CN115201813B - Sparse array-based meter wave TR MIMO radar low-altitude target height measurement method - Google Patents
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Abstract
The invention discloses a sparse array-based meter wave TR MIMO radar low-altitude target height measurement method, which is characterized by comprising the following steps of: s1, constructing a single-base meter wave sparse array TR MIMO radar system, and respectively calculating to obtain a transmitting direct waveguide vector a t(θd) and a reflecting waveguide vector a t(θs); s2, constructing a composite guide vector A (theta); s3, calculating received data Y, constructing a data covariance matrix R, and respectively performing real-value processing on the data covariance matrix R and a complex steering vector A (theta) to obtain a real covariance matrix R U and a real-value complex steering vector A U (theta); s4, searching spectral peaks according to the composite guide vector A (theta) and the data covariance matrix R or the real covariance matrix R U and the real value composite guide vector A U (theta), using a generalized MUSIC algorithm and a maximum likelihood algorithm, observing to obtain a spatial spectrum, and finding out an angle corresponding to the position of the peak, namely obtaining the target low elevation angle estimated valueS5, estimating the obtained target low elevation angleAnd converting to obtain the target height data H.
Description
Technical Field
The invention belongs to the technical field of meter wave TR MIMO radar, and particularly relates to a meter wave TR MIMO radar low-altitude target height measurement method based on a sparse array.
Background
The meter wave radar has great attention on the aspects of stealth target resistance and anti-radiation missile, however, the wavelength is longer, the main wave beam in pitching dimension is wider, and when a low-altitude target is detected, direct waves and ground reflection waves generally enter the radar from the main wave beam. Due to the limitation of the caliber and the working bandwidth of an antenna, the meter wave radar is difficult to distinguish direct waves from ground reflected waves in a space domain, a time domain and a frequency domain, and the angle measurement precision of a low elevation area of the meter wave radar is seriously affected by multipath effects. Multiple-input multiple-output (Multiple input multiple output, MIMO) radar realizes an equivalent large-scale virtual array with fewer array elements through a waveform diversity technique, and has an advantage incomparable with conventional array radars: the angle measurement precision is higher, the anti-interference capability is stronger, the anti-stealth effect is good, the multi-target tracking capability is strong, and the like. The time reversal (TIME REVERSAL, TR) technology has space-time focusing property, can effectively utilize reflected wave energy, reduce the influence of multipath effect on signal echo, and improve signal-to-noise ratio. The TR technology and the MIMO radar are combined to perform low-altitude target detection, so that the low-altitude ultra-low-altitude target parameter estimation accuracy can be improved, and the method has great significance.
In recent years, extensive scholars have studied the problem of estimating the direction of arrival (Direction Of Arrival, DOA) of a Mibo TR MIMO radar under the condition of low-altitude multipath reflection in depth, and have formed more results. Currently, the main processing methods include a rank multiplexing bidirectional space smoothing (Forward Backward Spatial Smoothing, FBSS) algorithm, a Capon algorithm, a multiple signal classification (Multiple Signal Classification, MUSIC) algorithm, a Toeplitz matrix reconstruction algorithm and the like. Liu Mengbo proposes a rank multiplexing FBSS MUSIC algorithm suitable for use under low-altitude multipath reflection conditions of a metric wave TR MIMO radar. The algorithm utilizes the focusing performance of the TR technology to effectively improve the angle measurement precision of a low-altitude target, but does not utilize the virtual aperture expansion capability of the MIMO system radar, and the parameter estimation performance is not greatly improved. Rao Kai proposes a Capon algorithm based on a meter wave TR MIMO radar multipath reflection condition, the algorithm has strong side lobe suppression capability, and has good estimation accuracy under multipath environment and low signal to noise ratio condition, but the algorithm cannot effectively distinguish direct waves and reflected waves with small angle intervals of incoming waves under the influence of the Capon algorithm, namely the algorithm is not suitable for DOA estimation of low-altitude and ultra-low-altitude targets. Liu Mengbo proposes a real-valued domain MUSIC algorithm based on TR MIMO radar. The algorithm effectively reduces the calculated amount by removing complex operations through real value transformation, has the decorrelation capability under the condition of not needing space smoothing, has relatively small loss of accuracy in target estimation, but also cannot effectively distinguish direct waves and reflected waves with small angle intervals of incoming waves, cannot overcome large spectrum values generated by small angles during spectrum peak searching, and is not suitable for DOA estimation of low-altitude and ultra-low-altitude targets. Liu Mengbo proposes a TR MIMO radar coherent target DOA estimation algorithm based on Toeplitz matrix reconstruction. The method adopts a Toeplitz matrix reconstruction algorithm to remove the coherence of the target, and utilizes an optimization iteration method to carry out DOA estimation based on a first order approximation theory, thereby further improving the accuracy of DOA estimation and reducing the computational complexity. However, due to the influence of multipath effects, the direct wave of the low-altitude target and the vector of the reflected wave guide are mutually coupled, and the algorithm has poor DOA estimation effect on the low-altitude target.
The algorithms proposed in the above documents all adopt a Uniform linear array (ULA LINEAR ARRAY) TR MIMO radar signal model, which has the problems of low accuracy of ultra-low altitude target parameter angle measurement (high) and large fluctuation of parameter estimation errors along with elevation angle changes due to multipath effects. With the continuous deep practice of combat, higher angular accuracy and stability are required for target detection and tracking.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a meter wave TR MIMO radar low-altitude target height measurement method based on a sparse array, which improves the meter wave TR MIMO radar angle measurement precision, particularly the angle measurement precision of an ultra-low altitude target and reduces the fluctuation of height measurement errors.
