CN107861109A - A kind of target micro-doppler curve extracting method based on order particles filtering - Google Patents
A kind of target micro-doppler curve extracting method based on order particles filtering Download PDFInfo
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Abstract
The invention discloses a kind of target micro-doppler curve extracting method based on order particles filtering, thinking is：Radar is determined, target be present in the range of detections of radar, relative to the Kinematic Decomposition of radar is target translation and target fine motion by target, the state model of kth moment target instantaneous Doppler frequency is established using order particles filter method；The observation vector that the target observation value of kth moment N number of Discrete Short Time Fourier Transform unit is formed is determined, establishes the observation model of kth moment target；Calculate state variable estimate corresponding to the instantaneous Doppler frequency of the moment of kth+1 target translationWith the instantaneous Doppler frequency of the moment of kth+1 target fine motion corresponding to state variable estimateAnd the instantaneous Doppler frequency estimation of the moment of kth+1 target isMake k value take 0 to K 1 respectively, respectively obtain the instantaneous Doppler frequency estimation of the 1st moment targetTo the instantaneous Doppler frequency estimation of K moment targetsAfter draw curve, the curve for extraction target micro-doppler curve.
Description
Technical Field
The invention belongs to the technical field of radar target identification, and relates to a target micro-Doppler curve extraction method based on high-order particle filtering, which is suitable for micro-Doppler curve extraction aiming at sinusoidal modulation.
Background
Micro-doppler curves are generally considered to uniquely characterize the motion characteristics of a target, with the ability to provide reliable information for radar target identification and classification; however, how to effectively extract the micro-doppler curve of the target remains a challenge in practical applications.
Generally, methods for extracting a micro doppler curve can be roughly divided into two types, wherein the first type is that a sub-signal dictionary is established according to a micro doppler signal model, and a radar echo of a target is matched with the established dictionary, so that corresponding model parameters are estimated; the method needs prior information of a target micro Doppler signal model, and when the model parameters are more, a high-dimensionality sub-signal dictionary needs to be constructed, so that the calculation amount is larger; taking the spinning target as an example, even if the translation of the spinning target is completely compensated, the sub-signal dictionary is also three-dimensional because it contains three unknown model parameters; the second method is to obtain a Time-instantaneous doppler plot by using a Time-frequency analysis method, and estimate Model parameters of a target according to an instantaneous doppler curve in the Time-instantaneous doppler plot, wherein the common Time-frequency analysis method includes Short Time Fourier Transform (STFT), wigner-Ville distribution, S method, time-varying Autoregressive Model (TVAR), and the like; the computational complexity of the commonly used time-frequency analysis methods is usually relatively low, but a clear time-instantaneous doppler map is required, and the number of scattering centers in a single range cell is required to be as small as possible; the former is often difficult to guarantee, and the latter can be realized by increasing the bandwidth of the radar emission signal.
Radon transform is a commonly used method for extracting a sinusoidal curve from a time-frequency plane in the current low signal-to-noise ratio environment, and it needs to assume that the target translation is completely compensated; however, this assumption is often difficult to achieve, especially for high frequency radars, a small compensation error may also result in very large micro-doppler modulations; therefore, it is necessary to describe the translation of the target by a third order or higher speed, but this results in a drastic increase in the computational complexity of Radon transform; in fact, the problem of extracting a micro doppler curve from a time-frequency plane under a low signal-to-noise ratio condition is consistent with the Tracking Before Detection (TBD) problem of a weak target, and the fluctuation of the target echo amplitude is very stable, but the micro doppler curve is mainly applied to a first-order markov process and cannot be directly extended to the extraction of the micro doppler curve.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, an object of the present invention is to provide a target micro doppler curve extraction method based on high-order particle filtering, which can be used for micro doppler curve extraction of sinusoidal modulation and can effectively estimate parameters of a sinusoidal micro doppler curve.
The realization idea of the invention is as follows: regarding the sine-modulated instantaneous Doppler curve as a high-order Markov process, and establishing a dynamic equation of a target; regarding a short-time Fourier transform result of a target radar echo as observation, and establishing an observation model of a target; and estimating static model parameters of the target by using a kernel smoothing method, and estimating state parameters of the target by using an auxiliary particle filtering method, thereby extracting and obtaining a micro Doppler curve of the target.
In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.
A target micro Doppler curve extraction method based on high-order particle filtering is characterized by comprising the following steps:
step 1, determining a radar, wherein a target exists in a radar detection range, and decomposing the motion of the target relative to the radar into target translation and target micromotion so as to obtain a short-time Fourier transform result of an echo signal of the target radar for M times; wherein M is the total times of obtaining target radar echo signals, and M is a positive integer greater than or equal to 1;
step 2, establishing a state model of the target instantaneous Doppler frequency at the kth moment by using a high-order particle filtering method; k is more than or equal to 0 and less than or equal to K-1, K represents the discrete time length of the short-time Fourier transform result of the target radar echo signal for M times, and K is a positive integer more than 1;
the short-time Fourier transform result of the M times of target radar echo signals comprises KxN discrete short-time Fourier transform units, N represents the total number of discrete frequency points contained in the short-time Fourier transform result of the M times of target radar echo signals, and K represents the discrete time length of the short-time Fourier transform result of the M times of target radar echo signals;
step 3, determining an observation vector formed by target observation values of N discrete short-time Fourier transform units at the kth moment according to the state model of the target instantaneous Doppler frequency at the kth moment, and further obtaining an observation model of the target at the kth moment; wherein N is less than or equal to M;
initialization: let K denote the kth time, K =0,1,2, \ 8230, the initial value of K-1, K is 0, K denotes the discrete time length of the short-time fourier transform result of the M times target radar echo signal;
step 4, according to the observation model of the target at the k moment, calculating to obtain a state variable estimation value corresponding to the translational instantaneous Doppler frequency of the target at the k +1 momentState variable estimation value corresponding to instantaneous Doppler frequency of target inching at the (k + 1) th moment
Step 5, according to the state variable estimated value corresponding to the instantaneous Doppler frequency of the target translation at the (k + 1) th momentState variable estimation value corresponding to instantaneous Doppler frequency of target inching at the (k + 1) th momentCalculating to obtain the instantaneous Doppler frequency estimated value of the target at the (k + 1) th moment
Step 6, respectively taking the value of K from 0 to K-1, repeating the steps 4 to 5, and further respectively obtaining the instantaneous Doppler frequency estimated value of the target at the 1 st momentInstantaneous Doppler frequency estimate to target at time KThen according to the instantaneous Doppler frequency estimated value of the target at the 1 st momentInstantaneous Doppler frequency estimate to target at time KAnd drawing to obtain a curve, wherein the obtained curve is the extracted target micro Doppler curve.
