topological feature extraction of persistent homology analysis in Sp4;

[0040] 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;

[0041] 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;

[0042] Auxiliary sensor module: includes airspeed sensor and magnetic compass, used to collect aircraft airspeed data and direction data as VIF bandwidth in Sp2 Optimization constraints;

[0043] FPGA accelerator: Equipped with a parallel computing unit, it is used to accelerate the topology 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;

[0044] Power management unit: Supports at least 10W power consumption and provides stable power supply for the IMU, processor, and FPGA.

[0045] Beneficial effects

[0046] The present invention provides an aviation positioning method based on inertial navigation, which has the following beneficial effects:

[0047] This invention optimizes the performance of inertial navigation systems (INS) through the synergistic effect of a virtual inertial field (VIF) and an adaptive topology filter (ATF). The VIF utilizes nonlinear mapping and dynamic weight optimization techniques using a radial basis function (RBF) kernel to accurately characterize the aircraft's dynamic motion trends. The ATF, based on topological data analysis (TDA), intelligently identifies and corrects error patterns, effectively overcoming the rapid growth of cumulative errors in traditional INS systems without external auxiliary signals (such as GPS). The VIF's nonlinear mapping overcomes the traditional method's reliance on linear motion models, enabling dynamic adaptation to complex flight conditions. The ATF, through topological data analysis, transcends the linear Gaussian error assumptions of traditional filters (such as the Kalman filter), significantly improving the intelligence and accuracy of error correction. Compared to the several-kilometer error often associated with traditional INS systems, this increased accuracy significantly enhances navigation reliability and safety during long-duration flights, providing strong technical support for long-range missions.

[0048] 2. The present invention combines the efficient parallel computing capabilities of an FPGA accelerator with the environmental adaptability of auxiliary sensor modules. The FPGA accelerates complex algorithms through hardware optimization, persistent coherence analysis, and filtering strategy selection to ensure real-time performance, with a processing time of no more than 5 milliseconds per cycle. The auxiliary sensor dynamically adjusts the VIF parameters, enabling the system to quickly adapt to changes in the flight environment. The hardware optimization design of the FPGA accelerator significantly improves computing efficiency, enabling the system to achieve real-time response in highly dynamic scenarios. The dynamic coupling mechanism between the auxiliary sensor and the VIF breaks through the limitations 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 in military and commercial aviation that require extremely high stability and reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 A diagram showing the steps of the method of the present invention;

[0050] Figure 2 This is a hardware structure diagram of the method of the present invention;

[0051] Figure 3 This is a graph showing the change of positioning error over time according to the present invention;

[0052] Figure 4 A comparison diagram of the true trajectory and the estimated trajectory of the present invention;

[0053] Figure 5 This is a scatter plot of error distribution of the present invention. DETAILED DESCRIPTION

[0054] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention. Specific embodiment one:

[0056] like Figures 1 to 5 As shown, an aviation positioning method based on inertial navigation includes the following steps:

[0057] Sp1: The aircraft's acceleration and angular velocity data are collected in real time through the inertial navigation system (INS). The accelerometer measures the acceleration of the aircraft in three orthogonal directions. , the gyroscope measures the angular velocity around three axes , the data acquisition 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;

[0058] Sp2: Based on the acceleration data and angular velocity data, a virtual inertia field (VIF) is constructed to characterize the dynamic motion trend of the aircraft. The construction of the virtual inertia field (VIF) further includes the following steps:

[0059] Sp2.1: In the preset time window Internally, collect acceleration and angular velocity , forming a dynamic data set ,The length of the time window is usually a few seconds, and the specific length is adjusted according to the ,dynamics of the aircraft;

[0060] Sp2.2: Validating the Dataset Using Radial Basis Function (RBF) Perform nonlinear mapping to generate a virtual inertia field:

[0061]

[0062] in, For historical position estimation; is the dynamic weight, which represents the contribution of each historical data point; For adaptive bandwidth, control the smoothness of VIF; is the spatial position;