In order to achieve the above purpose, the invention adopts the following technical scheme:
A meter wave TR MIMO radar low-altitude target height measurement method based on a sparse array comprises the following steps:
S1, constructing a single-base meter wave sparse array TR MIMO radar system, and respectively calculating guide vectors of a transmitted direct wave and a reflected wave of the single-base meter wave sparse array TR MIMO radar system to obtain a transmitted direct wave guide vector a t(θd) and a reflected wave guide vector a t(θs);
S2, constructing a composite guiding vector A (theta) according to the direct wave guiding vector a t(θd) and the reflecting wave guiding vector a t(θs);
S3, calculating received data Y, constructing a data covariance matrix R according to the calculated received data Y, performing eigenvalue decomposition on the constructed data covariance matrix R to obtain a noise subspace E n, performing real-value processing on the data covariance matrix R and a composite guide vector A (theta) respectively to obtain a real-value covariance matrix R U and a real-value composite guide vector A U (theta), and performing eigenvalue decomposition on a real-value covariance matrix R U to obtain a real-value noise subspace U n;
S4, searching spectral peaks according to the composite steering vector A (theta) and the data covariance matrix R or the real-valued composite steering vector A U (theta) and the real-valued covariance matrix R U by utilizing a generalized MUSIC algorithm and a maximum likelihood algorithm, observing to obtain a spatial spectrum, and finding out an angle corresponding to the position of the peak to obtain a target low elevation angle estimated value
S5, estimating the obtained target low elevation angleAnd converting to obtain the target height data H.
Preferably, in step S1, the antennas of the single-base meter-wave sparse array TR MIMO radar system are vertically disposed, the number of transmitting and receiving array elements is P t and P r, the positions of the array elements are d t and d r,θd, and θ s respectively represent the arrival angles of the direct wave and the reflected wave.
Preferably, in step S1, the expression of the transmitting direct waveguide direction vector a t(θd) and the reflecting waveguide direction vector a t(θs) is:
wherein, theta d and theta s respectively represent the arrival angles of the direct wave and the reflected wave, P t is the number of transmitting array elements, For the mth transmit element position, λ is the signal wavelength, (. Cndot.) T represents the transpose.
Preferably, in step S2, the expression of the composite steering vector is:
Where a t(θd) and a t(θs) refer to the transmit direct waveguide vector and the reflected waveguide vector, respectively, (. Cndot.) * represents the matrix conjugate.
Preferably, in step S3, the calculation formula of the received data is as follows:
Wherein, omega= [1 gamma 2]T, epsilon is the energy normalization factor of the energy, P r is the number of received array elements, For the complex reflection coefficient of the target under different pulses, f d is Doppler frequency, and W is noise after matched filtering and vectorization operation;
the calculation formula of the data covariance matrix is as follows:
Where Y is the received data, (. Cndot.) H represents the matrix conjugate transpose, and L represents the snapshot number.
Preferably, in step S3, the calculation formulas of the real-valued covariance matrix and the real-valued composite steering vector are respectively:
RU＝UHRfbU
AU(θ)＝UHA(θ)
where U is a unitary matrix, when the dimension of U is an odd number, When the dimension of U is even,/>II K is K x K switching matrix, specifically, the element on the opposite angle line is 1, the other elements are 0,I K are K x K unit matrix,/>(. Cndot.) H represents the matrix conjugate transpose, the A (θ) complex steering vector.
Preferably, in step S4, the spectral peak search formulas of the generalized MUSIC algorithm and the maximum likelihood algorithm according to the composite steering vector and the data covariance matrix are respectively as follows:
Where det represents determinant operation, trace is a trace operator, P a(θ)＝A(θ)(AH(θ)A(θ))-1AH (θ), R is a data covariance matrix, E n is a noise subspace obtained by decomposing a eigenvalue of R, I P is a unit matrix of p×p, and (-) H represents matrix conjugate transpose.
Preferably, in step S4, the spectral peak search formulas of the generalized MUSIC algorithm and the maximum likelihood algorithm according to the real covariance matrix and the real value composite steering vector are respectively as follows:
Wherein det represents determinant operation, trace is a trace operator, I P is a unit matrix of P×P, (. Cndot.) H represents matrix conjugate transpose, R U is real-valued covariance matrix, U n is real noise subspace obtained by performing feature decomposition on real-valued covariance matrix R U, A U (θ) is a real-valued composite steering vector.
Preferably, step S4 further includes a step of reducing the two-dimensional spectral peak search of the generalized MUSIC algorithm and the maximum likelihood algorithm to one-dimensional search according to the relationship between the direct wave incident angle θ d and the reflected wave incident angle θ s, and the relationship between the direct wave incident angle θ d and the reflected wave incident angle θ s is as follows:
θs＝-arctan(tanθd+2ha/R)
Wherein h a is the antenna erection height, and R is the target distance.
Preferably, in step S5, the calculation formula of the target height data is:
Wherein, For a target low elevation estimate, R is the target distance and h a is the antenna mount height.
