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CN-116794649-B - Clutter maneuvering target tracking method based on waveform selection

CN116794649BCN 116794649 BCN116794649 BCN 116794649BCN-116794649-B

Abstract

The invention discloses a clutter maneuvering target tracking method based on waveform selection, which is implemented according to the following steps of step 1, establishing a waveform model, step 2, establishing a state and measurement model, step 3, establishing a clutter model, step 4, establishing a filtering model, and step 5, realizing the minimization of posterior estimation errors through dynamic waveform selection based on a waveform scheduling algorithm of fractional Fourier transform. The invention reduces the calculation complexity of the tracking algorithm by improving the filtering algorithm and the dynamic waveform selection mode, improves the target tracking precision and improves the accuracy of maneuvering target state estimation.

Inventors

  • ZHANG HAOWEI
  • ZHANG QILIANG
  • HUANG JIEYU
  • XIE JUNWEI
  • LI ZHENGJIE
  • QI CHENG
  • DING ZIHANG

Assignees

  • 中国人民解放军空军工程大学

Dates

Publication Date
20260512
Application Date
20230626

Claims (10)

  1. 1. The clutter maneuvering target tracking method based on waveform selection is characterized by comprising the following steps of: Step 1, establishing a waveform model; Step 2, establishing a state and a measurement model; step 3, establishing a clutter model; step 4, establishing a filtering model; Step 5, a waveform scheduling algorithm based on fractional Fourier transform is used for realizing the minimization of posterior estimation errors through dynamic waveform selection; The method further comprises the steps of 2.1, establishing a state model for establishing an improved current statistical MCS model, 2.2, establishing a measurement model for a nonlinear measurement model, and processing clutter and nonlinear transformation by using an improved probability data interconnection filter MPDA and a square root volume Kalman filter on the basis of the improved current statistical MCS model.
  2. 2. The clutter in maneuvering target tracking method based on waveform selection according to claim 1, wherein the step 1 is specifically implemented according to the following steps: step 1.1, establishing a transmission waveform model in a narrow-band environment; (1) Wherein, the Is the energy of the signal waveform and, Is the carrier frequency of the signal, Is the complex envelope of the transmitted pulse; step 1.2, establishing a received waveform model; (2) Wherein, the Is the energy of the received signal; is an additional white noise; representing time delay; is the distance between the target and the radar; representing the speed of the target movement, and , Representing the speed of light; when the waveform time-bandwidth product satisfies the narrowband condition, The method is considered as follows: (3)。
  3. 3. The clutter in maneuvering target tracking method based on waveform selection according to claim 2, wherein the step 2 is specifically implemented according to the following steps: step 2.1, establishing a state model to establish an MCS model; (4) (5) Wherein, the In order to be a target state vector of the object, 、 And The position, velocity and acceleration in the x and y directions, respectively; Is the average value of first-order acceleration, process noise Zero mean Gaussian white noise, variance is ; And The specific form is as follows: (8) (9) Wherein, the Is the sampling interval; is shown at the moment Selected waveform of Is subjected to Is corresponding to a specific waveform Represented as ; Step 2.2, establishing a measurement model as a nonlinear measurement model; Assuming that the target moves in a two-dimensional plane and the distance, speed and direction are measured simultaneously, the nonlinear measurement model is as follows: (6) (7) Wherein, the Is a nonlinear transformation function; Measuring noise for a target measurement matrix Zero mean Gaussian white noise, variance is ; Representing the distance between the target and the radar, the radial velocity of the target and the azimuth of the target, respectively.
  4. 4. The clutter in maneuvering target tracking method based on waveform selection according to claim 3, wherein the step 3 is specifically implemented according to the following steps: Time of day under clutter conditions Expressed as measured values of (a): (10) Wherein, the Is the radar at the moment Is a measurement target total number; Step 3.1, Including distance, rate, and angle information, assuming that the false alarm number complies with the expectations The probability of false alarms is: (11) Wherein, the For the density of erroneous measurements, and To verify the door volume; Step 3.2, assuming that clutter is uniformly distributed in the verification gate, and under the assumption that only noise and targets exist, the test statistic follows the rule of exponential distribution; estimating delay and Doppler shift with peaks of a fuzzy function at time instants The detection probability of (2) is: (12) Wherein the method comprises the steps of Representing the desired probability of a false alarm, Representative time of day Is a signal to noise ratio of (c).
