CN116449326A - Broadband multi-target translational parameter estimation and compensation method - Google Patents
Broadband multi-target translational parameter estimation and compensation method Download PDFInfo
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Abstract
The invention discloses a broadband multi-target translational parameter estimation and compensation method, belonging to the field of radar signal processing; the method specifically comprises the following steps: firstly, calculating echo signals of N targets received by a radar; based on random Hough transformation, separating and extracting corresponding tracks of each target; then, the initial position and velocity and acceleration of each target are roughly estimated, and performing coarse compensation; redundant scattering points and aliased tracks are removed using CLEAN so that each target retains only one continuous scattering point. Then, estimating the residual acceleration and the residual translational velocity of the scattering point target based on the frequency spectrum characteristics, and calculating the final velocity estimation and acceleration estimation of the target; and finally, carrying out short-time Fourier transform on each row of distance units based on an R-D imaging algorithm of short-time Fourier transform on the radar echo signals after the fine compensation to obtain a three-dimensional Doppler-distance-time matrix, and obtaining an R-D image slice. The invention performs fine estimation and compensation on the motion parameters in the time-frequency domain.
Description
Technical Field
The invention belongs to the field of radar signal processing, and particularly relates to a broadband multi-target translational parameter estimation and compensation method.
Background
The different micro motions of the space target have different modulation characteristics on the radar echo, so that the scattering point of the target echo can generate serious envelop migration, and the migration is reflected on echo delay and micro Doppler characteristics and is an important basis for identifying and imaging the characteristics of the space target.
Therefore, the work based on the micro-motion feature has important research value, but most of the current researches are based on that the translational component of the target is accurately compensated, but the space target moving at high speed can generate complex modulation effects such as intra-pulse stretching, inter-pulse walking and the like on radar echo in practice.
When the radar detects space, a plurality of targets are always in the same wave gate, the distance between the targets is smaller, the targets in the wave gate are difficult to distinguish in the distance dimension, the targets fly at the initial speed and are under the action of aerodynamic force and earth attraction, the stress states are similar, the similar motion states are similar, the Doppler dimension is difficult to distinguish, and the conventional multi-target detection algorithm is only suitable for a plurality of stable targets and is difficult to be suitable for the scene.
Disclosure of Invention
Aiming at the problems of coupling and mutual interference during the separation of complex motion multi-target signals, the invention provides a broadband multi-target translational parameter estimation and compensation method, which is based on the separation of image domains and performs fine estimation and compensation on motion parameters in a time-frequency domain by utilizing the inching information of targets.
The method comprises the following specific steps:
step one, aiming at a scene that N targets are in the same wave gate when the radar detects the space, calculating echo signals received by the radar;
the echo signal calculation formula is:
wherein,,is a fast time, t m Is slow time, t is full time, f c Is the carrier frequency, kappa is the toneSlope of frequency, A ij Is the scattering intensity of the jth scattering point on the ith target, S i For the number of scattering points of the ith target, T p For pulse duration, c is the speed of light. />Is the radial distance of the jth scattering point on the ith target relative to the radar, where R i (t m ) Is the radial distance from the radar site to the origin of the reference coordinate system corresponding to the ith target, the change of which is regarded as translation, R ij (t m ) Is the distance from the jth scattering point in the target to the origin of coordinates, the change of which is regarded as inching; v represents the speed.
Step two, the echo signal of each target corresponds to one track in the one-dimensional range profile, and the corresponding track of each target is separated and extracted based on regional division random Hough transformation.
The method comprises the following specific steps:
(1) performing CFAR on the one-dimensional range profile sequence of each target, and extracting a target track to obtain a binary image;
(2) establishing a Cartesian coordinate system (x, y) in a one-dimensional range profile sequence space, and dividing the coordinates of x, y into a plurality of time blocks in an equalizing manner;
(3) carrying out classical random Hough transformation in each hour block to extract a straight line, and mapping the result to a rho-theta space;
(4) and (3) carrying out threshold detection on the rho-theta space to obtain a linear expression of the original one-dimensional range image sequence, constructing a corresponding mask according to the linear expression and the side lobe width of the echo signal, and separating the target signal from the one-dimensional image sequence.
Step three, utilizing a least square method to the corresponding track of each target to obtain the initial position R and the speed of each target through rough estimationAcceleration->Then, coarse compensation is performed.
The compensation method is as follows,
wherein f r Represents the sampling frequency point, f d Representing the doppler frequency, FFT (·) representing the fourier transform, IFFT (·) representing the inverse fourier transform,is the original echo signal.
And step four, removing redundant scattering points and aliasing tracks of the roughly compensated one-dimensional range profile sequence by using CLEAN, so that each target only keeps one continuous scattering point.
The CLEAN method specifically comprises the following steps:
(1) performing one-dimensional CFAR on the target one-dimensional range profile sequence after the rough compensation;
(2) envelope detection is carried out on the obtained result to obtain a distance unit and a time unit of the redundant scattering points of the target;
(3) firstly, hough transformation is carried out to obtain a linear equation of an aliased track, and then a mask with the width of only five distance units is constructed to select the aliased track;
(4) extracting the peak amplitude A of a slow time for a specific scattering point and an aliased track 1 Phase ofTime delay t 1 ；
(5) Inverting the target echo:and subtracting the original one-dimensional image sequence;
(6) the same operation is performed for each slow time until both the specific scatter points and the aliased tracks are eliminated by the CLEAN algorithm.
