CN114895268B - Aperture transition compensation method of distributed coherent radar - Google Patents

Abstract

The present invention discloses an aperture crossing compensation method for a distributed coherent radar, comprising: processing the echo signal received from the correction source direction to obtain a signal correlation matrix, and calculating the channel amplitude error; performing conjugate multiplication processing on the signal correlation matrix and the ideal steering vector autocorrelation matrix, extracting the phase error matrix, and extracting the system error matrix; calculating the phase error matrix and the array element position error matrix according to the relationship between the system error, the channel phase error, and the array element position error; calculating the receiving signal delay of different radar stations according to the target position and the array element position information, compensating the receiving signal after the system error correction, and realizing the full delay envelope correction processing of the signal; obtaining the phase compensation term, and performing phase compensation on the signal after the envelope correction. The present invention can utilize the correction source signal and the target signal received by each radar station to process the amplitude and phase error and aperture crossing problems of each array element, and realize the coherent synthesis of the array element receiving signal.

Description

A method for aperture transition compensation of distributed coherent radar

Technical Field

The invention belongs to the technical field of radar signal processing, and in particular relates to an aperture crossing compensation method for a distributed coherent radar.

Background technique

Distributed array radar is a radar that is arranged in a distributed array. The antenna array is split into multiple small-aperture sub-arrays and arranged in a dispersed manner. Without increasing the number of array elements, the physical aperture of the radar antenna array is expanded, thereby improving the radar detection performance.

For array antennas, the system error must be corrected before work. For the entire array radar system, the multi-channel transceiver channel contains multiple active devices, which often change with environmental conditions (such as temperature) and the age of the device, thus affecting the amplitude and phase characteristics of the entire transceiver channel. At the same time, due to the processing errors between different radars and other factors, the amplitude and phase errors of each radar channel will also be inconsistent, and these parts constitute the amplitude and phase errors. Due to the influence of factors such as antenna technology and installation skills, array radars will have array element position errors, which is mainly for short-range array radars. This type of position error can be ignored in most cases. When the array radar is relatively scattered and sparse, the position measurement error of the array element will be caused due to the undulating terrain; on the other hand, if the array radar is installed on a non-fixed platform, such as an aircraft, ship, or satellite, the relative position between the array elements is difficult to measure due to wind deformation, gravity deformation, platform vibration, and array installation errors. If the array elements of the entire radar array are installed on different moving platforms, position errors will be more inevitable. For occasions where the direction finding accuracy requirements are not high, traditional correction methods can meet the requirements. However, for high-precision angle measurement, it is necessary to study refined array system error correction methods. If the array error is not corrected, the antenna pattern characteristics will be seriously damaged, resulting in a decrease in antenna gain, a deterioration in sidelobe level, and a deterioration in beam pointing accuracy and angle measurement accuracy. Therefore, appropriate amplitude and phase correction must be provided to each channel to improve the angle measurement and beamforming performance.

When the radar works under broadband conditions, the aperture transit time brought by the array aperture will have a non-negligible impact, which will cause problems such as antenna beam pointing deviation, main lobe widening after pulse compression, and reduction of effective bandwidth, thus affecting the detection performance of the radar.

Since the physical aperture between dispersed radar arrays is large, the aperture transit time is greatly increased. When the aperture transit time is greater than the inverse of the signal bandwidth, aperture transit will occur. For distributed array radars, aperture transit is more likely to occur, which is an important issue affecting the application of distributed array radars.

Summary of the invention

In order to solve the above problems existing in the prior art, the present invention provides an aperture crossing compensation method for a distributed coherent radar. The technical problem to be solved by the present invention is achieved by the following technical solutions:

A distributed coherent radar aperture transition compensation method, the aperture transition compensation method comprising:

Step 1: The m-th radar station performs autocorrelation operation on the echo signals received from the N correction source directions in time division to obtain the signal correlation matrix R ^(k) , and obtains the channel amplitude error g _m of the m-th radar station according to the diagonal elements of the signal correlation matrix R ^(k) , m = 1, 2, ..., M;

Step 2: Substitute the autocorrelation matrix of the ideal steering vector a _d (θ _k ,φ _k ) into Perform a conjugate operation, multiply the conjugate operation result by the signal correlation matrix R ^(k) to obtain a phase error matrix W ^(k) , and extract a system error matrix ψ ^(k) from the phase error matrix W ^(k) ;

Step 3: Obtain the phase error matrix Φ ^{(k )} and the array element position error matrix [ΔX, ΔY, ΔZ] according to the system error matrix ψ (k), and obtain the amplitude and phase error correction matrix G _m of the mth radar station in combination with the estimated channel amplitude error g _m ;

Step 4: Obtain a received signal s _{m ′} (t) of the m-th radar station according to the amplitude-phase error correction matrix G _m and the received signal s _ref (t ₎ of the reference radar station, and compensate the received signal s _m (t) of the m-th radar station by an envelope compensation term W _p to obtain a compensated signal _{s m (} t)′;

Step 5: The compensated signal s _m (t)′ is subjected to total delay and phase compensation by a phase filter W _Broad to obtain an output signal s _{m_out} (t).

