CN105334507B - The detection method to offshore floating radar target based on polarization multiple features - Google Patents

The detection method to offshore floating radar target based on polarization multiple features Download PDF

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CN105334507B
CN105334507B CN201510795663.1A CN201510795663A CN105334507B CN 105334507 B CN105334507 B CN 105334507B CN 201510795663 A CN201510795663 A CN 201510795663A CN 105334507 B CN105334507 B CN 105334507B
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许述文
蒲佳
水鹏朗
薛健
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Xidian University
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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
    • 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
    • G01S7/414—Discriminating targets with respect to background clutter

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Abstract

The invention discloses a kind of detection method to offshore floating radar target based on polarization multiple features, comprise the following steps：(1) radar transmitter transmitting pulse signal, radar receiver receives echo data；According to echo data, H is built0Assuming that and H1Assuming that the received vector of detection unit and the received vector of reference unit in lower echo data, (2) try to achieve two polarization characteristics of detection unit and two polarization characteristics of reference unit respectively；(3) relative Doppler's peak height of relative the Doppler's peak height and reference unit of detection unit is calculated respectively；(4) assemblage characteristic of detection unit and the assemblage characteristic of reference unit are calculated respectively；(5) detection statistic of detection unit is calculated；(6) if the detection statistic of detection unit, which is more than in zero, detection unit, has target, H1Assuming that setting up；If the detection statistic of detection unit, which is not more than in zero, detection unit, is not present target, H0Assuming that setting up.

Description

Method for detecting sea surface floating radar target based on polarization multi-feature
Technical Field
The invention belongs to the technical field of radar target detection, and particularly relates to a method for detecting a radar target floating on the sea surface based on polarization multi-characteristics, which can be used for detecting a weak radar target floating on the sea surface under the background of sea clutter.
Background
Monitoring low-speed or floating weak radar targets on the sea surface, such as buoys, broken icebergs, boats, floating plates, and the like, is a main task of the sea surface monitoring radar. The nature of the sea clutter varies constantly with the radar parameters, the observation geometry of the radar and the sea surface conditions. When the high-resolution radar works at a small ground wiping angle, the echo signal of a weak radar target floating on the sea surface in the echo signals received by the radar receiver is too weak to be searched through simple energy integration. The radar with high azimuth resolution is generally adopted to detect the sea surface floating weak radar target, so that the level of sea clutter is reduced, the radar stays in one beam position for a long time to collect more information of the sea surface floating weak radar target and the environment, and the efficiency of the radar for detecting the sea surface floating weak radar target is reduced.
The traditional detection method based on the sea clutter statistical model is widely used for detecting the moving radar target under the sea clutter background. When the high-resolution radar works at a small ground-wiping angle, the sea clutter statistical model does not meet Gaussian distribution any more, and some non-Gaussian distributions, such as Weibull distribution, lognormal distribution, K distribution and other complex non-Gaussian distributions, are used for describing the sea clutter characteristics of the high-resolution radar when the high-resolution radar works at the small ground-wiping angle. Accordingly, various adaptive detectors have been proposed, such as a generalized likelihood ratio checker, an adaptive matched filter and an adaptive normalized matched filter, which are capable of working well on the premise that: the sea clutter and the echo signals of the radar target are completely separable in the doppler domain, but the detection probability of these detectors for the sea floating weak radar target is low.
The document Leung, H., and Lo, T.Chaotic radar signal processing over the sea. IEEE Journal of organic Engineering, 18, 3(1993), 287 295, starting from the assumption that the time sequence of the sea clutter data of high-resolution radar is correlated with the chaotic system, detects the target by analyzing the measured sea clutter data. The core of the detector proposed in this document is a non-linear predictor based on a prediction error hypothesis test, which can only be used to interpret the abnormal behavior of the time series received in the detection, since it presupposes: the sea clutter time sequence is disordered, but this premise has proven to be unrealistic. Subsequently, a radar target detection method based on radar echo signal energy characteristics is proposed, but because the detection information used by the method is single, the time required by characteristic extraction is long, and the observation time of a radar target is too long, a good effect is difficult to obtain for detecting a weak radar target floating on the sea surface.
Disclosure of Invention
In view of the above-mentioned shortcomings of the prior art, the present invention aims to provide a method for detecting a radar target floating on the sea surface based on polarization multi-features. The method extracts the polarization characteristics of the radar target and the sea clutter by utilizing the polarization information of the radar echo data, can improve the speed of characteristic extraction, and can obtain better radar detection performance aiming at the sea floating weak target in shorter observation time.