The invention has the beneficial effects that: the extraction process of the sine modulated micro Doppler curve is regarded as a state estimation problem, the instantaneous Doppler frequency of a target is regarded as a state to establish a dynamic equation, the short-time Fourier transform result of a target radar echo is regarded as observation to establish an observation equation, and the state parameters of the target are estimated by utilizing the auxiliary particle filtering combined with a kernel smoothing method, so that the extraction of the sine micro Doppler curve is realized.
Drawings
The invention is described in further detail below with reference to the following description of the drawings and the detailed description.
FIG. 1 is a flow chart of a target micro-Doppler curve extraction method based on high-order particle filtering according to the present invention;
FIG. 2 is a schematic diagram of a target model for electromagnetic simulation;
FIG. 3 is a schematic time-distance image of an electromagnetic simulation target;
FIG. 4a is a diagram of the results of micro-Doppler analysis of a smooth spinning target by short-time Fourier transform under noise-free conditions;
FIG. 4b is a diagram of the results of micro-Doppler analysis of a smooth spinning target by short-time Fourier transform at a signal-to-noise ratio of 5 dB;
FIG. 4c is a diagram of the results of micro-Doppler analysis of a smooth spinning target by short-time Fourier transform at 0dB signal-to-noise ratio;
FIG. 4d is a diagram of the results of micro-Doppler analysis of a smooth spinning target by the short-time Fourier transform method at a signal-to-noise ratio of-5 dB;
FIG. 5a is a graph of the results of instantaneous Doppler curve extraction in the absence of noise;
FIG. 5b is a graph of the instant Doppler curve extraction results of the present invention for a 5dB signal-to-noise ratio;
FIG. 5c is a graph of the instant Doppler curve extraction results of the present invention for a signal-to-noise ratio of 0 dB;
figure 5d is a graph of the results of the instant doppler curve extraction of the present invention for a-5 dB signal to noise ratio.
Detailed Description
Referring to fig. 1, it is a flow chart of a target micro doppler curve extraction method based on high order particle filtering according to the present invention; the target micro Doppler curve extraction method based on the high-order particle filtering comprises the following steps:
step 1, establishing a radar echo model modulated by sine micro Doppler and a signal form of discrete short-time Fourier transform of the radar echo model.
Determining a radar, wherein a target exists in a detection range of the radar, the motion of the target relative to the radar is decomposed into target translation and target micromotion, the target translation refers to the radial motion of the target along the sight line direction of the radar, the target micromotion refers to the micro motion of vibration, rotation, acceleration and the like of the target or the components of the target except for centroid translation, and each point on the target can generate different motion forms relative to the radar in the target micromotion process, so that different Doppler frequency shift amounts are corresponding to the different Doppler frequency shift amounts and are recorded as the instantaneous Doppler frequency of the target micromotion; then respectively setting the initial velocity v of the target translation 0 The second-order speed of the target translation is a, and the third-order speed of the target translation is b; setting the frequency of the target micro-motion to be omega, the amplitude of the target micro-motion to be E and the initial phase of the target micro-motion to be phi 0 (ii) a Reflecting the radar emission signal back to the radar echo signal through the target, recording the reflected signal as a target radar echo signal, respectively setting the amplitude of the target radar echo signal as rho, and setting the initial phase of the target radar echo signal as psi 0 Setting the wavelength of a radar transmitting signal as lambda and the pulse repetition period of a target radar echo signal as T r (ii) a And then, calculating to obtain an mth target radar echo signal x (m), wherein the expression of the mth target radar echo signal x (m) is as follows:
wherein, let M be the serial number of the target radar echo signal, M =0, \ 8230;, M-1, the mth time corresponds to mT r At the moment, M is the total number of times of obtaining the target radar echo signal, and M is a positive integer greater than or equal to 1; u (m) is the noise of the mth target radar echo signal x (m), and u (m) obeys a mean of 0 and a variance ofComplex gaussian distribution of (a); exp denotes an exponential function, j denotes an imaginary unit, and ρ denotes a meshAmplitude, v, of radar echo signals 0 Representing the initial velocity, T, of the translation of the target r Representing the pulse repetition period of the target radar return signal.
And performing short-time Fourier transform on the target radar echo signal x (0) of the 0 th time to the target radar echo signal x (M-1) of the M-1 th time by adopting a short-time Fourier transform method, and further obtaining a short-time Fourier transform result of the target radar echo signal of the M times.
