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Ítem Point pattern analysis and classification on compact two-point homogeneous spaces evolving time(Springer, 2023-02-14) Frías, María Pilar; Torres-Signes, Antoni; Ruiz-Medina, María DoloresThis paper introduces a new modeling framework for the statistical analysis of point patterns on a manifold Md; defined by a connected and compact two-point homogeneous space, including the special case of the sphere. The presented approach is based on temporal Cox processes driven by a L2ðMdÞ-valued log-intensity. Different aggregation schemes on the manifold of the spatiotemporal point-referenced data are implemented in terms of the time-varying discrete Jacobi polynomial transform of the log-risk process. The n-dimensional microscale point pattern evolution in time at different manifold spatial scales is then characterized from such a transform. The simulation study undertaken illustrates the construction of spherical point process models displaying aggregation at low Legendre polynomial transform frequencies (large scale), while regularity is observed at high frequencies (small scale). K-function analysis supports these results under temporal short, intermediate and long range dependence of the log-risk process.Ítem COVID-19 mortality analysis from soft-data multivariate curve regression and machine learning(Springer, 2021-04-19) Torres-Signes, Antoni; Frías, María Pilar; Ruiz-Medina, María DoloresA multiple objective space-time forecasting approach is presented involving cyclical curve log-regression, and multivariate time series spatial residual correlation analysis. Specifically, the mean quadratic loss function is minimized in the framework of trigonometric regression. While, in our subsequent spatial residual correlation analysis, maximization of the likelihood allows us to compute the posterior mode in a Bayesian multivariate time series soft-data framework. The presented approach is applied to the analysis of COVID-19 mortality in the first wave affecting the Spanish Communities, since March 8, 2020 until May 13, 2020. An empirical comparative study with Machine Learning (ML) regression, based on random k-fold cross-validation, and bootstrapping confidence interval and probability density estimation, is carried out. This empirical analysis also investigates the performance of ML regression models in a hard- and soft-data frameworks. The results could be extrapolated to other counts, countries, and posterior COVID-19 waves.Ítem Spatial Cox Processes in an Infinite-Dimensional Framework(Springer, 2021-04-29) Frías, María Pilar; Torres-Signes, Antoni; Ruiz-Medina, María DoloresWe introduce a new class of spatial Cox processes driven by a Hilbert-valued random log-intensity. We adopt a parametric framework in the spectral domain, to estimate its spatial functional correlation structure. Specifically, we consider a spectral functional, approach based on the periodogram operator, inspired on Whittle estimation methodology. Strong consistency of the parametric estimator is proved in the linear case. We illustrate this property in a simulation study under a Gaussian first-order Spatial Autoregressive Hilbertian scenario for the log-intensity model. Our method is applied to the spatial functional prediction of respiratory disease mortality in the Spanish Iberian Peninsula, in the period 1980–2015.Ítem A spatial functional count model for heterogeneity analysis in time(Springer, 2021-01-04) Torres-Signes, Antoni; Frías, María Pilar; Mateu, Jorge; Ruiz-Medina, María DoloresA spatial curve dynamical model framework is adopted for functional prediction of counts in a spatiotemporal log-Gaussian Cox process model. Our spatial functional estimation approach handles both wavelet-based heterogeneity analysis in time, and spectral analysis in space. Specifically, model fitting is achieved by minimising the information divergence or relative entropy between the multiscale model underlying the data, and the corresponding candidates in the spatial spectral domain. A simulation study is carried out within the family of log-Gaussian Spatial Autoregressive -valued processes (SAR processes) to illustrate the asymptotic properties of the proposed spatial functional estimators. We apply our modelling strategy to spatiotemporal prediction of respiratory disease mortality.