Estimating the residual acceleration of each target which only keeps one continuous scattering point based on the frequency spectrum characteristics;
the method comprises the following steps:
(1) predicting the residual acceleration according to the prior of the inching magnitude, and uniformly dividing to obtain an acceleration compensation sequence a com ；
(2) For the signal after coarse compensationPerforming time domain compensation, transforming to a frequency domain, and obtaining a spectrum peak value of the frequency domain:
(3) and then solving the maximum value in the spectrum peak value vector, wherein the corresponding acceleration compensation value is the target residual acceleration:
step six, precisely estimating the instantaneous frequency by utilizing a sliding window MUSIC, and estimating the residual translational velocity of each target which only keeps one continuous scattering point according to the frequency spectrum characteristic;
the algorithm comprises the following steps:
(1) given a window length W, selecting a proper window function, cutting off and windowing the signal;
(2) construction of an autocovariance matrix R using data x ；
(3) For auto-covariance matrix R x Performing feature decomposition, and sequencing the obtained feature value lambda and the feature vector Q; maximum value lambda of eigenvalue lambda 0 I.e. corresponding Q of Q 0 Tense into signal subspace, the remaining vectors in QTense into noise subspace Q N ；
(4) For determining the instantaneous normalized angular frequency of the signal, the vector v (f) =exp (2pi jft) of a given Doppler dimension m ) Thereby constructing a spectrum estimation formula:searching to obtain the instantaneous frequency f in the time window s ；
(5) Sliding a time window, and repeating the steps (2) to (5) until the Doppler search is completed;
obtaining the instantaneous frequency of a scattering point of the target after refining treatment, thereby estimating the translation quantity delta f of the target, and obtaining the estimated value of the residual translation speed:
Δv＝Δf×f s /2π
step seven, calculating final speed estimation and acceleration estimation of each target by using the residual acceleration and the residual translational speed of the target;
the speed estimation formula is:
wherein the method comprises the steps ofA speed that is a coarse estimate;
the acceleration estimation formula is:
wherein the method comprises the steps ofIs a coarse estimated acceleration.
And step eight, performing short-time Fourier transform on each row of distance units based on an R-D imaging algorithm of short-time Fourier transform on the radar echo signals subjected to fine compensation to obtain a three-dimensional Doppler-distance-time matrix, wherein each Doppler-distance time slice is an R-D image slice.
The invention has the advantages that:
1) Compared with the traditional parameter estimation, the method for estimating and compensating the translational parameters of the broadband multi-target makes full use of the micro-motion characteristics of the target, and performs more accurate and proper parameter estimation and motion compensation on the target echo.
2) The invention relates to a broadband multi-target translational parameter estimation and compensation method, which solves the problems that targets are difficult to separate in the distance and Doppler dimensions in the traditional method under the condition that a plurality of targets are in the same wave gate and the distance between the targets is smaller.
Drawings
FIG. 1 is a general flow chart of a wideband multi-objective translational parameter estimation and compensation method of the present invention;
FIG. 2 is a flowchart of an R-D imaging algorithm based on short-time Fourier transform according to the present invention;
Detailed Description
The invention will be described in further detail with reference to the drawings and examples.
The invention relates to a broadband multi-target translational parameter estimation and compensation method, which researches how to separate multi-target echo signals based on an image domain and perform accurate and proper parameter estimation and motion compensation in a time-frequency domain; by adopting image domain separation, the problems of coupling and mutual interference during separation between complex signal models are avoided, and the problem of track aliasing during image domain separation is restrained by adopting time-frequency domain refinement treatment.
The invention researches a method for estimating parameters of the broadband radar based on a space target and analyzing time frequency. Firstly, aiming at the characteristics that the motion characteristic of a space cone target is not stable, the influence of the translational speed on the radial distance is far greater than the influence of acceleration and micro motion on the radial distance in a certain observation time, and the characteristics that the traditional image detection algorithm has large operand, non-real time and the like; and extracting a linear track based on the regional random Hough, constructing a mask according to the signal side lobe and the target non-stationary characteristic, and extracting a target track through low-order fitting. And extracting distance information of each slow time of the target, performing coarse compensation on translation parameters through least square, and accurately estimating and eliminating the influence of sidelobe mutual interference between scattering points of the target and an aliased track on the micro-motion phase by using a CLEAN algorithm to obtain a spatial cone target one-dimensional distance image only comprising one scattering point, wherein the scattering point only comprises residual translation and micro-motion information. Finally, carrying out fine compensation on the residual translational motion, and estimating the residual acceleration of the target by using a peak value method according to the influence of micro Doppler, residual translational motion speed and residual translational motion acceleration on a signal spectrum so that a micro Doppler curve has no deflection; and then accurately cutting a noise subspace and a signal-noise subspace by using a sliding window MUSIC to realize high-precision estimation of the target instantaneous frequency for noise robustness, obtaining the time-frequency domain translation quantity of a time-frequency curve, and estimating the residual speed of the target. Finally, the separation, coherent compensation and R-D imaging of the broadband radar on a plurality of non-stationary targets in space are realized.
