In this paper, we present a novel [z log(z)]-based approach to the evaluation of estimators of the K-distributed clutter plus thermal noise parameters. In doing this, we start by deriving expressions of log-based moments of the received data, i.e., means of [log(z)] and [z log(z)], which are related to the parameters of the K plus noise distribution, the digamma, and the hypergeometric functions. Then, by accommodating a single pulse and noncoherent integration of N pulses, respectively, we first determine the new estimators in terms of log-based moments and first-and second-order moments. As the computation of these nonlinear estimates requires the use of numerical routines, we resort to the inverse of the harmonic mean of the received data to get equivalent but more interesting estimates in which expressions are independent of the confluent hypergeometric functions. Monte Carlo simulations show that the proposed estimators are more efficient than existing methods for various clutter plus noise situations.
Pareto plus noise clutter distribution has been introduced recently as a good candidate model for X-band high resolution maritime clutter returns. In this study, the authors derive a non-integer order moments estimator (NIOME) and [zlog(z)] based estimator to find the parameters of this distribution in the case of non-coherent integration of N-pulses. For this, the authors first develop an asymptotic formula of moments with non-integer order which is expressed in terms of the gamma and the generalised hypergeometric functions. Then, the authors derive [zlog(z)] based approach as a function of the log based moments and the generalised hypergeometric function. By accommodating a non-integer moments and moments of orders one and two, the proposed estimators are given so that non-linear estimates of the shape parameter are achieved using numerical computations. Through synthetic and real data, the authors show numerous examples demonstrating the applicability of the estimation procedures as a function of clutter-plus-noise parameters. The obtained results illustrate that the proposed NIOME method is asymptotically efficient especially for multiple looks case and high sample size.
A statistical model for high-resolution sea clutter, which we have called the compound inverse Gaussian (CIG) distribution, is proposed. The model is a mixture of the Rayleigh distribution and the inverse Gaussian (IG) distribution to model the speckle and the texture components, respectively. The CIG probability density function (pdf) is generalized to account for the additive thermal noise to achieve a good match to real data. The overall pdf is given in an integral form as a function of three parameters which are estimated from the recorded data based on the parametric curve-fitting estimation (PCFE) method of the complementary cumulative distributed function (CCDF). The Nelder-Mead (N-M) simplex algorithm is used to provide the best estimates of the pdf parameters. Using the IPIX backscatter database, the fitting of the CIG pdfs and the cumulative distributed functions (cdfs) are assessed and compared with the fitted Weibull, log-normal, Rician inverse Gaussian (RiIG), K plus noise, compound log-normal (CLN), and Pareto plus noise distributions. Experimental fitting results show that the sea-clutter amplitudes obey the proposed CIG model in most cases.
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