CN116794649A - Clutter maneuvering target tracking method based on waveform selection - Google Patents

Abstract

The invention discloses a clutter maneuvering target tracking method based on waveform selection, which is implemented according to the following steps: step1, establishing a waveform model; step2, 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 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.

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 existing literature "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 nonlinear systems and tracking problems in clutter environments, and uses particle filters to handle nonlinear transformations; however, the method has the problems of high calculation 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:

step1, establishing a waveform model;

step2, 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 step1 is specifically implemented according to the following steps:

step1.1, establishing a transmission waveform model in a narrow-band environment;

wherein E is _T Is the energy of the signal waveform, f _c Is the carrier frequency of the signal,is the complex envelope of the transmitted pulse;

step1.2, establishing a received waveform model;

wherein E is _R Is the energy of the received signal; n (t) is additional white noise; τ represents the time 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;

s when the waveform time bandwidth product satisfies the narrowband condition _R (t) is considered as:

the step2 is specifically implemented according to the following steps:

step2.1, establishing a state model to establish an MCS model;

wherein X is _k Is the target state vector, [ x ] _k ,y _k ]、And->The 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 Measuring a matrix as a target; process noise W _k Zero mean Gaussian white noise, variance Q _k ＝2ασ _a ² q _cs ；F _ACS And U _ACS The specific form is as follows:

wherein T is the sampling interval; epsilon _k Representing the waveform selected at time k, R _k Receiving epsilon _k Is a specific waveform corresponding to R _k Represented by R _k (ε _k )；

Step2.2, 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:

z _k ＝h(X _k )+V _k (6)

wherein z is _k For the target measurement matrix, measure noise V _k Zero mean Gaussian white noise, variance R _k ；r _k ,θ _k Representing 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:

wherein m is _k Is the total number of measurement targets of the radar at time k;

step 3.1, z ⁱ _k Including distance, rate, and angle information, assuming that the false alarm number complies with the expected ρV _k The probability of false alarms is:

wherein ρ is the density of the erroneous measurement, and V _k 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;

the delay and doppler shift are estimated with the peaks of the blurring function, the probability of detection at time k is:

wherein P is _f Representing the expected probability of false alarm, eta _k Representing the signal to noise ratio at time k.

Step 4 is specifically implemented according to the following steps:

step 4.1, establishing an MPDA model;

let beta be ⁱ _k Is the time k measurement z ⁱ _k Is of the associated probability, beta ⁰ _k If there is no associated probability from the target measurement value, the posterior error covariance matrix in mpdfs is:

wherein the method comprises the steps ofIs the Kalman filtering gain; s is S _k+1 ＝HP _k+1|k H ^T +R _k+1 Is an innovation covariance matrix; p (P) _k+1|k Is a predictive covariance matrix; alpha is the influence factor of the filter error covariance matrix:

wherein P is _d Is the probability of detection, and P _g Is a threshold probability; c _Γ Is an influence factor and represents the correlation gate to the innovation covariance matrix S _k+1 Is a function of (1);

when the measurement dimension is three-dimensional:

where γ is the correlation threshold, and γ=g ² G is the association area,is a defined error function;

R _k+1 corresponds to oneA specific waveform epsilon _k+1 (or waveform parameters), P _k+1|k+1 Also with epsilon _k+1 Correspondingly, define as P _k+1|k+1 (ε _k+1 ) The method comprises the steps of carrying out a first treatment on the surface of the When the modified Ricat equation is used to estimate P _k+1|k+1 ：

Wherein q is ₂ Is a scalar between 0 and 1, and is dependent on the clutter density ρ, the correlation threshold V _k+1 And the detection probability P at time k+1 _dk+1 ；q ₂ The approximate fit is:

wherein n is _Z =3 and V _k+1 ＝(4π/3)g ³ |S _k+1 | ^1/2 ；

Step 4.2, establishing an MPDA-SCKF model;

before data processing, R is defined as matrix A ^T An upper triangular matrix obtained by QR decomposition, the QR decomposition of matrix a being expressed as s=tria (a) =r ^T Wherein the matrix S is a lower triangular matrix, and the MPDAF-SCKF processing flow is as follows:

step 4.2.1, updating time;

and 4.2.2, measuring and updating.

