CN104793210A - Compressed sensing based onboard phased array radar low-altitude wind shear wind speed estimation method - Google Patents
Compressed sensing based onboard phased array radar low-altitude wind shear wind speed estimation method Download PDFInfo
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Abstract
A compressed sensing based onboard phased array radar low-altitude wind shear wind speed estimation method includes creating a transformation matrix of a reference distance unit and a to-be-detected distance unit according to a space-time interpolation method, acquiring an independently and identically distributed sample of a clutter covariance matrix forming the to-be-detected distance unit, and acquiring an estimated value of the clutter covariance matrix to achieve clutter rejection; taking radar main lobe length as prior information, and creating a generalized space guide vector of a wind shear field; taking signal spectral width as prior information, and creating a generalized time guide vector of the wind shear field; according to the generalized space guide vector and the generalized time guide vector, creating a wind speed based wind shear field space-time base dictionary and creating a sparse basis matrix; observing echo signals subjected to clutter rejection in the first step, and recovering the echo signals by the aid of the sparse basis matrix to achieve wind speed estimation. The method has the advantage that accurate wind field speed estimation results can be still acquired when the number of pulses is small and the signal-to-noise ratio is low.
Description
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly designs a compressed sensing-based low-altitude wind shear wind speed estimation method for an airborne phased array radar.
Technical Field
The low-altitude wind shear generally refers to a meteorological phenomenon that the wind direction and the wind speed change suddenly below 600m in height, and is one of the weather phenomena which threaten the safety of air transportation to the greatest extent. The wind shear phenomenon has the characteristics of short time, small dimension, high strength and the like, so that a series of problems of difficult detection, difficult forecast and the like are brought. When an airplane enters a strong wind shear area in the taking-off and landing stages, due to the lack of enough adjusting space, if the airplane is not operated properly, a flight accident is easily caused. Therefore, the research of the low-altitude wind shear detection technology becomes an important subject in the modern air transportation field.
The airborne weather radar can detect and early warn weather phenomena such as thunderstorm, wind shear, turbulence and the like, and is important equipment for detecting the airway weather information in real time by the airplane. However, when the radar is in the down-looking mode of operation, the wind shear echo is often in a strong clutter background. The accuracy of the wind shear field wind speed estimation result is directly influenced by the clutter suppression degree. Compared with the traditional single-antenna system meteorological radar, the phased array radar has the characteristics of high flexibility, high scanning speed, easiness in beam forming and the like. Because the airspace information of a target signal is added in the received echo, the phased array radar has a better clutter suppression effect than the traditional single-antenna system radar under a strong clutter background, the target can be better detected, and the phased array radar is widely valued. Some advanced weather radar research institutions in the world have started the research of a new generation of phased array weather radar. Space-time Adaptive Processing (STAP) is a key technology applied to phased array radar clutter suppression, and the STAP technology can effectively suppress ground clutter and improve the target detection capability of the radar at the same time by forming notches in a Space-time domain in a self-Adaptive manner. At present, the STAP technology is applied to the detection of point targets relative to the prepared land, but wind shear belongs to a distributed target, and the traditional STAP technology cannot be directly applied.
At present, a wind shear detection method for an airborne radar mainly aims at a radar with a single antenna system, but a wind speed estimation method applied to the radar with a phased array system is rarely mentioned. The traditional method for estimating the wind speed of the airborne single-antenna system meteorological radar mainly comprises a Pulse Pair method (PPP) based on time domain analysis and a Fast Fourier Transform (FFT) method based on frequency domain analysis. Although these methods have a good wind speed estimation performance when the number of pulses is large and the signal-to-noise ratio is high, the wind speed estimation performance is degraded when the number of pulses is small and the signal-to-noise ratio is low.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide a method for estimating a wind speed of a low altitude wind shear of an airborne phased array radar based on compressive sensing, which can improve the accuracy of parameter estimation.
In order to achieve the purpose, the method for estimating the low-altitude wind shear wind speed of the airborne phased array radar based on the compressed sensing comprises the following steps in sequence:
1) constructing a transformation matrix of a reference distance unit and a distance unit to be detected by using a space-time interpolation method, thereby obtaining independent same-distribution samples of a clutter covariance matrix constructing the distance unit to be detected, obtaining an estimated value of the clutter covariance matrix, and further realizing clutter suppression;
2) constructing a generalized space guide vector of a wind shear field by using the width of a radar main lobe as prior information;
3) constructing a generalized time-oriented vector of a wind shear field by using the signal spectral width as prior information;
4) constructing a wind shear field space-time basis dictionary based on wind speed by using the generalized space guide vector and the generalized time guide vector, and constructing a sparse basis matrix;
5) observing the echo signal subjected to clutter suppression in the step 1), and recovering the echo signal by using the sparse basis matrix to realize wind speed estimation.