According to the broadband multi-target translational parameter estimation and compensation method, as shown in fig. 1, a target one-dimensional image sequence is firstly subjected to linear detection by using random Hough transformation based on region division, then low-order fitting is carried out, and a mask is constructed according to a fitting result to carry out image domain separation. And carrying out least square rough estimation compensation on the separated result to obtain a target one-dimensional image sequence after rough compensation. In order to simplify the follow-up inching information extraction and reduce the operand, the redundant scattering points and the aliased tracks are subjected to CLEAN, the coupling of side lobes and the aliased tracks is reduced, and the coarse compensation is completed. After coarse compensation, motion information comprises inching, residual speed and residual acceleration, the residual acceleration is estimated precisely by a peak value method based on the frequency domain characteristics of signals, then the instantaneous frequency is solved based on a TVAR model to obtain a precise estimation result of the residual speed, and finally instantaneous R-D imaging based on short-time Fourier transformation is performed.
The method comprises the following specific steps:
step one, aiming at a scene that N targets are in the same wave gate when the radar detects the space, calculating echo signals received by the radar;
the transmitting signals of the broadband radar are as follows:
is a fast time, t m Is slow time, T p For pulse duration, f c Is the carrier frequency, t is the full time, and κ is the frequency modulation slope;
the echo signal calculation formula is:
wherein A is ij Is the scattering intensity of the jth scattering point on the ith target, S i The number of scattering points for the ith target, c is the speed of light,is the radial distance of the jth scattering point on the ith target relative to the radar, where R i (t m ) Is the radial distance from the radar site to the origin of the reference coordinate system corresponding to the ith target, the change of which is regarded as translation, R ij (t m ) Is the distance of the jth scattering point in the target to the origin of coordinates, the change of which is considered to be a jog. v represents the speed.
After radar echo matching and filteringExpressed as:
wherein f di ＝2v i λ represents the Doppler shift, v, for the ith target i Representing the speed of the ith target, lambda being the signal wavelength, alpha i ＝1-2v i And/c represents a time scaling factor, A ij Representing the scattering intensity of the jth scattering point on the ith target after being modulated, B representing the bandwidth,corresponding to Sa functionMost of the processing results of the microwave radar are Sa functions; the radar signal processing is only capable of cutting off signals to perform finite length processing, which is equivalent to adding rectangular windows to the signals, and the processing result corresponds to the frequency domain envelope of the rectangular windows, namely the Sa function, the main lobe of the function is narrow, but the side lobe is very high, and a large amount of spectrum energy leaks out of the side lobe to influence the resolution target and the subsequent signal processing, so that proper windowing and suppression are needed.
From the processing results, it can be seen that: because the motion of the target comprises acceleration and strong inching, the echo signal is a non-stationary signal, meanwhile, the high-speed moving target can generate modulation with great influence on the phase, pulse width and the like of the echo, and a common target compensation method such as envelope minimum entropy, a special display point method and the like can realize the compensation of the non-stationary target, but the general effect is poor, and especially the precision of coherent compensation in a polynomial form of a coherent radar system is superior to that of non-coherent compensation, and meanwhile, the influence on the phase change caused by the inching of the target is small, so that the method has important research value.
Step two, the echo signal of each target corresponds to one track in the one-dimensional range profile, and the corresponding track of each target is separated and extracted based on regional division random Hough transformation.
And (3) adopting an image domain separation method, and carrying out low-order fitting on the image domain at the cost of a certain degree of aliasing to construct a one-dimensional image sequence of the mask separation target. The Hough transform is a common method for image domain fitting, but has huge operand and lower use value, so that the improved Hough transform with lower operand needs to be explored.
The Hough transform is an algorithm for realizing straight line detection from an image through a one-to-many voting strategy, and describes the corresponding relation between two parameter spaces by defining the relation between points of the image space and curves in the parameter space, so that the problem which is difficult to solve in the image space is well solved in the parameter space.
An expression for a straight line in a given x-y coordinate system may be expressed as,
y＝k·x+b
wherein x is an x-axis coordinate obtained under a Cartesian coordinate system, y is a y-axis coordinate, k is a linear slope, b is a linear intercept, the method can also be written as,
b＝-x·a+y
the above equation can be regarded as a straight line equation in a cartesian coordinate system, and according to the transformation relationship of the ρ - θ space and the cartesian coordinate system,
x＝ρcosθ
y＝ρsinθ
wherein ρ is the shortest distance from the origin to the line, θ is the angle between the line and the x-axis, and is available,
ρ＝x cosθ+y sinθ
the Hough algorithm steps are as follows.
(1) Firstly, detecting characteristic points of an image, and extracting the characteristic points to obtain a corresponding binary image;
(2) according to the preset interval of rho and theta, carrying out parameter conversion on each characteristic point, and adding one to the pixel value corresponding to the conversion result;
(3) the image is detected in the ρ - θ space according to a preset threshold, and a point exceeding the threshold is considered to correspond to a straight line in the original image.
