Satellite ranging-assisted aircraft trajectory tail end positioning method

Abstract

The invention discloses a satellite ranging-assisted aircraft trajectory tail end positioning method, which comprises the following steps of: S1, positioning the current position of an aircraft by using an inertial navigation system, and calculating the spacing distance between the aircraft and a destination; calculating an estimated error of aircraft positioning based on a position error estimation method of Monte Carlo; s2, judging whether the aircraft enters a destination neighborhood range or not according to the spacing distance, if so, entering step S3, and otherwise, entering step S4; s3, judging whether the pre-estimated error is greater than an end point threshold value or not, if so, entering the step S5, and otherwise, returning to the step S1; s4, judging whether the pre-estimated error is greater than a process threshold value or not, if so, entering the step S5, and otherwise, returning to the step S1; and S5, positioning the aircraft by adopting a single-satellite fusion positioning algorithm based on unscented Kalman filtering, and returning to the step S1 after executing a preset duration.

Description

Technical Field

[0001] The present invention relates to an aircraft positioning technology, and in particular to an aircraft trajectory terminal positioning method assisted by satellite ranging. Background Art

[0002] To ensure accurate arrival of long-range aircraft at their destinations, inertial navigation combined with global navigation satellite systems (GNSS) is often used. However, to reduce reliance on GNSS during flight, adapt to complex electromagnetic environments, and achieve low-cost applications, aircraft navigation and positioning face dual challenges: First, maintaining high-precision navigation to ensure mission effectiveness; second, reducing reliance on navigation signals to ensure accurate positioning even after interference denial. Therefore, research is urgently needed to improve positioning accuracy for long-range aircraft without the support of GNSS.

[0003] In the field of navigation error reduction, satellite positioning assistance is the mainstream technology. However, continuous multi-satellite coordinated positioning consumes a large amount of satellite-to-ground communication resources and poses risks to link stability in highly dynamic scenarios. Furthermore, high-frequency satellite communications increase the probability of aircraft exposure, fundamentally conflicting with the requirements of covert missions. Therefore, minimizing resource consumption and maximizing battlefield concealment while maintaining high accuracy has become a technical bottleneck that urgently needs to be overcome in this field.

[0004] Currently, most research focuses on using simultaneous ranging measurements from multiple satellites to achieve positioning and navigation. This technical solution receives signals from at least four satellites and uses the ranging information to construct a set of equations to calculate the three-dimensional position coordinates and time offset of the user device. Satellite constellations (such as GPS and Beidou) are evenly distributed around the globe to ensure signal coverage. Distance is calculated by using the time difference in signal propagation, and high-precision positioning is achieved by combining data processing algorithms (such as the least squares method and Kalman filtering).

[0005] Simultaneous multi-satellite ranging and positioning technology requires the simultaneous use of communication resources from four or more satellites, which can easily lead to resource congestion during critical periods and make it difficult to meet the needs of simultaneous ranging for numerous aircraft. Furthermore, the receiver must simultaneously process multiple satellite signals, and the RF front-end must support multiple channels, significantly increasing device size and power consumption, hindering long-duration missions. Furthermore, in highly dynamic scenarios, such as hypersonic aircraft, multi-satellite link synchronization is unstable and prone to lock loss, compromising navigation accuracy and reliability.

[0006] Some existing research focuses on the ranging and positioning of ground targets using a single satellite. This involves using a single satellite to perform multiple ranging measurements of the target at multiple times, combining this with the satellite's ephemeris to construct a dynamic spatial arc and calculate the target's position. This technology is typically used to locate fixed ground facilities or stationary targets and is suitable for specific application scenarios, such as ground base stations and fixed monitoring points. However, it cannot be directly applied to the positioning and navigation of mobile targets such as aircraft, limiting its application scenarios. Therefore, further research is needed to fully utilize the one-dimensional ranging information in the one-to-one link between low-orbit satellites and aircraft to assist in improving the accuracy of aircraft trajectory positioning through multiple, short-term sequential measurements. Summary of the Invention

[0007] In response to the above-mentioned deficiencies in the prior art, the satellite ranging-assisted aircraft trajectory terminal positioning method provided by the present invention solves the problems in the existing navigation technology of high resource usage of multiple satellite ranging, poor stability in high-dynamic scenes, and the inability of single satellite time-sharing ranging to adapt to dynamic targets.

