A wing parachute system track reconstruction state estimation method and device, computer equipment and storage medium

Abstract

This application belongs to the technical field of paraglider systems, and relates to a method, apparatus, device, and medium for state estimation in paraglider system trajectory reconstruction. The method includes: acquiring the process equations and observation data of the paraglider system, obtaining the observation equations of the paraglider system, and obtaining the linear Kalman state transition equation to obtain prior and posterior estimation equations; obtaining the prior and posterior state errors based on the linear Kalman state transition equation, prior and posterior estimation equations, and obtaining the Kalman gain equation; defining the error covariance matrix and the prior error covariance matrix, solving the Kalman gain equation to obtain the Kalman gain and the matrix of undetermined coefficients of the Kalman gain equation; and obtaining the state reconstruction result of the paraglider system state based on the posterior estimation equation, Kalman gain, and the matrix of undetermined coefficients. This method can reconstruct the time history of each state variable of the paraglider system.

Description

Technical Field

[0001] This application relates to the field of paraglider system technology, and in particular to state estimation methods, apparatus, equipment and media for paraglider system trajectory reconstruction. Background Technology

[0002] The paraglider system is a typical nonlinear, multi-soft-body aircraft with highly complex dynamic characteristics. Establishing an accurate and reliable dynamic theoretical model is extremely difficult, and current understanding of paraglider systems is mostly obtained through experimental methods. Through paraglider flight tests, the system's flight performance and dynamic characteristics can be analyzed, providing a basis for optimizing and improving parameter configurations and control strategies.

[0003] Based on the data and kinematic relationships obtained during flight tests, the time histories of each state variable of the airdrop system can be obtained. This process is called reconstructed output or track reconstruction. Track reconstruction is of great significance for verifying the rationality of theoretical models and for sensor calibration. It can even be used for fault diagnosis during flight anomalies. In addition, when certain state quantities are inaccurate or unmeasurable, track reconstruction can restore the changes in these state quantities and replace the sensor measurement results.

[0004] In existing technologies, trajectory reconstruction methods include least squares estimation, output error method, and filtering error method. Least squares estimation assumes noise only exists in the system input and is relatively simple, but it is poorly applicable to complex problems. Output error method assumes noise is generated entirely by the measurement process; this method is computationally time-consuming and memory-intensive. Filtering error method assumes noise exists simultaneously in both the system process and the measurement process, but its algorithm is complex, computationally intensive, and rarely used in practice.

[0005] The paraglider airdrop system is a complex nonlinear multi-flexible body dynamic system. It is very difficult to install sensors on the canopy and lines. Furthermore, due to factors such as obstruction, fixation, and large deformation, the reliability of the measured data is low. Data such as the angle of attack is difficult to measure directly. If these state variables can be reconstructed and output, it will help to better understand the flight characteristics of the paraglider. Summary of the Invention

[0006] Therefore, it is necessary to provide a state estimation method, apparatus, device, and medium for reconstructing the trajectory of a paraglider system, which can reconstruct the time history of each state variable of the paraglider system, in order to address the above-mentioned technical problems.

[0007] A state estimation method for trajectory reconstruction of a paraglider system includes:

[0008] The process equations and observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data. Taylor expansions are performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations.

[0009] Based on the linear Kalman state transition equation, the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state are obtained.

[0010] Based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, the prior state error and the posterior state error are obtained; based on the prior state error, the posterior state error, and the posterior estimate equation, the Kalman gain equation is obtained; the error covariance matrix and the prior error covariance matrix are defined, and the Kalman gain equation is solved to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and the undetermined coefficient matrix of the Kalman gain equation is obtained;

[0011] Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction result of the paraglider system is obtained.