The main task of Hough transformation is to map the intercept and slope of a straight line to a rho-theta space, and convert the detection of the straight line into the detection of a peak value through a voting strategy.
However, this method has a major drawback in that the mapping concept is "one-to-many", a large number of mapping operations are required for each feature point, and the algorithm is computationally intensive. The random Hough transformation is proposed for the deficiency Xu Lei et al, and the algorithm replaces the mapping idea of 'one-to-many' through 'many-to-one' mapping, so that the time complexity of the algorithm is greatly reduced.
The basic idea of classical stochastic Hough transforms is to determine the mapping relationship based on image geometry, the basic metering method of which is also the voting mechanism. The geometric feature refers to the relation between the coordinates of the feature points and the equation of the curve to be extracted, for example, two points can determine a straight line, and then the extracted straight line randomly takes two feature points to determine a straight line; three points can determine a perfect circle, and then the extracted circle randomly takes three non-collinear feature points to determine the parameters of a circle.
The algorithm for extracting the straight line is as follows.
(1) Extracting feature points from the original image, and randomly selecting two feature points;
(2) according to the coordinates (x 1 ,x 2 )，(y 1 ,y 2 ) Determining a unique straight line:conversion to ρ - θ space: />ρ＝x 1 cosθ+y 1 sinθ；
(3) Adding one to the corresponding rho and theta coordinates, and stopping when the operation is performed for a certain number of times;
(4) and detecting rho and theta space according to a preset threshold value, wherein a point larger than the threshold value is considered to correspond to a straight line of the original image.
Compared with classical Hough, the classical stochastic Hohgh has much lower operand, and effectively improves the calculation speed and space utilization rate of the algorithm. However, in reality, there is a large amount of redundancy in classical random Hough, and the operation amounts of the redundancy and the nonsensical random operations are directly related to the number of the extracted feature points, and if the feature points cannot be pre-screened, a large amount of calculation force is wasted in the algorithm.
HRRP of multiple targets is often separable or partially crossed, and the trajectory of a spatially high-speed target in a certain observation time can be generally fitted by using a high-order polynomial, and when the observation time window is short, the fitting effect of a second-order polynomial is sufficient. However, the second order fitting corresponds to the Hough transformation, the parameter space is three-dimensional, the operation amount is large, and then the target track is separated in the image domain without estimating the target parameter with high precision, so that aiming at the problem of multi-target track cross aliasing, the low order fitting is adopted, namely, the straight line detection is carried out on a binary image obtained by CFAR, then a rectangular mask is constructed according to the estimation result, and the range images of the targets are separated one by one.
The random Hough transform based on region division is used for multi-objective, and the specific steps are as follows:
(5) performing CFAR on the one-dimensional range profile sequence of each target, and extracting a target track to obtain a binary image;
(6) establishing a Cartesian coordinate system (x, y) in a one-dimensional range profile sequence space, and dividing the coordinates of x, y into a plurality of time blocks in an equalizing manner;
since the radar received signal is processed here, the abscissa, i.e. the fast time dimension and the slow time dimension, are not balanced, so that the fast time dimension is much larger in the selection of the number of time blocks of the area division;
(7) carrying out classical random Hough transformation in each hour block to extract a straight line, and mapping the result to a rho-theta space;
(8) and (3) carrying out threshold detection on the rho-theta space to obtain a linear expression of the original one-dimensional range image sequence, constructing a corresponding mask according to the linear expression and the side lobe width of the echo signal, and separating the target signal from the one-dimensional image sequence.
The point exceeding the threshold is considered to correspond to a straight line in the original image.
In practice, the obtained one-dimensional range profile sequence often has the problem that target tracks are crossed, if a Canny and other edge detection algorithms are used for track extraction, the target tracks are often broken, the target tracks are not broken when a mask is constructed by polynomial fitting, and a part of signals are aliased.
Step three, utilizing a least square method to the corresponding track of each target to obtain the initial position R and the speed of each target through rough estimationAcceleration->Then, coarse compensation is performed.
Obtaining distance information R corresponding to each chirp of the target through one-dimensional CFAR according to the target track obtained in the step one w (t m ). The size of the space object is 1 m-2 m, the inching amplitude is also in the order of magnitude, and the speed of the space object is in the order of magnitude of thousands of meters per second, so the track information R obtained at the moment w (t m ) Mainly translation.
Suppose that at a certain observation time T o The inner radar receives M echoes, the target distance information of all the echoes can be expressed as,
R＝[R w (t 1 )…R w (t M )] T
the gaussian noise corresponding to each echo is,
e＝[e 1 …e M ] T
the parameters to be estimated are the parameters,
P＝[0.5a 0 ,v 0 ,R 0 ] T /α
wherein,,a 0 for coarse estimation of acceleration, v 0 For coarse speed estimation, R 0 Is the initial distance coarse estimation value.
The corresponding time series is that,
T＝[T 1 …T M ] T
it is in accordance with the physical meaning that,
R＝TP+e
wherein the cost function of the parameter P to be estimated under the least square criterion is
There is a case where the number of the group,
wherein inv (·) is the inverse of the matrix.