Compared with the prior art, the invention has the beneficial effects that:
According to the invention, the sparse array replaces a uniform linear array to serve as a transceiver antenna of the single-base meter wave TR MIMO radar, and compared with the uniform linear array, the sparse array is mainly utilized by virtue of a sparse structure, so that the expansion of the physical aperture of the array can be realized on the premise of a certain number of physical array elements, the virtual aperture expansion capability of the superimposed MIMO system radar greatly expands the effective array aperture, the hardware system overhead is reduced, the low-altitude target angle measurement (high) precision is improved, and the fluctuation of angle (high) measurement errors is reduced; simulation results show that the single-base meter wave sparse array TR MIMO radar has higher angle measurement (high) precision under the low-altitude multipath reflection condition, has more obvious advantages especially for ultra-low altitude targets, and has better effects when in low snapshot and low signal to noise ratio. Compared with two typical monostatic sparse array meter wave TR MIMO radars, under the same condition, the angle (high) accuracy of the mutual mass array is highest, the fluctuation of angle (high) measurement is minimum, and the second-order nested array is inferior. Compared with two typical algorithms, under the same condition, the generalized MUSIC algorithm suitable for the TR MIMO radar provided by the invention has the advantages of highest angle (high) accuracy and minimum angle (high) measurement error fluctuation.
Drawings
FIG. 1 is a graph of a meter wave TR MIMO radar horizontal ground reflection model provided by an embodiment of the invention;
FIG. 2 is a graph showing the variation of the calculation complexity of the algorithm according to the number of the transmitting array elements according to the embodiment of the present invention;
FIG. 3 is a graph of spectral peak searches for algorithms for arrays in the present invention;
FIG. 4 is a graph of spectral peak searches for ultra-low altitude targets for each algorithm of each array;
wherein fig. 4 (a) is a spectral peak search diagram at a target incident angle of 0.5 °; FIG. 4 (b) is a spectral peak search plot at a target angle of incidence of 1;
FIG. 5 is a graph showing the variation of each algorithm parameter estimation RMSE with elevation angle for each array;
wherein, fig. 5 (a) is a graph of the variation of the angle RMSE with the elevation angle; FIG. 5 (b) is a plot of elevation change of altitude RMSE;
FIG. 6 is a graph of the variation of each algorithm angle RMSE and target height with elevation angle for each array;
FIG. 6 (a) is a graph showing the variation of the angle RMSE with the elevation angle; FIG. 6 (b) is a graph of target altitude versus elevation angle;
FIG. 7 is a graph showing the variation of each algorithm parameter estimation RMSE with SNR for each array;
FIG. 7 (a) is a graph showing the variation of the angle RMSE with the elevation angle; FIG. 7 (b) is a plot of elevation change of altitude RMSE;
FIG. 8 is a graph showing the variation of each algorithm parameter estimation RMSE with snapshot number for each array;
FIG. 8 (a) is a graph showing the variation of the angle RMSE with the elevation angle; fig. 8 (b) is a graph of elevation angle versus altitude RMSE.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
The embodiment of the invention provides a sparse array-based meter wave TR MIMO radar low-altitude target height measurement method, which specifically comprises the following steps:
s1, constructing a single-base meter wave sparse array TR MIMO radar system, wherein as shown in FIG. 1, antennas of the radar system are vertically arranged, the number of transmitting and receiving array elements is P t and P r respectively, the positions of the array elements are d t and d r respectively, the ground is assumed to be smooth and flat, in the system, the transmitting and receiving arrays are closely spaced, the transmitting angle and the receiving angle (including the ground reflection angle) of a far-field target can be approximately equal, and theta d and theta s respectively represent the arrival angles of direct waves and reflected waves.
Transmitting signal of TR MIMO radarAre mutually orthogonal, which satisfies the following formula:
Wherein I P is a unit matrix, T is a pulse duration, (·) H represents a matrix conjugate transpose;
The signal transmitted at this time and propagated through the air medium to the target is:
where k 0＝2π/λ,[·]T represents the transpose of the matrix, ρ is the ground reflection coefficient, Δr is the wave path difference between the direct wave and the reflected wave, it is not difficult to find that the relationship between Δr≡2h asinθd,at(θd) and a t(θs) between the direct wave arrival angle and the antenna height H a is the transmitted direct wave and the reflected waveguide vector, and the direct vectors of the transmitted direct wave and the reflected wave of the single-base meter wave sparse array TR MIMO radar system are calculated respectively to obtain the transmitted direct waveguide vector a t(θd) and the reflected waveguide vector a t(θs), and the transmitted direct waveguide vector a t(θd) and the reflected waveguide vector a t(θs) are expressed as follows:
wherein, theta d and theta s respectively represent the arrival angles of the direct wave and the reflected wave, P t is the number of transmitting array elements, For the mth transmit element position, λ is the signal wavelength, (·) T denotes the transpose;
The signal expression received by the p-th array element is:
zp(t,τ)＝[ar,p(θd)+γar,p(θs)]β(τ)x(t)+vp(t,τ)
Wherein, For the complex reflection coefficient of the target under different pulses, f d is Doppler frequency;
The signal matrix received by the entire array can be written as:
Wherein the method comprises the steps of ,Ar＝ar(θd)+γar(θs),At＝at(θd)+γat(θs), For target complex reflection coefficients under different pulses, (·) T denotes a transpose, v (t, τ) is gaussian white noise, a r(θd) and a r(θs) are received direct wave and reflected waveguide vector, respectively, whose expressions are:
Wherein, theta d and theta s respectively represent the arrival angles of the direct wave and the reflected wave, Pr is the number of transmitting array elements, For the p-th transmit element position, λ is the signal wavelength, (·) T denotes the transpose.
