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

Abstract

The invention provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection, and solves the technical problems of dynamic model mismatch, prominent measurement noise contradiction and high tracking loss rate during existing high-speed maneuvering target tracking. The method comprises the following steps: calculating aerodynamic acceleration, reversely deducing aerodynamic parameters after decomposition, constructing a nine-dimensional state vector, and calculating information after state estimation; an acceleration derivative is estimated, a track inclination angle is extracted, an FrFT rotation angle is calculated, a two-dimensional waveform library is constructed, waveform parameters of a minimum covariance matrix trace are selected, and the waveform parameters and target maneuvering characteristics are matched in real time; constructing a double-closed-loop cooperative control architecture, fusing inner and outer loop control quantities through a joint correction mechanism, updating a covariance matrix and a nine-dimensional state vector, judging whether the tracking duration reaches a preset threshold, and if not, taking the tracking duration as an initial value of the next moment; otherwise, obtaining a target tracking result. The method can be widely applied to 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: 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; 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; 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 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; The double closed-loop collaborative 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 collaborative 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.

[0007] Preferably, the aerodynamic acceleration is decomposed by the 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; 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.

[0008] 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 that can minimize 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.

[0009] Preferably, the aerodynamic parameter sensitive term is obtained by decomposing the aerodynamic acceleration, and the extended Kalman filter fusing the aerodynamic parameters is constructed by constructing the Jacobian matrix.

[0010] 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: ; In the formula, is the velocity, is the time, is the gravity acceleration, is the aerodynamic acceleration, is the process noise.

[0011] Preferably, the linearized representation of the acceleration correction is the aerodynamic parameter difference vector, and the formula is: ; 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.

[0012] Preferably, the outer loop selects the waveform parameter that makes the noise covariance matrix minimum by calculating the noise covariance matrix under different waveform parameters, and calculates the noise covariance change caused by the waveform switching.

[0013] Preferably, the inner and outer loop control quantities include the inner loop gain and the 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 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, the covariance matrix is corrected, and the formula is as follows: = ; wherein, is the covariance matrix at the kth time, is the adjusted Kalman gain, is the observation matrix, is the noise covariance matrix, is the waveform parameter at the kth time, is the covariance matrix at the k-1th time.

[0014] Preferably, the process of calculating the aerodynamic acceleration includes: The measurement value obtained by the radar in the sampling period is converted into rectangular coordinates, and the velocity component is obtained by difference, and 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 y-axis direction, is the acceleration component in the z-axis direction, , , , , , respectively the velocity components in the horizontal, vertical and slant coordinate directions at the end of the first sampling period, , , respectively the velocity components in the horizontal, vertical and slant coordinate directions at the end of the second sampling period, is the sampling time interval of the radar, is the acceleration of gravity.

[0015] Preferably, the formula for calculating the innovation is as follows: 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.

[0016] The application has the beneficial effects that: the application proposes a high-speed maneuvering target tracking method combining parameter identification and waveform selection, first, 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 then the mass cross-sectional area decoupling is realized, solving the problem of poor adaptability of 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, based on the FrFT rotation angle adjustment strategy, the target acceleration derivative and the track inclination angle are dynamically associated, the waveform ambiguity function direction is adaptively optimized, the contradiction between range resolution and Doppler resolution is effectively balanced, and the problem of prominent measurement noise is solved, so as to improve the measurement accuracy in low-altitude environment; finally, the double closed-loop cooperative control architecture is constructed, the inner loop dynamically corrects the dynamic model through real-time identification of aerodynamic parameters, and the outer loop suppresses the measurement noise through waveform optimization, the inner loop corrects the aerodynamic parameters, the outer loop optimizes the waveform to suppress the noise, the double loops realize cooperative suppression of errors, 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

[0017] ​In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description only constitute some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor.