The measurement accuracy of the speed and distance in the commonly obtained target one-dimensional image sequence is the 3dB width of the frequency spectrum, namely the Rayleigh resolution, and the resolution is determined by specific parameters of the radar. The range resolution formula of the radar is as followsThe time of the M pulses, i.e. the observation time, is +.>The maximum error in the velocity is then,
it can be seen that the greater the number of pulses involved in the operation, the greater the accuracy of the least squares method. But the final speed, acceleration rough estimation error will be greater than theoretical due to the dramatic jog effect of the spatial target.
The compensation method is as follows,
wherein f r Represents the sampling frequency point, f d Representing Doppler frequency, FFT (·) representing Fourier transform, IFFT (·) representing inverse Fourier transform.A speed that is a coarse estimate;
the remaining translation may be expressed as,
the residual translational phase is given by the following,
and step four, removing redundant scattering points and aliasing tracks of the roughly compensated one-dimensional range profile sequence by using CLEAN, so that each target only keeps one continuous scattering point.
The target track after rough compensation is close to a straight line, and the distance and the phase of the one-dimensional image of the target are determined by the residual translation and the micro motion. The residual translational motion and the inching motion interfere with each other to influence the accurate estimation of each other.
The micro Doppler time-frequency curve without any translational component should be a periodic signal symmetrical about a time axis, so that the above extracted micro scattering points do not need to be distinguished from each other in specific positions, the micro periods of the cone top or the cone bottom are consistent, the amplitudes are different, and the residual translational components are the same, so that the positions of the scattering points in the cone do not need to be distinguished.
For the signals after coarse compensation and clear, the signal of each slow time point in a distance unit is extracted, and because the compensation method is coherent compensation, the instantaneous frequency time-frequency curve of the frequency solving target of the line of signals can be extracted.
Firstly, deriving a residual phase formula, substituting a cone precession micro Doppler expression into the residual phase formula to obtain,
f(t m )＝2/λ(Δv+Δat m +sinαsinθl p (t m )ω c cos(ω c t m ))
it can be seen that the effect of the residual speed on the time-frequency curve in the residual translation is to translate the time-frequency curve upwards or downwards; the residual acceleration affects the time-frequency curve by making the time-frequency curve have a certain skew.
For the original signal, the spectrum without translation and inching should be a single-frequency signal with concentrated energy, and the influence of the residual speed on the original signal is to shift the spectrum; the effect of the residual acceleration is to spread the signal from a single frequency to a band frequency, energy dispersive.
In conclusion, the translational velocity can be well estimated from the time-frequency domain processing of the inching, and the residual acceleration can be well estimated from the original signal frequency domain. This method of estimating the residual acceleration Δa is called a peak method, and the steps thereof are as follows.
(1) Predicting the residual acceleration according to the micro-motion magnitude a priori, wherein the residual acceleration range is [ -4m/s 2 ～4m/s 2 ]And uniformly dividing to obtain an acceleration compensation sequence a com ；
(2) For the signal after coarse compensationPerforming time domain compensation, transforming to a frequency domain, and obtaining a spectrum peak value of the frequency domain:
(3) and then solving the maximum value in the spectrum peak value vector, wherein the corresponding acceleration compensation value is the target residual acceleration:
then, the residual translational velocity Deltav needs to be estimated, and firstly, a time-frequency diagram of the target needs to be drawn to obtain the micro Doppler of the target. The time-frequency resolution of STFT and CWD is lower, the requirement of high-precision translational compensation is difficult to meet, the time-frequency resolution of the bilinear time-frequency conversion is obviously better than that of a linear time-frequency analysis method although the windowing truncation of an original signal is avoided, the time-frequency resolution is more sensitive to cross interference among multi-frequency component signals due to the use of signal convolution operation, and a false signal is introduced, so that the interference term of the multi-component signals is serious.
In summary, a TVAR is used here to analyze the micro-motion. TVAR is a broader autoregressive model, and the coefficients of TVAR model are time-varying unlike conventional autoregressive models, so that it has better analysis ability for non-stationary random signals, and in addition. TVAR models are commonly used in the financial and economic fields for analyzing data changes and are now often used for analyzing the instantaneous frequency of non-stationary signals. For the determination of its time-varying coefficients, it is generally represented by the sum of a set of basis functions with linear weights, so as to achieve a transition from the non-stationary time-varying problem to the stationary linear time-constant problem.
The differential equation of the TVAR model is as follows,
wherein x (N) is a non-stationary time sequence at time N, n=1, 2,3, …, N, w (N) is white gaussian noise, a k (n) is the time-varying coefficient of the kth order, and p is the model order. The time-varying autoregressive model is to fit a time-varying linear combination of the past p samples of the sequence to the sequence value at the predicted current time.
When the signal is a non-stationary signal, the instantaneous frequency changes over time, so a time-varying coefficient is required to describe this change. There are two general methods for determining the time-varying coefficients: the adaptive method iteratively calculates the time-varying coefficients and the basis function method calculates the time-varying coefficients with a certain criterion.
The dynamic model of the adaptive method is as follows,
the adaptive method is only suitable for the situation that the signal frequency changes slowly, when the signal transformation is more severe, the method is harder to track the time-varying coefficient, and the algorithm diverges when the signal frequency changes rapidly and cannot converge to a true value as a result of practical application.
