CONFORMAL RANGE MIGRATION ALGORITHM (CRMA) "KARMA"

• US 20060028371A1
• Filed: 08/17/2004
• Published: 02/09/2006
• Est. Priority Date: 08/04/2004
• Status: Active Grant

• Current Assignee: Raytheon Company (Rtx Corporation)
• Original Assignee: Raytheon Company (Rtx Corporation)
• Inventors: Lawrence, Michael E., Hansen, Charles T.
• Granted Patent: US 6,987,479 B1
• Time in Patent Office: Days
• US Class Current: 342/25.F
• CPC Class Codes: G01S 13/9019 Auto-focussing of the SAR signals
• CPC Class Codes: G01S 13/904 SAR modes
• CPC Class Codes: G01S 13/9088 Circular SAR [CSAR, C-SAR]

Abstract

Motion compensation for coherent combination of pulses facilitates a SAR image of a scene on earth'"'"'s surface. A great circle (406) is centered with respect to the earth'"'"'s center, The great circle (406) has an axis (412) perpendicular to a first plane. Axis (412) passes through the earth'"'"'s center. The first plane contains great circle (406) and includes the earth'"'"'s center. Great circle (406) has a first center defined by an intersection of the first plane and axis (412). The scene has one or more radar scatterers and is located on a surface (402). The radar system is mounted on a moving platform (400) moving with a component of motion in a direction along great circle (406). The radar comprises a radar receiver for digitizing the radar returns having a phase from scatterers on surface (402), and a computer for focusing the phase of said radar returns from the scatterers on surface (402). The surface (402) is located on a local scene centerline circle (408), the local scene centerline circle (408) defining a second plane. This second plane is parallel to the first plane. The local scene centerline circle (408) is centered on the axis at a second center, where the second center is displaced with respect to the first center along the axis by a distance (414). The phase of the radar returns received from the scene is compensated for the motion of the moving platform (400) using a cylindrical coordinate system referenced with respect to the second center to yield a SAR image.

Claims

1. A radar for acquiring a synthetic aperture image of a scene on earth, said earth having a great circle centered with respect to said earth'"'"'s center, said great circle having an axis perpendicular to a first plane, said axis passing through said earth'"'"'s center, said first plane containing said great circle including said earth'"'"'s center, said great circle having a first center defined by an intersection of said first plane and said axis, said scene having one or more radar scatterers on a surface, said radar system mounted on a moving platform moving with a component of motion in a direction along said great circle, said radar comprising:

a radar receiver for digitizing radar returns having a phase from scatterers on said surface, and

a computer for focusing said phase of said radar returns from said scatterers on said surface, said surface located on a local scene centerline circle, said local scene centerline circle defining a second plane, said second plane parallel to said first plane, said local scene centerline circle centered on said axis at a second center, said second center displaced with respect to said first center along said axis by a distance;

said phase of said radar returns received from said scene focused for the motion of said moving platform along said great circle using a cylindrical coordinate system referenced with respect to said second center.

2. A radar system as described in claim 1 wherein said phase of said radar returns is focused by computing a nominal moving platform track in a cylindrical coordinate system defined by ρ

, θ and

Z centered with respect to said second center where

ρ

is an object distance from said second center within said cylindrical coordinate system,

θ

is an angle in a third plane, said third plane perpendicular to said first plane and said second plane, said third plane passing through said second center, θ

=0 along said axis, and

Z is a height above said second center;

said ρ

, and θ

defining a scene center line approximated by a circle defined by a local radius of curvature, R_SCL (η

), said local radius of curvature defined by

$K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)=\frac{{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}^2<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)-L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\left(L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)·<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)\right)}{{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}^4}$$\mathrm{and}$$R_{\mathrm{SCL}}=\frac{1}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>};<br><br>$

a center of said circle defined by

$C_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)=L_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)+\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}$

and parametrized by

$L_{\mathrm{LSC},\mathrm{\eta <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=C_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)+\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right),<br><br>\widehat{\mathrm{\rho <br><br>}}=\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right),<br><br>\mathrm{and};<br><br>$$\widehat{\mathrm{\theta <br><br>}}=-\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right),$

said Z dimension given by a cross product,

{circumflex over (z)}={circumflex over (ρ

)}×

{circumflex over (θ

)}

where a position of a target is

x_T=ρ

_T{circumflex over (ρ

)}(θ

_T)+z_T{circumflex over (z)}

and where a nominal position of said moving platform is along a radius R_nav, said R_nav the radius of motion of said moving platform in said cylindrical coordinate system defined by a curvature of said scene centerline, said position of target further defined by

x_ac=R_nav{circumflex over (ρ

)}(θ

_ac)+Z_ac{circumflex over (z)}

and range to said target from said moving platform is

$R_T<br><br>\left({\mathrm{\theta <br><br>}}_{\mathrm{ac}}\right)=\sqrt{{\left({\mathrm{\rho <br><br>}}_T-R_{\mathrm{nav}}\right)}^2+{\left(z_T-Z_{\mathrm{nav}}\right)}^2+4<br><br>{\mathrm{\rho <br><br>}}_T<br><br>R_{\mathrm{nav}}<br><br>{\sin }^2<br><br>\left(\frac{{\mathrm{\theta <br><br>}}_T-{\mathrm{\theta <br><br>}}_{\mathrm{ac}}}{2}\right)}.$

3. A radar system as described in claim 2, wherein said radar focuses said phase using:

an along track spatial frequency parameter to compute said image from said radar returns, said along track spatial frequency parameter defined by K_θ

=K_x/R_SCL;

an along track matched filter defined by

$F_{\mathrm{MF}}=\exp <br><br>\left(-i<br><br>\left[R_{\mathrm{sc}}<br><br>\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}-K_R<br><br>R_s-K_{\mathrm{\theta <br><br>}}<br><br>\left({\mathrm{\Theta <br><br>}}_{\mathrm{sc}}\right)+\frac{\mathrm{\epsilon <br><br>}}{6}<br><br>\frac{\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}}{R_{\mathrm{sc}}}<br><br>{\left({\mathrm{\Theta <br><br>}}_{\mathrm{sc}}+\frac{R_{\mathrm{sc}}<br><br>K_{\mathrm{\theta <br><br>}}/\mathrm{\alpha <br><br>}}{\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}}\right)}^3\right]\right)$$\mathrm{where}$$R_{\mathrm{sc}}^2={\left(R_{\mathrm{SCL}}-R_{\mathrm{nav}}\right)}^2+{\left(Z_{\mathrm{SCL}}-Z_{\mathrm{ac}}\right)}^2+4<br><br>R_{\mathrm{SCL}}<br><br>R_{\mathrm{nav}}<br><br>{\sin }^2<br><br>\left(\frac{{\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c}{2}\right),<br><br>-R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\sin <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right)<br><br>\tan <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right)$$\mathrm{\alpha <br><br>}=R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\cos <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),<br><br>\mathrm{\Theta <br><br>}=\tan <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),<br><br>\mathrm{and}$$\mathrm{\epsilon <br><br>}=R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\sin <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),$

and where

θ

_o and Z_SCL describe an angular and an axial coordinate of said scene entry point in said local scene cylindrical coordinates;

θ

_c describes an angular coordinate of said center of said synthetic aperture imaging said scene entry point; and

θ

_o−

θ

_c describes the nominal angular offset between said moving platform position and an antenna pointing position in said scene cylindrical coordinates.

4. A method for acquiring a synthetic aperture image of a scene on earth using a radar, said earth having a great circle centered with respect to said earth'"'"'s center, said great circle having an axis perpendicular to a first plane, said axis passing through said earth'"'"'s center, said first plane containing said great circle including said earth'"'"'s center, said great circle having a first center defined by an intersection of said first plane and said axis, said scene having one or more radar scatterers on a surface, said radar system mounted on a moving platform moving with a component of motion in a direction along said great circle, said method comprising the steps of:

digitizing radar returns having a phase from scatterers on said surface, and

focusing said phase of said radar returns from said scatterers on said surface, said surface located on a local scene centerline circle, said local scene centerline circle defining a second plane, said second plane parallel to said first plane, said local scene centerline circle centered on said axis at a second center, said second center displaced with respect to said first center along said axis by a distance;

forming an image from said radar returns received from said scene, said returns focused for the motion of said moving platform along said great circle using a cylindrical coordinate system referenced with respect to said second center.

5. A method as described in claim 4 wherein said phase of said radar returns is focused by computing a nominal moving platform track in a cylindrical coordinate system defined by ρ

, θ and

Z centered with respect to said second center where

ρ

is an object distance from said second center within said cylindrical coordinate system,

θ

is an angle in a third plane, said third plane perpendicular to said first plane and said second plane, said third plane passing through said second center, θ

=0 along said axis, and

Z is a height above said second center;

said ρ

, and θ

defining a scene center line approximated by a circle defined by a local radius of curvature, R_SCL (η

), said local radius of curvature defined by

$K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)=\frac{{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}^2<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)-L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\left(L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)·<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)\right)}{{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}^4}$$\mathrm{and}$$R_{\mathrm{SCL}}=\frac{1}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}$

a center of said circle defined by

$C_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)=L_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)+\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}$

and parametrized by

$L_{\mathrm{LSC},\mathrm{\eta <br><br>}}<br><br>\left(\mathrm{\theta <br><br>}\right)=C_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)+\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>R_{\mathrm{SCL}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right),<br><br>\widehat{\mathrm{\rho <br><br>}}=\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right),<br><br>\mathrm{and}$$\widehat{\mathrm{\theta <br><br>}}=-\frac{K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>K_{\mathrm{SC}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\sin <br><br>\left(\mathrm{\theta <br><br>}\right)+\frac{L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)}{<br><br>L_{\mathrm{SC}}^{\mathrm{\prime <br><br>}}<br><br>\left(\mathrm{\eta <br><br>}\right)<br><br>}<br><br>\cos <br><br>\left(\mathrm{\theta <br><br>}\right);<br><br>$

said Z dimension given by a cross product,

{circumflex over (z)}={circumflex over (ρ

)}×

{circumflex over (θ

)}

where a position of a target is

x_T=ρ

_T{circumflex over (ρ

)}(θ

_T)+z_T{circumflex over (z)}

and where a nominal position of said moving platform is along a radius R_nav, said R_nav the radius of motion of said moving platform in said cylindrical coordinate system defined by a curvature of said scene centerline, said position of target further defined by

x_ac=R_nav{circumflex over (ρ

)}(θ

_ac)+Z_ac{circumflex over (z)},

and range to said target from said moving platform is

$R_T<br><br>\left({\mathrm{\theta <br><br>}}_{\mathrm{ac}}\right)=\sqrt{{\left({\mathrm{\rho <br><br>}}_T-R_{\mathrm{nav}}\right)}^2+{\left(z_T-Z_{\mathrm{nav}}\right)}^2+4<br><br>{\mathrm{\rho <br><br>}}_T<br><br>R_{\mathrm{nav}}<br><br>{\sin }^2<br><br>\left(\frac{{\mathrm{\theta <br><br>}}_T-{\mathrm{\theta <br><br>}}_{\mathrm{ac}}}{2}\right)}.$

6. A radar system as described in claim 5, wherein said phase is focused using:

an along track spatial frequency parameter for computing said image from said radar returns, said along track spatial frequency parameter defined by K_θ

=K_x/R_SCL;

an along track matched filter defined by

$F_{\mathrm{MF}}=\exp <br><br>\left(-i<br><br>\left[R_{\mathrm{sc}}<br><br>\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}-K_R<br><br>R_s-K_{\mathrm{\theta <br><br>}}<br><br>\left({\mathrm{\Theta <br><br>}}_{\mathrm{sc}}\right)+\frac{\mathrm{\epsilon <br><br>}}{6}<br><br>\frac{\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}}{R_{\mathrm{sc}}}<br><br>{\left({\mathrm{\Theta <br><br>}}_{\mathrm{sc}}+\frac{R_{\mathrm{sc}}<br><br>K_{\mathrm{\theta <br><br>}}/\mathrm{\alpha <br><br>}}{\sqrt{K_R^2-K_{\mathrm{\theta <br><br>}}^2/\mathrm{\alpha <br><br>}}}\right)}^3\right]\right)$$\mathrm{where}$$R_{\mathrm{sc}}^2={\left(R_{\mathrm{SCL}}-R_{\mathrm{nav}}\right)}^2+{\left(Z_{\mathrm{SCL}}-Z_{\mathrm{ac}}\right)}^2+4<br><br>R_{\mathrm{SCL}}<br><br>R_{\mathrm{nav}}<br><br>{\sin }^2<br><br>\left(\frac{{\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c}{2}\right),<br><br>-R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\sin <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right)<br><br>\tan <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right)$$\mathrm{\alpha <br><br>}=R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\cos <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),<br><br>\mathrm{\Theta <br><br>}=\tan <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),<br><br>\mathrm{and}$$\mathrm{\epsilon <br><br>}=R_{\mathrm{NAV}}<br><br>R_{\mathrm{SCL}}<br><br>\sin <br><br>\left({\mathrm{\theta <br><br>}}_o-{\mathrm{\theta <br><br>}}_c\right),$

and where

θ

_o and Z_SCL describe an angular and an axial coordinate of said scene entry point in said local scene cylindrical coordinates;

θ

_c describes an angular coordinate of said center of said synthetic aperture imaging said scene entry point; and

θ

_o−

θ

_c describes the nominal angular offset between said moving platform position and an antenna pointing position in said scene cylindrical coordinates.