A New Look at Boundedness of Error Covariance of Kalman Filtering
本文提出一种依赖系统参数的边界函数，将卡尔曼滤波误差协方差的有界性问题转化为该函数的均匀有界性研究，并深入分析了其动态行为与单调性，在最小条件下给出了定量结果。
In this correspondence paper, we provide a new look at the boundedness problems of error covariance of Kalman filtering. First, by utilizing the mathematical induction technique, a new bound function which is dependent on system parameters is proposed. In this manner, the boundedness problems of the error covariance can be converted to the study of the corresponding uniform bounds of the bound function. Second, based on such a bound function, the dynamic behaviors, monotonicities, and boundedness problems of error covariance are deeply explored. Consequently, a few quantitative results under minimal conditions about the uniform bounds on error covariance are obtained. Finally, examples are given to verify the correctness and effectiveness of our theoretical analyses.