The specific steps of the time update in the step 4.2.1 are as follows:

step1.1: factorization of

P _k|k ＝S _k|k (S _k|k ) ^T (18)

Step1.2: calculating a volume point and propagating the volume point

Wherein X is ⁱ _k|k And X ^i* _k+1|k Volume points and propagation volume points; m is the number of all volume points, n is the dimension of the state vector X, and satisfies the condition of m=2n; zeta type toy _i ＝(m/2) ^1/2 [1]，[1]Is a point set obtained by fully arranging or inverting the unit vectors in the n-dimensional space;

step1.3: calculating a state prediction mean and a square root of a state prediction error covariance;

wherein the weighted center matrix is:

the specific steps of the measurement update in step 4.2.1 are as follows:

step2.1: calculating volume points and performing nonlinear transformation:

step2.2: calculating a measurement prediction mean

Step2.3: calculating square root coefficients of a residual (innovation) covariance matrix:

wherein, the weighted center matrix is:

step2.4: calculating a residual covariance matrix:

step2.5: calculating a mutual covariance matrix between states and measurements

Wherein the weighted center matrix is:

step2.6: calculating a filter gain:

step2.7: calculating square root coefficients of the corresponding error covariance matrix and the posterior estimated error covariance matrix:

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:

S _k+1|k+1 ＝Chol(P _k+1|k+1 ) (37)

otherwise, the following formula is used:

assume that at kT time the state error covariance matrix is P _k|k 。

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.

The specific steps of the step 5.1 are as follows:

measuring noise covariance matrix R _k+1 The transmitted waveform parameter epsilon from time k+1 _k+1 Correlation (i.e. waveforms selected at time k), i.e. a (τ, f _d ) Is a fuzzy function of the transmit waveform s (t), namely:

with respect to delay τ and Doppler shift f _d The fee-house information matrix of (1) is:

where η is the signal to noise ratio; r is R _k+1 And A (τ, f) _d ) The relation between the two is:

R _k+1 (ε _k+1 )＝TJ ^-1 (ε _k+1 )T (42)

wherein t=diag (c/2, c/(2 f) _c ) Time delay τ and Doppler shift f) _d A matrix of Fischer-Tropsch information on distance and speed; j (J) ^-1 (ε _k+1 ) Is the lower bound of the Kramer for the selected waveform under unbiased estimation;

the selected waveform at time k is shown in equation (40) to determine R _k+1 The method comprises the steps of carrying out a first treatment on the surface of the The optimal waveform is selected by minimizing the estimation error at time k+1:

the selected waveform at time k affects the measurement error covariance matrix and also affects the state estimation error at time k+1; and selecting an optimal waveform through waveform scheduling, so that the target tracking performance under the clutter condition is greatly improved.

The specific steps of the step 5.2 are as follows:

assuming that the base transmit waveform is S ₀ (t) the blur function is A ₀ (τ,f _d ) The Fisher information matrix is J ₀ The corresponding measurement noise covariance matrix is R ₀ Fractional factor in fractional fourier transformIs applied to the basic emission waveform to realize orthogonality between the measurement error ellipse and the state error ellipse;

the fractional fourier transform is considered as a rotation operation of a coordinate system when the fractional fourier transform is used for parametersIs thatIs based on the transmitted waveform of the waveform, the blurring function of the waveform is by +.>Rotating to obtain a new waveform, wherein the obtained waveform is characterized in that:

wherein J _k+1 And R is _k+1 Respectively obtaining a Fischer-Tropsch information matrix and a covariance matrix after rotation;is a rotation matrix, satisfy->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;

let the state error covariance matrix at time k be P _k+1|k The score factor is:

wherein v is _P (i) And v _R (i) Respectively matrix P and matrix R _k Corresponds to the i-th element in the feature vector, wherein:

will beSubstituting formula (45) to obtain R _k+1 Then, a posterior state error covariance matrix P is obtained _k+1|k+1 The iteration is used for the next selection of waveforms.