[0018] Figure 1 The overall flowchart of a high-speed maneuvering target tracking method combining parameter identification and waveform selection provided by an embodiment of the present application is shown in the figure. Figure 2 The result diagram of waveform parameter selection at each time provided by an embodiment of the present application is shown in the figure, wherein (1) is a distribution diagram of pulse length selected at different time periods, and (2) is a distribution diagram of sweep width selected at different time periods. Figure 3 The target trajectory comparison diagram obtained by the present application and the fixed waveform method provided by an embodiment of the present application is shown in the figure. Figure 4 The aerodynamic parameter comparison diagram of parameter estimation and optimized trajectory calculation provided by an embodiment of the present application is shown in the figure. Figure 5 The tracking error comparison diagram in position between the present application and the traditional fixed waveform method provided by an embodiment of the present application is shown in the figure, wherein (1) is the root mean square error comparison diagram in X direction position between the present application and the fixed waveform, (2) is the root mean square error comparison diagram in Y direction position between the present application and the fixed waveform, and (3) is the root mean square error comparison diagram in Z direction position between the present application and the fixed waveform. Figure 6 The comparison diagram in speed between the present application and the traditional fixed waveform method and the real speed provided by an embodiment of the present application is shown in the figure, wherein (1) is the comparison diagram in X direction speed between the present application and the fixed waveform and the real X direction speed, (2) is the comparison diagram in Y direction speed between the present application and the fixed waveform and the real Y direction speed, and (3) is the comparison diagram in Z direction speed between the present application and the fixed waveform and the real Z direction speed. DETAILED DESCRIPTION

[0019] In order to make the technical problems, technical solutions and beneficial effects of the present application more clearly understood, the present application will be further described in detail below with reference to the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application, and are not used to limit the present application.

[0020] The application provides a high-speed maneuvering target tracking method combining parameter identification and waveform selection. First, a complex nine-dimensional joint state vector containing position, velocity 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 poor adaptability of a traditional tracking model (such as a CV / CA / Singer model) to nonlinear maneuvering. Second, a maneuvering guide waveform optimization mechanism is constructed, the rotation angle adjustment strategy based on fractional Fourier transform is used to realize real-time sensing of the target acceleration rate and the track characteristics, the waveform ambiguity function direction is adaptively optimized, the contradiction between the range resolution and the 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 the dynamic model through real-time identification of the aerodynamic parameters, the outer loop suppresses the measurement noise through waveform optimization, the double loops realize cooperative suppression of errors, and the joint control quantity is generated, thereby effectively improving the target tracking accuracy.

[0021] Please refer to Figure 1 A high-speed maneuvering target tracking method combining parameter identification and waveform selection is provided for an embodiment of the application, and the method comprises the following steps. S1: The measurement values obtained by a radar in a sampling period are converted into rectangular coordinates, the velocity components are obtained through difference, the aerodynamic acceleration is calculated according to the velocity components, the drag direction, the tangential and normal accelerations are obtained through decomposition, the aerodynamic parameters are back calculated according to the drag direction, the tangential and normal accelerations and the aerodynamic parameters defined by decoupling design, and a nine-dimensional state vector containing the target motion state and the aerodynamic parameters is constructed.

[0022] Specifically, in an optional embodiment, the measurement values obtained by the radar in the first three sampling periods are converted into rectangular coordinates through polar coordinate system measurement, the horizontal, vertical and longitudinal coordinates obtained by the measurement in the first sampling period are 、 、 The horizontal, vertical and longitudinal coordinates obtained by the measurement in the second sampling period are 、 、 The horizontal, vertical and longitudinal coordinates obtained by the measurement in the third sampling period are 、 、 And the formula is as follows: 、 、 ; In the formula, x, y and z respectively represent the horizontal, vertical and longitudinal coordinates obtained by the measurement in the sampling period, 、 、 is the unbiased conversion coefficient for the azimuth angle measurement accuracy in the first sampling period, ​​​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. , For the index of the sampling period, for The reciprocal, for The reciprocal, For radar in the The straight-line reference distance to the target measured in each sampling period. For radar in the The reference azimuth angle measured in each sampling period. For radar in the The reference pitch angle measured in each sampling period. For the first The error variance of radar measurement azimuth angle per sampling period. For the first The variance of the radar elevation angle measurement error per sampling period.

