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Due 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.

In this paper, the distributed filtering problem is addressed for a class of discrete-time stochastic systems over a sensor network with a given topology, susceptible to suffering deception attacks, launched by potential adversaries, which can randomly succeed or not with a known success probability, which is not necessarily the same for the different sensors. The system model integrates some random imperfections and features that are frequently found in real networked environments, namely: (1) fading measurements; (2) multiplicative noises in both the state and measurement equations; and (3) sensor additive noises cross-correlated with each other and with the process noise. According to the network communication scheme, besides its own local measurements, each sensor receives the measured outputs from its adjacent nodes. Based on such measurements, a recursive algorithm is designed to obtain the least-squares linear filter of the state. Thereafter, each sensor receives the filtering estimators previously obtained by its adjacent nodes, and these estimators are all fused to obtain the desired distributed filter as the minimum mean squared error matrix-weighted linear combination of them. The theoretical results are illustrated by a simulation example, where the efficiency of the developed distributed estimation strategy is discussed in terms of the error variances.

In this paper, a cluster-based approach is used to address the distributed fusion estimation problem (filtering and fixed-point smoothing) for discrete-time stochastic signals in the presence of random deception attacks. At each sampling time, measured outputs of the signal are provided by a networked system, whose sensors are grouped into clusters. Each cluster is connected to a local processor which gathers the measured outputs of its sensors and, in turn, the local processors of all clusters are connected with a global fusion center. The proposed cluster-based fusion estimation structure involves two stages. First, every single sensor in a cluster transmits its observations to the corresponding local processor, where least-squares local estimators are designed by an innovation approach. During this transmission, deception attacks to the sensor measurements may be randomly launched by an adversary, with known probabilities of success that may be different at each sensor. In the second stage, the local estimators are sent to the fusion center, where they are combined to generate the proposed fusion estimators. The covariance-based design of the distributed fusion filtering and fixed-point smoothing algorithms does not require full knowledge of the signal evolution model, but only the first and second order moments of the processes involved in the observation model. Simulations are provided to illustrate the theoretical results and analyze the effect of the attack success probability on the estimation performance.

This paper is concerned with the least-squares linear centralized estimation problem in multi-sensor network systems from measured outputs with uncertainties modeled by random parameter matrices. These measurements are transmitted to a central processor over different communication channels, and owing to the unreliability of the network, random one-step delays and packet dropouts are assumed to occur during the transmissions. In order to avoid network congestion, at each sampling time, each sensor’s data packet is transmitted just once, but due to the uncertainty of the transmissions, the processing center may receive either one packet, two packets, or nothing. Different white sequences of Bernoulli random variables are introduced to describe the observations used to update the estimators at each sampling time. To address the centralized estimation problem, augmented observation vectors are defined by accumulating the raw measurements from the different sensors, and when the current measurement of a sensor does not arrive on time, the corresponding component of the augmented measured output predictor is used as compensation in the estimator design. Through an innovation approach, centralized fusion estimators, including predictors, filters, and smoothers are obtained by recursive algorithms without requiring the signal evolution model. A numerical example is presented to show how uncertain systems with state-dependent multiplicative noise can be covered by the proposed model and how the estimation accuracy is influenced by both sensor uncertainties and transmission failures.

This paper is concerned with the distributed and centralized fusion filtering problems in sensor networked systems with random one-step delays in transmissions. The delays are described by Bernoulli variables correlated at consecutive sampling times, with different characteristics at each sensor. The measured outputs are subject to uncertainties modeled by random parameter matrices, thus providing a unified framework to describe a wide variety of network-induced phenomena; moreover, the additive noises are assumed to be one-step autocorrelated and cross-correlated. Under these conditions, without requiring the knowledge of the signal evolution model, but using only the first and second order moments of the processes involved in the observation model, recursive algorithms for the optimal linear distributed and centralized filters under the least-squares criterion are derived by an innovation approach. Firstly, local estimators based on the measurements received from each sensor are obtained and, after that, the distributed fusion filter is generated as the least-squares matrix-weighted linear combination of the local estimators. Also, a recursive algorithm for the optimal linear centralized filter is proposed. In order to compare the estimators performance, recursive formulas for the error covariance matrices are derived in all the algorithms. The effects of the delays in the filters accuracy are analyzed in a numerical example which also illustrates how some usual network-induced uncertainties can be dealt with using the current observation model described by random matrices.