In step 2), the method for constructing the generalized space steering vector of the wind shear field by using the width of the radar main lobe as prior information comprises the following steps: and constructing an angular signal density function based on azimuth and pitch by using the radar main lobe width, thereby constructing a distributed target space steering vector which is different from the traditional point target.
In step 3), the method for constructing the generalized time-oriented vector of the wind shear field by using the signal spectral width as prior information comprises the following steps: and constructing a spectrum spreading function of the meteorological echo by using the signal spectrum width, and constructing a meteorological target time guide vector which is different from the traditional point target.
In step 4), the generalized space-oriented vector and the generalized time-oriented vector are used to construct a wind shear field space-time basis dictionary based on wind speed, and the method for constructing the sparse basis matrix comprises the following steps: discretizing a wind speed interval to be estimated, establishing a discrete wind speed space to be estimated, establishing a time domain base dictionary by utilizing the discrete wind speed space, performing Kronecker product on a generalized space guide vector and the time domain base dictionary to obtain a space-time base dictionary of a wind speed-based space-shear field, and performing product on the space-time base dictionary and a random observation matrix to obtain a sparse base matrix.
In step 5), the method for observing the echo signal after clutter suppression in step 1) and recovering the echo signal by using the sparse basis matrix to realize wind speed estimation comprises the following steps: orthogonal projection is carried out on the observation signals to a one-dimensional subspace corresponding to each atom in the sparse basis matrix, projection errors are calculated, the projection errors are the minimum, namely the atom with the maximum correlation with the observation signals is the recovery atom of the echo signals; the central wind speed constituting the recovery atom is the central wind speed of the distance unit to be estimated.
The method for estimating the low-altitude wind shear wind speed of the airborne phased array radar based on the compressed sensing is characterized in that accurate space-time steering vectors of distributed meteorological targets are established by using prior information, and then signals are recovered by using the sparse characteristics of echoes of the accurate space-time steering vectors, so that parameter estimation is realized. The method can still obtain a more accurate wind field speed estimation result when the pulse number is less and the signal to noise ratio is lower.
Drawings
FIG. 1 is a flow chart of a compressed sensing-based airborne phased array radar low-altitude wind shear wind speed estimation method.
Fig. 2 is a diagram of an airborne forward-looking array radar array model.
Fig. 3 is a space-time two-dimensional spectrum of a radar receiving signal.
Fig. 4 is a spectrum diagram of a 35 th range bin wind shear echo.
FIG. 5 shows the wind speed estimation results at sampling pulse 64, SNR of 5dB, and SNR of 40 dB.
FIG. 6 shows the wind speed estimation results at sampling pulse 64, SNR 0dB, and SNR 40 dB.
FIG. 7 shows the wind speed estimation results at sampling pulse 32, signal-to-noise ratio of 5dB, and signal-to-noise ratio of 40 dB.
FIG. 8 shows the wind speed estimation results at sampling pulse 32, SNR 0dB, and SNR 40 dB.
Detailed description of the invention
The method for estimating the low-altitude wind shear wind speed of the airborne phased array radar based on the compressed sensing provided by the invention is described in detail below with reference to the accompanying drawings and specific examples.
As shown in fig. 1, the method for estimating the low-altitude wind shear wind speed of the airborne phased array radar based on the compressed sensing provided by the invention comprises the following steps in sequence:
1) constructing a transformation matrix of a reference distance unit and a distance unit to be detected by using a space-time interpolation method, thereby obtaining independent same-distribution data samples for constructing a clutter covariance matrix of the distance unit to be detected, obtaining an estimated value of the clutter covariance matrix, and further realizing clutter suppression;
the model of the airborne forward-looking array radar array is shown in figure 1, and the speed of the carrier is set as VRThe included angle between the speed direction of the carrier and the array axis of the antenna is 90 degrees, the number of antenna array elements is N, and the pulse repetition frequency is frThe coherent processing pulse number is K, and the array element spacing d is 0.5 lambda, wherein lambda is the wavelength of the radar emission pulse.
