Phase calibration of a stepped-chirp signal for a synthetic aperture radar

1. A Radar Calibration Processor (“RCP”) for calibrating the phase of a stepped-chirp signal utilized by a synthetic aperture radar (“SAR”), the RCP comprising:

a first non-periodic phase error (“NPPE”) calibrator;

a second NPPE calibrator; and

a periodic phase error (“PPE”) calibrator, wherein the PPE calibrator is in signal communication with the first NPPE calibrator,

wherein the first NPPE calibrator is in signal communication with the second NPPE calibrator,

wherein the PPE calibrator is configured to receive video phase history (“VPH”) data from the SAR and, in response, produces PPE calibrated data from the VPH data, and

wherein the VPH data includes a plurality of steps within a stepped-chirped waveform and a range frequency.

2. The RCP of claim 1 , wherein the PPE calibrator is further configured to

perform an azimuth compression on the VPH data to produce azimuth compressed input data,

concatenate the azimuth compressed input data into concatenated data,

define functional descriptions for optimization of the azimuth compressed input data,

establish an error model based on the functional descriptions,

search for optimum coefficients of one or more Legendre polynomials to determine a minimum image quality metric (“IQM”) for the error model,

determine an estimated PPE using the optimum coefficients of the error model, and

apply the estimated PPE to the azimuth compressed input data.

3. The RCP of claim 2 , wherein the configuration of the PPE calibrator to define the functional descriptions for optimization includes

(a) determining an expression for a PPE phase error of order O ppe starting from an order one for a phase calculation using Legendre polynomials with a length equal to a number of samples in a step, of the plurality of steps, of the stepped-chirp waveform, wherein the number of samples include a first sample and a last sample,

(b) applying a phase correction for the PPE phase error to the azimuth compressed data of all the steps in the range frequency,

(c) applying window weights to the concatenated data in the frequency range,

(d) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(e) repeating the steps (b) through (d) from the first sample to the last sample to produce a processed two-dimensional image, and

(f) determining the IQM from the processed two-dimensional image.

4. The RCP of claim 1 , wherein the first NPPE (“NPPE-1”) calibrator is configured to receive the PPE calibrated data having M frequency steps and, in response, produces NPPE-1 calibrated data, which has been calibrated for type-1 NPPE.

5. The RCP of claim 4 , wherein the NPPE-1 calibrator is configured to

(a) define functional descriptions for optimization and establishing an error model for a NPPE-1 phase error,

(b) search for optimum coefficients of Legendre polynomials to determine a minimum IQM in the error model for the NPPE-1 phase error utilizing a Broyden-Fletcher-Goldfarb-Shanno (“BFGS”) algorithm,

(c) determine an estimated NPPE-1 phase error using the optimum coefficients of the error model for a NPPE-1 phase error,

(d) apply the estimated NPPE to the azimuth compressed input data, wherein the NPPE-1 phase error is compensated for the order two through O nppe , and

(e) repeat steps (a) through (d) until all M frequency steps have been processed.

6. The RCP of claim 5 , wherein the configuration of the NPPE-1 calibrator to define the functional descriptions for optimization includes

(a) determining an expression of the NPPE-1 phase error of order O ppe starting from order two for a phase calculation using Legendre polynomials with the length equal to a number of samples in a step, of the plurality of steps, of the stepped-chirp waveform, wherein the number of samples include a first sample and a last sample,

(b) applying the phase correction to the azimuth compressed data of a step in the range frequency,

(c) applying window weights to the concatenated data in the frequency range,

(d) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(e) repeating the steps (b) through (d) from the first sample to the last sample to produce a processed two-dimensional image, and

(f) determining the IQM from the processed two-dimensional image.

7. The RCP of claim 4 , wherein the second NPPE (“NPPE-2”) calibrator is configured to receive the NPPE-1 calibrated data and, in response, produces NPPE-2 calibrated data, which has been calibrated for type-2 NPPE.

8. The RCP of claim 7 , wherein the NPPE-2 calibrator is configured to

(a) define functional descriptions for optimization and establishing an error model for a NPPE-2 phase error,

(b) search for optimum coefficients of Legendre polynomials of order zero and order one to determine a minimum IQM in the error model for the NPPE-2 phase error utilizing a Broyden-Fletcher-Goldfarb-Shanno (“BFGS”) algorithm,

(c) determine an 0order and firstorder estimated NPPE phase error using the optimum coefficients of the error model for the NPPE-2 phase error,

(d) repeat steps (a) through (c) until all M frequency steps have been processed.

9. The RCP of claim 8 , wherein the configuration of the NPPE-2 calibrator to define the functional descriptions for optimization includes

(a) taking two data segments from a first and a second frequency steps of the M frequency steps,

(b) determining an expression of the NPPE-2 phase error for a phase correction using Legendre polynomials of order zero and order one with a length equal to the number of range frequency samples in the second step,

(c) applying the phase correction in the range frequency of the azimuth compressed data of the second step,

(d) applying window weights to a concatenated data of the first and second steps using the phase adjusted data of the second step,

(e) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(f) repeating the steps (b) through (e) from the first sample to the last sample to produce a processed two-dimensional image, and

(g) determining the IQM from the processed two-dimensional image.

10. The RCP of claim 8 , wherein the RCP is configured to adjust constant and linear phases of all the M-1 steps in order to align them to the first step.