[0023] The horizontal, vertical, and axial coordinates obtained from the first, second, and third sampling periods are subtracted to calculate the velocity component, as shown in the following formula: ; ; In the formula, The velocity component in the x-axis direction at the end of the first sampling period. The velocity component in the ordinate direction at the end of the first sampling period. The velocity component in the vertical direction at the end of the first sampling period. The sampling time interval of the radar. The velocity component in the horizontal direction at the end of the second sampling period. The velocity component in the ordinate direction at the end of the second sampling period. This represents the velocity component in the vertical direction at the end of the second sampling period.

[0024] Calculate aerodynamic acceleration based on velocity components ,include , and The calculation formula is as follows: ; In the formula, for The acceleration component in the axial direction, for The acceleration component in the axial direction, for The acceleration component in the axial direction, This is the acceleration due to gravity.

[0025] 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: ; In the formula, Acceleration in the direction of resistance For tangential acceleration, Here, is the normal acceleration. The formula is as follows: ; 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.

[0026] Based on acceleration in the direction of resistance Tangential acceleration and normal acceleration and decoupling the aerodynamic parameter definition, the aerodynamic parameters are backstepped. The aerodynamic parameters include drag correlation coefficient , lift correlation coefficient and lift direction angle .

[0027] Specifically, the present application decouples the design of aerodynamic parameters. In the process of traditional aerodynamic parameter definition analysis, the aerodynamic parameters are decoupled, and the aerodynamic force is converted into unit mass force. That is: the drag coefficient and the lift coefficient are converted into drag correlation coefficient and lift correlation coefficient containing aircraft mass and reference area , realizing the decoupling of drag correlation coefficient and lift correlation coefficient . The formula for converting aerodynamic force into unit mass force is as follows: ; ; In the formula, is the lift, is the drag, is the lift coefficient, is the drag coefficient, is the aircraft mass, is the reference area, is the air density at the target current height (ρ0 is the sea level atmospheric density, h is the atmospheric altitude), is the sea level atmospheric density, is the atmospheric altitude), is the speed of the aircraft.

[0028] After normalization, the drag correlation coefficient and the lift correlation coefficient are obtained, realizing the decoupling of drag correlation coefficient and lift correlation coefficient .

[0029] According to the drag direction acceleration , the tangential acceleration and the normal acceleration and the aerodynamic parameter definition of decoupling design, the aerodynamic parameters are backstepped, and the formula is as follows: ; ; ; In the formula, is the drag correlation coefficient, is the lift correlation coefficient, The angle of projection of the lift vector onto the velocity plane in the body coordinate system is called the lift direction angle. The air density at the target's current altitude ( Atmospheric density at sea level (Atmospheric elevation) This refers to the speed of the aircraft.

[0030] According to the obtained , , , , , , , , Construct a system containing the target's motion state (position) , , speed , , ) and aerodynamic parameters , , The nine-dimensional state vector joint state modeling, by incorporating aerodynamic parameters into the state vector, provides a foundation for real-time identification. The constructed nine-dimensional state vector is as follows: .

[0031] S2: Decompose aerodynamic acceleration to obtain aerodynamic parameter sensitivity terms, construct the Jacobian matrix, and obtain an extended Kalman filter that fuses aerodynamic parameters. Use the extended Kalman filter that fuses aerodynamic parameters to perform state estimation on the nine-dimensional state vector, obtaining the state prediction value and covariance matrix. Combine this with radar measurements to calculate information, update aerodynamic parameters in real time, and complete the online identification of target maneuvering characteristics.

[0032] Decompose aerodynamic acceleration to obtain aerodynamic parameter sensitivity terms, and construct the Jacobian matrix. The process is as follows: First, aerodynamic acceleration is determined according to the aircraft coordinate system. The decomposition yields: ; In the formula, Aerodynamic acceleration, including , , , This is the coordinate transformation matrix. The air density at the target's current altitude. For the target speed, For lift correlation coefficient, For resistance correlation coefficient, The angle represents the direction of lift.

