Satellite ranging-aided end-of-track positioning method for aircraft

Abstract

The application discloses a satellite ranging auxiliary aircraft trajectory end positioning method, which comprises the following steps: S1, positioning the current position of the aircraft by using an inertial navigation system, and calculating the interval distance from the destination; then, calculating the estimation error of the aircraft positioning based on a Monte Carlo position error estimation method; S2, judging whether the aircraft enters the destination neighborhood range according to the interval distance, if yes, entering step S3, otherwise, entering step S4; S3, judging whether the estimation error is greater than the end threshold, if yes, entering step S5, otherwise, returning to step S1; S4, judging whether the estimation error is greater than the process threshold, if yes, entering step S5, otherwise, returning to step S1; S5, positioning the aircraft by using a single satellite fusion positioning algorithm based on an unscented Kalman filter, and returning to step S1 after a preset time length is executed.

Description

TECHNICAL FIELD

[0001] The present application relates to aircraft positioning technology, in particular to a satellite ranging assisted aircraft trajectory end positioning method. BACKGROUND

[0002] In order to enable a remote aircraft to accurately reach the destination, inertial navigation combined with global satellite navigation system positioning is usually used. However, in order to reduce the dependence on global satellite navigation system during flight, adapt to complex electromagnetic environment and low-cost application, aircraft navigation positioning faces double challenges: on the one hand, high-precision navigation needs to be maintained to ensure mission effectiveness; on the other hand, the dependence on navigation signals needs to be reduced to ensure the availability of positioning accuracy after being jammed. Therefore, it is urgent to study a method for improving the positioning accuracy of long-range flight without global satellite navigation system support.

[0003] In the field of navigation error suppression, satellite positioning assistance is the mainstream technology direction. However, continuous multi-satellite cooperative positioning requires a large amount of satellite-ground communication resources, and there is a risk of link stability in high dynamic scenarios. At the same time, high-frequency satellite communication also increases the exposure probability of the aircraft, which is fundamentally contradictory to the concealment task requirement. Therefore, how to minimize resource consumption and maximize battlefield concealment while ensuring high accuracy has become a technical bottleneck that needs to be broken through in this field.

[0004] Currently, existing researches are mostly focused on multi-satellite ranging for positioning and navigation. This technical solution receives signals from at least four satellites, uses ranging information to construct an equation set to solve the three-dimensional position coordinates and time deviation of the user equipment. Satellite constellations (such as GPS, Beidou) are uniformly distributed globally to ensure signal coverage, and the distance is calculated by the time difference of signal propagation, combined with data processing algorithms (such as least squares method, Kalman filter) to achieve high-precision positioning.

[0005] Multi-satellite ranging positioning technology needs to occupy the communication resources of more than 4 satellites at the same time, which may cause resource occupation risk in special periods, and is difficult to meet the needs of many aircrafts ranging at the same time. At the same time, the receiver needs to process multiple satellite signals at the same time, and the radio frequency front end needs to support multiple channels, which significantly increases the size and power consumption of the device, which is not conducive to the long-time mission of the aircraft. In addition, in high dynamic scenarios such as hypersonic aircraft, the multi-satellite link synchronization stability is poor, and it is easy to lose lock, which affects the accuracy and reliability of navigation.

[0006] Part of the existing research on single satellite to ground target ranging positioning, using through a single satellite at multiple times on the target for multiple ranging, combined with satellite ephemeris to build dynamic space arc, solve the target position. This technology is usually used for the positioning of ground fixed facilities or static target, suitable for some specific application scenarios, such as the positioning of ground base station, fixed monitoring point, etc., for the positioning and navigation of mobile target such as aircraft cannot be directly applied, the application scene is limited. Therefore, how to make full use of the one-dimensional ranging information in the one-to-one link between low earth orbit satellite and aircraft, through short time multiple sequential measurement to assist to improve the trajectory positioning accuracy of aircraft still needs further research. SUMMARY

[0007] In view of the above problems in the prior art, the satellite ranging assisted aircraft trajectory end positioning method provided by the present application solves the problems of high satellite ranging resource occupation, poor stability in high dynamic scene, and single satellite time-sharing ranging not suitable for dynamic target in the prior art.

