## 4 Results and Discussion
### Analysis of the Fit of the Measured Data  
To verify the fitting effect of the generalized Pareto distribution model on the statistical properties of heavy trailing sea clutter data and to analyze the adaptability of different parameter estimation methods for parameter estimation of real data, this section performs a goodness-of-fit analysis on the statistical properties of a set of high-intensity data from the IPIX radar dataset [39; 40] and an X-band radar open-source dataset [41; 42], respectively. Many scholars have carried out a large amount of research work on the perception of sea clutter properties based on the IPIX radar dataset, so this dataset is very reliable for the goodness-of-fit analysis. The effect of the distribution model on the sea clutter amplitude PDF fit is shown in Figure 10, and the two-parameter estimates of sea clutter data obtained via different parameter estimation methods are given in Table 3. Each dataset of the IPIX radar dataset contains 14 distance units, and a total of 131,702 data samples are collected for each distance unit. To reduce the running time, this experiment selects the non-target  
Figure 9: Parameter estimation performance as a function of shape parameters. (**a,b**) indicate the trends of RRMSE metrics with shape parameters for scale and shape parameters, respectively. distance unit within (pure clutter data) 50,000 data samples, as the object of parameter estimation. From Figure 10, it can be found that the PSO algorithm, compared to parameter estimation methods with explicit solutions, such as positive 2 nd/4 th-order and positive 1 st-order logarithmic moments, not only effectively solves the problem of non-closed expressions in the three types of parameter estimation methods shown in the figure but also provides a distribution model that fits the heavy-tailed part of the observed data (with amplitudes in the range of 4-6) with a fitting distance smaller than \(10^{-5}\). Another X-band radar open-source sea clutter dataset is taken for parameter estimation experiments, and this dataset is obtained through the radar working in scanning mode to avoid the influence of near-coast land clutter background; only the data when the radar is scanning to the sea are intercepted for the goodness-of-fit analysis. Each set of data in this dataset contains 1320 distance units, and there are a total of 7369 samples within each distance unit. This experiment selected the clutter data from within distance units 801 to 810, and then intercepted the samples at each distance unit corresponding to the 501 st to 3500 th, for a total sample size of 30,000 (pure clutter data). Figure 11 shows the fitting effect of the distribution model on the amplitude PDF of this group of data, and the two-parameter estimation results of this group of sea clutter data are shown in Table 3. It also reflects the fact that the particle swarm model introduced in this paper can fit the data. In addition, it also reflects that the problem of solving non-closed expressions for parameter estimation of the generalized Pareto distribution model has been effectively solved after the introduction of the particle swarm algorithm in this paper. Both sets of experiments above observe the fitting effect of the distribution model directly from the plots. To quantitatively characterize the strengths and weaknesses of the fitting effect and then make a more accurate analysis of the fitting effect, the results of the Kolmogorov-Smirnov (K-S) test, the mean square deviation (MSD) test, and the root mean square deviation (RMSD) tests for the IPIX radar data and X-band radar open-source measured data are given in Tables 4 and 5, respectively. The three test rules mentioned above are common methods for analyzing the fitting effect of distribution models, which are  
Figure 10: Fitting results of IPIX radar measured data.