In one embodiment of the present invention, step 1 comprises:

Step 1.1, obtain the projection d _m (θ _k ,φ _k ) of the vector formed by the mth radar station and the origin in the direction of the incoming wave;

Step 1.2, obtaining an ideal steering vector a _d (θ _k , φ _k ) according to the projection d _m (θ _k , φ _k );

Step 1.3, obtain the array amplitude and phase error matrix Γ;

Step 1.4, obtaining a time delay error Δτ _km of the kth signal relative to a reference array element when the kth signal arrives at the mth radar station according to the position error of the mth radar station, wherein the reference array element is the first radar station;

Step 1.5, obtaining a steering vector error Δa(θ _k ,φ _k ) according to the time delay error Δτ _km ;

Step 1.6, obtaining an actual steering vector a(θ _k ,φ _k ) according to the ideal steering vector a _d (θ _k ,φ _k ), the array amplitude and phase error matrix Γ and the steering vector error Δa(θ _k ,φ _k );

Step 1.7, obtain the array output vector X(t) according to the system total amplitude and phase error Γ′, the observation noise A(θ,φ) of the mth radar station, the complex amplitude vector S(t) of the correction source signal and the noise vector N(t), where A(θ,φ)＝[ _ad ( _θ1 , _φ1 ), _ad ( _θ2 , _φ2 ),…, _ad ( _θk , _φk ),…, _ad ( _θN , _φN )], Γ′＝Γ·[Δa( _θ1 , _φ1 ),Δa( _θ2 , _φ2 ),…,Δa( _θk , _φk ),…,Δa( _θN , _φN )];

Step 1.8: According to The signal correlation matrix R ^(k) is obtained, where E[·] is a mean operation, H is a matrix conjugate transpose operation, _RS is a signal autocorrelation matrix, is the noise power;

Step 1.9: Obtain the channel amplitude error g _m of the mth radar station according to the diagonal elements of the signal correlation matrix R ^(k) .

In one embodiment of the present invention, the projection d _m (θ _k , φ _k ) is:

d _m (θ _k ,φ _k )＝x _m cosθ _k cosφ _k +y _m cosθ _k sinφ _k +z _m sinθ _k

φ _k is the azimuth angle, θ _k is the elevation angle, k = 1, 2, ... N, the coordinates of the mth radar station are (x _m , y _m , z _m );

The ideal steering vector a _d (θ _k , φ _k ) is:

Among them, λ is the wavelength, T is the matrix transpose operation, and j is

The array amplitude-phase error moment Γ is:

_gm is the channel amplitude error of the mth radar station, _Φm is the phase error of the mth radar station;

The time delay error Δτ _km is:

Among them, the position error of the mth radar station is (Δx _m , Δy _m , Δz _m ), and c is the propagation speed of the signal;

The steering vector error Δa(θ _k ,φ _k ) is:

The actual steering vector a(θ _k ,φ _k ) is:

a(θ _k ,φ _k )=Γ·Δa(θ _k ,φ _k )·a _d (θ _k ,φ _k )

The array output vector X(t) is:

X(t)＝Γ'·A(θ,φ)S(t)+N(t)

Wherein, t is the system time, X(t) = [ _x1 (t), _x2 (t), …, _xm (t), …, _xM (t)] ^T , _xm (t) is the signal received by the m-th radar station, S(t) is the complex amplitude vector of the correction source signal, S(t) = [ _s1 (t), _s2 (t), …, _sk (t), …, _sN (t)] ^T , _sk (t) is the complex envelope of the k-th signal source in space, N(t) is the noise vector, N(t) = [ _n1 (t), _n2 (t), …, _nm (t), …, _nM (t)] ^T , _nm (t) is the observation noise of the m-th radar station;

The signal correlation matrix R ^(k) is:

Where, σ ² is the power of the signal source incident from the direction (θ ₁ ,φ ₁ ) reaching the radar station;

The channel amplitude error _gm is:

Among them, R _mm is the diagonal element of the signal correlation matrix R ^(k) .

In one embodiment of the present invention, step 2 comprises:

Step 2.1: Substitute the autocorrelation matrix of the ideal steering vector a _d (θ _k ,φ _k ) into Perform a conjugate operation, multiply the conjugate operation result with the signal correlation matrix R ^(k) , and pass the 2π phase ambiguity factor Correction to obtain the phase error matrix W ^(k) ;

Step 2.2, extracting phase information Ψ ^{(k ) from the phase error matrix W (k} );

Step 2.3: Obtain a system error matrix ψ ^{(k) according to the first row elements of the phase information Ψ (k )} .

In one embodiment of the present invention, the phase error matrix W ^(k) is:

in, is the total phase error of the m-th radar at the k-th correction source, angle(·) represents the phase information. is the multiplication of the corresponding position elements, conj(·) is the conjugate operation, β ^(k) is a column vector composed of the diagonal elements of Γ ^′(k) in order, Γ ^′(k) is the K-th element of the total amplitude-phase error Γ′ of the system, is the signal power, E is an M-dimensional all-1 matrix, and I is an M-dimensional identity matrix;

The phase information Ψ ^(k) is:

Where Ψ _1j ^(k) is the jth element in the first row of the matrix H ( ^k) formed by the upper triangular part of the phase error matrix W ^(k) , is the total phase error of the jth radar at the kth correction source, is an integer, is the 2π phase ambiguity correction term caused by the phase cycle;

The j-th element of the system error matrix ψ ^(k) is:

Among them, ΔΨ _1j ⁽ⁿ⁾ = Ψ _1j ⁽ⁿ⁺¹⁾ - Ψ _1j ⁽¹⁾ , n=1,2,3,...,N-1, k=n+1.

