CN115201813A - Meter-wave TR MIMO radar low-altitude target height finding method based on sparse array - Google Patents
Meter-wave TR MIMO radar low-altitude target height finding method based on sparse array Download PDFInfo
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Abstract
The invention discloses a meter wave TR MIMO radar low-altitude target height measurement method based on a sparse array, which is characterized by comprising the following steps of: s1, constructing a single-base ground meter wave sparse array TR MIMO radar system, and respectively calculating to obtain a guide vector a of a transmitted direct wave t (θ d ) And a reflected wave guide vector a t (θ s ) (ii) a S2, constructing a composite guide vector A (theta); s3, calculating received data Y, constructing a data covariance matrix R, and respectively performing real-valued processing on the data covariance matrix R and the composite guide vector A (theta) to obtain a real covariance matrix R U And the real-valued composite steering vector A U (θ); s4, according to the composite steering vector A (theta) and the data covariance matrixR or the real covariance matrix R U And real-valued composite steering vector A U (theta), performing spectrum peak search by using the generalized MUSIC algorithm and the maximum likelihood algorithm, observing to obtain a space spectrum, and finding out the angle corresponding to the position of the peak, namely obtaining the target low elevation angle estimated value
S5, obtaining a target low elevation angle estimated value
And converting to obtain target height data H.
Description
Technical Field
The invention belongs to the technical field of meter wave TR MIMO radars, 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 excellent performance and attracts much attention on resisting stealth targets and anti-radiation missiles, but the meter-wave radar has longer wavelength and wider pitch dimension main beams, and when a low-altitude target is detected, direct waves and ground reflected waves usually enter the radar from the main beams. Due to the limitation of the aperture and the working bandwidth of the antenna, the meter-wave radar is difficult to distinguish direct waves from ground reflected waves in an airspace, a time domain and a frequency domain, and the multipath effect seriously influences the angle measurement precision of the meter-wave radar in a low elevation angle region. The Multiple Input Multiple Output (MIMO) radar implements an equivalent large-scale virtual array with fewer array elements by a waveform diversity technique, and has advantages that a conventional array radar cannot compare with: the angle measurement precision is higher, the anti-interference ability is stronger, the anti-stealth effect is good, the multi-target tracking ability is strong, and the like. The Time Reversal (TR) technique has space-Time focusing, can effectively utilize the energy of reflected waves, reduce the influence of multipath effect on signal echoes, and improve the signal-to-noise ratio. The TR technology and the MIMO radar are combined to detect the low-altitude target, so that the parameter estimation precision of the low-altitude and ultra-low-altitude target can be improved, and the method has great significance.
In recent years, extensive scholars deeply research the problem Of estimating Direction Of Arrival (DOA) Of a meter wave TR MIMO radar under the condition Of low-altitude multipath reflection, and a plurality Of achievements are formed. At present, main processing methods include a row-column multiplexing bidirectional Spatial Smoothing (FBSS) algorithm, a Capon algorithm, a Multiple Signal Classification (MUSIC) algorithm, a Toeplitz matrix reconstruction algorithm, and the like. The Liu Meng wave provides a row-column multiplexing FBSS MUSIC algorithm suitable for the meter wave TR MIMO radar under the low-altitude multi-path reflection condition. The algorithm effectively improves the angle measurement precision of the low-altitude target by using the focusing performance of the TR technology, but does not utilize the expansion capability of the virtual aperture of the MIMO system radar, and the parameter estimation performance is not greatly improved. The Hookan proposes a Capon algorithm based on the multi-path reflection condition of the Mibowave TR MIMO radar, the algorithm has strong sidelobe suppression capability, and still has good estimation accuracy under the multi-path environment and the low signal-to-noise ratio condition, but the Capon algorithm cannot effectively distinguish direct waves and reflected waves with small incoming wave angle intervals under the influence of the Capon algorithm, namely the algorithm is not suitable for DOA estimation of low-altitude and ultra-low-altitude targets. The Liu Meng wave provides a real-value domain MUSIC algorithm based on a TR MIMO radar. The algorithm eliminates complex operation through real value transformation, thereby effectively reducing the calculated amount, has the capability of resolving coherence without spatial smoothing, and has relatively small loss of target estimation precision, but the algorithm also can not effectively distinguish direct waves and reflected waves with small angle intervals of incoming waves, can not overcome large spectral values generated by small angles during spectral peak search, and is not suitable for DOA estimation of low-altitude and ultra-low-altitude targets. The Liumeng wave provides a TR MIMO radar coherent target DOA estimation algorithm based on Toeplitz matrix reconstruction. According to the DOA estimation method, a Toeplitz matrix reconstruction algorithm is adopted, the coherence of a target is removed, the DOA estimation is carried out by using an optimization iteration method based on a first-order approximation theory, the DOA estimation precision is further improved, and the calculation complexity is reduced. However, due to the influence of multipath effect, the direct wave and the reflected wave guide vector of the low-altitude target are mutually coupled, and the DOA estimation effect of the algorithm on the low-altitude target is not good.