In the present invention, xlThe NK × 1-dimensional space-time snapshot data representing the L (L ═ 1,2, …, L) th cell to be detected is expressed as follows:
xl＝sl+cl+nl (1)
wherein s isl、cl、nlRespectively representing the wind shear field echo, clutter and noise of the first unit to be detected, wherein the clutter is assumed to have no fluctuation and no blur, and the noise is additive white Gaussian noise.
For the wind shear field in the ith distance unit, the sampling data of the radar can be written into an NxK matrix Sl. Wherein S islThe nth row and kth column elements of (1, 2, … N) th array element and kth (1, 2, … K) th pulse of the radar sample wind field echoes, and when there are Q meteorological scattering points in the irradiation range of the radar beam in the range unit, the specific expression is as follows:
whereinAndrespectively represent the spatial angular frequency and the temporal angular frequency of the qth (Q-1, 2, …, Q) meteorological scattering point, θq、Respectively representing the azimuth angle and the elevation angle of the meteorological scattering point relative to the radar, RqThe slope distance between the q scattering point and the carrier is obtained,is the antenna reception pattern. Will be S abovelSpread to form NK x 1 dimension column vector, that is, wind shear field echo snapshot sl. The echo signal within the radar full range unit can be expressed as:
X＝[x1 x2 … xL]T (3)
fig. 3 shows a space-time two-dimensional spectrum of a received signal under the conditions of a signal-to-noise ratio of 40dB and a signal-to-noise ratio of 5 dB. It can be seen that the forward looking array ground clutter is non-uniformly distributed in an ellipse, and the intensity of the ground clutter is much greater than that of the wind shear signal, which is almost completely swamped by the clutter.
Discretizing the horizontal azimuth angle of the No. l unit to be detected to obtain [ theta ]m}|m＝1,2,…MWhere M represents the number of discretized azimuths. Setting the clutter space-time guiding vector matrix corresponding to the detection unit as VlThe expression is as follows:
Vl＝[v(θ1) v(θ2) … v(θM)] (4)
wherein,(M-1, 2 … M) represents when the azimuth angle is θmTime, space-time steering vector of unit to be detected, vt(θm) And vs(θm) Respectively representing temporal and spatial steering vectors, wherein:
for the reference unit No. j adjacent to the unit to be detected, constructing a space-time steering vector matrix V of the clutter of the reference unitjThen, the interpolation transformation matrix of the l-th and j-th distance unit clutter can be obtained as follows:
Tj,l＝Vl(Vj)+ (6)
wherein (·)+Representing a pseudo-inverse operation. Transforming the matrix T by interpolationj,lAnd processing the received data of the reference distance unit to realize the distance dependency compensation of the received data of the j distance unit, so that the distance dependency compensation is consistent with the space-time distribution of the clutter in the distance unit to be detected:
yj＝Tj,lxj (7)
wherein x isjDenotes the received data before compensation of the j-th distance element, yjData after compensating for the distance dependency is shown.
The same method is utilized to process echo data (generally, P is required to be more than or equal to NK) of P reference units which are close to the distance unit to be detected and take the distance unit to be detected as the center, and P independent same-distribution (IID) data samples with the same clutter distribution characteristic as the distance unit to be detected can be obtained. At this time, the clutter covariance matrix of the unit to be detected is estimated by the following formula:
then, the estimatedThe signal obtained after clutter suppression is performed on the received data of the ith distance unit is as follows:
2) constructing a generalized space guide vector of a wind shear field by using the width of a radar main lobe as prior information;
in the invention, the width of the radar main lobe is used as the prior information of the wind shear field in the radar irradiation range, and the generalized space guide vector of the wind shear field is established.
When radar main lobe sideTo a pitch angle ofCentral azimuth angle thetaiWhen the method is used, the generalized space steering vector of the wind shear field in the irradiation range is set asThe expression is as follows:
whereinDenotes a central azimuth angle θiThe center pitch angle isA spatial steering vector of a point target in the azimuth;for deterministic angular signal density functions, according to the inventionRepresenting wind shear field at the central azimuth angle thetaiAnd center pitch angleThe extension of (c).Typically a unimodal symmetric function with the distributed source center DOA as the center of symmetry. Because the number of the meteorological particles in the radar main lobe range is large and none of the meteorological particles is in a leading position, according to the central limit theorem,can be expressed as:
wherein,σθdenotes thetaiThe angular spread in the direction of the shaft,to representThe angle in the direction expands.