A method for detecting a radar target floating on the sea surface based on polarization multi-feature is characterized by comprising the following steps:
step 1, firstly, transmitting a pulse signal through a radar transmitter, and receiving echo data formed by the pulse signal through sea surface scattering through a radar receiver; then, from the echo data, H is constructed0Assuming that the received vectors of the detecting unit and the reference unit in the echo data, and H1Assuming that the receiving vector of the detecting unit and the receiving vector of the reference unit are in the echo data, wherein H is0Assuming that only sea clutter is present, the H1The assumption represents the situation that the sea clutter and the target exist simultaneously;
step 2, according to H1Under the assumption, in the echo data, a receiving vector of a detection unit and a receiving vector of a reference unit respectively obtain two polarization characteristics of the detection unit and two polarization characteristics of the reference unit by using a model decomposition method based on unitary bi-component change, wherein the two polarization characteristics of the detection unit are respectively: the energy corresponding to the dihedral angle scattering mechanism of the detection unit and the energy corresponding to the volume scattering mechanism of the detection unit, the two polarization characteristics of the reference unit are respectively: dihedral scattering mechanism of reference cells corresponding to energy and volume of reference cellsThe scattering mechanism corresponds to energy;
step 3, according to H1Respectively calculating the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit under the assumption that the receiving vector of the detection unit and the receiving vector of the reference unit in the echo data;
step 4, respectively calculating the combination characteristic of the detection unit and the combination characteristic of the reference unit by using the two polarization characteristics of the detection unit and the two polarization characteristics of the reference unit, and the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit; the combined characteristics of the detection unit comprise energy corresponding to a dihedral angle scattering mechanism of the detection unit, energy corresponding to a volume scattering mechanism of the detection unit and relative Doppler peak height of the detection unit; the combined characteristics of the reference unit comprise energy corresponding to a dihedral angle scattering mechanism of the reference unit, energy corresponding to a volume scattering mechanism of the reference unit and relative Doppler peak height of the reference unit;
step 5, calculating a decision area of the detector by using a 3D feature space convex hull learning algorithm according to the combination features of the detection unit and the reference unit; calculating the detection statistic of the detection unit according to the decision area of the detector;
step 6, judging whether a target exists in the detection unit or not according to the detection statistic of the detection unit, and if the detection statistic of the detection unit is larger than zero, indicating that the target exists in the detection unit, H1If the detection statistic of the detection unit is not larger than zero, which indicates that no target exists in the detection unit, H0The assumption is true.
The invention has the beneficial effects that:
1) the invention utilizes the polarization information of the radar echo data, and has better target detection performance compared with the existing detector based on single energy information.
2) The method utilizes the polarization information of the radar echo data to extract the polarization characteristics of the radar target and the sea clutter, has higher characteristic extraction speed and shorter required observation time, and can obtain better target detection performance.
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The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a comparison graph of the detection effect of the actually measured sea clutter data under different false alarm probabilities when the observation time is 0.512 seconds by using the method of the present invention and the existing method, wherein the abscissa is the false alarm probability and the ordinate is the detection probability;
fig. 3 is a comparison graph of the detection effect of the actually measured sea clutter data at the observation time of 4.096 seconds under different false alarm probabilities by the method of the present invention and the existing method, wherein the abscissa is the false alarm probability and the ordinate is the detection probability.
Detailed Description
Referring to fig. 1, the method for detecting a radar target floating on the sea surface based on polarization multi-feature of the invention comprises the following specific steps:
step 1, firstly, transmitting a pulse signal through a radar transmitter, and receiving echo data formed by the pulse signal through sea surface scattering through a radar receiver; then, from the echo data, H is constructed0Assuming that the received vectors of the detecting unit and the reference unit in the echo data, and H1Assuming that the receiving vector of the detecting unit and the receiving vector of the reference unit are in the echo data, wherein H is0Assuming that only sea clutter is present, the H1It is assumed that a situation in which the sea clutter and the target coexist is represented.
Constructing H from the echo data0Suppose thatAnd H1Assuming that the receiving vector of the detection unit and the receiving vector of the reference unit in the echo data are as follows:
wherein x (n) represents a received vector of the detecting unit, xp(n) a received vector of the reference unit, c (n) a sea clutter vector of the detection unit, cp(N) represents a sea clutter vector of the reference unit, N represents a dimension of a reception vector of the detection unit or the reference unit, N represents a maximum dimension of the reception vector of the detection unit or the reference unit, P represents a P-th reference unit, and P represents a total number of the reference units.
The acceptance vector x (n) of the detection unit contains the components of the four polarization channels HH, VV, HV and VH of the radar, wherein the two components of the acceptance vector x (n) of the detection unit in the HH channel areAndthe two components of the acceptance vector x (n) of the detection unit in VV channel areAndthe acceptance vector x (n) of the detection unit has two components in the HV channelAndthe acceptance vector x (n) of the detection unit has two components in the VH channelAnd
acceptance vector x for reference unitp(n) contain the components of the four polarized channels HH, VV, HV, VH of the radar, where the acceptance vector x of the reference cellp(n) two components in the HH channel areAndacceptance vector x for reference unitp(n) two components in the VV channel areAndacceptance vector x for reference unitp(n) two components in the HV channel areAndacceptance vector x for reference unitp(n) two components in the VH channel areAnd
step 2, according to H1Under the assumption that a receiving vector of a detection unit and a receiving vector of a reference unit in echo data are obtained by using a model decomposition method based on unitary binary change, two polarization characteristics of the detection unit and two polarization characteristics of the reference unit are respectively obtained, and the two polarization characteristics of the detection unitRespectively as follows: the energy corresponding to the dihedral angle scattering mechanism of the detection unit and the energy corresponding to the volume scattering mechanism of the detection unit, the two polarization characteristics of the reference unit are respectively: the dihedral scattering mechanism of the reference cell corresponds to energy and the bulk scattering mechanism of the reference cell corresponds to energy.
