Abstract

Some quantitative characteristics of error covariance are studied for linear Kalman filters. These quantitative characteristics include the peak value and location in the matrix, the decay rate from peak to bottom, and some algebraic constraints of the elements in the covariance matrix. We mathematically prove a matrix upper bound and its quantitative characteristics for the error covariance of Kalman filters. Computational methods are developed to numerically estimate the elements in a matrix upper bound and its decay rate. The quantitative characteristics and the computational methods are illustrated using three examples, two linear systems and one nonlinear system of shallow water equations.

摘要

研究了线性卡尔曼滤波器的一些误差协方差的定量特征。这些定量特征包括峰值和在矩阵中的位置，从峰到谷的衰减率以及协方差矩阵中元素的一些代数约束。我们用数学方法证明了卡尔曼滤波器的误差协方差的矩阵上限及其定量特征。开发了计算方法以数字方式估计矩阵上限中的元素及其衰减率。通过三个例子，浅水方程组的两个线性系统和一个非线性系统，说明了定量特征和计算方法。