Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems

Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model

“…Regarding the intrinsic capabilities and limitations of the estimation procedure, some valuable insight can be gained by assessing the observability by means of the observability Gramian matrix Υ of the parameters [53], given here by [33] …”

Adaptive Kalman filter for actuator fault diagnosis

“…Discrete time systems have been considered in (Guyader and Zhang, 2003;Ţ iclea and Besançon, 2016), also in deterministic frameworks. In order to take into account random uncertainties with a numerically efficient algorithm, this paper considers stochastic systems in discrete time, with an adaptive Kalman filter, which is structurally inspired by adaptive observers (Zhang, 2002;Guyader and Zhang, 2003), but with well-established stochastic properties. The main contribution of this paper is an adaptive Kalman filter for discrete time LTV/LPV system joint stateparameter estimation in a stochastic framework, with rigorously proved stability and minimum variance properties.…”

Nonlinear joint state and parameter estimation: Application to a wastewater treatment plant

“…Unfortunately, the introduction of time-varying parameters in the system models, needed to accurately represent the system behaviour, leads to more challenging problems in estimation. In this case, conventional observers, essentially developped for time invariant systems cannot be directly used, and so-called adaptive observers developed for joint state and unknown parameter estimation are needed [21]. The main difficulty in estimating the state of such systems comes from the lack of knowledge on the parameter evolution.…”

“…Some results have been published on the time-varying systems problem. For example, the state estimation of linear systems with unknown constant or time-varying parameter is respectively addressed in [21] and [11]. Extensions to nonlinear systems are proposed in [1], [4], [16] and [22], but in those works, the parameter is assumed to be constant.…”