System, method and computer program product for reducing quadratic phase errors in synthetic aperture radar signals

• US 7,064,702 B1
• Filed: 03/01/2005
• Issued: 06/20/2006
• Est. Priority Date: 03/01/2005
• Status: Expired due to Fees

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Abatzoglou, Theagenis J.
• Primary Examiner(s): Lobo, Ian J.
• Application Number:
  US11/069,259
• Time in Patent Office: 476 Days
• Field of Search: 342/25.A, 342/25.B, 342/25.F, 342/25.R, 342/25.E
• US Class Current: 342/25.00F
• CPC Class Codes: G01S 13/9019 Auto-focussing of the SAR signals
• CPC Class Codes: G01S 13/904 SAR modes

Abstract

A method is provided for reducing quadratic phase errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions. The method includes receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines. A plurality of corrected samples and an initial quadratic phase error coefficient are identified based upon the slow-time samples. The corrected samples are processed according to a superresolution signal processing technique to thereby obtain a plurality of estimated Doppler frequencies for a plurality of point scatterers at each range line, after which a true signal for each range line is reconstructed based upon the plurality of estimated Doppler frequencies. A correction to the initial quadratic phase error coefficient is then obtained based upon the corrected samples, the true signals and the initial quadratic phase error coefficient.

Claims

1. A method of reducing quadratic phase errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions, the method comprising:

receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines;

identifying a plurality of corrected samples and an initial quadratic phase error coefficient based upon the slow-time samples;

processing the corrected samples according to a superresolution signal processing technique to thereby obtain a plurality of estimated Doppler frequencies for a plurality of point scatterers at each range line;

reconstructing a true signal for each range line based upon the plurality of estimated Doppler frequencies; and

obtaining a correction to the initial quadratic phase error coefficient based upon the corrected samples, the true signals and the initial quadratic phase error coefficient.

2. A method according to claim 1, wherein obtaining a correction comprises:

calculating a new phase estimate based upon the corrected samples, initial quadratic phase error coefficient and true signal; and

summing the initial phase estimate and the new phase estimate to thereby calculate the correction.

3. A method according to claim 2, wherein calculating a new phase estimate comprises calculating a new phase estimate α

_new by at least partially maximizing the following functional;

$F<br><br>\left(\mathrm{\alpha <br><br>}\right)=\underset{m}{\sum <br><br>}<br><br><br><br>{<br><br>\underset{n}{\sum <br><br>}<br><br><br><br>{\tilde{x}}_{m,n,l_{\max }}<br><br>{\stackrel{\_}{s}}_{m,n}<br><br>e^{-j<br><br><br><br>\mathrm{\alpha <br><br>}<br><br><br><br>n^2}<br><br>}^2,$

starting at α

=α

l_max, and wherein α

l_max represents the initial quadratic phase error coefficient, m represents a range line, n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line, {tilde over (x)}_m,n,lmax represents the corrected samples, and s_m,n represents the true signal.

4. A method according to claim 1, wherein processing the corrected samples comprises processing the corrected samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation.

5. A method according to claim 1, wherein reconstructing a true signal comprises reconstructing a true signal based upon a plurality of Doppler frequency steering matrices E_m, wherein the plurality of Doppler frequency steering matrices are represented as follows:

E_m=E(f_1,m, . . . , f_K,m),

and wherein f_k,m represents the estimated Doppler frequency for each of K point scatterers at each range line m.

6. A method according to claim 5, wherein reconstructing a true signal comprises reconstructing the true signal {right arrow over (s)}_m according to the following:

{right arrow over (s)}_m=E_m{right arrow over (z)}_m,

and wherein {right arrow over (z)}_m represents a plurality of estimated complex amplitudes of the scatterers at each range line.

7. A method according to claim 1 further comprising:

replacing the initial quadratic phase error coefficient with the correction;

calculating further corrected samples based upon the corrected samples and the correction; and

repeating the processing, reconstructing and obtaining steps,

wherein the replacing, calculating and repeating steps occur for at least one iteration.

8. A method according to claim 1 further comprising:

calculating a height of a scatterer above a point of reference based upon the correction.

9. A system for reducing quadratic phase errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions, the system comprising:

an autofocus processor for receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines,

wherein the autofocus processor is adapted to identify a plurality of corrected samples and an initial quadratic phase error coefficient based upon the slow-time samples,

wherein the autofocus processor is adapted to process the corrected samples according to a superresolution signal processing technique to thereby obtain a plurality of estimated Doppler frequencies for a plurality of point scatterers at each range line,

wherein the autofocus processor is adapted to reconstruct a true signal for each range line based upon the plurality of estimated Doppler frequencies, and

wherein the autofocus processor is adapted to obtain a correction to the initial quadratic phase error coefficient based upon the corrected samples, the true signals and the initial quadratic phase error coefficient.

10. A system according to claim 9, wherein the autofocus processor is adapted to obtain the correction by calculating a new phase estimate based upon the corrected samples, initial quadratic phase error coefficient and true signal, and summing the initial phase estimate and the new phase estimate to thereby calculate the correction.