The beneficial effects of the invention are as follows: on the basis of improving the current statistical (MCS, modified current statistical) model, an improved probability data interconnection filter (MPDAF, modified probabilistic data association filter) and a square root volume Kalman filter (SCKF, square-root Kalman filte) are used for processing clutter and nonlinear transformation, so that the filter estimation error is reduced, the filter precision is improved, and meanwhile, the method has the advantage of low calculation complexity. The invention reduces the calculation complexity of the tracking algorithm by improving the filtering algorithm and the dynamic waveform selection mode, and improves the target tracking precision. The invention has strong adaptability and good tracking performance when the maneuvering target is maneuvering, and improves the accuracy of maneuvering target state estimation.

Drawings

FIG. 1 (a) is the present inventionA waveform diagram generated at the time;

FIG. 1 (b) is the present inventionA waveform diagram generated at the time;

FIG. 1 (c) is the present inventionA waveform diagram generated at the time;

FIG. 2 (a) is an elliptical non-orthogonal view of the prediction error of the present invention;

FIG. 2 (b) is an elliptical orthogonal view of the prediction error of the present invention;

FIG. 3 is a flow chart of the adaptive MPDA-SCKF processing operation of the present invention;

FIG. 4 is a maneuver target acceleration diagram of the present invention;

FIG. 5 (a) is a position root mean square error plot;

FIG. 5 (b) is a velocity root mean square error plot;

FIG. 5 (c) is an acceleration root mean square error plot;

fig. 6 is a rotation angle plot of the fourier transform of the waveform of the present invention.

Detailed Description

The invention will be described in detail below with reference to the drawings and the detailed description.

Example 1

The invention discloses a clutter maneuvering target tracking method based on waveform selection, which is implemented according to the following steps:

step1, establishing a waveform model;

step2, 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.

Example 2

The invention discloses a clutter maneuvering target tracking method based on waveform selection, which is implemented according to the following steps:

step1, establishing a waveform model;

step1.1, establishing a transmission waveform model in a narrow-band environment;

wherein E is _T Is the energy of the signal waveform, f _c Is the carrier frequency of the signal,is the complex envelope of the transmitted pulse;

step1.2, establishing a received waveform model;

wherein E is _R Is the energy of the received signal; n (t) is additional white noise; τ represents the time 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;

s when the waveform time bandwidth product satisfies the narrowband condition _R (t) is considered as:

step2, establishing a state and a measurement model;

step2.1, establishing a State model

The MCS model is built as follows:

wherein X is _k Is the target state vector, [ x ] _k ,y _k ]、And->The 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 Measuring a matrix as a target; process noise W _k Zero mean Gaussian white noise, variance Q _k ＝2ασ _a ² q _cs ；F _ACS And U _ACS The specific form is as follows:

wherein T is the sampling interval; epsilon _k Representing the waveform (or waveform parameter) selected at time k, and R _k Receiving epsilon _k Is a specific waveform corresponding to R _k Represented by R _k (ε _k )。

Step2.2, establishing a 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:

z _k ＝h(X _k )+V _k (6)

wherein z is _k For the target measurement matrix, measure noise V _k Zero mean Gaussian white noise, variance R _k ；r _k ,θ _k Respectively representing the distance between the target and the radar, the radial speed of the target and the azimuth angle of the target;

step 3, establishing a clutter model

The measurement of time k under clutter conditions is expressed as:

wherein m is _k Is the total number of measurement targets of the radar at time k;

step 3.1, z ⁱ _k Including distance, rate, and angle information, assuming that the false alarm number complies with the expected ρV _k The probability of false alarms is:

wherein ρ is the density of the erroneous measurement, and V _k 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;

the delay and doppler shift are estimated with the peaks of the blurring function, the probability of detection at time k is:

wherein P is _f Representing the expected probability of false alarm, eta _k Representing the signal to noise ratio at time k.

Step 4, establishing a filtering model

Step 4.1, establishing an MPDA model

Let beta be ⁱ _k Is the time k measurement z ⁱ _k Is of the associated probability, beta ⁰ _k If there is no associated probability from the target measurement, then the posterior error co-ordinates in MPDAFThe difference matrix is:

wherein the method comprises the steps ofIs the Kalman filtering gain; s is S _k+1 ＝HP _k+1|k H ^T +R _k+1 Is an innovation covariance matrix; p (P) _k+1|k Is a predictive covariance matrix; alpha is the influence factor of the filter error covariance matrix:

wherein P is _d Is the probability of detection, and P _g Is a threshold probability; c _Γ Is an influence factor and represents the correlation gate to the innovation covariance matrix S _k+1 Is a function of (a) and (b).

