CN107422317A - Low angle target arrival direction estimation method based on smoothing matrix collection - Google Patents

Low angle target arrival direction estimation method based on smoothing matrix collection Download PDF

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CN107422317A
CN107422317A CN201710656447.8A CN201710656447A CN107422317A CN 107422317 A CN107422317 A CN 107422317A CN 201710656447 A CN201710656447 A CN 201710656447A CN 107422317 A CN107422317 A CN 107422317A
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CN107422317B (en
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师俊朋
胡国平
张小飞
周豪
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Air Force Engineering University of PLA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/418—Theoretical aspects

Abstract

The invention discloses the low angle target arrival direction estimation method based on smoothing matrix collection, it is related to radar signal and technical field of information processing, it is front and rear to smoothing matrix collection (Forward Backward SMS, FB SMS) method builds new smoothing matrix by rearranging the auto-covariance battle array of the sub- face battle array of each every trade, and algorithm can be by improving the information utilization optimal estimating performance of sample covariance matrix；Spatial diversity smoothing matrix collection (Spatial Differencing SMS, SD SMS) method by the noise to the sub- face battle array of every trade and non-noise part carry out respectively spatial diversity and it is front and rear reduce data degradation to smoothing processing, compared to traditional distinctions algorithm, its coloured noise rejection is more preferable.

Description

Low angle target arrival direction estimation method based on smoothing matrix collection
Technical field
The present invention relates to radar signal and technical field of information processing, more particularly to the low angle mesh based on smoothing matrix collection Mark arrival direction estimation method.
Background technology
Multi-target two-dimensional DOA (angle of pitch, azimuth) estimations are widely used to the neck such as radar, sonar and radio communication Domain.Arrival direction estimation, which is carried out, using array manifolds such as L-type battle array, parallel linear array and uniform surface battle arrays also therefore achieves huge progress. Wherein, class algorithm in subspace obtains great development, such as MUSIC, ESPRIT.But under the environment of low latitude, direct signal and reflection The coherence of signal makes traditional subspace class algorithm failure.Front-rear space smooth (FBSS) algorithm can by it is front and rear to Submatrix covariance matrix space summation decorrelation LMS, but certain free degree can be lost.Therefore, handled using uniform surface battle array space smoothing Virtual submatrix is formed to overcome aperture loss to achieve greater advance, such as two-dimentional MUSIC, two-dimentional real value ESPRIT algorithms.And Such algorithm has been used for MIMO radar DOA estimations, joint DOD and DOA estimations etc..On the basis of two-dimensional space smoothing algorithm, profit New theoretical system is also form with the front and rear spatial diversity algorithm that difference operation is carried out to submatrix, such as initial submatrix and backward submatrix Difference operation, it is adjacent it is front and rear to submatrix difference operation, it is front and rear to the Hermition difference operations of submatrix and backward submatrix, it is asymmetric front and rear To difference operation etc..But the major defect of existing space smoothing and spatial diversity algorithm has：
1. two-dimensional space smoothing algorithm can only utilize limited data message, especially for uniform surface battle array, do not utilize Data message amount is bigger.And under the conditions of coloured noise, estimation performance is weaker.
2. two-dimensional space difference algorithm produces very big data degradation in difference operation is carried out, and with the increasing of array aperture Increase greatly.Therefore, under the conditions of big array aperture, it is weaker than space for white noise and coloured noise spatial diversity algorithm performance Smoothing algorithm.
The content of the invention
The embodiments of the invention provide the low angle target arrival direction estimation method based on smoothing matrix collection, can solve existing There is problem present in technology.