Respectively setting k as a discrete time variable of a short-time Fourier transform result of the M times of target radar echo signals, and l as a discrete frequency variable of a short-time Fourier transform result of the M times of target radar echo signals, wherein the signal form of the (k, l) th discrete short-time Fourier transform unit of the short-time Fourier transform result of the M times of target radar echo signals is z (k, l):
wherein, x [ (N-N) ol )k+n]Denotes the (N-N) ol ) k + N times of target radar echo signals, N =0, \8230;, N-1, w (N) represents a window function at the nth discrete frequency point in the short-time Fourier transform result of the M times of target radar echo signals, N represents the total number of discrete frequency points contained in the short-time Fourier transform result of the M times of target radar echo signals, and N represents the total number of discrete frequency points contained in the short-time Fourier transform result of the M times of target radar echo signals ol The number of overlapped points of the window function w (N) and the target radar echo signals of M times when sliding is represented, N is less than or equal to M, K represents the discrete time length of the short-time Fourier transform result of the target radar echo signals of M times, represents rounding-down, and N, M and K are positive integers greater than or equal to 1 respectively.
And 2, regarding the instantaneous Doppler frequency of the target as a state, and establishing a state model of the instantaneous Doppler frequency of the target at the kth moment by using a high-order particle filtering method.
The instantaneous Doppler frequency of the target is divided into two parts to be used for establishing a dynamic equation for the instantaneous Doppler frequency caused by the translational part and the instantaneous Doppler frequency caused by the jogging part respectively, so that a state model of the instantaneous Doppler frequency of the target at the kth moment is obtained.
According to the radar echo signal (1) of the target, the instantaneous Doppler frequency gamma of the mth target radar echo signal x (m) can be obtained m Can be expressed as:
wherein, the first and the second end of the pipe are connected with each other,ω＝ΩT r ，v 0 representing the initial velocity of the translation of the target, a representing the second-order velocity of the translation of the target, T r The pulse repetition period of a target radar echo signal is represented, lambda represents the wavelength of a radar transmitting signal, b represents the third-order speed of translation of a target, E represents the amplitude of micro-motion of the target, and omega represents the frequency of the micro-motion of the target.
In order to extract the instantaneous Doppler frequency curve of the target by adopting particle filtering, the instantaneous Doppler frequency gamma of the 0 th target radar echo signal x (0) is measured 0 Instantaneous Doppler frequency gamma to M-1 st target radar echo signal x (M-1) M-1 Considering the target observation value as a short-time Fourier transform result of the target radar echo signal of M times, and recording the total observation time length of the target observation value as K ', wherein K' is equal to K in value; setting the step length of short-time Fourier transform as Deltat, and then the state equation of target translation at the moment k +1 is as follows:
wherein d is k+1 Initial velocity v of target translation at the k +1 th moment 0 Induced instantaneous Doppler frequency, d k Is at k timeInitial velocity v of translational motion of engraved target 0 Induced instantaneous Doppler frequency, eta k+1 Instantaneous Doppler frequency, η, due to second order velocity a of the target translation at time k +1 k The instantaneous doppler frequency caused by the second order velocity a of the target translation at time k,the instantaneous doppler frequency caused by the third order velocity b of the target translation at the time point k +1,instantaneous Doppler frequency caused by three-order speed b of target translation at the kth moment;instantaneous Doppler frequency caused by third-order speed b of target translation at moment k +1Is in process noise, andobey mean of 0 and variance ofA gaussian distribution of (a).
Let the state vector of the translation of the target at the k +1 th time be beta k+1 ，Superscript T denotes transpose; the state transition matrix for the translation of the object is psi,the process noise vector of the target translation at the k +1 th moment is xi k+1 ， Instantaneous Doppler frequency due to third-order velocity b of target translation at time k +1The process noise of (1); further, the state equation of the target translation at the k +1 th moment is obtained as follows:
β k+1 ＝Ψβ k +ξ k+1 (6)
let the state variable of the target inching at the k +1 th time be g k+1 If the target inching at the k +1 th moment is determined as follows:
wherein, t k+1 ＝t k +△t，g k State variable, g, representing the target jog at time k k ＝A'cos(ωt k +φ 0 )，t k+1 Denotes the (k + 1) th time, t k Denotes the kth time, deltat denotes the set time interval, phi 0 An initial phase representing a target jog;ω＝ΩT r ，T r the pulse repetition period of a target radar echo signal is represented, lambda represents the wavelength of a radar transmitting signal, E represents the amplitude of target micro-motion, omega represents the frequency of the target micro-motion, sin represents a sine function, and cos represents a cosine function; sgn (·) represents a sign function satisfying:
wherein the content of the first and second substances,since the target observation is discretized in the time dimension, the differential part in equation (7)The method cannot be directly calculated and needs to be obtained by adopting approximate calculation of a first-order derivative or a higher-order derivative.
Using approximation of the p-derivativeThen, P is more than or equal to 1 and less than or equal to P, P represents the set highest order, P is a positive integer greater than or equal to 1, and the value of the set highest order P is 4 in the embodiment; and further calculating to obtain a state equation of the target inching at the k +1 th moment after the p-order derivative is approximated:
wherein ω = Ω T r ，T r Representing the pulse repetition period of the target radar echo signal, omega representing the frequency of the target micro-motion, Δ t representing the step size of the short-time Fourier transform, D p (g k ) State variable g representing target inching at time k k Sgn represents a sign function; respectively jogging the state variables g of the target at the k-th time k Is recorded as D (1) (g k ) The state variable g of the target inching at the k-th time is set k Is denoted as D (2) (g k ) The state variable g of the target inching at the k-th time is set k Is denoted as D (3) (g k-1 ) The state variable g of the target inching at the k-th time is set k Is recorded as D (4) (g k-1 ) The expressions are respectively:
D (1) (g k )＝(g k -g k-1 ) (10a)
according to the formula (9), g k And g k-P To g k-1 The historical states at the P moments are related, so that the instantaneous Doppler frequency of the target micromotion is a high-order dynamic process; note that the state variable g of the target jog at the k-th time is k The p-th derivative of (A) is only present when the observation time k ≧ p.