[0012] In one embodiment, the process equations of the paraglider system and the observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data; Taylor expansions are performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations, including:

[0013] Obtaining the process equations for the parachute system:

[0014]

[0015] In the formula, x true f(x) represents the true state vector of the system. true ) is a nonlinear function of the state vector; w is the process noise;

[0016] Obtain observation data of the parachute system, and derive the observation equations for the parachute system based on the observation data:

[0017] y true =h(x true )+v (3)

[0018] In the formula, y true For x true The measured value; h(x) true ) is a nonlinear function of the state vector; v is the observation noise;

[0019] Define the state error vector x and the observation error vector y as follows:

[0020] x = x true -x referemce (5)

[0021] y = y true -y referemce (6)

[0022] in:

[0023] y referemce =h(x referemce )+v

[0024] The process equation in x reference Taylor expansion yields the process differential equation:

[0025]

[0026] In the formula, F is the Jacobi matrix of the function f;

[0027] The observation equation in x reference Taylor expansion yields the observation differential equation:

[0028]

[0029] In the formula, H is the Jacobi matrix of the h function;

[0030] For the process differential equation, the solution has the following form:

[0031] x k+1 =Φ k+1,k x k (10)

[0032] In the formula, x k Let be the true state vector of the paraglider system at time k;

[0033] Based on equations (9) and (10), the linear Kalman state transition equation is obtained:

[0034] x k+1 =Φ k+1,k x k +w k (11)

[0035] y k =H k x k +v k (12)

[0036] in:

[0037] Φ k+1,k =I+FΔt (13)

[0038]

[0039] In the formula, y k Δt represents the measurement value obtained through observation or measurement, and Δt is the time interval between the (k+1)th and the kth measurement values.

[0040] In one embodiment, obtaining the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state based on the linear Kalman state transition equation includes:

[0041] Based on the linear Kalman state transition equation, a priori estimate of the parachute system state is defined. Define the posterior estimate of the state of the parachute system Assuming the posterior estimation result is a linear combination of the prior estimation result and the measurement result, the posterior estimation equation for the parachute system state is obtained as follows:

[0042]

[0043] In the formula, J k Let K be the matrix of undetermined coefficients. k For Kalman gain.

[0044] In one embodiment, the prior state error and the posterior state error are obtained based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, including:

[0045] Based on the linear Kalman state transition equation (11), the prior and posterior estimation equations (15), the prior state error is obtained. and posterior state error

[0046]

[0047]

[0048] In one embodiment, the Kalman gain equation is obtained based on the prior state error, the posterior state error, and the posterior estimation equation, including:

[0049] Substituting the prior state error, i.e., equation (16), into the posterior estimation equation, i.e., equation (15), we get:

[0050]

[0051] Substituting equation (12) into equation (18), we get:

[0052]

[0053] Substituting equation (19) into the posterior state error, i.e., equation (17), we get:

[0054]

[0055] According to the orthogonality rule of stochastic processes, the posterior state error and measured value y iThe relationship is:

[0056]

[0057] Substituting equation (20) into equation (21), we get:

[0058]

[0059] Substituting equation (12) (let k = i) into equation (22), we get:

[0060]

[0061] Based on the random measurement process noise, the lack of correlation between measurement noise and the measurement process, and the orthogonality criterion, we obtain from equation (23):

[0062]

[0063] because For equation (26) to always hold true, then we have:

[0064] J k =IK k H k (27)

[0065] Substituting equation (27) into equation (15), we obtain the Kalman gain equation:

[0066]

[0067] In the formula, K k For Kalman gain.

[0068] In one embodiment, the error covariance matrix and the prior error covariance matrix are defined, and the Kalman gain equation is solved to obtain the Kalman gain that minimizes the trace of the error covariance matrix, including:

[0069] Define the error covariance matrix P k :

[0070]

[0071] According to equations (20), (27), and (29), we get:

[0072]

[0073] Define the prior error covariance matrix

[0074]

[0075] According to equation (31):

[0076]

[0077] In formula (33), P k The trace of the Kalman gain K k The partial derivatives are zero, so:

[0078]

[0079] Solving equation (34) yields:

[0080]

[0081] In one embodiment, the state reconstruction result of the paraglider system state is obtained based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, including:

[0082]

[0083]

[0084] J k =IK k H k

[0085] in For the state reconstruction result, K k For Kalman gain, J k This is the matrix of undetermined coefficients.

[0086] A state estimation device for trajectory reconstruction of a paraglider system includes:

[0087] The acquisition module is used to acquire the process equations of the paraglider system and the observation data of the paraglider system, and to obtain the observation equations of the paraglider system based on the observation data; Taylor expansion is performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations.

[0088] The estimation module is used to obtain the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state based on the linear Kalman state transition equation.