A kind of low angle target arrival direction estimation method based on smoothing matrix collection, including：
The low angle target echo signal model established under the conditions of uniform surface battle array；
Uniform surface battle array in the low angle target echo signal model is divided into the sub- face battle array of multiple every trades with sliding type；
Under white noise, using the diagonal of the covariance matrix of first row face battle array as boundary, extract from top to bottom Data message, descending smoothing matrix collection is built according to the data message of extraction；
Backward smoothing processing is carried out to the descending smoothing matrix collection, obtains descending backward smoothing matrix collection；
Using the diagonal of the covariance matrix of first row face battle array as boundary, data message, root are extracted from top to bottom Up smoothing matrix collection is built according to the data message of extraction；
Backward smoothing processing is carried out to the up smoothing matrix collection, obtains up backward smoothing matrix collection；
The descending of each row face battle array is extracted using the descending smoothing matrix collection and descending backward smoothing matrix collection It is front and rear to extract each row to extraction data, while using the up smoothing matrix collection and up backward smoothing matrix collection Face battle array it is up front and rear to extraction data；
According to each row face battle array it is descending before and after to extraction data and it is up it is front and rear calculate to extraction data it is final Front-rear space smooth collection, to the front-rear space smooth collection carry out singular value decomposition after, using two dimensional ESPRIT algorithm Solve DOA estimates；
Under coloured noise, using the diagonal of the covariance matrix of first row face battle array as boundary, carry from top to bottom After taking data message, difference computing is carried out to the noise section of the data message of extraction, while before and after being carried out to non-noise part To smoothing processing, descending difference submatrix is obtained；
Using the diagonal of the covariance matrix of first row face battle array as boundary, data message is extracted from top to bottom Afterwards, difference computing is carried out to the noise section of the data message of extraction, while non-noise part carried out front and rear to smooth place Reason, obtain up difference submatrix；
Extract the descending difference of each row face battle array respectively using the descending difference submatrix and up difference submatrix Smoothing matrix collection and up difference smoothing matrix collection；
It is smooth that final spatial diversity is calculated according to the descending difference smoothing matrix collection and up difference smoothing matrix collection Matrix stack, two dimensional ESPRIT Algorithm for Solving DOA estimates are used to the spatial diversity smoothing matrix collection.
The low angle target arrival direction estimation method based on smoothing matrix collection in the embodiment of the present invention has advantages below：
1.FB-SMS utilizes more sample covariance matrix information, and it estimates performance than Traditional Space smoothing method performance more It is excellent；
Difference computings and cross covariance array (non-noise portion of the 2.SD-SMS using auto-covariance array (noise section) Point) it is front and rear can effectively suppress coloured noise to processing, and reduce the data degradation of difference computing, it estimates that performance is obvious Lifting.
Brief description of the drawings
In order to illustrate more clearly about the embodiment of the present invention or technical scheme of the prior art, below will be to embodiment or existing There is the required accompanying drawing used in technology description to be briefly described, it should be apparent that, drawings in the following description are only this Some embodiments of invention, for those of ordinary skill in the art, on the premise of not paying creative work, can be with Other accompanying drawings are obtained according to these accompanying drawings.
Fig. 1 is the low angle target echo signal model established；
Fig. 2 (a) is the schematic diagram of first row face battle array；
Fig. 2 (b) is the covariance matrix schematic diagram of first row face battle array；
Fig. 3 is FB-SMS simulation result；
Fig. 4 is SD-SMS simulation result；
Variation relations of the Fig. 5 for mean square error under white noise with signal to noise ratio；
Variation relations of the Fig. 6 for mean square error under white noise with fast umber of beats；
Variation relations of the Fig. 7 for mean square error under coloured noise with signal to noise ratio；
Variation relations of the Fig. 8 for mean square error under coloured noise with fast umber of beats.
Embodiment
Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete Site preparation describes, it is clear that described embodiment is only part of the embodiment of the present invention, rather than whole embodiments.It is based on Embodiment in the present invention, those of ordinary skill in the art are obtained every other under the premise of creative work is not made Embodiment, belong to the scope of protection of the invention.