The basis functions commonly used in the method for solving the time-varying coefficients are: legend basis functions, walsh basis functions, DCT basis functions, and Fourier basis functions. This approach treats the time-varying coefficients as a linear combination of basis functions,
wherein g j (n) is a basis function, a ij For the converted time-invariant coefficient, M 0 Is the basis function dimension.
Equation (4.20) is substituted into the differential equation of the TVAR model,
Y N ＝X N Φ N +E N
wherein, the signal sequence is that,
Y N ＝[x(p+1),x(p+2),…,x(N)] T
the time-invariant coefficient sequence is that,
Φ N ＝[a 10 …a 1m ,a 20 …a 2m …a p0 …a pm ] T
the white gaussian noise sequence is given by the following,
E N ＝[e(p+1),e(p+2)…e(N)] T
the matrix of signal sequences and basis function sequences is,
the method for estimating the time-varying coefficient by the TVAR model comprises a least square method, a mean square estimation method and the like.
The formula of the fourier basis function is,
g n (k)＝exp[-j2πnk/N]
g n (k) Is to calculate the 2 pi N/N sine and cosine component in the signal at a sampling frequency of 2 pi k/N over 0-2 pi.
The model residual of the least squares method is noted as follows,
E N ＝Y N -X N Φ N
the idea of the least squares method is to minimize the sum of squares of the residuals under the least squares criterion, whose cost function is,
the least square estimate of the model time-varying coefficients is,
after estimating the time-varying coefficients of the TVAR model, a complex polynomial equation can be constructed,
z p +a 1 (n)z p-1 +a 2 (n)z p-2 +…+a p ＝0
wherein z=e -jω The physical meaning is the normalized instantaneous frequency of the signal at that instant.
After solving the polynomial, the z value of each component can be obtained, the real instantaneous frequency of which can be obtained by the following equation,
f k (n)＝angle(z k (n))×f s /2π
f k (n) is the instantaneous frequency of the k-order component, f s Is the sampling rate of the signal, what is worth say here f s Not a fast time sampling rate of the echo, because the processed signal is a signal of multiple chirp over a distance cell, the corresponding sampling rate should be the pulse repetition frequency of the radar.
Under a space target scene, the target distance radar station is tens to hundreds of kilometers, and the signal to noise ratio of the processed signal is lower; especially, the micro-motion extracted by the broadband radar has a span unit phenomenon, a target signal on part of time sequences is not a signal main lobe, but a signal side lobe, and the signal-to-noise ratio is low; in addition, the micro Doppler has poor energy aggregation effect at the time point of severe partial frequency change, and the overall treatment effect is not ideal. It is necessary to find an instantaneous frequency estimation algorithm with good noise reduction performance.
The results obtained in the steps comprise micro motion and residual translation, the magnitude of which is equivalent, but because the processing results of the microwave radar are mostly Sa functions, the sidelobes of the microwave radar are very high, the interference on adjacent distance units is larger, and particularly, the influence on the phase of a target is larger. Although only one target exists, the spatial target is an extended target, the frequency spectrum leakage of adjacent scattering points is serious, and the extraction influence on micro-motion is large. The translation of different scattering points is the same, so that the translation compensation can be completed by processing a single scattering point, and the compensated one-dimensional image sequence is subjected to CLEAN, redundant scattering points are removed, and each target only maintains one continuous scattering point.
In addition, the radial distance between multiple targets is relatively short, the targets are often indistinguishable in distance dimension, and the target tracks are overlapped in a coherent accumulation time, and the overlapping can influence subsequent signal processing, especially micro-extraction, and can directly influence the phase of micro-motion signals, so that the fine processing of the signals is influenced, and the processing precision of an algorithm is reduced. Therefore, the cross aliasing of the multi-target tracks needs to be further removed, and the invention also uses the CLEAN algorithm to process the aliasing part, so as to reduce the influence of the aliasing part on the micro-extraction. Because the scattering points of the same target are leveled after the rough compensation and mainly concentrated in several to more than ten distance units, aliasing signals of other targets are in a one-dimensional range profile sequence with the target in a mode of high slope, uncompensated and nearly straight line, hough transformation straight line detection is firstly carried out on the aliasing signals, a target straight line equation is extracted, and then a mask with a very narrow width is constructed to carry out clear operation on the aliasing flight path.
The CLEAN method is only a principle, can be flexibly changed according to the use requirement, does not have strict algorithm steps, is mainly used for reducing noise, side lobes and weak targets, and is widely applied to the fields of computer vision and microwave radar.
The CLEAN method specifically comprises the following steps:
1. performing one-dimensional CFAR on the target one-dimensional range profile sequence after the rough compensation;
2. envelope detection is carried out on the obtained result to obtain a distance unit and a time unit of the redundant scattering points of the target;
3. firstly, hough transformation is carried out to obtain a linear equation of an aliased track, and then a mask with the width of only five distance units is constructed to select the aliased track;
4. extracting the peak amplitude A of a slow time for a specific scattering point and an aliased track 1 Phase ofTime delay t 1 ；
5. Inverting the target echo:and subtracting the original one-dimensional image sequence;
6. the same operation is performed for each slow time until both the specific scatter points and the aliased tracks are eliminated by the CLEAN algorithm.