[0033] Then, the aerodynamic acceleration The aerodynamic force vector part in the expression is , and the formula is as follows: ; Next, the aerodynamic acceleration is expanded according to the chain rule, and the following formula is obtained: ; Among them, the direction change term is: ; The modulus change term is: ; In summary, the partial derivative of the aerodynamic acceleration with respect to the velocity, that is, the aerodynamic parameter sensitivity term, is: ; In the formula, , , are the orthogonal bases of the velocity coordinate system, and the formula is as follows: ; In the formula, is the velocity in the axis direction, is the velocity in the axis direction.

[0034] After obtaining the aerodynamic parameter sensitivity term, the Jacobian matrix is established, and the formula is as follows: ; In the formula, is a zero matrix of 3 rows and 3 columns, is a unit matrix of 3 rows and 3 columns, 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.

[0035] The extended Kalman filter integrating the aerodynamic parameters is used to estimate the nine-dimensional state vector , and the state prediction value and the covariance matrix are obtained. The discretized prediction equation is: ; In the formula, is the state prediction value based on the observation information at k−1 time at k time, is the state estimation value at k−1 time, is the sampling time interval of the 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, T is the matrix transpose operator, is the process noise covariance.

[0036] In the measurement update stage, the measurement value obtained by the radar in the sampling period , the state prediction value and the covariance matrix are used to calculate the innovation, and the innovation is updated iteratively to continuously correct the aerodynamic parameters to adapt to the target maneuver. The formula for calculating the innovation is as follows: ; 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 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.

[0037] 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 match the waveform parameters with the target maneuver characteristics in real time.

[0038] 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 component of the target in the horizontal, vertical and longitudinal coordinates at time K, and the track tilt angle is obtained; in order to minimize the range-Doppler coupling, the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuver direction, and the FrFT (Fractional Fourier Transform) rotation angle is calculated according to the orthogonal track tilt angle and the acceleration derivative. A two-dimensional waveform library containing pulse length and 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 that can minimize 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 using the FrFT, the guided waveform parameters are matched with the target maneuver characteristics, and the optimization of the maneuver guided waveform is completed.

[0039] Firstly, the target maneuvering strength is estimated, and the trace variation rate of the state prediction covariance matrix is used to reflect the target maneuvering strength. Specifically, the acceleration derivative (the variation rate of acceleration) is determined according to the trace variation rate of the state prediction covariance matrix, and the double-step difference is used to enhance the acceleration derivative The estimation robustness is determined by the following formula: ; In the formula, is the double-step difference enhanced acceleration derivative, is the state prediction covariance matrix at time k, is the state prediction covariance matrix at the last time, is the trace of the matrix, is the time step.

[0040] Then, the track geometric features are extracted, and the track geometric features are determined by the track inclination angle (which determines the direction of the lift force). The track inclination angle is extracted, and the formula is as follows: ; In the formula, is the track inclination angle, , , are the velocity vectors of the target in the , , directions at time k, respectively.

[0041] In order to minimize the distance-Doppler coupling, the main lobe direction of the waveform ambiguity function is orthogonal to the target maneuvering direction, and at this time, the FrFT (Fractional Fourier Transform) rotation angle can be determined by the track inclination angle and the acceleration derivative The formula is as follows: ; In the formula, is the FrFT rotation angle, is the double-step difference enhanced acceleration derivative, is the target speed at time k, is the track inclination angle.

[0042] Then, a two-dimensional waveform library containing the pulse length and the sweep width is constructed, which is used for waveform selection optimization, and the formula is as follows: ; In the formula, the pulse length controls the range resolution, the sweep controls the Doppler resolution, is the two-dimensional waveform library.

[0043] The main lobe direction of the waveform ambiguity function is dynamically adjusted based on the FrFT technology, and the waveform parameter capable of minimizing the trace of the prediction covariance matrix is selected, and the formula is as follows: ; In the formula, is the optimal waveform parameter at the k+1 moment, is the candidate waveform parameter, including the pulse length and the sweep , is a two-dimensional waveform library, is the trace of a matrix, is the prediction covariance matrix.