The low angle target arrival direction estimation method based on smoothing matrix collection provided in the embodiment of the present invention, this method bag Include：
Low angle target echo signal model is established, the model of foundation is as shown in figure 1, multipath effect is preferable mirror-reflection Model and ignore atmospheric refraction and earth curvature and influence；Uniform surface battle array has M × N number of bay, and adjacent array element is at intervals of half-wave It is long, and the height of uniform surface battle array is h；K irrelevant far field narrow band signal source sk(t) k=1,2 ..., K incident angle is (αk, θk).Then echo-signal is made up of direct signal and reflected signal, and its model is specially：
In formula, θdkAnd θrkThe direct projection elevation angle and the reflection elevation angle of respectively k-th target, θdk≈-θrk= θk, αkFor azimuth, βkFor multipath reflection coefficient； uk=sin θkcosαk, vk=sin θksinαk；Z (t) is Average is 0, variance σ2And separate white Gaussian noise；For ease of calculating, if βk=exp [j (π -2 π Δs Rk/ λ)], Δ Rk≈2h sinθk, Δ RkFor multipath range difference.It will be expressed as after echo-signal vectorization：
X (t)=vec (X (t))=(AxοAy)s(t)+z(t) (2)
In formula, z(t) =vec (Z (t)).IfFormula (2) is represented by：
When fast umber of beats is L (t=1,2 ..., L), echo-signal x (t) covariance matrix is represented by：
In formula, A=AxοAy, Rs=E [s (t) sH(t)] it is signal source covariance matrix.
Under the conditions of white noise, uniform surface battle array is divided into multiple row faces battle array.By taking first row face battle array as an example, assisted with it Variance matrix diagonal is boundary, extracts data message from top to bottom and builds descending smoothing matrix collection；Then, extract from top to bottom Data message simultaneously builds corresponding preceding up smoothing matrix collection；Similarly, it is smooth to build downlink and uplink corresponding to the battle array of each row face Matrix stack.
Respectively in x-axis and y-axis direction structure QxAnd QyIndividual forward direction submatrix, corresponding submatrix array number is PxAnd Py, then uniform surface Battle array is segmented into QxQyIndividual sub- face battle array, its size are Px×Py, Qx=M-Px+ 1, Qy=N-Py+1.QxqyIndividual sub- face battle array can represent For：
In formula,WithRespectively array manifold matrix AxAnd AyPreceding PxAnd PyRow composition, qx =1 ..., Qx, qy=1 ..., Qy,For corresponding noise Vector.Now, each row face battle array is by QyIndividual sub- face battle array composition.By taking first row face battle array as an example, it is set tox1,nFor xnPreceding PxOK, n=1 ..., N.Using the diagonal of its covariance matrix as boundary, first Each column data information is extracted from top to bottom, then the n-th row (n=1 ..., Qy- 1) it is represented by：
Wherein,
z1(t), z1,n(t) it is respectively corresponding noise vector, Remaining PyColumn data is represented by：
From (6) and (10), reconstruct descending forward direction smoothing matrix set and be represented by：
Wherein,To improve estimation performance and decorrelation energy, to matrix R1Progress after It can be obtained to smoothing processing：
Wherein,dk=(M-1) uk+(N-1)vk, by (12) descending backward smoothing matrix collection can be obtained and be combined into (13)：
Similarly, using diagonal as boundary, extract each column data information from top to bottom, then It is classified as：
Wherein,
WhereinThen last PyColumn data can table It is shown as：
From (18) and (20), the up forward direction of reconstruct is slided set of matrices and is represented by：
Wherein,Up backward smoothing matrix collection be：
Q can similarly be obtainedxThe descending of individual sub- face battle array front and rear be to smoothing matrix collection with up：
Wherein
The front-rear space smooth collection (FB-SMS) that can be obtained finally by (20)-(23) is：
Matrix stack RfbHave the following properties that：Work as QxQy＞ 2K, Qx＞ 1, QyDuring ＞ 1, matrix RfbOrder be 2K.Then to RfbEnter After row singular value decomposition (SVD), two dimensional ESPRIT Algorithm for Solving DOA estimates can be used.
Under coloured noise, understood according to formula (6) and (15), only first submatrix includes noise matrix, other submatrixs by Cross-correlation matrix forms.