The specific substeps of step 2 are:
2.1 according to H1Assuming that the receiving vectors of the detecting unit and the receiving vectors of the reference unit in the echo data are as follows, calculating a polarization scattering matrix S of the detecting unit and a polarization scattering matrix S' of the reference unit:
where HH, VV, HV and VH denote the four polarized channels of the radar, SHHA polarization scattering matrix, S, representing the HH polarization channel of the detection cellHVA polarization scattering matrix, S, representing the HV polarization channel of the detection cellVHPolarization scattering matrix, S, representing the VH polarization channels of the detection cellsVVPolarization scattering matrix, S 'representing detection unit VV polarization channel'HHA polarization scattering matrix, S ', representing the HH polarization channel of the reference cell'HVA polarization scattering matrix, S ', representing a reference cell HV polarization channel'VHA polarization scattering matrix, S ', representing a reference cell VH polarization channel'VVA polarization scattering matrix representing the polarization channel of the reference cell VV,andfor the two components of the detection unit's acceptance vector x (n) in the HH channel,andfor the two components of the detection cell's acceptance vector x (n) at VV channel,andtwo components in the HV channel are accepted vectors x (n) for the detection unit,andtwo components in the VH channel are accepted vectors x (n) for the detection units,andis an acceptance vector x of the reference unitp(n) in the two components of the HH channel,andis an acceptance vector x of the reference unitp(n) at both components of the VV channel,andis an acceptance vector x of the reference unitp(n) at both components of the HV channel,andis an acceptance vector x of the reference unitp(N) in two components of the VH channel, N denotes the dimension of the receiving vector of the detection unit or the reference unit, N is 1, 2.. N, N denotes the maximum dimension of the receiving vector of the detection unit or the reference unit, i is an imaginary unit;
2.2, according to the polarization scattering matrix S of the detection unit and the polarization scattering matrix S 'of the reference unit, the coherent matrix T of the detection unit and the coherent matrix T' of the reference unit are obtained:
wherein |. non chlorine2Represents the square of the norm (·)*Representing the conjugation;
2.3 according to the coherent matrix T of the detection unit and the coherent matrix T' of the reference unit, obtaining two polarization characteristics of the detection unit and two polarization characteristics of the reference unit by using a model decomposition method based on the unitary-bivariate change;
firstly, obtaining a rotation matrix T (theta) of the detection unit and a rotation matrix T ' (theta ') of the reference unit by carrying out rotation change on a coherent matrix T of the detection unit and a coherent matrix T ' of the reference unit:
wherein,re {. is used for representing the real part of a complex number, and the superscript represents conjugation;
then, according to the rotation matrix T (θ) of the detection unit and the rotation matrix T ' (θ ') of the reference unit, a unitary transformation matrix T () of the detection unit and a unitary transformation matrix T ' ():
T11()＝T11(θ)＝|SHH+SVV|2
T22()＝T22(θ)cos22+T33(θ)sin22+Im{T23(θ)}sin4
T33()＝T33(θ)cos22+T22(θ)sin22-Im{T23(θ)}sin4
T11′(′)＝T′11(θ′)＝|S′HH+S′VV|2
T22′(′)＝T22′(θ′)cos22′+T33′(θ′)sin22′+Im{T23′(θ′)}sin4′
T33′(′)＝T33′(θ′)cos22′+T22′(θ′)sin22′-Im{T23′(θ′)}sin4′
wherein,im {. is } represents taking the imaginary part of the complex number;
finally, according to unitary transformation matrix T () of the detecting unit and unitary transformation matrix T' () of the reference unit, obtaining their decomposition expressions:
T()＝PsT()surface+PdT()double+PvT()vol+PcT()helix
T′()＝P′sT′()surface+P′dT′()double+Pv′T′()vol+Pc′T′()helix
wherein, T ()surface、T()double、T()vol、T()helixRespectively representing four sub unitary transformation matrixes T' corresponding to a surface scattering mechanism, a dihedral angle scattering mechanism, a volume scattering mechanism and a spiral scattering mechanism of the detection unitsurface、T′()double、T′()vol、T′()helixRespectively representing sub unitary transformation matrixes P corresponding to a surface scattering mechanism, a dihedral angle scattering mechanism, a volume scattering mechanism and a spiral scattering mechanism of the reference unitsRepresenting the energy, P, corresponding to the surface scattering mechanism of the detection celldDihedral scattering mechanism pair representing detection cellsIn response to energy, PvRepresenting the energy, P, corresponding to the bulk scattering mechanism of the detection cellcRepresenting the energy, P, corresponding to the helical scattering mechanism of the detection cells' denotes the energy, P, corresponding to the surface scattering mechanism of the reference celld' indicates the energy, P, corresponding to the dihedral scattering mechanism of the reference cellv' denotes the energy, P, corresponding to the volume scattering mechanism of the reference cellc' denotes the energy corresponding to the helical scattering mechanism of the reference cell.
Step 3, according to H1And respectively calculating the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit by assuming the receiving vector of the detection unit and the receiving vector of the reference unit in the echo data.
The specific substeps of step 3 are:
3.1 according to H1Assuming that the receiving vector of the detecting unit and the receiving vector of the reference unit in the echo data are respectively calculated, the Doppler amplitude spectrum X (f) of the detecting unit is calculatedd) And Doppler amplitude spectrum X' (f) of the reference celld)：
Wherein x (n) represents a received vector of the detecting unit, xp(n) denotes a received vector of the reference unit, fdRepresenting the Doppler frequency, TrIs the pulse repetition frequency, N represents the dimension of the received vector of the detection unit or the reference unit, N represents the maximum dimension of the received vector of the detection unit or the reference unit;
3.2 Doppler amplitude spectrum X (f) from the detection unitd) And Doppler amplitude spectrum X' (f) of the reference celld) Separately calculating the positions of Doppler peaks in the Doppler amplitude spectrum of the detection unitsAnd height Peak (x), and the location of the Doppler peak in the Doppler amplitude spectrum of the reference cellAnd height Peak' (x):
wherein,it means that the maximum value is taken for operation,denotes the Doppler frequency f at which {. DEG } is maximizeddTaking the value of (A);
3.3 Doppler amplitude spectrum according to the position of Doppler peakAnd a height peak (x), calculating a relative doppler peak height RPH of the detection unit:
wherein Δ represents the Doppler number set, Δ [ -1，-2]∪[2，1]，1＝50Hz，2The symbol # Δ represents the position of the doppler peak in the doppler amplitude spectrum of the detection unit at 5HzThe number of doppler bins Δ;
3.4 location of Doppler peaks in the Doppler amplitude spectrum from the reference cellAnd height Peak '(x), calculating relative doppler Peak height RPH' of the reference cell:
wherein the symbol # Δ' represents the position of the Doppler peak in the Doppler amplitude spectrum of the reference cellThe number falling into the doppler set Δ.
