A high-speed maneuvering target tracking method combining parameter identification and waveform selection

Abstract

The application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection, and solves the technical problems of existing high-speed maneuvering target tracking, such as mismatch of dynamic model, prominent contradiction of measurement noise and high loss rate. It comprises the following steps: calculating aerodynamic acceleration, decomposing and backstepping aerodynamic parameters, constructing a nine-dimensional state vector, calculating new information after state estimation; estimating acceleration derivative, extracting flight path tilt angle, calculating FrFT rotation angle, constructing a two-dimensional waveform library, selecting waveform parameters minimizing the trace of the covariance matrix, and real-time matching of waveform parameters and target maneuvering characteristics; constructing a double closed-loop cooperative control architecture, fusing inner and outer loop control quantities through a joint correction mechanism, updating the covariance matrix and the nine-dimensional state vector, judging whether the tracking time length reaches the preset threshold, if not, taking it as the initial value at the next moment; otherwise, obtaining the target tracking result. The application can be widely applied in the technical field of target tracking.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of target tracking, and more particularly relates to a high-speed maneuvering target tracking method combining parameter identification and waveform selection. BACKGROUND

[0002] High-speed maneuvering target tracking is a key technical challenge in the field of civil radars. Due to targets such as low-altitude unmanned aerial vehicles and hypersonic aircraft, such targets have the characteristics of small radar scattering cross section, strong maneuverability, high speed and complex motion characteristics, which leads to the failure of traditional tracking methods. The key to realizing effective target tracking is to realize that the established target motion model can match the actual target motion model, and to perform adaptive filtering processing. For high-speed maneuvering targets, the aerodynamic characteristics change dramatically with the flight attitude, and the traditional tracking model (such as the CV / CA / Singer model) does not consider the coupling relationship between aerodynamic force and motion attitude. The fixed parameter model cannot describe such nonlinear changes. The nonlinear changes of the aerodynamic parameters will lead to model mismatch when the target performs high maneuvering flight, and the prediction will deviate significantly, and the trajectory will diverge.

[0003] The existing Chinese invention patent with the publication number CN116909303B provides a process noise adaptive adjustment method for near-space target tracking. Through adaptive adjustment, the adverse effects of model error changes on target tracking are weakened, and the tracking accuracy and stability are improved. The size of the process noise variance of the extended state is adjusted using an adaptive adjustment factor. When the model error is large, the process noise is increased, and when the model error is small, the process noise is reduced.

[0004] However, the fixed parameter radar waveform of this patent cannot simultaneously meet the needs of high range resolution and high Doppler resolution. Narrow pulses improve range resolution but reduce Doppler resolution, and wide frequency sweeps improve speed resolution but reduce range accuracy. This contradiction will cause serious range-velocity coupling errors in strong maneuvering target tracking. The fixed parameter adjustment method of this patent cannot dynamically balance the two, and significant measurement noise is generated in strong maneuvering target tracking. In addition, the existing scheme treats state estimation and waveform selection as independent modules, which causes the aerodynamic parameter identification to rely on historical data, resulting in response lag, and the waveform selection is not related to the real-time maneuvering direction of the target, causing the model error and the measurement noise to form a positive feedback, further deteriorating the tracking accuracy. SUMMARY

[0005] The purpose of the embodiments of the present application is to provide a high-speed maneuvering target tracking method combining parameter identification and waveform selection, to solve the technical problems of model mismatch, prominent measurement noise contradiction and high loss rate in high-speed maneuvering target tracking in the prior art.

[0006] To achieve the above object, the embodiment of the present application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection, comprising the following steps:

[0007] The aerodynamic acceleration is calculated according to the radar measurement value, the aerodynamic parameters are defined based on the decoupling design after decomposition, and the nine-dimensional state vector is constructed;

[0008] The extended Kalman filter fusing the aerodynamic parameters is constructed, the state prediction value and the covariance matrix are obtained by state estimation on the nine-dimensional state vector, the innovation is calculated combined with the radar measurement value, and the aerodynamic parameters are updated in real time;

[0009] The acceleration derivative is estimated according to the trace change rate of the covariance matrix, the flight path inclination angle is extracted according to the target speed component, the FrFT rotation angle is calculated by using the two, the two-dimensional waveform library is constructed, the waveform parameters minimizing the trace of the covariance matrix are selected, and the waveform parameters are matched with the target maneuvering characteristics in real time;

[0010] The double closed-loop cooperative control architecture is constructed, the aerodynamic parameters are corrected in the inner loop, the waveform is optimized to suppress noise in the outer loop, the inner and outer loop control quantities are fused through the joint correction mechanism, the error cooperative suppression is realized, the covariance matrix and the nine-dimensional state vector are updated, whether the tracking time length reaches the preset threshold is judged, if not, the covariance matrix and the nine-dimensional state vector are taken as the initial values at the next time; otherwise, the target tracking result is obtained.