[0063] Sp2.3: Jointly optimize based on the real-time motion characteristics of the aircraft, such as the rate of change of acceleration and angular velocity and ,The optimization method introduces airspeed data (collected by auxiliary sensor module) as a constraint condition, and uses gradient descent method to adjust in real time and , VIF is based on the currently measured acceleration and angular velocity , predict the next moment state and position of the aircraft ,speed , as a reference for INS integration to minimize the deviation between VIF prediction and actual motion. The joint optimization further includes introducing the aircraft's airspeed data as a constraint to adjust the VIF bandwidth , real-time optimization through gradient descent method , ensuring VIF's prediction accuracy for highly dynamic flight. VIF provides predictions of the aircraft's future state through nonlinear modeling and dynamic optimization, making up for the limitations of traditional INS that relies solely on integration;

[0064] Sp3: Predict the aircraft's position and velocity based on the virtual inertial field (VIF), compare them with the position and velocity measured by the inertial navigation system (INS), and generate an error distribution. The generation of the error distribution specifically includes:

[0065] Sp3.1: Acceleration based on INS data collection and angular velocity , isomorphic integral calculation to obtain the measured position and speed , the calculation formula is:

[0066]

[0067] in: is the velocity vector calculated by INS, which changes with time t and is in m / s; is the initial time, which is the time when the flight starts; is the current time point; is the acceleration vector, which changes with time and is expressed in m / s 2 , provided by IMU; is the time differential, which represents the time increment in the integral; is the initial velocity vector in m / s, usually input externally or set to zero;

[0068]

[0069] in: is the position vector calculated by INS, which changes with time t and is in meters; is the initial time; t is the current time point; is the velocity vector, which changes with time Change, in m / s, is calculated by the above formula; is the time differential; is the initial position vector, in meters, usually input externally or set to zero;

[0070] Sp3.2: Using VIF to predict the next moment's position and speed ;

[0071] Sp3.3: Calculate the error vector , and generate the error distribution within the time window , the error distribution reflects the characteristics of the INS cumulative error and provides input for the adaptive filtering;

[0072] 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 (INS). The adaptive topology filter (ATF) further includes the following:

[0073] Sp4.1: Error distribution Persistent homology analysis is applied to extract topological features, including the number of connected components (Betti-0) and the number of rings (Betti-1). The number of connected components (Betti-0) represents the discrete clusters in the error distribution; the number of rings (Betti-1) represents the periodic structure in the error distribution.

[0074] Sp4.2: Adaptively select filtering strategies based on topological features. If Betti-0 is dominant (discrete error is significant), correct the discrete error through cluster analysis (such as K-means). If Betti-1 is significant (periodic error is significant), suppress the periodic error through frequency domain filtering (such as Fourier transform).

[0075] Sp4.3: Dynamically adjust INS state estimates based on the selected strategy, generate corrected position and velocity, and calculate error distribution Topological persistence, identifying abnormal error points, eliminating abnormal points, recalculating topological features and updating filtering strategies. ATF intelligently identifies error patterns through topological data analysis (TDA) to achieve targeted corrections.

[0076] 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 estimate of the aircraft. The fusion of the prediction results and the correction results further includes the following:

[0077] Sp5.1: Fusion of VIF predicted positions via Kalman filtering ,speed Position and velocity after ATF correction:

[0078] Kalman filter model:

[0079] Measurement update: Combine VIF prediction and ATF correction to optimize state estimation;

[0080] Sp5.2: Update the dynamic weight of VIF based on the fusion result , realize closed-loop optimization of prediction and correction, and update the dynamic weight of VIF according to the fusion results :

[0081]

[0082] in, is the error function between prediction and fusion results, is the learning rate;

[0083] Through fusion and optimization, the output position and velocity estimates are ensured to have both prediction accuracy and correction stability.

