A synthetic-aperture-radar apparatus, comprising: a radar transceiver, configured to emit electromagnetic pulses towards a surveillance area and to provide a radar signal (S SAR) in response to reception of echoes of the electromagnetic pulses; and a processing unit, configured to produce synthetic-aperture-radar images of moving objects present in the surveillance area starting from the radar signal (S SAR); wherein the processing unit comprises: a first processing module, configured to apply a process of translational motion compensation to a central reference point of a moving object in a subaperture of the radar signal (S SAR); a second processing module, configured to execute a first phase-compensation process with the single central reference point as reference; and a third processing module, configured to estimate a phase component (φ CP (i); φ 1 (i),..., φ K (i)) of at least one auxiliary point (CP; CP 1,..., CP K) of the moving object distinct from the central reference point; characterized in that the third processing module is further configured to apply phase compensation to the radar signal (S SAR) as a function of the phase component (φ CP (i); φ 1 (i),..., φ K (i)) of the auxiliary point (CP; CP 1,..., CP K) and of a normalization parameter to a distance in range (rb CRP -rb CP) between the central reference point and the auxiliary point (CP; CP 1,..., CP K), and in that the third processing module is further configured to determine a start instant for production of SAR images from the radar signal (S SAR) on the basis of a Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K) and of a derivative of the Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K). a radar transceiver, configured to emit electromagnetic pulses towards a surveillance area and to provide a radar signal (S SAR) in response to reception of echoes of the electromagnetic pulses; and a processing unit, configured to produce synthetic-aperture-radar images of moving objects present in the surveillance area starting from the radar signal (S SAR); wherein the processing unit comprises: a first processing module, configured to apply a process of translational motion compensation to a central reference point of a moving object in a subaperture of the radar signal (S SAR); a second processing module, configured to execute a first phase-compensation process with the single central reference point as reference; and a third processing module, configured to estimate a phase component (φ CP (i); φ 1 (i),..., φ K (i)) of at least one auxiliary point (CP; CP 1,..., CP K) of the moving object distinct from the central reference point; characterized in that the third processing module is further configured to apply phase compensation to the radar signal (S SAR) as a function of the phase component (φ CP (i); φ 1 (i),..., φ K (i)) of the auxiliary point (CP; CP 1,..., CP K) and of a normalization parameter to a distance in range (rb CRP -rb CP) between the central reference point and the auxiliary point (CP; CP 1,..., CP K), and in that the third processing module is further configured to determine a start instant for production of SAR images from the radar signal (S SAR) on the basis of a Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K) and of a derivative of the Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K). a first processing module, configured to apply a process of translational motion compensation to a central reference point of a moving object in a subaperture of the radar signal (S SAR); a second processing module, configured to execute a first phase-compensation process with the single central reference point as reference; and a third processing module, configured to estimate a phase component (φ CP (i); φ 1 (i),..., φ K (i)) of at least one auxiliary point (CP; CP 1,..., CP K) of the moving object distinct from the central reference point; characterized in that the third processing module is further configured to apply phase compensation to the radar signal (S SAR) as a function of the phase component (φ CP (i); φ 1 (i),..., φ K (i)) of the auxiliary point (CP; CP 1,..., CP K) and of a normalization parameter to a distance in range (rb CRP -rb CP) between the central reference point and the auxiliary point (CP; CP 1,..., CP K), and in that the third processing module is further configured to determine a start instant for production of SAR images from the radar signal (S SAR) on the basis of a Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K) and of a derivative of the Doppler coordinate of the auxiliary point (CP; CP 1,..., CP K).