Ítem Multisensor Fusion Estimation for Systems with Uncertain Measurements, Based on Reduced Dimension Hypercomplex Techniques(MDPI, 2022-07-18) Fernández-Alcalá, Rosa María; Jiménez-López, José Domingo; Navarro-Moreno, Jesús; Ruiz-Molina, Juan CarlosThe prediction and smoothing fusion problems in multisensor systems with mixed uncertainties and correlated noises are addressed in the tessarine domain, under Tk-properness conditions. Bernoulli distributed random tessarine processes are introduced to describe one-step randomly delayed and missing measurements. Centralized and distributed fusion methods are applied in a Tk-proper setting, k = 1, 2, which considerably reduce the dimension of the processes involved. As a consequence, efficient centralized and distributed fusion prediction and smoothing algorithms are devised with a lower computational cost than that derived from a real formalism. The performance of these algorithms is analyzed by using numerical simulations where different uncertainty situations are considered: updated/delayed and missing measurements.Ítem Distributed optimal fusion filtering for singular systems with random transmission delays and packet dropout compensations(Elsevier, 2023) Hu, Jun; Wang, Chen; Caballero-Águila, Raquel; Liu, HongjianThis paper is concerned with the fusion filtering problem for time-varying singular systems with random transmission delays (RTDs) and packet dropout (PD) compensations. Here, the phenomena of RTDs and PDs are both characterized by Bernoulli distributed random variables with different probabilities. Generally, the current sensor measurement and one-step delayed sensor measurement can be received by filter. When the sensor measurement is lost, based on the strategy of PD compensations, the one-step predictor of current sensor measurement is used as compensator. Then, the new augmented systems with stochastic parameter matrices and correlated noises are introduced based on the measurement compensation model. Utilizing the innovation analysis approach, the local filters (LFs) dependent on probabilities and corresponding estimation error covariance matrices are derived for augmented systems. Moreover, the matrix-weighted distributed fusion filter (DFF) is designed for original singular systems on the basis of the state transformation. Compared with the LFs, it is not difficult to see that the presented DFF has better precision. In the end, some comparison simulation experiments are carried out to verify the effectiveness of the proposed fusion filtering algorithm.Ítem Distributed fusion filtering for multi-sensor nonlinear networked systems with multiple fading measurements via stochastic communication protocol(Elsevier, 2024) Hu, Jun; Hu, Zhibin; Caballero-Águila, Raquel; Yi, XiaojianThis paper studies the distributed fusion filtering (DFF) issue for a class of nonlinear delayed multi-sensor networked systems (MSNSs) subject to multiple fading measurements (MFMs) under stochastic communication protocol (SCP). The phenomenon of MFMs occurs randomly in the network communication channels and is characterized by a diagonal matrix with certain statistical information. In order to decrease the overload of communication network and save network resources, the SCP that can regulate the information transmission between sensors and estimators is adopted. The primary aim of the tackled problem is to develop the DFF method for nonlinear delayed MSNSs in the presence of MFMs and SCP based on the inverse covariance intersection fusion rule. In addition, the local upper bound (UB) of the filtering error covariance (FEC) is derived and minimized by means of suitably designing the local filter gain. Moreover, the boundedness analysis regarding the local UB is proposed with corresponding theoretical proof. Finally, two simulation examples with comparative illustrations are given to display the usefulness and feasibility of the derived theoretical results.Ítem Distributed resilient fusion filtering for nonlinear systems with multiple missing measurements via dynamic event-triggered mechanism(Elsevier, 2023) Hu, Jun; Hu, Zhibin; Caballero-Águila, Raquel; Chen, Cai; Fan, Shuting; Yi, XiaojianThis paper investigates the distributed resilient fusion filtering (DRFF) issue under inverse covariance intersection (ICI) fusion criterion and dynamic event-triggered mechanisms (DETMs), where the physical plant is described by stochastic nonlinear multi-sensor networked systems (MSNSs) with time-varying system parameters and multiple missing measurements (MMMs). The measurements from various sensor nodes to the fusion center may undergo the missing data, where this phenomenon is depicted by means of random variables governed by certain statistical principles. In addition, the DETM is adopted to regulate the communication process from each sensor node to fusion center, which can alleviate the network transmission situations with communication overload and energy consumption limitation. The purpose of the addressed issue is to construct a set of local resilient filters (LRFs) for stochastic nonlinear MSNSs with MMMs via the DETM, which can guarantee that the minimized upper bounds are derived and the desirable filter gain with easy-to-implementation form is given. Subsequently, via the obtained LRFs, a unified framework of the DRFF approach is formulated through using the ICI fusion criterion. In addition, the monotonicity analysis of the obtained upper bound in regard to the triggered parameter is examined by providing rigorous theoretical proof. Finally, the simulations with comparison experiment are provided to illustrate the validity of presented DRFF technique.