[0008] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: A method for positioning an aircraft trajectory end point using satellite ranging assistance is provided, comprising: S1. Use the inertial navigation system to locate the current position of the aircraft and calculate the distance between it and the destination; then calculate the estimated error of the aircraft positioning based on the Monte Carlo position error estimation method; S2. Determine whether the aircraft has entered the vicinity of the destination based on the interval distance. If so, proceed to step S3; otherwise, proceed to step S4. S3, determine whether the estimated error is greater than the endpoint threshold, if so, proceed to step S5, otherwise return to step S1; S4, determine whether the estimated error is greater than the process threshold, if so, proceed to step S5, otherwise return to step S1; S5. Use the single-satellite fusion positioning algorithm based on unscented Kalman filtering to locate the aircraft, and after executing the preset time, return to step S1.

[0009] Furthermore, the method for positioning an aircraft using a single-satellite fusion positioning algorithm based on an unscented Kalman filter includes: S51, discretizing the aircraft nominal trajectory state equation and the single-satellite pseudorange measurement equation; S52. Given the initial state and initial error covariance matrix: in, is the initial state of the aircraft’s position and velocity; is the estimated value of the initial state; is the mathematical expectation operator, which represents the theoretical optimal estimate; T is the transpose; is the initial error covariance matrix, which represents the uncertainty of the initial state estimate; S53. Construct sigma point: in, is the i-th sigma point at time k, i.e. the sampling point; is the mean position and velocity of the aircraft at time k; is the i-th column of the result matrix obtained by calculation in the brackets; n is the number of state dimensions; is the error covariance matrix at time k; is the scale parameter, is the scale parameter; S54. Calculate the system prediction mean: , , in, for The predicted mean of the k+1 time observations obtained by weighted summation; For the general Substitute into the single-star pseudorange measurement equation The predicted measurement values ​​obtained; For the general Substitute into the state equation The predicted sigma point at time k+1 is obtained; is the state equation of the aircraft nominal trajectory; is the acceleration of the aircraft at time k; S55. Calculate the prior prediction value of the state error covariance matrix at time k : in, The predicted sigma point after propagation The mean of the predicted state at time k+1 obtained by weighted average; All are weights; is the prior prediction value of the state error covariance matrix at time k; is the system noise covariance matrix; S56. Calculate the Kalman gain matrix: in, is the Kalman gain matrix at time k+1; is the covariance of the correlation strength between the reaction state and the observation at time k+1; is the prior prediction value of the measurement error covariance matrix at time k+1; is the measurement noise covariance matrix; S57. Calculate the state estimation result and the posterior estimate of the covariance matrix: in, is the estimated value of the state at time k+1; is the measurement value obtained by satellite tracking measurement at time k+1; is the posterior estimate of the covariance matrix at time k+1; is the prior prediction value of the state error covariance matrix at time k+1.

[0010] The beneficial effects of the above technical solution are as follows: the unscented Kalman filter (UKF) can avoid the first-order linearization truncation error of the extended Kalman filter (EKF) for nonlinear systems by accurately propagating the statistical distribution of state quantities through deterministic sampling (Sigma points). Combined with the single-satellite pseudo-range measurement equation and utilizing the state constraints provided by the aircraft kinematic model, the underdetermined positioning problem of single-satellite ranging is transformed into an observable problem in state space, fundamentally solving the adaptability defects of single-satellite positioning of dynamic targets.

[0011] Furthermore, the weights are calculated The expression is: in, and They are The initial value of .