[0008] In order to achieve the above invention purpose, the technical scheme adopted by the present application is:

[0009] The present application provides a satellite ranging assisted aircraft trajectory end positioning method, which comprises:

[0010] S1, the current position of the aircraft is positioned by using the inertial navigation system, and the interval distance between the aircraft and the destination is calculated. Then the estimated error of the aircraft positioning is calculated based on the Monte Carlo position error estimation method;

[0011] S2, according to the interval distance, it is judged whether the aircraft enters the destination neighborhood range, if yes, step S3 is entered, otherwise step S4 is entered;

[0012] S3, it is judged whether the estimated error is greater than the end point threshold, if yes, step S5 is entered, otherwise step S1 is returned;

[0013] S4, it is judged whether the estimated error is greater than the process threshold, if yes, step S5 is entered, otherwise step S1 is returned;

[0014] S5, the aircraft is positioned by using the single satellite fusion positioning algorithm based on unscented Kalman filter, and after a preset time is executed, step S1 is returned.

[0015] Further, the method for positioning the aircraft by using the single satellite fusion positioning algorithm based on unscented Kalman filter comprises:

[0016] S51, the nominal trajectory state equation and the single satellite pseudo-range measurement equation of the aircraft are discretized;

[0017] S52, the initial state and the initial error covariance matrix are given:

[0018]

[0019] where, is the initial state of the aircraft position and velocity; is the initial state estimate; is the mathematical expectation operator, representing the theoretically optimal estimate; T is the transpose; is the initial error covariance matrix, representing the uncertainty of the initial state estimate;

[0020] S53, construct sigma points:

[0021]

[0022] where, is the i-th sigma point at time k, i.e., the sampling point; is the mean of the position and velocity of the aircraft at time k; is the i-th column of the resulting matrix calculated inside the parentheses; n is the dimension number of the state quantity; is the error covariance matrix at time k; is a scaling parameter, is a scaling parameter;

[0023] S54, calculate the system prediction mean:

[0024] , ,

[0025] where, is the weighted sum of the observation prediction mean at time k+1; is the predicted measurement value obtained by substituting into the single-star pseudorange measurement equation ; is the predicted sigma point at time k+1 obtained by substituting into the state equation ; is the state equation of the nominal trajectory of the aircraft; is the acceleration of the aircraft at time k;

[0026] S55, calculate the prior prediction value of the state error covariance matrix at time k :

[0027]

[0028] where, is the propagated predicted sigma point The predicted state mean value at the k+1 moment is obtained by weighted average according to the weights; are weights; is the prior prediction value of the state error covariance matrix at the k moment; is the system noise covariance matrix;

[0029] S56, the Kalman gain matrix is calculated:

[0030]

[0031] wherein, is the Kalman gain matrix at the k+1 moment; is the correlation strength covariance of the reaction state and observation at the k+1 moment; is the prior prediction value of the measurement error covariance matrix at the k+1 moment; is the measurement noise covariance matrix;

[0032] S57, the state estimation result and the posterior estimation value of the covariance matrix are calculated:

[0033]

[0034] wherein, is the state estimation value at the k+1 moment; is the measurement value obtained by satellite tracking measurement at the k+1 moment; is the posterior estimation value of the covariance matrix at the k+1 moment; is the prior prediction value of the state error covariance matrix at the k+1 moment.

[0035] The beneficial effects of the above technical solutions are: the unscented Kalman filter (UKF) can accurately propagate the statistical distribution of the state quantity through deterministic sampling (Sigma point), which can avoid the first-order linearization truncation error of the extended Kalman filter (EKF) for a nonlinear system, and in combination with the single satellite pseudorange measurement equation, the state constraint provided by the spacecraft kinematics model is used to convert the underdetermined positioning problem of single satellite ranging into an observable problem in the state space, and fundamentally solve the adaptability defects of dynamic target single satellite positioning.