In this paper, the information fusion estimation problem is investigated for a class of multisensor linear systems affected by different kinds of stochastic uncertainties, using both the distributed and the centralized fusion methodologies. It is assumed that the measured outputs are perturbed by one-step autocorrelated and cross-correlated additive noises, and also stochastic uncertainties caused by multiplicative noises and randomly missing measurements in the sensor outputs are considered. At each sampling time, every sensor output is sent to a local processor and, due to some kind of transmission failures, one-step correlated random delays may occur. Using only covariance information, without requiring the evolution model of the signal process, a local least-squares (LS) filter based on the measurements received from each sensor is designed by an innovation approach. All these local filters are then fused to generate an optimal distributed fusion filter by a matrix-weighted linear combination, using the LS optimality criterion. Moreover, a recursive algorithm for the centralized fusion filter is also proposed and the accuracy of the proposed estimators, which is measured by the estimation error covariances, is analyzed by a simulation example.

This paper is concerned with the optimal fusion estimation problem in networked stochastic systems with bounded random delays and packet dropouts, which unavoidably occur during the data transmission in the network. The measured outputs from each sensor are perturbed by random parameter matrices and white additive noises, which are cross-correlated between the different sensors. Least-squares fusion linear estimators including filter, predictor and fixed-point smoother, as well as the corresponding estimation error covariance matrices are designed via the innovation analysis approach. The proposed recursive algorithms depend on the delay probabilities at each sampling time, but do not to need to know if a particular measurement is delayed or not. Moreover, the knowledge of the signal evolution model is not required, as the algorithms need only the first and second order moments of the processes involved. Some of the practical situations covered by the proposed system model with random parameter matrices are analyzed and the influence of the delays in the estimation accuracy are examined in a numerical example.

The distributed fusion state estimation problem is addressed for sensor network systems with random state transition matrix and random measurement matrices, which provide a unified framework to consider some network-induced random phenomena. The process noise and all the sensor measurement noises are assumed to be one-step autocorrelated and different sensor noises are one-step cross-correlated; also, the process noise and each sensor measurement noise are two-step cross-correlated. These correlation assumptions cover many practical situations, where the classical independence hypothesis is not realistic. Using an innovation methodology, local least-squares linear filtering estimators are recursively obtained at each sensor. The distributed fusion method is then used to form the optimal matrix-weighted sum of these local filters according to the mean squared error criterion. A numerical simulation example shows the accuracy of the proposed distributed fusion filtering algorithm and illustrates some of the network-induced stochastic uncertainties that can be dealt with in the current system model, such as sensor gain degradation, missing measurements, and multiplicative noise.

The problem of least-squares linear filtering is explored for a specific type of networked systems, where the measurements are affected by random parameters and experience random delays and packet dropouts. To prevent network congestion, only one packet is transmitted per sampling interval. However, due to these phenomena, either a single packet, two packets, or no data at all may be received at each sampling time. In the latter case, the estimator compensates by utilizing a predicted value. An innovation-based method is used to derive a recursive filter that does not require the signal dynamics, but only some statistical properties (first-order and second-order moments) of the stochastic processes in the observation model.

Networked systems usually face different random uncertainties that make the performance of the least-squares (LS) linear filter decline significantly. For this reason, great attention has been paid to the search for other kinds of suboptimal estimators. Among them, the LS quadratic estimation approach has attracted considerable interest in the scientific community for its balance between computational complexity and estimation accuracy. When it comes to stochastic systems subject to different random uncertainties and deception attacks, the quadratic estimator design has not been deeply studied. In this paper, using covariance information, the LS quadratic filtering and fixed-point smoothing problems are addressed under the assumption that the measurements are perturbed by a time-correlated additive noise, as well as affected by random parameter matrices and exposed to random deception attacks. The use of random parameter matrices covers a wide range of common uncertainties and random failures, thus better reflecting the engineering reality. The signal and observation vectors are augmented by stacking the original vectors with their second-order Kronecker powers; then, the linear estimator of the original signal based on the augmented observations provides the required quadratic estimator. A simulation example illustrates the superiority of the proposed quadratic estimators over the conventional linear ones and the effect of the deception attacks on the estimation performance.