The algorithms proposed in the above documents all adopt a Uniform Linear Array (ULA) TR MIMO radar signal model, which has the problems of low accuracy of angle measurement of ultra-low altitude target parameters and large fluctuation of parameter estimation errors affected by multipath effects with changes of elevation angles. With the continuous deepening of the battle practice, the target detection and tracking needs higher angle measurement precision and stability.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, provides a method for measuring the height of a low-altitude target of a meter-wave TR MIMO radar based on a sparse array, improves the angle measurement precision of the meter-wave TR MIMO radar, especially the angle measurement precision of the low-altitude target, and reduces the fluctuation degree of height measurement errors.
In order to achieve the purpose, the invention adopts the technical scheme that:
a meter-wave TR MIMO radar low-altitude target height finding method based on a sparse array comprises the following steps:
s1, constructing a single-base ground meter wave sparse array TR MIMO radar system, and respectively calculating guide vectors of transmitted direct waves and reflected waves of the single-base ground meter wave sparse array TR MIMO radar system to obtain a guide vector a of the transmitted direct waves t (θ d ) And the reflected wave guide vector a t (θ s )；
S2, guiding the vector a according to the transmitted direct wave t (θ d ) And a reflected wave guide vector a t (θ s ) Constructing a composite steering vector A (theta);
s3, calculating received data Y, constructing a data covariance matrix R according to the received data Y obtained through calculation, and performing characteristic value decomposition on the constructed data covariance matrix R to obtain a noise subspace E n Respectively carrying out real-valued processing on the data covariance matrix R and the composite guide vector A (theta) to obtain a real-valued covariance matrix R U And real-valued composite steering vector A U (θ) and for the real-valued covariance matrix R U Carrying out eigenvalue decomposition to obtain a real-valued noise subspace U n ；
S4, according to the composite guide vector A (theta) and the data covariance matrix R or the real-value composite guide vector A U (theta) and the real-valued covariance matrix R U Performing spectrum peak search by using the generalized MUSIC algorithm and the maximum likelihood algorithm, observing to obtain a space spectrum, and finding out the angle corresponding to the position of the peak, namely obtaining the target low elevation angle estimated value
S5, obtaining a target low elevation angle estimated value
And converting to obtain target height data H.
Preferably, in step S1, the antennas of the monostatic meter wave sparse array TR MIMO radar system are vertically arranged, and the number of transmitting and receiving array elements is P t And P r The array element position is d t And d r ，θ d And theta s Representing the angle of arrival of a direct wave and a reflected wave, respectively.
Preferably, in step S1, the transmitted direct wave guide vector a t (θ d ) And a reflected wave guide vector a t (θ s ) The expression of (a) is:
wherein, theta d And theta s Representing the angle of arrival, P, of the direct and reflected waves, respectively t In order to determine the number of the transmitting array elements,
is the m-th transmitting array element position, lambda is the signal wavelength, (. DEG) T Representing a transposition.
Preferably, in step S2, the expression of the composite guide vector is:
wherein, a t (θ d ) And a t (θ s ) Respectively, a transmitted direct guide vector and a reflected guide vector, (. Cndot.) * Representing the matrix conjugate.
Preferably, in step S3, the calculation formula of the received data is as follows:
wherein ω = [1 γ γ γ γ γ = 2 ] T ε is the energy normalization factor, P r In order to receive the number of array elements,
for complex reflection coefficient of target under different pulses, f d The frequency is Doppler frequency, and W is noise after matched filtering and vectorization operation;
the calculation formula of the data covariance matrix is as follows:
wherein, Y is received data, (·) H Representing the matrix conjugate transpose and L represents the fast beat number.
Preferably, in step S3, the calculation formulas of the real-valued covariance matrix and the real-valued composite steering vector are respectively:
R U ＝U H R fb U
A U (θ)＝U H A(θ)
wherein, U is unitary matrix, when the dimension of U is odd,
when the dimension of U is an even number,
Π K a K x K switching matrix, in particular with 1 for the element on the anti-diagonal and 0 for the other elements K Is a unit array of K multiplied by K,
(·) H representing the matrix conjugate transpose, a (θ) composite 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 trace operator, P a (θ)＝A(θ)(A H (θ)A(θ)) -1 A H (theta), R is a data covariance matrix, E n Noise subspace, I, obtained for eigenvalue decomposition of R P Is a P unit array H Representing a 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-valued composite steering vector are respectively as follows:
where det represents determinant operation, trace is trace-solving operator, I P Is a P unit array H Representing the conjugate transpose of the matrix, R U Is a real-valued covariance matrix, U n For real-valued covariance matrix R U The real noise subspace obtained by performing the feature decomposition,
A U (θ) is the real-valued composite steering vector.
Preferably, step S4 further includesSearching two-dimensional spectral peak containing generalized MUSIC algorithm and maximum likelihood algorithm according to incident angle theta of direct wave d Incident angle theta with the reflected wave s The relation between the two is reduced to a step of one-dimensional search, and the incident angle theta of the direct wave is d Incident angle theta with the reflected wave s The relationship between them is as follows:
θ s ＝-arctan(tanθ d +2h a /R)
wherein h is a The antenna erection height is defined, and R is the target distance.
Preferably, in step S5, the calculation formula of the target height data is:
wherein, the first and the second end of the pipe are connected with each other,
for a target low elevation estimate, R is the distance of the target, h a The height of the antenna is set up.