Difference computing is carried out to the noise section of formula (6), had：
Other cross-correlation submatrixs (non-noise part) can use front-rear space smooth technical finesse：
Wherein,It can be obtained by (27) and (28), the n-th row (n=1 ..., Qy- 1) difference of data Matrix is represented by：
Remaining PyThe difference matrix of column data is represented by：
Wherein,By (29) and (31) can must under Row spatial diversity smoothing matrix collection (SD-SMS) is：
Then extracting the up difference smoothing matrix collection of data message structure from top to bottom is
Wherein,
Similarly, qxDownlink and uplink difference smoothing matrix collection is respectively corresponding to the battle array of individual row face
Wherein,
It can then be obtained by formula (36) and (37)：
To RdDOA estimates can be tried to achieve using two dimensional ESPRIT algorithm.
Exploitativeness to illustrate the invention, now emulate as follows.Simulated conditions are：Uniform surface battle array is highly h=20m, battle array First number is M=N=12, signal wavelength 1m, and incoming signal power isColoured noise is second order AR models, coefficient a= [1,-0.7,0.6]；Monte Carlo simulation number 300.
Experiment 1：Fig. 3 and Fig. 4 sets forth FB-SMS and SD-SMS simulation result, simulation times 100, target position Put respectively α1=[10 °, 20 °, 40 °], θ1=[20 °, 35 °, 50 °] and α2=[5 °, 15 °, 25 °], θ2=[25 °, 35 °, 45°]；Submatrix size Px=Py=9, SNR=5dB, fast umber of beats are L=500.From Fig. 3 and Fig. 4, in white noise and coloured noise FB-SMS and SD-SMS can accurately estimate all target locations in the case of two kinds.
Experiment 2：Performance evaluation under the conditions of white noise.This experiment carry out white noise under the conditions of inventive algorithm (FB-SMS, SD-SMS), mean square error (RMSE) curve of FBSS algorithms, spatial diversity algorithm (AFB-SDS) and CRB is with signal to noise ratio, snap Several variation relations.Fig. 5 gives variation relation of the mean square error with signal to noise ratio, submatrix size Px=Py=9, fast umber of beats L= 500；Fig. 6 gives variation relation of the mean square error with fast umber of beats, submatrix size Px=Py=9, signal to noise ratio snr=5dB.By Fig. 5 Understand that under the conditions of white noise, FB-SMS algorithms using more data messages due to estimating better performances with Fig. 6；SD- SMS is estimated performance and is weaker than FBSS due to larger data degradation；Because SD-SMS only uses difference computing to autocorrelation matrix, And AFB-SDS uses difference operation to submatrix covariance, so SD-SMS data degradations are less than AFB-SMS, and better performances are estimated.
Experiment 3：Performance evaluation under the conditions of coloured noise.Fig. 7, which is provided, gives variation relations of the RMSE with signal to noise ratio, Px=Py =9, L=500；Fig. 8 gives variation relations of the RMSE with fast umber of beats, Px=Py=9, SNR=5dB.From Fig. 7 and Fig. 8, When coloured noise is second order AR models, SD-SMS has preferably estimation performance than FB-SMS.This is due to that SD-SMS can have The influence of the reduction coloured noise covariance matrix off-diagonal element of effect.Wherein, due to excellent using more data information, FB-SMS performances In FBSS；Due to producing larger data degradation, AFB-SDS performances are most weak.
It should be understood by those skilled in the art that, embodiments of the invention can be provided as method, system or computer program Product.Therefore, the present invention can use the reality in terms of complete hardware embodiment, complete software embodiment or combination software and hardware Apply the form of example.Moreover, the present invention can use the computer for wherein including computer usable program code in one or more The computer program production that usable storage medium is implemented on (including but is not limited to magnetic disk storage, CD-ROM, optical memory etc.) The form of product.
The present invention is the flow with reference to method according to embodiments of the present invention, equipment (system) and computer program product Figure and/or block diagram describe.It should be understood that can be by every first-class in computer program instructions implementation process figure and/or block diagram Journey and/or the flow in square frame and flow chart and/or block diagram and/or the combination of square frame.These computer programs can be provided The processors of all-purpose computer, special-purpose computer, Embedded Processor or other programmable data processing devices is instructed to produce A raw machine so that produced by the instruction of computer or the computing device of other programmable data processing devices for real The device for the function of being specified in present one flow of flow chart or one square frame of multiple flows and/or block diagram or multiple square frames.