[0089] The calculation module is used to obtain the prior state error and the posterior state error based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation; to obtain the Kalman gain equation based on the prior state error, the posterior state error, and the posterior estimate equation; to define the error covariance matrix and the prior error covariance matrix, to solve the Kalman gain equation, to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and to obtain the undetermined coefficient matrix of the Kalman gain equation;

[0090] The reconstruction module is used to obtain the state reconstruction result of the paraglider system state based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix.

[0091] A computer device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program performing the following steps:

[0092] The process equations and observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data. Taylor expansions are performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations.

[0093] Based on the linear Kalman state transition equation, the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state are obtained.

[0094] Based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, the prior state error and the posterior state error are obtained; based on the prior state error, the posterior state error, and the posterior estimate equation, the Kalman gain equation is obtained; the error covariance matrix and the prior error covariance matrix are defined, and the Kalman gain equation is solved to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and the undetermined coefficient matrix of the Kalman gain equation is obtained;

[0095] Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction result of the paraglider system is obtained.

[0096] A computer-readable storage medium having a computer program stored thereon, the computer program performing the following steps when executed by a processor:

[0097] The process equations and observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data. Taylor expansions are performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations.

[0098] Based on the linear Kalman state transition equation, the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state are obtained.

[0099] Based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, the prior state error and the posterior state error are obtained; based on the prior state error, the posterior state error, and the posterior estimate equation, the Kalman gain equation is obtained; the error covariance matrix and the prior error covariance matrix are defined, and the Kalman gain equation is solved to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and the undetermined coefficient matrix of the Kalman gain equation is obtained;

[0100] Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction result of the paraglider system is obtained.

[0101] The aforementioned method, apparatus, equipment, and medium for reconstructing the trajectory of a paraglider system is a paraglider system trajectory reconstruction method based on Kalman state estimation. It assumes the presence of noise in both the system and the measurement process, and is applicable to various trajectory reconstruction problems with wide applicability. Specifically, when the true state variables of the paraglider system at a certain moment are unknown, a priori estimates of the state variables at the next moment are obtained using a dynamic theory model (i.e., process equations). Measurements of paraglider flight data are obtained through observation or measurement. Based on these measurements, the aforementioned extended Kalman filtering method is used to estimate the true values. Combined with the dynamic and kinematic relationships of the dynamic theory model, the time histories of other state variables, such as the angle of attack, which cannot be measured, are reconstructed. This restores the dynamic state changes of various state variables of the nonlinear paraglider system over a certain time period. In situations where the understanding of the paraglider system is insufficient or the dynamic model is incomplete, this provides a reference for model correction and flight characteristic analysis. Attached Figure Description

[0102] Figure 1 This is a diagram illustrating an application scenario of the state estimation method for trajectory reconstruction of a paraglider system in one embodiment.

[0103] Figure 2 This is a flowchart illustrating the state estimation method for trajectory reconstruction of a paraglider system in one embodiment;

[0104] Figure 3 Here is a diagram showing the horizontal velocity reconstruction result and deviation in one embodiment, where (a) is the horizontal velocity reconstruction result diagram and (b) is the horizontal velocity deviation diagram;

[0105] Figure 4 Here is a height reconstruction result and deviation map in one embodiment, where (a) is the height reconstruction result map and (b) is the height deviation map;

[0106] Figure 5 Here is a diagram showing the reconstructed heading angle and the deviation in one embodiment, where (a) is the diagram showing the reconstructed heading angle and (b) is the diagram showing the deviation heading angle.

[0107] Figure 6 Here is a diagram showing the pitch angle reconstruction result and deviation in one embodiment, where (a) is the pitch angle reconstruction result diagram and (b) is the pitch angle deviation diagram;

[0108] Figure 7 Here is a roll angle reconstruction result and deviation diagram in one embodiment, where (a) is the roll angle reconstruction result diagram and (b) is the roll angle deviation diagram;

[0109] Figure 8 Here is a diagram showing the 3D trajectory reconstruction result and deviation in one embodiment, where (a) is the 3D trajectory reconstruction result diagram and (b) is the 3D trajectory deviation diagram;

[0110] Figure 9 This is a comparison diagram of the reconstructed angle of attack, sideslip angle, and lift-to-drag ratio in one embodiment, where (a) is the reconstructed angle of attack, (b) is the reconstructed sideslip angle, and (c) is the reconstructed lift-to-drag ratio.

