We investigate non-Gaussian noise second-order filtering and fixed-order smoothing problems for non-Gaussian stochastic discrete systems with packet dropouts. We present a novel Kalman-like nonlinear non-Gaussian noise estimation approach based on the packet dropout probability distribution and polynomial filtering technique. By means of properties of Kronecker product we first introduce a second-order polynomial extended system and then analyze the means and variances of the Kronecker powers of the extended system noises. To generate noise estimators in forms of filtering and smoothing, we use the innovation approach. We give an example to illustrate that the presented algorithm has better robustness against packet dropouts than conventional linear minimum variance estimation.

我们研究具有数据包丢失的非高斯随机离散系统的非高斯噪声二阶滤波和固定阶平滑问题。我们提出了一种基于数据包丢失概率分布和多项式滤波技术的新型卡尔曼式非线性非高斯噪声估计方法。利用克罗内克积的性质，我们首先引入了一个二阶多项式扩展系统，然后分析了扩展系统噪声的克罗内克幂的均值和方差。为了生成滤波和平滑形式的噪声估计器，我们使用了创新方法。我们举一个例子来说明所提出的算法比传统的线性最小方差估计具有更好的鲁棒性。