According to the principle of time reversal, the signal matrix of the receiving end in the signal matrix formula received by the whole array is conjugated and time-reversed, energy normalization is carried out, and the signal matrix is transmitted again. The transmitting signal model is epsilon z * (-t, tau), epsilon is an energy normalization factor, and the signal matrix expression of the TR MIMO radar receiving end is as follows:
Wherein [ (DEG ] * represents matrix conjugation); v (t, τ) is gaussian white noise; w (t, τ) is the cumulative noise, Transpose is represented for the target complex reflection coefficient ,Ar＝ar(θd)+γar(θs),At＝at(θd)+γat(θs),(·)T for different pulses, it is known from literature that w (t, τ) can be approximated as gaussian white noise due to the time-reversed focusing effect;
Using transmitted signals The method comprises the following steps of:
Vectorizing the above method to obtain:
wherein A is a composite guide vector, Vec represents a vectorization operation,/>The product of kron is represented, W is noise after matched filtering and vectorization operation, and because the original noise W (t, tau) is approximate to Gaussian white noise, the literature knows that W is still Gaussian white noise after matched filtering and vectorization operation;
S2, constructing a composite guiding vector A (theta) according to the direct wave guiding vector a t(θd) and the reflected wave guiding vector a t(θs), wherein the expression of the composite guiding vector is as follows:
Wherein a t(θd) and a t(θs) refer to the transmit direct waveguide vector and the reflected waveguide vector, respectively, (·) * represents the matrix conjugate;
The covariance matrix R is:
In the method, in the process of the invention, And/>The signal power and the noise power are represented respectively, A (theta) is a composite steering vector, namely the steering vector matrix provided by the invention, and is different from the steering vector in the common MUSIC algorithm, and the steering vector matrix is still orthogonal with the noise subspace under the interference of the TR MIMO radar multipath coherent signals;
S3, calculating received data Y, wherein the calculation formula of the received data is as follows:
Wherein, omega= [1 gamma 2]T, epsilon is the energy normalization factor of the energy, P r is the number of received array elements, For the complex reflection coefficient of the target under different pulses, f d is Doppler frequency, and W is noise after matched filtering and vectorization operation;
Constructing a data covariance matrix R according to the calculated received data Y, wherein the calculation formula of the data covariance matrix is as follows:
Wherein Y is the received data, (. Cndot.) H represents the matrix conjugate transpose, and L represents the snapshot number;
And the eigenvalue decomposition is carried out on the constructed data covariance matrix R to obtain a noise subspace E n, so that the MIMO radar greatly increases the operation amount while enhancing the system performance, the engineering practice is inconvenient, and the receiving retransmission of the TR technology also increases the calculation redundancy, so that the TR MIMO radar system has huge calculation amount. The calculation formula of the received data is a P multiplied by L dimensional array received signal matrix, the covariance matrix is found to be a complex matrix, and in order to further reduce the calculation complexity of the algorithm provided by the invention, the received data can be subjected to real value processing by utilizing the unitary matrix. Defining a unitary matrix as follows:
Wherein, pi K is a KxK switching matrix, the element on the opposite angle line is 1, the other elements are 0,I K are KxK unit matrix, if P is odd number, the real value processing is carried out by adopting U 2K+1 formula, and K= (P-1)/2; if P is even, the real-valued processing is performed using the formula U 2K, and k=p/2.
According to the nature of the unitary matrix, the unitary matrix can change the Centro-Hermitian matrix into a real matrix through unitary transformation, but R is not the Centro-Hermitian matrix, so that it needs to be subjected to a bi-directional smoothing to be converted into the Centro-Hermitian matrix:
Then, real-value processing is carried out on the data covariance matrix R and the composite guide vector A (theta) respectively to obtain a real covariance matrix R U and a real-value composite guide vector A U (theta), and the calculation formulas of the real covariance matrix R U and the real-value composite guide vector A U (theta) are respectively as follows:
RU＝UHRfbU
AU(θ)＝UHA(θ)
Wherein U is a unitary matrix, (. Cndot.) H represents the matrix conjugate transpose, A (θ) is the composite steering vector, and the eigenvalue decomposition is performed on the real covariance matrix R U to obtain the noise subspace U n;
S4, performing spectral peak search according to the composite steering vector A (theta) and the data covariance matrix R or the real covariance matrix R U and the real value composite steering vector A U (theta) by using a generalized MUSIC algorithm and a maximum likelihood algorithm, wherein the spectral peak search formula of the generalized MUSIC algorithm according to the composite steering vector and the data covariance matrix is as follows:
wherein det represents determinant operation, P a(θ)＝A(θ)(AH(θ)A(θ))-1AH(θ),En is a noise subspace obtained by decomposing the characteristic value of R, and (-) H represents matrix conjugate transpose;
similarly, the space projection matrix of the maximum likelihood algorithm is constructed by using the steering vector matrix A (θ) provided by the embodiment of the invention as follows:
Pa(θ)＝A(θ)(AH(θ)A(θ))-1AH(θ)
Wherein A (θ) is a complex steering vector, (. Cndot.) H represents a matrix conjugate transpose;
The maximum likelihood algorithm spectral peak search formula is as follows:
Wherein trace is a trace operator, P a(θ)＝A(θ)(AH(θ)A(θ))-1AH (θ), R is a data covariance matrix, and I P is a unit matrix of P×P;
The spectral peak search formula of the generalized MUSIC algorithm according to the real covariance matrix and the real value composite steering vector is as follows:
Wherein det represents determinant operation, (. H) represents matrix conjugate transpose, U n is a real noise subspace obtained by performing feature decomposition on a real-valued covariance matrix R U, and A U (theta) is a real-valued composite guide vector;
Defining a real-valued spatial projection matrix as follows:
The real-valued maximum likelihood algorithm spectral peak search formula is as follows:
wherein trace is a trace operator, I P is a unit matrix of P x P, R U is a real-valued covariance matrix,
And reducing the two-dimensional spectral peak search of the generalized MUSIC algorithm and the maximum likelihood algorithm to one-dimensional search according to the relationship between the direct wave incident angle theta d and the reflected wave incident angle theta s, wherein the relationship between the direct wave incident angle theta d and the reflected wave incident angle theta s is as follows:
θs＝-arctan(tanθd+2ha/R)
Wherein h a is the antenna erection height, and R is the target distance;
Then observing the obtained spatial spectrum, finding out the angle corresponding to the position of the wave crest, and obtaining the estimated value of the target low elevation angle
S5, estimating the obtained target low elevation angleConverting to obtain target height data H, wherein the calculation formula of the target height data is as follows:
Wherein, For a target low elevation estimate, R is the target distance and h a is the antenna mount height.