[0111] Figure 10 This is a structural block diagram of a state estimation device for trajectory reconstruction of a paraglider system in one embodiment;

[0112] Figure 11 This is an internal structural diagram of a computer device in one embodiment. Detailed Implementation

[0113] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0114] It should be noted that all directional indicators (such as up, down, left, right, front, back, etc.) in the embodiments of this application are only used to explain the relative positional relationship and movement of each component in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicator will also change accordingly.

[0115] Furthermore, the use of terms such as "first" and "second" in this application is for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of those features. In the description of this application, "multiple sets" means at least two sets, such as two sets, three sets, etc., unless otherwise explicitly specified.

[0116] In this application, unless otherwise expressly specified and limited, the terms "connection," "fixed," etc., should be interpreted broadly. For example, "fixed" can mean a fixed connection, a detachable connection, or an integral part; it can mean a mechanical connection, an electrical connection, a physical connection, or a wireless communication connection; it can mean a direct connection or an indirect connection through an intermediate medium; it can mean the internal communication of two elements or the interaction between two elements, unless otherwise expressly limited. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0117] Furthermore, the technical solutions of the various embodiments of this application can be combined with each other, but only if they are based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such combination of technical solutions does not exist and is not within the scope of protection claimed by this application.

[0118] The method provided in this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. Terminal 102 may include, but is not limited to, various personal computers, laptops, smartphones, tablets, and portable wearable devices. Server 104 may be a server corresponding to various portal websites or work system backends.

[0119] This application provides a state estimation method for trajectory reconstruction of a paraglider system, such as... Figure 2 As shown, in one embodiment, the method is applied to Figure 1 Taking the terminal in the example, the explanation includes:

[0120] Step 202: Obtain the process equations and observation data of the paraglider system, and obtain the observation equations of the paraglider system based on the observation data; perform Taylor expansion on the process equations and observation equations respectively to obtain the linear Kalman state transition equations.

[0121] Specifically:

[0122] Obtaining the process equations of the parachute system: The parachute system is a typical nonlinear continuous dynamic system, and its state is described by the following nonlinear differential equations:

[0123]

[0124] In the formula, x true Let x be the true state vector of the system. true The derivative of the system's true state vector with respect to time, including velocity and angular velocity components; f(x true ) is a nonlinear function of the state vector; w is the process noise;

[0125] Process noise w is defined as:

[0126]

[0127] In the formula, E is the expected value, and w n Let n be the process noise vector at time n. Q is the transpose of the process noise vector at time k. k Let be a constant representing the magnitude of process noise;

[0128] During the actual observation and measurement of the parachute system's state, observation data of the parachute system is acquired, and the observation equation of the parachute system is obtained based on the observation data. The observation equation is also expressed in a nonlinear form:

[0129] y true =h(x true )+v (3)

[0130] In the formula, y true For x at time k true The measured value; h(x) true ) is a nonlinear function of the state vector, determined by the measurement method, specifically existing technology; v is the observation noise;

[0131] The observation noise v is defined as:

[0132]

[0133] In the formula, v n Let be the measurement noise vector at time n. R is the transpose of the measurement noise vector at time k. k A constant representing the magnitude of the measurement noise;

[0134] Define the state error vector x and the observation error vector y as follows:

[0135] x = x true -x referemce (5)

[0136] y = y true -y referemce (6)

[0137] in:

[0138] y referemce =h(x referemce )+v

[0139] In the formula, x referemce For reference track, y referemce For reference measurement value, h(x) referemce) is a nonlinear function of the state vector, determined by the measurement method;

[0140] When the reference track is close enough to the actual track, the deviation between the two can be approximated by the first few terms of the Taylor expansion of the deviation.

[0141] Ignoring the noise term w, the process equation, i.e., equation (1), is applied to x. reference Taylor expansion is as follows:

[0142]

[0143] Taking the first two terms of equation (7), we have the process differential equation:

[0144]

[0145] In the formula, F is the Jacobi matrix of the function f;

[0146] Similarly, the observation equation, i.e., equation (3), is applied to x. reference Taylor expansion yields the observation differential equation:

[0147]

[0148] In the formula, H is the Jacobi matrix of the h function;

[0149] For the process differential equation, i.e., equation (8), the solution has the following form:

[0150] x k+1 =Φ k+1,k x k (10)

[0151] In the formula, x k Let Φ be the true state vector of the parachute system at time k. k+1,k This is the state transition matrix from time k to time k+1;