[0036] Further, the expression of the weight is:

[0037]

[0038]

[0039] wherein, and are initial values of .

[0040] The beneficial effects of the above technical solutions are: the scale parameter in the weight design The dispersion degree of the Sigma point and the mean value is controlled, and the sampling range is adjusted to match the nonlinearity strength of the system; the distribution parameter High-order moment information is introduced, which can optimize the probability consistency of covariance weight distribution; and the cooperation of the two ensures the high-order moment approximation ability of the Sigma point set to the state posterior distribution, and significantly improves the convergence stability of the state estimation in the high-maneuvering scene.

[0041] Further, the expression of the nominal trajectory state equation of the aircraft is

[0042]

[0043] Among them, is the nominal displacement vector of the aircraft; is the nominal acceleration vector of the aircraft; is the nominal velocity vector of the aircraft; is the conversion matrix from the navigation coordinate system to the geocentric inertial coordinate system; is the acceleration of the aircraft in the navigation coordinate system measured by the inertial navigation system; is the constant drift existing in the accelerometer; is the gravity acceleration vector; is the conversion matrix from the navigation coordinate system to the geocentric inertial coordinate system;

[0044] The expression of the conversion matrix from the navigation coordinate system to the geocentric inertial coordinate system is

[0045]

[0046]

[0047]

[0048] Among them, is the conversion matrix from the geocentric terrestrial coordinate to the geocentric inertial coordinate; is the conversion matrix from the navigation coordinate system to the geocentric terrestrial coordinate system; is the reference point latitude and longitude; and are the initial time and the reference angle of the earth rotation at time t, respectively; is the angular velocity of the earth rotation.

[0049] The beneficial effects of the above technical solutions are: the state equation explicitly separates the inertial navigation error term from the real dynamics, and establishes an analytically modeled noise input channel for Monte Carlo error estimation; the coordinate conversion chain is coupled with the angular velocity of the earth rotation​ , strictly compensate the relative rotation accumulation effect between the navigation coordinate system and the inertial coordinate system, and eliminate the frame bias in long-time navigation tasks.

[0050] Further, the expression of the acceleration of the aircraft in the navigation coordinate system measured by the inertial navigation system is

[0051]

[0052] wherein, is the real acceleration of the aircraft; is the acceleration system noise.

[0053] Further, the expression of the single-satellite pseudorange measurement equation

[0054]

[0055] wherein, are position vectors of the satellite and the aircraft at the i-th moment, respectively; is the length of the vector, and here represents the distance from the satellite to the aircraft; is a column vector composed of the distances from the satellite to the aircraft measured at three moments; and are position vectors of the satellite and the aircraft at the i-1-th moment, respectively; and are position vectors of the satellite and the aircraft at the i-2-th moment, respectively, is the displacement vector of the aircraft between the i-th moment and the i-1-th moment; is the displacement vector of the aircraft between the i-1-th moment and the i-2-th moment; is the measurement noise.

[0056] The beneficial effects of the above technical solution are that the displacement vector is used to construct the position correlation constraint between adjacent moments, the single-satellite pseudorange measurement value is expanded into a space-time joint observation value, the design utilizes the continuity of the aircraft motion, converts the geometric positioning problem of single-satellite ranging into a state estimation problem with dynamic constraints, and can break through the strong hypothesis limit of the target motion state in the traditional single-satellite positioning.

[0057] Further, the expression of the process threshold is

[0058]

[0059] wherein, is the process threshold; is the maximum position deviation tolerance of the chain-building cone,​​​ A safety coefficient for building a link.

[0060] Further, the expression for calculating the end threshold value is:

[0061] ,

[0062] wherein, the end threshold value; the final task landing point accuracy requirement; the inertial navigation error accumulation model satisfying function; the neighborhood range radius; the end safety operation area of ; the horizontal speed of the aircraft; the measurement interval of the satellite adjacent two times of ranging.