When the measurement dimension is three-dimensional:

where γ is the correlation threshold, and γ=g ² G is the association area,is a defined error function.

R _k+1 Corresponds to a specific waveform epsilon _k+1 (or waveform parameters), P _k+1|k+1 Also with epsilon _k+1 Correspondingly, define as P _k+1|k+1 (ε _k+1 ). When the modified Ricat equation is used to estimate P _k+1|k+1 ：

Wherein q is ₂ Is a scalar between 0 and 1, and is dependent on the clutter density ρ, the correlation threshold V _k+1 And the detection probability P at time k+1 _dk+1 。q ₂ The approximate fit is:

wherein n is _Z =3 and V _k+1 ＝(4π/3)g ³ |S _k+1 | ^1/2 。

Step 4.2, establishing an MPDA-SCKF model;

before data processing, R is defined as matrix A ^T An upper triangular matrix obtained by QR decomposition, the QR decomposition of matrix a being expressed as s=tria (a) =r ^T The matrix S is a lower triangular matrix, and as shown in FIG. 3, the MPDAF-SCKF processing flow is as follows:

step 4.2.1, time update

Assume that at kT time the state error covariance matrix is P _k|k 。

Step1.1: factorization of

P _k|k ＝S _k|k (S _k|k ) ^T (18)

Step1.2: calculating a volume point and propagating the volume point

Wherein X is ⁱ _k|k And X ^i* _k+1|k The volume points and the propagation volume points, respectively. m is the number of all volume points, n is the dimension of the state vector X, and the condition of m=2n is satisfied. Zeta type toy _i ＝(m/2) ^1/2 [1]，[1]Is a point set obtained by fully arranging or inverting the unit vectors of the n-dimensional space.

Step1.3: the state prediction mean and the square root of the state prediction error covariance are calculated.

Wherein the weighted center matrix is:

step 4.2.2, measurement update

Step2.1: calculating volume points and performing nonlinear transformation:

step2.2: calculating a measurement prediction mean

Step2.3: calculating square root coefficients of a residual (innovation) covariance matrix:

wherein, the weighted center matrix is:

step2.4: calculating a residual covariance matrix:

step2.5: calculating a mutual covariance matrix between states and measurements

Wherein the weighted center matrix is:

step2.6: calculating a filter gain:

step2.7: calculating square root coefficients of the corresponding error covariance matrix and the posterior estimated error covariance matrix:

/>

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:

S _k+1|k+1 ＝Chol(P _k+1|k+1 ) (37)

otherwise, the following formula is used:

and 5, a waveform scheduling algorithm based on fractional Fourier transform, and the minimization of posterior estimation errors is realized through dynamic waveform selection.

Step 5.1, calculating the lower bound of the Keramelteon

Measuring noise covariance matrix R _k+1 The transmitted waveform parameter epsilon from time k+1 _k+1 Correlation (i.e. waveforms selected at time k), i.e. a (τ, f _d ) Is a fuzzy function of the transmit waveform s (t), namely:

with respect to delay τ and Doppler shift f _d The fee-house information matrix of (1) is:

where η is the signal to noise ratio. R is R _k+1 And A (τ, f) _d ) The relation between the two is:

R _k+1 (ε _k+1 )＝TJ ^-1 (ε _k+1 )T (42)

wherein t=diag (c/2, c/(2 f) _c ) Time delay τ and Doppler shift f) _d A matrix of fischer-tropsch information about distance and speed. J (J) ^-1 (ε _k+1 ) Is to unbiased estimationLower cladmerol bound for the selected waveform.

The selected waveform at time k is shown in equation (40) to determine R _k+1 。

Therefore, the optimal waveform is selected by minimizing the estimation error at time k+1:

the selected waveform at time k affects the measurement error covariance matrix and also affects the state estimation error at time k+1. Therefore, the optimal waveform is selected through waveform scheduling, so that the performance of target tracking under clutter conditions is greatly improved.

Step 5.2 optimized waveform selection based on fractional Fourier transform

Assuming that the fundamental transmit waveform (one rectangular pulse) is S ₀ (t) the blur function is A ₀ (τ,f _d ) The Fisher information matrix is J ₀ The corresponding measurement noise covariance matrix is R ₀ . Fractional factor in fractional fourier transformIs applied to the fundamental transmit waveform to achieve orthogonality between the measurement error ellipses and the state error ellipses.