Combining the equation of state of the target translation at the kth time given by the formula (5), and considering that random disturbance exists in both the frequency and the amplitude of the target micromotion in practical application, therefore, establishing a state model of the target instantaneous Doppler frequency at the kth time as follows:
wherein, g k+1,p State variables, g, representing the target jog at time k +1 after approximation of the p-th derivative k,p State variable, beta, representing the target jog at time k after approximation of the p-th derivative k+1 State variable, beta, representing target translation at time k +1 k State variable, ξ, representing the target translation at time k k+1 Representing the process noise vector, upsilon, of the target translation at time k +1 k+1 State variable g representing the target jog at time k +1 after approximation of the p-th derivative k+1,p Is process noise of, and upsilon k+1 Obedience mean of 0 and variance of(ii) a gaussian distribution of; d p (g k ) State variable g representing target inching at time k k Sgn represents the sign function and Ψ represents the state transition matrix for the translation of the object.
At this time, the instantaneous Doppler frequency γ of the target at the k-th time k Can be expressed as:
γ k ＝tβ k +g k (12)
where t denotes a set state vector at the kth time, and t = [ 10 ].
And 3, regarding the short-time Fourier transform result of the target radar echo signal for M times as observation according to the state model of the target instantaneous Doppler frequency at the kth moment, and establishing an observation model of the target at the kth moment.
The target observation value is a short-time Fourier transform result of the target radar echo signal for M times, the short-time Fourier transform result of the target radar echo signal for M times comprises K multiplied by N discrete short-time Fourier transform units, N represents the total number of discrete frequency points contained in the short-time Fourier transform result of the target radar echo signal for M times, and K represents the discrete time length of the short-time Fourier transform result of the target radar echo signal for M times.
Let z k An observation vector formed by target observation values of N discrete short-time Fourier transform units at the kth time, z k ＝[z(k,0),…,z(k,l),…,z(k,N-1)] T Z (K, l) represents the signal form of the (K, l) th discrete short-time Fourier transform unit of the short-time Fourier transform result of the target radar echo signal of M times, K is more than or equal to 0 and less than or equal to K-1, l is more than or equal to 0 and less than or equal to N-1, and superscript T represents transposition.
Given the state variable of the target instantaneous Doppler frequency at time k as g k,p ,β k Setting a state variable g containing the target inching at the kth moment after the approximation of the p-th derivative k,p The static model parameter in (1) is theta k ，θ k ＝[A,ω] T Let the point spread function of the (k, l) th discrete short-time Fourier transform unit be h (k, l; g) k,p ,θ k ,β k ) Let h stand for k Is the point spread function vector of K x N discrete short time fourier transform units at time K.
Furthermore, the point spread function h (k, l; g) of the (k, l) -th discrete short-time Fourier transform unit k,p ,θ k ,β k ) There may be an unknown phase shift exp j phi k }，φ k Denotes the phase shift phase, φ, of the (k, l) th discrete short-time Fourier transform element k Obey uniform division on [0,2 π ]Cloth; considering additive noise n of (k, l) th discrete short-time Fourier transform unit k Presence of n, n k Obedience mean of 0 and variance ofComplex Gaussian distribution of (I) N Representing an N-dimensional identity matrix; observation vector z composed of target observation values of N discrete short-time Fourier transform units at k time k Satisfies the following conditions:
z k ＝exp{jφ k }h k +n k (13)
the observation equation is described by a joint likelihood ratio function of the target (i.e. the ratio of the likelihood function when the target is present to the likelihood function when the target is not present); assuming that the phase shift phi of the point spread function of the (k, l) th discrete short-time Fourier transform unit is known, the observation vector z formed by the target observation values of the N discrete short-time Fourier transform units at the k time k Has a target condition joint likelihood ratio function of L (z) k |g k,p ,θ k ,β k ,φ k )：
Wherein phi is k Representing the phase shift phase of the (k, l) th discrete short-time Fourier transform unit; mixing L (z) k |g k,p ,θ k ,β k Phi) phase shift phase phi of the (k, l) th discrete short-time Fourier transform unit k Is integrated in the distribution range [0,2 pi) of the first time point and then an observation vector z formed by target observation values of N discrete short-time Fourier transform units at the kth time point is obtained k Is determined by the joint likelihood function ratio L (z) k |g k,p ,θ k ,β k ) The expression is as follows:
wherein the superscript H denotes the conjugate transpose, I 0 (. -) represents a modified Bessel function, θ k State variable g representing the target jog at the kth moment comprised in the approximation of the p-th derivative k,p The parameters of the static model in (1),state variable g representing target inching at time k +1 after approximation of p-th derivative k+1,p Process noise v k+1 Variance of (d φ) k Is shown by k Differentiation of (2).
An observation vector z composed of target observation values of the N discrete short-time Fourier transform units at the kth time k Is a joint likelihood function ratio L (z) k |g k,p ,θ k ,β k ) Is an observed model of the target at the kth moment.
Initialization: let K denote the kth time, K =0,1,2, \ 8230, and the initial value of K-1, K is 0.
