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

• US 6,603,424 B1
• Filed: 07/31/2002
• Issued: 08/05/2003
• Est. Priority Date: 07/31/2002
• Status: Expired due to Fees

• Current Assignee: The Boeing Co.
• Original Assignee: The Boeing Co.
• Inventors: Abatzoglou, Theagenis J.
• Primary Examiner(s): Tarcza, Thomas H.
• Assistant Examiner(s): Andrea, Brian K
• Application Number:
  US10/209,093
• Time in Patent Office: 370 Days
• Field of Search: 342/25, 342/159, 342/195, 342/196
• US Class Current: 342/25.00R
• CPC Class Codes: G01S 13/9019 Auto-focussing of the SAR signals
• CPC Class Codes: G01S 13/904 SAR modes

Abstract

A system is provided for reducing errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions. The system comprises an autofocus processor for receiving a plurality of slow-time samples. The autofocus processor can estimate a phase error for each slow-time sample by a maximum likelihood technique and thereafter compensate the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples. The implementation of the maximum likelihood technique is done by a superresolution technique along slow-time samples which also estimates a plurality of Doppler frequencies and amplitudes for a plurality of point scatterers at each range line. Further, the autofocus processor can also predict the performance of the autofocus technique by computing a resulting root mean square error of the estimated phase error which is derived form the corresponding Cramer Rao bound.

Claims

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

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

estimating a phase error for each slow-time sample;

compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples;

processing the range-line samples according to a superresolution signal processing technique to thereby obtain a plurality of 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 Doppler frequencies; and

obtaining a correction to the estimated phase error for each slow-time sample based upon the range-line samples and the true signals.

2. A method according to claim 1, wherein, if a root mean square error (RMSE) of the correction to the estimated phase error for each slow-time sample is greater than a predetermined threshold, said method further comprises replacing the slow-time samples with the range-line samples and thereafter repeating the compensating, processing, reconstructing, obtaining and replacing steps until the RMSE of the correction for each slow-time sample is less than the predetermined threshold.

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

4. A method according to claim 1, wherein compensating the plurality of slow-time samples comprises compensating the plurality of slow-time samples based upon a diagonal random phasor matrix.

5. A method according to claim 4, wherein compensating the plurality of slow-time samples comprises multiplying the slow-time samples {right arrow over (x)}_m by a complex conjugate of the diagonal random phasor matrix to obtain a plurality of range-line samples, {right arrow over (y)}_m wherein {right arrow over (x)}_m represents a plurality of slow-time samples for each range line m, and {right arrow over (y)}_m represents a plurality of range-line samples for each range line.

6. 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, Ê

_m, wherein the plurality of Doppler frequency steering matrices are represented as follows;

7. A method according to claim 6, wherein reconstructing a true signal for each range line comprises reconstructing the true signal according to the following:

8. A method according to claim 7, wherein reconstructing a true signal further comprises determining the plurality of complex amplitudes of the scatterers at each range line according to the following:

9. A method according to claim 7, wherein obtaining a correction comprises obtaining a correction δ

{circumflex over (φ

)}_n to the estimated phase error for each slow-time sample according to the following;

$\mathrm{\delta <br><br>}<br><br>{\widehat{\mathrm{\phi <br><br>}}}_n=\arg <br><br>\left\{\underset{m}{\sum <br><br>}<br><br>y_{n,m}<br><br>{\stackrel{\_}{\hat{s}}}_{n,m}\right\},$

and wherein n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line.

10. A method of determining an accuracy of estimated phase errors in synthetic aperture radar signals, wherein the signals are from a plurality of range lines that each includes a plurality of azimuth positions, said method comprising:

calculating true signals for a plurality of slow-time samples for the plurality of range lines, wherein the plurality of slow-time samples represent radar signals for a plurality of azimuth positions for a plurality of range lines;

determining a true signal power for each slow-time sample summed over the plurality of range lines and a total true signal power, wherein the true signal powers are based upon the true signals and the total true signal power is based upon amplitudes of the scatterers;

determining a Cramer Rao Bound (CRB) based upon a clutter-plus-receiver noise power, the true signal powers, a dominate scatterer power, the number of slow time samples and the total true signal power; and

determining a root mean square error based upon the CRB.

11. A method according to claim 10 further comprising estimating the clutter-plus-receiver noise power based upon a uniform clutter noise and a receiver noise model, wherein the clutter-plus-receiver noise power is determined before determining the CRB.

12. A method according to claim 10 further comprising selecting a plurality of signal scatterer parameters, wherein the plurality of point scatterer parameters are determined before determining the true signals, and wherein calculating the true signals is based upon the point scatterer parameters.

