**Figure 1.**
Radar and target moving at speed v away from the radar.

**Figure 1.**
Radar and target moving at speed v away from the radar.

**Figure 2.**
Sweeping of a step frequency continuous wave (SFCW) radar: f_{1} is the initial frequency, Δf is the step frequency, B is the bandwidth, Δt is the tone duration, N is the number of frequencies, and τ is the sweep time.

**Figure 2.**
Sweeping of a step frequency continuous wave (SFCW) radar: f_{1} is the initial frequency, Δf is the step frequency, B is the bandwidth, Δt is the tone duration, N is the number of frequencies, and τ is the sweep time.

**Figure 3.**
Example of the Doppler range shift. The green curve is the inverse fast Fourier transform (IFFT) amplitude of a static target, the red curve is the IFFT amplitude of a target moving away from the radar (in the radar-target direction) at speed v = 10 m/s.

**Figure 3.**
Example of the Doppler range shift. The green curve is the inverse fast Fourier transform (IFFT) amplitude of a static target, the red curve is the IFFT amplitude of a target moving away from the radar (in the radar-target direction) at speed v = 10 m/s.

**Figure 4.**
Plot of the mathematical function A_{N}(x).

**Figure 4.**
Plot of the mathematical function A_{N}(x).

**Figure 5.**
Simulation set-up of the free-falling target.

**Figure 5.**
Simulation set-up of the free-falling target.

**Figure 6.**
Simulated time-range map of the free-falling target.

**Figure 6.**
Simulated time-range map of the free-falling target.

**Figure 7.**
Plot of the peak range in time. The green line is the effective range of the target, the red line is the range of the peaks without the Doppler correction, and the blue dotted line is the range of the peaks with the Doppler correction.

**Figure 7.**
Plot of the peak range in time. The green line is the effective range of the target, the red line is the range of the peaks without the Doppler correction, and the blue dotted line is the range of the peaks with the Doppler correction.

**Figure 8.**
Speed of the falling target (**green line**) and the estimated speed by phase difference between two subsequent sweeps (**red line**).

**Figure 8.**
Speed of the falling target (**green line**) and the estimated speed by phase difference between two subsequent sweeps (**red line**).

**Figure 9.**
Range of error evaluated for different signal-to-noise ratios (SNR). The red line is an interpolating straight line of slope −1.

**Figure 9.**
Range of error evaluated for different signal-to-noise ratios (SNR). The red line is an interpolating straight line of slope −1.

**Figure 10.**
Picture of the radar prototype.

**Figure 10.**
Picture of the radar prototype.

**Figure 11.**
Picture of the experimental set-up for detecting a free-falling corner reflector by radar.

**Figure 11.**
Picture of the experimental set-up for detecting a free-falling corner reflector by radar.

**Figure 12.**
Time-range map of the measured IFFT (experimental set-up shown in

Figure 8).

**Figure 12.**
Time-range map of the measured IFFT (experimental set-up shown in

Figure 8).

**Figure 13.**
Measured plots of the peaks’ range in time (experimental set-up shown in

Figure 8). The green line is the theoretical range of the target, the red line is the range of the peaks without the Doppler correction, and the blue dotted line is the range of the peaks with the Doppler correction.

**Figure 13.**
Measured plots of the peaks’ range in time (experimental set-up shown in

Figure 8). The green line is the theoretical range of the target, the red line is the range of the peaks without the Doppler correction, and the blue dotted line is the range of the peaks with the Doppler correction.

**Figure 14.**
Difference between the effective range and the measured range with the Doppler correction during the fall.

**Figure 14.**
Difference between the effective range and the measured range with the Doppler correction during the fall.

**Figure 15.**
Detection of a small unmanned aerial vehicle (UAV) using an SFCW radar.

**Figure 15.**
Detection of a small unmanned aerial vehicle (UAV) using an SFCW radar.

**Figure 16.**
Two different flight maneuvers: (**1**) take-off and rapid running away and (**2**) rapid vertical take-off.

**Figure 16.**
Two different flight maneuvers: (**1**) take-off and rapid running away and (**2**) rapid vertical take-off.

**Figure 17.**
Detection of a small UAV using an SFCW radar. Time-range map without the Doppler correction during maneuver 1 (i.e., take-off and rapid running away).

**Figure 17.**
Detection of a small UAV using an SFCW radar. Time-range map without the Doppler correction during maneuver 1 (i.e., take-off and rapid running away).

**Figure 18.**
Recorded acceleration modulus of the UAV during maneuver 1 (i.e., take-off and rapid running away).

**Figure 18.**
Recorded acceleration modulus of the UAV during maneuver 1 (i.e., take-off and rapid running away).

**Figure 19.**
Detection of a small UAV using an SFCW radar. Time-range map with the Doppler correction during maneuver 1 (i.e., take-off and rapid running away).

**Figure 19.**
Detection of a small UAV using an SFCW radar. Time-range map with the Doppler correction during maneuver 1 (i.e., take-off and rapid running away).

**Figure 20.**
Maneuver 1 (i.e., take-off and rapid running away). Range plots at time t = 4.92 without the Doppler correction (**in red**) and with the Doppler correction (**in green**).

**Figure 20.**
Maneuver 1 (i.e., take-off and rapid running away). Range plots at time t = 4.92 without the Doppler correction (**in red**) and with the Doppler correction (**in green**).

**Figure 21.**
Detection of a small UAV using a SFCW radar. Time-range map without the Doppler correction during maneuver 2 (i.e., rapid take-off).

**Figure 21.**
Detection of a small UAV using a SFCW radar. Time-range map without the Doppler correction during maneuver 2 (i.e., rapid take-off).

**Figure 22.**
Recorded vertical acceleration of the UAV during maneuver 2 (i.e., rapid take-off).

**Figure 22.**
Recorded vertical acceleration of the UAV during maneuver 2 (i.e., rapid take-off).

**Figure 23.**
Detection of a small UAV using a SFCW radar. Time-range map with the Doppler correction during maneuver 2 (i.e., rapid take-off).

**Figure 23.**
Detection of a small UAV using a SFCW radar. Time-range map with the Doppler correction during maneuver 2 (i.e., rapid take-off).

**Figure 24.**
Maneuver 2 (i.e., rapid take-off). Range plots at time 1.20 s without the Doppler correction (**in red**) and with the Doppler correction (**in green**).

**Figure 24.**
Maneuver 2 (i.e., rapid take-off). Range plots at time 1.20 s without the Doppler correction (**in red**) and with the Doppler correction (**in green**).