[0011] Preferably, the aerodynamic acceleration is decomposed by a coordinate matrix to obtain the resistance direction, the tangential and normal accelerations, and the aerodynamic parameters are defined based on the decoupling design combined with the backstepping aerodynamic parameters;

[0012] The decoupling design of the aerodynamic parameter definition refers to decoupling the aerodynamic parameters in the traditional aerodynamic parameter definition analysis process, and converting the drag coefficient and the lift coefficient in the aerodynamic parameters into the drag-related coefficient and the lift-related coefficient containing the mass and the reference area of the maneuvering target.

[0013] Preferably, the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuvering direction, the FrFT rotation angle is calculated according to the flight path inclination angle and the acceleration derivative after the orthogonal, the optimal waveform is selected as the waveform parameter minimizing the trace of the covariance matrix by using the mapping relationship between the predicted covariance matrix and the Cramer-Rao lower bound matrix with the FrFT rotation angle as the guide, and the adaptive matching of the waveform parameters and the target maneuvering characteristics is realized.

[0014] Preferably, the aerodynamic acceleration is decomposed to obtain the aerodynamic parameter sensitive term, and the extended Kalman filter fusing the aerodynamic parameters is constructed by constructing the Jacobian matrix.

[0015] Preferably, the change of the aerodynamic parameters is converted into the acceleration correction amount based on the state equation and the Jacobian matrix in the inner loop, and the state equation is:

[0016] ;

[0017] wherein, is the velocity, is the time, is the gravity acceleration, is the aerodynamic acceleration, is the process noise.

[0018] Preferably, the linearized representation of the acceleration correction is an aerodynamic parameter difference vector, and the formula is:

[0019] ;

[0020] wherein, is the aerodynamic parameter difference vector, is the increment of the drag correlation coefficient, is the lift correlation coefficient estimated at the kth time, is the difference of the lift direction angle.

[0021] Preferably, the outer loop selects the waveform parameter that minimizes the noise covariance matrix by calculating the noise covariance matrix under different waveform parameters, and calculates the noise covariance change caused by the waveform switching.

[0022] Preferably, the inner and outer loop control quantities include an inner loop gain and an outer loop gain, the inner loop gain is constructed based on the aerodynamic parameter sensitivity term in the Jacobian matrix, and the outer loop gain is determined by the difference of the trace of the Cramer-Rao lower bound matrix of the waveform parameter;

[0023] According to the noise covariance change and the inner and outer loop control quantities, a joint correction quantity is calculated, the Kalman gain is adjusted based on the Kalman gain and the joint correction quantity, the covariance matrix is corrected, and the formula is as follows:

[0024] = ;

[0025] wherein, is the covariance matrix at k time, is the adjusted Kalman gain, is the observation matrix, is the noise covariance matrix, is the waveform parameter at k time, is the covariance matrix at k-1 time.

[0026] Preferably, the process of calculating the aerodynamic acceleration includes:

[0027] The measurement value obtained by the radar in the sampling period is converted into rectangular coordinates, and the difference is obtained to obtain the velocity component, and the aerodynamic acceleration is calculated according to the velocity component, and the formula is as follows:

[0028] ;

[0029] wherein, is the acceleration component in the x-axis direction, is the acceleration component in the x-axis direction, is the acceleration component in the x-axis direction, , , are respectively the velocity components in the x, y, z coordinate directions at the end of the first sampling period, , , are respectively the velocity components in the x, y, z coordinate directions at the end of the second sampling period, is the sampling time interval of the radar, is the gravitational acceleration.

[0030] Preferably, the formula for calculating the innovation is as follows:

[0031] ;

[0032] wherein, is the innovation, is the innovation covariance, is the Kalman gain, is the actual observation value of the radar in the kth sampling period, is the Jacobian matrix of the measurement function, is the state prediction covariance at time k, is a nonlinear measurement function that maps the state space prediction value to the radar observation space, is the state prediction value at time k, is the measurement noise covariance matrix.

[0033] The application has the beneficial effects that: the application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection. Firstly, by constructing a nine-dimensional state vector containing position, velocity and aerodynamic parameters, the unified description of motion state and aerodynamic parameters is realized, and the decoupling of mass cross-sectional area is realized, thereby solving the problem of poor adaptability of the traditional CV / CA model to nonlinear maneuvering, so as to realize the matching of the dynamic model. Secondly, the maneuvering guide waveform optimization mechanism is constructed, the target acceleration derivative and the track inclination angle are dynamically associated based on the FrFT rotation angle adjustment strategy, the waveform ambiguity function direction is adaptively optimized, the contradiction between the range resolution and the Doppler resolution is effectively balanced, and the problem of prominent measurement noise is solved, thereby improving the measurement accuracy in the low-altitude environment. Finally, the double closed-loop cooperative control architecture is constructed. The inner loop dynamically corrects the dynamic model by real-time identification of the aerodynamic parameters, and the outer loop suppresses the measurement noise by waveform optimization. The inner loop corrects the aerodynamic parameters, and the outer loop optimizes the waveform to suppress the noise. The double loops realize cooperative error suppression, generate inner and outer control quantities, update the covariance matrix and the nine-dimensional state vector, judge whether the tracking time length reaches the preset threshold, if yes, take the covariance matrix and the nine-dimensional state vector as the initial values at the next moment, realize the closed-loop feedback, otherwise, end the tracking process, obtain the target tracking result, and realize high-precision tracking. BRIEF DESCRIPTION OF DRAWINGS

[0034] In order to more clearly illustrate the technical solutions in the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the application, and other drawings can be obtained by those skilled in the art without creative labor.

