非高斯噪声下Kalman滤波熵理论算法研究

Kalman Filter Algorithm under Non-Guassian Noises Using Entropy Theory

从一个新的角度结合具体的算法讲述了Kalman滤波器的原理,并对噪声为非高斯情况下结合熵的理论提出了假设,解决了噪声为非高斯情形下的滤波器设计的瓶颈。传统的Kalman滤波器是在噪声为高斯的情形下得出的最优滤波估计,但是现实生活中大多数噪声却是未知的、不确定性并且非高斯的。为了清楚说明熵原理应用于非高斯滤波器的设计结果,运用了数学统计的方法,对比滤波效果,说明了其可行性,证明了这种方法更适应于对噪声情况未知、参数不明确的情况,为研究广义噪声的随机系统提出了一种新的通用的解决途径。

Describes the principle of the Kalman filter from a new perspective, where a specified algorithm has been developed on the assumption that the entropy theory could be used for the design of the Kalman filter under non - Guassian noises. Traditional Kalman filter has got the optimal filter estimate under Guassian noises without thinking that there are always some unknown, uncertain even no - Guassian noises in reality. In order to clarify the experiment resuk using the entropy theory for non - Guassian filter design, the mathematical statistics are applied in the paper so as to illustrate the filtering effects for the explanation of its feasibility. It has also been shown that the proposed filtering even fits for unknown possibility or ambiguity parameter of noises in Kalman filter design. Also provides a new and universal way for studying the generalized noises of stochastic systems.