CN104375115B - Polarization sensitive array based non-circular signal DOA and polarization parameter joint estimation method - Google Patents

Abstract

The invention belongs to the technical field of array signal direction finding and particularly relates to a polarization sensitive array based non-circular signal DOA and polarization parameter joint estimation method. Compared with most of methods in the field, the polarization sensitive array based non-circular signal DOA and polarization parameter joint estimation method can be used for the more general situation that circular signals and non-circular signals are mixed. By establishing a planar dual-polarization sensitive array based long vector receive data model and utilizing the non-circular characteristic of the signals, the circular signals and the non-circular signals in mixed incidence signal are separated to be sequentially estimated, mutual interference of two types of signals is reduced, and accordingly the performance of estimating various signals is improved. In addition, the four-dimensional searching process of a spectral function is reduced to be two-dimensional searching process for solving the problem of huge operation amount, the operation times of the method are decreased, and the estimating accuracy is not reduced. The polarization sensitive array based non-circular signal DOA and polarization parameter joint estimation method successively fills up the blank of polarization sensitive array based methods for non-circular signal direction finding.

Description

Not rounded signal DOA and polarization parameter combined estimation method under polarization sensitive array

Technical field

The invention belongs to array signal direction finding technology field is and in particular to not rounded signal DOA under a kind of polarization sensitive array With polarization parameter combined estimation method, it is to be mixed with not rounded signal based on the round signal that is applied to of planar bipolar sensitization array DOA under condition of incidence and polarization parameter combined estimation method.

Background technology

If it is possible to reasonably in the estimation problem to signal direction of arrival (direction of arrival, DOA) Using some unique characteristics information of incoming wave signal, the such as not rounded characteristic of signal, polarization characteristic etc. is it is possible to extra by these Information improve algorithm estimation performance.

The not rounded characteristic of signal refers to that the statistical property of signal does not have rotational invariance, in Array Signal Processing problem In, that is, the pseudocovariance matrix being equivalent to signal is not zero.Not rounded signal is widely used in Modern Communication System, such as The DOA of the modulated signals such as BPSK, MSK, GMSK, therefore not rounded signal estimates that having become one of array signal process technique grinds Study carefully focus.

Meanwhile, spatial electromagnetic ripple signal, for aerial array in addition to DOA information, also has polarization of electromagnetic wave Characteristic, it describes the electric field intensity feature over time of electromagnetic wave at any point in communication space, is electromagnetic wave A kind of build-in attribute.If therefore obtaining it is also possible to obtain polarization of electromagnetic wave information while the DOA information of incoming wave signal, The information to incoming wave signal that just can increase controls degree, thus improve the receiving ability of aerial array, also optimizes signal The estimation performance of DOA.

The classical DOA estimation method based on Electromagnetic Vector Sensor Array adopts long vector (long vector, LV) number According to model, when polarization parameter is unknown, the high dimensional search of LV data model can lead to operand huge, is difficult in engineer applied Middle realization.

And current, utilize the combined estimation method of the DOA of signal not rounded characteristic and polarization characteristic and polarization parameter still simultaneously It is so blank out.

Content of the invention

(1) technical problem to be solved

The technical problem to be solved in the present invention is：How the DOA of a kind of utilization signal not rounded characteristic and polarization characteristic is provided Combined estimation method with polarization parameter.

(2) technical scheme

For solving above-mentioned technical problem, the present invention provides not rounded signal DOA and polarization parameter under a kind of polarization sensitive array Combined estimation method, the method specifically includes following steps：

Step S1：For the uniform transverse electro-magnetic wave in q far field, incide the planar bipolarization sensitivity aerial array of M array element Situation, set up the long vector matrix model of array received data：

Wherein：

A=[a₁a₂… a_q] be polarization sensitive aerial array spatial domain steering vector matrix；

Steering vector for i-th signal；Superscript^TThe transposition of representing matrix；

