Robust parameter estimation for the Double K distribution in heavy-tailed sea clutter using a multi-population genetic algorithm

Abstract The Double K (KK) distribution, a hierarchical compound model in which the texture component follows a K-distribution, provides a flexible framework for heavy-tailed sea clutter under high sea states, but its practical use depends on reliable estimation of multiple coupled parameters. This study proposes a KK-distribution parameter estimation method based on a multi-population genetic algorithm (MPGA). The method formulates parameter estimation as a nonlinear optimization problem that jointly minimizes the discrepancies between the theoretical and empirical probability density function (PDF) and cumulative distribution function (CDF) at histogram sampling points. Relative to the standard genetic algorithm (SGA), the MPGA preserves population diversity and mitigates premature convergence in multi-parameter search. Monte Carlo simulations show that the proposed method delivers higher estimation accuracy and stronger convergence stability than the SGA, while additional tests clarify how sample size and histogram bin width affect estimation performance. Additional comparisons with particle swarm optimization and differential evolution, together with statistical tests, ablation analysis, and hyperparameter sensitivity experiments, further characterize the accuracy–cost trade-off of the proposed estimator. Experiments on measured sea-clutter data show that the KK model with MPGA-estimated parameters fits heavy-tailed behavior more accurately than the K distribution and the generalized Pareto distribution. For the McMaster University Intelligent Pixel Processing (IPIX) datasets, the proposed method achieves Kolmogorov-Smirnov (K-S) distances of 0.0128 and 0.0164 and root-mean-square deviation (RMSD) values of 0.0042 and 0.0060, all lower than the benchmark values. Additional X-band measured datasets under sea states 2–4 support the practical applicability of the KK fitting framework across different clutter conditions. These results indicate that the proposed method provides an effective and practical solution for KK-distribution parameter estimation and heavy-tailed sea-clutter modeling.