Ítem Distributed fusion filtering for uncertain systems with coupled noises, random delays and packet loss prediction compensation(Taylor & Francis, 2023) Caballero-Águila, Raquel; Linares-Pérez, JosefaThe design of recursive estimation algorithms in networked systems is an important research challenge from both theoretical and practical perspectives. The growing number of application fields are demanding the development of new mathematical models and algorithms that accommodate the effect of the unavoidable network-induced uncertainties. Special relevance have transmission delays and packet dropouts, which may yield a significant degradation in the performance of conventional estimators. This paper discusses the distributed fusion estimation problem in a class of linear stochastic uncertain systems whose measurement noises are cross-correlated and coupled with the process noise. The uncertainty of the system is not only described by additive noises, but also by multiplicative noise in the state equation and random parameter matrices in the measurement model. Both one-step delays and packet dropouts can randomly occur during the transmission of the sensor measurements to the local processors and a compensation strategy based on measurement prediction is used. Under the least-squares criterion and using an innovation approach, a recursive algorithm for the local filtering estimators is designed. These local estimators are then fused at a processing centre, where the distributed fusion filter is generated as the least-squares matrix-weighted linear combination of the local ones.Ítem Two Compensation Strategies for Optimal Estimation in Sensor Networks with Random Matrices, Time-Correlated Noises, Deception Attacks and Packet Losses(MDPI, 2022-11-04) Caballero-Águila, Raquel; Hu, Jun; Linares-Pérez, JosefaDue to its great importance in several applied and theoretical fields, the signal estimation problem in multisensor systems has grown into a significant research area. Networked systems are known to suffer random flaws, which, if not appropriately addressed, can deteriorate the performance of the estimators substantially. Thus, the development of estimation algorithms accounting for these random phenomena has received a lot of research attention. In this paper, the centralized fusion linear estimation problem is discussed under the assumption that the sensor measurements are affected by random parameter matrices, perturbed by time-correlated additive noises, exposed to random deception attacks and subject to random packet dropouts during transmission. A covariance-based methodology and two compensation strategies based on measurement prediction are used to design recursive filtering and fixed-point smoothing algorithms. The measurement differencing method —typically used to deal with the measurement noise time-correlation— is unsuccessful for these kinds of systems with packet losses because some sensor measurements are randomly lost and, consequently, cannot be processed. Therefore, we adopt an alternative approach based on the direct estimation of the measurement noises and the innovation technique. The two proposed compensation scenarios are contrasted through a simulation example, in which the effect of the different uncertainties on the estimation accuracy is also evaluated.Ítem Unreliable networks with random parameter matrices and time-correlated noises: distributed estimation under deception attacks(AIMSPRESS - American Institute of Mathematical Sciences, 2023-07-05) Caballero-Águila, Raquel; García-Ligero, María Jesús; Hermoso-Carazo, Aurora; Linares-Pérez, JosefaThis paper examines the distributed filtering and fixed-point smoothing problems for networked systems, considering random parameter matrices, time-correlated additive noises and random deception attacks. The proposed distributed estimation algorithms consist of two stages: the first stage creates intermediate estimators based on local and adjacent node measurements, while the second stage combines the intermediate estimators from neighboring sensors using least-squares matrix-weighted linear combinations. The major contributions and challenges lie in simultaneously considering various network-induced phenomena and providing a unified framework for systems with incomplete information. The algorithms are designed without specific structure assumptions and use a covariance-based estimation technique, which does not require knowledge of the evolution model of the signal being estimated. A numerical experiment demonstrates the applicability and e ectiveness of the proposed algorithms, highlighting the impact of observation uncertainties and deception attacks on estimation accuracy.