It is the lagging phase that m-th array element is with respect to reference point,It is respectively incident orientation angle and the angle of pitch of i-th signal, (x_m,y_m) be m array element position coordinateses, λ be signal wave Long；

S (t)=[s₁(t) s₂(t) … s_q(t)]^TIt is signal phasor；

N_k(t)=[n_k1(t) n_k2(t) … n_kM(t)]^T, k=1,2 is additive noise vector；

V_k=diag (V_k1,V_k2,…,V_kq), k=1,2 is receiving voltage V_kiThe diagonal matrix constituting；

V_ki=E_0ih_k ^T(x,y)ξ_i, E_0iRepresent the beam power of i-th signal, h_k(x, y) represents two orthogonal antennas relatively Effective length in coordinate plane o-xy；

γ_i,η_iRepresent the polarization of i-th signal respectively Argument and polarization phases are poor；

Step S2：Calculate the covariance matrix R=E [XX of X (t) respectively^H] and pseudocovariance matrix R'=E [XX^T], upper angle Mark^HThe conjugate transpose of representing matrix；

Step S3：Pseudocovariance matrix R' is carried out with singular value decomposition, and the local derviation relation being met using extreme value of a function point, Construct the two-dimensional space Power estimation function after the dimension-reduction treatment estimated for not rounded signal：

By this function pair two-dimensional directional parameterScan for trying to achieve extreme value, thus obtaining all not rounded signals Arrival bearing；

Step S4：Two-dimensional directional parameter using the not rounded signal having been estimated thatDirectly calculate each not rounded letter Number corresponding polarization parameter

Step S5：Not rounded signal parameter using estimationObtain the estimation of not rounded signal guide matrix：

Thus the estimation of not rounded signal covariance matrix can be obtained further

Step S6：Construction difference matrixFeature decomposition is carried out to it, and according to the dimensionality reduction side in step S3 Two-dimensional space Power estimation function after the dimension-reduction treatment that method construction is estimated for circle signal：

Obtain the arrival bearing of all round signals by searching for extreme value；

Step S7：According to the computational methods in step S4, using the two-dimensional directional parameter of the round signal having been estimated thatDirectly calculate the corresponding polarization parameter of round signal

Wherein, in step S5, the estimation of construction not rounded signal covariance matrixIt is divided into two kinds of situations：

Step S5a：When rate conditions such as incoming signal satisfactions, have：

Step S5a：When incoming signal is unsatisfactory for constant power condition, but not rounded signal satisfaction is maximum not rounded rate signal When, have：

Wherein superscriptThe pseudoinverse of representing matrix, has：

(3) beneficial effect

Compared with prior art, the present invention possesses following beneficial effect：

Compared to this field most methods, the method for the present invention be can be used for circle signal and mixed incidence with not rounded signal More general scenario.By setting up the long vector receiving data model under planar bipolar sensitization array, the not rounded using signal is special Property by mixing incoming signal in round signal separately estimated successively with not rounded signal, decrease mutually dry between two class signals Disturb, thus improving the estimation performance to various types of signal.It is simultaneous for the huge problem of operand, by the four-dimension search of spectral function Process is reduced to two-dimensional search process, has both reduced the operation number of times of the method, and has not sacrificed estimated accuracy.The method Successfully fill up the blank being applied to not rounded signal direction-finding method under polarization sensitive array.

Brief description

Fig. 1 is space incident signal schematic representation.

Fig. 2 is electric field intensityQuadrature component schematic diagram.

Fig. 3 is typical four tortuous arm unit layouts.

Specific embodiment

For making the purpose of the present invention, content and advantage clearer, with reference to the accompanying drawings and examples, to the present invention's Specific embodiment is described in further detail.