[0063] The beneficial effects of the above technical solutions are: the process threshold value can directly map the geometric accessibility boundary of satellite link building, and the safety coefficient is designed based on the probability distribution characteristics of inertial navigation error, which ensures that the correction is triggered before the link interruption and maintains the closed-loop controllability of the navigation system; the end threshold value fuses the inertial navigation error accumulation model and the spatial boundary conditions of the end operation area , and establishes the mathematical association between error propagation and task accuracy. Through the neighborhood radius , the triggering time is adaptively adjusted to ensure the landing point accuracy from the control theory level.

[0064] Further, the method for obtaining the estimated error value in step S1 comprises:

[0065] S21, generating a plurality of acceleration noise sequences by obtaining the acceleration noise power spectrum or variance of static measurement;

[0066] S22, inputting each group of acceleration noise sequences into the nominal trajectory state equation of the aircraft, and calculating the position error sample set by vertical integration;

[0067] S23, statistically analyzing the position error distribution of each group of independent samples, and extracting the standard deviation 95% confidence interval boundary value as the estimated error value.

[0068] The beneficial effects of this invention are as follows: This solution is applied to aircraft in the startup state that have not yet reached their destination. It continuously provides autonomous navigation information through an inertial navigation system, and only when the error accumulates to a certain threshold does it heuristically select a satellite for connection and ranging information acquisition, ensuring link stability. By fusing inertial navigation data with satellite ranging information, errors are effectively corrected, achieving high-precision, low-resource-consumption navigation. This method is suitable for moving targets such as aircraft, especially in long-endurance, high-dynamic, and resource-constrained scenarios, improving navigation accuracy and reliability while enhancing battlefield stealth and meeting the navigation needs of modern aircraft in complex environments. Attached Figure Description

[0069] Figure 1 A flowchart of a satellite ranging-assisted aircraft trajectory end-point localization method.

[0070] Figure 2 A schematic diagram of the mission scenario for the satellite-assisted positioning phase.

[0071] Figure 3 This is a schematic diagram of a heuristic navigation process.

[0072] Figure 4 This is a spatiotemporal relationship diagram of the dual-threshold triggering mechanism.

[0073] Figure 5 This is a schematic diagram of the destination area.

[0074] Figure 6 For spacecraft and satellite trajectory maps.

[0075] Figure 7 This is a comparison chart of simulation results for the positioning algorithm's errors in each direction.

[0076] Figure 8 This is a scatter plot of the Euclidean distance distribution of the aircraft's landing points. Detailed Implementation

[0077] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0078] To facilitate understanding of the positioning method in this scheme, Figure 2 A schematic diagram of the satellite-assisted positioning phase is provided, illustrating the spatial scenario in which the spacecraft establishes a laser link with a single satellite and performs ranging during flight.

[0079] refer to Figure 1, Figure 1 A flow chart of a satellite ranging aided aircraft trajectory end positioning method is shown; as Figure 1 and Figure 3 The method S provided by the scheme comprises steps S1-S5, Figure 3 The double threshold refers to the threshold in steps S3 and S4 of the scheme.

[0080] In step S1, the current position of the aircraft is positioned by using the inertial navigation system, and the interval distance from the destination is calculated; then the estimated error of the aircraft positioning is calculated based on the Monte Carlo position error estimation method.

[0081] In implementation, the method for obtaining the estimated error value in step S1 of the scheme preferably comprises:

[0082] S21, obtaining a static measured acceleration noise power spectrum or variance to generate a plurality of sets of acceleration noise sequences;

[0083] S22, inputting each set of acceleration noise sequences into the nominal trajectory state equation of the aircraft, and calculating the position error sample set by vertical integration;

[0084] S23, statistically analyzing the position error distribution of each group of independent samples, and extracting the 95% confidence interval boundary value of the standard deviation as the estimated error value.

[0085] In step S2, according to the interval distance, it is judged whether the aircraft enters the destination neighborhood range, if yes, step S3 is entered, otherwise step S4 is entered; in order to facilitate the understanding of the scheme, Figure 5 A schematic diagram of the destination area range is given.

