Synthetic aperture radar processing

• US 9,880,277 B2
• Filed: 05/01/2015
• Issued: 01/30/2018
• Est. Priority Date: 05/01/2014
• Status: Active Grant

• Current Assignee: Utah State University Research Foundation (Utah State University)
• Original Assignee: Utah State University Research Foundation (Utah State University)
• Inventors: Knight, Chad P., Gunther, Jacob H.
• Primary Examiner(s): Windrich, Marcus E
• Application Number:
  US14/702,272
• Publication Number:
  US 20150316647A1
• Time in Patent Office: 1,005 Days
• Field of Search: 342 25 R- 5 F
• CPC Class Codes: G01S 13/90 using synthetic aperture techniques , e.g. synthetic aperture radar [SAR] techniques
• CPC Class Codes: G01S 13/904 SAR modes
• CPC Class Codes: G01S 13/9052 Spotlight mode
• CPC Class Codes: G01S 7/358 using I/Q processing

Abstract

For synthetic aperture radar (SAR) processing, a SAR receives a plurality of SAR signals. The SAR generates a piecewise approximation of the plurality of SAR signals over a coherent processing interval. The piecewise approximation may mitigate phase reflection components of each SAR signal. The SAR further generates an estimate of the scene from the piecewise approximation.

Claims

1. A method for synthetic aperture radar (SAR) processing comprising:

receiving, by use of a processor, a plurality of SAR signals;

generating a piecewise approximation of the plurality of SAR signals over a coherent processing interval, wherein the piecewise approximation is a function of a linear fit, an aspect filter, a spatial filter, and a sparsity constraint and mitigates phase reflection components of each SAR signal; and

generating an estimate of a scene from the piecewise approximation.

2. The method of claim 1, wherein the aspect filter calculates w_f∥

Fx_m∥

_p, wherein F is an aspect filter matrix, x_m is an absolute pixel vector, Fx_m are normalized to a given unit p, and w_f is an aspect filter weight.

3. The method of claim 1, wherein the spatial filter calculates w_g∥

Gx_m∥

_f, wherein G is a spatial filter matrix, x_m is an absolute pixel vector, Gx_m are normalized to a given unit f, and w_g is a spatial filter weight.

4. The method of claim 1, wherein the sparsity constraint calculates w_m∥

x_m∥

q, wherein x_m is an absolute pixel vector normalized to a given unit q, and w_m is a sparsity weight.

5. The method of claim 1, wherein the piecewise approximation of the plurality of SAR signals is calculated by minimizing ∥

Ax−

b∥

₂+w_f∥

Fx_m∥

_p+w_m∥

x_m∥

_q+w_g∥

Gx_m∥

_f subject to √

{square root over ((x_k,l^r)+(x_k,lⁱ)²)}≦

x_mk,l for all pixel coordinates k, l, where x_m is an absolute pixel vector, Fx_m is the aspect filter, Gx_m is the spatial filter, and w_m is the sparsity constraint.

6. The method of claim 1, wherein A is a spatial impulse response matrix, x is a pixel vector and c^T is a transpose of a constraint cone defined by ∥

Ax_i−

b∥

₂≦

c^T+d where d is a constant and the piecewise approximation of the plurality of SAR signals is calculated by minimizing c^Tx subject to Ax=b.

7. A program product comprising a computer readable storage medium that stores code executable by a processor, the executable code comprising code to perform:

receiving a plurality of SAR signals;

generating a piecewise approximation of the plurality of SAR signals over a coherent processing interval, wherein the piecewise approximation is a function of a linear fit, an aspect filter, a spatial filter, and a sparsity constraint and phase reflection components of each SAR signal; and

generating an estimate of a scene from the piecewise approximation.

8. The program product of claim 7, wherein the aspect filter calculates w_f∥

Fx_m∥

_p, wherein F is an aspect filter matrix, x_m is an absolute pixel vector, Fx_m are normalized to a given unit p, and w_f is an aspect filter weight.

9. The program product of claim 7, wherein the spatial filter calculates w_g∥

Gx_m∥

_f, wherein G is a spatial filter matrix, x_m is an absolute pixel vector, Gx_m are normalized to a given unit f, and w_g is a spatial filter weight.

10. The program product of claim 7, wherein the sparsity constraint calculates w_m∥

x_m∥

_q, wherein x_m is an absolute pixel vector normalized to a given unit q, and w_m is a sparsity weight.

11. The program product of claim 7, wherein the piecewise approximation of the plurality of SAR signals is calculated by minimizing ∥

Ax−

b∥

₂+w_f∥

Fx_m∥

_p+w_m∥

x_m∥

_q+w_g∥

Gx_m∥

_f subject to √

{square root over ((x_k,l^r)+(x_k,lⁱ)²)}≦

x_mk,l for all pixel coordinates k, l, where x_m is an absolute pixel vector, Fx_m is the aspect filter, Gx_m is the spatial filter, and w_m is the sparsity constraint.

12. The program product of claim 7, wherein A is a spatial impulse response matrix, x is a pixel vector and c^T is a transpose of a constraint cone defined by ∥

Ax_i−

b∥

₂≦

c^T+d where d is a constant and the piecewise approximation of the plurality of SAR signals is calculated by minimizing c^Tx subject to Ax=b.

13. An apparatus comprising:

a processor;

a memory that stores code executable by the processor, the code comprising;

code that receives a plurality of SAR signals;

code that generates a piecewise approximation of the plurality of SAR signals over a coherent processing interval, wherein the piecewise approximation is a function of a linear fit, an aspect filter, a spatial filter, and a sparsity constraint and mitigates phase reflection components of each SAR signal; and

code that generates an estimate of a scene from the piecewise approximation.

14. The apparatus of claim 13, wherein the aspect filter calculates w_f∥

Fx_m∥

_p, wherein F is an aspect filter matrix, x_m is an absolute pixel vector, Fx_m are normalized to a given unit p, and w_f is an aspect filter weight.

15. The apparatus of claim 13, wherein the spatial filter calculates w_g∥

Gx_m∥

_f, wherein G is a spatial filter matrix, x_m is an absolute pixel vector, Gx_m are normalized to a given unit f, and w_g is a spatial filter weight.

16. The apparatus of claim 13, wherein the sparsity constraint calculates w_m∥

x_m∥

_q, wherein x_m is an absolute pixel vector normalized to a given unit q, and w_m is a sparsity weight.

17. The apparatus of claim 13, wherein the piecewise approximation of the plurality of SAR signals is calculated by minimizing ∥

Ax−

b∥

₂+w_f∥

Fx_m∥

_p+w_m∥

x_m∥

_q+w_g∥

Gx_m∥

_f subject to √

{square root over ((x_k,l^r)+(x_k,lⁱ)²)}≦

x_mk,l for all pixel coordinates k, l, where x_m is an absolute pixel vector, Fx_m is the aspect filter, Gx_m is the spatial filter, and w_m is the sparsity constraint.