These computer program instructions, which may be alternatively stored in, can guide computer or other programmable data processing devices with spy Determine in the computer-readable memory that mode works so that the instruction being stored in the computer-readable memory, which produces, to be included referring to Make the manufacture of device, the command device realize in one flow of flow chart or multiple flows and/or one square frame of block diagram or The function of being specified in multiple square frames.
These computer program instructions can be also loaded into computer or other programmable data processing devices so that counted Series of operation steps is performed on calculation machine or other programmable devices to produce computer implemented processing, so as in computer or The instruction performed on other programmable devices is provided for realizing in one flow of flow chart or multiple flows and/or block diagram one The step of function of being specified in individual square frame or multiple square frames.
Although preferred embodiments of the present invention have been described, but those skilled in the art once know basic creation Property concept, then can make other change and modification to these embodiments.So appended claims be intended to be construed to include it is excellent Select embodiment and fall into having altered and changing for the scope of the invention.
Obviously, those skilled in the art can carry out the essence of various changes and modification without departing from the present invention to the present invention God and scope.So, if these modifications and variations of the present invention belong to the scope of the claims in the present invention and its equivalent technologies Within, then the present invention is also intended to comprising including these changes and modification.

Claims (9)

  1. A kind of 1. low angle target arrival direction estimation method based on smoothing matrix collection, it is characterised in that including：
    The low angle target echo signal model established under the conditions of uniform surface battle array；
    Uniform surface battle array in the low angle target echo signal model is divided into the sub- face battle array of multiple every trades with sliding type；
    Under white noise, using the diagonal of the covariance matrix of first row face battle array as boundary, data are extracted from top to bottom Information, descending smoothing matrix collection is built according to the data message of extraction；
    Backward smoothing processing is carried out to the descending smoothing matrix collection, obtains descending backward smoothing matrix collection；
    Using the diagonal of the covariance matrix of first row face battle array as boundary, data message is extracted from top to bottom, according to carrying The data message taken builds up smoothing matrix collection；
    Backward smoothing processing is carried out to the up smoothing matrix collection, obtains up backward smoothing matrix collection；
    The descending front and rear of each row face battle array is extracted using the descending smoothing matrix collection and descending backward smoothing matrix collection Each row face battle array is extracted to extraction data, while using the up smoothing matrix collection and up backward smoothing matrix collection It is up front and rear to extraction data；
    According to each row face battle array it is descending before and after to extraction data and it is up it is front and rear to extraction data calculate it is final before Backward space smoothing collection, after carrying out singular value decomposition to the front-rear space smooth collection, using two dimensional ESPRIT Algorithm for Solving DOA estimates；
    Under coloured noise, using the diagonal of the covariance matrix of first row face battle array as boundary, number is extracted from top to bottom It is believed that after breath, difference computing is carried out to the noise section of the data message of extraction, while non-noise part is carried out front and rear to flat Sliding processing, obtains descending difference submatrix；
    It is right after extracting data message from top to bottom using the diagonal of the covariance matrix of first row face battle array as boundary The noise section of the data message of extraction carries out difference computing, at the same non-noise part is carried out it is front and rear to smoothing processing, obtain Up difference submatrix；
    The descending difference for extracting each row face battle array respectively using the descending difference submatrix and up difference submatrix is smooth Matrix stack and up difference smoothing matrix collection；
    Final spatial diversity smoothing matrix is calculated according to the descending difference smoothing matrix collection and up difference smoothing matrix collection Collection, two dimensional ESPRIT Algorithm for Solving DOA estimates are used to the spatial diversity smoothing matrix collection.
