Expanded Swerling target models

Radar target fluctuation models were first introduced by Swerling in the 1950s and they proved to be very useful. Swerling soon realized, however, that his original four models were inadequate and generalized them through use of the gamma distribution. These generalized results still had serious limitations in modeling fluctuating targets. For some targets the Swerling I correlated model produced an overly pessimistic value for P_D at large signal-to-noise ratios (SNRs) while the Swerling III correlated model produced an overly optimistic one. As a result, other fluctuation models, such as the log-normal and Weibull, remain useful in spite of their own limitations. Two new models that expand on the generalized Swerling model are presented here. They are physically motivated and can produce the desired P_D levels at high SNR values. They are described in detail and both the moment generating functions (MGFs) and P_D expressions are determined. They provide a significant advance in our modeling capabilities through their flexibility for modeling many different types of target radar cross section (RCS) responses. These new models apply to both the case where the pulse-to-pulse target responses are correlated as well as the case where they are uncorrelated, thereby overcoming the limitations of the log-normal and Weibull models.