Ítem Tessarine signal processing under the T -properness condition(Elsevier, 2020-09) Navarro-Moreno, Jesús; Fernández-Alcalá, Rosa María; Jiménez-López, José Domingo; Ruiz-Molina, Juan CarlosThe paper analyzes the processing of 4D commutative hypercomplex or tessarine signals under properness conditions. Firstly, the concept of T-properness is introduced and a procedure to test experimentally whether a tessarine random signal is proper or not is proposed. Then, for the class of T-proper signals, the linear minimum mean square error estimation problem is addressed. In this regard, it should be highlighted that although the tessarine algebra is not a Hilbert space, a metric which guarantees the existence and unicity of the optimal estimator is defined. Moreover, the equivalence, under T-properness conditions, between the optimal estimator based on a tessarine widely linear processing and the one based on a tessarine strictly linear (TSL) processing is also shown, attaining thus a notable reduction in computational burden. Finally, two T-proper models, a TSL state-space model, and a TSL stationary model, from which the optimal estimator can be recursively obtained are considered. In both cases, simulated examples are developed where the superiority of TSL processing over the counterparts in the quaternion domain is exhibited.Ítem Widely Linear Estimation for Multisensor Quaternion Systems with Mixed Uncertainties in the Observations(Elsevier, 2019) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.The optimal widely linear state estimation problem for quaternion systems with multiple sensors and mixed uncertainties in the observations is solved in a unified framework. For that, we devise a unified model to describe the mixed uncertainties of sensor delays, packet dropouts and uncertain observations by using three Bernoulli distributed quaternion random processes. The proposed model is valid for linear discrete-time quaternion stochastic systems measured by multiple sensors and it allows us to provide filtering, prediction and smoothing algorithms for estimating the quaternion state through a widely linear processing. Simulation results are employed to show the superior performance of such algorithms in comparison to standard widely linear methods when mixed uncertainties are present in the observations.Ítem Semi-Widely Linear Estimation Algorithms of Quaternion Signals with Missing Observations and Correlated Noises(Elsevier, 2020) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.The paper deals with the estimation problem of a discrete-time vectorial quaternion signal which is observed through a linear dynamic system with intermittent observations and autocorrelated and cross-correlated noises. Under $\mathbb{C}^{\eta}$-properness conditions, a semi-widely linear processing is considered to provide filtering, fixed-point and fixed-lag smoothing algorithms for estimating the quaternion state. The proposed solutions give a substantial reduction in computational burden in relation to the widely linear estimation techniques, this benefit being impossible to be fully captured by using a real number framework. The feasibility and performance of the aforementioned algorithms are illustrated by means of simulation examples.Ítem Proper Adaptive Filtering in Four-Dimensional Cayley-Dickson Algebras(Elsevier, 2023) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.A family of hypercomplex algebras in four dimensions (4D) is proposed to devise adaptive filters. Such a family, called $\beta$-quaternions, has multiplication rules for the complex units that depend on a parameter $\beta$, and this family contains, as particular cases, both standard Hamilton quaternions and split quaternions. In this framework, two notions of properness for random vectors are introduced and their implications on the statistical processing involved are analyzed. Then, statistical tests to check properness in practice and a method to select the best algebra where the properness conditions could hold are provided. Also, proper adaptive filters are suggested and row and column updating problems are studied. The main advantage of the techniques proposed compared with the standard ones is that a notable reduction in the computational burden is achieved. Finally, simulation examples validate the proper adaptive filters and demonstrate that our scheme performs better than the traditional quaternion domain.