In one embodiment of the present invention, step 3 comprises:

Step 3.1: Substitute the system error matrix ψ ^(k) into The obtained result is the non-all-zero row matrix ψ' ^(k) of the system error of the kth correction source;

Step 3.2, obtain the difference Δψ'(k') of the system error non-zero row matrix according to the system error non-zero row matrix ψ' ⁽¹⁾ of the first correction source and the system error non-zero row matrix ψ'^{(k'+1) of} the k'th correction source;

Step 3.3, based on the least squares method, obtain the array element position error matrix [ΔX, ΔY, ΔZ] according to the difference Δψ'^(k') of the non-zero row matrix of the system error;

Step 3.4, obtaining the phase error of each radar station according to the system error non-all-zero row matrix ψ' ^(k) and the array element position error matrix [ΔX, ΔY, ΔZ];

Step 3.5: Obtain the amplitude and phase error correction matrix G _m of the m th radar station according to the phase error Φ _m and the channel amplitude error g _m of the m th radar station.

In one embodiment of the present invention, the system error matrix ψ ^(k) is substituted into The result is:

The system error non-all-zero row matrix ψ' ^(k) is:

The difference Δψ'^(k') of the non-zero row matrix of the system error is:

Δψ'^(k')=ψ' ⁽¹⁾ -ψ'^(k'+1)

The array element position error matrix [ΔX, ΔY, ΔZ] is:

The phase error of each radar station is:

The amplitude and phase error correction matrix _Gm is:

In one embodiment of the present invention, the transmission signal s _t (t) of the radar station is:

Where a(t) is the complex envelope of the signal, and f _c is the carrier frequency of the signal;

The received signal s _ref (t) of the reference radar station is:

τ _r =2R/c, c is the electromagnetic wave propagation speed, R is the distance of the target relative to the reference radar station; the received signal s _m '(t) of the mth radar station is:

Among them, τ _m =L _m (θ,φ)/c, L _m (θ,φ) = x _m cosθcosφ+y _m cosθsinφ+z _m sinθ;

The received signal s _m (t) of the m-th radar station is:

The compensated signal s _m (t)′ is:

in,

In one embodiment of the present invention, the phase filter W _Broad is:

The output signal s _{m_out} (t) is:

Beneficial effects of the present invention:

The aperture crossing compensation method of the present invention utilizes the prior information of the signal and the target position under the premise of the system error correction of each radar station to complete the complete correction of the received signal envelope movement and the compensation processing of the signal phase, thereby realizing the coherent processing of each received signal. The aperture crossing compensation method of the present invention is suitable for the application of broadband signal coherent synthesis processing of distributed radar.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a schematic flow chart of an aperture crossing compensation method for a distributed coherent radar provided in an embodiment of the present invention;

FIG2 is a flow chart of an implementation method of an aperture crossing compensation method for a distributed coherent radar provided in an embodiment of the present invention;

FIG3a is a schematic diagram of a coordinate system constructed with three radar stations provided in an embodiment of the present invention;

FIG3b is a schematic diagram of the arrangement of a three-station simulation example provided by an embodiment of the present invention;

FIG4a is a schematic diagram of channel amplitude errors between channels of a distributed array provided by an embodiment of the present invention;

FIG4b is a schematic diagram of phase errors between channels of a distributed array provided by an embodiment of the present invention;

FIG4c is a schematic diagram of array element position errors of each sub-array of a distributed array provided by an embodiment of the present invention;

FIG5a is a schematic diagram of a curve showing a change in amplitude standard deviation of amplitude and phase errors with a signal-to-noise ratio according to an embodiment of the present invention;

FIG5b is a schematic diagram of a curve showing a change in phase standard deviation of amplitude and phase errors versus signal-to-noise ratio provided by an embodiment of the present invention;

FIG5c is a schematic diagram of a curve showing a change in the position standard deviation of the position error in the x-axis direction as a function of the signal-to-noise ratio provided by an embodiment of the present invention;

FIG5d is a schematic diagram of a curve showing a change in the position standard deviation in the y-axis direction of the position error as a function of the signal-to-noise ratio provided by an embodiment of the present invention;

FIG5e is a schematic diagram of a curve showing a change in the _z -axis position standard deviation of the position error as a function of the signal-to-noise ratio provided by an embodiment of the present invention;

6a is a schematic diagram of the maximum distance difference between the echo received by the distributed array radar to three stations provided by an embodiment of the present invention;

FIG6b is a schematic diagram of the azimuth and elevation angle ranges of the distributed array radar aperture crossing phenomenon provided by an embodiment of the present invention;

FIG7a is a schematic diagram of the average distance loss caused by performing only phase compensation when aperture crossing occurs according to an embodiment of the present invention;

FIG7b is a schematic diagram of average distance loss after being processed by the method of the present invention when aperture crossing phenomenon exists, provided by an embodiment of the present invention;

FIG7c is a schematic diagram of average distance loss after integer delay and phase compensation when aperture crossing occurs according to an embodiment of the present invention;

7d is a schematic diagram of curves showing changes in the average distance loss versus the signal-to-noise ratio for three methods when the incoming wave direction is 30° in azimuth and 30° in elevation, provided by an embodiment of the present invention.

Detailed ways

The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

Please refer to Figures 1 and 2. Figure 1 is a schematic flow chart of an aperture transition compensation method for a distributed coherent radar provided by an embodiment of the present invention, and Figure 2 is an implementation flow chart of an aperture transition compensation method for a distributed coherent radar provided by an embodiment of the present invention. An embodiment of the present invention provides an aperture transition compensation method for a distributed coherent radar, and the aperture transition compensation method includes:

Step 1: The m-th radar station performs autocorrelation operation on the echo signals received from the N correction source directions in time division to obtain the signal correlation matrix R ^(k) , and obtains the channel amplitude error g _m of the m-th radar station according to the diagonal elements of the signal correlation matrix R ^(k) , where m = 1, 2, ..., M.

Specifically, there are M radar stations in total. Each radar station performs autocorrelation operation on the echo signals received from N correction source directions in time division to obtain the signal correlation matrix R ^(k) . The diagonal element characteristics are extracted to calculate the relative channel amplitude error of each station (taking m=1 radar station as a reference): g ₁ , g ₂ , …, g _m , …, g _M , which is used for channel amplitude error correction.