[0086] In step S3, it is judged whether the estimated error is greater than the end threshold, if yes, step S5 is entered, otherwise step S1 is returned;

[0087] In step S4, it is judged whether the estimated error is greater than the process threshold, if yes, step S5 is entered, otherwise step S1 is returned;

[0088] During the flight of the aircraft, the inertial navigation system of the aircraft has certain errors, and continuous use of inertial navigation will cause cumulative errors, so if the navigation is switched too late, the inertial navigation error will be too large, which may cause the aircraft to enter a dangerous area (such as obstacles, no-fly zones, etc.), increase the task risk, and even cause the aircraft to deviate from the predetermined trajectory, the navigation system fails, and the satellite and the aircraft cannot realize the link establishment.

[0089] Therefore, the present solution sets an error threshold, and switches the positioning algorithm to navigate when the inertial navigation error accumulates to the threshold. Similarly, if the positioning algorithm is switched too early, the error accumulation will still occur after switching back to the inertial navigation positioning method, resulting in a large final aircraft landing point error. Therefore, it is necessary to ensure that the aircraft is in a state of high precision within a certain range from the destination to avoid subsequent precision error accumulation. If the requirement is not met, the positioning algorithm is switched to ensure that the final landing point precision meets the requirements.

[0090] In implementation, the expression for calculating the process threshold is preferably:

[0091]

[0092] wherein, is the process threshold; is the maximum position deviation tolerance of the chain building cone, is a safe chain building coefficient, which is 0.7 through multiple simulation experiments.

[0093] The process threshold of the present solution is the maximum allowed error boundary during flight, and its essence is determined by the geometric constraints of satellite laser chain building. The narrow beam characteristics of laser communication require that the aircraft must be located within the chain building cone of the satellite. If the inertial navigation error causes the aircraft to deviate outside the cone, the chain building will be interrupted and the correction ability will be lost. When the above threshold is reached, the satellite navigation algorithm proposed in the present solution is enabled, which can suppress the positioning precision.

[0094] In implementation, the expression for calculating the end point threshold is preferably:

[0095] ,

[0096] wherein, is the end point threshold; is the final task landing point precision requirement; is the inertial navigation error accumulation model satisfying function; is the neighborhood range radius; is the end safety operation area of ; is the horizontal speed of the aircraft; is the measurement interval of the adjacent two ranging of the satellite.

[0097] In implementation, theoretically, the algorithm switching determined by the end point threshold is closer to the destination, the time of the final positioning precision error accumulation is shorter, and the precision of reaching the destination is higher.

[0098] In step S5, the single-satellite fusion positioning algorithm based on the unscented Kalman filter is used to position the aircraft, and after a preset time length is executed, the step S1 is returned to. The preset time length is 3 seconds, that is, the single-satellite fusion positioning algorithm is executed for 3 seconds, and then the step S1 is returned to use the inertial navigation system for navigation.

[0099] In an embodiment of the present application, the method for positioning the aircraft by using the single-satellite fusion positioning algorithm based on the unscented Kalman filter comprises:

[0100] S51, the nominal trajectory state equation of the aircraft and the single-satellite pseudorange measurement equation are discretized; wherein the nominal trajectory state equation of the aircraft The expression of the nominal trajectory state equation of the aircraft is:

[0101]

[0102] wherein, is the nominal displacement vector of the aircraft; is the nominal acceleration vector of the aircraft; is the nominal velocity vector of the aircraft; is the conversion matrix from the navigation coordinate system to the geocentric inertial coordinate system; is the acceleration of the aircraft in the navigation coordinate system measured by the inertial navigation system; is the constant drift existing in the accelerometer; is the gravity acceleration vector; is the conversion matrix from the navigation coordinate system to the geocentric inertial coordinate system.

[0103] The expression of the single-satellite pseudorange measurement equation is:

[0104]

[0105] wherein, and are the position vectors of the satellite and the aircraft at i moment, respectively; is the length of the vector, which here represents the distance from the satellite to the aircraft; is a column vector composed of the distances from the satellite to the aircraft measured at three moments; and are the position vectors of the satellite and the aircraft at i-1 moment, respectively; and are the position vectors of the satellite and the aircraft at i-2 moment, respectively, ; is the displacement vector of the aircraft between i moment and i-1 moment; is the displacement vector of the aircraft between i-1 moment and i-2 moment; is the measurement noise.