11. The RCP of claim 10 , further including an antenna gain calibrator.

12. A method for calibrating the phase of a stepped-chirp signal utilized by a synthetic aperture radar (“SAR”), the method comprising:

estimating a first non-periodic phase error (“NPPE”);

estimating for a second NPPE calibration after the first NPPE (“NPPE-1”) has been estimated; and

estimating a periodic phase error (“PPE”),

wherein the PPE is estimate prior to estimating the first NPPE,

wherein estimating the PPE includes

receiving video phase history (“VPH”) data from the SAR and

producing a PPE calibrated data from the VPH data in response to receiving the VPH data and

wherein the VPH data includes a plurality of steps within a stepped-chirped waveform and a range frequency.

13. The method of claim 12 , wherein estimating the PPE further includes

performing an azimuth compression on the VPH data to produce azimuth compressed input data,

concatenating the azimuth compressed input data into concatenated data,

defining functional descriptions for optimization of the azimuth compressed input data,

establishing an error model based on the functional descriptions,

searching for optimum coefficients of one or more Legendre polynomials to determine a minimum image quality metric (“IQM”) for the error model,

determining an estimated PPE using the optimum coefficients of the error model, and

applying the estimated PPE to the azimuth compressed input data.

14. The method of claim 13 , wherein defining functional descriptions for optimization includes

(a) determining an expression for a PPE phase error of order O ppe starting from an order one for a phase calculation using Legendre polynomials with a length equal to a number of samples in a step, of the plurality of steps, of the stepped-chirp waveform, wherein the number of samples include a first sample and a last sample,

(b) applying a phase correction for the PPE phase error to the azimuth compressed data of all the steps in the range frequency,

(c) applying window weights to the concatenated data in the frequency range,

(d) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(e) repeating the steps (b) through (d) from the first sample to the last sample to produce a processed two-dimensional image, and

(f) determining the IQM from the processed two-dimensional image.

15. The method of claim 12 , wherein estimating the NPPE-1 phase error includes

receiving the PPE calibrated data having M frequency steps and

producing NPPE-1 calibrated data, which has been calibrated for type-1 NPPE, in response to receiving the PPE calibrated data.

16. The method of claim 15 , wherein the estimating the NPPE-1 phase error further includes

(a) defining functional descriptions for optimization and establishing an error model for a NPPE-1 phase error,

(b) searching for optimum coefficients of Legendre polynomials to determine a minimum IQM in the error model for the NPPE-1 phase error utilizing a Broyden-Fletcher-Goldfarb-Shanno (“BFGS”) algorithm,

(c) determining an estimated NPPE-1 phase error using the optimum coefficients of the error model for a NPPE-1 phase error,

(d) applying the estimated NPPE to the azimuth compressed input data, wherein the NPPE-1 phase error is compensated for the order two through O nppe , and

(e) repeating steps (a) through (d) until all M frequency steps have been processed.

17. The method of claim 16 , wherein defining functional descriptions for optimization includes

(a) determining an expression of the NPPE-1 phase error of order O ppe starting from order two for a phase calculation using Legendre polynomials with the length equal to a number of samples in a step, of the plurality of steps, of the stepped-chirp waveform, wherein the number of samples include a first sample and a last sample,

(b) applying the phase correction to the azimuth compressed data of a step in the range frequency,

(c) applying window weights to the concatenated data in the frequency range,

(d) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(e) repeating the steps (b) through (d) from the first sample to the last sample to produce a processed two-dimensional image, and

(f) determining the IQM from the processed two-dimensional image.

18. The method of claim 12 , wherein estimating the NPPE-2 phase error includes

receiving the NPPE-1 calibrated data and

producing NPPE-2 calibrated data, which has been calibrated for type-2 NPPE, in response to receiving the NPPE-1 calibrated data.

19. The method of claim 18 , wherein estimating the NPPE-2 phase error further includes

(a) defining functional descriptions for optimization and establishing an error model for a NPPE-2 phase error,

(b) searching for optimum coefficients of Legendre polynomials of order zero and order one to determine a minimum IQM in the error model for the NPPE-2 phase error utilizing a Broyden-Fletcher-Goldfarb-Shanno (“BFGS”) algorithm,

(c) determining an 0 order and first order estimated NPPE phase error using the optimum coefficients of the error model for the NPPE-2 phase error,

(d) repeating steps (a) through (c) until all M frequency steps have been processed.

20. The method of claim 19 , wherein defining functional descriptions for optimization includes

(a) taking two data segments from a first and a second frequency steps of the M frequency steps,

(b) determining an expression of the NPPE-2 phase error for a phase correction using Legendre polynomials of order zero and order one with a length equal to the number of range frequency samples in the second step,

(c) applying the phase correction in the range frequency of the azimuth compressed data of the second step,

(d) applying window weights to a concatenated data of the first and second steps using the phase adjusted data of the second step,

(e) applying a fast Fourier transform (“FFT”) on the concatenated data for range compression,

(f) repeating the steps (b) through (e) from the first sample to the last sample to produce a processed two-dimensional image, and

(g) determining the IQM from the processed two-dimensional image.

21. The method of claim 20 , further including adjusting constant and linear phases of all the M steps in order to align them to the first step.

22. The method of claim 21 , further including calibrating an antenna gain prior to estimating the PPE phase error.

23. A Radar Calibration Processor (“RCP”) for calibrating the phase of a stepped-chirp signal utilized by a synthetic aperture radar (“SAR”), the RCP comprising:

means for estimating a first non-periodic phase error (“NPPE”);

means for estimating for a second NPPE calibration after the first NPPE (“NPPE-1”) has been estimated; and

means for estimating a periodic phase error (“PPE”),

wherein the PPE is estimate prior to estimating the first NPPE,

wherein estimating the PPE includes

receiving video phase history (“VPH”) data from the SAR and

producing a PPE calibrated data from the VPH data in response to receiving the VPH data and

wherein the VPH data includes a plurality of steps within a stepped-chirped waveform and a range frequency.