In a specific embodiment, step 1 may include steps 1.1 to 1.9, wherein:

Step 1.1. Obtain the projection d _m (θ _k ,φ _k ) of the vector formed by the m-th radar station and the origin in the direction of the incoming wave.

Specifically, assume that M radar stations form a uniform linear array, and each radar station is composed of a planar array formed by a number of array elements. The coordinates of the mth radar station in a given coordinate system are ( _xm , _ym , _zm ), m = 1, 2, …, M, where ( _x1 , _y1 , _z1 ) = (0, 0, 0), and N independent narrow-band point correction sources are incident from the far field in the form of plane waves (wavelength is λ). The azimuth angle of the kth correction source in the direction of the incoming wave is _φk and the elevation angle is _θk , k = 1, 2, …N. Then the direction vector in this direction is a( _θk , _φk ) = [ _{cosθkcosφk , cosθksinφk , sinθk} ] ^T , and the projection _dm ( _θk , _φk ) of the vector formed by each radar station and the origin in this direction is:

d _m (θ _k ,φ _k )＝x _m cosθ _k cosφ _k +y _m cosθ _k sinφ _k +z _m sinθ _k

Where T is the matrix transpose operation.

Step 1.2: Obtain the ideal steering vector a _d (θ _k , φ _k ) according to the projection d _m (θ _k , φ _k ).

Specifically, the ideal steering vector a _d (θ _k ,φ _k ) of the array radar can be expressed as:

Among them, j is

Step 1.3: Obtain the array amplitude and phase error matrix Γ.

Specifically, the array amplitude and phase error matrix Γ is expressed as the following diagonal matrix:

Wherein, g _m is the channel amplitude error of the mth radar station, Φ _m is the phase error of the mth radar station, which is based on the amplitude and phase errors of the first radar station (g ₁ =1, Φ ₁ =0).

Step 1.4: Obtain the time delay error Δτ _km of the kth signal relative to the reference array element when it arrives at the mth radar station according to the position error of the mth radar station. The reference array element is the first radar station.

Specifically, assuming that the position error of the radar station is (Δx _m , Δy _m , Δz _m ), where the first radar station is still used as the reference radar station, that is, (Δx ₁ , Δy ₁ , Δz ₁ ) = (0, 0, 0), the time delay error Δτ _km caused by the kth signal arriving at the mth radar station relative to the reference radar station can be expressed as:

Where c is the propagation speed of the signal.

Step 1.5: Obtain the steering vector error Δa(θ _k ,φ _k ) according to the time delay error Δτ _km . The steering vector error Δa(θ _k ,φ _k ) is:

Step 1.6: Obtain the actual steering vector a(θ _k ,φ _k ) based on the ideal steering vector a _d (θ _k ,φ _k ), the array amplitude and phase error matrix Γ and the steering vector error Δa(θ _k ,φ _k ).

Specifically, the actual steering vector of the kth signal after being affected by the array amplitude and phase error Γ and the array element position error becomes a(θ _k ,φ _k ) as follows:

a(θ _k ,φ _k )=Γ·Δa(θ _k ,φ _k )·a _d (θ _k ,φ _k )

Among them, · is the dot product, that is, the corresponding elements of the two matrices are multiplied.

Step 1.7. Obtain the array output vector X(t) based on the system total amplitude and phase error Γ′, the observation noise A(θ, φ) of the mth radar station, the complex amplitude vector S(t) of the correction source signal, and the noise vector N(t), where A(θ, φ) = [ _ad (θ ₁ , φ ₁ ), _ad (θ ₂ , φ ₂ ),…, _ad (θ _k ,φ _k ),…, _ad (θ _N ,φ _N )], Γ′ = Γ·[Δa(θ ₁ ,φ ₁ ),Δa(θ ₂ ,φ ₂ ),…,Δa(θ _k ,φ _k ),…,Δa(θ _N ,φ _N )].

Specifically, the array output vector X(t) is:

X(t)＝Γ ^' ·A(θ,φ)S(t)+N(t)

Where t is the system time, X(t) = [ _x1 (t), _x2 (t),…, _xm (t),…, _xM (t)] ^T , _xm (t) is the signal received by the m-th radar station, S(t) is the complex amplitude vector of the correction source signal, S(t) = [ _s1 (t), _s2 (t),…, _sk (t),…, _sN (t)] ^T , _sk (t) is the complex envelope of the k-th signal source in space, N(t) is the noise vector, N(t) = [ _n1 (t), _n2 (t),…, _nm (t),…, _nM (t)] ^T , _nm (t) is the observation noise of the m-th radar station, and A(θ, φ) is the array flow type, which is related to the signal incident angle and array arrangement.

Step 1.8, according to The signal correlation matrix R ^(k) is obtained, where E[·] is a mean operation, H is a matrix conjugate transpose operation, _RS is a signal autocorrelation matrix, is the noise power;.

Specifically, according to the formula The signal correlation matrix R ^(k) of the array at these N correction positions is obtained as follows:

Where σ ² is the power of the signal source incident from the direction of (θ ₁ ,φ ₁ ) reaching the radar station. The radar position error will affect the phase of the received signal but will not affect the radar gain.

Step 1.9: Obtain the channel amplitude error g _m of the mth radar station according to the diagonal elements of the signal correlation matrix R ^(k) .

Specifically, since the diagonal part of R ^(k) does not contain phase information, the radar channel amplitude error can be directly estimated as:

Where R _mm is the diagonal element of the signal correlation matrix R ^(k) .

