Vibrometry and sound reproduction of acoustic sources on moving platforms using radar

A radar system, comprising:

• a radar configured to receive a signal from a moving object;
• and
• a motion compensator configured to:
• determine respective time delays that maximize respective correlations between respective reference pulses and respective pulse profiles in the signal for each pulse profile in a plurality of pulse profiles in the signal,
• determine a delay vector based on the respective time delays,
• determine a velocity of the object based on the delay vector,
• determine an acceleration of the object based on the delay vector,
• determine an optimized velocity, based on the determined velocity, such that the optimized velocity minimizes entropy,
• determine an optimized acceleration, based on the determined acceleration, such that the optimized acceleration minimizes entropy,
• align the plurality of pulse profiles based on the optimized velocity and the optimized acceleration, thereby generating ranged aligned data,
• convert the ranged aligned data to a range-Doppler map,
• minimize a two dimensional (2D) entropy of the range-Doppler map,
• determine an estimate for a quadratic phase error based on the minimized 2D entropy of the range-Doppler map, and
• perform a phase gradient autofocus (PGA) process on the ranged aligned data, based on the indirect estimate for the quadratic phase error, thereby generating a motion compensated signal.

A radar system, comprising:

• a radar configured to:
• send a signal towards a moving object, and
• receive a return signal;
• and
• a motion compensator configured to:
• receive the return signal from the radar,
• determine a direct estimate for a velocity of the object based on the return signal,
• determine a direct estimate for an acceleration of the object based on the return signal,
• determine respective indirect estimates for the velocity and acceleration based on an entropy optimization of the determined direct estimate for the velocity and the determined direct estimate for the acceleration, thereby generating ranged aligned data,
• determine an indirect estimate for quadratic phase error in the ranged aligned data based on entropy optimization, and
• perform a phase gradient autofocus (PGA) process on the ranged aligned data, based on the indirect estimate for the quadratic phase error, thereby generating a motion compensated signal.