[0152] By adding noise terms w and v, and according to equations (8), (9), and (10), the linear Kalman state transition equation is obtained:

[0153] x k+1 =Φ k+1,k x k +w k (11)

[0154] y k =H k x k +v k (12)

[0155] in:

[0156] Φ k+1,k=I+FΔt (13)

[0157]

[0158] In the formula, y k Let w be the measured value obtained through observation or measurement, Δt be the time interval between the (k+1)th and kth measurements, and w be the measured value. k Let v be the process noise vector at time k. k Let H be the measurement noise vector at time k. k Let I be the Jacobi matrix of the measurement function h, and let I be the identity matrix.

[0159] Step 204: Based on the linear Kalman state transition equation, obtain the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state.

[0160] Specifically:

[0161] Define the prior estimate of the state of the parachute system That is, estimating the system state at time k before obtaining the measured value, denoted as

[0162] Define the posterior estimate of the state of the parachute system That is, the measured value y at time k k After generation, a new estimate is obtained. That is, the desired state reconstruction result of the paraglider system of this invention;

[0163] Based on the linear Kalman state transition equations, namely equations (11) and (12), the posterior estimation result, i.e., the reconstruction result, is expressed as a linear combination of the prior estimation and the measurement result, thus obtaining the posterior estimation equation of the parachute system state:

[0164]

[0165] In the formula, J k Let K be the matrix of undetermined coefficients. k For Kalman gain.

[0166] Step 206: Based on the linear Kalman state transition equation, prior estimation, and posterior estimation equation, obtain the prior state error and posterior state error; based on the prior state error, posterior state error, and posterior estimation equation, obtain the Kalman gain equation; define the error covariance matrix and the prior error covariance matrix, solve the Kalman gain equation to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and obtain the undetermined coefficient matrix of the Kalman gain equation.

[0167] Specifically:

[0168] Based on the linear Kalman state transition equations (11) and (12), and the prior and posterior estimation equations (15), the prior state error is obtained. and posterior state error

[0169]

[0170]

[0171] Substituting the prior state error, i.e., equation (16), into the posterior estimation equation, i.e., equation (15), we get:

[0172]

[0173] Substituting equation (12) into equation (18), we get:

[0174]

[0175] Substituting equation (19) into the posterior state error, i.e., equation (17), we get:

[0176]

[0177] According to the orthogonality rule of stochastic processes, the posterior state error and measured value y i The relationship is:

[0178]

[0179] Substituting equation (20) into equation (21), we get:

[0180]

[0181] Substituting equation (12) (let k = i) into equation (22), we get:

[0182]

[0183] According to the definition of random measurement process noise, i.e., observation noise, i.e., equation (4), the last term of equation (23) is zero:

[0184]

[0185] Since the measurement noise is unrelated to the measurement process, the last term of equation (24) is also zero:

[0186]

[0187] According to the orthogonality criterion, the last term of equation (25) is also zero:

[0188]

[0189] because For equation (26) to always hold true, then we have:

[0190] J k =IK k H k (27)

[0191] Substituting equation (27) into equation (15), we obtain the Kalman gain equation:

[0192]

[0193] In the formula, K k For Kalman gain.

[0194] To find K k The optimal value is defined by the error covariance matrix P. k :

[0195]

[0196] Substituting equation (27) into equation (20), we get:

[0197]

[0198] Substituting equation (30) into equation (29), we get:

[0199]

[0200] Define the prior error covariance matrix

[0201]

[0202] According to equation (4):

[0203]

[0204] Assume v k and Unrelated, that is:

[0205]

[0206] Then equation (31) becomes:

[0207]

[0208] In formula (33), P k The trace of the Kalman gain K k The partial derivatives are zero, so:

[0209]

[0210] Solving equation (34) yields:

[0211]

[0212] The Kalman gain value obtained from equation (35) makes the error covariance matrix P k Minimizing the trace is equivalent to minimizing the posterior state error. Its length is the smallest.

[0213] From equations (27) and (35), we obtain the matrix of undetermined coefficients J. k and K k :

[0214]

[0215] Step 208: Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction result of the paraglider system is obtained.