Compared with the prior art, the invention has the beneficial effects that:
according to the invention, the sparse array replaces the uniform linear array to serve as the receiving and transmitting antenna of the monostatic millimeter wave TR MIMO radar, and the sparse structure of the sparse array is mainly utilized, so that compared with the uniform linear array, the expansion of the physical aperture of the array can be realized on the premise of a certain number of physical array elements, the expansion capability of the virtual aperture of the radar with the overlapped MIMO system greatly expands the effective array aperture, the cost of a hardware system is reduced, the angle (high) precision of a low-altitude target is improved, and the fluctuation degree of the angle (high) measurement error is reduced; simulation results show that the single-base millimeter wave sparse array TR MIMO radar has higher angle (high) measurement precision under the condition of low-altitude multipath reflection, has more obvious advantages especially for an ultra-low-altitude target, and has better effect under the conditions of low snapshot and low signal-to-noise ratio. Compared with two typical single-base sparse array metric wave TR MIMO radars, under the same condition, the expanded co-prime array has the highest angle (high) measurement precision, the minimum angle (high) measurement fluctuation and the second-order nested array order. Compared with two typical algorithms, under the same condition, the generalized MUSIC algorithm applicable to the TR MIMO radar has the highest angle (high) measurement precision and the minimum angle (high) measurement error fluctuation.
Drawings
Fig. 1 is a diagram of a model of horizontal ground reflection of a meter-wave TR MIMO radar according to an embodiment of the present invention;
FIG. 2 is a graph of the computational complexity of the algorithm provided by the embodiment of the present invention as a function of the number of transmit array elements;
FIG. 3 is a spectral peak search plot for each algorithm of each array in the present invention;
FIG. 4 is a spectrum peak search chart of each algorithm of each array for an ultra-low altitude target;
wherein, fig. 4 (a) is a spectrum peak search chart at a target incident angle of 0.5 °; FIG. 4 (b) is a spectral peak search plot at a target incident angle of 1 °;
FIG. 5 is a graph of the variation of the RMSE with elevation angle for each algorithm parameter estimate for each array;
wherein, FIG. 5 (a) is a diagram of the variation of angle RMSE with the elevation angle; FIG. 5 (b) is a graph of height RMSE as a function of elevation;
FIG. 6 is a graph of the algorithm angles RMSE of each array and the variation of the target altitude with elevation;
wherein, FIG. 6 (a) is a graph of the variation of the angle RMSE with the elevation angle; FIG. 6 (b) is a graph of target height as a function of elevation;
FIG. 7 is a graph of the variation of the RMSE with the SNR for each algorithm parameter estimate for each array;
wherein, FIG. 7 (a) is a diagram of the variation of angle RMSE with the elevation angle; FIG. 7 (b) is a graph of height RMSE as a function of elevation;
FIG. 8 is a graph of the variation of the estimated RMSE of each algorithm parameter of each array with the number of snapshots;
wherein, FIG. 8 (a) is a graph of the variation of the angle RMSE with the elevation angle; fig. 8 (b) is a graph of height RMSE as a function of elevation.
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 by 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 method for measuring the height of a low-altitude target of a meter-wave TR MIMO radar based on a sparse array, which specifically comprises the following steps:
s1, constructing a single-base ground meter wave sparse array TR MIMO radar system, wherein as shown in figure 1, antennas of the radar system are vertically arranged, and the number of transmitting and receiving array elements is P t And P r The array element position is d t And d r Assuming that the terrain is smooth and flat, in this system, the transmit and receive arrays are closely spaced, the transmit and receive angles (including the ground reflection angle) may be approximately equal for far field targets, where θ d And theta s Representing the angle of arrival of a direct wave and a reflected wave, respectively.
Transmitting signal of TR MIMO radar
Are mutually orthogonal and satisfy the following formula:
wherein, I P Is a unit array, T is a pulse duration, (. DEG) H Representing a matrix conjugate transpose;
the signals of the transmitting signals which are propagated through the air medium and reach the target are as follows:
wherein k is 0 ＝2π/λ，[·] T Represents the transposition of the matrix, rho is the ground reflection coefficient, delta R is the wave path difference between the direct wave and the reflected wave, and the arrival angle of the direct wave and the antenna height H can be easily found by observing figure 1 a The relationship betweenIs DeltaR ≈ 2H a sinθ d ，a t (θ d ) And a t (θ s ) Respectively transmitting direct wave and reflected wave guide vectors, respectively calculating the guide vectors of the transmitted direct wave and the reflected wave of the single-base ground meter wave sparse array TR MIMO radar system to obtain a guide vector a of the transmitted direct wave t (θ d ) And the reflected wave guide vector a t (θ s ) Transmitting the direct wave guide vector a t (θ d ) And a reflected wave guide vector a t (θ s ) The expression of (a) is:
wherein, theta d And theta s Representing the angle of arrival, P, of the direct and reflected waves, respectively t In order to determine the number of the transmitting array elements,
is the m-th transmitting array element position, lambda is the signal wavelength, (. DEG) T Representing a transposition;
then the expression of the signal received by the pth array element is:
z p (t,τ)＝[a r,p (θ d )+γa r,p (θ s )]β(τ)x(t)+v p (t,τ)
wherein the content of the first and second substances,
for the complex reflection coefficient of the target under different pulses, f d Is the Doppler frequency;
the matrix of signals received by the entire array can be written as:
wherein A is r ＝a r (θ d )+γa r (θ s )，A t ＝a t (θ d )+γa t (θ s )，
For different pulse target complex reflection coefficient, (.) T Denotes transposition, v (t, τ) is Gaussian white noise, a r (θ d ) And a r (θ s ) Respectively receiving direct wave and reflected wave guide vectors, and respectively having the expressions:
wherein, theta d And theta s Respectively representing the angles of arrival of the direct wave and the reflected wave, Pr in order to determine the number of the transmitting array elements,
for the position of the p-th transmitting array element, λ is the signal wavelength, (. Cndot.) T Indicating transposition.
