Multipath resolving correlation interferometer direction finding
First Claim
1. A method for determining the azimuth and elevation to an aircraft at long range that is transmitting an electromagnetic signal while flying at a low altitude above water, the signal being received using a plurality of vertically polarized antennas and horizontally polarized antennas in an antenna array, the received signal is received directly from the aircraft subject to electromagnetic scattering perturbations and is received via multi-path reflections from the surface of the water, and there is a calibration manifold having stored array steering vectors that is used to correct for the perturbations, the method comprising the steps of:
- (a) forming a first plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of vertically polarized antennas;
(b) forming a second plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of horizontally polarized antennas;
(c) calculating signal eigenvalues and associated eigenvectors for each of the plurality of covariance matrices formed in steps (a) and (b) for the signal received directly from the aircraft and received via multi-path reflections from the surface of the water;
(d) comparing the signal eigenvalues for the first plurality of covariance matrices with the signal eigenvalues for the second plurality of covariance matrices to determine if the received signal has stronger vertical or horizontal polarization, and selecting the signal eigenvector associated with the signal having the stronger polarization for subsequent processing in steps (e) and (f);
(e) performing a global correlation maximum search, assuming mirror sea-state reflection conditions using the signal eigenvector selected in step (d) with steering vectors retrieved from the calibration array manifold to determine a first azimuth and elevation; and
(f) performing a conjugate gradient based correlation search using the selected signal eigenvector and the array manifold in the region of the first azimuth and elevation to determine accurate azimuth and elevation information to the aircraft.
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Accused Products
Abstract
Apparatus and a method utilizing correlation interferometer direction finding for determining the azimuth and elevation to an aircraft at long range and flying at low altitudes above water with a transmitting radar while resolving multipath signals. The signals from the radar are received both directly and reflected from the surface of the water using horizontally polarized and vertically polarized antenna arrays, are digitized and are stored in separate covariant matrices. Eigenvalues for the eigenvectors of the matrices processed on signal samples recorded on horizontally polarized X arrays are compared to the eigenvalues for the eigenvectors of the covariance matrices processed on signal samples recorded on vertically polarized X arrays. Incident field polarization is associated with the antenna array measurements that yield the strongest eigenvalue. The eigenvector and eigenvalues for the strongest signal are selected and used for subsequent signal processing. An initial global search assuming mirror sea-state reflection conditions using the signal eigenvector having the strongest eigenvalue is performed to yield an approximate elevation α and azimuth β to the aircraft. The approximate values are then used as the starting point for a subsequent conjugate gradient search to determine accurate elevation α and azimuth β to the aircraft.
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Citations
20 Claims
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1. A method for determining the azimuth and elevation to an aircraft at long range that is transmitting an electromagnetic signal while flying at a low altitude above water, the signal being received using a plurality of vertically polarized antennas and horizontally polarized antennas in an antenna array, the received signal is received directly from the aircraft subject to electromagnetic scattering perturbations and is received via multi-path reflections from the surface of the water, and there is a calibration manifold having stored array steering vectors that is used to correct for the perturbations, the method comprising the steps of:
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(a) forming a first plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of vertically polarized antennas; (b) forming a second plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of horizontally polarized antennas; (c) calculating signal eigenvalues and associated eigenvectors for each of the plurality of covariance matrices formed in steps (a) and (b) for the signal received directly from the aircraft and received via multi-path reflections from the surface of the water; (d) comparing the signal eigenvalues for the first plurality of covariance matrices with the signal eigenvalues for the second plurality of covariance matrices to determine if the received signal has stronger vertical or horizontal polarization, and selecting the signal eigenvector associated with the signal having the stronger polarization for subsequent processing in steps (e) and (f); (e) performing a global correlation maximum search, assuming mirror sea-state reflection conditions using the signal eigenvector selected in step (d) with steering vectors retrieved from the calibration array manifold to determine a first azimuth and elevation; and (f) performing a conjugate gradient based correlation search using the selected signal eigenvector and the array manifold in the region of the first azimuth and elevation to determine accurate azimuth and elevation information to the aircraft. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A method comprising determining the azimuth and elevation to an aircraft at long range and transmitting an electromagnetic signal while flying at a low altitude above water, wherein the signal is received using a plurality of vertically polarized antennas and horizontally polarized antennas in an antenna array, wherein the received signal is received directly from the aircraft and is received via multi-path reflections from the surface of the water, wherein the azimuth and elevation to the aircraft are defined by a conjugate gradient based correlation search of covariance matrices containing the signals received by the vertically polarized antennas and the horizontally polarized antennas in digitized form representing the real and imaginary components of the received signal, and wherein the following equation is used to process the digitized information stored in the covariance matrices is searched to find the azimuth and elevation to the aircraft using the equation:
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where |R(α
,β
)|2 is the correlation squared and the maximum value is searched for during the conjugate gradient based correlation search, α
is the elevation angle to the aircraft transmitting the signal, β
is the azimuth angle to the aircraft transmitting the signal, ρ
d is the direct complex coefficient, ρ
r is the reflected complex coefficient, * is a complex conjugate, na is the number of antennas in the beam forming array utilized to receive the signals transmitted by the aircraft, Apol are calibration vectors as a function of α and
β
, and Upol is the eigenvector resolved received signal vector and is composed of the directly received signal component and the reflected signal component and is equal the sum of the eigenvectors of the signals from the vertically polarized antennas and the horizontally polarized antennas.- View Dependent Claims (9, 10, 11)
and the denominator of the equation in claim 8 is defined as equal to and the closed form maximization process is further simplified by letting H and G terms be defined as then the G and H terms are inserted into the equation in claim 8 to get a revised equation where the characteristic equation of Hermitian forms [H−
γ
G]=0 and the largest root of this equation is the maximum of the ratio of Hermitian forms iswhere |R(α
,β
)|2 has this form and the maximum value of |R(α
,β
)|2 at angles α
, β
, −
α
+Δ
α
, and, β
+Δ
β
is the solution to the determinant equationwhere this determinant equation is solved by the quadratic equation
α
×
γ
max2+b×
γ
max+c=0
α
=G11×
G22+|G12|2
b=−
(H11×
G22+H22×
G11)+(H12×
G21+H21×
G12)
c=H11×
H22−
H12×
H21=0and the maximum value of |R(α
,β
)|2 is therefore
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12. A method for determining the azimuth and elevation to an aircraft at long range that is transmitting an electromagnetic signal while flying at a low altitude above water, the signal being received using a plurality of vertically polarized antennas and horizontally polarized antennas in an antenna array, the received signal is received directly from the aircraft subject to electromagnetic scattering perturbations and is received via multi-path reflections from the surface of the water, and there is a calibration manifold having stored array steering vectors that is used to correct for the perturbations, the method comprising the steps of:
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(a) forming a first plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of vertically polarized antennas; (b) forming a second plurality of covariance matrices from a like plurality of sets of samples of the electromagnetic signal received by the plurality of horizontally polarized antennas; (c) calculating signal eigenvalues and associated eigenvectors for each of the plurality of covariance matrices formed in steps (a) and (b) for the signal received directly from the aircraft and received via multi-path reflections from the surface of the water; (d) comparing the signal eigenvalues for the first plurality of covariance matrices with the signal eigenvalues for the second plurality of covariance matrices to determine if the received signal has stronger vertical or horizontal polarization, and selecting the signal eigenvector associated with the signal having the stronger polarization for subsequent processing in steps (e) and (f); and (e) performing a conjugate gradient based correlation search using the selected signal eigenvector and the array manifold in the region of the first azimuth and elevation to determine accurate azimuth and elevation information to the aircraft. - View Dependent Claims (13, 14, 15, 16, 17, 18, 19, 20)
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Specification