[0216] Specifically:

[0217] Using equations (15), (27), and (35), we obtain the result based on the measured value y. k Parachute system state reconstruction results

[0218] in For the state reconstruction result, K k For Kalman gain, J k The matrix represents the undetermined coefficients. The state reconstruction results include: three-dimensional position, horizontal velocity, attitude angles (roll, pitch, and yaw), and angle of attack / sideslip.

[0219] It should be noted that after obtaining the state reconstruction result, the error covariance matrix also needs to be updated. In the state estimation at the next time step k+1, the error covariance matrix P updated at the previous time step will be used. k That is to say, there is The specific process is as follows.

[0220] Multiply by the right side of both sides of equation (35) Summarized as follows:

[0221]

[0222] Expanding equation (33), according to equation (36), the error covariance matrix after obtaining the measured value is obtained from P. k - Updated to P k have:

[0223]

[0224] The aforementioned state estimation method for paraglider system trajectory reconstruction is a Kalman state estimation-based method. It assumes noise in both the system and the measurement process and is applicable to various trajectory reconstruction problems, with wide applicability. Specifically, when the true state variables of the paraglider system at a certain moment are unknown, a priori estimates of the state variables at the next moment are obtained using a dynamic theory model (i.e., process equations). Measurements of paraglider flight data are obtained through observation or measurement. Based on these measurements, the aforementioned extended Kalman filter method is used to estimate the true values. Combined with the dynamic and kinematic relationships of the dynamic theory model, the time histories of other state variables, such as the angle of attack, which cannot be measured, are reconstructed. This restores the dynamic state changes of various state variables in the nonlinear paraglider system over a certain time period. When the understanding of the paraglider system is insufficient or the dynamic model is incomplete, this provides a reference for model correction and flight characteristic analysis. This application improves the Kalman filter method, which is only applicable to linear systems, to extend its application to nonlinear systems. By linearizing the nonlinear system equations, the state estimation results for complex nonlinear systems have smaller errors and better performance, achieving better trajectory reconstruction results.

[0225] It should be understood that, although Figure 2 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified in this document, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 2 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but may be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but may be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0226] In a specific embodiment, taking a six-degree-of-freedom paraglider system dynamics model as an example, the system's state equation is described by the following equation:

[0227]

[0228]

[0229] In the formula, m is the mass matrix of the parachute system; m add I is the added mass matrix of the parachute system; I is the moment of inertia matrix; I add The additional moment of inertia matrix; u, v, w are the three components of the parachute velocity in the body coordinate system; p, q, r are the three angular velocity components of the parachute's rotation around the body coordinate system; F aF is the vector of aerodynamic force in the body coordinate system. g F is the vector of gravity in the body coordinate system. am M is the vector of the additional inertial force in the body coordinate system. a M is the vector of aerodynamic torque in the volume coordinate system. ai The vector of the additional inertial torque in the body coordinate system.

[0230] The noise terms are assumed to follow a Gaussian distribution with a mean of 0 and a variance of 1. The observation matrix, state transition matrix, and covariance matrix of the initial state variables are all identity matrices I. Kalman state estimation is used to reconstruct the state variables of the paraglider system during the hovering phase, restoring the changes in the system state over that time period. The reconstructed state variables include altitude, horizontal velocity, attitude angles (heading angle, roll angle, pitch angle), and 3D trajectory. Model simulation results, trajectory reconstruction results, and measurement results are presented. The relative deviations between the model simulation results, reconstruction results, and measurement values ​​are shown below. Figures 3 to 8 As shown.

[0231] Figures 3 to 8 The results show that, compared with the theoretical model, the trajectory reconstruction results have a significantly smaller relative deviation from the measurement results. Under the premise that the measurement results are more reliable, the trajectory reconstruction results can be considered to be closer to the actual flight state of the paraglider system.

[0232] Based on the reconstruction results and dynamic relationships, the time histories of other state variables that are not directly measured, such as angle of attack, sideslip angle, and lift-to-drag ratio, can also be derived. These can serve as a reference for analyzing paraglider flight performance. Figure 9 As shown.

[0233] according to Figure 9 Comparing the results from the model with the EKF results (i.e., the reconstructed results), when the paraglider system hovers at an altitude of 1200m-2200m, the angle of attack is approximately 20°, the sideslip angle is -3 to -4°, and the lift-to-drag ratio is approximately 2.5, which is consistent with the design conditions of this type of paraglider. Moreover, all three parameters exhibit periodic fluctuations, with the fluctuation period being approximately equal to the change period of the heading angle (approximately 70s). In other words, when the paraglider is in stable hovering flight, the angle of attack, sideslip angle, and lift-to-drag ratio are also fluctuating stably. This phenomenon can also be observed in the measurement results of horizontal speed and roll angle, which indirectly confirms the reliability of the reconstructed results.