As shown in FIGS. 1 (a) - (c), are differentThe waveform obtained in this case, the fractional Fourier transform is regarded as a rotation operation of the coordinate system when the fractional Fourier transform is used for the parameters +.>Is based on the transmitted waveform of the waveform, the blurring function of the waveform is by +.>And rotating to obtain a new waveform. The obtained waveform features are: />

Wherein J _k+1 And R is _k+1 The Fischer-Tropsch information matrix and the (measurement noise) covariance matrix obtained after rotation, respectively.Is a rotation matrix, satisfy->Since the blurring function is independent of the angular dimension, there is no rotational transformation in this dimension of the angle. Orthogonalization is achieved by rotation transformation. And is therefore referred to as an error orthogonalization method. As shown in fig. 2, fig. 2 (a) shows a case where the prediction error ellipse and the measurement error are not orthogonal; whereas in fig. 2 (b) two error ellipses are orthogonal. When the two error ellipses are orthogonal, the overlapping area is minimum, and the minimum tracking error can be obtained. Rotation angle->Obtained by the formula (44), assuming that the state error covariance matrix at the time k is P _k+1|k The score factor is:

wherein v is _P (i) And v _R (i) Respectively matrix P and matrix R _k Corresponds to the i-th element in the feature vector. Wherein:

will beSubstituting formula (45) to obtain R _k+1 . Then, a posterior state error covariance matrix P is obtained _k+1|k+1 . The iteration is used for the next selection of waveforms.

Example 3

The invention establishes a foundation for establishing an MPDA-SCKF model in the next step by establishing the MPDAF based on the clutter maneuvering target tracking method in the waveform selection; the modified Ricat equation in PDAF is used as an approximate solution under the condition of large-area association by using the modified Ricat equation as a covariance matrix of the next state error. In contrast, the mpd af-corrected licarpa's equation is a condition that is precisely solved and does not require extensive correlation. Thus, mpdfs are taken as update trackers; by adopting the error ellipse orthogonalization method, when two error ellipses are orthogonalized, the overlapping area is minimum, the minimum tracking error is obtained, the calculated amount is low, and the physical meaning is visual.

From the figure

As can be seen from fig. 5 (a) to (c), the proposed algorithm has excellent performance both in strong maneuvers and in weak maneuvers. The proposed algorithm has the lowest root mean square error and the fastest convergence speed, especially in case of abrupt state transitions.

As shown in fig. 6, the rotation angle of the waveform fourier transform in the proposed algorithm is shown, the rotation angle selecting the optimal waveform in the dynamic variation. Therefore, the minimum tracking precision can be achieved, and the tracking performance is effectively improved. In contrast, two filters that fix the waveform cannot effectively utilize waveform scheduling, making tracking performance lower than the proposed algorithm.

Table 1 shows the average error, tracking loss rate, and run time of the algorithm.

TABLE 1 average error, tracking loss rate, run time

The invention achieves minimum average error and tracking loss rate. In addition, the tracking loss rates of IMM-PDA-PF, MCS-PDA-SCKF-WWS and the proposed algorithm are very close. In contrast, the tracking loss rate of both filters of the fixed waveform is twice that of the proposed algorithm. Therefore, waveform scheduling can actually improve tracking performance in clutter environments.

The simulation is carried out under the environment of high signal-to-noise ratio, and the tracking loss rate of all algorithms is relatively low; furthermore, it can be seen that not only is the average error greater, but also the run time is at a maximum of three times that of the proposed algorithm. In contrast, the proposed algorithm has the lowest average error while maintaining validity. The proposed algorithm runs slightly longer on the basis of two filters of fixed waveform, due to the waveform scheduling. But tracking performance is effectively improved.