And 4, estimating the state variable and the static model parameter { g ] of the radar echo signal of the target at the kth moment by using an auxiliary particle filter algorithm auxiliary particle filter method according to the observation model of the target at the kth moment k,p ,θ k ,β k Obtaining a state variable estimated value corresponding to the instantaneous Doppler frequency of the target translation at the k +1 th momentState variable estimation value corresponding to instantaneous Doppler frequency of target jogging at the (k + 1) th moment
Specifically, according to the observation model of the target at the k-th moment, estimating the state variable and the static model parameter { g } of the radar echo signal of the target at the k-th moment by using an auxiliary particle filter algorithm in combination with a kernel smoothing method k,p ,θ k ,β k }，θ k State variable g representing the target jog at the kth moment comprised in the approximation of the p-th derivative k,p Of (2) a static model parameter of (a) k ＝[A,ω] T ，ω＝ΩT r 。
Set the particle set at the k-th time asThe particle set at the k moment isIn which contains N s Particles of N s Denotes the total number of particles, N s Is a positive integer greater than 0;a state variable corresponding to the instantaneous Doppler frequency of the target jiggle in the ith particle at the kth time,a state variable corresponding to the instantaneous Doppler frequency of the target translation in the ith particle at the kth moment,representing target static model parameters in the ith particle at the kth moment; wherein the 0 th time particles are combined into A state variable corresponding to the instantaneous Doppler frequency of the target jiggling in the ith particle at the 0 th time,a state variable corresponding to the instantaneous Doppler frequency of the target translation in the ith particle at the 0 th moment,representing the target static model parameters in the ith particle at time 0.
(1) Respectively calculating the k-th timeThe ith particleCorresponding a priori estimatorNamely, the prior estimator of the state variable corresponding to the instantaneous Doppler frequency of the target micro-motion in the ith particle at the (k + 1) th time isThe prior estimator of the state variable corresponding to the instantaneous Doppler frequency of the target translation in the ith particle at the (k + 1) th moment isThe prior estimator of the parameters of the target static model in the ith particle at the kth time isThe expressions are respectively:
where-represents the generation of random numbers from a given distribution, h represents a set smoothing factor, 0<h<1，State variable g representing the target jog at the kth moment after approximation of the p-th derivative k,p The static model parameter θ in k Is estimated from the mean value of the measured signal, a first level weight representing an ith particle at a kth time; when the value of k is 0, the value of k is,
(2) Calculating the first-stage weight of the ith particle at the (k + 1) th timeComprises the following steps:
where, oc represents a proportional relationship,representObservation vector z formed by target observation values of N discrete short-time Fourier transform units corresponding to the (k + 1) th time k+1 The ratio of the joint likelihood functions of (a),indicates the ith particle at the k timeA corresponding a priori estimator.
(3) First order weight for ith particle at time k +1Normalization processing is carried out to obtain the first-stage weight of the ith particle at the k +1 th moment after normalization processing
(4) Let i take 1 to N respectively s And (3) is repeatedly executed, and then the 1 st particle at the k +1 th time after the normalization processing is respectively obtainedFirst level weighting of childrenTo the nth time of the k +1 th time after normalization processing s First order weight of each particleAnd is recorded as the k +1 th time N after normalization processing s First order weight of each particle
In order to improve the degradation problem of the particle filter, the k-th time N after normalization processing is carried out s First order weight of particleAnd using a symmetric resampling algorithm to collect particles at the k momentResampling is carried out to reduce the number of small weight particles and improve the number of effective particles, and then a new particle set at the kth moment is obtainedThe new set of particles at the k-th timeIn which contains N s Particles of N s Denotes the total number of particles, N s Is a positive integer greater than 0;indicates the ith time j The state variable corresponding to the instantaneous Doppler frequency of the target's micromotion in each particle,indicates the kth time i j The state variable corresponding to the instantaneous doppler frequency of the target translation in each particle,indicates the ith time j Target static model parameters in individual particles, i j Represents the jth from 1 \ 8230n s The number of particles obtained after repeated extraction from each particle, i j ∈{1,…,N s Is said to belong.
(5) Determine a mean value ofVariance is h 2 V k+1 Gaussian distribution of Indicates the ith time j A priori estimates of the parameters of the static model of the object in each particle, h represents a set smoothing factor, 0<h&1; and from the mean value ofVariance is h 2 V k+1 Gaussian distribution ofRandomly generating static model parameters in the jth particle at the (k + 1) th moment
Wherein, theta k+1 State variable g representing the target jog at time k +1, comprised after approximation of the p-th derivative k+1,p Static model parameter of (1), V k Indicates the k-th time N s The variance estimates of the individual particles are then calculated,
(6) From the probability distributionRandomly generating a target inching state variable of the jth particle at the (k + 1) th momentAnd from the probability distributionRandomly generating a target translation state variable of the jth particle at the (k + 1) th moment
Wherein the content of the first and second substances,indicates givenAndposterior probability distribution of state variables corresponding to instantaneous Doppler frequency of target micromotion at the (k + 1) th moment, g k+1,p A state variable representing the target jog at time k +1 after approximation of the p-th derivative,indicates givenThe posterior probability distribution of the state variable corresponding to the instantaneous Doppler frequency of the target translation at the (k + 1) th moment,indicates the ith time j The state variable corresponding to the instantaneous Doppler frequency of the target translation in each particle.