The performance of the method provided by the embodiment of the invention is analyzed as follows
(1) Parameter estimation performance
The foregoing is thatThe formula of (2) is a signal model of a received signal after matching and filtering under the condition of multipath reflection of the meter wave TR MIMO radar, compared with the traditional MIMO radar, the signal model has the advantages that the amplitude of the TR MIMO radar signal has P r times of gain, the signal energy has P r 2 times of gain, the signal to noise ratio is greatly improved, the TR MIMO radar transmitting array is mainly used for expanding the virtual aperture, and the receiving array is used for improving the signal gain. When P t≥Pr, the meter wave TR MIMO radar has higher low-altitude target DOA estimation accuracy and resolution and greater degrees of freedom. In summary, in order to improve the performance of TR MIMO radar parameter estimation, the transmitting array may utilize a sparse array to expand the effective array aperture, and no special requirement is required for the receiving array structure, so long as the number of receiving array elements can be effectively increased.
(2) Computational complexity
The complexity of the method provided by the embodiment of the invention mainly comprises the following parts: ① Constructing a covariance matrix; ② Covariance matrix feature decomposition; ③ The spectral peak searches for three parts. The real-valued processing algorithm adds to the real-valued processing algorithm complexity. Note that: the real-valued processing algorithm requires additional computation of covariance matrices R fb and R U compared to the non-real-valued processing algorithm, which introduces little computational complexity, neglecting here, since both the switching matrix n P and the unitary transformation matrix U P are sparse. In addition, addition is omitted here, only multiplication being considered. Further, one complex multiplication corresponds to four real multiplications.
The generalized MUSIC algorithm and the maximum likelihood algorithm which are suitable for the low-altitude target height measurement of the meter wave TR MIMO radar and provided by the embodiment of the invention are respectively called GMUSIC algorithm and ML algorithm for short, and the two algorithms which are subjected to real value processing are respectively called UGMUSIC algorithm and UML algorithm for short.
CGMUSIC＝4Pt 4L+4Pt 6+4Θ(32Pt 2+8Pt 4)
CML＝4Pt 4(L+Pt 2)+4Θ(32Pt 2+4Pt 4+Pt 6)
CUGMUSIC＝Pt 4L+Pt 6+Θ(32Pt 2+8Pt 4)
CUML＝Pt 4(L+Pt 2)+Θ(32Pt 2+4Pt 4+Pt 6)
Wherein L represents the snapshot number, P t represents the number of transmitting array elements, and Θ represents the searching times of spectrum peaks.
Fig. 2 is a graph showing the change of algorithm computation complexity along with the number P t of transmitting array elements, the snapshot number l=30, the target number n=1, and the frequency Θ=1000. As can be seen from fig. 2, the GMUSIC algorithm has lower computational complexity than the ML algorithm, and as the number of array elements increases, the computational complexity of the algorithm subjected to real-value processing has a greater advantage. Obviously, the calculation complexity can be greatly reduced through real value processing, and the calculation time is saved by about 75%.
Experimental simulation
When the array elements of the sparse array are equal in number, the physical aperture sizes of the simple mutual mass array (SCA), the extended mutual mass array (ECA) and the second-order Nested Array (NA) are similar, and the parameter estimation performance is not much different. According to the result of the literature simulation experiment, the GMUSIC algorithm has similar performance to the ML algorithm, but the GMUSIC algorithm has lower calculation complexity. Therefore, according to the similarity degree of the array structure and the algorithm precision, two typical sparse arrays, namely a second-order Nested Array (NA) and a unfolding mutual quality array (UCA), are taken as objects, the GMUSIC algorithm which is suitable for the Mitsui sparse array TR MIMO radar and the Uniform Linear Array (ULA) which respectively adopts FBSSMUSIC, UGMUSIC and GMUSIC algorithms provided by the embodiment of the invention are adopted to simulate, the results are compared and analyzed in performance, and the influence of factors such as target elevation angle (height), signal-to-noise ratio, snapshot number and the like on the elevation angle estimation performance of each algorithm of each array is mainly analyzed, so that a general conclusion is obtained.