In particular, and fixing the waveformCompared with the MCS-MPDA-SCKF, the position estimation precision of the proposed algorithm is improved by 32.46%, the speed estimation precision is improved by 25.62%, and the acceleration estimation precision is improved by 10.37%. The run time was increased by 13.23%. And fix waveform->Compared with MCS-MPDA-SCKF, the position estimation precision of the provided algorithm is improved by 34.83%, the speed estimation precision is improved by 35.73%, and the acceleration estimation precision is improved by 24.17%. At the same time, the run time was increased by 12.98%. Simulation results show that compared with a method for fixing waveforms, the method has lower track tracking loss ratio and higher tracking precision. Meanwhile, compared with the two existing methods, the method has the advantages of simple structure and high precision.

The invention solves the problems of nonlinear measurement and target tracking in clutter environment, combines MPDAF and SCKF into a new filter based on MCS motion model, and dynamically selects waveforms through effective waveform configuration. Compared with a filter with fixed waveform, the invention realizes low RMSE, low ME and TLP under the condition of maintaining reasonable increment of computational complexity, and has simpler structure and higher estimation precision.

Claims (10)

1. The clutter maneuvering target tracking method based on waveform selection is characterized by comprising the following steps of:

step1, establishing a waveform model;

step2, 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.

2. The clutter in maneuvering target tracking method based on waveform selection according to claim 1, wherein the step1 is specifically implemented according to the following steps:

step1.1, establishing a transmission waveform model in a narrow-band environment;

wherein E is _T Is the energy of the signal waveform, f _c Is the carrier frequency of the signal,is the complex envelope of the transmitted pulse;

step1.2, establishing a received waveform model;

wherein E is _R Is the energy of the received signal; n (t) is additional white noise; τ represents the time 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;

s when the waveform time bandwidth product satisfies the narrowband condition _R (t) is considered as:

3. the clutter in maneuvering target tracking method based on waveform selection according to claim 2, wherein the step2 is specifically implemented according to the following steps:

step2.1, establishing a state model to establish an MCS model;

wherein X is _k Is the target state vector, [ x ] _k ,y _k ]、And->Respectively represents x and yPosition, velocity and acceleration of direction; />Is the average value of first-order acceleration; h (·) is a nonlinear transformation function; z _k Measuring a matrix as a target; process noise W _k Zero mean Gaussian white noise, variance Q _k ＝2ασ _a ² q _cs ；F _ACS And U _ACS The specific form is as follows:

wherein T is the sampling interval; epsilon _k Representing the waveform selected at time k, R _k Receiving epsilon _k Is a specific waveform corresponding to R _k Represented by R _k (ε _k )；

Step2.2, 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:

z _k ＝h(X _k )+V _k (6)

wherein z is _k For the target measurement matrix, measure noise V _k Zero mean Gaussian white noise, variance R _k ；r _k ,θ _k Respectively represent the distance between the target and the radar and the radial direction of the targetSpeed and azimuth of the target.

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:

the measurement of time k under clutter conditions is expressed as:

wherein m is _k Is the total number of measurement targets of the radar at time k;

step 3.1, z ⁱ _k Including distance, rate, and angle information, assuming that the false alarm number complies with the expected ρV _k The probability of false alarms is:

wherein ρ is the density of the erroneous measurement, and V _k 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;

the delay and doppler shift are estimated with the peaks of the blurring function, the probability of detection at time k is:

wherein P is _f Representing the expected probability of false alarm, eta _k Representing the signal to noise ratio at time k.

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;

let beta be ⁱ _k Is the time k measurement z ⁱ _k Is of the associated probability, beta ⁰ _k If there is no associated probability from the target measurement value, the posterior error covariance matrix in mpdfs is:

wherein the method comprises the steps ofIs the Kalman filtering gain; s is S _k+1 ＝HP _k+1|k H ^T +R _k+1 Is an innovation covariance matrix; p (P) _k+1|k Is a predictive covariance matrix; alpha is the influence factor of the filter error covariance matrix:

wherein P is _d Is the probability of detection, and P _g Is a threshold probability; c _Γ Is an influence factor and represents the correlation gate to the innovation covariance matrix S _k+1 Is a function of (1);

when the measurement dimension is three-dimensional:

where γ is the correlation threshold, and γ=g ² G is the association area,is a defined error function;

R _k+1 corresponds to a specific waveform epsilon _k+1 (or waveform parameters), P _k+1|k+1 Also with epsilon _k+1 Corresponding, fixMeaning P _k+1|k+1 (ε _k+1 ) The method comprises the steps of carrying out a first treatment on the surface of the When the modified Ricat equation is used to estimate P _k+1|k+1 ：