11. A system according to claim 10, wherein the autofocus processor is adapted to calculate the new phase estimate α

_new by at least partially maximizing the following functional;

$F<br><br>\left(\mathrm{\alpha <br><br>}\right)=\underset{m}{\sum <br><br>}<br><br><br><br>{<br><br>\underset{n}{\sum <br><br>}<br><br><br><br>{\tilde{x}}_{m,n,l_{\max }}<br><br>{\stackrel{\_}{s}}_{m,n}<br><br>e^{-j<br><br><br><br>\mathrm{\alpha <br><br>}<br><br><br><br>n^2}<br><br>}^2$

starting at α

=α

_lmax, and wherein α

_lmax represents the initial quadratic phase error coefficient, m represents a range line, n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line, {tilde over (x)}_m,n,lmax represents the corrected samples, and s_m,n represents the true signal.

12. A system according to claim 9, wherein the autofocus processor is adapted to process the corrected samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation.

13. A system according to claim 9, wherein the autofocus processor is adapted to reconstruct the true signal based upon a plurality of Doppler frequency steering matrices E_m, wherein the plurality of Doppler frequency steering matrices are represented as follows:

E_m=E(f_1,m, . . . , f_K,m),

and wherein f_k,m represents the estimated Doppler frequency for each of K point scatterers at each range line m.

14. A system according to claim 13, wherein the autofocus processor is adapted to reconstruct the true signal {right arrow over (s)}_m according to the following:

{right arrow over (s)}_m=E_m{right arrow over (z)}_m,

and wherein {right arrow over (z)}_m represents a plurality of estimated complex amplitudes of the scatterers at each range line.

15. A system according to claim 9, wherein, for at least one iteration, the autofocus processor is further adapted to replace the initial quadratic phase error coefficient with the correction, calculate further corrected samples based upon the corrected samples and the correction, and again process the corrected samples, reconstruct a true signal and obtain a correction.

16. A computer program product of reducing quadratic phase errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions, the computer program product comprising a computer-readable storage medium having computer-readable program code portions stored therein, the computer-readable program portions comprising:

a first executable portion for receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines;

a second executable portion for identifying a plurality of corrected samples and an initial quadratic phase error coefficient based upon the slow-time samples;

a third executable portion for processing the corrected samples according to a superresolution signal processing technique to thereby obtain a plurality of estimated Doppler frequencies for a plurality of point scatterers at each range line;

a fourth executable portion for reconstructing a true signal for each range line based upon the plurality of estimated Doppler frequencies; and

a fifth executable portion for obtaining a correction to the initial quadratic phase error coefficient based upon the corrected samples, the true signals and the initial quadratic phase error coefficient.

17. A computer program product according to claim 16, wherein the fifth executable portion is adapted to obtain the correction by calculating a new phase estimate based upon the corrected samples, initial quadratic phase error coefficient and true signal, and summing the initial phase estimate and the new phase estimate to thereby calculate the correction.

18. A computer program product according to claim 17, wherein the fifth executable portion is adapted to calculate the new phase estimate α

_new by at least partially maximizing the following functional;

$F<br><br>\left(\mathrm{\alpha <br><br>}\right)=\underset{m}{\sum <br><br>}<br><br><br><br>{<br><br>\underset{n}{\sum <br><br>}<br><br><br><br>{\tilde{x}}_{m,n,l_{\max }}<br><br>{\stackrel{\_}{s}}_{m,n}<br><br>e^{-j<br><br><br><br>\mathrm{\alpha <br><br>}<br><br><br><br>n^2}<br><br>}^2,$

starting at α

=α

_lmax, and wherein α

_lmax represents the initial quadratic phase error coefficient, m represents a range line, n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line, {tilde over (x)}_m,n,lmax represents the corrected samples, and s_m,n represents the true signal.

19. A computer program product according to claim 16, wherein the third executable portion is adapted to process the corrected samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation.

20. A computer program product according to claim 16, wherein the fourth executable portion is adapted to reconstruct the true signal based upon a plurality of Doppler frequency steering matrices E_m, wherein the plurality of Doppler frequency steering matrices are represented as follows:

E_m=E(f_1,m, . . . , f_K,m),

and wherein f_k,m represents the estimated Doppler frequency for each of K point scatterers at each range line m.

21. A computer program product according to claim 20, wherein the fourth executable portion is adapted to reconstruct the true signal {right arrow over (s)}_m according to the following:

{right arrow over (s)}_m=E_m{right arrow over (z)}_m,

and wherein {right arrow over (z)}_m represents a plurality of estimated complex amplitudes of the scatterers at each range line.

22. A computer program product according to claim 16 further comprising:

a sixth executable portion for replacing the initial quadratic phase error coefficient with the correction; and

a seventh executable portion for calculating further corrected samples based upon the corrected samples and the correction; and

an eighth executable portion for repeating the processing, reconstructing and obtaining steps,

wherein the sixth, seventh and eighth executable portions are adapted to perform the replace, calculate and repeat steps for at least one iteration.