The basic conditions of the simulation experiments are consistent, namely, three single-base meter wave TR MIMO radars are assumed to adopt arrays which are vertically arranged into one-dimensional linear arrangement as receiving and transmitting antennas, and the radar receiving and transmitting antennas are separated and have the same structure. Antenna 1 is ULA, antenna 2 is second order NA, antenna 3 is UCA, and the number of each array transmitting and receiving array element is P t＝Pr = 10. The ULA array element distance d is half wavelength of a received signal, and the physical array element positions of the ULA array element distance d are {0, d,2d,3d,4d,5d,6d,7d,8d,9d }; the physical array element positions of the second-order NA are {0, d,2d,3d,4d,5d,11d,17d,23d,29d }; the physical array element positions of UCAs are {0,6d,12d,18d,24d,29d,34d,39d,44d,49d }; the radar working frequency is 300Mhz, the number of space targets is n=1, the height of a receiving and transmitting antenna at the bottom end is 4m, the ground reflection coefficient is-0.9, and the added noise is Gaussian white noise. The angle measurement precision of Monte Carlo repetition experiments and different algorithms of different arrays are compared, the number of Monte Carlo repetition experiments is I=300, and a one-dimensional Root Mean Square Error (RMSE) formula is as follows:
Wherein: i is the number of Monte Carlo tests, Is the target angle measured the kth time.
Experiment 1 Each array space spectrum imaging contrast experiment
The experimental conditions of the group are that the incidence angle of the target direct wave is 2 degrees, the SNR=0 dB, the snapshot number L=20, the target distance is 200km, the angle search range is 0-10 degrees, and the search interval is 0.1 degrees. FIG. 3 is a graph of spectral peak searches for various algorithms for various arrays, with the peak being the elevation estimate. As can be seen from FIG. 3, ① meter wave TR MIMO radars of each array can accurately measure the low elevation angle of the target, but the sparse array is sharper than the uniform linear array in low elevation angle spectrum peak, and the meter wave TR MIMO radar of the sparse array has better angle measurement performance. ② Compared with two typical sparse array meter wave TR MIMO radars, under the same condition, the method has the advantages of sharper spreading of the spectrum peak of the mutual mass array, best performance and second-order nested array. ③ Compared with three algorithms, under the same condition, the GMUSIC algorithm and UGMUSIC algorithm which are suitable for the meter wave TR MIMO radar provided by the embodiment of the invention have sharper spectral peaks and better performance, and the rank multiplexing FBSSMUSIC algorithm provided by the literature is inferior. The main reasons are that the FBSSMUSIC algorithm of rank multiplexing does not utilize the virtual aperture of the MIMO radar, and the GMUSIC algorithm without decoherence has better performance than the FBSSMUSIC decoherence algorithm.
Experiment 2 ultra-low altitude target imaging contrast experiment of each array
The experimental conditions of the group are that the signal-to-noise ratio SNR=0 dB, the snapshot number L=20, the target distance is 200km, the target direct wave incident angle is 0.5 DEG and 1 DEG respectively, the angle search range is 0 DEG to 10 DEG, and the search interval is 0.1 deg. FIG. 4 is a graph of spectral peak search for ultra-low altitude targets for each algorithm for each array, where the peak is the elevation estimate. As can be seen from FIG. 4, ① meter wave sparse array TR MIMO radar can accurately measure ultra-low altitude target elevation angle, meter wave uniform linear array TR MIMO radar can measure target elevation angle only when target elevation angle is 1 degree, and sparse array is sharper than uniform linear array ultra-low altitude target space spectrum peak, meter wave sparse array TR MIMO radar ultra-low altitude angle measurement performance is better. ② Compared with two typical sparse array meter wave TR MIMO radars, under the same condition, the ultra-low-altitude target space spectrum peak of the mutual mass array is more sharp, the performance is better, and the second-order nested array is inferior. ③ Compared with three algorithms, under the same condition, GMUSIC and UGMUSIC algorithms suitable for the meter wave TR MIMO radar provided by the embodiment of the invention have sharper spatial spectrum peaks and better performance than the ultra-low altitude target elevation angle spatial spectrum peaks of a row multiplexing FBSSMUSIC algorithm. The reason is the same as in experiment 1.
Experiment 3 elevation angle influence parameter estimation precision experiment
The experimental condition of the group is that the SNR is = -10dB, the snapshot number is L=5, and the target distance is 200km. The elevation angle varies in the range of 0.5 deg. to 8 deg., and the variation interval is 0.5 deg.. The angular search range is 0 ° to 10 ° with a search interval of 0.01 °. Fig. 5 is a graph of the variation of RMSE with elevation angle for each algorithm parameter estimate for each array. As can be seen from fig. 5, the elevation angle ① and the angle measurement (height) error have a substantially negative correlation, but have a certain fluctuation variation in the section along with the elevation angle variation, and the main reason is that the elevation angle variation brings about the periodic variation of the multipath attenuation coefficient phase, thereby influencing the algorithm effect. As the elevation angle becomes larger, the interval between the direct wave and the multipath becomes larger, the algorithm effect is gradually reduced under the influence of the phase of the attenuation coefficient, the angle estimation performance is in an overall rising trend, and the angle measurement precision tends to be stable when the elevation angle is larger than a certain range; ② Under the condition of the same elevation angle, the angle measurement (high) precision of the sparse array meter wave TR MIMO radar is higher than that of a uniform linear array. ③ Compared with two typical sparse array meter wave TR MIMO radars, under the condition of the same elevation angle, the highest precision of the mutual mass array angle measurement (high) is developed, and the second order nested array is inferior. ④ Compared with three algorithms, under the condition of the same elevation angle, the GMUSIC algorithm parameter estimation RMSE suitable for the meter wave TR MIMO radar provided by the embodiment of the invention has the advantages of minimum performance, the real value GMUSIC algorithm and the worst rank multiplexing FBSSMUSIC algorithm. The real-valued GMUSIC algorithm results in reduced performance of parameter estimation due to the real-valued processing of the missing signal imaginary information. The reason for the worst performance of the rank multiplexing FBSSMUSIC algorithm is the same as experiment 1.