[0106] S52, given the initial state and initial error covariance matrix:

[0107]

[0108] where, is the initial state of the aircraft position and velocity; is the initial state estimate; is the mathematical expectation operator, representing the theoretically optimal estimate (usually assumed to be known or determined by the nominal trajectory); T is the transpose; is the initial error covariance matrix, representing the uncertainty of the initial state estimate;

[0109] S53, construct sigma points:

[0110]

[0111] where, is the i-th sigma point at time k, i.e., the sampling point; is the mean of the position and velocity of the aircraft at time k; is the i-th column of the resulting matrix calculated in the parentheses; n is the dimension number of the state quantity; is the error covariance matrix at time k; is a scaling parameter, is a scaling parameter;

[0112] S54, calculate the system prediction mean:

[0113] , ,

[0114] where, is the weighted sum of the observation prediction mean at time k+1; is the predicted measurement value obtained by bringing into the single-star pseudorange measurement equation ; is the predicted sigma point at time k+1 obtained by bringing into the state equation ; is the state equation of the nominal trajectory of the aircraft; is the acceleration of the aircraft at time k;

[0115] S55, calculate the prior prediction value of the state error covariance matrix at time k :

[0116]

[0117] wherein, is the propagated predicted sigma point is the predicted state mean value at time k+1 obtained by weighted average according to the weights; are weights; is the prior prediction value of the state error covariance matrix at time k; is the system noise covariance matrix;

[0118] S56, calculate the Kalman gain matrix:

[0119]

[0120] wherein, is the Kalman gain matrix at time k+1; is the correlation strength covariance between the state at time k+1 and the observation; is the prior prediction value of the measurement error covariance matrix at time k+1; is the measurement noise covariance matrix;

[0121] S57, calculate the state estimation result and the posteriori estimation value of the covariance matrix:

[0122]

[0123] wherein, is the state estimation value at time k+1; is the measurement value obtained by satellite tracking measurement at time k+1; is the posteriori estimation value of the covariance matrix at time k+1; is the prior prediction value of the state error covariance matrix at time k+1.

[0124] In implementation, the expression of the calculation weight is:

[0125] ,

[0126]

[0127] wherein, and are initial values of .

[0128] The expression of the conversion matrix of the navigation coordinate system to the geocentric inertial coordinate system is:

[0129]

[0130]

[0131]

[0132] wherein, is the transformation matrix from the geocentric inertial coordinate to the geocentric body coordinate; is the transformation matrix from the navigation coordinate system to the geocentric body coordinate system; is the reference point latitude and longitude; and are the earth rotation reference angles at the initial time and at the time t, respectively; is the earth rotation angular velocity.

[0133] is the expression of the acceleration of the aircraft in the navigation coordinate system measured by the inertial navigation system

[0134]

[0135] wherein, is the real acceleration of the aircraft; is the acceleration system noise.

[0136] The scheme adopts a double threshold mechanism to control the navigation system switching in steps S1-S5: the process threshold is set according to the geometric tolerance of satellite chain building, which can ensure that the inertial navigation cumulative error approaches the critical point of communication interruption to trigger satellite correction; the end threshold fuses the terminal operation area and the task accuracy constraint, and only enables satellite positioning when the landing point accuracy is close to out of control. Each satellite positioning only performs a fixed short window single satellite cooperative mode, and returns to pure inertial navigation immediately after the end. This design compresses the satellite communication frequency to the necessary minimum level, and makes the aircraft in a passive inertial navigation dominated state for most of the voyage, which ensures the navigation accuracy while essentially improving the battlefield stealth.

[0137] The inertial navigation system is effectively fused with single satellite ranging, and satellite cooperative navigation is performed through heuristic strategy. The inertial navigation error is corrected, while the resource consumption is minimized and the battlefield stealth is maximized, while ensuring high-precision navigation, improving the navigation performance and reliability of the aircraft in long-time mission.