According to the principle of time reversal, the signal matrix at the receiving end in the signal matrix formula received by the whole array is subjected to conjugation and time reversal, energy normalization is carried out, and the signal is transmitted again. The transmitted signal is modeled as ε z * And (-t, tau), epsilon is an energy normalization factor, and the signal matrix expression of the TR MIMO radar receiving end is as follows:
wherein [ ·] * Representing a matrix conjugate; v (t, τ) is white Gaussian noise; w (t, τ) is the accumulated noise,
for complex reflection coefficients of objects under different pulses, A r ＝a r (θ d )+γa r (θ s )，A t ＝a t (θ d )+γa t (θ s )，(·) T Representing transposition, it is known from literature that w (t, τ) can be approximated as white gaussian noise due to the time-reversed focusing effect;
using transmission signals
The above formula is matched and filtered to obtain:
vectorizing the above equation:
wherein A is a composite guide vector,
vec represents the vectoring operation and,
representing a kron product, wherein W is noise after matched filtering and vectorization operation, and the original noise W (t, tau) is approximate to Gaussian white noise, so that the fact that W is still Gaussian white noise after matched filtering and vectorization operation can be known from literature;
s2, guiding the vector a according to the transmitted direct wave t (θ d ) And a reflected wave guide vector a t (θ s ) And constructing a composite steering vector A (theta), wherein the expression of the composite steering vector is as follows:
wherein, a t (θ d ) And a t (θ s ) Respectively, a direct wave guide vector and a reflected wave guide vector (·) * Representing a matrix conjugate;
the covariance matrix R is then:
in the formula (I), the compound is shown in the specification,
and
respectively representing signal power and noise power, wherein A (theta) is a composite steering vector which is a steering vector matrix provided by the invention, and the steering vector matrix is different from a steering vector in a common MUSIC algorithm and still orthogonal to a noise subspace under the interference of a TR MIMO radar multipath coherent signal;
s3, calculating the received data Y, wherein the calculation formula of the received data is as follows:
wherein ω = [1 γ γ γ γ γ = 2 ] T ε is the energy normalization factor, P r In order to receive the number of array elements,
for the complex reflection coefficient of the target under different pulses, f d The Doppler frequency is W, and the noise is subjected to matched filtering and vectorization operation;
and constructing a data covariance matrix R according to the received data Y obtained by calculation, wherein the calculation formula of the data covariance matrix is as follows:
wherein, Y is received data, (-) H Representing matrix conjugate transpose, L represents fast beat number;
and performing characteristic value decomposition on the constructed data covariance matrix R to obtain a noise subspace E n The MIMO radar greatly increases the operation amount while enhancing the system performance, which is inconvenient for engineering practice, and the receiving and retransmitting of the TR technology also increases the calculation redundancy, so 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 a complex matrix which can be easily found, and in order to further reduce the calculation complexity of the algorithm provided by the invention, the received data can be processed by a unitary matrix in a real value mode. Defining a unitary matrix as follows:
therein, II K A K x K switching matrix with 1 element on the anti-diagonal and 0, I elements K Is a K × K unit array, if P is an odd number, U is adopted 2K+1 The formula is processed in real value, and K = (P-1)/2; if P is even number, U is adopted 2K The formula is real-valued, and K = P/2.