Ítem Biased Regression Algorithms in the Quaternion Domain(Elsevier, 2024) Ruiz Molina, Juan Carlos; Navarro Moreno, Jesús; Fernández Alcalá, Rosa Mª; Jiménez López, José D.The ill-conditioned matrix problem in quaternion linear regression models is addressed in this paper and several dimension-reduction based regression methods for circumventing this problem are suggested. The algorithms are formulated in a general way and can be easily adapted to different scenarios: widely linear, semi-widely linear and strictly linear processing, in accordance with the properness properties presented by quaternion random vectors. A comparison with existing solutions is carried out by using both laboratory data and a color face database.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 A modelling of the number of almazaras by municipality in Andalusia(2022) Cueva-López, Valentina; Rodríguez-Avi, José; Olmo-Jiménez, María José; Rodríguez-Reinoso, JuliaAn almazara (oil mill) is an essential piece in the production of olive oil since it is the place where the olive is milled and the olive oil is obtained. They are usually linked to producer cooperatives. They are structures that require specialized machinery and that on multiple occasions are underutilised, given the presence of several of them at very close distances. In addition, they characterise the mainly olive grove municipalities and their study provides a valuable information of economic interest. From a statistical point of view, the “number of oil mills per municipality” is a count data variable that exhibits overdispersion. In this study, we focus on the oil mills found in municipalities of Andalusia. First, we make a descriptive study of the variable. Second, we model this data according to the most suitable probabilistic model. Finally, several generalized linear regression models based on different geographic and socioeconomic variables are proposed and the best one (using the Akaike information criterion) is selected.Ítem An Optimal Linear Fusion Estimation Algorithm of Reduced Dimension for T-Proper Systems with Multiple Packet Dropouts(MDPI, 2023-04-17) Fernández Alcalá, Rosa María; Jiménez López, José Domingo; Le Bihan, Nicolas; Cheong Took, CliveThis paper analyses the centralized fusion linear estimation problem in multi-sensor systems with multiple packet dropouts and correlated noises. Packet dropouts are modeled by independent Bernoulli distributed random variables. This problem is addressed in the tessarine domain under conditions of 𝕋1 and 𝕋2-properness, which entails a reduction in the dimension of the problem and, consequently, computational savings. The methodology proposed enables us to provide an optimal (in the least-mean-squares sense) linear fusion filtering algorithm for estimating the tessarine state with a lower computational cost than the conventional one devised in the real field. Simulation results illustrate the performance and advantages of the solution proposed in different settings.Ítem Distributed fusion filtering for multi-sensor nonlinear networked systems with multiple fading measurements via stochastic communication protocol(Elsevier, 2024-06-24) Hu, Jun; Hu, Zhibin; Caballero-Águila, Raquel; Yi, XiaojianThis paper studies the distributed fusion filtering (DFF) issue for a class of nonlinear delayed multi-sensor networked systems (MSNSs) subject to multiple fading measurements (MFMs) under stochastic communication protocol (SCP). The phenomenon of MFMs occurs randomly in the network communication channels and is characterized by a diagonal matrix with certain statistical information. In order to decrease the overload of communication network and save network resources, the SCP that can regulate the information transmission between sensors and estimators is adopted. The primary aim of the tackled problem is to develop the DFF method for nonlinear delayed MSNSs in the presence of MFMs and SCP based on the inverse covariance intersection fusion rule. In addition, the local upper bound (UB) of the filtering error covariance (FEC) is derived and minimized by means of suitably designing the local filter gain. Moreover, the boundedness analysis regarding the local UB is proposed with corresponding theoretical proof. Finally, two simulation examples with comparative illustrations are given to display the usefulness and feasibility of the derived theoretical results.