[0084] Specific working process and operation logic: IMU startup, real-time acquisition and , data is transmitted to the embedded processor through the data interface, the initial position and speed Set by external input or default value; IMU collects data at a frequency of at least 100Hz, and 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 ,predict and , the processor calculates based on INS data and , compare the VIF prediction results and generate error distribution The processor performs persistent homology analysis on 𝐸E, extracts topological features, selects filtering strategies based on the features, corrects INS state estimation, removes outliers and updates the strategy, uses Kalman filtering to fuse VIF predictions and ATF correction results, outputs the final p and v, updates VIF weights, and forms a closed-loop optimization. The system executes the above steps in a loop and outputs high-precision position and velocity estimates in real time. Specific embodiment two:

[0086] like Figures 1 to 5 As shown, according to the content of the above specific embodiment, the following content is further disclosed: Preferably, the hardware composition of the aerial positioning method includes:

[0087] Inertial Measurement Unit (IMU): includes a three-axis accelerometer and a three-axis gyroscope, used to collect aircraft acceleration data in real time and angular velocity data By integrating the acceleration, the aircraft's speed and position changes can be calculated. The data from the three-axis gyroscope is used to track the aircraft's attitude, such as pitch, yaw, and roll. The IMU sampling frequency must be at least 100Hz to ensure that rapidly changing motion information is captured in highly dynamic flight scenarios and to avoid data omissions. Aviation-grade IMUs typically require the accelerometer's bias stability to be better than 0.01g and the gyroscope's bias stability to be better than 0.1° / h. This high-precision and low-noise feature can significantly reduce the impact of cumulative errors on positioning accuracy. IMUs are widely used in inertial navigation systems (INS) and are key components for autonomous positioning of aircraft, drones, missiles, and other aircraft.

[0088] Embedded processor: Equipped with a main frequency of at least 1 GHz and a floating-point unit, it is used to perform virtual inertial field (VIF) construction, error distribution calculation, and real-time operation of the adaptive topology filter (ATF). The embedded processor uses hardware-accelerated algorithms to calculate the radial basis function (RBF) kernel in Sp2 and extract topological features for persistent homology analysis in Sp4. With a main frequency of at least 1 GHz and a floating-point unit, it supports high-performance real-time computing. Responsible for executing virtual inertial field (VIF) construction, error distribution calculation, and real-time operation of the adaptive topology filter (ATF), the processor is the computational core of the system. The processor uses the radial basis function (RBF) kernel to perform nonlinear mapping on 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 power. The processor compares INS measurement data with VIF predictions, calculates error vectors, and generates error distributions. This distribution provides the basis for subsequent filtering and optimization. The processor performs persistent coherence analysis to extract topological features from the data and selects appropriate filtering strategies based on these features to ensure the robustness of the positioning results. To improve computational 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 these tasks within each sampling period (approximately 10ms) to ensure the system's real-time responsiveness.

[0089] Storage module: The capacity is not less than 4GB, used to store historical motion data within the time window and error distribution , supports dynamic update of VIF, capacity is not less than 4GB, supports high read and write speed, and stores historical movement data within the time window and error distribution Provide data support for dynamic updates of VIF; for historical motion data :Includes acceleration, angular velocity and timestamp, used for VIF construction and update; for error distribution : Record error vectors and support ATF topology analysis and filtering optimization. The storage module must have high read and write speeds to meet the needs of real-time data updates and fast access. A ring buffer or sliding window mechanism is used to ensure dynamic management of data within the time window, always retaining the latest data and overwriting expired data. Depending on system requirements, high-speed flash memory (such as NAND Flash) can be selected for data persistence, or DRAM for faster access speeds. The storage module is used in aviation systems to support real-time data processing and historical data analysis. It is a key link in the dynamic adjustment algorithm. The storage module provides the necessary data foundation for VIF and ATF, ensuring that the system can perform adaptive optimization based on historical information.

[0090] Data interface: Supports data transmission with a sampling frequency of at least 100Hz to ensure 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 losslessly. It uses 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 must support a clock synchronization mechanism to ensure the time consistency between IMU data and processor calculations to avoid data offset. In an aviation environment, the data interface must have an anti-electromagnetic interference design (such as a shielded cable or differential signal) to ensure transmission reliability. The data interface ensures efficient communication between hardware components and is the basis for system collaboration.