Step 4, respectively calculating the combination characteristic of the detection unit and the combination characteristic of the reference unit by using the two polarization characteristics of the detection unit and the two polarization characteristics of the reference unit, and the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit; the combined characteristics of the detection unit comprise energy corresponding to a dihedral angle scattering mechanism of the detection unit, energy corresponding to a volume scattering mechanism of the detection unit and relative Doppler peak height of the detection unit; the combined characteristics of the reference unit comprise the energy corresponding to a dihedral angle scattering mechanism of the reference unit, the energy corresponding to a volume scattering mechanism of the reference unit and the relative Doppler peak height of the reference unit.
The specific substeps of step 4 are:
4.1 Using two polarization characteristics of the detection cell, i.e. the dihedral scattering mechanism of the detection cell corresponds to the energy PdEnergy P corresponding to the volume scattering mechanism of the detection unitvAnd the relative doppler peak height RPH of the detection unit, calculating the combined characteristic CF of the detection unit:
CF＝[Pd，Pv，RPH]；
4.2 use of two polarization characteristics of the reference cell, i.e. the dihedral scattering mechanism of the reference cell corresponds to the energy Pd' corresponding energy P to the volume scattering mechanism of the detection unitv', and relative doppler peak height RPH ' of the detection unit, calculate the combined characteristic CF ' of the detection unit:
CF′＝[Pd′，Pv′，RPH′]。
step 5, calculating a decision area of the detector by using a 3D feature space convex hull learning algorithm according to the combination features of the detection unit and the reference unit; and calculating the detection statistic of the detection unit according to the decision area of the detector.
The specific substeps of step 5 are:
5.1 calculating a decision area omega of the detector by using a 3D feature space convex hull learning algorithm according to the combined feature CF' of the reference unit;
first, a false alarm probability P is setfaAnd obtaining a convex hull omega 'according to the combination characteristic CF' of the reference unit:
Ω′＝{CF′j，j＝1，2，...，J}
wherein J represents the dimension of the combined feature CF 'of the reference unit, and J represents the maximum dimension, CF'jA jth feature representing a combined feature CF' of the reference cell;
the resulting convex hull Ω' is then represented as the decision region Ω of the detector with the outer surface triangle vertices:
wherein SP {. is } represents a closed space surrounded by triangles,representing a vertex asThe shape of the triangle of (a) is,three vertexes arranged in a clockwise direction from the outer side of the convex contour of the triangle on the qth convex hull, Q being 1, 2.
5.2 calculating a detection statistic xi of the detection unit according to the combination characteristic CF of the detection unit and the decision area omega of the detector:
where det (-) denotes the determinant of the matrix.
Step 6, judging whether a target exists in the detection unit or not according to the detection statistic of the detection unit, and if the detection statistic of the detection unit is larger than zero, indicating that the target exists in the detection unit, H1If the detection statistic of the detection unit is not larger than zero, which indicates that no target exists in the detection unit, H0The assumption is true.
The effect of the present invention can be further illustrated by the following simulation experiments:
1) simulation conditions are as follows:
in the simulation experiment, actually measured sea clutter data is adopted to test the detection performance of the method.
The actually measured sea clutter data that adopts in the simulation experiment is the data of the sea clutter that IPIX high resolution radar obtained, and this IPIX high resolution radar has 9.3 GHz's carrier frequency, and the beam width is 0.9 degree, and range resolution is 30m, and the distance sampling interval is 15 meters, and this IPIX high resolution radar sends coherent pulse train under H and the alternative polarization mode of V, and pulse repetition frequency is Tr2000Hz and the radar receiver also has two channels with H and V polarizations. Each set of data contains data collected simultaneously for the four polarized channels HH, VV, HV and VH. And 4 of the 14 continuous distance units are selected as detection units, and 10 are selected as reference units.
2) Simulation content and result analysis:
the method and the existing detection method based on energy characteristics (the existing method for short) are respectively adopted to carry out target detection on the actually measured sea clutter data, the detection results of the two detection methods are compared by analyzing the detection probabilities under different false alarm probabilities, and the higher the detection probability is, the better the detection performance is.
Simulation experiment 1:
when the observation time is 0.512 seconds, comparing the detection probability of the actually measured sea clutter data under different false alarm probabilities by the method of the invention and the existing method, as shown in fig. 2; in fig. 2, the false alarm probability changes from 0.005 to 0.01, the black circle curve represents the detection probability curve of the method of the present invention, the black inverted triangle curve represents the detection probability curve of the existing method in the HV polarization channel, the black regular triangle curve represents the detection probability curve of the existing method in the VH polarization channel, the black square curve represents the detection probability curve of the existing method in the HH polarization channel, and the black "×" curve represents the detection probability curve of the existing method in the VV polarization channel.