[0234] This application also provides a state estimation device for trajectory reconstruction of a paraglider system, such as... Figure 10 As shown, in one embodiment, it includes: an acquisition module 1002, an estimation module 1004, a calculation module 1006, and a reconstruction module 1008, wherein:

[0235] The acquisition module 1002 is used to acquire the process equations of the paraglider system and the observation data of the paraglider system, and to obtain the observation equations of the paraglider system based on the observation data; and to perform Taylor expansion on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations.

[0236] The estimation module 1004 is used to obtain the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state based on the linear Kalman state transition equation.

[0237] The calculation module 1006 is used to obtain the prior state error and the posterior state error based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation; to obtain the Kalman gain equation based on the prior state error, the posterior state error, and the posterior estimate equation; to define the error covariance matrix and the prior error covariance matrix, to solve the Kalman gain equation, to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and to obtain the undetermined coefficient matrix of the Kalman gain equation;

[0238] The reconstruction module 1008 is used to obtain the state reconstruction result of the paraglider system state based on the posterior estimation equation, Kalman gain and undetermined coefficient matrix.

[0239] Specific limitations regarding the state estimation device for paraglider system trajectory reconstruction can be found in the limitations of the state estimation method for paraglider system trajectory reconstruction described above, and will not be repeated here. Each module in the aforementioned device can be implemented entirely or partially through software, hardware, or a combination thereof. These modules can be embedded in or independent of the processor in a computer device, or stored in the memory of a computer device as software, so that the processor can call and execute the corresponding operations of each module.

[0240] In one embodiment, a computer device is provided, which may be a terminal, and its internal structure diagram may be as follows: Figure 11As shown, the computer device includes a processor, memory, network interface, display screen, and input devices connected via a system bus. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The network interface is used to communicate with external terminals via a network connection. When executed by the processor, the computer program implements a state estimation method for paraglider system trajectory reconstruction. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad mounted on the computer device casing, or an external keyboard, touchpad, or mouse.

[0241] Those skilled in the art will understand that Figure 11 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0242] In one embodiment, a computer device is provided, including a memory and a processor, the memory storing a computer program, the processor executing the computer program to implement the steps of the method described above.

[0243] In one embodiment, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described above.

[0244] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0245] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0246] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A state estimation method for trajectory reconstruction of a paraglider system, characterized in that, include: The process equations of the paraglider system and the observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data. Taylor expansions of the process equation and the observation equation are performed respectively to obtain the linear Kalman state transition equation; Based on the linear Kalman state transition equation, the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state are obtained. Based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, the prior state error and the posterior state error are obtained; based on the prior state error, the posterior state error, and the posterior estimate equation, the Kalman gain equation is obtained; the error covariance matrix and the prior error covariance matrix are defined, and the Kalman gain equation is solved to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and the undetermined coefficient matrix of the Kalman gain equation is obtained; Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction result of the paraglider system is obtained; The linear Kalman state transition equation is: (11) (12) in: (13) (14) In the formula, These are measured values ​​obtained through observation or measurement. For the first k+1 The and the first k The time interval between measurements F for f The Jacobi matrix of the function, For parachute system in k The true state vector at time t, For the first k The measurement noise vector at any given time; Based on the linear Kalman state transition equations, the prior estimate and posterior estimate equations of the parachute system state are obtained as follows: Based on the linear Kalman state transition equation, a priori estimate of the parachute system state is defined. Define the posterior estimate of the state of the parachute system. Assuming the posterior estimation result is a linear combination of the prior estimation result and the measurement result, the posterior estimation equation for the parachute system state is obtained as follows: (15) In the formula, J k The matrix of undetermined coefficients, K k Kalman gain; Based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation, the prior state error and the posterior state error are obtained as follows: Based on the linear Kalman state transition equation (11), the prior and posterior estimation equations (15), the prior state error is obtained. and posterior state error : (16) (17)； Based on the prior state error, the posterior state error, and the posterior estimation equation, the Kalman gain equation is obtained as follows: Substituting the prior state error, i.e., equation (16), into the posterior estimation equation, i.e., equation (15), we get: (18) Substituting equation (12) into equation (18), we get: (19) Substituting equation (19) into the posterior state error, i.e., equation (17), we get: (20) According to the orthogonality rule of stochastic processes, the posterior state error and measured values The relationship is: (21) Substituting equation (20) into equation (21), we get: (22) Then let equation (12) (let) k=i Substituting into equation (22), we get: (23) Based on the random measurement process noise, the lack of correlation between measurement noise and the measurement process, and the orthogonality criterion, we obtain from equation (23): (26) because To make equation (26) always hold true, we have: (27) Substituting equation (27) into equation (15), we obtain the Kalman gain equation: (28) In the formula, K k This is the Kalman gain.