(7) Estimating a second-level weight of a jth particle at a time instant k +1j＝1,…,N s ：
Wherein the content of the first and second substances,representing a new set of particles at a given time (k + 1)Observation vector z formed by target observation values of N discrete short-time Fourier transform units corresponding to the (k + 1) th time k+1 The ratio of the joint likelihood functions of (a),to representObservation vector z formed by target observation values of N discrete short-time Fourier transform units corresponding to the (k + 1) th time k+1 The posterior probability of (a) is,represents a new set of particles at time k +1Middle (i) j Particles ofA corresponding a-priori estimate of the amount of,indicates the ith time at the k +1 th time j The state variable corresponding to the instantaneous doppler frequency of the target's micromotion in a particle,indicates the ith time at the k +1 th time j The state variable corresponding to the instantaneous Doppler frequency of the target translation in each particle,indicates the ith time at the k +1 th time j Target static model parameters in individual particles, z k+1 And the observation vector is formed by target observation values of N discrete short-time Fourier transform units at the (k + 1) th time.
(8) Second-level weight for jth particle at time k +1Normalization processing is carried out to obtain the second-level weight of the jth particle at the k +1 moment after normalization processing
(9) Using new set of particles at time k +1As the weighted average of the k +1 th time N s State variable estimation of individual particleAnd a k +1 th time N s Mold of particleStatic parameter estimationThe expressions are respectively:
wherein the content of the first and second substances,the state variable estimated value corresponding to the instantaneous Doppler frequency representing the target inching at the (k + 1) th moment,the state variable estimated value corresponding to the instantaneous Doppler frequency of the target translation at the k +1 th moment,state variable g representing the target jog contained at time k +1 after approximation of the p-th derivative k+1,p The estimated values of the parameters of the static model in (1),a state variable corresponding to the instantaneous Doppler frequency of the target jog in the jth particle at the (k + 1) th time,a state variable corresponding to the instantaneous Doppler frequency of the target translation in the jth particle at the (k + 1) th moment,represents the target static model parameter, theta, in the jth particle at time k +1 k+1 State variable g representing the target jog at time k +1, comprised after approximation of the p-th derivative k+1,p The static model parameters in (1).
Step 5, according to the state variable estimated value corresponding to the instantaneous Doppler frequency of the target translation at the (k + 1) th momentState variable estimation value corresponding to instantaneous Doppler frequency of target jogging at the (k + 1) th momentCalculating to obtain the instantaneous Doppler frequency estimated value of the target at the (k + 1) th moment
Concretely, the estimated values of the state variable and the model static parameter are substituted into the formula (12), and the estimated value of the instantaneous Doppler frequency of the target at the k +1 moment is obtained through calculationThe expression is as follows:
step 6, respectively taking the value of K from 0 to K-1, repeating the steps 4 to 5, and further respectively obtaining the instantaneous Doppler frequency estimated value of the target at the 1 st momentInstantaneous Doppler frequency estimate to target at time KThen, the instantaneous Doppler frequency estimated value of the target at the 1 st moment is obtainedInstantaneous Doppler frequency estimate to target at time KAnd drawing to obtain a curve, wherein the obtained curve is the extracted target micro Doppler curve.
The effect of the invention is further verified and explained by the following electromagnetic simulation experiment.
(1) Electromagnetic simulation experiment parameter setting
In the experiment, a radar observation sample is generated by adopting professional 3-dimensional electromagnetic simulation software CST Studio 2015. The target adopts a simple smooth cone model, as shown in fig. 2, the material is an ideal good conductor; wherein, the radius of the bottom surface of the cone is 0.1m, and the height is 0.3m.
Simulated radar parameters are set as follows: the carrier frequency is 10.01GHz, the frequency range is 9.5 GHz-10.5 GHz, the pulse repetition frequency is 360Hz, and the residence time is 0.5s; the spin angular frequency of the target is 2 pi rad/s, and the residual speed of the translation is v 0 =1.5m/s, second order residual velocity a =0.01m/s 2 The third-order residual speed is b = -0.09m/s 3 (ii) a The signal-to-noise ratio is defined as the ratio of the average energy of a single echo to the noise power; the micro-Doppler analysis is realized by an STFT method, and a Chebyshev window function with the side lobe attenuation coefficient of 100dB and the length of 128 points is adopted; the order of the auxiliary particle filter is 5 and the resulting number of particles is 500.
(2) Contents of electromagnetic simulation experiment
1) Examining the scattering centers of the cone top and cone bottom correspondence of the pyramid target to be separable in distance, as shown in fig. 3, the distance-time image of the target is obtained by generating a set of broadband data; in fig. 3, the abscissa is time in(s), the ordinate is distance, and the coordinate is (m).
2) The performance of the micro-doppler analysis of the STFT method under different signal-to-noise ratios is shown in fig. 4a, 4b, 4c and 4d, wherein fig. 4a, 4b, 4c and 4d are graphs of the results of the micro-doppler analysis of the STFT method on a smooth spinning target under noise-free, 5dB, 0dB and-5 dB signal-to-noise ratios, respectively; the abscissa in fig. 4a, 4b, 4c, 4d is time in(s) and the ordinate is doppler frequency in (Hz).
3) The performance of extracting the instantaneous doppler curve under different signal-to-noise ratios according to the present invention is shown in fig. 5a, fig. 5b, fig. 5c, and fig. 5d, wherein fig. 5a, fig. 5b, fig. 5c, and fig. 5d are graphs of the results of extracting the instantaneous doppler curve under the signal-to-noise ratios of no noise, 5dB, 0dB, and-5 dB, respectively; the abscissa in fig. 5a, 5b, 5c, 5d is time in(s) and the ordinate is doppler frequency in (Hz).