[0044] 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, so as to select the optimal waveform parameter to minimize the prediction covariance matrix. The mapping relationship is adjusted by adjusting the waveform parameter and the radar echo signal-to-noise ratio, and the tracking accuracy is improved, and the formula is as follows: ; In the formula, is the CRLB matrix of the time delay-Doppler shift, is a coordinate conversion matrix, is the radar echo signal-to-noise ratio based on the spatial position and distance attenuation, is the waveform parameter.

[0045] The CRLB matrix of the time delay-Doppler shift is specifically implemented as: ; In the formula, is the time delay, is the Doppler shift, is a signal-to-noise ratio attenuation factor, is the waveform ambiguity function, which is directly related to the waveform parameter (the reflects the pulse length influences the range resolution, reflects the sweep bandwidth influences the velocity resolution, and the non-diagonal item reflects the distance-Doppler coupling strength.

[0046] The FrFT is used to perform time-frequency analysis on the echo signal to obtain the representation of the signal in the time-frequency joint domain, the Doppler rate of change of the target maneuver is extracted, and the FrFT rotation angle is matched with the Doppler rate of change of the target maneuver (the rate of change of the Doppler shift with time), the guided waveform parameter is matched with the characteristics of the target maneuver, and the formula is as follows: ; In the formula, the kernel function , is an input signal, specifically a target echo signal received by a radar, is a time variable, is an imaginary unit.

[0047] S4: Construct a double closed-loop collaborative control framework, correct the aerodynamic parameters in the inner loop, and optimize the waveform to suppress noise in the outer loop. Through the joint correction mechanism, the inner and outer loop control quantities are fused to realize error collaborative suppression. Update the covariance matrix and nine-dimensional state vector, and judge whether the tracking time length reaches the preset threshold. If not, take the covariance matrix and nine-dimensional state vector as the initial value at the next time; otherwise, obtain the target tracking result.

[0048] Specifically, the double closed-loop collaborative mechanism breaks the positive feedback of model error and measurement noise by constructing an inner loop (correcting aerodynamic parameters) and an outer loop (optimizing waveform 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.

[0049] The inner loop is described by the state equation of the target motion, wherein is the velocity, is the gravitational acceleration, is the aerodynamic acceleration, is the process noise.

[0050] According to the state equation and the Jacobian matrix, the following formula is obtained: ; In the formula, is the change of aerodynamic acceleration, is the increment of drag-related coefficient, is the drag-related coefficient estimated at the kth moment, is the drag-related coefficient estimated at the (k-1)th moment, is the increment of lift-related coefficient, is the lift-related coefficient estimated at the kth moment, is the lift-related coefficient estimated at the kth moment, is the lift-related coefficient estimated at the (k-1)th moment, is the difference of lift direction angle.

[0051] By changing the aerodynamic acceleration , the change of aerodynamic parameters is converted into acceleration correction. The aerodynamic parameter difference vector is a linear expression of the acceleration correction, which can be expressed as: ; The outer loop optimizes the noise characteristics of the measurement by waveform selection to minimize the noise covariance matrix.

[0052] Specifically, the waveform parameter that minimizes the noise covariance matrix is selected by calculating the noise covariance matrix under different waveform parameters. The specific formula is as follows: ; In the formula, is the noise covariance matrix obtained based on the optimized waveform parameter, 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.

[0053] By outer loop control (waveform optimization noise suppression), the noise covariance change brought by waveform switching is calculated: ; In the formula, is the noise covariance change, is the noise covariance matrix obtained based on the optimized waveform parameter, is the noise covariance matrix obtained based on the previously used waveform parameter.

[0054] The joint correction mechanism fuses the inner and outer loop control quantities to realize error collaborative suppression, and the formula is as follows: ; In the formula, is the joint correction quantity, is the inner loop gain, is the outer loop gain, is the noise covariance change, is the matrix vectorization operation.

[0055] Wherein, the inner loop gain is constructed based on the aerodynamic parameter sensitivity term in the Jacobian matrix: ; In the formula, is the adaptive convergence factor, , is the radar echo signal-to-noise ratio, .