[0138] The positioning effect of the terminal positioning method provided by the scheme will be described below in combination with simulation:

[0139] The aircraft model is defined as a mass point with initial velocity, only subjected to thrust, resistance and gravity, wherein the thrust direction is fixed, and the resistance direction is opposite to the velocity direction. The launch point and each parameter of the aircraft are set with reference to Table 1;

[0140] Table 1 Launch point and model parameters of the aircraft

[0141] ​

[0142] The satellite orbit model is defined as a two-body orbit, i.e., the acceleration only considers the effect of gravity, and the initial position and velocity vector are obtained through orbit root number conversion. For details of the conversion process, refer to "Orbital Mechanics", and the satellite orbit root number is set with reference to Table 2.

[0143] Table 2. Satellite model orbit root number

[0144]

[0145] The end position of the aircraft trajectory is determined according to the relevant parameters in Table 1 and Table 2, and the simulation results of the aircraft and satellite trajectories are shown in the following table. Figure 6

[0146] At the same time, the simulation also obtains the horizontal positioning error, vertical positioning error, and combined positioning error simulation results of the aircraft flight process using only inertial navigation and using the process of the present application. For details, refer to Figure 7 . The simulation results show that the final aircraft position error is lower relative to inertial navigation through three times of error suppression, and only three single satellites are used, the satellite resource occupation time is also less, the resource consumption is reduced, the battlefield concealment is improved, and the effectiveness of the error estimation method is verified.

[0147] Figure 8 The 1000 times of aircraft landing point positioning results obtained by using only inertial navigation and using the process of the present application are shown, which intuitively shows the effectiveness of the present application in improving positioning accuracy. At the same time, by drawing the 95% confidence ellipse boundary, the improvement of navigation accuracy is quantified, and the positioning error of the final landing point is reduced by 40%.

[0148] In Figure 8 , by simulating 1000 times of flight in the same scene, the results show that the positioning method of the present application improves the navigation accuracy and significantly reduces the error compared with the traditional inertial navigation. Calculate the 95% confidence interval radius, and the error of the present application is reduced by 20% compared with the traditional scheme.

[0149] At the same time, compared with the satellite tracking navigation strategy throughout the whole process, the communication resource occupation time is only concentrated in the three ranging moments, and the device power consumption is reduced. These significant effects show that the present application can effectively solve the problems of high resource occupation, large error, and poor stability of existing navigation technology, and provide a more accurate, stable, and efficient solution for long-time, high-dynamic navigation of aircraft.​

Claims

1. A satellite ranging aided aircraft trajectory end positioning method, characterized by, Comprise: S1, adopt inertial navigation system to position the current position of the aircraft, and calculate its interval distance with the destination; then calculate the estimation error of the aircraft positioning based on the Monte Carlo position error estimation method; S2, according to the interval distance, judge whether the aircraft enters the destination neighborhood range, if yes, enter step S3, otherwise enter step S4; S3, judge whether the estimation error is greater than the end threshold, if yes, enter step S5, otherwise return to step S1; S4, judge whether the estimation error is greater than the process threshold, if yes, enter step S5, otherwise return to step S1; S5, adopt single star fusion positioning algorithm based on unscented Kalman filter to position the aircraft, and return to step S1 after executing the preset time length; The expression for calculating the process threshold is: wherein, is a process threshold value; is a maximum position deviation tolerance of the build chain cone, is a safety build chain coefficient; The expression for calculating the end threshold is: ， wherein, is an end point threshold value; is a final mission landing accuracy requirement; is an inertial navigation error accumulation model satisfying function; is a neighborhood range radius; is a terminal safety operation zone; is an aircraft horizontal speed; is a measurement interval of adjacent two ranging of a satellite; The method for obtaining the estimation error value in step S1 comprises: S21, obtain the acceleration noise power spectrum or variance of static measurement to generate a plurality of acceleration noise sequences; S22, input each group of acceleration noise sequence into the nominal trajectory state equation of the aircraft, and calculate the position error sample set by vertical integral; S23, statistics the position error distribution of each group of independent samples, and extract the standard deviation 95% confidence interval boundary value as the estimation error value.