[0012] The beneficial effects of the above technical solution are: the scale parameter in the weight design Control the degree of discreteness between the Sigma point and the mean, and adjust the sampling range to match the nonlinear strength of the system; distribution parameters The introduction of high-order moment information can optimize the probabilistic consistency of covariance weight distribution; the two work together to ensure the Sigma point set's ability to approximate the high-order moments of the state posterior distribution, significantly improving the convergence stability of state estimation in high-maneuverability scenarios.

[0013] Furthermore, the state equation of the aircraft nominal trajectory is The expression is: in, is the nominal displacement vector of the aircraft; is the vehicle nominal acceleration vector; is the vehicle nominal velocity vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The inertial navigation system measures the acceleration of the aircraft in the navigation coordinate system; is the constant drift present in the accelerometer; is the gravitational acceleration vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The expression of the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system is: in, is the transformation matrix from Earth-centered Earth-fixed coordinates to Earth-centered inertial coordinates; is the transformation matrix from the navigation coordinate system to the Earth-centered Earth-fixed coordinate system; is the latitude and longitude of the reference point; and are the reference angles of the Earth's rotation at the initial moment and at time t, respectively; is the angular velocity of the Earth's rotation.

[0014] The beneficial effects of the above technical solution are: the state equation explicitly separates the inertial guidance error term With the real dynamics, establish an analytically modelable noise input channel for Monte Carlo error estimation; coordinate transformation chain Coupled Earth rotation angular velocity , strictly compensate for the cumulative effect of relative rotation between the navigation coordinate system and the inertial coordinate system, and eliminate the frame deviation in long-duration missions.

[0015] Furthermore, the inertial navigation system measures the acceleration of the aircraft in the navigation coordinate system The expression is: in, is the true acceleration of the aircraft; is the acceleration system noise.

[0016] Furthermore, the single-star pseudorange measurement equation The expression is: in, are the position vectors of the satellite and the spacecraft at time i respectively; To find the length of the vector, here we mean to find the distance from the satellite to the spacecraft; is a column vector consisting of the distances from the satellite to the spacecraft measured at three moments; and are the position vectors of the satellite and the spacecraft at time i-1 respectively; and are the position vectors of the satellite and the spacecraft at time i-2, ; is the displacement vector of the aircraft between time i and time i-1; is the displacement vector of the aircraft between time i-1 and time i-2; To measure noise.

[0017] The beneficial effects of the above technical solution are: through the displacement vector By constructing position correlation constraints at adjacent moments, the single-satellite pseudorange measurement value is expanded into a joint space-time observation value. This design utilizes the continuity of spacecraft motion to transform the geometric positioning problem of single-satellite ranging into a state estimation problem with dynamic constraints, which can break through the strong assumptions of traditional single-satellite positioning on the target motion state.

[0018] Furthermore, the expression for calculating the process threshold is: in, is the process threshold; is the maximum position deviation tolerance of the chain-building cone, is the safety chain building factor.

[0019] Furthermore, the expression for calculating the endpoint threshold is: , in, is the endpoint threshold; The final mission landing accuracy requirement; The inertial error accumulation model satisfies the function; is the neighborhood radius; for The terminal safety operation area; is the horizontal speed of the aircraft; It is the measurement interval between two adjacent satellite ranging measurements.

[0020] The beneficial effects of the above technical solution are: process threshold Can directly map the geometric reachability boundary of satellite link building, safety factor Designed based on the probability distribution characteristics of inertial navigation errors to ensure triggering of corrections before link interruption and maintain closed-loop controllability of the navigation system; endpoint threshold Fusion inertial navigation error accumulation model and terminal operation area The spatial boundary conditions of the error propagation are used to establish the mathematical relationship between error propagation and task accuracy. Adaptively adjust the trigger timing to ensure landing accuracy from the control theory level.

