Abstract
The paper deals with Kalman (or H2) smoothing problem for wireless sensor networks (WSNs) with multiplicative noises. Packet loss occurs in the observation equations, and multiplicative noises occur both in the system state equation and the observation equations. The Kalman smoothers which include Kalman fixed‐interval smoother, Kalman fixedlag smoother, and Kalman fixed‐point smoother are given by solving Riccati equations and Lyapunov equations based on the projection theorem and innovation analysis. An example is also presented to ensure the efficiency of the approach. Furthermore, the proposed three Kalman smoothers are compared.
Highlights
The linear estimation problem has been one of the key research topics of control community according to 1
Kalman filtering which usually uses state space equation is better than Wiener filtering, since it is recursive, and it can be used to deal with time-variant system 1, 2, 5
The standard Kalman filtering cannot be directly used in the estimation on wireless sensor networks WSNs since packet loss occurs, and sometimes multiplicative noises occur 6, 7
Summary
The linear estimation problem has been one of the key research topics of control community according to 1. Under the performance of H2 index, Kalman filtering 2–4 is an important approach to study linear estimation besides Wiener filtering. Kalman filtering which usually uses state space equation is better than Wiener filtering, since it is recursive, and it can be used to deal with time-variant system 1, 2, 5. This has motivated many previous researchers to employ Kalman filtering to study linear time variant or linear time-invariant estimation, and Kalman filtering has been a popular and efficient approach for the normal linear system. The standard Kalman filtering cannot be directly used in the estimation on wireless sensor networks WSNs since packet loss occurs, and sometimes multiplicative noises occur 6, 7
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