As can be seen from FIG. 2, the detection performance of the method of the present invention is significantly better than that of the existing method in the four polarization channels of HH, VV, HV and VH at the observation time of 0.512 seconds.
Simulation experiment 2:
when the observation time is 0.512 seconds, comparing the detection probability of the actually measured sea clutter data under different false alarm probabilities by the method of the invention and the existing method, as shown in fig. 2; in fig. 2, the false alarm probability changes from 0.005 to 0.01, the black circle curve represents the detection probability curve of the method of the present invention, the black inverted triangle curve represents the detection probability curve of the existing method in the HV polarization channel, the black regular triangle curve represents the detection probability curve of the existing method in the VH polarization channel, the black square curve represents the detection probability curve of the existing method in the HH polarization channel, and the black "×" curve represents the detection probability curve of the existing method in the VV polarization channel.
As can be seen from FIG. 3, the detection performance of the method of the present invention is significantly better than that of the existing method in the four polarization channels of HH, VV, HV and VH at the observation time of 4.096 seconds.
In conclusion, the sea surface floating weak radar target detection method based on the polarization multi-feature is stable in detection performance and superior to the existing detection performance based on the energy feature detection method.
It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention; thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (5)

1. A method for detecting a radar target floating on the sea surface based on polarization multi-feature is characterized by comprising the following steps:
step 1, firstly, transmitting a pulse signal through a radar transmitter, and receiving echo data formed by the pulse signal through sea surface scattering through a radar receiver; then, from the echo data, H is constructed0Assuming that the received vectors of the detecting unit and the reference unit in the echo data, and H1Assuming that the receiving vector of the detecting unit and the reference unit in the echo data are connectedReceive a vector, wherein the H0Assuming that only sea clutter is present, the H1The assumption represents the situation that the sea clutter and the target exist simultaneously;
in step 1, H is constructed according to the echo data0Hypothesis and H1Assuming that the receiving vector of the detection unit and the receiving vector of the reference unit in the echo data are as follows:
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>H</mi> <mn>0</mn> </msub> <mo>:</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>c</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>H</mi> <mn>1</mn> </msub> <mo>:</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>s</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>c</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mi>n</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>N</mi> <mo>,</mo> <mi>p</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>...</mn> <mo>,</mo> <mi>P</mi> </mrow>
wherein x (n) represents a received vector of the detecting unit, xp(n) a received vector of the reference unit, c (n) a sea clutter vector of the detection unit, cp(N) represents a sea clutter vector of the reference unit, N represents a dimension of a reception vector of the detection unit or the reference unit, N represents a maximum dimension of the reception vector of the detection unit or the reference unit, P represents a P-th reference unit, and P represents a total number of the reference units;
the acceptance vector x (n) of the detection unit contains the components of the four polarization channels HH, VV, HV and VH of the radar, wherein the two components of the acceptance vector x (n) of the detection unit in the HH channel areAndthe two components of the acceptance vector x (n) of the detection unit in VV channel areAndthe acceptance vector x (n) of the detection unit has two components in the HV channelAndthe acceptance vector x (n) of the detection unit has two components in the VH channelAnd
acceptance vector x for reference unitp(n) contain the components of the four polarized channels HH, VV, HV, VH of the radar, where the acceptance vector x of the reference cellp(n) two components in the HH channel areAndacceptance vector x for reference unitp(n) two components in the VV channel areAndacceptance vector x for reference unitp(n) two components in the HV channel areAndacceptance vector x for reference unitp(n) two components in the VH channel areAnd
step 2, according to H1Under the assumption, in the echo data, a receiving vector of a detection unit and a receiving vector of a reference unit respectively obtain two polarization characteristics of the detection unit and two polarization characteristics of the reference unit by using a model decomposition method based on unitary bi-component change, wherein the two polarization characteristics of the detection unit are respectively: the energy corresponding to the dihedral angle scattering mechanism of the detection unit and the energy corresponding to the volume scattering mechanism of the detection unit, the two polarization characteristics of the reference unit are respectively: the energy corresponding to the dihedral angle scattering mechanism of the reference unit and the energy corresponding to the volume scattering mechanism of the reference unit;
step 3, according to H1Respectively calculating the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit under the assumption that the receiving vector of the detection unit and the receiving vector of the reference unit in the echo data;
step 4, respectively calculating the combination characteristic of the detection unit and the combination characteristic of the reference unit by using the two polarization characteristics of the detection unit and the two polarization characteristics of the reference unit, and the relative Doppler peak height of the detection unit and the relative Doppler peak height of the reference unit; the combined characteristics of the detection unit comprise energy corresponding to a dihedral angle scattering mechanism of the detection unit, energy corresponding to a volume scattering mechanism of the detection unit and relative Doppler peak height of the detection unit; the combined characteristics of the reference unit comprise energy corresponding to a dihedral angle scattering mechanism of the reference unit, energy corresponding to a volume scattering mechanism of the reference unit and relative Doppler peak height of the reference unit;
step 5, calculating a decision area of the detector by using a 3D feature space convex hull learning algorithm according to the combination features of the detection unit and the reference unit; calculating the detection statistic of the detection unit according to the decision area of the detector;
step 6, judging whether a target exists in the detection unit or not according to the detection statistic of the detection unit, and if the detection statistic of the detection unit is larger than zero, indicating that the target exists in the detection unit, H1If the detection statistic of the detection unit is not larger than zero, which indicates that no target exists in the detection unit, H0The assumption is true.
