Stochastic Estimation for Two-State Linear Dynamic Systems With Additive Cauchy Noises
Stochastic Estimation for Two-State Linear Dynamic Systems With Additive Cauchy Noises
复制标题
具有加性柯西噪声的二态线性动态系统的随机估计
DOI：
10.1109/tac.2015.2422478
复制
发表时间：
2015
影响因子：
6.8
通讯作者：
M. Idan
中科院分区：
文献类型：
--
作者：
Javier H. Fernández;J. Speyer;M. Idan
针对柯西分布式过程和测量噪声驱动的二态线性系统，开发了一种高效的递归状态估计器。对于一般的矢量状态系统，估计器基于递归传播条件概率密度函数 (cpdf) 的特征函数，其中表达该特征函数的和中的项数随着每次测量更新而增长。条件均值和条件误差方差都是测量历史的函数。对于具有两个状态的系统，所提出的估计器通过利用在一般矢量状态情况下尚未开发的关系，大大减少了表达 cpdf 特征函数所需的项数。此外，通过使用最近测量的固定滑动窗口，所提出的两种状态估计器的效率得到提高，可以实现实时计算的精确近似。这样，每次测量更新的计算复杂度最终变得恒定，并且可以处理任意数量的测量。演示了柯西估计器在柯西和高斯模拟中的数值性能，并与卡尔曼滤波器进行了比较。
An efficient recursive state estimator is developed for two-state linear systems driven by Cauchy distributed process and measurement noises. For a general vector-state system, the estimator is based on recursively propagating the characteristic function of the conditional probability density function (cpdf), where the number of terms in the sum that expresses this characteristic function grows with each measurement update. Both the conditional mean and the conditional error variance are functions of the measurement history. For systems with two states, the proposed estimator reduces substantially the number of terms needed to express the characteristic function of the cpdf by taking advantage of relationships not yet developed in the general vector-state case. Further, by using a fixed sliding window of the most recent measurements, the improved efficiency of the proposed two-state estimator allows an accurate approximation for real-time computation. In this way, the computational complexity of each measurement update eventually becomes constant, and an arbitrary number of measurements can be processed. The numerical performance of the Cauchy estimator in both Cauchy and Gaussian simulations was demonstrated and compared to the Kalman Filter.