For solving problem of the prior art, the present invention adopts the long vector data model of polarization sensitive aerial array, utilizes The not rounded characteristic of signal is separately estimated mixing the round signal in incoming signal with not rounded signal, and by spectral function Local derviation said conditions are treated and are estimated parameter dimensionality reduction optimization, thus substantially reducing the operand in search procedure.This method make use of letter Number not rounded characteristic improve information utilization, improve the estimation performance of method, can simultaneously be effectively do not counted by search Calculate the polarization information of mixing incoming signal.

Specifically, not rounded signal DOA and polarization parameter Combined estimator side under polarization sensitive array provided by the present invention Method, the method is gone for circle signal and is mixed the more generally situation such as incident with not rounded signal, specifically includes following steps：

Step S1：For q far field uniform transverse electro-magnetic wave (Transverse Electromagnetic Wave, TEM Wave), incide the situation of the planar bipolarization sensitivity aerial array of M array element, set up the long vector square of array received data Battle array model：

Wherein：

A=[a₁a₂… a_q] be polarization sensitive aerial array spatial domain steering vector matrix；

Steering vector for i-th signal；Superscript^TThe transposition of representing matrix；

It is the lagging phase that m-th array element is with respect to reference point,It is respectively incident orientation angle and the angle of pitch of i-th signal, (x_m,y_m) be m array element position coordinateses, λ be signal wave Long；

S (t)=[s₁(t) s₂(t) … s_q(t)]^TIt is signal phasor；

N_k(t)=[n_k1(t) n_k2(t) … n_kM(t)]^T, k=1,2 is additive noise vector；

V_k=diag (V_k1,V_k2,…,V_kq), k=1,2 is receiving voltage V_kiThe diagonal matrix constituting；

V_ki=E_0ih_k ^T(x,y)ξ_i, E_0iRepresent the beam power of i-th signal, h_k(x, y) represents two orthogonal antennas relatively Effective length in coordinate plane o-xy；

γ_i,η_iRepresent the polarization of i-th signal respectively Argument and polarization phases are poor；

Step S2：Calculate the covariance matrix R=E [XX of X (t) respectively^H] and pseudocovariance matrix R'=E [XX^T], upper angle Mark^HThe conjugate transpose of representing matrix；

Step S3：Pseudocovariance matrix R' is carried out with singular value decomposition, and the local derviation relation being met using extreme value of a function point, Construct the two-dimensional space Power estimation function after the dimension-reduction treatment estimated for not rounded signal：

By this function pair two-dimensional directional parameterScan for trying to achieve extreme value, thus obtaining all not rounded signals Arrival bearing；

Step S4：Two-dimensional directional parameter using the not rounded signal having been estimated thatDirectly calculate each not rounded The corresponding polarization parameter of signal

Step S5：Not rounded signal parameter using estimationObtain the estimation of not rounded signal guide matrix：

Thus the estimation of not rounded signal covariance matrix can be obtained further

Step S6：Construction difference matrixIt is carried out with feature decomposition, and according to the dimension reduction method in step S3 Two-dimensional space Power estimation function after the dimension-reduction treatment that construction is estimated for circle signal：

Obtain the arrival bearing of all round signals by searching for extreme value；

Step S7：According to the computational methods in step S4, using the two-dimensional directional parameter of the round signal having been estimated thatDirectly calculate the corresponding polarization parameter of round signal

Wherein, in step S5, the estimation of construction not rounded signal covariance matrixIt is divided into two kinds of situations：

Step S5a：When rate conditions such as incoming signal satisfactions, have：

Step S5a：When incoming signal is unsatisfactory for constant power condition, but not rounded signal satisfaction is maximum not rounded rate signal When, have：

Wherein superscriptThe pseudoinverse of representing matrix, has：

In step sl, initially set up the mathematical model that far field uniform TEM ripple incides planar bipolar sensitization array, If i-th signal incident direction isDirection vector, the azimuth of incoming signal is defined as vectorProjection and x in xoy face The angle of axle, symbol θ_iRepresent；The angle of pitch is defined as vectorThe angle of z-axis, symbol is usedRepresent, signal i incides M battle array The polarized antenna arrays initial point of unit is as shown in Figure 1；