  5. 5. The clutter in maneuvering target tracking method based on waveform selection according to claim 4, wherein the step 4 is specifically implemented according to the following steps: Step 4.1, establishing an MPDA model; Assume that Is the moment of time Measurement value Is used to determine the probability of association of (a) with (b), If there is no associated probability from the target measurement, then the posterior error covariance matrix in MPDAF is: (13) Wherein the method comprises the steps of Is the Kalman filtering gain; is an innovation covariance matrix; Is a predictive covariance matrix; Is the influencing factor of the filter error covariance matrix: (14) Wherein the method comprises the steps of Is the detection probability, and Is a threshold probability; is an influence factor and represents the correlation gate to the innovation covariance matrix Is a function of (1); When the measurement dimension is three-dimensional: (15) Wherein the method comprises the steps of For the associated threshold, and , In order to associate the regions with each other, Is a defined error function; corresponding to a specific waveform Or a waveform parameter, Also with Correspondingly, is defined as When the modified Ricat equation is used to estimate : (16) Wherein the method comprises the steps of Is a scalar between 0 and 1, and is dependent on the clutter density lambda, the correlation threshold And Probability of detection of time of day ; The approximate fit is: (17) Wherein the method comprises the steps of And ; Step 4.2, establishing an MPDA-SCKF model; definition prior to data processing Is a matrix Upper triangular matrix obtained by QR decomposition, matrix The QR decomposition of (C) is expressed as Wherein the matrix The processing flow of the MPDAF-SCKF is as follows: Step 4.2.1, updating time; and 4.2.2, measuring and updating.
  6. 6. The method for tracking maneuvering targets in clutter based on waveform selection according to claim 5, wherein the specific steps of time update in step 4.2.1 are: step1.1, factorization; (18) step1.2, calculating volume points and transmitting the volume points; (19) (20) Wherein the method comprises the steps of And Volume points and propagation volume points; For all the number of volume points, Is a state vector And satisfy the dimensions of Conditions of (2); , Is to The unit vectors of the dimensional space are subjected to full arrangement or point set obtained by negation; (21) Step1.3, calculating the state prediction mean and the square root of the state prediction error covariance; (22) (23) Wherein the weighted center matrix is: (24)。
  7. 7. The method for tracking maneuvering targets in clutter based on waveform selection according to claim 6, wherein the specific steps of measurement updating in step 4.2.1 are as follows: Step2.1, calculating volume points and performing nonlinear transformation: (25) (26) step2.2, calculating a measurement prediction mean value; (27) Step2.3, calculating square root coefficients of the residual covariance matrix: (28) Wherein, the weighted center matrix is: (29) Step2.4, calculating a residual covariance matrix: (30) Step2.5 calculating a mutual covariance matrix between states and measurements (31) Wherein the weighted center matrix is: (32) step2.6, calculating the filter gain: (33) step2.7, calculating square root coefficients of the corresponding error covariance matrix and the posterior estimated error covariance matrix: (34) (35) Step2.8, updating the corresponding state matrix and the corresponding error covariance matrix: if no measurement result is accurate, the following formula is adopted for updating: (36) (37) Otherwise, the following formula is used: (38) (39) Is assumed to be in The moment state error covariance matrix is 。
  8. 8. The method for tracking maneuvering targets in clutter based on waveform selection according to claim 7, wherein the specific steps of the step 5 are as follows: step 5.1, calculating the lower bound of the Keramelteon And 5.2, selecting an optimized waveform based on fractional Fourier transform.
  9. 9. The method for tracking maneuvering targets in clutter based on waveform selection according to claim 8, wherein the step 5.1 specifically comprises the following steps: Measuring noise covariance matrix And (3) with Time of day transmit waveform parameters Correlation, i.e. at time Selected waveforms, i.e. Is a transmitted waveform Is a fuzzy function of (1), namely: (40) With respect to time delay And Doppler shift The fee-house information matrix of (1) is: (41) Wherein the method comprises the steps of Is the signal to noise ratio; And The relation between the two is: (42) Wherein the method comprises the steps of Time delay of And Doppler shift A matrix of Fischer-Tropsch information on distance and speed; is the lower bound of the Kramer for the selected waveform under unbiased estimation; the time of day is shown in equation (40) Is determined by the selected waveform of (a) By minimizing the time of day To select the optimal waveform: (43) Time of day The selected waveform of (a) affects the measurement error covariance matrix and also affects the time of day And selecting an optimal waveform through waveform scheduling, thereby greatly improving the target tracking performance under the clutter condition.
  10. 10. The method for tracking maneuvering targets in clutter based on waveform selection according to claim 9, wherein the step 5.2 specifically comprises the following steps: assuming that the base transmit waveform is The blur function is The Fisher information matrix is The corresponding measurement noise covariance matrix is Fractional factor in fractional fourier transform Is applied to the basic emission waveform to realize orthogonality between the measurement error ellipse and the state error ellipse; The fractional fourier transform is regarded as a rotation operation of a coordinate system when the fractional fourier transform is used for parameters of Is based on the transmitted waveform, the fuzzy function of the waveform is realized by Rotating to obtain a new waveform, wherein the obtained waveform is characterized in that: (44) (45) Wherein the method comprises the steps of And Respectively obtaining a Fischer-Tropsch information matrix and a covariance matrix after rotation; Is a rotation matrix, satisfies Because the fuzzy function is irrelevant to the angle dimension, rotation transformation does not exist in the angle dimension, and orthogonalization is realized through the rotation transformation; Assume time of day The state error covariance matrix is when The score factor is: (46) Wherein the method comprises the steps of And Respectively a matrix Sum matrix Corresponding to the maximum eigenvalue in the eigenvector A number of elements, wherein: (47) (48) Will be Substituting formula (45) to obtain Then, obtaining a posterior state error covariance matrix The iteration is used for the next selection of waveforms.

