Fourth-order-product phase difference autofocus

• US 5,200,754 A
• Filed: 11/27/1991
• Issued: 04/06/1993
• Est. Priority Date: 11/27/1991
• Status: Expired due to Fees

• Current Assignee: Hughes Aircraft Company (Rtx Corporation)
• Original Assignee: Hughes Aircraft Company (Rtx Corporation)
• Inventors: Niho, Yoji G.
• Primary Examiner(s): TUBBESING, THEODORE
• Application Number:
  US07/799,505
• Time in Patent Office: 496 Days
• Field of Search: 342/25
• US Class Current: 342/25.00D
• CPC Class Codes: G01S 13/9011 with frequency domain processing of the SAR signals in azimuth G01S13/9005 takes precedence
• CPC Class Codes: G01S 13/9019 Auto-focussing of the SAR signals

Abstract

The present invention is a computational method, defined by a computational algorithm, that automatically corrects synthetic array radar (SAR) focus errors more accurately than conventional procedures. The novel feature is that the present method estimates residual phase errors by forming fourth-order subarray products in lieu of conventional second-order subarray products. As a result, a pull-in range for residual phase errors is vastly improved. The present invention advances the state of the art by creating a SAR autofocus method that has an unlimited pull-in range for both a quadratic and a cubic phase errors. The invention thus extends the operational range and resolution of SAR systems, and enables the effective use of the SAR sensor with a limited (less expensive) motion compensation subsystem. The present invention provides for a phase difference autofocus method that estimates the residual quadratic and cubic phase error that often requires only one autofocus iteration.

Claims

1. A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of:

dividing an array of range compressed VPH data into first and second subarrays;

forming a third subarray of range compressed VPH data comprising a portion of the array;

complex-conjugate multiplying the first subarray with the third subarray to produce a first second-order-product subarray;

complex-conjugate multiplying the third subarray with the second subarray to produce a second second-order-product subarray;

complex-conjugate multiplying the first second-order-product subarray with the second second-order-product subarray to produce a first fourth-order-product subarray;

time reversing and complex-conjugate multiplying the second second-order-product subarray with the first second-order-product subarray to produce a second fourth-order-product subarray;

separately performing Fourier transforms on the first and second fourth-order-product subarrays to produce respective FFT filter banks;

separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals;

summing the respective autofocus functionals over all range bins;

respectively determining the locations of the peak response values of the autofocus functionals;

computing quadratic and cubic phase error values from the respective peak response locations;

combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and

multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

2. The method of claim 1 wherein:

the array of data is divided into first and second equal subarrays comprising respective halves of the array; and

the third subarray comprises a center portion of the array.

3. The method of claim 2 which further comprises the step of:

separately amplitude weighting the first and second fourth-order-product subarrays prior to performing the Fourier transforms on them.

4. A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of:

dividing an array of range compressed VPH data into first and second equal subarrays that comprise respective halves of the data comprising the array;

forming a third subarray of range compressed VPH data comprising a center portion of the array, and which comprises the same amount of data as the first and second subarrays;

complex-conjugate multiplying the first subarray with the third array to produce a first second-order-product subarray;

complex-conjugate multiplying the third subarray with the second array to produce a second second-order-product subarray;

complex-conjugate multiplying the first second-order-product subarray with the second second-order-product subarray to produce a first fourth-order-product subarray;

time reversing and complex-conjugate multiplying the second second-order-product subarray with the first second-order-product subarray to produce a second fourth-order-product subarray;

separately performing Fourier transforms on the first and second fourth-order-product subarrays to produce respective FFT filter banks;

separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals;

summing the respective autofocus functionals over all range bins;

respectively determining the locations of the peak response values of the autofocus functionals;

computing quadratic and cubic phase error values from the respective peak response locations;

combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and

multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

5. The method of claim 4 which further comprises the step of:

separately amplitude weighting the first and second fourth-order-product subarrays prior to performing the Fourier transforms on them.

