Estimation of the k-distributed clutter plus thermal noise parameters using higher order and fractional moments

The estimation of the K-distributed radar clutter plus thermal noise parameters can be improved by employing fractional moments instead of the existing higher order moments. In order to achieve this, we provide first an asymptotic expression of the moments in terms of the confluent and Gauss hypergeometric functions. For fractional orders of the latter, the new estimation method is derived so that the estimates of the shape parameter are achieved via numerical computations of nonlinear equations. For lower fractional orders of moments and different values of the parameters, the numerical simulations demonstrate the effectiveness of the proposed estimation procedure when compared with the standard higher order moments method.