3) Constructing a generalized time-oriented vector of a wind shear field by using the signal spectral width as prior information;
the wind-shear field echo is random in time and has spectral broadening, and its received signal can be written as the following uniform form for the wind-shear field in the l-th range bin:
wherein z isl,n,kRepresenting the complex amplitude of the received signal, fdDoppler frequency, f, representing wind shear echo signalssRepresenting spatial angular frequencies. For a wind shear field of a single distance unit, it is generally consideredWherein f is0Representing the central Doppler frequency, σ, of the echofRepresenting the spectral width of the wind shear signal echo within the range bin. That is, the echo signal of a single range bin received by each array element can be considered as a signal with a constant central doppler frequency (corresponding to the central wind speed within the range bin) and a continuous doppler spread (corresponding to the wind speed gradient magnitude). The generalized time-oriented vector of the wind shear field can be obtained as follows:
wherein g (σ)f) Representing the frequency spread function, the expression of which is as follows:
represents the azimuth angle thetaiAnd a pitch angleTime-oriented vector of point target with velocity v.
4) Constructing a wind shear field space-time basis dictionary based on wind speed by using the generalized space guide vector and the generalized time guide vector, and constructing a sparse basis matrix;
establishing a discretized velocity space of the central wind speed { v } according to a priori wind speed estimation rangew}|w＝1,2,…,WWhere W represents the number of discretized velocities. Then constructing a K multiplied by W dimensional time domain basis dictionary according to the wind speed space and the generalized time guiding vector of the wind shear field deduced in the step 2):
the space generalized guide of the time domain base dictionary and the wind shear fieldVector of directionAnd (3) making a Kronecker product, and constructing a wind shear field space-time basis dictionary with dimension of NK multiplied by W:
then using a space-time two-basis dictionary, a sparse basis matrix can be constructed:
Ψ＝ΦΘST (17)
wherein, phi represents T multiplied by NK dimension random observation matrix, and T < NK.
5) Observing the echo signal subjected to clutter suppression in the step 1), and recovering the echo signal by using the sparse basis matrix to realize wind speed estimation.
Observing the wind shear field echo data of the ith distance unit to obtain:
wherein,representing observed data; n islIs a noise component; rholIs a sparse coefficient vector. RholThe non-zero element in (A) reflects the number sum of atoms participating in restoring the wind field echo signalLocation. In a smaller space range, the central wind speed of the wind shear field is approximately constant, namely rho can be consideredlOnly one of the non-zero elements in (a). At this time, ρlThe solution of (a) can be summarized as the following optimization problem:
wherein | · | purple sweet2Is represented by2Norm, | · | luminance0Is represented by0A norm; matching terms to signalsIn l0Space-time basis dictionary theta under norm constraintSTOnly one atom of (a) participates in signal recovery, which is expressed as the maximum energy accumulation of the signal at that atom, i.e., the solution of the optimization problem equation (18) can be given by:
wherein ρ represents the position of the atom participating in signal recovery in the space-time basis dictionary, Θ'ρRepresenting a space-time basis dictionary ΘSTThe p-th atom of (a). The solution is to observe the signalOrthogonal projection is carried out on the one-dimensional subspace corresponding to each atom in the space-time base dictionary, projection errors are calculated, and the atom with the minimum projection error with the observation signal (namely the atom with the maximum correlation with the observation signal) is the recovery atom of the echo signal.
Central wind velocity v constituting the recovery atomρI.e. the central wind speed of the distance unit to be estimated:
Vl＝vρ,(l＝1,2,…L) (21)
the effect of the method for estimating the low-altitude wind shear wind speed of the airborne phased array radar based on the compressive sensing can be further illustrated by the following simulation results.
Setting simulation parameters: the low-altitude wind shear field is distributed at the 8.5-16.5km front part of the airplane. The antenna array is a forward-looking ideal uniform linear array with an array element number N equal to 8, the array element spacing is realized, the horizontal azimuth angle of a main lobe beam is 60 degrees, the pitch angle is 0 degree, the beam width is 3.5 degrees, the wavelength of the airborne weather radar is 0.05m, the pulse repetition frequency is 7000Hz, the minimum resolution distance of the radar is 150m, the noise-to-noise ratio is 40dB, and the signal-to-noise ratio is 5 dB; the speed of the carrier is 75m/s, the flying height is 600m, and the normalized Doppler spectrum is wide.
