Shape Parameter Estimation of <i>K</i>-Distributed Sea Clutter Using Neural Network and Multisample Percentile in Radar Industry
Jian Xue, Mengling Sun, Jun Liu, Shuwen Xu, Meiyan Pan
Abstract
In this paper, we consider the problem of robustly and accurately estimating the shape parameters of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> -distributed sea clutter in the maritime radar industry. Outliers formed by non-sea-surface echoes have a significant negative impact on the estimation accuracy. To improve the estimation performance, we first propose a bipercentiles feedforward neural network for the shape parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> (BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> ), which utilizes a ratio of two percentiles and a two-hidden-layer feedforward neural network. The BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can learn the mathematical relationship between the shape parameter and the ratio of two percentiles, and can work in environments where the number of outliers is approximately known. Moreover, to solve the case where the number of outliers is not known due to dynamic changes in the environment, we also design another neural network (referred to as MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> ), which consists of multiple BP-FFNNs- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> and a multi-class classification network. The MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can perceive the change in the proportion of outliers, so an accurate estimate can be obtained from an unaffected BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> . Finally, training and test data are constructed to train and evaluate the proposed methods, respectively. Experimental results demonstrate that the BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> performs better than traditional moments-based estimators, and has almost the same performance as the tri-percentile estimator. Compared with the tri-percentile estimator, the BP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> avoids table lookups, and produces a continuous estimate. The MBP-FFNN- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\eta$</tex-math></inline-formula> can achieve more than 97% overall classification accuracy on simulated and measured data, and thus an accurate estimate of the shape parameter can be obtained when the number of outliers varies.