Meanwhile, according to orthogonal vectorWith the coordinate transformation relation of rectangular coordinate system in space o-xyz, can arrive The electric field intensity of ripple signalMatrix form：

Electric field intensityIn two orthogonal unit vectorsDirection on decompose as shown in Figure 2；

Typical planar bipolar antenna such as Sinuous Antenna, includes two cross-polarized antennas in single bore, Under normal circumstances, can the horizontal polarization in reception space and vertical polarization signal simultaneously, when with the addition of suitable hardware, can To receive the signal of left-handed and right-hand polarization, typical four tortuous arm unit layouts are as shown in Figure 3；

If two orthogonal antennas are respectively h with respect to the effective length of coordinate system o-xyz₁,h₂It is contemplated that array element is in xoy putting down Face, h₁,h₂Z-axis durection component inoperative, order：

Then two-way cross-polarized antennas to the receiving voltage of i-th signal are：

v_ai=h₁ ^TΕ_i=E_0ih₁ ^T(x,y)ξ_i

v_bi=h₂ ^TΕ_i=E_0ih₂ ^T(x,y)ξ_i.

If first array element is set as reference array element, received by the two-way orthogonal antenna of m-th bay Time-domain signal is：

In subsequent steps, using the not rounded characteristic of signal, by incident for the mixing containing circle signal and not rounded signal letter Number separately estimated successively, corresponding matrix is carried out after singular value decomposition or Eigenvalues Decomposition, using the orthogonality of subspace Relation pair two dimension direction parameter is estimated, then calculates the corresponding two-dimentional polarization parameter of each signal again.

Wherein,

1st, the calculating of the covariance matrix R in step S2 and pseudocovariance matrix R'

It is impossible to directly obtain the theoretical value of R and R' in practical application engineering, but can be by time-limited observation data X (t) approximately to obtain.Had according to maximum likelihood principle：

Wherein, L is fast umber of beats of sampling.

2nd, the space spectral function that not rounded signal is estimated in step S3Structure

If in q far field TEM ripple, circle signal has q_cIndividual, not rounded signal has q_ncIndividual.The pseudocovariance matrix R' of observation data Carry out singular value decomposition, have：

According to the orthogonality of subspace, U_n-ncThe space opened with the array manifold matrix of not rounded signalOrthogonal.If by matrix U_n-ncIt is written asThen have：

Wherein, a_i-ncSteering vector for i-th not rounded signal.Order

The then estimation spectral function to not rounded signalIt is so structured that：

Wherein, | | | |_FThe Frobenius norm of representing matrix.Notice that vector a is parameterFunction, and become Amount ρ, δ is parameterFunction, therefore typically require and carry out four-dimensional search, operand is very big.In order to reduce operand The dimensionality reduction of line parameter can be entered first, make spectral functionRespectively parameter (γ, η) is asked with local derviation and makes it be zero, Have：

May certify that following formula is set up：

By simultaneous equations spectral function abbreviation can be：

Now dimensionality reduction, can be by two-dimensional parameter to conventional binary function for spectral functionScan for asking Obtain extreme value, thus obtaining q_ncThe arrival bearing of individual not rounded signal

3rd, the calculating to not rounded polarizations parameter in step S4

When the arrival bearing's parameter obtaining not rounded signalAfterwards, can calculate further to respectively obtain corresponding not rounded The polarization parameter of signalAccording to the functional relationship in the 2nd point of specific embodiment, simultaneous can obtain：

For estimated parameterThe steering vector building, when coordinate system and the reference of polarization sensitive aerial array Coordinate system overlaps, and that is, antenna polarization vector meets h₁=[1 0]^T, h₂=[0 1]^T, and make：

The polarization parameter of i-th not rounded signal of estimation can be obtained after then arranging：

4th, the corresponding covariance matrix of not rounded signal in step S5Method of estimation