[0021] Furthermore, the method for obtaining the estimated error value in step S1 includes: S21. Obtaining a statically measured acceleration noise power spectrum or variance to generate multiple groups of acceleration noise sequences; S22, inputting each set of acceleration noise sequences into the aircraft nominal trajectory state equation, and obtaining a position error sample set by vertical integration calculation; S23. Statistically calculate the position error distribution of each group of independent samples and extract the 95% confidence interval boundary value of the standard deviation as the estimated error value.

[0022] The beneficial effects of the present invention are as follows: This solution is applied to aircraft that are in the startup state and have not yet reached their destination. This solution continuously provides autonomous navigation information through the inertial navigation system. Only when the error accumulates to a certain threshold, a satellite is heuristically selected to link and obtain ranging information to ensure link stability. The inertial navigation data is integrated with the satellite ranging information to effectively correct the error and achieve high-precision, low-resource navigation. This method is suitable for mobile targets such as aircraft, especially in long-duration, high-dynamic and resource-constrained scenarios, to improve navigation accuracy and reliability, while enhancing battlefield concealment and meeting the navigation needs of modern aircraft in complex environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 Flowchart of the method for positioning the end of an aircraft trajectory assisted by satellite ranging.

[0024] Figure 2 Schematic diagram of the mission scenario in the satellite-assisted positioning phase.

[0025] Figure 3 Schematic diagram of the heuristic navigation process.

[0026] Figure 4 This is the spatiotemporal relationship diagram of the dual-threshold trigger mechanism.

[0027] Figure 5 This is a schematic diagram of the destination area.

[0028] Figure 6 It is a trajectory map of aircraft and satellites.

[0029] Figure 7 This is a comparison chart of the simulation results of the positioning algorithm's various directions of error.

[0030] Figure 8 This is a scatter plot of the Euclidean distance distribution of the aircraft landing points. DETAILED DESCRIPTION

[0031] The specific embodiments of the present invention are described below to facilitate understanding of the present invention by those skilled in the art. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the concepts of the present invention are protected.

[0032] In order to facilitate the understanding of the positioning method of this solution, Figure 2 A schematic diagram of the mission scenario in the satellite-assisted positioning phase is given, which shows the spatial scenario of the aircraft establishing a laser link and ranging with a single satellite during flight.

[0033] refer to Figure 1 , Figure 1 FIG. 1 shows a flow chart of a method for positioning an aircraft trajectory end assisted by satellite ranging; FIG. Figure 1 and Figure 3 As shown, the method S provided in this solution includes steps S1 to S5. Figure 3 The double thresholds referred to are the thresholds in steps S3 and S4 below in this solution.

[0034] In step S1, the inertial navigation system is used to locate the current position of the aircraft and calculate the distance between it and the destination; then the estimated error of the aircraft positioning is calculated based on the Monte Carlo position error estimation method.

[0035] During implementation, the method for obtaining the estimated error value in step S1 of this solution preferably includes: S21. Obtaining a statically measured acceleration noise power spectrum or variance to generate multiple groups of acceleration noise sequences; S22, inputting each set of acceleration noise sequences into the aircraft nominal trajectory state equation, and obtaining a position error sample set by vertical integration calculation; S23. Statistically calculate the position error distribution of each group of independent samples and extract the 95% confidence interval boundary value of the standard deviation as the estimated error value.

[0036] In step S2, based on the interval distance, it is determined whether the aircraft has entered the vicinity of the destination. If so, it proceeds to step S3, otherwise it proceeds to step S4. In order to facilitate the understanding of the solution, Figure 5 A schematic diagram of the destination area is given.

[0037] In step S3, it is determined whether the estimated error is greater than the end point threshold. If so, the process proceeds to step S5, otherwise it returns to step S1; In step S4, it is determined whether the estimated error is greater than the process threshold. If so, the process proceeds to step S5, otherwise it returns to step S1; During flight, the aircraft's inertial navigation system (INS) has certain errors. Continuous use of INS can lead to cumulative errors. Therefore, if you switch to INS too late, the INS error can be too large, potentially causing the aircraft to enter dangerous areas (such as obstacles or no-fly zones), increasing mission risk. It can even cause the aircraft to deviate from its planned trajectory, leading to navigation system failure and the inability to establish a link between the satellite and the aircraft.