(3) Analyzing the electromagnetic simulation experiment result:
1) Fig. 3 shows the time-dependent variation of the distance-time image obtained from electromagnetic simulation data, from which fig. 3 two parallel straight lines are clearly visible, indicating that the scattering centers corresponding to the cone top and the cone bottom of the spinning cone target are separable in distance.
2) As can be seen from fig. 4a, 4b, 4c, and 4d, as the signal-to-noise ratio decreases, the performance of the micro doppler analysis on the electromagnetic simulation data by the STFT method gradually decreases, and the distortion degree of the micro doppler curve in the time-frequency diagram gradually increases; when the signal-to-noise ratio is-5 dB, the micro Doppler curve in the time-frequency diagram cannot be clearly shown and is almost submerged by noise.
3) As can be seen from fig. 5a, 5b, 5c, and 5d, the method of the present invention can effectively extract the micro doppler curve in the noise environment; when the noise is not generated or the signal-to-noise ratio is 5dB, the result of the micro Doppler curve obtained by extraction is very close to the true value, and when the signal-to-noise ratio is 0dB or-5 dB, the micro Doppler curve obtained by extraction has partial distortion, but the result is basically satisfactory.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
Claims (6)
1. A target micro Doppler curve extraction method based on high-order particle filtering is characterized by comprising the following steps:
step 1, determining a radar, wherein a target exists in a radar detection range, and decomposing the motion of the target relative to the radar into translation of the target and micromotion of the target so as to obtain a short-time Fourier transform result of an echo signal of the target radar for M times; wherein M is the total times of obtaining target radar echo signals, and M is a positive integer greater than or equal to 1;
the short-time Fourier transform result of the M-time target radar echo signals comprises K multiplied by N discrete short-time Fourier transform units, N represents the total number of discrete frequency points contained in the short-time Fourier transform result of the M-time target radar echo signals, and K represents the discrete time length of the short-time Fourier transform result of the M-time target radar echo signals;
step 2, establishing a state model of the target instantaneous Doppler frequency at the kth moment by using a high-order particle filtering method; k is more than or equal to 0 and less than or equal to K-1, K represents the discrete time length of the short-time Fourier transform result of the target radar echo signal for M times, and K is a positive integer more than or equal to 1;
step 3, determining an observation vector formed by target observation values of N discrete short-time Fourier transform units at the kth moment according to the state model of the target instantaneous Doppler frequency at the kth moment, and further obtaining an observation model of the target at the kth moment; wherein N is less than or equal to M;
initialization: let K denote the kth time, K =0,1,2, \ 8230, the initial value of K-1, K is 0;
step 4, according to the observation model of the target at the k moment, calculating to obtain a state variable estimation value corresponding to the translational instantaneous Doppler frequency of the target at the k +1 momentState variable estimation value corresponding to instantaneous Doppler frequency of target jogging at the (k + 1) th moment
Step 5, according to the state variable estimated value corresponding to the instantaneous Doppler frequency of the target translation at the (k + 1) th momentState variable estimation value corresponding to instantaneous Doppler frequency of target inching at the (k + 1) th momentCalculating to obtain the instantaneous Doppler frequency estimated value of the target at the (k + 1) th moment
Step 6, respectively taking the value of K from 0 to K-1, repeating the steps 4 to 5, and further respectively obtaining the instantaneous Doppler frequency estimated value of the target at the 1 st momentInstantaneous Doppler frequency estimate to target at time KThen, the instantaneous Doppler frequency estimated value of the target at the 1 st moment is obtainedInstantaneous Doppler frequency estimate to target at time KAnd drawing to obtain a curve, wherein the obtained curve is the extracted target micro Doppler curve.
2. The method for extracting target micro-doppler curve based on high-order particle filtering as claimed in claim 1, wherein in step 1, the target radar echo signal is an echo signal of a radar transmitting signal reflected back to a radar through a target;
the short-time Fourier transform result of the M times of target radar echo signals is obtained by the following steps:
respectively setting the amplitude of the echo signal of the target radar as rho and the initial phase of the echo signal of the target radar as psi 0 Setting the wavelength of radar emission signal as lambda and the pulse repetition period of target radar echo signal as T r (ii) a And then calculating to obtain an mth target radar echo signal x (m), wherein the expression of the mth target radar echo signal x (m) is as follows:
wherein, let M be the serial number of the target radar echo signal, M =0, \ 8230;, M-1, the mth time corresponds to mT r At the moment, M is the total times of obtaining target radar echo signals; u (m) is noise of a mth target radar echo signal x (m), exp represents an exponential function, j represents an imaginary number unit, rho represents the amplitude of the target radar echo signal, a represents the second-order speed of the translation of the target, b represents the third-order speed of the translation of the target, omega represents the frequency of the micro-motion of the target, E represents the amplitude of the micro-motion of the target, and phi represents the amplitude of the micro-motion of the target 0 Initial phase, v, representing target jogging 0 Representing an initial velocity of translation of the target;
and then, carrying out short-time Fourier transform on the 0 th time target radar echo signal x (0) to the M-1 st time target radar echo signal x (M-1) by adopting a short-time Fourier transform method, and further obtaining a short-time Fourier transform result of the M times target radar echo signal.