[0091] Auxiliary sensor module: includes airspeed sensor and magnetic compass, used to collect aircraft airspeed data and direction data as VIF bandwidth in Sp2 The optimization constraints are: the airspeed sensor measures the speed of the aircraft relative to the air and outputs airspeed data, which is used to dynamically adjust the bandwidth of the VIF. To adapt to the motion characteristics at different flight speeds, the magnetic compass measures the aircraft's magnetic heading and provides direction information to assist in the initialization and directionality 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 positioning accuracy. The auxiliary sensor provides additional environmental information in different flight phases (such as takeoff, cruise, and landing) to enhance 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.

[0092] FPGA accelerator: Equipped with a parallel computing unit, it is used to accelerate the topology 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, FPGA accelerator is equipped with parallel computing units, the processing time does not exceed 5ms / cycle, accelerates the topological filtering strategy selection and fusion calculation of ATF, improves system performance, FPGA uses parallel processing units to accelerate the topological feature extraction and error distribution in persistent homology analysis For tasks such as cluster analysis and frequency domain filtering, dedicated circuits are designed using hardware description languages ​​(such as VHDL or Verilog) to efficiently execute computationally intensive tasks, ensuring processing time is controlled within 5ms. FPGAs act as coprocessors, communicating with embedded processors via high-speed buses (such as PCIe), receiving task instructions and returning results. FPGAs are commonly used in aviation navigation systems for real-time signal processing and complex algorithm acceleration, significantly improving computational efficiency. FPGA accelerators reduce the burden on embedded processors through hardware optimization, ensuring real-time performance even under high system loads.

[0093] Power Management Unit: Supports at least 10W power consumption and provides stable power supply for IMU, processor and FPGA. The power management unit supports at least 10W power consumption and provides stable and reliable power supply for IMU, embedded processor and FPGA. Through the voltage regulator and filtering circuit, it ensures the stability of the power supply voltage and reduces the impact of power supply noise on sensor and processor performance. It supports dynamic power consumption adjustment and optimizes energy consumption according to system load. It is particularly suitable for battery-powered devices such as drones. It has overcurrent and overvoltage protection mechanisms to ensure safe operation of the system under abnormal conditions.

[0094] Working Mechanism: The IMU collects raw data and transmits it to the embedded processor via a data interface. The processor then constructs the VIF using historical data from the storage module and optimizes parameters based on auxiliary sensor data. An FPGA accelerator handles the complex ATF calculations, ensuring real-time performance. A power management unit supports all components. The FPGA accelerator's efficient parallel computing and the auxiliary sensor module's environmental adaptability ensure that this hardware architecture not only meets real-time requirements but also significantly improves the system's computing power and positioning accuracy, making it particularly suitable for highly dynamic flight scenarios. Specific embodiment three:

[0096] like Figures 1 to 5 As shown, based on the content in the above specific embodiments, the following contents are further disclosed:

[0097] To further verify the feasibility and technical features of the technical solution of this application, an experiment was designed to compare the positioning accuracy of the dumb 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 its credibility. The specific experiments include the following:

[0098] Simulated flight scenario:

[0099] Tools and Data: The open-source flight simulator JSBSim was used to generate realistic flight paths, including straight flight, turns (shallow and sharp), climbs, descents, and turbulence scenarios, simulating actual aviation missions.

[0100] Data generation: The simulator outputs real position, velocity, and attitude data, as well as IMU data (acceleration and angular velocity), adding different noise levels (such as Gaussian white noise with standard deviations of 0.01g and 0.1° / s) to test the system's adaptability to sensor quality;

[0101] Flight duration: Each set of experiments ran for 10 hours to simulate long-duration flight conditions;

[0102] The system is implemented as follows:

[0103] Standard INS: Based on IMU data, position and velocity are calculated through numerical integration without any error correction mechanism, reflecting the drift characteristics of traditional INS:

[0104]

[0105] in: is the velocity vector calculated by INS, which changes with time t and is in m / s; is the initial time, which is the time when the flight starts; is the current time point; is the acceleration vector, which changes with time and is expressed in m / s 2 , provided by IMU; is the time differential, which represents the time increment in the integral; is the initial velocity vector in m / s, usually input externally or set to zero;

