What is the Swerling target model and how does it affect the probability of detection calculation?

The Swerling target models describe four statistical models (Swerling I through IV) for the fluctuation of a target's radar cross section (RCS) over time, which profoundly affects the probability of detection (Pd) calculation for radar systems. Real targets do not have a fixed RCS; instead, the RCS fluctuates due to: the target's aspect angle changing relative to the radar (as the target moves or rotates), the relative phases of multiple scattering centers on the target changing with frequency and angle, and environmental effects (atmospheric scintillation, sea surface reflections). The four Swerling models are: Swerling I (RCS follows a chi-squared distribution with 2 degrees of freedom (exponential distribution), and is constant within a scan but independent from scan to scan; models a target with one dominant scatterer; the RCS has a large variance), Swerling II (same exponential RCS distribution as Swerling I, but the RCS fluctuates independently from pulse to pulse; models a target with fast fluctuation), Swerling III (RCS follows a chi-squared distribution with 4 degrees of freedom, constant within a scan but independent scan to scan; models a target with a dominant scatterer plus many smaller scatterers; the variance is lower than Swerling I), and Swerling IV (same chi-squared 4-DOF distribution as Swerling III, with pulse-to-pulse fluctuation). The effect on detection: for a given average SNR and desired Pd: Swerling I/II targets require 5-10 dB more SNR than a non-fluctuating target (Swerling 0) to achieve Pd = 0.9. Swerling III/IV require approximately 2-5 dB more. Pulse-to-pulse fluctuation (Swerling II, IV) benefits from non-coherent integration because the integration averages over the RCS fluctuation.