一种瑞利分布k阶原点矩的计算方法

A calculating method of kth order origin moment of Rayleigh distribution

瑞利分布作为雷达杂波最基本的非高斯分布模型,广泛应用于雷达建模与分析.针对服从瑞利分布的随机变量的k阶原点矩闭解式的求解问题,通过递推思想,导出了服从瑞利分布的随机变量的k阶原点矩的解析式,在此基础上得到了在雷达中常用的一阶、二阶、三阶和四阶原点矩.最后通过Monte Carlo仿真,验证了理论分析结果的正确性,为雷达杂波服从瑞利分布时的参数估计和杂波建模等提供了理论支撑.

As the most basic non-Gaussian distribution model of radar clutter, Rayleigh distribution is widely used in radar modeling and analysis. In order to get the closed solution of the kth order origin moment of random variables that follow Rayleigh distribution, the paper derives the analytic formula of kth order origin moment by recursion thought, on the basis of which the first, the second, the third and the fourth order origin moments commonly used in radar are obtained. Finally the paper verifies the correctness of the theoretical analysis results by Monte Carlo simulation, and provides a theoretical support for parameters estimation and clutter modeling when radar clutter follows Rayleigh distribution.