[0106]

[0107] in: is the position vector calculated by INS, which changes with time t and is in meters; is the initial time; t is the current time point; is the velocity vector, which changes with time Change, in m / s, is calculated by the above formula; is the time differential; is the initial position vector, in meters, usually input externally or set to zero;

[0108] Traditional INS + dynamic model: This approach uses a Kalman filter combined with a predefined aircraft dynamic model (such as one assuming constant acceleration or simple dynamics based on thrust and drag calculations) for error correction. The dynamic model relies on aircraft parameters (such as mass and thrust) and performs well in low-dynamic scenarios, but may fail in high-dynamic scenarios due to model inaccuracies. The Kalman filter update formula (simplified to two steps: prediction and update) is:

[0109] predict:

[0110]

[0111] in:

[0112] The state prediction vector (including position and velocity) at the current moment k, based on the estimate at the previous moment;

[0113] is the state transfer matrix, describing the system dynamics (e.g., constant acceleration model);

[0114] is the state estimation vector at the previous moment 𝑘−1k−1;

[0115] The control input matrix maps the control quantity to the state;

[0116] For control input vectors (e.g. thrust), the units depend on the model;

[0117] renew:

[0118]

[0119] is the state estimation vector at the current time k, which integrates prediction and measurement;

[0120] is the Kalman gain matrix, balancing the weights of prediction and measurement;

[0121] is the measurement vector (here is the INS integration result);

[0122] is the measurement matrix, which maps the state to the measurement space;

[0123] is the predicted state vector;

[0124] It relies on the accuracy of the dynamic model and is limited by nonlinear errors in highly dynamic scenes.

[0125] This application method:

[0126] VIF construction: Using historical IMU data, a virtual inertial field is generated through the RBF kernel to predict the position and velocity at the next moment;

[0127]

[0128] in: : Virtual inertia field function, changes with position and time Change, in units of dimensionless field values;

[0129] The summation symbol, Historical data points are accumulated;

[0130] No. The dynamic weight of each historical data point is dimensionless and adjusted by the optimization algorithm;

[0131] is an exponential function with the base being the natural logarithm ;

[0132] is the current position x and the historical position The Euclidean distance of , in m;

[0133] 2 is a constant, the scaling factor in the denominator;

[0134] is the square of the adaptive bandwidth, in units of , the range of influence of the control field;

[0135] ATF correction: error distribution Apply persistent homology analysis to extract topological features (Betti-0 and Betti-1) and adaptively select filtering strategies (such as cluster analysis or frequency domain filtering);

[0136] Error distribution:

[0137]

[0138] in:

[0139]

[0140] in: is the error distribution set, representing the error vectors at multiple time points;

[0141] is a collection symbol, including Error vector ;

[0142] is the error vector, which changes with time change;

[0143] is the position vector measured by INS, in meters;

[0144] is the position vector predicted by VIF, in meters;

[0145] is the velocity vector measured by INS, in m / s;

[0146] is the velocity vector predicted by VIF, in m / s;

[0147] The VIF prediction and ATF correction results are fused through Kalman filtering to output the final estimate, which relies on external signals or predefined models, is data-driven, and adapts to high-dynamic scenarios.

[0148] Run and compare: In each set of flight scenarios, run three systems, record the position error (Euclidean distance) and velocity error (vector difference), and calculate it by root mean square error (RMSE):

[0149]

[0150] in:

[0151] is the root mean square error, a statistical indicator for measuring positioning accuracy, with the unit being m;

[0152] is the averaging factor, is the total number of time steps;

[0153] For the summation symbol, for all time steps From 1 to Accumulation

[0154] To estimate the position vector, over time Change, in m;

[0155] is the real position vector, over time Change, unit is m.

[0156] The error growth curve over time focuses on the performance after 10 hours and the error performance in specific segments (such as high-dynamic turns) to verify the contributions of VIF and ATF.