3. The method for extracting a target micro-doppler curve based on higher order particle filtering as claimed in claim 2, wherein in step 2, the state model of the target instantaneous doppler frequency at the kth time is represented by:
wherein the content of the first and second substances,g k+1,p state variables, g, representing the target jog at time k +1 after approximation of the p-th derivative k,p State variable, beta, representing the target jog at time k after approximation of the p-th derivative k+1 State variable, beta, representing target translation at time k +1 k State variable, ξ, representing the target translation at time k k+1 Representing the process noise vector, upsilon, of the target translation at time k +1 k+1 State variable g representing target inching at time k +1 after approximation of p-th derivative k+1,p Process noise of D p (g k ) State variable g representing target inching at time k k Of the p-th order of derivative, and g k The P-th derivative of (2) exists only when k is more than or equal to P, P is more than or equal to 1 and less than or equal to P, P represents the set highest order, and P is a positive integer more than or equal to 1; sgn denotes a sign function, Ψ denotes a state transition matrix for translation of the target, ω = Ω T r ，T r The pulse repetition period of the target radar echo signal is shown, omega shows the frequency of target micro-motion, and delta t shows the step size of short-time Fourier transform.
4. The method as claimed in claim 3, wherein in step 3, the observation vector formed by the target observations of the N discrete short-time fourier transform units at the kth time is z k ，z k ＝[z(k,0),…,z(k,l),…,z(k,N-1)] T Z (k, l) represents the signal form of the (k, l) th discrete short-time Fourier transform unit of the short-time Fourier transform result of the M times target radar return signal,
k is more than or equal to 0 and less than or equal to K-1, l is more than or equal to 0 and less than or equal to N-1, and the superscript T represents transposition operation;
the observation model of the target at the kth moment is specifically an observation vector z formed by target observation values of N discrete short-time Fourier transform units at the kth moment k Is a joint likelihood function ratio L (z) k |g k,p ,θ k ,β k ) The expression is as follows:
wherein, L (z) k |g k,p ,θ k ,β k ,φ k ) An observation vector z composed of target observation values of N discrete short-time Fourier transform units at the k-th time k Is combined with the target condition of the likelihood ratio function phi k Representing the phase shift phase, h, of the (k, l) th discrete short-time Fourier transform element k Indicating the K time K × NThe vector of the point spread function of the discrete short-time fourier transform unit,state variable g representing the target jog at time k +1 after approximation of the p-th derivative k+1,p Process noise v k+1 Variance of (a), theta k State variable g representing the target jog at the kth moment after approximation of the p-th derivative k,p Static model parameter of (1), d φ k Is indicative of phi k Is differentiated, the superscript H denotes the conjugate transpose, I 0 (. Cndot.) represents a modified Bessel function.
5. The method for extracting a target micro-doppler curve based on high-order particle filtering as claimed in claim 4, wherein in step 4, the estimated value of the state variable corresponding to the instantaneous doppler frequency of the translation of the target at the k +1 th time pointState variable estimation value corresponding to instantaneous Doppler frequency of target inching at the (k + 1) th momentThe expressions are respectively:
wherein the content of the first and second substances,a state variable corresponding to the instantaneous Doppler frequency of the target jog in the jth particle at the (k + 1) th time,a state variable corresponding to the instantaneous Doppler frequency of the target translation in the jth particle at the (k + 1) th moment,representing the second level weight of the jth particle at time k +1 after the normalization process, represents the second level weight of the jth particle at time k +1, representing a new set of particles at a given time k +1Observation vector z formed by target observation values of N discrete short-time Fourier transform units corresponding to the (k + 1) th time k+1 The ratio of the joint likelihood functions of (a),to representAn observation vector z formed by target observation values of N discrete short-time Fourier transform units corresponding to the (k + 1) th time k+1 The posterior probability of (a) is,represents a new set of particles at time k +1Middle (i) th j Particles of
A corresponding a priori estimator; wherein, the first and the second end of the pipe are connected with each other,indicates the ith time at the k +1 th time j The state variable corresponding to the instantaneous Doppler frequency of the target's micromotion in each particle,indicates the ith time at the k +1 th time j The state variable corresponding to the instantaneous doppler frequency of the target translation in each particle,indicates the ith time at the k +1 th time j Target static model parameters in individual particles, z k+1 An observation vector formed by target observation values of N discrete short-time Fourier transform units at the (k + 1) th time;
the new set of particles at the k-th timeThe obtaining process comprises the following steps: estimating state variables and static model parameters { g) of radar echo signals of the target at the kth moment according to the observation model of the target at the kth moment k,p ,θ k ,β k }，θ k State variable g representing the target jog at the kth moment comprised in the approximation of the p-th derivative k,p The static model parameters in (1); set the particle set at the k-th time asThe k-th time particle set isIn which contains N s Particles of N s Denotes the total number of particles, N s Is a positive integer greater than 0;indicates in the ith particle at the kth timeThe state variable corresponding to the instantaneous doppler frequency of the target's micromotion,a state variable corresponding to the instantaneous Doppler frequency of the target translation in the ith particle at the kth moment,representing target static model parameters in the ith particle at the kth moment;
then for the particle set at the k timeResampling is carried out, and a new particle set at the k-th moment is obtainedThe new set of particles at the k-th timeIn which contains N s Particles of N s Denotes the total number of particles, N s Is a positive integer greater than 0;indicates the ith time j The state variable corresponding to the instantaneous Doppler frequency of the target's micromotion in each particle,indicates the kth time i j The state variable corresponding to the instantaneous Doppler frequency of the target translation in each particle,indicates the kth time i j Target static model parameters in individual particles, i j Represents the j-th slave 1 of 8230N s The number of particles obtained after repeated extraction from each particle, i j ∈{1,…,N s Denotes belonging to by.
6. The method as claimed in claim 4, wherein in step 5, the instantaneous Doppler frequency estimate of the target at the (k + 1) th time isThe expression is as follows:
where t represents the state vector at the set k-th time.
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