2. The method for detecting the sea surface floating radar target based on the polarized multi-feature as claimed in claim 1, wherein the specific sub-steps of the step 2 are as follows:
2.1 according to H1Assuming that the receiving vectors of the detecting unit and the receiving vectors of the reference unit in the echo data are as follows, calculating a polarization scattering matrix S of the detecting unit and a polarization scattering matrix S' of the reference unit:
<mrow> <mi>S</mi> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> </msub> </mtd> <mtd> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mi>I</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mi>Q</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mi>I</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mi>Q</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mi>I</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mi>Q</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mi>I</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mi>Q</mi> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
<mrow> <msup> <mi>S</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> <mtd> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>,</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>I</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>Q</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>I</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>Q</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>I</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>Q</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>=</mo> <msubsup> <mi>x</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>I</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msubsup> <mi>ix</mi> <mrow> <mi>V</mi> <mi>H</mi> </mrow> <mrow> <mo>&amp;prime;</mo> <mi>Q</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
where HH, VV, HV and VH denote the four polarized channels of the radar, SHHA polarization scattering matrix, S, representing the HH polarization channel of the detection cellHVA polarization scattering matrix, S, representing the HV polarization channel of the detection cellVHPolarization scattering matrix, S, representing the VH polarization channels of the detection cellsVVPolarization scattering matrix, S 'representing detection unit VV polarization channel'HHA polarization scattering matrix, S ', representing the HH polarization channel of the reference cell'HVA polarization scattering matrix, S ', representing a reference cell HV polarization channel'VHA polarization scattering matrix, S ', representing a reference cell VH polarization channel'VVA polarization scattering matrix representing the polarization channel of the reference cell VV,andfor the two components of the detection unit's acceptance vector x (n) in the HH channel,andfor the two components of the detection cell's acceptance vector x (n) at VV channel,andtwo components in the HV channel are accepted vectors x (n) for the detection unit,andtwo components in the VH channel are accepted vectors x (n) for the detection units,andis an acceptance vector x of the reference unitp(n) in the two components of the HH channel,andis an acceptance vector x of the reference unitp(n) two in the VV channelThe components of the first and second images are,andis an acceptance vector x of the reference unitp(n) at both components of the HV channel,andis an acceptance vector x of the reference unitp(N) in two components of the VH channel, N denotes the dimension of the receiving vector of the detection unit or the reference unit, N is 1, 2.. N, N denotes the maximum dimension of the receiving vector of the detection unit or the reference unit, i is an imaginary unit;
2.2, according to the polarization scattering matrix S of the detection unit and the polarization scattering matrix S 'of the reference unit, the coherent matrix T of the detection unit and the coherent matrix T' of the reference unit are obtained:
<mrow> <mi>T</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>|</mo> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msup> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <mo>*</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <msup> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <mo>*</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <msup> <mrow> <mo>(</mo> <mrow> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> </msub> <mo>-</mo> <msub> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> </msub> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mo>|</mo> <msub> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> </msub> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
<mrow> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mo>|</mo> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <msup> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>*</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <msup> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>*</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>+</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <msup> <mrow> <mo>(</mo> <mrow> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>H</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <mo>-</mo> <msubsup> <mi>S</mi> <mrow> <mi>V</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> </mrow> <mo>)</mo> </mrow> <mo>*</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mn>2</mn> <mo>|</mo> <msubsup> <mi>S</mi> <mrow> <mi>H</mi> <mi>V</mi> </mrow> <mo>&amp;prime;</mo> </msubsup> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein |. non chlorine2Represents the square of the norm (·)*Representing the conjugation;
2.3 according to the coherent matrix T of the detection unit and the coherent matrix T' of the reference unit, obtaining two polarization characteristics of the detection unit and two polarization characteristics of the reference unit by using a model decomposition method based on the unitary-bivariate change;
firstly, a coherent matrix T of a detection unit and a coherent matrix T 'of a reference unit are subjected to rotation change to obtain a rotation matrix T (theta) of the detection unit and a rotation matrix T' (theta) of the reference unit:
<mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;lsqb;</mo> <mi>T</mi> <mo>&amp;rsqb;</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;theta;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>H</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>23</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>32</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>33</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