[0038] Therefore, this solution sets an error threshold and switches the positioning algorithm for navigation when the inertial navigation error accumulates to this threshold. Similarly, if the positioning algorithm is switched too early to allow the aircraft's positioning accuracy to converge, errors will still accumulate after switching back to the inertial navigation positioning method, resulting in a large error in the final landing point accuracy. Therefore, it is necessary to ensure that the aircraft is in a high-precision state when it is within a certain distance from the destination to avoid subsequent accumulation of accuracy errors. If the requirements are not met, the positioning algorithm is switched to ensure that the final landing point accuracy meets the requirements.

[0039] During implementation, the preferred expression for calculating the process threshold value of this solution is: in, is the process threshold; is the maximum position deviation tolerance of the chain-building cone, is the safety chain establishment coefficient, and the value here is taken as 0.7 through multiple simulation experiments.

[0040] This solution's process threshold represents the maximum allowable error during flight. This threshold is determined by the geometric constraints of satellite laser communication. The narrow beam characteristics of laser communication require the aircraft to be located within the satellite's communication cone. If inertial navigation errors cause the aircraft to deviate outside this cone, communication interruption will occur, resulting in loss of correction capability. When this solution passes this threshold, the proposed satellite navigation algorithm is activated, suppressing positioning accuracy.

[0041] During implementation, the preferred expression for calculating the endpoint threshold value in this solution is: , in, is the endpoint threshold; The final mission landing accuracy requirement; The inertial error accumulation model satisfies the function; is the neighborhood radius; for The terminal safety operation area; is the horizontal speed of the aircraft; It is the measurement interval between two adjacent satellite ranging measurements.

[0042] In the implementation process, theoretically, the closer the algorithm switching determined by the endpoint threshold is to the destination, the shorter the time for the final positioning accuracy error to accumulate, and the higher the accuracy of reaching the destination.

[0043] In step S5, the aircraft is positioned using a single-satellite fusion positioning algorithm based on an unscented Kalman filter. After executing for a preset duration, the system returns to step S1. This solution preselects a preset duration of 3 seconds, meaning that after executing the single-satellite fusion positioning algorithm for 3 seconds, the system returns to step S1 and uses the inertial navigation system for navigation.

[0044] In one embodiment of the present invention, a method for positioning an aircraft using a single-satellite fusion positioning algorithm based on an unscented Kalman filter includes: S51, discretize the aircraft nominal trajectory state equation and the single-satellite pseudo-range measurement equation; wherein the aircraft nominal trajectory state equation The expression is: in, is the nominal displacement vector of the aircraft; is the vehicle nominal acceleration vector; is the vehicle nominal velocity vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The inertial navigation system measures the acceleration of the aircraft in the navigation coordinate system; is the constant drift present in the accelerometer; is the gravitational acceleration vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system.

[0045] Single-star pseudorange measurement equation The expression is: in, are the position vectors of the satellite and the spacecraft at time i respectively; To find the length of the vector, here we mean to find the distance from the satellite to the spacecraft; is a column vector consisting of the distances from the satellite to the spacecraft measured at three moments; and are the position vectors of the satellite and the spacecraft at time i-1 respectively; and are the position vectors of the satellite and the spacecraft at time i-2, ; is the displacement vector of the aircraft between time i and time i-1; is the displacement vector of the aircraft between time i-1 and time i-2; To measure noise.