Step 2: Substitute the autocorrelation matrix of the ideal steering vector a _d (θ _k ,φ _k ) into A conjugate operation is performed, and the conjugate operation result is multiplied by the signal correlation matrix R ^(k) to obtain a phase error matrix W ^(k) , and a system error matrix ψ ^(k) is extracted from the phase error matrix W ^(k) .

Specifically, the autocorrelation matrix of the ideal steering vector a _d (θ _k , φ _k ) of the distributed radar station is The conjugate operation is performed and the result is multiplied with the signal correlation matrix to obtain the phase error matrix W ^(k) , and then the system error matrix ψ ^(k) is extracted for the estimation of channel phase error and array element position error.

In a specific embodiment, step 2 may include steps 2.1 to 2.3, wherein:

Step 2.1: Substitute the autocorrelation matrix of the ideal steering vector a _d (θ _k ,φ _k ) into Perform conjugate operation, multiply the conjugate operation result with the signal correlation matrix R ^(k) , and pass the 2π phase ambiguity factor Correction is performed to obtain the phase error matrix W ^(k) .

Specifically, the total amplitude and phase error vector Γ′ of the system can be obtained:

in, is the total phase error of the amplitude error and the position error.

For the total phase information, angle(R _ij ^(k) )(angle(·) means taking its phase information) is composed of the phase error, position error and delay of the signal reaching the i-th and j-th radar stations, so the autocorrelation matrix is constructed first Eliminate the phase effect caused by the delay of the signal reaching the radar station and use a 2π phase ambiguity factor Correction, get the radar station phase error matrix W ^(k) :

Take the upper triangular part to form the matrix H ^(k) :

in,

in, is the total phase error of the mth radar at the kth correction source, is the multiplication of the corresponding position elements, conj(·) is the conjugate operation, β ^(k) is the column vector composed of the diagonal elements of Γ ^′(k) in order, Γ ^′(k) is the Kth element of the total amplitude and phase error Γ′ of the system, is the signal power, E is an M-dimensional all-1 matrix, and I is an M-dimensional identity matrix.

Step 2.2: Extract phase information Ψ ^(k) from the phase error matrix W ^(k) . The phase information Ψ ^(k) is:

Depend on It can be seen that:

Where Ψ _1j ^(k) is the first row of the matrix H ^(k) formed by the upper triangular part of the phase error matrix W ^(k) , is the total phase error of the jth radar at the kth correction source, the total phase error It can be obtained from the first row ψ ( ^k) of Ψ ( ^k ) after 2π ambiguity correction, where is an integer, is the 2π phase ambiguity correction term caused by the phase period.

Step 2.3: Obtain the system error matrix ψ ^(k) according to the first row elements of the phase information Ψ ^(k) . The j-th element of the system error matrix ψ ^(k) is:

Among them, ΔΨ _1j ⁽ⁿ⁾ = Ψ _1j ⁽ⁿ⁺¹⁾ - Ψ _1j ⁽¹⁾ , n=1,2,3,...,N-1, k=n+1.

Step 3: Obtain the phase error matrix Φ ^{(k )} and the array element position error matrix [ΔX, ΔY, ΔZ] according to the system error matrix ψ (k), and obtain the amplitude and phase error correction matrix G _m of the mth radar station in combination with the estimated channel amplitude error g _m .

Specifically, according to the relationship between the total system error, the channel phase error and the array element position error, the system error matrix ψ ^(k) is used to obtain the phase error matrix Φ ^(k) and the array element position error matrix [ΔX, ΔY, ΔZ]. Combined with the estimated channel amplitude error g _m , the amplitude and phase errors of the radar system are corrected.

In a specific embodiment, step 3 may include steps 3.1 to 3.5, wherein:

Step 3.1: Substitute the system error matrix ψ ^(k) into The obtained result is the non-all-zero row matrix ψ' ^(k) of the system error of the kth correction source.

Specifically, substitute the system error matrix ψ ^(k) into have to

Right now:

Therefore, the non-all-zero row matrix of the system error ψ' ^(k) is:

Step 3.2: Obtain the difference Δψ'(k') of the system error non-zero row matrix according to the system error non-zero row matrix ψ' ⁽¹⁾ of the first correction source and the system error non-zero row matrix ψ' ^{( k'+1)} of the k'th correction source, where k'=1, 2, N-1.

Specifically, using the above relationship obtained from different correction source data, let:

Δψ'^(k')=ψ' ⁽¹⁾ -ψ'^(k'+1) .

Step 3.3: Based on the least squares method, the array element position error matrix [ΔX, ΔY, ΔZ] is obtained according to the difference Δψ'^(k') of the non-zero row matrix of the system error.

specifically:

When N time-sharing co-frequency narrowband correction sources are known, we can obtain:

Solving the above equation using the least squares method yields the position error:

Where, C ⁺ is the generalized inverse of C, C ⁺ = C ^H ·(C·C ^H ) ^-1 ; in actual processing, And their angular difference should be as large as possible, requiring rank(C)=3. If the difference between θ _k and φ _k is very small, the two rows of matrix C will be nearly correlated. When the generalized inverse is calculated, the characteristics of the solution will be very poor, resulting in a large error in the calculated coordinates [ΔX, ΔY, ΔZ].

Step 3.4: Obtain the phase error of each radar station based on the system error non-all-zero row matrix ψ' ^(k) and the array element position error matrix [ΔX, ΔY, ΔZ].

Specifically, substitute [ΔX, ΔY, ΔZ] into The phase error of each radar station can be obtained as:

The radar amplitude, phase and position error parameters thus obtained are used to correct the radar array.