Experiment 4 elevation angle influence measurement error relief experiment
The experimental condition of this group is that the signal-to-noise ratio snr= -10dB, the snapshot number l=5. The target height 7000m, the adjacent flight, the elevation angle change range is 2.5 degrees to 10 degrees, the change interval is 0.5 degrees, namely the range of the distance between the target and the radar is about 160479m to 40311m, the angle search range is 0 degrees to 11 degrees, and the search interval is 0.01 degrees. Fig. 6 is a graph of the angular RMSE of each algorithm and the target height as a function of elevation angle for each array. As can be seen from fig. 6, the error between the measured target height and the actual target height measured by each algorithm of each array ① does not change linearly with the distance, but changes in a fluctuating manner, because the elevation angle changes to bring about the periodic change of the multipath fading coefficient phase, the multipath interference effect changes periodically with the elevation angle change, and thus the algorithm effect is affected. ② Under the condition of the same elevation angle, the fluctuation degree of the angle measurement (high) error of the sparse array meter wave TR MIMO radar is lower than that of the uniform linear array. ③ Compared with two typical sparse array meter wave TR MIMO radars, under the condition of the same elevation angle, the error fluctuation degree of the measurement angle (high) of the mutual mass array is minimum, and the two-order nested arrays are inferior. ④ Compared with three typical algorithms, under the same condition, the GMUSIC algorithm parameter estimation error fluctuation degree for the meter wave TR MIMO radar provided by the embodiment of the invention is minimum and has the best performance. The real value GMUSIC algorithm is inferior, while the rank multiplexing FBSSMUSIC algorithm is the most undulating. The reason is the same as in experiment 3.
Experiment 5 signal to noise ratio influencing angle measurement (high) accuracy experiment
The experimental conditions are that the incidence angle of the target direct wave is 3 degrees, the snapshot number is L=5, and the target distance is 200km. The value of the SNR is changed, the change range is-20 dB to 0dB, and the change interval is 1dB. The angular search range is 0 ° to 10 ° with a search interval of 0.005 °. Fig. 7 is a graph of RMSE as a function of SNR for each algorithm parameter estimate for each array. As can be seen from fig. 7, the signal-to-noise ratio of ① has a positive correlation with the angular (high) precision of each algorithm of each array, and after the signal-to-noise ratio is greater than a certain range, the improvement of the angular (high) precision tends to be gentle; ② Under the condition of the same signal-to-noise ratio, the low-altitude target angle measurement (high) precision of the sparse array meter wave TR MIMO radar is higher than that of the uniform linear array. ③ Compared with two typical sparse array meter wave TR MIMO radars, under the condition of the same signal-to-noise ratio, the highest accuracy of the mutual mass array angle measurement (high) is developed, and the second-order nested array is performed. ④ Compared with three algorithms, under the condition of the same signal-to-noise ratio, the GMUSIC algorithm parameter estimation accuracy suitable for the meter wave TR MIMO radar provided by the embodiment of the invention is highest, and the performance is best. The real value GMUSIC algorithm is inferior, while the rank multiplexing FBSSMUSIC algorithm measures the worst. The reason is the same as in experiment 3.
Experiment 6 the snapshot count affects the angle (high) precision experiment:
The experimental condition is that the incidence angle of the target direct wave is 3 degrees, the SNR= -10dB, and the target distance is 200km. Changing the value of the snapshot number L, wherein the change range is 2 times to 20 times, the change interval is 2 times, the angle search range is 0 degree to 10 degrees, and the search interval is 0.01 degree. FIG. 8 is a graph showing the variation of each algorithm parameter estimation RMSE with snapshot number for each array. As can be seen from fig. 8, the number of ① snapshots has a positive correlation with the angular accuracy of each algorithm of each array, and after the number of snapshots is greater than a certain range, the improvement of the angular (high) accuracy tends to be gentle; ② Under the condition of the same snapshot count, the low-altitude target angle measurement (high) precision of the sparse array meter wave TR MIMO radar is higher than that of the uniform linear array. ③ Compared with two typical sparse array meter wave TR MIMO radars, under the condition of the same snapshot number, the highest accuracy of the mutual mass array angle measurement (high) is developed, and the second-order nested array is performed. ④ Compared with three algorithms, under the condition of the same snapshot number, the GMUSIC algorithm parameter estimation precision suitable for the meter wave TR MIMO radar provided by the embodiment of the invention is highest, and the performance is best. The real value GMUSIC algorithm is inferior, while the rank multiplexing FBSSMUSIC algorithm measures the worst. The reason is the same as in experiment 3.
In summary, the embodiment of the invention introduces the sparse array as the receiving and transmitting antenna into the single-base meter wave TR MIMO radar system, provides a low-altitude target height measurement method suitable for the single-base sparse array meter wave TR MIMO radar, and the simulation experiment compares parameters of a typical sparse array and a uniform linear array with equal array element numbers, and the algorithm provided by the embodiment of the invention and a classical algorithm, thereby verifying the superiority of the sparse array meter wave TR MIMO radar and the effectiveness of the method.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: many changes, modifications, substitutions and variations may be made to the embodiments without departing from the spirit and principles of the invention, the scope of which is defined by the claims and their equivalents.
