Abstract
We consider the problem of remote estimation with time delay and multiplicative noise for multichannel systems. First, we apply the reorganized innovation analysis approach to construct the original delay system into a new delay-free system. Secondly, the delay-free system will be reconstructed by the quadratic filtering method to obtain an augmented system. Then, Kalman filtering theory and projection formula are used to solve two Riccati equations and one Lyapunov equation for the augmented system, and the quadratic filter for the measurement delay system on the packet loss network can be obtained. Finally, we use a numerical example to illustrate the effectiveness of the method.
Highlights
In recent years, the problem of missing measurements caused by unreliable channel transmission has been the focus of many scholars [1,2,3]. e research on the problem of packet loss can be roughly divided into two directions: one is to solve the linear estimator based on the minimum mean square error method and the other is to use the quadratic filtering method
Zhang et al [6] propose an estimator that can be applied to an infinite horizon, and its iteration only includes solving a Riccati equation. is estimator avoids the convergence analysis problem caused by the calculation of the Lyapunov equation in traditional estimation methods. e authors in [7] apply the recombination innovation analysis method to obtain an optimal linear filter, which solves the remote estimation problem of the packet loss network with the measurement delay system obeying Bernoulli distribution
Cacace et al [13] add the packet loss factor to the measurement model and use the quadratic filtering method to obtain a filter iteration equation with a smaller estimation error. e Kronecker algebraic rules are used in [14] to discuss the stochastic properties of augmented noise in augmented systems. en, the linear estimation of the discrete-time non-Gaussian system is obtained by the projection formula
Summary
The problem of missing measurements caused by unreliable channel transmission has been the focus of many scholars [1,2,3]. e research on the problem of packet loss can be roughly divided into two directions: one is to solve the linear estimator based on the minimum mean square error method and the other is to use the quadratic filtering method. E research on the problem of packet loss can be roughly divided into two directions: one is to solve the linear estimator based on the minimum mean square error method and the other is to use the quadratic filtering method. E authors in [7] apply the recombination innovation analysis method to obtain an optimal linear filter, which solves the remote estimation problem of the packet loss network with the measurement delay system obeying Bernoulli distribution. Cacace et al [13] add the packet loss factor to the measurement model and use the quadratic filtering method to obtain a filter iteration equation with a smaller estimation error. E main contribution of this paper is to effectively combine the quadratic filtering method with the innovation recombination theory; so as to obtain the quadratic filtering scheme of the discrete-time system with packet loss and measurement delay. If the dimensions are not explicitly stated, matrices are assumed to have compatible dimensions with algebraic operations
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