  2. 2. the method as described in claim 1, it is characterised in that multipath effect is preferable specular reflectance model and ignores air Refraction and earth curvature influence；Uniform surface battle array has M × N number of bay, and adjacent array element is at intervals of half-wavelength, and uniform surface battle array Highly it is h；K irrelevant far field narrow band signal source sk(t), k=1,2 ..., K incident angle is (αk,θk)；Wherein, αkAnd θk The azimuth and the elevation angle of respectively k-th target, then echo-signal be made up of direct signal and reflected signal, its model is specific For：
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    In formula, θdkAnd θrkThe direct projection elevation angle and the reflection elevation angle of respectively k-th target, θdk≈-θrk=θk, αk For azimuth, βkFor multipath reflection coefficient； uk=sin θkcosαk, vk=sin θksinαk；Z (t) is Average is 0, variance σ2And separate white Gaussian noise；For ease of calculating, if βk=exp [j (π -2 π Δs Rk/ λ)], Δ Rk≈2h sinθk, Δ RkFor multipath range difference, will be expressed as after echo-signal vectorization：
    In formula,
    <mrow> <msub> <mi>A</mi> <mi>y</mi> </msub> <mo>=</mo> <msubsup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>v</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>v</mi> <mi>K</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>a</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mo>-</mo> <msub> <mi>v</mi> <mi>K</mi> </msub> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mi>N</mi> <mo>&amp;times;</mo> <mn>2</mn> <mi>K</mi> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mrow> <mo>&amp;lsqb;</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mn>1</mn> </msub> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>s</mi> <mi>K</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <msub> <mi>&amp;beta;</mi> <mi>K</mi> </msub> <msub> <mi>s</mi> <mi>K</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>2</mn> <mi>K</mi> <mo>&amp;times;</mo> <mn>1</mn> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> </mrow>
    Z (t)=vec (Z (t)), ifFormula (2) is represented by：
    <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mn>2</mn> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mi>N</mi> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <mi>x</mi> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>x</mi> </msub> <msub> <mi>&amp;Phi;</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <mi>x</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>z</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
    When fast umber of beats is L, t=1,2 ..., during L, echo-signal x (t) covariance matrix is represented by：
    <mrow> <msub> <mi>R</mi> <mn>0</mn> </msub> <mo>=</mo> <mi>E</mi> <mo>&amp;lsqb;</mo> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mi>L</mi> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>t</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <mi>x</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <msup> <mi>x</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>AR</mi> <mi>s</mi> </msub> <msup> <mi>A</mi> <mi>H</mi> </msup> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <mi>M</mi> <mi>N</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
    In formula,Rs=E [s (t) sH(t)] it is signal source covariance matrix.
  3. 3. method as claimed in claim 2, it is characterised in that step will be uniform in the low angle target echo signal model Face battle array is divided into multiple row faces battle array with sliding type and specifically included：
    Respectively in x-axis and y-axis direction structure QxAnd QyIndividual forward direction submatrix, corresponding submatrix array number is PxAnd Py, then uniform surface battle array can To be divided into QxQyIndividual row face battle array, its size are Px×Py, Qx=M-Px+ 1, Qy=N-Py+ 1, qxqyIndividual row face battle array can represent For：
    <mrow> <msub> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <msub> <mi>q</mi> <mi>y</mi> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>z</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <msub> <mi>q</mi> <mi>y</mi> </msub> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
    In formula, WithRespectively array manifold matrix AxAnd AyPreceding PxAnd PyRow composition, qx= 1,…,Qx, qy=1 ..., Qy, For corresponding noise vector Amount, now, each row face battle array is by QyIndividual row face battle array composition, then first row face battle array can be set tox1,nFor xnPreceding PxOK, n=1 ..., N.