Description

Clutter maneuvering target tracking method based on waveform selection Technical Field The invention belongs to the technical field of radar tracking, and relates to a clutter maneuvering target tracking method based on waveform selection. Background The radar transmits electromagnetic waves to a target object and receives echoes reflected by the electromagnetic waves, so that information of the target is obtained, and the cognitive radar adapts to a dynamically changing environment by changing waveforms due to closed-loop feedback of a receiver to a transmitter, so that tracking performance of the whole system is improved. With the increasing complexity of the air and ground detection environments, the increasing mobility of the targets and the gradual improvement of the capability of the signal processor, the requirements on the target tracking technology are continuously improved, and the problems of high calculation complexity and poor tracking precision of the target tracking technology under clutter environment and the tracking of maneuvering targets still exist. The conventional document "Jiantao Wang,Yuliang Qin,Hongqiang Wang,et al.Dynamic waveform selection for manoeuvering target tracking in clutter,IET Radar Sonar Navig.,2013,Vol.7,Iss.7,pp.815-825" discloses a nonlinear system and a tracking problem under clutter environment, and uses a particle filter to process nonlinear transformation, but has the problems of high computational complexity and inconvenience for practical application. The method is mainly characterized in that the existing research selects the optimal waveform through traversing calculation of each parameter, so that higher calculation load is caused, the waveform selection algorithm cannot be practically applied to engineering, and meanwhile, the waveform selection can influence the measurement error of the target, so that the tracking precision of the target is influenced. Disclosure of Invention The invention aims to provide a clutter maneuvering target tracking method based on waveform selection, which solves the problems of high computational complexity and low precision in the prior art. The technical scheme adopted by the invention is that the method for tracking the maneuvering target in the clutter based on waveform selection is implemented according to the following steps: Step 1, establishing a waveform model; Step 2, establishing a state and a measurement model; step 3, establishing a clutter model; step 4, establishing a filtering model; And 5, a waveform scheduling algorithm based on fractional Fourier transform, and the minimization of posterior estimation errors is realized through dynamic waveform selection. The present invention is also characterized in that, The step 1 is specifically implemented according to the following steps: step 1.1, establishing a transmission waveform model in a narrow-band environment; Where E T is the energy of the signal waveform, f c is the carrier frequency, Is the complex envelope of the transmitted pulse; step 1.2, establishing a received waveform model; Wherein E R is the energy of the received signal, n (t) is the additional white noise, τ represents the delay, r is the distance between the target and the radar; representing the speed of the target movement, and C represents the speed of light; When the waveform time-bandwidth product satisfies the narrowband condition, s R (t) is regarded as: The step 2 is specifically implemented according to the following steps: step 2.1, establishing a state model to establish an MCS model; wherein X k is a target state vector, [ X k,yk ] AndThe position, velocity and acceleration in the x and y directions, respectively; is the average value of first-order acceleration, h (·) is a nonlinear transformation function, z k is a target measurement matrix, process noise W k is zero-mean gaussian white noise, and variances are Q k＝2ασa2qcs;FACS and U ACS in the specific form: Wherein T is the sampling interval, ε k represents the waveform selected at time k, and R k is affected by ε k, and R k corresponding to a particular waveform is denoted R k(εk); step 2.2, establishing a measurement model as a linear measurement model; Assuming that the target moves in a two-dimensional plane and the distance, speed and direction are measured simultaneously, the nonlinear measurement model is as follows: zk＝h(Xk)+Vk (6) Wherein z k is a target measurement matrix, the measurement noise V k is zero-mean Gaussian white noise, the variance is R k;rk, Θ k represents the distance between the target and the radar, the radial velocity of the target, and the azimuth of the target, respectively. The step 3 is specifically implemented according to the following steps: The measurement of time k under clutter conditions is expressed as: Where m k is the total number of measurement targets of the radar at time k; step 3.1, z ik includes distance, velocity and angle information, assuming that the number of false alarms