According to the property of unitary matrix, unitary matrix can change Centro-Hermitian matrix into real matrix by unitary transformation, but R is not Centro-Hermitian matrix, so that it needs to be processed with bidirectional smoothing to convert into Centro-Hermitian matrix:
then, real-valued processing is carried out on the data covariance matrix R and the composite steering vector A (theta) respectively to obtain a real covariance matrix R U And real valueComposite steering vector A U (θ), the real covariance matrix R U And real-valued composite steering vector A U The calculation formula of (θ) is:
R U ＝U H R fb U
A U (θ)＝U H A(θ)
wherein, U is a unitary matrix,
(·) H representing the matrix conjugate transpose, A (theta) is the composite steering vector, and for the real covariance matrix R U Decomposing the characteristic value to obtain a noise subspace U n ；
S4, according to the composite guide vector A (theta) and the data covariance matrix R or the real covariance matrix R U And the real-valued composite steering vector A U (θ), performing a spectral peak search using the generalized MUSIC algorithm and the maximum likelihood algorithm, wherein a 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 the determinant operation, P a (θ)＝A(θ)(A H (θ)A(θ)) -1 A H (θ)，E n A noise subspace obtained by performing eigenvalue decomposition on R, (. Cndot.) H Representing a matrix conjugate transpose;
similarly, the space projection matrix of the maximum likelihood algorithm is constructed by using the steering vector matrix A (theta) provided by the embodiment of the invention as follows:
P a (θ)＝A(θ)(A H (θ)A(θ)) -1 A H (θ)
wherein, A (theta) is a composite guide vector (·) H Representing a matrix conjugate transpose;
then the maximum likelihood algorithm spectral peak search formula is as follows:
wherein trace is the trace-finding operator, P a (θ)＝A(θ)(A H (θ)A(θ)) -1 A H (θ), R is a data covariance matrix, I P A P × P unit array;
the spectral peak search formula of the generalized MUSIC algorithm based on the real covariance matrix and the real-valued composite steering vector is as follows:
where det represents the determinant operation, (. Cndot.) H Representing the conjugate transpose of the matrix, U n For real-valued covariance matrix R U A real noise subspace, A, obtained by performing a feature decomposition U (theta) is a real-valued composite steering vector;
defining a real-valued spatial projection matrix as follows:
then the real-valued maximum likelihood algorithm spectral peak search formula is as follows:
wherein trace is the trace-finding operator, I P Is a P × P unit array, R U Is a real-valued covariance matrix,
searching the two-dimensional spectral peak of the generalized MUSIC algorithm and the maximum likelihood algorithm according to the incident angle theta of the direct wave d Incident angle theta with reflected wave s The relation between the two is reduced to a step of one-dimensional search, and the incident angle theta of the direct wave is d Incident angle theta with the reflected wave s The relationship between them is as follows:
θ s ＝-arctan(tanθ d +2h a /R)
wherein h is a Setting the height of the antenna, wherein R is the distance of a target;
then observing to obtain a space spectrum, finding out the angle corresponding to the position of the wave crest, namely obtaining the target low elevation angle estimated value
S5, obtaining a target low elevation angle estimated value
Converting to obtain target height data H, wherein the calculation formula of the target height data is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for a target low elevation estimate, R is the distance of the target, h a The height of the antenna is set up.
The following is an analysis of the performance of the method provided by the embodiments of the invention
(1) Performance of parameter estimation
As described above
The formula is a signal model of a received signal after matched filtering under the condition of multipath reflection of the meter wave TR MIMO radar, and the formula shows that compared with the traditional MIMO radar, the signal amplitude of the TR MIMO radar has P r Multiple gain, signal energy having P r 2 The signal-to-noise ratio is greatly improved due to the multiple gain, 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 is present t ≥P r In time, the meter wave TR MIMO radar has higher low-altitude target DOA estimation precisionDegree and resolution and greater degrees of freedom. In summary, in order to improve the TR MIMO radar parameter estimation performance, the transmitting array may use the sparse array to expand the effective array aperture, and no special requirement is required for the receiving array structure, as long as the number of receiving array elements can be effectively increased.
(2) Complexity of calculation
The complexity of the method provided by the embodiment of the invention mainly comprises the following parts: (1) constructing a covariance matrix; (2) carrying out covariance matrix characteristic decomposition; (3) the spectral peak search was three parts. The real-valued processing algorithm also adds to the real-valued processing algorithm complexity. Note that: compared with the unreal value processing algorithm, the real value processing algorithm needs to calculate the covariance matrix R additionally fb And R U Due to the switching matrix pi P And unitary transformation matrix U P Are all sparse, so they bring little computational complexity, and are ignored here. In addition, here, the addition is omitted and only the multiplication is considered. In addition, one complex multiplication corresponds to four real multiplications.
The generalized MUSIC algorithm and the maximum likelihood algorithm which are suitable for the height measurement of the low-altitude target of the meter-wave TR MIMO radar and are provided by the embodiment of the invention are respectively abbreviated as GMUSIC algorithm and ML algorithm, and the two algorithms which are subjected to real value processing are respectively abbreviated as UGMUSIC algorithm and UML algorithm.
C GMUSIC ＝4P t 4 L+4P t 6 +4Θ(32P t 2 +8P t 4 )
C ML ＝4P t 4 (L+P t 2 )+4Θ(32P t 2 +4P t 4 +P t 6 )
C UGMUSIC ＝P t 4 L+P t 6 +Θ(32P t 2 +8P t 4 )
C UML ＝P t 4 (L+P t 2 )+Θ(32P t 2 +4P t 4 +P t 6 )
Wherein L represents the number of beats, P t For the number of transmitting elements, [ theta ] isNumber of spectral peak searches.
FIG. 2 is a diagram illustrating the calculation complexity of the algorithm according to the number P of transmitting array elements according to the embodiment of the present invention t The variation graph has a snapshot number L =30, a target number n =1, and a spectrum peak search frequency Θ =1000. As can be seen from FIG. 2, the GMUSIC algorithm has lower computational complexity than the ML algorithm, and the computational complexity of the algorithm subjected to real-valued processing has greater advantage as the number of array elements increases. Obviously, the computational complexity can be greatly reduced by real-valued processing, saving about 75% of the computational time.