Step 3.5: Obtain the amplitude and phase error correction matrix G _m of the m th radar station according to the phase error Φ _m and the channel amplitude error g _m of the m th radar station.

Specifically, when the azimuth angle of the incoming wave direction is φ and the elevation angle is θ, the amplitude and phase error correction matrix _Gm of the mth radar station is:

When the radar station receives the signal, the echo signal of each radar station is multiplied by its respective amplitude and phase error correction matrix, thus completing the amplitude and phase error correction.

Step 4: Obtain the received signal s _{m ′} (t) of the m-th radar station according to the amplitude and phase error correction matrix G _m and the received signal s _ref (t ₎ of the reference radar station, and compensate the radar station received signal s _m (t) by the envelope compensation term W _p to obtain the compensated signal _{s m (} t)′.

In this embodiment, according to the a priori target position and the corrected radar station position information, the received signal delay τ _m of different radar stations is obtained, and the signal envelope compensation coefficient W _p of each station is calculated to compensate the received signal after the system error correction, so as to realize the full delay envelope correction processing of the signal.

Specifically, when the azimuth angle of the incoming wave direction is φ and the elevation angle is θ, the direction vector of this direction is a _d (θ, φ) = [cosθcosφ, cosθsinφ, sinθ], and the projection of the vector formed by the radar station and the origin on this direction vector is:

L _m (θ,φ)＝x _m cosθcosφ+y _m cosθsinφ+z _m sinθ

Then, on this direction vector, the path difference between the mth radar station and the m'th radar station can be written as |L _m' (θ,φ)-L _m (θ,φ)|, where the maximum value is:

D _max (θ,φ)＝max{|L _m' (θ,φ)-L _m (θ,φ)|},m,m'＝1,2,…,M

Then, the aperture crossing phenomenon will occur when D _max (θ, φ)>c/B, where c is the propagation speed of electromagnetic waves and B is the signal bandwidth.

Assume the radar transmission signal is s _t (t), we have:

The signal complex envelope a(t) is a baseband linear frequency modulation sub-pulse with a bandwidth of B, a pulse width of T, and a modulation frequency of μ = B/T, that is, is a rectangular function with a pulse width of T, which can be expressed as:

Assuming that the target is a single scattering point, if the distance of the target relative to the reference radar station is R, then the corresponding delay is:

τ _r =2R/c

Then let the received signal of the reference radar station be s _ref (t), we have:

The envelope delay of the received signal at the mth radar station relative to the received signal at the reference radar station is:

τ _m =L _m (θ, φ)/c

Then let the received signal of the mth radar station be s _m '(t), then we have:

When the time corresponding to the radial distance R is taken as the reference point, the signal received by the mth radar station is in the form of:

Among them, μ is the signal modulation frequency, rect(·) is the rectangular window function; what is related to the envelope movement is Because it is related to both τ _m and t; It is just a range window and has no effect on the phase. The shift of the range window may cause 1 to 2 sampling points to fail to participate in the coherent accumulation. However, a linear frequency modulation pulse is always obtained by many sampling points. The shift of the range window has little effect, so this item can be ignored. In the processing of envelope movement, what needs to be compensated is It can be compensated by designing the envelope compensation term _Wp , which is as follows:

The signal form after envelope compensation is:

Step 5: After the compensated signal s _m (t)′ is fully delayed and phase compensated by the phase filter W _Broad , an output signal s _{m_out} (t) is obtained.

According to the transmission signal, radar station and target information, the phase compensation term required for the coherence of different radar stations is obtained, and its conjugate is taken as the phase filter W _Broad . After phase compensation processing, the signal after envelope correction is subjected to matched filtering and coherent synthesis processing to extract the peak amplitude information.

In phase compensation, the term to be compensated is Therefore, the signal after matched filtering can be filtered through the phase filter W _Broad to achieve phase compensation. The response of the filter is:

At this time, the output signal after full delay and phase compensation can be expressed as:

The aperture crossing problem has been eliminated, and the coherence between the signals of each array element has been achieved. After that, pulse compression and coherent synthesis are performed, and the peak amplitude information Ap is extracted, and the performance comparison between different algorithms is performed. The performance improvement of the method of the present invention can be seen by comparing the accumulated gain of the existing method of compensating only the phase and the method of integer delay and compensating the phase.

Simulation

In order to prove the effectiveness of the present invention, the following simulation comparison test is used to further illustrate it.

(1) Simulation conditions:

As shown in Fig. 3b, the distributed radar array includes three radar stations. The three radars are arranged in an equidistant linear array with a spacing of d = 30m, that is, the ideal positions of the three radars are (0, 0, 0), (0, 30, 0), and (0, 60, 0), respectively. The waveform parameters of the signal are set as follows: carrier frequency f _c = 2.31GHz, pulse bandwidth B = 100MHz, time width T _p = 10us, radar amplitude and phase errors are: g _i is 0 to 1dB, Φ _i is -5 to 5 degrees; the radar position error is evenly distributed in the range of 0.5cm to 3cm; the signal is a linear frequency modulation signal with a baseband frequency of 2.31GHZ and a signal-to-noise ratio of 20dB. The directions of the waves from the four co-frequency narrowband correction sources are (10°, -5°), (30°, 40°), (60°, -40°), and (80°, 60°). 3a is a schematic diagram of a coordinate system constructed with three radar stations in the present invention, wherein the angle φ between the projection vector of the incoming wave vector onto the xy plane and the x-axis is defined as the azimuth angle, and the angle θ between the incoming wave vector and the xy plane is defined as the elevation angle.