2. The aircraft trajectory end positioning method according to claim 1, wherein, The method for positioning the aircraft by using single star fusion positioning algorithm based on unscented Kalman filter comprises: S51, discretize the nominal trajectory state equation of the aircraft and the single star pseudorange measurement equation; S52, give the initial state and the initial error covariance matrix: wherein, is an initial state of the aircraft position velocity; is an initial state estimate; is a mathematical expectation operator, representing a theoretically optimal estimate; T is transpose; is an initial error covariance matrix, representing uncertainty of the initial state estimate; S53, construct sigma point: wherein, is the ith sigma point at time k, i.e. a sample point; is the position and velocity mean of the aircraft at time k; is the ith column of the resulting matrix calculated in the brackets; n is the dimension of the state vector; is the error covariance matrix at time k; is a proportional parameter, is a scaling parameter; S54, calculate the system prediction mean: ， ， wherein, is a weighted sum to obtain the predicted mean of the measurement at time k+1; is into the single-satellite pseudorange measurement equation to obtain the predicted measurement value; is into the state equation to obtain the predicted sigma point at time k+1; is the nominal trajectory state equation for the aircraft; is the acceleration of the aircraft at time k; S55, calculate the priori prediction value of the state error covariance matrix at time k : wherein, is the predicted state mean at time k+1; is the predicted state mean at time k+1; are weight values; is the prior prediction of the state error covariance matrix at time k; is the system noise covariance matrix; S56, calculate the Kalman gain matrix: wherein, is the Kalman gain matrix at time k + 1 ; is the association strength covariance between the reaction state and the observation at time k + 1 ; is the prior prediction of the measurement error covariance matrix at time k + 1 ; is the measurement noise covariance matrix; is the prior prediction of the measurement error covariance matrix; S57, calculate the posterior estimation value of state estimation result and covariance matrix: wherein, is the state estimate value at time k+1; is the measurement value obtained by satellite tracking measurement at time k+1; is the posteriori estimate value of the covariance matrix at time k+1; is the priori prediction value of the state error covariance matrix at time k+1.

3. The aircraft trajectory end positioning method according to claim 2, wherein, The expression for calculating the process threshold is: weight The expression for the weight is: wherein and are respectively the initial value of the variable 4. The aircraft trajectory end positioning method according to claim 2, wherein, Aircraft nominal trajectory state equation The expression is: wherein, is a nominal displacement vector of the aircraft; is a nominal acceleration vector of the aircraft; is a nominal velocity vector of the aircraft; is a transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; is an acceleration of the aircraft in the navigation coordinate system measured by the inertial navigation system; is a constant drift present in the accelerometer; is a gravitational acceleration vector; is a transformation matrix from the navigation coordinate system to the geocentric inertial coordinate system; The expression for calculating the end threshold is: The expression for calculating the process threshold is: The expression for calculating the end threshold is: wherein, is the transformation matrix from the geocentric inertial coordinate to the geocentric body-fixed coordinate; is the transformation matrix from the navigation coordinate system to the geocentric body-fixed coordinate system; is the reference point latitude and longitude; and are the earth rotation reference angles at the initial time and at the time t, respectively; is the earth rotation angular velocity.

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

6. The aircraft trajectory end positioning method according to Claim 2, wherein, The single satellite pseudorange measurement equation The expression for the single satellite pseudorange measurement equation is: where, and are the position vectors of the satellite and the aircraft at time i, respectively; is the distance between the satellite and the aircraft, and is the length of the vector is a column vector composed of the distances between the satellite and the aircraft measured at three time instants; and are the position vectors of the satellite and the aircraft at time i-1, respectively; and are the position vectors of the satellite and the aircraft at time i-2, respectively, ; is the displacement vector of the aircraft between time i and i-1; is the displacement vector of the aircraft between time i-1 and i-2; is the measurement noise.

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