After passing clear, the sidelobe energy leaked by redundant scattering points is effectively inhibited, the aliased tracks are effectively cleared, and obstacles are cleared for micro-motion extraction and subsequent further refinement processing.
Estimating the residual acceleration of each target which only keeps one continuous scattering point based on the frequency spectrum characteristics;
firstly, deriving a residual phase formula, substituting a cone precession micro Doppler expression into the residual phase formula to obtain,
f(t m )＝2/λ(Δv+Δat m +sinαsinθl p (t m )ω c cos(ω c t m ))
it can be seen that the effect of the residual speed on the time-frequency curve in the residual translation is to translate the time-frequency curve upwards or downwards; the residual acceleration affects the time-frequency curve by making the time-frequency curve have a certain skew.
For the original signal, the spectrum without translation and inching should be a single-frequency signal with concentrated energy, and the influence of the residual speed on the original signal is to shift the spectrum; the effect of the residual acceleration is to spread the signal from a single frequency to a band frequency, energy dispersive.
In conclusion, the translational velocity can be well estimated from the time-frequency domain processing of the inching, and the residual acceleration can be well estimated from the original signal frequency domain. This method of estimating the residual acceleration Δa is called a peak method, and the steps thereof are as follows.
The method comprises the following steps:
(4) according to the prior prediction of the magnitude of the residual acceleration of the inching magnitude, the embodiment selects the range of the residual acceleration to be [ -4m/s 2 ～4m/s 2 ]And uniformly dividing to obtain an acceleration compensation sequence a com ；
(5) For the signal after coarse compensationPerforming time domain compensation, transforming to a frequency domain, and obtaining a spectrum peak value of the frequency domain:
(6) and then solving the maximum value in the spectrum peak value vector, wherein the corresponding acceleration compensation value is the target residual acceleration:
step six, precisely estimating the instantaneous frequency by utilizing a sliding window MUSIC, and estimating the residual translational velocity of each target which only keeps one continuous scattering point according to the frequency spectrum characteristic;
the invention adopts a sliding window MUSIC method to reduce noise of micro Doppler signals of a target scattering point one-dimensional range profile sequence. The MUSIC is a parameter estimation realized by decomposing covariance matrix, constructing a spectrum estimation function after cutting signal subspace and noise subspace, and carrying out spectrum peak search on azimuth direction. The basis of MUSIC cutting signal-noise subspace and noise subspace is that the correlation of the signal and noise is very weak, the proper direction of the signal in space is very strong, but the proper direction of the signal and noise is nearly orthogonal, and the spectrum estimation function is constructed through the orthogonality, so that the noise and the signal can be cut, the noise can be almost completely taken out, and the noise robustness is very strong.
The algorithm comprises the following steps:
1. given a window length W, selecting a proper window function, cutting off and windowing the signal;
2. construction of an autocovariance matrix R using data x ；
3. For auto-covariance matrix R x Performing feature decomposition, and sequencing the obtained feature value lambda and the feature vector Q; maximum value lambda of eigenvalue lambda 0 I.e. corresponding Q of Q 0 Tense into signal subspace, the remaining vectors in QTense into noise subspace Q N ；
4. For determining the instantaneous normalized angular frequency of the signal, the vector v (f) =exp (2pi jft) of a given Doppler dimension m ) Thereby constructing a spectrum estimation formula:searching to obtain the instantaneous frequency f in the time window s ；
5. Sliding a time window, and repeating the steps (2) to (5) until the Doppler search is completed;
obtaining the instantaneous frequency of a scattering point of the target after refining treatment, thereby estimating the translation quantity delta f of the target, and obtaining the estimated value of the residual translation speed:
Δv＝Δf×f s /2π
step seven, calculating final speed estimation and acceleration estimation of each target by using the residual acceleration and the residual translational speed of the target;
the speed estimation formula is:
wherein the method comprises the steps ofA speed that is a coarse estimate;
the acceleration estimation formula is:
wherein the method comprises the steps ofIs a coarse estimated acceleration.
And step eight, performing short-time Fourier transform on each row of distance units based on an R-D imaging algorithm of short-time Fourier transform on the radar echo signals subjected to fine compensation to obtain a three-dimensional Doppler-distance-time matrix, wherein each Doppler-distance time slice is an R-D image slice.
As shown in FIG. 2, for the received radar echo, only micro motion and low-level translation of the signal after fine compensation can be regarded as not including the translation, and at the moment, defocusing can occur due to micro motion of a target when the signal matrix is subjected to two-dimensional R-D imaging, so that the R-D imaging algorithm based on the short-time Fourier transform is used for carrying out the short-time Fourier time-frequency transform on each row of distance units, a three-dimensional Doppler-distance-time matrix is obtained, and then one Doppler-distance time slice is taken out at will to be the R-D image slice.
