Fast phase difference autofocus

A phase difference autofocus method for removing phase errors from synthetic array radar data, said method comprising the steps of:

• dividing a full array of each range bin in the synthetic array radar data into two subarrays;
• complex-conjugate multiplying the the two subarrays together to produce a cross spectrum;
• aligning the phases of a current cross spectrum with a presently accumulated cross spectrum sum by multiplying the current cross spectrum with a complex phasor and adding it to a presently accumulated cross spectrum sum;
• adding the current phase aligned cross spectrum to the previously accumulated cross spectrum sum to update the cross spectrum sum;
• whereby when all range bins have been processed, a final cross spectrum sum is produced;
• applying an amplitude weighting function to the final cross spectrum sum;
• performing an FFT on the amplitude-weighted cross spectrum sum to produce a cross correlation function;
• magnitude-detecting the cross correlation function to detect a peak location of the cross correlation function;
• multiplying the filter location of the peak by a scale factor to compute a center-to-end phase error estimate signal;
• and
• generating a phase correction signal using the phase error estimate signal and removing the phase error from the synthetic array radar data by multiplying the data with the phase estimate signal.

A phase difference autofocus method that removes phase errors from synthetic array radar data, said method comprising the steps of:

• dividing a full array from each range bin of the synthetic array radar data into two subarrays X.sub.n (m), Y.sub.n (m) of length M;
• complex-conjugate multiplying the two subarrays together to produce a cross spectrum r.sub.n (m);
• computing a phasor e.sup.jyn by complex-conjugate multiplying the cross spectrum r.sub.n (m) with the presently accumulated sum SUM.sub.n-1 (m), adding all terms of the resulting product, and then extracting its phase y.sub.n to form the phasor e.sup.jyn ;
• integrating the phase aligned cross spectrum r.sub.n (m) e.sup.jyn across all range bins to produce a cross spectrum sum comprising a summed value SUM.sub.n (m)=SUM.sub.n-1 (m)+r.sub.n (m) e.sup.jyn,
• applying an amplitude weighting function to the cross spectrum sum SUM.sub.N (m);
• performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
• magnitude-detecting the cross correlation function to determine the location t.sub.xy of the peak response therein;
• computing a quadratic phase error estimate .phi..sub.q =-2p t.sub.xy M.sup.2 /(4LK);
• generating a phase error correction signal e.sup.j .phi.q (m/M)2, -M<m<M;
• and
• removing the phase error from the synthetic array radar data by multiplying the data with the phase error correction signal.

A phase difference autofocus method that removes phase errors from synthetic array radar data, said method comprising the steps of:

• dividing each range bin of the synthetic array radar data into two subarrays;
• producing a cross spectrum of the two subarrays;
• aligning the phases of each cross spectrum with an accumulated sum of cross spectrums;
• adding the phase aligned cross spectrum to the accumulated cross spectrum sum;
• processing all range bins to compute a final cross spectrum sum;
• applying an amplitude weighting function to the final cross spectrum sum;
• performing an FFT on the amplitude weighted cross spectrum sum to produce a cross correlation function;
• magnitude-detecting the cross correlation function;
• producing a phase error correction signal;
• and
• removing the phase error from synthetic array radar data by multiplying the data with the phase error correction signal.

A fast phase difference autofocus method for removing phase errors from synthetic array radar signals, said method comprising the steps of:

• dividing each range bin of the synthetic array radar data into two subarrays;
• complex-conjugate multiplying the two subarrays together to produce a cross spectrum;
• determining a complex phasor for the cross spectrum to align its phase so that the cross spectrum can be coherently added to the accumulated sum of cross spectrums from previously processed range bins by:
• complex-conjugate multiplying the current cross spectrum and a previously accumlated sum of cross spectrums to produce a second order cross spectrum product;
• summing all terms of the second order cross spectrum product to form a complex sample;
• and
• extracting the phase of the complex sample;
• multiplying the cross spectrum with the complex phasor and adding it to the accumulated sum of cross spectrums from previously processed range bins;
• repeating the process over all range bins to form the final cross spectrum sum from all range bins;
• applying an amplitude weighting function to the final cross spectrum sum;
• performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
• magnitude-detecting the cross correlation function and determining a peak location of the cross correlation function;
• multiplying the peak location by a scale factor to compute a center-to-end phase error estimate;
• and
• generating a phase error correction signal and removing the phase error from the synthetic array radar data by multiplying the data with the phase error correction signal.

A fast phase difference autofocus method generating a phase error correction signal that is used to remove phase errors from synthetic array radar signals, said method comprising the steps of:

• dividing each range bin of the synthetic array radar data into two subarrays;
• complex-conjugate multiplying the two subarrays together to produce a cross spectrum;
• determining a complex phasor for the cross spectrum to align its phase so that the cross spectrum can be coherently added to the accumulated sum of cross spectrums from previously processed range bins;
• multiplying the cross spectrum with the complex phasor and adding it to the accumulated sum of cross spectrums from previously processed range bins;
• repeating the previous three steps for all range bins to form the final cross spectrum sum from all range bins;
• applying an amplitude weighting function to the final cross spectrum sum;
• performing an FFT to the amplitude-weighted cross spectrum sum to produce a cross correlation function;
• magnitude-detecting the cross correlation function and determining a peak location of the cross correlation function;
• multiplying the peak location by a scale factor to compute a center-to-end phase error estimate;
• and
• generating a phase error correction signal that is adapted to remove the phase error from the synthetic array radar data by multiplying the data with the phase error correction signal.