Simulation of experiments
When the array elements of the sparse array are equal, the physical aperture sizes of a simple co-prime array (SCA), an extended co-prime array (ECA) and a second-order Nested Array (NA) are close, and the parameter estimation performance is not much different. According to the conclusion of literature simulation experiments, 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 an unfolded cross-prime array (UCA), are taken as objects, the GMUSIC algorithm suitable for the Meter-wave sparse array TR MIMO radar and the Uniform Linear Array (ULA) adopting the FBSSMUSIC, UGMUSIC and GMUSIC algorithms are adopted for simulation, the results are compared and subjected to performance analysis, the influence of factors such as target elevation (height), signal-to-noise ratio and fast beat number on the elevation estimation performance of each algorithm of each array is analyzed in an important way, and a general conclusion is obtained.
The basic conditions of the simulation experiments are consistent, that is, three monostatic meter wave TR MIMO radars adopt an array which is vertically arranged into one-dimensional linear arrangement as a receiving and transmitting antenna, and the receiving and transmitting antennas of the radars are separately arranged and have the same structure. The antenna 1 is ULA, the antenna 2 is second-order NA, the antenna 3 is UCA, and the number of the transmitting and receiving array elements of each array is P t ＝P r =10. The space d of the ULA array elements is half-wavelength of a received signal, and the physical array element positions 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 and 29d }; the physical array position of the UCA is {0,6d,12d,18d,24d,29d,34d,39d,44d,49d }; the radar working frequency is 300Mhz, the number of space targets is n =1, and the height of the bottom receiving and transmitting antenna4m, the ground reflection coefficient is-0.9, and the added noise is white Gaussian noise. The angle measurement precision of different algorithms of different arrays is compared by adopting a Monte Carlo repeated experiment, the Monte Carlo repeated experiment frequency I =300 times, and a one-dimensional Root Mean Square Error (RMSE) formula is as follows:
in the formula: i is the number of Monte Carlo trials,
is the target angle measured at the kth time.
The experimental conditions of the group are that the incident angle of the target direct wave is 2 degrees, the signal-to-noise ratio SNR =0dB, the snapshot number L =20, the target distance is 200km, the angle search range is 0 degree to 10 degrees, and the search interval is 0.1 degree. Fig. 3 is a spectrum peak search diagram of each algorithm of each array, and the peak position is an elevation angle estimated value. As can be found from the figure 3, the array meter-wave TR MIMO radars (1) can accurately measure the low elevation angle of the target, but the sparse array has sharper spectral peak at low elevation angle than the uniform linear array, and the angle measurement performance of the sparse array meter-wave TR MIMO radar is better. (2) Compared with two typical sparse array meter wave TR MIMO radars, the spread co-prime array spectral peak is sharper, the performance is best and the second-order nested array is inferior under the same condition. (3) Compared with three algorithms, under the same condition, the GMUSIC and UGMUSIC algorithms applicable to the meter-wave TR MIMO radar have sharper spectrum peaks and better performance, and the rank multiplexing FBSSMUSIC algorithm provided by the literature is inferior. The main reason is that the FBSSMUSIC algorithm of row-column 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.
The experimental conditions of the group are that the signal-to-noise ratio SNR =0dB, the snapshot number L =20, the target distance is 200km, the incident angles of the target direct waves are 0.5 degrees and 1 degrees respectively, the angle search range is 0 degree to 10 degrees, and the search interval is 0.1 degrees. Fig. 4 is a spectrum peak search diagram of each array algorithm for an ultra-low altitude target, and the peak position is an elevation angle estimated value. As can be seen from fig. 4, both (1) the m-wave sparse array TR MIMO radar can accurately measure the elevation angle of the ultra-low altitude target, the m-wave uniform linear array TR MIMO radar can measure the elevation angle of the target barely when the elevation angle of the target is 1 °, the sparse array is sharper than the uniform linear array ultra-low altitude target spatial spectrum peak, and the m-wave sparse array TR MIMO radar has better ultra-low altitude angle measurement performance. (2) Compared with two typical sparse array meter wave TR MIMO radars, the spread co-prime array ultra-low-altitude target space spectrum peak is sharper, the performance is better, and the second-order nested array is inferior under the same condition. (3) Compared with three algorithms, under the same condition, the GMUSIC and UGMUSIC algorithms suitable for the meter-wave TR MIMO radar provided by the embodiment of the invention have sharper ultralow target elevation angle space spectrum peaks and better performance than the line-column multiplexing FBSSMUSIC algorithm. The reason is the same as in experiment 1.