[0035] Figure 1 The whole flowchart of a high-speed maneuvering target tracking method combining parameter identification and waveform selection provided by an embodiment of the application is shown in the figure.

[0036] Figure 2 The result diagram of waveform parameter selection at each moment provided by an embodiment of the application is shown in the figure, wherein (1) is a distribution diagram of pulse length selected in different time periods, and (2) is a distribution diagram of sweep width selected in different time periods.

[0037] Figure 3 The target trajectory comparison diagram obtained by the application and the fixed waveform method provided by an embodiment of the application is shown in the figure.

[0038] Figure 4 The comparison diagram of aerodynamic parameters calculated by parameter estimation and optimized trajectory provided by an embodiment of the application is shown in the figure.

[0039] Figure 5The application provides a comparison chart of tracking errors in positions of the application and a traditional fixed waveform method, wherein (1) is a comparison chart of root mean square errors in X direction positions of the application and the fixed waveform, (2) is a comparison chart of root mean square errors in Y direction positions of the application and the fixed waveform, and (3) is a comparison chart of root mean square errors in Z direction positions of the application and the fixed waveform.

[0040] Figure 6 The application provides a comparison chart of speeds of the application and a traditional fixed waveform method and real speeds, wherein (1) is a comparison chart of X direction speeds of the application and the fixed waveform and real X direction speeds, (2) is a comparison chart of Y direction speeds of the application and the fixed waveform and real Y direction speeds, and (3) is a comparison chart of Z direction speeds of the application and the fixed waveform and real Z direction speeds. DETAILED DESCRIPTION

[0041] In order to make the technical problems, technical solutions and beneficial effects of the application clearer, the application is further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the application and do not limit the application.

[0042] The application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection. Firstly, a complex nine-dimensional joint state vector containing positions, speeds and aerodynamic parameters is constructed to establish a joint state space, so that the motion state and the aerodynamic parameters are uniformly described, thereby solving the problem that a traditional tracking model (such as a CV / CA / Singer model) is poor in adaptability to nonlinear maneuvers. Secondly, a maneuvering guide waveform optimization mechanism is constructed, a rotation angle adjustment strategy based on fractional Fourier transform is used to realize real-time sensing of target acceleration rate and track features, and the direction of a waveform fuzzy function is adaptively optimized, so that the contradiction between distance resolution and Doppler resolution is effectively balanced, and the measurement accuracy is improved in a low-altitude environment. Finally, a double-closed-loop cooperative control architecture is constructed, the inner loop dynamically corrects a dynamic model through real-time identification of aerodynamic parameters, the outer loop suppresses measurement noise through waveform optimization, the double loops realize cooperative suppression of errors, generate a joint control quantity, and effectively improve the target tracking accuracy.

[0043] Please refer to Figure 1 The application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection, comprising the following steps.

[0044] S1: Convert the measurements acquired by the radar during the sampling period into rectangular coordinates, perform differential to obtain velocity components, calculate aerodynamic acceleration based on velocity components, decompose to obtain drag direction, tangential and normal acceleration, back-infer aerodynamic parameters based on drag direction, tangential, normal acceleration and decoupled design aerodynamic parameters, and construct a nine-dimensional state vector containing target motion state and aerodynamic parameters.

[0045] Specifically, in an optional embodiment, the measurements from the first three sampling cycles of the radar are... , , The measurements are converted from polar coordinates to rectangular coordinates to obtain the horizontal, vertical, and triangular coordinates acquired during the first sampling period. , , The horizontal, vertical, and axial coordinates obtained from the second sampling period. , , And the horizontal, vertical and horizontal coordinates obtained from the third sampling period , , The formula is as follows:

[0046] ;

[0047] In the formula, , , These are the horizontal, vertical, and axial coordinates obtained from the measurements during the sampling period. For the first Each sampling period represents the unbiased conversion coefficient for azimuth measurement accuracy. For the first Each sampling period represents the unbiased conversion coefficient for pitch angle measurement accuracy. This represents the straight-line distance between the radar and the target measured in the first sampling period. The target azimuth angle measured by the radar in the first sampling period. This is the target elevation angle measured by the radar in the first sampling period, which is the angle between the target and the horizontal plane. This represents the straight-line distance between the radar and the target measured in the second sampling period. The target azimuth angle measured by the radar in the second sampling period. The target elevation angle measured by the radar in the second sampling period. This represents the straight-line distance between the radar and the target measured in the third sampling period. The target azimuth angle measured by the radar in the third sampling period. The target elevation angle measured by the radar in the third sampling period. , is the index of the sampling period, is the index of the sampling period, is the reciprocal of, is the reciprocal of, is the reciprocal of, is the straight-line reference distance of the target measured by the radar in the th sampling period, is the reference azimuth angle measured by the radar in the th sampling period, is the reference elevation angle measured by the radar in the th sampling period, is the error variance of the azimuth angle measured by the radar in the th sampling period, is the error variance of the elevation angle measured by the radar in the th sampling period.