[0046] S52. Given the initial state and initial error covariance matrix: in, is the initial state of the aircraft’s position and velocity; is the estimated value of the initial state; Mathematical expectation operator, representing the theoretically optimal estimate (usually assumed to be known or determined by a nominal trajectory); T is the transpose; is the initial error covariance matrix, which represents the uncertainty of the initial state estimate; S53. Construct sigma point: in, is the i-th sigma point at time k, i.e. the sampling point; is the mean position and velocity of the aircraft at time k; is the i-th column of the result matrix obtained by calculation in the brackets; n is the number of state dimensions; is the error covariance matrix at time k; is the scale parameter, is the scale parameter; S54. Calculate the system prediction mean: , , in, for The predicted mean of the k+1 time observations obtained by weighted summation; For the general Substitute into the single-star pseudorange measurement equation The predicted measurement values ​​obtained; For the general Substitute into the state equation The predicted sigma point at time k+1 is obtained; is the state equation of the aircraft nominal trajectory; is the acceleration of the aircraft at time k; S55. Calculate the prior prediction value of the state error covariance matrix at time k : in, The predicted sigma point after propagation The mean of the predicted state at time k+1 obtained by weighted average; All are weights; is the prior prediction value of the state error covariance matrix at time k; is the system noise covariance matrix; S56. Calculate the Kalman gain matrix: in, is the Kalman gain matrix at time k+1; is the covariance of the correlation strength between the reaction state and the observation at time k+1; is the prior prediction value of the measurement error covariance matrix at time k+1; is the measurement noise covariance matrix; S57. Calculate the state estimation result and the posterior estimate of the covariance matrix: in, is the estimated value of the state at time k+1; is the measurement value obtained by satellite tracking measurement at time k+1; is the posterior estimate of the covariance matrix at time k+1; is the prior prediction value of the state error covariance matrix at time k+1.

[0047] When implemented, this solution preferably calculates the weights The expression is: , in, and They are The initial value of .

[0048] The expression of the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system is: in, is the transformation matrix from Earth-centered Earth-fixed coordinates to Earth-centered inertial coordinates; is the transformation matrix from the navigation coordinate system to the Earth-centered Earth-fixed coordinate system; is the latitude and longitude of the reference point; and are the reference angles of the Earth's rotation at the initial moment and at time t, respectively; is the angular velocity of the Earth's rotation.

[0049] Measure the acceleration of the aircraft in the navigation coordinate system for the inertial navigation system The expression is: in, is the true acceleration of the aircraft; is the acceleration system noise.

[0050] This solution uses a dual-threshold mechanism to control the switching of the navigation system in steps S1 to S5: the process threshold is set according to the geometric tolerance of the satellite link establishment, which can ensure that satellite correction is triggered when the cumulative error of the inertial navigation approaches the critical point of communication interruption; the end threshold integrates the terminal operation area and the mission accuracy constraint, and enables satellite positioning only before the landing accuracy is on the verge of getting out of control. Each satellite positioning only executes the single-star collaborative mode with a fixed short-term window, and immediately returns to pure inertial navigation after the end. This design reduces the frequency of satellite communications to the necessary minimum level and keeps the aircraft in a passive inertial navigation-dominated state for most of its flight, thereby achieving a substantial improvement in battlefield concealment while ensuring navigation accuracy.

[0051] The system effectively integrates the inertial navigation system with single-satellite ranging, and uses heuristic strategies to conduct satellite collaborative navigation. This corrects inertial navigation errors while minimizing resource consumption and maximizing battlefield concealment, while ensuring high-precision navigation and improving navigation performance and reliability during long-duration missions.

[0052] The following is an explanation of the positioning effect of the terminal positioning method provided by this solution using simulation: The aircraft model is defined as a point mass with an initial velocity and only subjected to thrust, drag, and gravity. The thrust direction is fixed, and the drag direction is opposite to the velocity direction. The launch point and aircraft parameter settings refer to Table 1. Table 1 Aircraft launch point model parameters The satellite orbit model is defined as a two-body orbit, that is, the acceleration only considers the effect of gravity. The initial position and velocity vector are obtained through orbital element conversion. The specific conversion process is referred to "Orbital Mechanics". The satellite orbit element setting is referred to Table 2.