13. A method according to claim 10, wherein calculating the true signals comprises:

receiving the plurality of slow-time samples and thereafter estimating a phase error for each slow-time sample;

compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples;

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

reconstructing a true signal for each range line based upon the plurality of Doppler frequencies.

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

an autofocus processor capable of receiving a plurality of slow-time samples representing radar signals for a plurality of azimuth positions for a plurality of range lines, wherein said autofocus processor is also capable of estimating a phase error for each slow-time sample and thereafter compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples, wherein said autofocus processor is further capable of processing the range-line samples according to a superresolution signal processing technique to thereby obtain a plurality of Doppler frequencies for a plurality of point scatterers at each range line, wherein said autofocus processor is further capable of reconstructing a true signal for each range line based upon the plurality of Doppler frequencies and thereafter obtaining a correction to the estimated phase error for each slow-time sample based upon the range-line samples and the true signals.

15. A system according to claim 14, wherein said autofocus processor is also capable of replacing the slow-time samples with the range-line samples when a root mean square error (RMSE) of the estimated phase error correction for each slow-time sample is greater than a predetermined threshold, wherein said autofocus processor is additionally capable of compensating the slow-time samples, processing the range-line samples, reconstructing the true signal, obtaining the correction, and replacing the slow-time samples until the RMSE of the correction for each slow-time sample is less than the predetermined threshold.

16. A system according to claim 14, wherein said autofocus processor is capable of processing the range-line samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation.

17. A system according to claim 14, wherein said autofocus processor is capable of compensating the plurality of slow-time samples based upon a diagonal random phasor matrix.

18. A system according to claim 17, wherein said autofocus processor is capable of compensating the plurality of slow-time samples by multiplying the slow-time samples {right arrow over (x)}_m by a complex conjugate of the diagonal random phasor matrix to obtain a plurality of range-line samples, {right arrow over (y)}_m wherein {right arrow over (x)}_m represents a plurality of slow-time samples for each range line m, and {right arrow over (y)}_m represents a plurality of range-line samples for each range line.

19. A system according to claim 14, wherein said autofocus processor is capable of reconstructing a true signal based upon a plurality of Doppler frequency steering matrices, Ê

_m, wherein the plurality of Doppler frequency steering matrices are represented as follows;

20. A system according to claim 19, wherein said autofocus processor is capable of reconstructing a true signal for each range line according to the following:

21. A system according to claim 20, wherein said autofocus processor is capable of reconstructing a true signal by further determining the plurality of complex amplitudes of the scatterers at each range line according to the following:

22. A system according to claim 20, wherein said autofocus processor is capable of obtaining a correction δ

{circumflex over (φ

)}_n to the estimated phase error for each slow-time sample according to the following;

$\mathrm{\delta <br><br>}<br><br>{\widehat{\mathrm{\phi <br><br>}}}_n=\arg <br><br>\left\{\underset{m}{\sum <br><br>}<br><br>y_{n,m}<br><br>{\stackrel{\_}{\hat{s}}}_{n,m}\right\},$

and wherein n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line.

23. A system for determining an accuracy of estimated phase errors in synthetic aperture radar signals, wherein the signals are from a plurality of range lines that each includes a plurality of azimuth positions, said system comprising:

a processing element capable of calculating true signals for a plurality of slow-time samples for the plurality of range lines, wherein the plurality of slow-time samples represent radar signals for a plurality of azimuth positions for a plurality of range lines, wherein said processing element is also capable of determining a true signal power for each slow-time sample summed over the plurality of range lines and a total true signal power, wherein the true signal powers are based upon the true signals and the total true signal power is based upon amplitudes of the scatterers, said processing element additionally being capable of determining a Cramer Rao Bound (CRB) based upon a clutter-plus-receiver noise power, the true signal powers, a dominant scatterer power, the number of slow time samples and the total true signal power, and wherein said processing element is further capable of determining a root mean square error based upon the CRB.

24. A system according to claim 23, wherein said processing element is also capable of estimating the clutter-plus-receiver noise power based upon a uniform clutter noise and a receiver noise model.

25. A system according to claim 23, wherein said processing element is also capable of selecting a plurality of signal scatterer, and wherein the true signals are calculated based upon the point scatterer parameters.

26. A system according to claim 23, wherein said processing element is capable of calculating the, true signals by:

receiving the plurality of slow-time samples and thereafter estimating a phase error for each slow-time sample;

compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples;

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

reconstructing a true signal for each range line based upon the plurality of Doppler frequencies.