[0048] The horizontal, vertical and longitudinal coordinates measured in the first, second and third sampling periods are differentiated to calculate the velocity components, and the formulas are as follows:

[0049] ;

[0050] ;

[0051] In the formula, is the velocity component in the horizontal coordinate direction at the end of the first sampling period, is the velocity component in the vertical coordinate direction at the end of the first sampling period, is the velocity component in the longitudinal coordinate direction at the end of the first sampling period, is the sampling time interval of the radar, is the velocity component in the horizontal coordinate direction at the end of the second sampling period, is the velocity component in the vertical coordinate direction at the end of the second sampling period, is the velocity component in the longitudinal coordinate direction at the end of the second sampling period.

[0052] The aerodynamic acceleration is calculated according to the velocity components , and , and the calculation formulas are as follows:

[0053] ;

[0054] In the formula, is the acceleration component in the axis direction, is the acceleration component in the axis direction, is the acceleration component in the axis direction, This is the acceleration due to gravity.

[0055] aerodynamic acceleration , , Through coordinate transformation matrix By decomposing the components, we can obtain the acceleration in the direction of resistance. Tangential acceleration and normal acceleration The formula is as follows:

[0056] ;

[0057] In the formula, Acceleration in the direction of resistance For tangential acceleration, Here, is the normal acceleration. The formula is as follows:

[0058] ;

[0059] In the formula, This is the coordinate transformation matrix. For the magnitude of the target velocity, For the target velocity on the horizontal plane ( - The size of the projection on the plane For the goal Velocity components on the axis, For the goal Velocity components on the axis, For the goal Velocity components on the axis.

[0060] Based on acceleration in the direction of resistance Tangential acceleration and normal acceleration The aerodynamic parameters are defined in the decoupled design, and then inversely derived. These aerodynamic parameters include drag correlation coefficients. Lift correlation coefficient and lift direction angle .

[0061] Specifically, this application employs decoupling design for aerodynamic parameters. In the traditional aerodynamic parameter definition and analysis process, the aerodynamic parameters are decoupled, converting aerodynamic forces into forces per unit mass. That is, the drag coefficient is... and lift coefficient Convert to include aircraft mass and reference area resistance correlation coefficient Correlation coefficient with lift , the drag correlation coefficient and the lift correlation coefficient are decoupled. The formula of converting aerodynamic force to unit mass force is as follows:

[0062] ;

[0063] ;

[0064] wherein, is the lift, is the drag, is the lift coefficient, is the drag coefficient, is the mass of the aircraft, is the reference area, is the air density at the target current height (ρ0), is the sea level atmospheric density, is the atmospheric altitude), is the speed of the aircraft.

[0065] After normalization, the drag correlation coefficient and the lift correlation coefficient are obtained, and the drag correlation coefficient and the lift correlation coefficient are decoupled.

[0066] According to the drag direction acceleration , the tangential acceleration and the normal acceleration and the decoupling designed aerodynamic parameter definition, the aerodynamic parameters are back calculated, and the formula is as follows:

[0067] ;

[0068] ;

[0069] ;

[0070] wherein, is the drag correlation coefficient, is the lift correlation coefficient, is the projection angle of the lift vector in the speed plane in the body coordinate system, which is called the lift direction angle, is the air density at the target current height (ρ0), is the sea level atmospheric density, is the atmospheric altitude), is the speed of the aircraft.

[0071] According to the obtained , 、 、 、 、 、 、 、 Construct a nine-dimensional state vector joint state model containing target motion state (position 、 、 Velocity 、 、 ) and aerodynamic parameters 、 、 By including aerodynamic parameters in the state vector, provide a basis for real-time identification, and the constructed nine-dimensional state vector is: .

[0072] S2: Decompose aerodynamic acceleration to obtain aerodynamic parameter sensitive terms, construct Jacobian matrix, and get extended Kalman filter fused with aerodynamic parameters. Through the extended Kalman filter fused with aerodynamic parameters, the state estimation of the nine-dimensional state vector is carried out, and the state prediction value and covariance matrix are obtained, combined with the radar measurement value to calculate the innovation, real-time update the aerodynamic parameters, complete the online identification of target maneuvering characteristics.

[0073] Decompose aerodynamic acceleration to obtain aerodynamic parameter sensitive terms, construct Jacobian matrix, the process is as follows:

[0074] First, according to the aircraft coordinate system, the aerodynamic acceleration is decomposed to obtain:

[0075] ;

[0076] In the formula, is the aerodynamic acceleration, including 、 、 , is the coordinate transformation matrix, is the air density at the current height of the target, is the target speed, is the lift-related coefficient, is the drag-related coefficient, is the lift direction angle.

[0077] Then, let the aerodynamic acceleration The aerodynamic force vector part in the expression is , the formula is as follows:

[0078] ;

[0079] Next, the aerodynamic acceleration According to the chain rule, the following formula is obtained:

[0080] ;

[0081] The direction change term is:

[0082] ;

[0083] The modulus change term is:

[0084] ;

[0085] Therefore, the partial derivative of the aerodynamic acceleration with respect to the velocity, i.e., the aerodynamic parameter sensitivity term, is:

[0086] ;

[0087] where , , are the orthogonal bases of the velocity coordinate system, and the formulas are as follows:

[0088] ;

[0089] where is the velocity in the x-axis direction, is the velocity in the y-axis direction, is the velocity in the z-axis direction.