According to all not rounded signal two dimension DOA parameters having been estimated thatThe corresponding sky of not rounded signal can be obtained Domain steering vector matrixIf incoming signal is constant power signal, in conjunction with the pole having been estimated that Change parameterThe induced voltage matrix that reference array element two-way cross polarization passage can be obtained is：

Then the pseudocovariance matrix R' of observation data can arrange and be：

OrderObviously, matrixFor column full rank, definable matrixAndMoore- Penrose is inverse to beThen have：

If q_ncIn individual not rounded signal, comprise q_nc1Individual maximum not rounded rate signal and q_nc2Individual general not rounded rate signal.Then above formula Can be written as：

Not rounded rate due to general not rounded rate signal meets 0<ρ<1, in order to remove not rounded phase place impact it is clear that can profit Use following relation：

So far, can obtain mixing the full detail of not rounded signal section in incoming signal, the i.e. association of not rounded signal section The estimation of variance matrixFor：

If incoming signal is unsatisfactory for constant power condition, but when being entirely maximum not rounded rate signal in not rounded signal, then It is tied to form vertical just like ShiShimonoseki：

The now estimation of the covariance matrix of not rounded signal sectionFor：

5th, the space spectral function that circle signal is estimated in step S6Structure

In order to estimate two-dimentional DOA parameter and the polarization parameter of circle signal further, calculate difference matrix first Feature decomposition is carried out to it, hasWherein, U_s-c,U_n-cIt is respectively circle signal covariance matrix Signal subspace and noise subspace, Σ_S,Σ_nThe diagonal matrix being constituted by its corresponding eigenvalue.Therefore there is noise in the same manner Subspace U_n-cThe space opened with circle signal corresponding array manifold matrixOrthogonal, by noise subspace U_n-cIt is written asThe Estimation of Spatial Spectrum function of round signal then can be builtIn order to avoid the four-dimension is searched The huge problem of operand of rope, reuses the local derviation relation of spectral function, by estimating spectral function abbreviation can be：

Now can be by scanning for trying to achieve extreme value to two-dimensional parameter, thus obtaining the arrival bearing of remaining circle signal

6th, the calculating to circle polarizations parameter in step S7

Rely on the two-dimentional DOA parameter of estimated round signalIts corresponding polarization ginseng can be calculated in the same manner Number.Order：

The polarization parameter of i-th round signal of estimation can be obtained

The present invention using signal not rounded characteristic it is proposed that be applied to planar bipolar sensitization array DOA and polarization ginseng Number combined estimation methods, improve the estimated accuracy of signal DOA parameter, and compared to the classical polarization sensitive array that is applied to Direction-finding method significantly reduces operand and estimates it is possible to make combining to polarization parameter while not expending extra operand Meter.

To sum up, the present invention is directed to the not rounded signal situation simultaneously incident with circle signal, has initially set up plane polarization sensitive The receiving data LV model of array, and using the not rounded characteristic of signal, two class signals are separately estimated：Prior estimation not rounded signal DOA and polarization parameter, recycle estimator to make estimation to the circle DOA of signal and polarization parameter.It is simultaneous for LV data The huge problem of the operand of model, treats and estimates parameter and carry out dimension-reduction treatment, reduce the parameter dimensions in search procedure, having Decrease to effect and while operand, also ensure that estimated accuracy.

The above is only the preferred embodiment of the present invention it is noted that ordinary skill people for the art For member, on the premise of without departing from the technology of the present invention principle, some improvement can also be made and deform, these improve and deform Also should be regarded as protection scope of the present invention.