  4. 4. method as claimed in claim 3, it is characterised in that under white noise, with the association side of first row face battle array The diagonal of poor matrix is boundary, extracts data message from top to bottom, and descending smoothing matrix collection is built according to the data message of extraction, Specifically include：
    Using the diagonal of its covariance matrix as boundary, each column data information is extracted from top to bottom first, then the n-th row, n=1 ..., Qy- 1, it is represented by：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msub> <mi>&amp;Phi;</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    <mrow> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>s</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>z</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mi>n</mi> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
    z1(t), z1,n(t) it is respectively corresponding noise vector, Remaining PyColumn data is represented by：
    <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>10</mn> <mo>)</mo> </mrow> </mrow>
    From formula (6) and (10), reconstruct descending forward direction smoothing matrix set and be represented by：
    <mrow> <msub> <mi>R</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    Step carries out backward smoothing processing to the descending smoothing matrix collection, obtains descending backward smoothing matrix collection and specifically includes：
    To improve estimation performance and decorrelation energy, to matrix R1Carrying out backward smoothing processing can obtain：
    <mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>12</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,dk=(M-1) uk+(N-1)vk, by formula (12) descending backward smoothing matrix collection can be obtained and be combined into (13)：
    <mrow> <msubsup> <mi>R</mi> <mn>1</mn> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>14</mn> <mo>)</mo> </mrow> </mrow>
    Step extracts data message, root from top to bottom using the diagonal of the covariance matrix of first row face battle array as boundary Up smoothing matrix collection is built according to the data message of extraction to specifically include：
    Using diagonal as boundary, extract each column data information from top to bottom, then It is classified as：
    <mrow> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mi>H</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> <mi>H</mi> </msubsup> <mo>}</mo> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msub> <mi>&amp;Phi;</mi> <mi>y</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mi>n</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    <mrow> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>
    WhereinThen last PyColumn data is represented by：
    <mrow> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>I</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>
    From formula (15) and (17), the up forward direction of reconstruct is slided set of matrices and is represented by：
    <mrow> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> </msub> <mo>=</mo> <mo>&amp;lsqb;</mo> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>18</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    Step carries out backward smoothing processing to the up smoothing matrix collection, obtains up backward smoothing matrix collection and specifically includes：
    Up backward smoothing matrix collection be：
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> <mi>b</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <mo>&amp;rsqb;</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mi>&amp;Pi;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mi>&amp;Pi;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>b</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>19</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  5. 5. method as claimed in claim 4, it is characterised in that qxIndividual row face battle array it is descending with it is up front and rear to smooth square Battle array collects：
    <mrow> <msub> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>20</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Pi;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mi>C</mi> <mn>0</mn> </msub> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>21</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>s</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>22</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Theta;A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>}</mo> <mo>+</mo> <msup> <mi>&amp;sigma;</mi> <mn>2</mn> </msup> <msub> <mover> <mi>C</mi> <mo>&amp;OverBar;</mo> </mover> <mn>0</mn> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>23</mn> <mo>)</mo> </mrow> </mrow>
    Wherein
    <mrow> <msub> <mo>&amp;Pi;</mo> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>24</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mover> <mo>&amp;Pi;</mo> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>25</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  6. 6. method as claimed in claim 5, it is characterised in that according to each row face battle array it is descending before and after to extraction number According to it is up it is front and rear calculate final front-rear space smooth collection to extraction data, specifically include：
    <mrow> <msup> <mi>R</mi> <mrow> <mi>f</mi> <mi>b</mi> </mrow> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>Q</mi> <mi>x</mi> </msub> </mrow> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> </munderover> <mo>{</mo> <mo>&amp;lsqb;</mo> <msub> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <msub> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> </msub> <mo>&amp;rsqb;</mo> <mo>+</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>b</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>26</mn> <mo>)</mo> </mrow> </mrow>
    To RfbAfter carrying out singular value decomposition, using two dimensional ESPRIT Algorithm for Solving DOA estimates.