[0157] The results are analyzed as follows:

[0158] Standard INS: The error increases quadratically with time and may reach more than 5000 meters after 10 hours because there is no correction mechanism;

[0159] Traditional INS + dynamic model: The error is small in low-dynamic scenarios (100-500 meters), but in high-dynamic scenarios, the error may reach 1000 meters due to model inaccuracy;

[0160] This application method: Through VIF prediction and ATF correction, the positioning error is controlled within 15 meters during a 10-hour flight, which is significantly better than other methods.

[0161] The key indicator comparison table is as follows:

[0162] System Type 10-hour positioning error (mean, m) Maximum error (m) High dynamic scene performance Standard INS 5000+ 10000+ Fast drift Traditional INS+dynamic model 100-500 1000 Limited and highly model-dependent This application method (VIF+ATF) <15 <50 Robust, error stable

[0163] This application does not rely on external signals or predefined dynamic models. VIF learns motion trends through data-driven learning, and ATF intelligently corrects errors through topological analysis. Different from the limitations of traditional methods, this application is more robust in high-dynamic scenarios, reflecting the synergistic effect of VIF and ATF.

[0164] This experiment quantitatively compares the positioning accuracy of this proposed method with existing systems through simulated flight scenarios, validating the effectiveness of its core technologies (VIF and ATF). The results are expected to demonstrate the high accuracy and robustness of this proposed method without external auxiliary signals, making it particularly suitable for navigation missions in military aviation and extreme environments. The experimental design accounted for varying noise levels and dynamic conditions to ensure the broad applicability and statistical significance of the results. Specific embodiment four:

[0166] like Figures 1 to 5 As shown, based on the content in the above specific embodiments, the following contents are further disclosed:

[0167] To further verify the feasibility of this application, the following are examples of actual applications of this application, as shown below:

[0168] Case 1: Long-distance flight navigation in military covert reconnaissance missions:

[0169] During a covert military reconnaissance mission, an unmanned reconnaissance aircraft was tasked with conducting a 12-hour flight in hostile airspace. The mission required the aircraft to maintain high-precision positioning without GPS signals to ensure accurate geotagging of the reconnaissance data. Due to strong electromagnetic interference deployed by the enemy, traditional INS systems exhibited rapid error accumulation in simulation tests, reaching several kilometers after eight hours, making them unable to meet the mission requirements. Implementing the technical solution of this application, the system first uses an inertial measurement unit (IMU) to collect real-time aircraft acceleration and angular velocity data at a 100Hz frequency. This data is received by an embedded processor and stored in a 4GB memory module. The processor uses this data to construct a virtual inertial field (VIF). Using a radial basis function (RBF) kernel, it nonlinearly maps historical motion data to generate a dynamic field to predict the aircraft's position and velocity trends. Simultaneously, auxiliary data from an airspeed sensor and magnetic compass are used to optimize the VIF's bandwidth and weighting to ensure the prediction is suitable for the reconnaissance aircraft's high-speed cruising conditions. The system then compares the VIF predictions with the position and velocity calculated by the INS integral to generate an error distribution, which is then analyzed by an adaptive topology filter (ATF). The ATF uses persistent homology analysis to extract topological features of the error distribution and discovers significant periodic components (high Betti-1 values) in the error. Frequency-domain filtering is then used to suppress these periodic errors while also removing outliers to improve correction accuracy. The FPGA accelerator plays a key role in this process, completing topological analysis and filtering strategy selection within 5 milliseconds through parallel computing units, ensuring real-time performance. Finally, a Kalman filter integrates the VIF predictions and ATF correction results to output real-time position and velocity estimates. The entire process is supported by a stable power supply from the power management unit. Actual flight data shows that positioning error remained within 18 meters throughout the 12-hour mission, far exceeding the 6,000-meter error of a traditional INS. This successfully completed the reconnaissance mission, ensuring the geographic accuracy of the data and mission confidentiality.