Claims (3)
1. The broadband multi-target translational parameter estimation and compensation method is characterized by comprising the following specific steps:
step one, aiming at a scene that N targets are in the same wave gate when the radar detects the space, calculating echo signals received by the radar;
the echo signal calculation formula is:
wherein,,is a fast time, t m Is slow time, t is full time, f c Is the carrier frequency, kappa isFrequency modulation slope, A ij Is the scattering intensity of the jth scattering point on the ith target, S i For the number of scattering points of the ith target, T p For pulse duration, c is the speed of light;is the radial distance of the jth scattering point on the ith target relative to the radar, where R i (t m ) Is the radial distance from the radar site to the origin of the reference coordinate system corresponding to the ith target, the change of which is regarded as translation, R ij (t m ) Is the distance from the jth scattering point in the target to the origin of coordinates, the change of which is regarded as inching; v represents the speed;
step two, the echo signal of each target corresponds to one track in the one-dimensional range profile, and the corresponding track of each target is separated and extracted based on regional division random Hough transformation;
step three, utilizing a least square method to the corresponding track of each target to obtain the initial position R and the speed of each target through rough estimationAcceleration->Then performing coarse compensation;
the compensation method is as follows,
wherein f r Represents the sampling frequency point, f d Representing the doppler frequency, FFT (·) representing the fourier transform, IFFT (·) representing the inverse fourier transform,is the original echo signal;
step four, removing redundant scattering points and aliased tracks of the roughly compensated one-dimensional range profile sequence by using CLEAN, so that each target only keeps one continuous scattering point;
estimating the residual acceleration of each target which only keeps one continuous scattering point based on the frequency spectrum characteristics;
the method comprises the following steps:
(1) predicting the residual acceleration according to the prior of the inching magnitude, and uniformly dividing to obtain an acceleration compensation sequence a com ；
(2) For the signal after coarse compensationPerforming time domain compensation, transforming to a frequency domain, and obtaining a spectrum peak value of the frequency domain:
(3) and then solving the maximum value in the spectrum peak value vector, wherein the corresponding acceleration compensation value is the target residual acceleration:
step six, precisely estimating the instantaneous frequency by utilizing a sliding window MUSIC, and estimating the residual translational velocity of each target which only keeps one continuous scattering point according to the frequency spectrum characteristic;
the algorithm comprises the following steps:
(1) given a window length W, selecting a proper window function, cutting off and windowing the signal;
(2) construction of an autocovariance matrix R using data x ；
(3) For auto-covariance matrix R x Performing feature decomposition, and sequencing the obtained feature value lambda and the feature vector Q; maximum value lambda of eigenvalue lambda 0 I.e. corresponding Q of Q 0 Tense into signal subspace, the remaining vectors in QTense into noise subspace Q N ；
(4) For determining the instantaneous normalized angular frequency of the signal, the vector v (f) =exp (2pi jft) of a given Doppler dimension m ) Thereby constructing a spectrum estimation formula:searching to obtain the instantaneous frequency f in the time window s ；
(5) Sliding a time window, returning to the step (2), and repeating until the Doppler search is completed;
obtaining the instantaneous frequency of a scattering point of the target after refining treatment, thereby estimating the translation quantity delta f of the target, and obtaining the estimated value of the residual translation speed:
Δv＝Δf×f s /2π
step seven, calculating final speed estimation and acceleration estimation of each target by using the residual acceleration and the residual translational speed of the target;
the speed estimation formula is:
wherein the method comprises the steps ofA speed that is a coarse estimate;
the acceleration estimation formula is:
wherein the method comprises the steps ofAcceleration for coarse estimation;
and step eight, performing short-time Fourier transform on each row of distance units based on an R-D imaging algorithm of short-time Fourier transform on the radar echo signals subjected to fine compensation to obtain a three-dimensional Doppler-distance-time matrix, wherein each Doppler-distance time slice is an R-D image slice.
2. The method for estimating and compensating wideband multi-objective translational parameters of claim 1, wherein said step two is specifically as follows:
(1) performing CFAR on the one-dimensional range profile sequence of each target, and extracting a target track to obtain a binary image;
(2) establishing a Cartesian coordinate system (x, y) in a one-dimensional range profile sequence space, and dividing the coordinates of x, y into a plurality of time blocks in an equalizing manner;
(3) carrying out classical random Hough transformation in each hour block to extract a straight line, and mapping the result to a rho-theta space;
(4) and (3) carrying out threshold detection on the rho-theta space to obtain a linear expression of the original one-dimensional range image sequence, constructing a corresponding mask according to the linear expression and the side lobe width of the echo signal, and separating the target signal from the one-dimensional image sequence.
3. The method for estimating and compensating wideband multi-objective translational parameters according to claim 1, wherein the clear method in the fourth step specifically comprises:
(1) performing one-dimensional CFAR on the target one-dimensional range profile sequence after the rough compensation;
(2) envelope detection is carried out on the obtained result to obtain a distance unit and a time unit of the redundant scattering points of the target;
(3) firstly, hough transformation is carried out to obtain a linear equation of an aliased track, and then a mask with the width of only five distance units is constructed to select the aliased track;
(4) extracting the peak amplitude A of a slow time for a specific scattering point and an aliased track 1 Phase ofTime delay t 1 ；
(5) Inverting the target echo:and subtracting the original one-dimensional image sequence;
(6) the same operation is performed for each slow time until both the specific scatter points and the aliased tracks are eliminated by the CLEAN algorithm.
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