  7. 7. method as claimed in claim 4, it is characterised in that difference computing is carried out to the noise section of formula (6), had：
    The non-noise part of other cross-correlation submatrixs can use front-rear space smooth technical finesse：
    <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>{</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>H</mi> </msubsup> <mo>+</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <mo>.</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> <mo>+</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>*</mo> </msup> <msubsup> <mi>x</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>T</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>}</mo> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msub> <mi>A</mi> <mi>P</mi> </msub> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mi>n</mi> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>28</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,It can be obtained by (27) and (28), the n-th row (n=1 ..., Qy- 1) difference matrix of data It is represented by：
    <mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>29</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>T</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>,</mo> <mn>...</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>30</mn> <mo>)</mo> </mrow> </mrow>
    Remaining PyThe difference matrix of column data is represented by：
    <mrow> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mo>*</mo> </msubsup> <msub> <mi>J</mi> <mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>31</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,Descending sky can be obtained by (29) and (31) Between difference smoothing matrix collection (SD-SMS) be：
    <mrow> <msubsup> <mi>R</mi> <mn>1</mn> <mi>d</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mi>R</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> <mi>d</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <mn>1</mn> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>32</mn> <mo>)</mo> </mrow> </mrow>
    Then extracting the up difference smoothing matrix collection of data message structure from top to bottom is
    <mrow> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mn>1</mn> <mi>d</mi> </msubsup> <mo>=</mo> <mo>&amp;lsqb;</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> <mi>d</mi> </msubsup> <mo>&amp;rsqb;</mo> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>33</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <msub> <mi>J</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> </msub> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>34</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <mn>1</mn> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <mi>&amp;Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>35</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow> 5
  8. 8. method as claimed in claim 7, it is characterised in that can be obtained according to formula (32) and (33), qxIndividual row face battle array is corresponding Downlink and uplink difference smoothing matrix collection be respectively：
    <mrow> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>36</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>=</mo> <msub> <mi>A</mi> <mi>P</mi> </msub> <mo>{</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>37</mn> <mo>)</mo> </mrow> </mrow>
    Wherein,
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mi>n</mi> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msub> <mi>R</mi> <mi>s</mi> </msub> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>,</mo> <mn>...</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <msub> <mi>Q</mi> <mi>y</mi> </msub> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mi>n</mi> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>+</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>+</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>/</mo> <mn>2</mn> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>38</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mi>&amp;Gamma;</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>Q</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>Q</mi> <mi>y</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>&amp;Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>39</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msub> <mo>=</mo> <mo>{</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>P</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <msub> <mi>P</mi> <mi>y</mi> </msub> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mn>1</mn> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>+</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <msub> <mi>P</mi> <mi>y</mi> </msub> <mo>-</mo> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>...</mn> <mo>,</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>y</mi> <mrow> <mover> <mi>n</mi> <mo>&amp;OverBar;</mo> </mover> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <msub> <mi>P</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <msub> <mi>P</mi> <mi>x</mi> </msub> <mi>H</mi> </msubsup> <mo>}</mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>40</mn> <mo>)</mo> </mrow> </mrow>
    <mrow> <msub> <mover> <mi>&amp;Gamma;</mi> <mo>&amp;OverBar;</mo> </mover> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>,</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>R</mi> <mi>s</mi> </msub> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <mo>-</mo> <msup> <mi>&amp;Theta;</mi> <mo>*</mo> </msup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <mn>1</mn> <mo>-</mo> <msub> <mi>q</mi> <mi>x</mi> </msub> </mrow> </msubsup> <msubsup> <mi>R</mi> <mi>s</mi> <mo>*</mo> </msubsup> <msubsup> <mi>&amp;Phi;</mi> <mi>x</mi> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>&amp;Theta;</mi> <mo>)</mo> </mrow> <msubsup> <mi>A</mi> <mi>P</mi> <mi>H</mi> </msubsup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>41</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
  9. 9. method as claimed in claim 8, it is characterised in that poor according to downlink and uplink corresponding to each row face battle array Different smoothing matrix collection establishes final spatial diversity smoothing matrix collection：
    <mrow> <msup> <mi>R</mi> <mi>d</mi> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <msub> <mi>Q</mi> <mi>x</mi> </msub> </mfrac> <munderover> <mo>&amp;Sigma;</mo> <mrow> <msub> <mi>q</mi> <mi>x</mi> </msub> <mo>=</mo> <mn>1</mn> </mrow> <msub> <mi>Q</mi> <mi>x</mi> </msub> </munderover> <mo>{</mo> <msubsup> <mi>R</mi> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>,</mo> <msubsup> <mover> <mi>R</mi> <mo>&amp;OverBar;</mo> </mover> <msub> <mi>q</mi> <mi>x</mi> </msub> <mi>d</mi> </msubsup> <mo>}</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>42</mn> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
    Two dimensional ESPRIT Algorithm for Solving DOA estimates are used to it.
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