低位截断瑞利噪声的统计推理

预警雷达抗噪声压制干扰评估通常需要对量化后的瑞利噪声样本进行估计,在实际雷达系统中受硬件采样位数限制有时会舍弃噪声样本的低位数据,相当于进一步提高了噪声的量化误差,这时采用截断后的噪声样本计算均值会造成很大的估计偏差。为了有效运用低位截断后的噪声样本进行噪声估计,基于多项分布和瑞利分布推导了分布参数的最大似然估计方法,并证明了对数似然函数的凸函数性质以及后验分布为对数凹分布的性质,在此基础上提出了无信息先验贝叶斯估计方法和共轭先验贝叶斯估计方法。仿真数据实验验证了所提的极大似然估计、无信息先验贝叶斯估计和共轭先验贝叶斯估计算法的有效性,且对比分析了贝叶斯估计相对于极大似然估计的优越性。

Statistical inference toward lower digits truncated Rayleigh noise

The anti -noise jamming evaluation toward surveillance radar often needs to estimate quantized Rayleigh noise samples. In addition, due to the conversion digit number restriction of hardwares, real radar systems sometimes discard the low bit data, which increases the quantization error. In that case, calculating the average of these truncated data would cause large biases. In order to efficiently estimate the truncated noise samples, we derive the maximum likelihood estimation for their distribution parameters is derived, and the convex function property for the logarithm likelihood function as well as the logarithm concave distribution property for the posterior distribution are proved. Based on that, we propose Bayesian estimation methods under noninformative/conjugate priors. Simulation experiments demonstrate the effectiveness of the proposed maximum likelihood estimation, and noninformative/conjugate priors based Bayesian estimation. By comparison with the maximum likelihood estimation, the advantage of the Bayesian estimation is analyzed.