(2) Simulation content and results:

Simulation 1, the amplitude, phase and position diagram of each array element when the distributed radar array system has amplitude and phase errors and array element position errors. The results are shown in Figures 4a, 4b and 4c. It can be seen that when there is a system error, there are errors in the amplitude and phase between the array elements, and thus the received data cannot be coherently synthesized. At the same time, the error in the array element position will also affect the phase of each array element.

Simulation 2, the simulation involves the amplitude and phase error correction method. After 10,000 Monte Carlo experiments, the average is taken. The results are shown in Figures 5a, 5b, 5c, 5d, and 5e. It can be seen that with the improvement of the signal-to-noise ratio, the performance of the amplitude and phase error correction method used is better, and the estimation of the amplitude error, phase error, and position error of each array element is more accurate.

Simulation 3, a schematic diagram of the maximum distance difference of the distributed radar array obtained by the method of the present invention and a schematic diagram of the azimuth and elevation angle range when the aperture crossing exists are simulated. The results are shown in Figures 6a and 6b. It can be seen that the aperture crossing phenomenon does not exist at every angle, but only occurs when the maximum spacing between array elements and the azimuth and elevation angles meet certain conditions.

Simulation 4 is a comparison chart of the processing results of the distributed array radar aperture crossing problem obtained by simulating the method of the present invention. The results are shown in Figures 7a, 7b, 7c, and 7d. The average processing loss of the received signal distance after processing by the method of the present invention is compared with the average loss of the distance after processing by the phase compensation method only and the integer delay + phase compensation method. It can be seen that the average loss of the distance caused by the processing by the present method is the smallest, and the coherent synthesis of the array element receiving signal can be better realized.

In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims (7)

1. An aperture transition compensation method of a distributed coherent radar, which is characterized by comprising the following steps:

Step 1, an mth radar station performs autocorrelation operation on echo signals received from N correction source directions in a time-sharing manner to obtain a signal correlation matrix R ^(k), so as to obtain a channel amplitude error g _m of the mth radar station according to diagonal elements of the signal correlation matrix R ^(k), wherein m=1, 2, … and M;

step 2, autocorrelation matrix of ideal steering vector a _d(θ_k,φ_k) Performing conjugate operation, and multiplying the conjugate operation result with the signal correlation matrix R ^(k) to obtain a phase error matrix W ^(k) and extracting a system error matrix psi ^(k) from the phase error matrix W ^(k);

Step 3, obtaining a phase error matrix phi ^(k) and an array element position error matrix [ delta X, delta Y, delta Z ] according to the system error matrix phi ^(k), and obtaining an amplitude-phase error correction matrix G _m of the mth radar station by combining the estimated channel amplitude error G _m;

Step 4, obtaining a receiving signal s _m ' (t) of the mth radar station according to the amplitude-phase error correction matrix Gm and a receiving signal s _ref (t) of the reference radar station, so as to obtain a receiving signal s _m (t) of the mth radar station according to the receiving signal s _m ' (t) and the amplitude-phase error correction matrix G _m, and compensating the receiving signal s _m (t) of the radar station through an envelope compensation term W _p to obtain a compensated signal s _m (t) ';

Step 5, the compensated signal s _m (t)' is subjected to full delay and phase compensation by a phase filter W _Broad to obtain an output signal s _{m_out} (t);

The step 2 comprises the following steps:

Step 2.1, autocorrelation matrix of ideal steering vector a _d(θ_k,φ_k) Performing conjugate operation, multiplying the conjugate operation result with the signal correlation matrix R ^(k), and performing 2 pi phase fuzzy factorCorrecting to obtain a phase error matrix W ^(k);

Step 2.2, extracting phase information ψ ^(k) from the phase error matrix W ^(k);

Step 2.3, obtaining a system error matrix ψ ^(k) according to the first row element of the phase information ψ ^(k);

the phase error matrix W ^(k) is:

Wherein, For the total phase error of the mth radar at the kth correction source, angle (·) represents taking the phase information thereof, multiplying the corresponding position elements, conj (·) is conjugate operation, β ^(k) is a column vector composed of diagonal elements of Γ ' ^(k) in order, Γ ' ^(k) is the kth element of the total amplitude phase error Γ ' of the system,E is an M-dimensional full 1 matrix, and I is an M-dimensional identity matrix;

The phase information ψ ^(k) is:

Wherein ψ _1j ^(k) is the first row j-th element of matrix H ^(k) which is the upper triangular part of the phase error matrix W ^(k), The total phase error of the source at the kth correction for the jth radar, Is an integer of the number of the times,A2 pi phase ambiguity correction term caused by the phase period;

the j-th element of the systematic error matrix ψ ^(k) is:

Where Δψ _1j ⁽ⁿ⁾＝Ψ_1j ⁽ⁿ⁺¹⁾-Ψ_1j ⁽¹⁾, n=1, 2,3, …, N-1, k=n+1.

2. The method for compensating for aperture transition of distributed coherent radar according to claim 1, wherein said step 1 comprises:

step 1.1, obtaining projection d _m(θ_k,φ_k of a vector formed by an mth radar station and an origin in an incoming wave direction);

Step 1.2, obtaining an ideal guiding vector a _d(θ_k,φ_k) according to the projection d _m(θ_k,φ_k);

Step 1.3, acquiring an array amplitude-phase error matrix Γ;

Step 1.4, obtaining a delay error delta tau _km of a kth signal reaching an mth radar station relative to a reference array element according to the position error of the mth radar station, wherein the reference array element is the first radar station;

step 1.5, obtaining a guiding vector error delta a (theta _k,φ_k) according to the time delay error delta tau _km;