2. The state estimation method for trajectory reconstruction of a paraglider system according to claim 1, characterized in that, The process equations of the paraglider system and the observation data of the paraglider system are obtained, and the observation equations of the paraglider system are obtained based on the observation data. Taylor expansions of the process equation and the observation equation yield the linear Kalman state transition equations, including: Obtaining the process equations for the parachute system: (1) In the formula, This represents the system's true state vector. It is a nonlinear function of the state vector; w This is process noise; Obtain observation data of the parachute system, and derive the observation equations for the parachute system based on the observation data: (3) In the formula, To The measured value; It is a nonlinear function of the state vector; v To observe noise; Define the state error vector x and observation error vector y for: (5) (6) in: In the formula, For reference flight path, For reference measurement value; The process equation is in Taylor expansion yields the process differential equation: (8) In the formula, F for f The Jacobi matrix of the function; The observation equation is in Taylor expansion yields the observation differential equation: (9) In the formula, H for h The Jacobi matrix of the function; For the process differential equation, the solution has the following form: (10) In the formula, For parachute system in k The true state vector at any given time; Based on equations (9) and (10), the linear Kalman state transition equation is obtained: (11) (12) in: (13) (14) In the formula, These are measured values ​​obtained through observation or measurement. For the first k+1 The and the first k The time interval between measurements Let k be the process noise vector at time k. For measurement function h Jacobi matrix, It is the identity matrix. For the reason k Time's up k The state transition matrix at time +1.

3. The state estimation method for trajectory reconstruction of a paraglider system according to claim 2, characterized in that, Define the error covariance matrix and the prior error covariance matrix, and solve the Kalman gain equation to obtain the Kalman gain that minimizes the trace of the error covariance matrix, including: Define the error covariance matrix P k : (29) According to equations (20), (27), and (29), we get: (31) Define the prior error covariance matrix : According to equation (31), we have: (33) In formula (33) P k The trace of Kalman gain K k The partial derivatives are zero, so: (34) Equation (34) can be solved to obtain: (35)。 4. The state estimation method for trajectory reconstruction of a paraglider system according to claim 3, characterized in that, Based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix, the state reconstruction results of the paraglider system include: in For the state reconstruction result, K k For Kalman gain, J k This is the matrix of undetermined coefficients.

5. A state estimation device for trajectory reconstruction of a paraglider system, characterized in that, The state estimation method for trajectory reconstruction of a paraglider system according to any one of claims 1 to 4 includes: The acquisition module is used to acquire the process equations of the paraglider system and the observation data of the paraglider system, and to obtain the observation equations of the paraglider system based on the observation data; Taylor expansion is performed on the process equations and the observation equations respectively to obtain the linear Kalman state transition equations. The estimation module is used to obtain the prior estimate of the parachute system state and the posterior estimate equation of the parachute system state based on the linear Kalman state transition equation. The calculation module is used to obtain the prior state error and the posterior state error based on the linear Kalman state transition equation, the prior estimate, and the posterior estimate equation; to obtain the Kalman gain equation based on the prior state error, the posterior state error, and the posterior estimate equation; to define the error covariance matrix and the prior error covariance matrix, to solve the Kalman gain equation, to obtain the Kalman gain that minimizes the trace of the error covariance matrix, and to obtain the undetermined coefficient matrix of the Kalman gain equation; The reconstruction module is used to obtain the state reconstruction result of the paraglider system state based on the posterior estimation equation, Kalman gain, and undetermined coefficient matrix.

6. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method according to any one of claims 1 to 4.

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