[0090] After obtaining the aerodynamic parameter sensitivity term, the Jacobian matrix J is established as follows:

[0091] ;

[0092] where is a 3x3 zero matrix, is a 3x3 identity matrix, is the partial derivative of the aerodynamic acceleration with respect to the position, is the partial derivative of the aerodynamic acceleration with respect to the velocity, is the partial derivative of the aerodynamic acceleration with respect to the aerodynamic parameter.

[0093] The extended Kalman filter with fused aerodynamic parameters is used to estimate the nine-dimensional state vector , and the state prediction value and covariance matrix are obtained. The discretized prediction equation is:

[0094] ;

[0095] where is the state prediction value based on the observation information at time k−1 at time k, ​​is the state estimation value at time k-1, is the sampling time interval of radar, is the covariance matrix at time k, is the Jacobian matrix containing the sensitivity terms of aerodynamic parameters for linearizing the nonlinear function, is the estimated error covariance matrix at time k-1, and T is the matrix transpose operator, is the process noise covariance.

[0096] In the measurement update stage, the measurement value obtained by the radar in the sampling period is used , the state prediction value and the covariance matrix to calculate the innovation, and the innovation is updated by iteration to continuously correct the aerodynamic parameters to adapt to the target maneuver. The formula for calculating the innovation is as follows:

[0097] ;

[0098] In the formula, is the innovation, is the innovation covariance, is the Kalman gain, is the actual observation value of the radar in the kth sampling period, is the Jacobian matrix of the measurement function, is the state prediction covariance at time k, is the nonlinear measurement function for mapping the state space prediction value to the radar observation space, is the state prediction value at time k, is the measurement noise covariance matrix.

[0099] S3: Estimate the acceleration derivative according to the trace rate of the covariance matrix, extract the track tilt angle according to the target velocity component, calculate the FrFT rotation angle according to the acceleration derivative and the track tilt angle, construct a two-dimensional waveform library, select the waveform parameters that minimize the trace of the covariance matrix, and real-time match the waveform parameters with the target maneuver characteristics.

[0100] Specifically, the acceleration derivative is estimated according to the trace rate of the covariance matrix; the track geometric feature is extracted according to the velocity components of the target in the horizontal, vertical and longitudinal coordinates at the K moment, to obtain the track inclination angle; in order to minimize the range-Doppler coupling, the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuvering direction, and the FrFT (Fractional Fourier Transform) rotation angle is calculated according to the track inclination angle and the acceleration derivative after the orthogonality. A two-dimensional waveform library containing the pulse length and the sweep width is constructed, the main lobe direction of the waveform ambiguity function is dynamically adjusted based on the FrFT technology, and the waveform parameters capable of minimizing the trace of the predicted covariance matrix are selected; the mapping relationship between the waveform parameters and the tracking accuracy is established through the CRLB (Cramer-Rao Lower Bound), the echo signal is analyzed by using the FrFT, the matching between the steering waveform parameters and the target maneuvering characteristics is realized, and the optimization of the maneuvering steering waveform is completed.

[0101] Firstly, the target maneuvering intensity is estimated, and the trace rate of the state prediction covariance matrix is used to reflect the target maneuvering intensity. Specifically, the acceleration derivative (the rate of change of acceleration) is determined according to the trace rate of the state prediction covariance matrix The acceleration derivative is enhanced by double-step difference

[0102] ;

[0103] In the formula, is the acceleration derivative enhanced by double-step difference, is the state prediction covariance matrix at the K moment, is the state prediction covariance matrix at the last moment, is the trace of the matrix, is the time step.

[0104] Then, the track geometric feature is extracted, and the track geometric feature is determined by the track inclination angle (determining the direction of the lift force). The track inclination angle is extracted, and the formula is as follows:

[0105] ;

[0106] In the formula, is the track inclination angle, , , are the velocity vectors of the target in the , , directions at the k moment, respectively.

[0107] In order to minimize the range-Doppler coupling, the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuvering direction, and the FrFT (Fractional Fourier Transform) rotation angle can be calculated through the track inclination angle and the acceleration derivative is determined as follows:

[0108] ;

[0109] where, is the FrFT rotation angle, is the double-step difference enhanced acceleration derivative, is the target velocity size at time k, is the flight path tilt angle.

[0110] Then, a two-dimensional waveform library containing pulse length and sweep width is constructed for waveform selection optimization, as follows:

[0111] ;

[0112] where, pulse length controls the range resolution, sweep controls the Doppler resolution, is the two-dimensional waveform library.

[0113] Based on the FrFT technology, the main lobe direction of the waveform ambiguity function is dynamically adjusted, and the waveform parameters that can minimize the trace of the prediction covariance matrix are selected, as follows:

[0114] ;

[0115] where, is the optimal waveform parameter at time k+1, is the candidate waveform parameter, including pulse length and sweep , is the two-dimensional waveform library, is the trace of the matrix, is the prediction covariance matrix.