<mrow> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>&amp;lsqb;</mo> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mo>&amp;rsqb;</mo> <msup> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>-</mo> <mi>sin</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> <mtd> <mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mi>H</mi> </msup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>11</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>12</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>13</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>21</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>22</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>23</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>31</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>32</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msubsup> <mi>T</mi> <mn>33</mn> <mo>&amp;prime;</mo> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
wherein,re {. is used for representing the real part of a complex number, and the superscript represents conjugation;
then, according to the rotation matrix T (θ) of the detection unit and the rotation matrix T ' (θ ') of the reference unit, a unitary transformation matrix T () of the detection unit and a unitary transformation matrix T ' ():
<mrow> <mi>T</mi> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>11</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>22</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>T</mi> <mn>31</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>T</mi> <mn>33</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>
T11()＝T11(θ)＝|SHH+SVV|2
<mrow> <msub> <mi>T</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>21</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mn>21</mn> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;delta;</mi> <mo>-</mo> <msub> <mi>jT</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;delta;</mi> </mrow>
<mrow> <msub> <mi>T</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>31</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;delta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mn>31</mn> <mo>*</mo> </msubsup> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>T</mi> <mn>13</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <mi>&amp;delta;</mi> <mo>-</mo> <msub> <mi>jT</mi> <mn>12</mn> </msub> <mrow> <mo>(</mo> <mi>&amp;theta;</mi> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <mi>&amp;delta;</mi> </mrow>
T22()＝T22(θ)cos22+T33(θ)sin22+Im{T23(θ)}sin4
T33()＝T33(θ)cos22+T22(θ)sin22-Im{T23(θ)}sin4
<mrow> <msup> <mi>T</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>11</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>12</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>13</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>21</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>22</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>31</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msup> <msub> <mi>T</mi> <mn>33</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced> </mrow>3
T11′(′)＝T′11(θ)＝|S′HH+S′VV|2
<mrow> <msup> <msub> <mi>T</mi> <mn>12</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mi>T</mi> <mn>21</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mn>21</mn> <mrow> <mo>*</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mi>T</mi> <mn>12</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msup> <msub> <mi>jT</mi> <mn>13</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> </mrow>
<mrow> <msup> <msub> <mi>T</mi> <mn>13</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mi>T</mi> <mn>31</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msubsup> <mi>T</mi> <mn>31</mn> <mrow> <mo>*</mo> <mo>&amp;prime;</mo> </mrow> </msubsup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mo>=</mo> <msup> <msub> <mi>T</mi> <mn>13</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mn>2</mn> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> <mo>-</mo> <msup> <msub> <mi>jT</mi> <mn>12</mn> </msub> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msup> <mi>&amp;theta;</mi> <mo>&amp;prime;</mo> </msup> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mn>2</mn> <msup> <mi>&amp;delta;</mi> <mo>&amp;prime;</mo> </msup> </mrow>
T22′(′)＝T22′(θ′)cos22′+T33′(θ′)sin22′+Im{T23′(θ′)}sin4′
T33′(′)＝T33′(θ′)cos22′+T22′(θ′)sin22′-Im{T23′(θ′)}sin4′
wherein,im {. is } represents taking the imaginary part of the complex number;
finally, according to unitary transformation matrix T () of the detecting unit and unitary transformation matrix T' () of the reference unit, obtaining their decomposition expressions:
T()＝PsT()surface+PdT()double+PvT()vol+PcT()helix
T′()＝Ps′T′()surface+P′dT′()double+Pv′T′()vol+Pc′T′()helix
wherein, T ()surface、T()double、T()vol、T()helixRespectively representing four sub unitary transformation moments corresponding to a surface scattering mechanism, a dihedral angle scattering mechanism, a volume scattering mechanism and a spiral scattering mechanism of the detection unitBattle array, T' ()surface、T′()double、T′()vol、T′()helixRespectively representing sub unitary transformation matrixes P corresponding to a surface scattering mechanism, a dihedral angle scattering mechanism, a volume scattering mechanism and a spiral scattering mechanism of the reference unitsRepresenting the energy, P, corresponding to the surface scattering mechanism of the detection celldRepresenting the energy, P, corresponding to the dihedral scattering mechanism of the detection cellvRepresenting the energy, P, corresponding to the bulk scattering mechanism of the detection cellcRepresenting the energy, P, corresponding to the helical scattering mechanism of the detection cells' denotes the energy, P, corresponding to the surface scattering mechanism of the reference celld' indicates the energy, P, corresponding to the dihedral scattering mechanism of the reference cellv' denotes the energy, P, corresponding to the volume scattering mechanism of the reference cellc' denotes the energy corresponding to the helical scattering mechanism of the reference cell.
3. The method for detecting the sea surface floating radar target based on the polarized multi-feature as claimed in claim 1, wherein the specific sub-steps of the step 3 are as follows:
3.1 according to H1Assuming that the receiving vector of the detecting unit and the receiving vector of the reference unit in the echo data are respectively calculated, the Doppler amplitude spectrum X (f) of the detecting unit is calculatedd) And Doppler amplitude spectrum X' (f) of the reference celld)：
<mrow> <mi>X</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>N</mi> </msqrt> </mfrac> <mo>|</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>d</mi> </msub> <msub> <mi>nT</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> </mrow>
<mrow> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <msqrt> <mi>N</mi> </msqrt> </mfrac> <mo>|</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>x</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <mo>-</mo> <mn>2</mn> <msub> <mi>&amp;pi;f</mi> <mi>d</mi> </msub> <msub> <mi>nT</mi> <mi>r</mi> </msub> <mo>)</mo> </mrow> <mo>|</mo> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> </mrow>