Claims (10)
1. A meter wave TRMIMO radar low-altitude target height measurement method based on a sparse array is characterized by comprising the following steps:
S1, constructing a single-base meter wave sparse array TRMIMO radar system, and respectively calculating guide vectors of a transmitted direct wave and a reflected wave of the single-base meter wave sparse array TRMIMO radar system to obtain a transmitted direct waveguide vector a t(θd) and a reflected waveguide vector a t(θs);
S2, constructing a composite guiding vector A (theta) according to the direct wave guiding vector a t(θd) and the reflecting wave guiding vector a t(θs);
S3, calculating received data Y, constructing a data covariance matrix R according to the calculated received data Y, performing eigenvalue decomposition on the constructed data covariance matrix R to obtain a noise subspace E n, performing real-value processing on the data covariance matrix R and a composite guide vector A (theta) respectively to obtain a real-value covariance matrix R U and a real-value composite guide vector A U (theta), and performing eigenvalue decomposition on a real-value covariance matrix R U to obtain a real-value noise subspace U n;
S4, searching spectral peaks according to the composite steering vector A (theta) and the data covariance matrix R or the real-valued composite steering vector A U (theta) and the real-valued covariance matrix R U by utilizing a generalized MUSIC algorithm and a maximum likelihood algorithm, observing to obtain a spatial spectrum, and finding out an angle corresponding to the position of the peak to obtain a target low elevation angle estimated value
S5, estimating the obtained target low elevation angleAnd converting to obtain the target height data H.
2. The method for measuring the height of the low-altitude target of the meter wave TRMIMO radar based on the sparse array according to claim 1, wherein in the step S1, the antennas of the single-base meter wave sparse array TRMIMO radar system are vertically placed, the number of transmitting and receiving array elements is P t and P r respectively, and the positions of the array elements are d t and d r,θd and θ s respectively represent the arrival angles of the direct wave and the reflected wave.
3. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method of claim 1, wherein in step S1, the expressions of the transmit direct waveguide vector a t(θd) and the reflective waveguide vector a t(θs) are:
wherein, theta d and theta s respectively represent the arrival angles of the direct wave and the reflected wave, P t is the number of transmitting array elements, For the mth transmit element position, λ is the signal wavelength, (. Cndot.) T represents the transpose.
4. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method of claim 1, wherein in step S2, the expression of the composite steering vector is:
Where a t(θd) and a t(θs) refer to the transmit direct waveguide vector and the reflected waveguide vector, respectively, (. Cndot.) * represents the matrix conjugate.
5. The sparse array-based meter wave TR MIMO radar low-altitude target height measurement method of claim 1, wherein in step S3, the calculation formula of the received data is as follows:
Wherein, omega= [1 gamma 2]T, epsilon is the energy normalization factor of the energy, P r is the number of received array elements, For the complex reflection coefficient of the target under different pulses, f d is Doppler frequency, and W is noise after matched filtering and vectorization operation;
the calculation formula of the data covariance matrix is as follows:
Where Y is the received data, (. Cndot.) H represents the matrix conjugate transpose, and L represents the snapshot number.
6. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method according to claim 1, wherein in step S3, the calculation formulas of the real-valued covariance matrix and the real-valued composite steering vector are respectively:
RU＝UHRfbU
AU(θ)＝UHA(θ)
where U is a unitary matrix, when the dimension of U is an odd number, When the dimension of U is even,/>II K is K x K switching matrix, specifically, the element on the opposite angle line is 1, the other elements are 0,I K are K x K unit matrix,/>(. Cndot.) H represents the matrix conjugate transpose, the A (θ) complex steering vector.
7. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method according to claim 1, wherein in step S4, the spectral peak search formulas according to the generalized MUSIC algorithm and the maximum likelihood algorithm of the composite steering vector and the data covariance matrix are respectively as follows:
Where det represents determinant operation, trace is a trace operator, P a(θ)＝A(θ)(AH(θ)A(θ))-1AH (θ), R is a data covariance matrix, E n is a noise subspace obtained by decomposing a eigenvalue of R, I P is a unit matrix of p×p, and (-) H represents matrix conjugate transpose.
8. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method according to claim 1, wherein in step S4, the spectral peak search formulas of the generalized MUSIC algorithm and the maximum likelihood algorithm according to the real-valued covariance matrix and the real-valued composite steering vector are respectively as follows:
Wherein det represents determinant operation, trace is a trace operator, I P is a unit matrix of P×P, (. Cndot.) H represents matrix conjugate transpose, R U is real-valued covariance matrix, U n is real noise subspace obtained by performing feature decomposition on real-valued covariance matrix R U, A U (θ) is a real-valued composite steering vector.
9. The sparse array-based metric wave TRMIMO radar low-altitude target height measurement method of claim 1, wherein step S4 further comprises the step of reducing the two-dimensional spectral peak search of the generalized MUSIC algorithm and the maximum likelihood algorithm to a one-dimensional search according to the relationship between the direct wave incident angle θ d and the reflected wave incident angle θ s, said relationship between the direct wave incident angle θ d and the reflected wave incident angle θ s being as follows:
θs＝-arctan(tanθd+2ha/R)
Wherein h a is the antenna erection height, and R is the target distance.
10. The sparse array-based meter wave TRMIMO radar low-altitude target height measurement method of claim 1, wherein in step S5, the calculation formula of the target height data is:
Wherein, For a target low elevation estimate, R is the target distance and h a is the antenna mount height.
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