[0053] Table 2 Satellite model orbit elements According to the relevant parameters in Table 1 and Table 2, the aircraft trajectory terminal positioning method of this scheme is executed, and the aircraft and satellite trajectories are simulated as follows Figure 6 shown.

[0054] At the same time, this solution also obtains the simulation results of the horizontal positioning error, vertical positioning error and combined positioning error of the aircraft during flight using only inertial navigation and the process of the present invention through simulation. For details, refer to Figure 7Simulation results show that the three-way error suppression makes the final aircraft position error lower than that of inertial navigation. In addition, only a single satellite is used three times, which reduces the time occupied by satellite resources, reduces resource consumption, improves battlefield concealment, and verifies the effectiveness of the error estimation method.

[0055] Figure 8 The results of 1,000 aircraft landing point positioning tests using both inertial navigation alone and the process of the present invention are presented, visually demonstrating the effectiveness of the present invention in improving positioning accuracy. The improvement in navigation accuracy was also quantified by plotting 95% confidence ellipse boundaries, ultimately reducing the positioning error of the landing point by 40%.

[0056] exist Figure 8 In a study conducted on 1,000 simulated flights in the same scenario, the results showed that this proposed positioning method improved navigation accuracy and significantly reduced errors compared to traditional inertial navigation. Calculating the 95% confidence interval radius showed that this approach reduced errors by 20% compared to traditional approaches.

[0057] Furthermore, compared to full-range satellite tracking navigation strategies, communication resource usage is concentrated only during the three ranging moments, reducing device power consumption. These significant results demonstrate that this solution effectively addresses the high resource usage, large errors, and poor stability issues of existing navigation technologies, providing a more accurate, stable, and efficient solution for long-duration, high-dynamic navigation of aircraft.

Claims

1. A satellite ranging-assisted aircraft trajectory terminal positioning method, characterized in that: include: S1. Use the inertial navigation system to locate the current position of the aircraft and calculate the distance between it and the destination; then calculate the estimated error of the aircraft positioning based on the Monte Carlo position error estimation method; S2. Determine whether the aircraft has entered the vicinity of the destination based on the interval distance. If so, proceed to step S3; otherwise, proceed to step S4. S3, determine whether the estimated error is greater than the endpoint threshold, if so, proceed to step S5, otherwise return to step S1; S4, determine whether the estimated error is greater than the process threshold, if so, proceed to step S5, otherwise return to step S1; S5. Use the single-satellite fusion positioning algorithm based on unscented Kalman filtering to locate the aircraft, and after executing the preset time, return to step S1.

2. The method for locating the end of an aircraft trajectory according to claim 1, wherein: Methods for positioning an aircraft using a single-satellite fusion positioning algorithm based on unscented Kalman filtering include: S51, discretizing the aircraft nominal trajectory state equation and the single-satellite pseudorange measurement equation; S52. Given the initial state and initial error covariance matrix: in, is the initial state of the aircraft’s position and velocity; is the estimated value of the initial state; is the mathematical expectation operator, which represents the theoretical optimal estimate; T is the transpose; is the initial error covariance matrix, which represents the uncertainty of the initial state estimate; S53. Construct sigma point: in, is the i-th sigma point at time k, i.e. the sampling point; is the mean position and velocity of the aircraft at time k; is the i-th column of the result matrix obtained by calculation in the brackets; n is the number of state dimensions; is the error covariance matrix at time k; is the scale parameter, is the scale parameter; S54. Calculate the system prediction mean: ， ， in, for The predicted mean of the k+1 time observations obtained by weighted summation; For the general Substitute into the single-star pseudorange measurement equation The predicted measurement values ​​obtained; For the general Substitute into the state equation The predicted sigma point at time k+1 is obtained; is the state equation of the aircraft nominal trajectory; is the acceleration of the aircraft at time k; S55. Calculate the prior prediction value of the state error covariance matrix at time k : in, The predicted sigma point after propagation The mean of the predicted state at time k+1 obtained by weighted average; All are weights; is the prior prediction value of the state error covariance matrix at time k; is the system noise covariance matrix; S56. Calculate the Kalman gain matrix: in, is the Kalman gain matrix at time k+1; is the covariance of the correlation strength between the reaction state and the observation at time k+1; is the prior prediction value of the measurement error covariance matrix at time k+1; is the measurement noise covariance matrix; is the prior prediction value of the measurement error covariance matrix; S57. Calculate the state estimation result and the posterior estimate of the covariance matrix: in, is the estimated value of the state at time k+1; is the measurement value obtained by satellite tracking measurement at time k+1; is the posterior estimate of the covariance matrix at time k+1; is the prior prediction value of the state error covariance matrix at time k+1.