[0170] Case 2: High-latitude navigation during polar scientific research flights:

[0171] During a polar expedition, a research aircraft was required to conduct a 10-hour flight in the Arctic to collect ice thickness and climate data. Due to geomagnetic anomalies and auroral interference in high-latitude regions, GPS signals were frequently interrupted. Simulations using a traditional INS-based dynamic model showed errors exceeding 500 meters after 6 hours, failing to meet the high-precision positioning requirements for the expedition data. Using the proposed method, the system collects aircraft acceleration and angular velocity data via an IMU, which is then transmitted via a data interface to an embedded processor. The processor constructs a VIF using historical data stored in a storage module, generates a continuous field using an RBF kernel, and dynamically adjusts the bandwidth and weighting based on airspeed sensor data to predict the aircraft's motion under the cold and turbulent polar conditions. Due to the frequent turbulence during polar flight, the error distribution between the VIF predictions and the INS measurements exhibits complex patterns. The ATF then intervenes, using topological data analysis to identify discrete clusters (high Betti-0 values) and periodic structures (high Betti-1 values) in the errors. For discrete clusters, ATF corrects instantaneous errors through cluster analysis; for periodic structures, frequency domain filtering is used to suppress long-term drift. The FPGA accelerator completes these calculations in less than 5 milliseconds, ensuring the system's real-time responsiveness in turbulence. During the fusion stage, the Kalman filter integrates the VIF prediction and ATF correction results, and updates the VIF weights through closed-loop optimization, allowing the system to adapt to the dynamic changes in the polar environment. The entire system is provided with stable power supply by the power management unit to ensure continuous operation under low temperature conditions. Ultimately, the positioning error was controlled within 15 meters during the 10-hour flight, which significantly improved the spatial resolution of the scientific research data compared to the 500-meter error of traditional methods, ensuring the scientific value of the mission.

[0172] Case 3: High-dynamic logistics distribution of commercial cargo drones:

[0173] In a highly dynamic logistics delivery mission involving a commercial cargo drone, the drone was required to carry out a six-hour cargo delivery in an urban environment. The route involved frequent takeoffs and landings, sharp turns, and high-altitude turbulence. The error of a traditional INS system rapidly increased in this highly dynamic scenario, reaching 800 meters after four hours, threatening delivery safety. Implementing this method, the drone's IMU collected acceleration and angular velocity data at a 100Hz frequency. This data was received and stored by an embedded processor. The processor used this data to construct a VIF, generating a dynamic field using an RBF kernel. This prediction model was optimized by combining airspeed sensor and magnetic compass data to accurately capture the drone's motion trends in sharp turns and turbulence. After generating the error distribution, the ATF analyzed its topology and found that the errors in this highly dynamic scenario exhibited a mixture of discrete clusters and periodicity. The ATF then adaptively selected a strategy combining cluster analysis and frequency-domain filtering to correct for both transient and long-term errors. The FPGA accelerator supported the ATF's real-time processing through parallel computing, ensuring that complex calculations were completed within 5 milliseconds, meeting the drone's rapid response requirements. The Kalman filter integrates the VIF predictions and ATF corrections to output high-precision position and velocity estimates. It also dynamically adjusts VIF parameters through closed-loop optimization, enabling the system to adapt to the changing conditions of urban environments. The power management unit provides stable power to all components, ensuring continuous operation of the drone under high loads. In actual missions, positioning error remained within 12 meters over a six-hour flight, far exceeding the 800-meter error of traditional INS. This ensures accurate and safe cargo delivery and improves logistics efficiency.

[0174] In the three cases, VIF accurately predicted the aircraft's motion trends in different scenarios (stealth cruising, polar turbulence, and urban high dynamics) through data-driven nonlinear mapping, overcoming the traditional INS's reliance on external signals or predefined models. ATF used topological data analysis to identify complex error patterns and adaptively selected filtering strategies to effectively suppress error accumulation under long-term flight and high-dynamic conditions, demonstrating its intelligence and robustness. FPGA accelerators and auxiliary sensor modules ensured the system's real-time response and environmental adaptability in high-dynamic scenarios, significantly improving its performance in practical applications. The cases showed that positioning errors during long-term flights were controlled within 12-18 meters, far exceeding the hundreds to thousands of meters of errors of traditional methods. The system maintained stable operation under conditions such as turbulence and sharp turns, meeting military, scientific research, and commercial needs.