[0116] Through the mapping relationship between the prediction covariance matrix and the Cramer-Rao lower bound (CRLB) matrix, the influence of the waveform parameter on the system performance can be evaluated, and the optimal waveform parameter is selected to minimize the prediction covariance matrix. By adjusting the waveform parameter and the radar echo signal-to-noise ratio, this mapping relationship is adjusted to improve the tracking accuracy, as follows:

[0117] ;

[0118] where, is the CRLB matrix of the delay-Doppler shift, is the coordinate conversion matrix, SNR of radar echo based on spatial position and distance attenuation, is a waveform parameter.

[0119] The CRLB matrix calculation of time delay-Doppler shift is specifically implemented as:

[0120]

[0121] wherein, is a time delay, is a Doppler shift, is a SNR attenuation factor, is a waveform ambiguity function, which is directly related to the waveform parameter, reflects the pulse length affects the range resolution, reflects the sweep bandwidth affects the velocity resolution, and the off-diagonal element reflects the strength of the range-Doppler coupling.

[0122] The FrFT is used to perform time-frequency analysis on the echo signal to obtain a representation of the signal in a time-frequency joint domain, and the Doppler rate of change of the target maneuver is extracted through the FrFT rotation angle The Doppler rate of change of the target maneuver (the rate of change of the Doppler shift with time) is matched, the guided waveform parameter is matched with the characteristics of the target maneuver, and the formula is as follows:

[0123]

[0124] wherein, the kernel function , is an input signal, specifically a target echo signal received by a radar, is a time variable, is an imaginary unit.

[0125] S4: A double closed-loop cooperative control framework is constructed, the inner loop corrects the aerodynamic parameters, the outer loop optimizes the waveform to suppress noise, the inner and outer loop control quantities are fused through a joint correction mechanism to realize cooperative suppression of errors, the covariance matrix and the nine-dimensional state vector are updated, it is judged whether the tracking time length reaches a preset threshold, if not, the covariance matrix and the nine-dimensional state vector are taken as the initial values at the next time; otherwise, the target tracking result is obtained.

[0126] Specifically, the double closed-loop cooperative mechanism breaks the positive feedback of model errors and measurement noise by constructing an inner loop (correcting aerodynamic parameters) and an outer loop (optimizing waveforms to suppress noise). The inner loop corrects the aerodynamic parameters in real time based on the sensitivity of the dynamic equation, and the outer loop suppresses the coupling of measurement noise through waveform optimization.

[0127] The inner loop is composed of a state equation ​​The motion of the target is described, wherein is the velocity, is the gravitational acceleration, is the aerodynamic acceleration, is the process noise.

[0128] According to the state equation and the Jacobian matrix, the following formula is obtained:

[0129] ;

[0130] In the formula, is the change amount of the aerodynamic acceleration, is the increment of the drag correlation coefficient, is the drag correlation coefficient estimated at the kth moment, is the drag correlation coefficient estimated at the (k-1)th moment, is the increment of the lift correlation coefficient, is the lift correlation coefficient estimated at the kth moment, is the lift correlation coefficient estimated at the kth moment, is the lift correlation coefficient estimated at the (k-1)th moment, is the difference of the lift direction angle.

[0131] By the change amount of the aerodynamic acceleration , the change of the aerodynamic parameter is converted into the acceleration correction amount. The aerodynamic parameter difference vector is the linearization expression of the acceleration correction amount, which can be expressed as:

[0132] ;

[0133] The outer loop optimizes the measurement noise characteristics by waveform selection to minimize the noise covariance matrix.

[0134] Specifically, by calculating the noise covariance matrix under different waveform parameters, the waveform parameters that minimize the noise covariance matrix are selected. The specific formula is as follows:

[0135] ;

[0136] In the formula, is the noise covariance matrix obtained based on the optimized waveform parameters, is the speed of light, is the pulse length, is the radar echo signal-to-noise ratio, is the center carrier frequency, is the variance of the velocity measurement noise, is the frequency modulation slope, , is the effective pulse duration.

[0137] Noise covariance change caused by waveform switching is calculated by outer loop control (waveform optimization noise suppression):

[0138]

[0139] In the formula, Noise covariance change, Noise covariance matrix based on optimized waveform parameters, Noise covariance matrix based on previously used waveform parameters.

[0140] Joint correction mechanism, fusion inner and outer loop control, realize error collaborative suppression, formula as follows:

[0141]

[0142] In the formula, Joint correction amount, Inner loop gain, Outer loop gain, Noise covariance change, Matrix vectorization operation.

[0143] Wherein, inner loop gain Based on the sensitivity of aerodynamic parameters in Jacobian matrix:

[0144]

[0145] In the formula, Adaptive convergence factor, , Radar echo signal-to-noise ratio,

[0146] Outer loop gain Determined by the difference of trace change rate of CRLB matrix:

[0147]

[0148] In the formula, The preset weight coefficient, the value range is [0.2, 0.8].

[0149] Double loop realizes coupling through covariance matrix Complete tracking closed loop.