[0056] The outer loop gain The trace rate difference of the CRLB matrix determines: ; In the formula, is a preset weight coefficient, and the value range is [0.2, 0.8].

[0057] The double loop realizes coupling by the covariance matrix , and completes the tracking closed loop.

[0058] The Kalman gain based on the standard method , injects the double loop control quantity, and obtains the adjusted Kalman gain: ; In the formula, is the adjusted Kalman gain, is the Kalman gain at K time, is the joint correction amount, is the covariance matrix at k-1 time, is the transpose of the observation matrix, is the inverse of the measurement noise covariance matrix.

[0059] The covariance robustness is updated, and the modified covariance matrix enhances the suppression ability to the model-noise coupling error, and the formula is as follows: = ; In the formula, 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.

[0060] 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 the complete closed loop of modeling->identification->optimization->update.

[0061] The tracking result is output and the loop is judged, and the result output at each filtering period (k time) 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, and is the tracking result of the target at the time. Subsequently, the algorithm judges whether the preset total tracking time length is reached, if the tracking has not ended, the output results and at k time are used as the initial values of the filtering calculation at the next time (k+1 time), and new radar measurement values are waited. Input, the above-mentioned all tracking process is executed cyclically, the continuous tracking of the target is realized; if the tracking is completed, the tracking process is ended, and the target tracking result is obtained.

[0062] Embodiment 1: The application is compared with the tracking path of fixed waveform for simulation experiment.

[0063] Suppose that the starting position of the maneuvering target is [2470, 2050, 1400] m, the starting speed is [70, -200, 2] , the initial acceleration is [-1, 1, 25] , the duration of motion observation is 190s, the sampling interval T is 0.5s, the pulse length , the sweep width , and the Monte Carlo simulation is used for 100 times.

[0064] Under the above simulation conditions, the maneuvering target is tracked by the application and the method of fixed waveform respectively, wherein, Figure 2 is the selection result of the waveform parameters of the application at each time, wherein (1) is the distribution diagram of the pulse length selected in different time periods, and (2) is the 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 the comparison diagram of the target trajectory obtained by the application and the method of fixed waveform. It can be seen from the diagram that the tracking trajectory of the application more accurately simulates the actual motion path of the maneuvering target, so the tracking result of the application is more accurate, and the tracking process is more stable compared with the existing method of fixed waveform.

[0065] Embodiment 2: The comparison simulation experiment of the aerodynamic parameter estimated value of the application and the real aerodynamic parameter.

[0066] Under the simulation conditions in embodiment 1, the aerodynamic parameters directly calculated by the application and the optimized trajectory are compared, and the comparison result diagram is as shown in Figure 4 , and the ARMSE is as shown in Table 1. Combined with Figure 4 and Table 1, it can be seen 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.

[0067] Table 1: Average root mean square error (ARMSE) of aerodynamic parameter estimation

[0068] Embodiment 3: The tracking error comparison simulation experiment of the application and the fixed waveform.

[0069] Under the simulation conditions in embodiment 1, the tracking errors of the application and the traditional method of fixed waveform are compared, Figure 5Figures 1-3 are comparison charts of tracking errors in position between the application and the conventional fixed waveform method, wherein (1) is a comparison chart of root mean square errors in X direction position between the application and the fixed waveform, (2) is a comparison chart of root mean square errors in Y direction position between the application and the fixed waveform, and (3) is a comparison chart of root mean square errors in Z direction position between the application and the fixed waveform.

[0070] Figure 6 Figures 4-6 are comparison charts of velocities between the application and the conventional fixed waveform method and real velocities, wherein (1) is a comparison chart of velocities in X direction between the application and the fixed waveform and real X direction velocity, (2) is a comparison chart of velocities in Y direction between the application and the fixed waveform and real Y direction velocity, and (3) is a comparison chart of velocities in Z direction between the application and the fixed waveform and real Z direction velocity, and Table 2 is a comparison of ARMSEs of different tracking methods.