27. A computer program product for reducing errors in synthetic aperture radar signals from a plurality of range lines where each range line includes a plurality of azimuth positions, said 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 estimating a phase error for each slow-time sample;

a third executable portion for compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples;

a fourth executable portion for processing the range-line samples according to a superresolution signal processing technique to thereby obtain a plurality of Doppler frequencies for a plurality of point scattersers at each range line;

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

a sixth executable portion for obtaining a correction to the estimated phase error for each slow-time sample based upon the range-line samples and the true signals.

28. A computer program product according to claim 27 further comprising a seventh executable portion for replacing the slow-time samples with the range-line samples when a root mean square error (RMSE) of the estimated phase error correction for each slow-time sample is greater than a predetermined threshold, wherein said third executable portion compensates the slow-time samples, said fourth executable portion processes the range-line samples, said fifth executable portion reconstructs the true signal, said sixth executable portion obtains the correction, and said seventh executable portion replaces the slow-time samples until the RMSE of the correction for each slow-time sample is less than the predetermined threshold.

29. A computer program product according to claim 27, wherein said fourth executable portion processes the range-line samples according to a superresolution signal processing technique including Constrained Total Least Squares parameter estimation.

30. A computer program product according to claim 27, wherein said third executable portion compensates the plurality of slow-time samples based upon a diagonal random phasor matrix.

31. A computer program product according to claim 30, wherein said third executable portion compensates the plurality of slow-time samples by multiplying the slow-time samples {right arrow over (x)}_m by a complex conjugate of the diagonal random phasor matrix to obtain a plurality of range-line samples, {right arrow over (y)}_m, wherein {right arrow over (x)}_m represents a plurality of slow-time samples for each range line m, and {right arrow over (y)}_m represents a plurality of range-line samples for each range line.

32. A computer program product according to claim 27, wherein said fifth executable portion reconstructs a true signal based upon a plurality of Doppler frequency steering matrices, Ê

_m, wherein the plurality of Doppler frequency steering matrices are represented as follows;

33. A computer program product according to claim 32, wherein said fifth executable portion reconstructs a true signal for each range line according to the following:

34. A computer program product according to claim 33, wherein said fifth executable portion reconstructs a true signal by further determining the plurality of complex amplitudes of the scatterers at each range line according to the following:

35. A computer program product according to claim 33, wherein said sixth executable portion obtains a correction δ

{circumflex over (φ

)}_n to the estimated phase error for each slow-time sample according to the following;

$\mathrm{\delta <br><br>}<br><br>{\widehat{\mathrm{\phi <br><br>}}}_n=\arg <br><br>\left\{\underset{m}{\sum <br><br>}<br><br>y_{n,m}<br><br>{\stackrel{\_}{\hat{s}}}_{n,m}\right\},$

and wherein n=−

N, . . . , 0, . . . N represents each of 2N+1 slow-time samples at each range line.

36. A computer program product for determining an accuracy of estimated phase errors in synthetic aperture radar signals, wherein the signals are from a plurality of range lines that each includes a plurality of azimuth positions, said 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 calculating true signals for a plurality of slow-time samples for the plurality of range lines, wherein the plurality of slow-time samples represent radar signals for a plurality of azimuth positions for a plurality of range lines;

a second executable portion for determining a true signal power for each slow-time sample summed over the plurality of range lines and a total true signal power, wherein the true signal powers are based upon the true signals and the total true signal power is based upon amplitudes of the scatterers;

a third executable portion for determining a Cramer Rao Bound (CRB) based upon a clutter-plus-receiver noise power, the true signal powers, a dominant scatterer power, the number of slow time samples and the total true signal power; and

a fourth executable portion for determining a root mean square error based upon the CRB.

37. A computer program product according to claim 36 further comprising a fifth executable portion for estimating the clutter-plus-receiver noise power based upon a uniform clutter noise and a receiver noise model, wherein said fifth executable portion determines the clutter-plus-receiver noise before said third executable portion determines the CRB.

38. A computer program product according to claim 36 further comprising a fifth executable portion for selecting a plurality of signal scatterer parameters based upon a Fisher information matrix, wherein said fifth executable portion determines the plurality of point scatterer parameters before said first executable portion calculates the true signals, and wherein said first executable portion calculates the true signals is based upon the point scatterer parameters.

39. A computer program product according to claim 36, wherein said first executable portion calculates the true signals by:

receiving the plurality of slow-time samples and thereafter estimating a phase error for each slow-time sample;

compensating the plurality of slow-time samples by the estimated phase errors to obtain a plurality of range-line samples;

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

reconstructing a true signal for each range line based upon the plurality of Doppler frequencies.