3. The method for locating the end of an aircraft trajectory according to claim 2, wherein: calculate Weight The expression is: in, and They are The initial value of .

4. The method for locating the end of an aircraft trajectory according to claim 2, wherein: Aircraft nominal trajectory state equation The expression is: in, is the nominal displacement vector of the aircraft; is the vehicle nominal acceleration vector; is the vehicle nominal velocity vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The inertial navigation system measures the acceleration of the aircraft in the navigation coordinate system; is the constant drift present in the accelerometer; is the gravitational acceleration vector; is the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The expression of the transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system is: in, is the transformation matrix from Earth-centered Earth-fixed coordinates to Earth-centered inertial coordinates; is the transformation matrix from the navigation coordinate system to the Earth-centered Earth-fixed coordinate system; is the latitude and longitude of the reference point; and are the reference angles of the Earth's rotation at the initial moment and at time t, respectively; is the angular velocity of the Earth's rotation.

5. The method for locating the end of an aircraft trajectory according to claim 4, wherein: Measure the acceleration of the aircraft in the navigation coordinate system for the inertial navigation system The expression is: in, is the true acceleration of the aircraft; is the acceleration system noise.

6. The method for positioning the end of an aircraft trajectory according to claim 2, wherein: The single-star pseudorange measurement equation The expression is: in, are the position vectors of the satellite and the spacecraft at time i respectively; To find the length of the vector, here we mean to find the distance from the satellite to the spacecraft; is a column vector consisting of the distances from the satellite to the spacecraft measured at three moments; and are the position vectors of the satellite and the spacecraft at time i-1 respectively; and are the position vectors of the satellite and the spacecraft at time i-2, ; is the displacement vector of the aircraft between time i and time i-1; is the displacement vector of the aircraft between time i-1 and time i-2; To measure noise.

7. The method for positioning the end of an aircraft trajectory according to claim 1, wherein: The expression for calculating the process threshold is: in, is the process threshold; is the maximum position deviation tolerance of the chain-building cone, is the safety chain building factor.

8. The method for positioning the end of an aircraft trajectory according to claim 1, wherein: The expression for calculating the endpoint threshold is: ， in, is the endpoint threshold; The final mission landing accuracy requirement; The inertial guidance error accumulation model satisfies the function; is the neighborhood radius; for The terminal safety operation area; is the horizontal speed of the aircraft; It is the measurement interval between two adjacent ranging measurements of the satellite.

9. The method for positioning the end of an aircraft trajectory according to claim 1, wherein: The method for obtaining the estimated error value in step S1 includes: S21. Obtaining a statically measured acceleration noise power spectrum or variance to generate multiple groups of acceleration noise sequences; S22, inputting each set of acceleration noise sequences into the aircraft nominal trajectory state equation, and obtaining a position error sample set by vertical integration calculation; S23. Statistically calculate the position error distribution of each group of independent samples and extract the 95% confidence interval boundary value of the standard deviation as the estimated error value.

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