[0150] Based on the standard method of Kalman gain , inject double loop control amount, get adjusted Kalman gain:

[0151] ​​​​​​

[0152] wherein, is the adjusted Kalman gain, is the Kalman gain at time k, is the joint correction, is the covariance matrix at time k-1, is the transpose of the observation matrix, is the inverse of the measurement noise covariance matrix.

[0153] The covariance robust update is performed, and the corrected covariance matrix enhances the suppression ability of the model-noise coupling error, and the formula is as follows:

[0154] = ;

[0155] wherein, is the covariance matrix at time k, is the adjusted Kalman gain, is the observation matrix, is the noise covariance matrix, is the waveform parameter at time k, is the covariance matrix at time k-1.

[0156] The closed-loop feedback updates the covariance matrix and the nine-dimensional state vector, and they are used as the initial values of the filtering calculation at the next time together, forming a complete closed loop of modeling → identification → optimization → update.

[0157] The tracking result is output and the loop is judged, and the result output at each filtering period (time k) is the updated nine-dimensional state vector and the corresponding covariance matrix , which contains the optimal position, speed estimation and aerodynamic parameter of the target at the current time, is the tracking result of the target at the time, then the algorithm judges whether the preset total tracking time reaches, if the tracking has not ended, the output result and at time k are used as the initial values of the filtering calculation at the next time (time k+1), and the new radar measurement value is input, and the above tracking process is executed in a loop to realize the continuous tracking of the target; if the tracking is completed, the tracking process is ended, and the tracking result of the target is obtained.

[0158] Embodiment 1: The tracking path of the present application is compared with the fixed waveform simulation experiment.

[0159] It is assumed that the initial position of the maneuvering target is [2470, 2050, 1400] m, the initial speed is [70, -200, 2] , and the initial acceleration is [-1, 1, 25] , the motion observation duration is 190s, the sampling interval T is 0.5s, in the waveform selection range, the pulse length , the sweep width , 100 times of Monte Carlo simulation are used.

[0160] Under the simulation conditions described above, the moving target is tracked by the method of the application and the fixed waveform method respectively, wherein, Figure 2 is the result of selecting the waveform parameters at each time of the application, wherein (1) is a distribution diagram of the pulse length selected in different time periods, and (2) is a distribution diagram of the sweep width selected in different time periods. It can be seen from the diagram that the optimal waveform parameters are selected at each time. Please refer to Figure 3 , is a comparison diagram of the target trajectory obtained by the method of the application and the fixed waveform method. It can be seen from the diagram that the tracking trajectory of the application more accurately simulates the actual motion path of the moving target, and therefore, compared with the existing fixed waveform method, the tracking result of the application is more accurate, and the tracking process is more stable.

[0161] Example 2: Comparison simulation experiment of the aerodynamic parameter estimated value of the application and the real aerodynamic parameter.

[0162] Under the simulation conditions in Example 1, the aerodynamic parameters directly calculated by the method of the application and the optimized trajectory are compared, and the comparison result diagram is as shown in Figure 4 , and the ARMSE is shown in Table 1. It can be seen from Figure 4 and Table 1 that the estimated aerodynamic parameters of the application are consistent with the real values, and the change can also verify the maneuverability of the trajectory.

[0163] Table 1: Average root mean square error (ARMSE) of aerodynamic parameter estimation

[0164]

[0165] Example 3: Tracking error comparison simulation experiment of the application and the fixed waveform.

[0166] Under the simulation conditions in Example 1, the tracking errors of the method of the application and the traditional fixed waveform are compared, Figure 5 is a comparison diagram of the tracking errors in position of the method of the application and the traditional fixed waveform, wherein (1) is a comparison diagram of the root mean square errors in X direction position of the method of the application and the fixed waveform, (2) is a comparison diagram of the root mean square errors in Y direction position of the method of the application and the fixed waveform, and (3) is a comparison diagram of the root mean square errors in Z direction position of the method of the application and the fixed waveform.

[0167] Figure 6Figures 1-3 are comparison charts of the tracking method of the present application and the conventional fixed waveform method in speed and real speed, wherein (1) is a comparison chart of the tracking method of the present application and the conventional fixed waveform method in X direction speed and real X direction speed, (2) is a comparison chart of the tracking method of the present application and the conventional fixed waveform method in Y direction speed and real Y direction speed, and (3) is a comparison chart of the tracking method of the present application and the conventional fixed waveform method in Z direction speed and real Z direction speed. Table 2 is a comparison of ARMSE of different tracking methods.

[0168] In combination with Figure 5 , Figure 6 and Table 2, it can be seen that the tracking method of the present application is less than the tracking error of the conventional fixed waveform method in overall trend, and the overall effect is more stable, and the tracking precision is higher.

[0169] Table 2 Comparison of ARMSE of different tracking methods

[0170]

[0171] Those skilled in the art can appreciate that the units and algorithm steps of each example described in combination with the embodiments disclosed herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether the functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. A person skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0172] The above-described embodiments are only used to illustrate the technical solutions of the present application, but not limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.