6. A phase difference autofocus computational method for use in processing range compressed video phase history (VPH) data of a SAR data to correct for phase errors contained therein, said method comprising the steps of:

dividing an array of range compressed VPH data into first and second equal subarrays {X(n)}, {Y(n)};

forming a third subarray {Z(n)} of range compressed VPH data comprising a center portion of the array;

complex-conjugate multiplying the first subarray {X(n)} with the third subarray {Z(n)} to produce a first second-order-product subarray {P(n)};

complex-conjugate multiplying the third subarray {Z(n)} with the second subarray {Y(n)} to produce a second second-order-product subarray {Q(n)};

complex-conjugate multiplying the first second-order-product subarray {P(n)} with the second second-order-product subarray {Q(n)} to produce a first fourth-order-product subarray {H(n)};

time reversing and complex-conjugate multiplying the second second-order-product subarray {Q(n)} with the first second-order-product subarray {P(n)} to produce a second fourth-order-product subarray {G(n)};

separately amplitude weighting the first and second fourth-order-product subarrays {G(n)}, {H(n)};

separately performing Fourier transforms on the amplitude weighted first and second fourth-order-product subarrays {G(n)}, {H(n)} to produce respective FFT filter banks;

separately performing magnitude-detections on respective FFT filter banks to produce respective autofocus functionals;

summing the respective autofocus functionals over all range bins;

respectively determining the locations of the peak response values of the autofocus functionals;

computing quadratic and cubic phase error values from the respective peak response locations;

combining the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal; and

multiplying the range compressed VPH data with the phase error correction signal to produce phase-corrected VPH data.

7. The method of claim 6 wherein:

the dividing an array into first and second subarrays and forming a third subarray comprises creating first, second and third subarrays of length 2N+1 defined by

space="preserve" listing-type="equation">X(n)=S(n-L)=σ

e.sup.jφ

(n-L), -N<

n<

N,

space="preserve" listing-type="equation">Y(n)=S(n+L)=σ

e.sup.jφ

(n+L), -N<

n<

N, and

space="preserve" listing-type="equation">Z(n)=S(n)=σ

e.sup.jφ

(n), -N<

n<

N,

and wherein a full array of length 2M+1 is defined by

space="preserve" listing-type="equation">S(m)=σ

e.sup.jφ

(m), -M,<

m<

M,

defines the locations of the first and second subarrays, σ

is a magnitude and φ

(m) is a phase variation having the form

space="preserve" listing-type="equation">φ

(m)=2π

(A+Bm+Cm.sup.2 +Dm.sup.3), -M≦

m≦

M,

for constants A, B, C and D;

the complex conjugate multiplying the first subarray {X(n)} with the third subarray {Z(n)} to produce a first second-order-product subarray {P(n)} is defined by P(n)=X*(n) Z(n) and the complex-conjugate multiplying the third subarray {Z(n)} with the second subarray {Y(n)} to produce a second second-order-product subarray {Q(n)} is defined by Q(n)=Z*(n) Y(n);

the separately amplitude weighting the first and second fourth-order-product subarrays {G(n)} and {H(n)} are defined by

space="preserve" listing-type="equation">G(n)=P(n)Q*(-n), -N≦

n≦

N, and

space="preserve" listing-type="equation">H(n)=P*(n) Q(n), -N≦

n≦

N,

and are predetermined as

space="preserve" listing-type="equation">G(n)=σ

.sup.4 e.sup.+j2π

4CLn, and

space="preserve" listing-type="equation">H(n)=σ

.sup.4 e.sup.+j2π

6DL.spsp.2 n;

respectively determining the locations of the autofocus functional is determined by;

the peak response is located at τ

_g =4CLK if a K-point FFT is performed on the first fourth-order-product subarray {G(n)}, and

the peak response is located at τ

_h =6DL² K if a K-point FFT is performed on the second fourth-order-product subarray {H(n)}; and

the computing the quadratic and cubic phase error values in accordance with a predefined relationship to produce a phase error correction signal is specified as center-to-end quadratic phase error Φ

_q is given by Φ

_q =2π

τ

_g M² /(4LK), and the center-to-end cubic phase error Φ

_c is given by Φ

_c =2π

τ

_g M³ /(6LK).