Claims (1)

1. under a kind of polarization sensitive array not rounded signal DOA and polarization parameter combined estimation method it is characterised in that the method tool Body comprises the following steps：

Step S1：For the uniform transverse electro-magnetic wave in q far field, incide the feelings of the planar bipolarization sensitivity aerial array of M array element Shape, sets up the long vector matrix model of array received data：

$X\left(t\right)=\left[\begin{array}{c}{X}_1\left(t\right)\\ X_2\left(t\right)\end{array}\right]=\left[\begin{array}{c}{\mathrm{AV}}_1\\ {\mathrm{AV}}_2\end{array}\right]S\left(t\right)+\left[\begin{array}{c}{N}_1\left(t\right)\\ N_2\left(t\right)\end{array}\right];$

Wherein：

A=[a₁a₂… a_q] be polarization sensitive aerial array spatial domain steering vector matrix；

$a_i={\left[\begin{array}{cccc}{e}^{-j{\mathrm{\&phi;}}_{1i}}& e^{-j{\mathrm{\&phi;}}_{2i}}& ...& e^{-j{\mathrm{\&phi;}}_{\mathrm{Mi}}}\end{array}\right]}^T$ Steering vector for i-th signal；Superscript^TThe transposition of representing matrix；

It is the lagging phase that m-th array element is with respect to reference point, It is respectively incident orientation angle and the angle of pitch of i-th signal, (x_m,y_m) be m array element position coordinateses, λ be signal wavelength；

S (t)=[s₁(t) s₂(t) … s_q(t)]^TIt is signal phasor；

N_k(t)=[n_k1(t) n_k2(t) … n_kM(t)]^T, k=1,2 is additive noise vector；

V_k=diag (V_k1,V_k2,…,V_kq), k=1,2 is receiving voltage V_kiThe diagonal matrix constituting；

V_ki=E_0ih_k ^T(x,y)ξ_i, E_0iRepresent the beam power of i-th signal, h_k(x, y) represents two orthogonal antennas with respect to coordinate It is the effective length of plane o-xy；

γ_i,η_iRepresent the polarization argument of i-th signal respectively Poor with polarization phases；

Step S2：Calculate the covariance matrix R=E [XX of X (t) respectively^H] and pseudocovariance matrix R'=E [XX^T], superscript^HTable Show the conjugate transpose of matrix；

Step S3：Pseudocovariance matrix R' is carried out with singular value decomposition, and the local derviation relation being met using extreme value of a function point, construction Two-dimensional space Power estimation function after the dimension-reduction treatment estimated for not rounded signal：

By this function pair two-dimensional directional parameterScan for trying to achieve extreme value, thus obtaining the incoming wave side of all not rounded signals To；

Step S4：Two-dimensional directional parameter using the not rounded signal having been estimated thatDirectly calculate each not rounded signal pair The polarization parameter answered

Step S5：Not rounded signal parameter using estimationObtain the estimation of not rounded signal guide matrix：

${\tilde{A}}_{\mathrm{nc}}\stackrel{\mathrm{\&Delta;}}{=}\left[\begin{array}{c}{\hat{A}}_{\mathrm{nc}}{\stackrel{\&OverBar;}{V}}_{1-\mathrm{nc}}\\ {\hat{A}}_{\mathrm{nc}}{\stackrel{\&OverBar;}{V}}_{2-\mathrm{nc}}\end{array}\right];$

Thus the estimation of not rounded signal covariance matrix can be obtained further

Step S6：Construction difference matrixIt is carried out with feature decomposition, and according to the dimension reduction method construction in step S3 Two-dimensional space Power estimation function after the dimension-reduction treatment estimated for circle signal：

Obtain the arrival bearing of all round signals by searching for extreme value；

Step S7：According to the computational methods in step S4, using the two-dimensional directional parameter of the round signal having been estimated thatDirectly Connect and calculate the corresponding polarization parameter of round signal

Wherein, in step S5, the estimation of construction not rounded signal covariance matrixIt is divided into two kinds of situations：

Step S5a：When rate conditions such as incoming signal satisfactions, have：

Step S5a：When incoming signal is unsatisfactory for constant power condition, but when not rounded signal satisfaction is maximum not rounded rate signal, have：

Wherein superscriptThe pseudoinverse of representing matrix, has：