Claims

1. A high-speed maneuvering target tracking method combining parameter identification and waveform selection, characterized in that, The method comprises the following steps: The aerodynamic acceleration is calculated according to radar measurement values, and the aerodynamic parameters are defined by backstepping based on decomposition, and a nine-dimensional state vector is constructed; An extended Kalman filter fusing aerodynamic parameters is constructed to perform state estimation on the nine-dimensional state vector to obtain state prediction values and a covariance matrix, and new information is calculated in combination with the radar measurement values to update the aerodynamic parameters in real time; The acceleration derivative is estimated according to the trace rate of the covariance matrix, the flight path inclination angle is extracted according to the target speed component, the FrFT rotation angle is calculated using the two, a two-dimensional waveform library is constructed, the waveform parameter that minimizes the trace of the covariance matrix is selected, and the waveform parameter is matched with the target maneuvering characteristics in real time; A double closed-loop collaborative control architecture is constructed, the aerodynamic parameters are corrected in the inner loop, the waveform is optimized in the outer loop to suppress noise, the inner and outer loop control quantities are fused through a joint correction mechanism to realize collaborative suppression of errors, the covariance matrix and the nine-dimensional state vector are updated, and it is determined whether the tracking time length reaches a preset threshold; if not, the covariance matrix and the nine-dimensional state vector are taken as initial values at the next time; Otherwise, the target tracking result is obtained; The aerodynamic acceleration is decomposed by a coordinate matrix to obtain resistance direction, tangential and normal accelerations, and the aerodynamic parameters are defined by backstepping based on the decomposition; The aerodynamic parameter definition refers to decoupling the aerodynamic parameters in the traditional aerodynamic parameter definition analysis process to convert the drag coefficient and the lift coefficient in the aerodynamic parameters into drag-related coefficients and lift-related coefficients containing the mass and reference area of the maneuvering target; The aerodynamic acceleration is decomposed to obtain the aerodynamic parameter sensitivity term, and the extended Kalman filter fusing aerodynamic parameters is constructed by constructing a Jacobian matrix; The inner loop converts the change of the aerodynamic parameters into acceleration correction quantity based on a state equation and the Jacobian matrix, and the state equation is: ； wherein is the velocity, is the time, is the gravitational acceleration, is the aerodynamic acceleration, is the process noise; The outer loop calculates the noise covariance matrix under different waveform parameters, selects the waveform parameter that minimizes the noise covariance matrix, and calculates the noise covariance change caused by waveform switching; The inner and outer loop control quantities include inner loop gain and outer loop gain, the inner loop gain is constructed based on the aerodynamic parameter sensitivity term in the Jacobian matrix, and the outer loop gain is determined by the difference of the trace of the Cramer-Rao lower bound matrix of the waveform parameter; The joint correction quantity is calculated according to the noise covariance change and the inner and outer loop control quantities, the Kalman gain is adjusted based on the Kalman gain and the joint correction quantity, the covariance matrix is corrected, and the formula is as follows: = ； wherein is the covariance matrix at time k, is the adjusted Kalman gain, is the observation matrix, is the noise covariance matrix, is the waveform parameter at time k, is the covariance matrix at time k-1.

2. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuvering direction, the FrFT rotation angle is calculated according to the flight path inclination angle and the acceleration derivative after orthogonalization, the optimal waveform that minimizes the trace of the covariance matrix is selected as the optimal waveform by mapping the prediction covariance matrix and the Cramer-Rao lower bound matrix with the FrFT rotation angle as the guide, and adaptive matching of the waveform parameter and the target maneuvering characteristics is realized. ​ 3. The method of claim 1, wherein the joint parameter estimation and waveform selection for high-speed maneuvering target tracking is characterized by: The linearization of the acceleration correction is expressed as a vector of aerodynamic parameter differences, and the formula is: ； wherein is the aerodynamic parameter difference vector, is the increment of the drag related coefficient, is the lift related coefficient estimated at the kth time instant, is the difference of the lift direction angle.

4. The method of claim 1, wherein the joint parameter estimation and waveform selection for high-speed maneuvering target tracking is characterized by: The process of calculating the aerodynamic acceleration includes: The measurement obtained by the radar in the sampling period is converted into a rectangular coordinate, and the velocity component is obtained by difference. The aerodynamic acceleration is calculated according to the velocity component, and the formula is as follows: ； wherein is the acceleration component in the x-axis direction, is the acceleration component in the x-axis direction, is the acceleration component in the x-axis direction, , , are the velocity components in the x, y, z coordinate directions at the end of the first sampling period, respectively, , , are the velocity components in the x, y, z coordinate directions at the end of the second sampling period, respectively, is the sampling time interval of the radar, is the gravitational acceleration.

5. The method of claim 1, wherein the joint parameter estimation and waveform selection for high-speed maneuvering target tracking is characterized by: The formula for calculating the innovation is as follows: ； wherein, is the innovation, is the innovation covariance, is the Kalman gain, is the actual radar observation at the kth sampling period, is the Jacobian matrix of the measurement function, is the state prediction covariance at time k, is a nonlinear measurement function that maps the state space prediction to the radar observation space, is the state prediction at time k, is the measurement noise covariance matrix.

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