Wherein q is ₂ Is a scalar between 0 and 1, and is dependent on the clutter density ρ, the correlation threshold V _k+1 And the detection probability P at time k+1 _dk+1 ；q ₂ The approximate fit is:

wherein n is _Z =3 and V _k+1 ＝(4π/3)g ³ |S _k+1 | ^1/2 ；

Step 4.2, establishing an MPDA-SCKF model;

before data processing, R is defined as matrix A ^T An upper triangular matrix obtained by QR decomposition, the QR decomposition of matrix a being expressed as s=tria (a) =r ^T Wherein the matrix S is a lower triangular matrix, and the MPDAF-SCKF processing flow is as follows:

step 4.2.1, updating time;

and 4.2.2, measuring and updating.

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 of

P _k|k ＝S _k|k (S _k|k ) ^T (18)

Step1.2: calculating a volume point and propagating the volume point

Wherein X is ⁱ _k|k And X ^i* _k+1|k Volume points and propagation volume points; m is the number of all volume points, n is the dimension of the state vector X, and satisfies the condition of m=2n; zeta type toy _i ＝(m/2) ^1/2 [1]，[1]Is a point set obtained by fully arranging or inverting the unit vectors in the n-dimensional space;

step1.3: calculating a state prediction mean and a square root of a state prediction error covariance;

wherein the weighted center matrix is:

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:

step2.2: calculating a measurement prediction mean

Step2.3: calculating square root coefficients of a residual (innovation) covariance matrix:

wherein, the weighted center matrix is:

step2.4: calculating a residual covariance matrix:

step2.5: calculating a mutual covariance matrix between states and measurements

Wherein the weighted center matrix is:

step2.6: calculating a filter gain:

step2.7: calculating square root coefficients of the corresponding error covariance matrix and the posterior estimated error covariance matrix:

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:

S _k+1|k+1 ＝Chol(P _k+1|k+1 ) (37)

otherwise, the following formula is used:

assume that at kT time the state error covariance matrix is P _k|k 。

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. 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 R _k+1 The transmitted waveform parameter epsilon from time k+1 _k+1 Correlation (i.e. waveforms selected at time k), i.e. a (τ, f _d ) Is a fuzzy function of the transmit waveform s (t), namely:

with respect to delay τ and Doppler shift f _d The fee-house information matrix of (1) is:

where η is the signal to noise ratio; r is R _k+1 And A (τ, f) _d ) The relation between the two is:

R _k+1 (ε _k+1 )＝TJ ^-1 (ε _k+1 )T (42)

wherein t=diag (c/2, c/(2 f) _c ) Time delay τ and Doppler shift f) _d A matrix of Fischer-Tropsch information on distance and speed; j (J) ^-1 (ε _k+1 ) Is the lower bound of the Kramer for the selected waveform under unbiased estimation;

the selected waveform at time k is shown in equation (40) to determine R _k+1 The method comprises the steps of carrying out a first treatment on the surface of the The optimal waveform is selected by minimizing the estimation error at time k+1:

the selected waveform at time k affects the measurement error covariance matrix and also affects the state estimation error at time k+1; and selecting an optimal waveform through waveform scheduling, so that the target tracking performance under the clutter condition is greatly improved.

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 S ₀ (t) the blur function is A ₀ (τ,f _d ) The Fisher information matrix is J ₀ The corresponding measurement noise covariance matrix is R ₀ Fractional factor in fractional fourier transformIs 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 ofIs based on the transmitted waveform of the waveform, the blurring function of the waveform is by +.>Rotating to obtain a new waveform, wherein the obtained waveform is characterized in that:

wherein J _k+1 And R is _k+1 Respectively obtaining a Fischer-Tropsch information matrix and a covariance matrix after rotation;is a rotation matrix, satisfy->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;

let the state error covariance matrix at time k be P _k+1|k The score factor is:

wherein v is _P (i) And v _R (i) Respectively matrix P and matrix R _k Corresponds to the i-th element in the feature vector, wherein:

will beSubstituting formula (45) to obtain R _k+1 Then, a posterior state error covariance matrix P is obtained _k+1|k+1 The iteration is used for the next selection of waveforms.