FIG. 3 is a space-time two-dimensional spectrum of a radar receiving signal under the conditions of a noise-to-noise ratio of 40dB and a signal-to-noise ratio of 5 dB. It can be seen that the forward looking array ground clutter is non-uniformly distributed in an ellipse, and the intensity of the ground clutter is much greater than that of the wind shear signal, which is almost completely swamped by the clutter.
Fig. 4 is a graph of the spectrum of the wind shear signal for distance cell No. 35, and it can be seen that there is only one large peak in the spectrum, which corresponds to the center wind speed of the distance gate.
Fig. 5-8 show simulation results of different signal-to-noise ratios and different sampling pulses, and it can be seen that the wind speed is inversely distributed within the range of 8.5-16.5km, when there are more pulses and the signal-to-noise ratio is higher, the performance of the FFT method and the resolution ratio provided by the FFT method are equivalent to each other, along with the gradual reduction of the number of pulses and the signal-to-noise ratio, the performance of the FFT method and the resolution ratio provided by the FFT method are reduced, and the estimated wind speed gradually deviates from the actual wind speed, but the method of the present invention still can maintain higher estimation accuracy.
Claims (5)
1. A compressed sensing-based low-altitude wind shear wind speed estimation method for an airborne phased array radar is characterized by comprising the following steps of:
1) constructing a transformation matrix of a reference distance unit and a distance unit to be detected by using a space-time interpolation method, thereby obtaining independent same-distribution data samples for constructing a clutter covariance matrix of the distance unit to be detected, obtaining an estimated value of the clutter covariance matrix, and further realizing clutter suppression;
2) constructing a generalized space guide vector of a wind shear field by using the width of a radar main lobe as prior information;
3) constructing a generalized time-oriented vector of a wind shear field by using the signal spectral width as prior information;
4) constructing a wind shear field space-time basis dictionary based on wind speed by using the generalized space guide vector and the generalized time guide vector, and constructing a sparse basis matrix;
5) observing the echo signal subjected to clutter suppression in the step 1), and recovering the echo signal by using the sparse basis matrix to realize wind speed estimation.
2. The compressed sensing-based low-altitude wind shear wind speed estimation method for the airborne phased array radar according to claim 1, is characterized in that: in step 2), the method for constructing the generalized space steering vector of the wind shear field by using the width of the radar main lobe as prior information comprises the following steps: and constructing an angular signal density function based on azimuth and pitch by using the radar main lobe width, thereby constructing a distributed target space steering vector which is different from the traditional point target.
3. The compressed sensing-based low-altitude wind shear wind speed estimation method for the airborne phased array radar according to claim 1, is characterized in that: in step 3), the method for constructing the generalized time-oriented vector of the wind shear field by using the signal spectral width as prior information comprises the following steps: and constructing a spectrum spreading function of the meteorological echo by using the signal spectrum width, and constructing a meteorological target time guide vector which is different from the traditional point target.
4. The compressed sensing-based low-altitude wind shear wind speed estimation method for the airborne phased array radar according to claim 1, is characterized in that: in step 4), the generalized space-oriented vector and the generalized time-oriented vector are used to construct a wind shear field space-time basis dictionary based on wind speed, and the method for constructing the sparse basis matrix comprises the following steps: discretizing a wind speed interval to be estimated, establishing a discrete wind speed space to be estimated, establishing a time domain base dictionary by utilizing the discrete wind speed space, performing Kronecker product on a generalized space guide vector and the time domain base dictionary to obtain a space-time base dictionary of a wind speed-based space-shear field, and performing product on the space-time base dictionary and a random observation matrix to obtain a sparse base matrix.
5. The compressed sensing-based low-altitude wind shear wind speed estimation method for the airborne phased array radar according to claim 1, is characterized in that: in step 5), the method for observing the echo signal subjected to clutter suppression in step 1) and recovering the echo signal by using a sparse basis matrix to realize wind speed estimation comprises the following steps: orthogonal projection is carried out on the observation signals to a one-dimensional subspace corresponding to each atom in the sparse basis matrix, projection errors are calculated, the projection errors are the minimum, namely the atom with the maximum correlation with the observation signals is the recovery atom of the echo signals; the central wind speed constituting the recovery atom is the central wind speed of the distance unit to be estimated.
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