Wherein x (n) represents a received vector of the detecting unit, xp(n) denotes a received vector of the reference unit, fdRepresenting the Doppler frequency, TrIs the pulse repetition frequency, N represents the dimension of the received vector of the detection unit or the reference unit, N represents the maximum dimension of the received vector of the detection unit or the reference unit;
3.2 Doppler amplitude spectrum X (f) from the detection unitd) And Doppler amplitude spectrum X' (f) of the reference celld) Separately calculating the positions of Doppler peaks in the Doppler amplitude spectrum of the detection unitsAnd height Peak (x), and the location of the Doppler peak in the Doppler amplitude spectrum of the reference cellAnd height Peak' (x):
<mrow> <mi>P</mi> <mi>e</mi> <mi>a</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> </munder> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>}</mo> </mrow>4
<mrow> <msubsup> <mi>f</mi> <mi>d</mi> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> </munder> <mo>{</mo> <mi>X</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>}</mo> </mrow>
<mrow> <msup> <mi>Peak</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> </munder> <mo>{</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>}</mo> </mrow>
<mrow> <msubsup> <mi>f</mi> <mi>d</mi> <mrow> <mo>&amp;prime;</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>arg</mi> <munder> <mrow> <mi>m</mi> <mi>a</mi> <mi>x</mi> </mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> </munder> <mo>{</mo> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>&amp;le;</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;le;</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <msub> <mi>T</mi> <mi>r</mi> </msub> </mrow> </mfrac> <mo>}</mo> </mrow>
wherein,it means that the maximum value is taken for operation,denotes the Doppler frequency f at which {. DEG } is maximizeddTaking the value of (A);
3.3 from Doppler peaks in the Doppler amplitude spectrum of the detection cellPosition ofAnd a height peak (x), calculating a relative doppler peak height RPH of the detection unit:
<mrow> <mi>R</mi> <mi>P</mi> <mi>H</mi> <mo>=</mo> <mfrac> <mrow> <mi>P</mi> <mi>e</mi> <mi>a</mi> <mi>k</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mrow> <mo>#</mo> <mi>&amp;Delta;</mi> </mrow> </mfrac> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;Element;</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mi>max</mi> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;Delta;</mi> </mrow> </msub> <mi>X</mi> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
wherein Δ represents the Doppler number set, Δ [ -1，-2]∪[2，1]，1＝50Hz，2The symbol # Δ represents the position of the doppler peak in the doppler amplitude spectrum of the detection unit at 5HzThe number of doppler bins Δ;
3.4 location of Doppler peaks in the Doppler amplitude spectrum from the reference cellAnd height Peak '(x), calculating relative doppler Peak height RPH' of the reference cell:
<mrow> <msup> <mi>RPH</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <msup> <mi>Peak</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mfrac> <mn>1</mn> <mrow> <mo>#</mo> <msup> <mi>&amp;Delta;</mi> <mo>&amp;prime;</mo> </msup> </mrow> </mfrac> <msub> <mi>&amp;Sigma;</mi> <mrow> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>&amp;Element;</mo> <msubsup> <mi>f</mi> <mi>d</mi> <mrow> <mo>&amp;prime;</mo> <mi>max</mi> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>&amp;Delta;</mi> </mrow> </msub> <msup> <mi>X</mi> <mo>&amp;prime;</mo> </msup> <mrow> <mo>(</mo> <msub> <mi>f</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> </mrow> </mfrac> </mrow>
wherein the symbol # Δ' represents the position of the Doppler peak in the Doppler amplitude spectrum of the reference cellThe number falling into the doppler set Δ.
4. The method for detecting the sea surface floating radar target based on the polarized multi-feature as claimed in claim 1, wherein the specific sub-steps of the step 4 are as follows:
4.1 Using two polarization characteristics of the detection cell, i.e. the dihedral scattering mechanism of the detection cell corresponds to the energy PdEnergy P corresponding to the volume scattering mechanism of the detection unitvAnd the relative doppler peak height RPH of the detection unit, calculating the combined characteristic CF of the detection unit:
CF＝[Pd，Pv，RPH]；
4.2 use of two polarization characteristics of the reference cell, i.e. the dihedral scattering mechanism of the reference cell corresponds to the energy Pd' corresponding energy P to the volume scattering mechanism of the detection unitv', and relative doppler peak height RPH ' of the detection unit, calculate the combined characteristic CF ' of the detection unit:
CF′＝[Pd′，Pv′，RPH′]。
5. the method for detecting the sea surface floating radar target based on the polarized multi-feature as claimed in claim 1, wherein the specific sub-steps of the step 5 are as follows:
5.1 calculating a decision region omega of the detector by using a 3D feature space convex hull learning algorithm according to the combined feature CF' of the reference unit;
first, a false alarm probability P is setfaAnd obtaining a convex hull omega 'according to the combination characteristic CF' of the reference unit:
Ω′＝{CF′j，j＝1，2，...，J}
wherein J represents the dimension of the combined feature CF 'of the reference unit, and J represents the maximum dimension, CF'jA jth feature representing a combined feature CF' of the reference cell;
the resulting convex hull Ω' is then represented as the decision region Ω of the detector with the outer surface triangle vertices:
<mrow> <mi>&amp;Omega;</mi> <mo>&amp;equiv;</mo> <mi>S</mi> <mi>P</mi> <mo>{</mo> <mi>t</mi> <mi>r</mi> <mi>i</mi> <mi>a</mi> <mi>n</mi> <mi>g</mi> <mi>l</mi> <mi>e</mi> <mrow> <mo>(</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mo>,</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>}</mo> </mrow>
wherein SP {. is } represents a closed space surrounded by triangles,representing a vertex asThe shape of the triangle of (a) is,three vertexes arranged in a clockwise direction from the outer side of the convex contour of the triangle on the qth convex hull, Q being 1, 2.
5.2 calculating a detection statistic xi of the detection unit according to the combination characteristic CF of the detection unit and the decision area omega of the detector:
<mrow> <mi>&amp;xi;</mi> <mo>=</mo> <mi>m</mi> <mi>a</mi> <mi>x</mi> <mo>{</mo> <mi>det</mi> <mrow> <mo>(</mo> <mo>&amp;lsqb;</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <mi>C</mi> <mi>F</mi> <mo>,</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <mi>C</mi> <mi>F</mi> <mo>,</mo> <msubsup> <mi>v</mi> <mi>q</mi> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <mi>C</mi> <mi>F</mi> <mo>&amp;rsqb;</mo> <mo>)</mo> </mrow> <mo>}</mo> </mrow>
where det (-) denotes the determinant of the matrix.
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