[0071] In combination with Figure 5 , Figure 6 and Table 2, it can be seen that the tracking method of the application is less than the tracking error of the conventional fixed waveform method in the overall trend, the overall effect is more stable, and the tracking precision is higher.

[0072] Table 2 Comparison of ARMSEs of different tracking methods

[0073] 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 application.

[0074] The above-described embodiments are only used to illustrate the technical solutions of the application, but not limit it; although the 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 to some 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 application, and should be included in the protection scope of the 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: calculating aerodynamic acceleration according to radar measurement values, decomposing to define backstepping aerodynamic parameters based on decoupling design aerodynamic parameters, and constructing a nine-dimensional state vector; constructing an extended Kalman filter fusing aerodynamic parameters to perform state estimation on the nine-dimensional state vector to obtain state prediction values and a covariance matrix, and combining the radar measurement values to calculate innovation and update aerodynamic parameters in real time; estimating acceleration derivatives according to a trace rate of the covariance matrix, extracting a track inclination angle according to a target speed component, calculating a FrFT rotation angle using the two, constructing a two-dimensional waveform library, selecting waveform parameters that minimize the trace of the covariance matrix, and matching the waveform parameters with target maneuvering characteristics in real time; constructing a double closed-loop collaborative control architecture, correcting aerodynamic parameters in the inner loop, and optimizing waveforms to suppress noise in the outer loop, fusing inner and outer loop control quantities through a joint correction mechanism to achieve error collaborative suppression, updating the covariance matrix and the nine-dimensional state vector, and determining 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 for the next time; otherwise, a target tracking result is obtained.

2. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein: the aerodynamic acceleration is decomposed by a coordinate matrix to obtain drag direction, tangential and normal accelerations, and backstepping aerodynamic parameters are defined in combination with decoupling design aerodynamic parameters; the decoupling design aerodynamic parameter definition refers to decoupling aerodynamic parameters in a traditional aerodynamic parameter definition analysis process, and converting drag and lift coefficients in the aerodynamic parameters into drag and lift related coefficients containing the mass and reference area of the maneuvering target.

3. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein: the main lobe direction of a waveform ambiguity function is orthogonal to the target maneuvering direction, the FrFT rotation angle is calculated according to the track inclination angle and the acceleration derivative after orthogonalization, the FrFT rotation angle is used as a guide to select waveform parameters that minimize the trace of the covariance matrix as optimal waveforms through the mapping relationship between the prediction covariance matrix and the Cramer-Rao lower bound matrix, and adaptive matching of waveform parameters and target maneuvering characteristics is realized.

4. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein: the aerodynamic acceleration is decomposed to obtain aerodynamic parameter sensitive items, and an extended Kalman filter fusing aerodynamic parameters is constructed.

5. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 4, wherein: the inner loop converts changes in the aerodynamic parameters into acceleration correction quantities based on a state equation and the Jacobian matrix, and the state equation is: ； where, is the velocity, is the time, is the gravitational acceleration, is the aerodynamic acceleration, is the process noise.

6. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 5, wherein: the linearization of the acceleration correction quantity is represented as an aerodynamic parameter difference vector, 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.

7. The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 6, wherein: The outer loop calculates noise covariance matrix under different waveform parameters, selects the waveform parameter that makes the noise covariance matrix minimum, and calculates noise covariance change caused by waveform switching. 8.The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 7, wherein: 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 aerodynamic parameter sensitivity terms in the Jacobian matrix, and the outer loop gain is determined by differences in matrix traces of Cramer-Rao lower bound of the waveform parameters; A joint correction quantity is calculated according to the noise covariance change and the inner and outer loop control quantities, Kalman gain is adjusted based on the Kalman gain and the joint correction quantity, a 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. 9.The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein: The process of calculating the aerodynamic acceleration includes: The measurement values obtained by the radar in a sampling period are converted into rectangular coordinates, and the velocity components are obtained by difference, the aerodynamic acceleration is calculated according to the velocity components, 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. 10.The high-speed maneuvering target tracking method of joint parameter identification and waveform selection according to claim 1, wherein: 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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