The experimental conditions in this set were SNR = -10dB, number of snapshots L =5, and target distance 200km. The variation range of the elevation angle is 0.5 degrees to 8 degrees, and the variation interval is 0.5 degrees. The angle search range is 0 ° to 10 °, and the search interval is 0.01 °. FIG. 5 is a graph of the RMSE estimate for each algorithm parameter estimate for each array as a function of elevation. As can be seen from fig. 5, (1) the elevation angle size and the angle measurement (height) error are approximately in a negative correlation relationship, but a certain fluctuation change can be presented in an interval along with the elevation angle change, mainly because the elevation angle change brings the periodic change of the multipath attenuation coefficient phase, thereby affecting the algorithm effect. Along with the increase of the elevation angle, the interval between direct waves and multipath is increased, the influence of the attenuation coefficient phase on the algorithm effect is gradually reduced, the integral angle estimation performance is in an ascending trend, and the angle measurement precision tends to be stable after the elevation angle is larger than a certain range; (2) under the condition of the same elevation angle, the angle (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, the spread co-prime array has the highest angle measurement (high) precision and the second-order nested array is the second order under the condition of the same elevation angle. (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 is the smallest, the performance is the best, the real-value GMUSIC algorithm is the second, and the line-column multiplexing FBSSMUSIC algorithm is the worst. The real-valued GMUSIC algorithm degrades the performance of parameter estimation due to loss of signal imaginary part information by real-valued processing. The reason why the row-column multiplexing FBSSMUSIC algorithm has the worst performance is the same as that of experiment 1.
The experimental conditions in this set were SNR = -10dB, number of snapshots L =5. The target height 7000m, near flight, varies from 2.5 ° to 10 ° in elevation angle with a variation interval of 0.5 °, i.e. the range of variation of the distance between the target and the radar is approximately 160479m to 40311m, the range of angular search is 0 ° to 11 °, and the search interval is 0.01 °. FIG. 6 is a graph of the algorithm angles RMSE for each array and the variation of target height with elevation. As can be seen from fig. 6, (1) the error between the target height measured by each algorithm of each array and the actual target height 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, and the algorithm effect is further affected. (2) Under the condition of the same elevation angle, the fluctuation degree of angle (height) measurement errors 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, the spread co-prime array angle measurement (height) error fluctuation is minimum under the condition of the same elevation angle, and the second-order nested array is the second-order nested array. (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 the performance is best. The real-valued GMUSIC algorithm is next to the real-valued GMUSIC algorithm, and the row-column multiplexing FBSSMUSIC algorithm has the largest fluctuation degree. The reason is the same as experiment 3.
The experimental conditions in this set were a target direct wave incidence angle of 3 °, fast beat number L =5, and a target distance of 200km. The value of SNR is changed in the range of-20 dB to 0dB and the change interval is 1dB. The angle search range is 0 ° to 10 °, and the search interval is 0.005 °. FIG. 7 is a graph of the RMSE versus SNR variation for each algorithm parameter estimate for each array. As can be seen from fig. 7, (1) the signal-to-noise ratio has a positive correlation with the angle (height) measurement precision of each algorithm of each array, and after the signal-to-noise ratio is greater than a certain range, the improvement of the angle (height) measurement precision tends to be smooth; (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, the spread co-prime array has the highest angle measurement (high) precision and the second-order nested array is the second order under the condition of the same signal-to-noise ratio. (4) Compared with three algorithms, under the condition of the same signal to noise ratio, the GMUSIC algorithm parameter estimation method applicable to the meter wave TR MIMO radar has the highest accuracy and the best performance. The real-valued GMUSIC algorithm is the second, and the line-column multiplexing FBSSMUSIC algorithm has the worst measurement accuracy. The reason is the same as experiment 3.
the experimental conditions in this set were a target direct wave incidence angle of 3 °, a signal-to-noise ratio SNR = -10dB, and a target distance of 200km. The value of the fast beat number L is changed, the change range is 2 times to 20 times, the change interval is 2 times, the angle search range is 0 degrees to 10 degrees, and the search interval is 0.01 degrees. FIG. 8 is a graph of the variation of the estimated RMSE with snapshot number for each array algorithm parameter. As can be seen from fig. 8, (1) the snapshot number is in positive correlation with the angle measurement accuracy of each algorithm of each array, and after the snapshot number is greater than a certain range, the improvement of the angle measurement (high) accuracy tends to be smooth; (2) under the condition of the same fast beat number, the low-altitude target 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, the spread co-prime array has the highest angle measurement (high) precision and the second-order nested array is the second order under the condition of the same fast beat number. (4) Compared with three algorithms, under the condition of equal fast beat number, the GMUSIC algorithm applicable to the metric wave TR MIMO radar has the highest parameter estimation precision and the best performance. The real-valued GMUSIC algorithm is the second, and the line-column multiplexing FBSSMUSIC algorithm has the worst measurement accuracy. The reason is the same as experiment 3.
In summary, the sparse array is used as a receiving and transmitting antenna and introduced into a monostatic meter wave TR MIMO radar system, a low-altitude target height measurement method suitable for the monostatic sparse array meter wave TR MIMO radar is provided, a simulation experiment carries out parameter comparison on a typical sparse array and a uniform linear array with equal array elements, and an algorithm provided by the embodiment of the invention and a classical algorithm, so that the superiority of the sparse array meter wave TR MIMO radar in comparison with the uniform linear array TR MIMO radar and the effectiveness of the method are verified.
While embodiments of the present invention have been shown and described, it will be understood by those of ordinary skill in the art that: various changes, modifications, substitutions and alterations can be made to the embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.