[0175] It should be noted that, in this document, relational terms such as first and second, etc., are used only 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 "comprises," "comprising," or any other variants thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or device. In the absence of further restrictions, 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.

[0176] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to these embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the appended claims and their equivalents.

Claims

1. An aviation positioning method based on inertial navigation, characterized in that: The aerial positioning method comprises the following steps: Sp1: Real-time acquisition of aircraft acceleration and angular velocity data through the inertial navigation system; Sp2: Based on the acceleration data and angular velocity data, a virtual inertia field is constructed to characterize the dynamic motion trend of the aircraft. The construction of the virtual inertia field 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 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 , the virtual inertial field is based on the currently measured acceleration and angular velocity , predict the next moment state and position of the aircraft ,speed , serves as a reference for the integration of the inertial navigation system to minimize the deviation between the virtual inertial field prediction and the actual motion; Sp3: Predicting the position and velocity of the aircraft based on the virtual inertial field, and comparing them with the position and velocity measured by the inertial navigation system to generate an error distribution; Sp4: Use the adaptive topology filter to analyze the topological structure of the error distribution, adaptively adjust the filter parameters, and correct the accumulated error of the inertial navigation system. The adaptive topology filter further includes the following: 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 selects filtering strategies based on topological features. If Betti-0 is dominant, cluster analysis is used to correct discrete errors. If Betti-1 is significant, frequency domain filtering is used to suppress periodic errors. Sp4.3: Dynamically adjust the state estimate of the inertial navigation system based on the selected strategy to generate corrected position and velocity; Sp5: Fusion of virtual inertial field prediction results and adaptive topology filter correction results to output real-time position and velocity estimates of the aircraft.

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

3. The inertial navigation-based aviation positioning method according to claim 1, characterized in that: The fusion prediction result and correction result in Sp5 further include the following contents: Sp5.1: Position predicted by fusing virtual inertial field through Kalman filtering ,speed and the position and velocity after correction using the topological filter; Sp5.2: Update the dynamic weight of the virtual inertial field based on the fusion results , achieving closed-loop optimization of prediction and correction.

4. The inertial navigation-based aviation positioning method according to claim 1, wherein: The joint optimization in step Sp2.3 further includes introducing the aircraft's airspeed data as a constraint condition to adjust the virtual inertial field bandwidth , real-time optimization through gradient descent method , ensuring the prediction accuracy of the virtual inertial field for high dynamic flight.

5. The aerial positioning method based on inertial navigation according to claim 1, characterized in that: The step Sp4 further includes calculating the error distribution The topological persistence is determined, abnormal error points are identified, and after removing the abnormal points, the topological features are recalculated and the filtering strategy is updated.

6. The aviation positioning method based on inertial navigation according to any one of claims 1 to 5, characterized in that: The hardware components of the aerial positioning method include: Inertial measurement unit: includes a three-axis accelerometer and a three-axis gyroscope, used to collect aircraft acceleration data in real time and angular velocity data ; Embedded processor: Equipped with a main frequency of at least 1GHz and a floating-point arithmetic unit, it is used to perform the construction of the virtual inertial field, error distribution calculation, and real-time operation of the adaptive topology filter. The embedded processor uses hardware acceleration algorithms to realize the calculation of the radial basis function kernel in Sp2 and the topological feature extraction of the persistent homology analysis in Sp4; Storage module: The capacity is not less than 4GB, used to store historical motion data within the time window and error distribution , supports dynamic update of virtual inertial field; Data interface: supports data transmission with a sampling frequency of at least 100 Hz, ensuring real-time interaction between the inertial measurement unit data and the processor; Auxiliary sensor module: includes airspeed sensor and magnetic compass, used to collect aircraft airspeed data and direction data as the virtual inertial field bandwidth in Sp2 Optimization constraints; FPGA accelerator: Equipped with a parallel computing unit, it is used to accelerate the topology filtering strategy selection of the self-used topology filter 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. Cluster analysis and frequency domain filtering; Power management unit: Supports at least 10W power consumption and provides stable power supply for the inertial measurement unit, processor, and FPGA.

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