SIAM Journal on Control and Optimization, Volume 59, Issue 4, Page 2454-2476, January 2021.
This paper studies the steady-state Kalman filtering over the random delay and packet drop channel, motivated by the state estimation in wireless sensor networks and networked control systems. Such systems induce both packet drops and time-varying delays. Assuming the Bernoulli processes for random delays and packet drops and enforcing nonrepetitive observations, we show that the channel states associated with random delays and packet drops form a finite Markov chain, and can thus be modeled as a finite state discrete Markov process. Furthermore, the composite system consisting of the process model and output communication channels results in a special type of the Markov jump linear systems. Design results for the steady-state Kalman filter over the channel of random delays and packet drops are presented, including the stabilizability and detectability conditions in the mean-square sense. The steady-state Kalman filtering results over the random delay and packet drop channel are illustrated by a numerical example.

中文翻译：

---

随机延迟和丢包信道上的卡尔曼滤波

SIAM Journal on Control and Optimization，第 59 卷，第 4 期，第 2454-2476 页，2021 年 1 月。
本文研究了随机延迟和丢包信道上的稳态卡尔曼滤波，其动机是无线传感器网络和网络控制系统中的状态估计。这种系统会导致数据包丢失和时变延迟。假设随机延迟和丢包的伯努利过程并强制执行非重复观察，我们表明与随机延迟和丢包相关的信道状态形成有限马尔可夫链，因此可以建模为有限状态离散马尔可夫过程。此外，由过程模型和输出通信通道组成的复合系统导致了一种特殊类型的马尔可夫跳跃线性系统。给出了随机延迟和丢包信道上稳态卡尔曼滤波器的设计结果，包括均方意义上的稳定性和可检测性条件。随机延迟和丢包信道上的稳态卡尔曼滤波结果用数值例子说明。