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Ítem Wide-Sense Markov Signals on the Tessarine Domain. A Study under Properness Conditions(Elsevier, 2021) Ruiz Molina, Juan CarlosThe quaternion algebra is not always the best choice for processing 4D hypercomplex signals. This paper aims to explore tessarines as an alternative algebra to solve the estimation problem. More concretely, wide-sense Markov signals in the tessarine domain are introduced and their properties under properness properties are analyzed. Firstly, the $\mathbb{T}_2$-properness condition in the tessarine setting is defined and then, the linear estimation problem under tessarine processing is addressed. The equivalence between the optimal estimator based on tessarine widely linear processing and the one based on tessarine $\mathbb{T}_2$ processing is proved, thus attaining a notable reduction in computational burden. Next, the $\mathbb{T}_i$-proper wide-sense Markov signals, $i=1,2$, are defined and a forwards representation for modeling them is suggested. Finally, the estimation problem with intermittent observations for this class of signals is tackled. Specifically, based on the forwards representation, two algorithms for the problems of filtering, prediction and fixed-interval smoothing are devised. Numerical simulations are developed where the superiority of the $\mathbb{T}_i$ estimators, $i=1,2$, over their counterparts in the quaternion domain is shown.Ítem Hybrid-attack-resistant distributed state estimation for nonlinear complex networks with random coupling strength and sensor delays(Elsevier, 2024-06-21) Lei, Bingxin; Hu, Jun; Caballero-Águila, Raquel; Chen, CaiIn this paper, a recursive distributed hybrid-attack-resistant state estimation (SE) scheme is proposed for a class of time-varying nonlinear complex networks (NCNs) subject to random coupling strength (RCS) and random sensor delays (RSDs) under hybrid attacks. A hybrid-attack model is considered to characterize the random occurrence of denial-of-service (DoS) attacks and deception attacks. The objective of the problem to be solved is to develop a recursive distributed estimation method such that, in the presence of RCS, RSDs and hybrid attacks, a locally optimized upper bound (UB) on the estimation error covariance (EEC) is ensured. By employing the mathematical induction method, a UB is firstly derived on the EEC. Subsequently, the obtained UB is minimized by appropriately designing the estimator gain (EG). Furthermore, a sufficient criterion guaranteeing the exponential boundedness (EB) of SE error is elaborated in the mean square sense (MSS). Finally, simulation experiments with localization applications of multiple mobile indoor robots are conducted to illustrate the applicability of the proposed SE scheme.Ítem DGLMExtPois: Advances in Dealing with Over and Under-dispersion in a Double GLM Framework(The R Foundation, 2022-12) Sáez-Castillo, Antonio J.; Conde-Sánchez, Antonio; Martínez, FranciscoIn recent years the use of regression models for under-dispersed count data, such as COM-Poisson or hyper-Poisson models, has increased. In this paper the DGLMExtPois package is presented. DGLMExtPois includes a new procedure to estimate the coefficients of a hyper-Poisson regression model within a GLM framework. The estimation process uses a gradient-based algorithm to solve a nonlinear constrained optimization problem. The package also provides an implementation of the COM-Poisson model, proposed by Huang (2017), to make it easy to compare both models. The functionality of the package is illustrated by fitting a model to a real dataset. Furthermore, an experimental comparison is made with other related packages, although none of these packages allow you to fit a hyper-Poisson model.