Step 1.6, obtaining an actual guiding vector a (theta _k,φ_k) according to the ideal guiding vector a _d(θ_k,φ_k), the array amplitude-phase error matrix Γ and the guiding vector error delta a (theta _k,φ_k);

Step 1.7, obtaining an array output vector X (t) according to the total amplitude-phase error Γ' of the system, the observation noise A (theta, phi) of the mth radar station, the complex amplitude vector S (t) of the corrected source signal and the noise vector N (t), wherein ,A(θ,φ)＝[a_d(θ₁,φ₁),a_d(θ₂,φ₂),…,a_d(θ_k,φ_k),…,a_d(θ_N,φ_N)],Γ′＝Γ·[Δa(θ₁,φ₁),Δa(θ₂,φ₂),…,Δa(θ_k,φ_k),…,Δa(θ_N,φ_N)];

Step 1.8 according toObtaining the signal correlation matrix R ^(k), wherein E is mean value operation, H is matrix conjugate transpose operation, R _S is signal autocorrelation matrix,Is the noise power;

and step 1.9, obtaining a channel amplitude error g _m of the mth radar station according to diagonal elements of the signal correlation matrix R ^(k).

3. The method of aperture transition compensation for a distributed coherent radar according to claim 2, wherein the projection d _m(θ_k,φ_k) is:

d_m(θ_k,φ_k)＝x_mcosθ_kcosφ_k+y_mcosθ_ksinφ_k+z_msinθ_k

Wherein phi _k is azimuth angle, theta _k is pitch angle, k=1, 2, … N, and the coordinate of the mth radar station is (x _m,y_m,z_m);

The ideal steering vector a _d(θ_k,φ_k) is:

Wherein lambda is wavelength, T is matrix transpose operation, j is

The array amplitude-phase error moment Γ is:

Wherein g _m is the channel amplitude error of the mth radar station, and Φ _m is the phase error of the mth radar station;

the delay error Δτ _km is:

the position error of the mth radar station is (delta x _m,Δy_m,Δz_m), and c is the propagation speed of the signal;

the steering vector error Δa (θ _k,φ_k) is:

The actual guiding vector a (θ _k,φ_k) is:

a(θ_k,φ_k)＝Γ·Δa(θ_k,φ_k)·a_d(θ_k,φ_k)

Wherein, is a dot product;

the array output vector X (t) is:

X(t)＝Γ'·A(θ,φ)S(t)+N(t)

Wherein t is the system time, X (t) = [ X ₁(t),x₂(t),…,x_m(t),…,x_M(t)]^T,x_m (t) is the signal received by the mth radar station, S (t) is the complex amplitude vector of the correction source signal, S (t) = [ S ₁(t),s₂(t),…,s_k(t),…,s_N(t)]^T,s_k (t) is the complex envelope of the kth signal source in space, N (t) is the noise vector, and N (t) = [ N ₁(t),n₂(t),…,n_m(t),…,n_M(t)]^T,n_m (t) is the observation noise of the mth radar station;

The signal correlation matrix R ^(k) is:

wherein σ ² is the power of the signal source incident from the (θ ₁,φ₁) direction to the radar station;

the channel amplitude error g _m is:

Wherein R _mm is a diagonal element of the signal correlation matrix R ^(k).

4. The method for compensating for aperture transitions of a distributed coherent radar according to claim 3, wherein said step 3 comprises:

step 3.1, substituting the system error matrix psi ^(k) into the system error matrix Obtaining a system error non-all-zero row matrix phi' ^(k) of a kth correction source according to the obtained result;

step 3.2, obtaining a difference value delta phi '^(k') of the system error non-zero row matrix according to the system error non-zero row matrix phi' ⁽¹⁾ of the first correction source and the system error non-zero row matrix phi '^(k'+1) of the kth correction source, wherein k' =1, 2, n-1;

Step 3.3, obtaining an array element position error matrix [ delta X, delta Y, delta Z ] according to a difference delta phi' ^(k') of a system error non-zero row matrix based on a least square method;

Step 3.4, obtaining the phase error of each radar station according to the system error non-all-zero row matrix psi' ^(k) and the array element position error matrix [ delta X, delta Y, delta Z ];

And 3.5, obtaining an amplitude-phase error correction matrix G _m of the mth radar station according to the phase error phi _m and the channel amplitude error G _m of the mth radar station.

5. The method for compensating for aperture transition of distributed coherent radar according to claim 4, wherein said systematic error matrix ψ ^(k) is substituted intoThe results obtained were:

Namely:

the systematic error non-all-zero row matrix ψ' ^(k) is:

the difference Δψ' ^(k') of the system error non-zero row matrix is:

Δψ'^(k'⁾＝ψ'⁽¹⁾-ψ'^(k'+1)

the array element position error matrix [ delta X, delta Y, delta Z ] is as follows:

the phase errors of the individual radar stations are:

the amplitude and phase error correction matrix G _m is:

6. The method of claim 5, wherein the radar station's transmit signal s _t (t) is:

Wherein a (t) is a signal complex envelope, and f _c is a signal carrier frequency;

the received signal s _ref (t) of the reference radar station is:

Where τ _r =2r/c, c is the electromagnetic wave propagation speed, R is the distance of the target relative to the reference radar station;

The reception signal s _m' (t) of the mth radar station is:

Wherein τ _m＝L_m(θ,φ)/c,L_m(θ,φ)＝x_mcosθcosφ+y_mcosθsinφ+z_m sin θ;

The receiving signal s _m (t) of the mth radar station is:

wherein mu is the signal modulation frequency, and rect (·) is a rectangular window function;

the compensated signal s _m (t)' is:

Wherein,

7. The method of claim 6, wherein the phase filter W _Broad is:

The output signal s _{m_out} (t) is: