Robust predictive deconvolution system and method

• US 7,106,250 B2
• Filed: 09/23/2004
• Issued: 09/12/2006
• Est. Priority Date: 09/03/2003
• Status: Expired due to Fees

• Current Assignee: The United States of America As Represented By The Secretary of Agriculture
• Original Assignee: the united states of america as represented by the secretary of the navy
• Inventors: Blunt, Shannon D., Gerlach, Karl R.
• Primary Examiner(s): Gregory, Bernarr E.
• Application Number:
  US10/947,784
• Publication Number:
  US 20050057392A1
• Time in Patent Office: 719 Days
• Field of Search: 342 25 R- 26 D, 342/27, 342/28, 342 82-103, 342/118, 342128-144, 342159-175, 342189-197, 342200-205, 375130-153
• US Class Current: 342/195
• CPC Class Codes: G01S 13/284 using coded pulses
• CPC Class Codes: G01S 13/9094 Theoretical aspects
• CPC Class Codes: G01S 7/2921 based on data belonging to one radar period

Abstract

A method for processing a received, modulated pulse (i.e. waveform) that requires predictive deconvolution to resolve a scatterer from noise and other scatterers includes receiving a return signal; obtaining L+(2M−1)(N−1) samples y of the return signal, where y(l)={tilde over (x)}^T(l) s+v(l); applying RMMSE estimation to each successive N samples to obtain initial impulse response estimates [{circumflex over (x)}₁{−(M−1)(N−1)}, . . . , {circumflex over (x)}₁{−1}, {circumflex over (x)}₁ {0}, . . . , {circumflex over (x)}₁{L−1}, . . . , {circumflex over (x)}₁{L}, {circumflex over (x)}₁{−1 +(M−1)(N−1)}]; computing power estimates {circumflex over (ρ)}₁(l)=|{circumflex over (x)}₁(l)|^α for l=−(M−1)(N−1), . . . , L−1+(M−1)(N−1) and 0<α≦2; computing MMSE filters according to w(l)=ρ(l) (C(l)+R)⁻¹s, where ρ(l)=E[|x(l)|^α] is the power of x(l), for 0<α≦2, and R=E[v(l) v^H(l)] is the noise covariance matrix; applying the MMSE filters to y to obtain [{circumflex over (x)}₂{−(M−2)(N−1)}, . . . , {circumflex over (x)}₂{−1}, {circumflex over (x)}₂{0}, . . . , {circumflex over (x)}₂{L−1}, {circumflex over (x)}₂{L}, . . . , {circumflex over (x)}₂{L−1+(M−2)(N−1)}]; and repeating (d)–(f) for subsequent reiterative stages until a desired length-L range window is reached, thereby resolving the scatterer from noise and other scatterers. The RMMSE predictive deconvolution approach provides high-fidelity impulse response estimation. The RMMSE estimator can reiteratively estimate the MMSE filter for each specific impulse response coefficient by mitigating the interference from neighboring coefficients that is a result of the temporal (i.e. spatial) extent of the transmitted waveform. The result is a robust estimator that adaptively eliminates the spatial ambiguities that occur when a fixed receiver filter is used.

Claims

1. A method for processing a received, modulated pulse that requires predictive deconvolution to resolve a scatterer from noise and other scatterers, comprising:

a) receiving a return signal;

b) obtaining L+(2M−

1)(N−

1) samples y of the return signal, where y(l)={tilde over (x)}^T(l) s+v(l);

c) applying RMMSE estimation to each successive N samples to obtain initial impulse response estimates [{circumflex over (x)}₁{−

(M−

1)(N−

1)}, . . . , {circumflex over (x)}₁{−

1}, {circumflex over (x)}₁{−

0}, . . . , {circumflex over (x)}₁{L−

1}, {circumflex over (x)}₁{L}, . . . , {circumflex over (x)}₁{L−

1+(M−

1)(N−

1)}];

d) computing power estimates {circumflex over (ρ

)}(l)=|{circumflex over (x)}¹(l)|⁶⁰ for (l)=−

(M−

1)(N−

1), . . . , L−

1+(M−

1)(N−

1) and 0<

α

≦

2;

(e) computing MMSE filters according to w(l)=ρ

(l) (C(l) R)<sup>−

1</sup>s , where ρ

(l)=E[|x(l)|_α

] is the power of x(l), for 0<

α

≦

2, and R=E[v(l)v^H(l)] is the noise covariance matrix;

(f) applying the MMSE filters to y to obtain [{circumflex over (x)}₂{−

(M−

2)(N−

1)}, . . . , {circumflex over (x)}₂{−

1}, {circumflex over (x)}₂{0}, . . . , {circumflex over (x)}₂{L−

1}, {circumflex over (x)}₂{L}, . . . , {circumflex over (x)}₂{L−

1+(M−

2)(N−

1}]; and

(g) repeating (d)–

(f) for subsequent reiterative stages until a desired length-L range window is reached, thereby resolving the scatterer from noise and other scatterers.

2. A method as in claim 1, wherein the RMMSE estimation is performed with a plurality of parallel processors.

3. A method as in claim 1, further comprising setting a nominal level for which the power estimates are not allowed to fall below.

4. A method as in claim 1, wherein the y samples are obtained via A/D) conversion.

5. A method as in claim 1, wherein the method is applied in range profiling.

6. A method as in claim 1, wherein the method is applied in a weather radar system.

7. A method as in claim 1, wherein the method is applied in image recognition for Synthetic Aperture Radar (SAR).

8. A method as in claim 1, wherein the method is applied in image recognition for Inverse SAR (ISAR).

9. A method as in claim 1, wherein the method is applied in remote sensing.

10. A method as in claim 1, wherein the method is applied in ultrasonic non-destructive evaluation for structural integrity.

11. A method as in claim 1, wherein the method is applied in seismic estimation.

12. A method as in claim 1, wherein the method is applied in biomedical imaging.

13. A method as in claim 1, wherein the method is applied in inverse filtering of optical images.

14. A radar receiver system comprising;

a receiver;

a processor including a Reiterative Minimum Mean-Square Error estimation (RMMSE) radar pulse compression algorithm, wherein the RMSSE radar pulse compression algorithm comprises;

(a) obtaining L+(2M−

1)(N−

1) samples y of a radar return signal, where y(l)={circumflex over (x)}^T(l) s+v(l);

(b) applying RMMSE pulse compression to each set of N contiguous samples to obtain initial radar impulse response estimates [{circumflex over (x)}₁{−

(M−

1)(N−

1)}, . . . , {circumflex over (x)}₁{−

1},{circumflex over (x)}₁{0}, . . . , {circumflex over (x)}₁{L−

1},{circumflex over (x)}₁{L}, . . . , {circumflex over (x)}₁{L−

1+(M−

1)(N−

1)}];

(c) computing power estimates {circumflex over (ρ

)}1(l)=|{circumflex over (x)}₁(l)|^α

for (l)=−

(M−

1)(N−

1), . . . , L−

1+(M−

1)(N−

1) and 0<

α

≦

2;

(d) computing range-dependent filters according to w(l)=ρ

(l) (C(l) R)<sup>−

1</sup>s, where ρ

(l)=E[|x(l)|^α

] is the power of x(l), for 0<

α

≦

2, and R=E[v(l) v^H(l)] is the noise covariance matrix;

(e) applying the range-dependent filters to y to obtain [{circumflex over (x)}₂{−

(M−

2)(N−

1)}, . . . , {circumflex over (x)}₂{−

1}, {circumflex over (x)}₂{0}, . . . , {circumflex over (x)}₂{L−

1}, {circumflex over (x)}₂{L}, . . . ,{circumflex over (x)}₂{L−

1+(M−

2)(N−

1)}]; and

(f) repeating (c)–

(e) for subsequent reiterative stages until a desired length-L range window is reached; and

a target detector.

15. A radar receiver system as in claim 14, further comprising a plurality of parallel processors for performing the RMMSE pulse compression.

16. A radar receiver system as in claim 14, wherein a nominal level is set for which the power estimates are not allowed to fall below.

17. A radar receiver system as in claim 14, further comprising an analog-to-digital (A/D) converter.

18. A radar receiver system as in claim 14, further comprising an analog-to-digital (A/D) converter for obtaining the y samples.

19. A radar receiver system as in claim 14, wherein the system is an airport radar system.

20. A radar receiver system as in claim 14, wherein the system is a weather radar system.

21. A method for processing a received, modulated radar pulse to resolve a radar target from noise or other targets, comprising:

a) receiving a radar return signal;

b) obtaining L+(2M−

1)(N−

2) samples y of the radar return signal, where y(l)={circumflex over (x)}^T(l) s+v(l);

c) applying RMMSE pulse compression to each successive N samples to obtain initial radar impulse response estimates [{circumflex over (x)}₁{−

(M−

1)(N−

1)}, . . . , {circumflex over (x)}₁{−

1}{circumflex over (x)}₁{0}, . . . , {circumflex over (x)}₁{L−

1}, {circumflex over (x)}₁{L}, . . . , {circumflex over (x)}₁{L−

1+(M−

1)(N−

1)}];

d) computing power estimates {circumflex over (ρ

)}₁(l)=|{circumflex over (x)}₁(l)|^α

for l=−

(M−

1)(N−

l), . . . , L−

1(M−

1) and 0<

α

≦

2;

(e) computing range-dependent filters according to w(l)=ρ

(l) (C(l)+R)<sup>−

1</sup>s, where ρ

(l)=E[|x(l)|^α

] is the power of x(l), for 021 α

≦

2, and R=E[v(l)v^H(l)] is the noise covariance matrix;

(f) applying the range-dependent filters to y to obtain [{circumflex over (x)}₂{−

(M−

2)(N−

1)}, . . . , {circumflex over (x)}₂{−

1}, . . . , {circumflex over (x)}₂{0}, . . . , {circumflex over (x)}₂{L−

1}, {circumflex over (x)}₂{L}, . . . , {circumflex over (x)}₂{L−

1+(M−

2)(N−

1)}]; and

(g) repeating (d)–

(f) for subsequent reiterative stages until a desired length-L range window is reached, thereby resolving the radar target from noise or other targets.

22. A method as in claim 21, wherein the RMMSE pulse compression is performed with a plurality of parallel processors.

23. A method as in claim 21, wherein the y samples of the radar return signal are obtained via A/D conversion.

24. A method as in claim 21, further comprising setting a nominal level for which the power estimates are not allowed to fall below.

25. A method as in claim 21, wherein the method is applied in an airport radar system.

26. A method as in claim 21, wherein the method is applied in a weather radar system.

27. A method as in claim 21, wherein the y samples of the radar return signal are obtained via A/D Conversion.

28. A method as in claim 21, wherein a plurality of radar targets are resolved and separately identified.