Claims (10)
1. A low-altitude target height measurement method of a meter-wave TRMIMO radar 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 transmitted direct waves and reflected waves of the single-base meter wave sparse array TRMIMO radar system to obtain a guide vector a of the transmitted direct waves t (θ d ) And the reflected wave guide vector a t (θ s )；
S2, guiding the vector a according to the transmitted direct wave t (θ d ) And the reflected wave guide vector a t (θ s ) Constructing a composite guide vector A (theta);
s3, calculating received data Y, constructing a data covariance matrix R according to the received data Y obtained through calculation, and performing characteristic value decomposition on the constructed data covariance matrix R to obtain a noise subspace E n Respectively carrying out real-valued processing on the data covariance matrix R and the composite steering vector A (theta) to obtain a real-valued covariance matrix R U And real-valued composite steering vector A U (θ) and for the real-valued covariance matrix R U Decomposing the characteristic value to obtain a real-value noise subspace U n ；
S4, according to the composite guide vector A (theta) and the data covariance matrix R or the real-value composite guide vector A U (theta) and the real-valued covariance matrix R U Using generalized MUSIC algorithm and maximum likelihood calculationThe method carries out spectrum peak search, observes and obtains a space spectrum, finds out the angle corresponding to the position of the peak, namely obtains the target low elevation angle estimated value
S5, obtaining a target low elevation angle estimated value
And converting to obtain target height data H.
2. The method for measuring the height of the low-altitude target of the TRMIMO radar based on the sparse array as claimed in claim 1, wherein in step S1, the antennas of the TRMIMO radar system with the monostatic TRMIMO sparse array are vertically arranged, and the number of transmitting and receiving array elements is P respectively t And P r The array element position is d t And d r ，θ d And theta s Representing the arrival angles of the direct wave and the reflected wave, respectively.
3. The sparse array-based meter-wave TRMIMO radar low-altitude target altimetry method of claim 1, wherein in step S1, the transmitted direct wave steering vector a t (θ d ) And the reflected wave guide vector a t (θ s ) The expression of (a) is:
wherein, theta d And theta s Representing the angle of arrival, P, of the direct and reflected waves, respectively t In order to determine the number of the transmitting array elements,
for the m-th transmitting array element position, λ is the signal wavelength, (. Alpha.) T Indicating transposition.
4. The sparse array-based meter-wave TRMIMO radar low-altitude target height measurement method according to claim 1, wherein in step S2, the expression of the composite steering vector is as follows:
wherein, a t (θ d ) And a t (θ s ) Respectively, a direct wave guide vector and a reflected wave guide vector (·) * Representing the matrix conjugate.
5. The sparse-array-based meter-wave TR MIMO radar low-altitude target elevation measurement method according to claim 1, wherein in step S3, the calculation formula of the received data is as follows:
wherein ω = [1 γ γ γ γ γ = 2 ] T ε is the energy normalization factor, P r In order to receive the number of array elements,
for the complex reflection coefficient of the target under different pulses, f d The Doppler frequency is W, and the noise is subjected to matched filtering and vectorization operation;
the calculation formula of the data covariance matrix is as follows:
wherein, Y is received data, (·) H Representing the matrix conjugate transpose, L represents the fast beat number.
6. The sparse array-based meter-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:
R U ＝U H R fb U
A U (θ)＝U H A(θ)
wherein, U is unitary matrix, when the dimension of U is odd,
when the dimension of U is an even number,
Π K a K x K switching matrix, in particular with 1 for the element on the anti-diagonal and 0 for the other elements K Is a unit array of K multiplied by K,
(·) H representing the matrix conjugate transpose, a (θ) composite steering vector.
7. The sparse array-based meter-wave TRMIMO radar low-altitude target height finding 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 composite steering vector and the data covariance matrix are respectively as follows:
wherein, the first and the second end of the pipe are connected with each other,det stands for determinant operation, trace is the trace-seeking operator, P a (θ)＝A(θ)(A H (θ)A(θ)) -1 A H (θ), R is a data covariance matrix, E n Noise subspace, I, obtained for eigenvalue decomposition of R P Is a P unit array H Representing a matrix conjugate transpose.
8. The sparse array-based meter-wave TRMIMO radar low-altitude target height finding 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 covariance matrix and the real-valued composite steering vector are respectively as follows:
where det represents determinant operation, trace is trace operator, I P Is a P unit array H Representing the conjugate transpose of the matrix, R U Is a real-valued covariance matrix, U n For real-valued covariance matrix R U The real noise subspace obtained by performing the feature decomposition,
A U (θ) is the real-valued composite steering vector.
9. The method according to claim 1, wherein step S4 further comprises searching two-dimensional spectral peaks of the generalized MUSIC algorithm and the maximum likelihood algorithm according to the incident angle θ of the direct wave d Incident angle theta with the reflected wave s The relation between the two is reduced to a step of one-dimensional search, and the incident angle theta of the direct wave is d Incident angle theta with reflected wave s The relationship between them is as follows:
θ s ＝-arctan(tanθ d +2h a /R)
wherein h is a The antenna erection height is defined, and R is the target distance.
10. The sparse array-based meter-wave TRMIMO radar low-altitude target height measurement method according to claim 1, wherein in step S5, the calculation formula of the target height data is as follows:
wherein, the first and the second end of the pipe are connected with each other,
for a target low elevation estimate, R is the distance of the target, h a The height of the antenna is set up.
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