Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.This research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigaciónand Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Least-Squares Filtering Algorithm in Sensor Networks with Noise Correlation and Multiple Random Failures in Transmission

This paper addresses the least-squares centralized fusion estimation problem of discrete-time random signals from measured outputs, which are perturbed by correlated noises. These measurements are obtained by different sensors, which send their information to a processing center, where the complete set of data is combined to obtain the estimators. Due to random transmission failures, some of the data packets processed for the estimation may either contain only noise (uncertain observations), be delayed (randomly delayed observations), or even be definitely lost (random packet dropouts). These multiple random transmission uncertainties are modelled by sequences of independent Bernoulli random variables with different probabilities for the different sensors. By an innovation approach and using the last observation that successfully arrived when a packet is lost, a recursive algorithm is designed for the filtering estimation problem. The proposed algorithm is easily implemented and does not require knowledge of the signal evolution model, as only the first- and second-order moments of the processes involved are used. A numerical simulation example illustrates the feasibility of the proposed estimators and shows how the probabilities of the multiple random failures influence their performance

Covariance-Based Estimation for Clustered Sensor Networks Subject to Random Deception Attacks

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 research is supported by Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación and Fondo Europeo de Desarrollo Regional FEDER (grant no. MTM2017-84199-P)

Optimal Fusion Estimation with Multi-Step Random Delays and Losses in Transmission

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.This research is supported by the “Ministerio de Economía y Competitividad” and “Fondo Europeo de Desarrollo Regional” FEDER (Grant No. MTM2014-52291-P)

Networked Fusion Filtering from Outputs with Stochastic Uncertainties and Correlated Random Transmission Delays

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

Distributed Fusion Estimation for Multisensor Multirate Systems with Stochastic Observation Multiplicative Noises

This paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises. The dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update period. Moreover, different sensors have the different sampling rates and observations of sensors are subject to the stochastic uncertainties of multiplicative noises. At first, local filters at the observation sampling points are obtained based on the observations of each sensor. Further, local estimators at the state update points are obtained by predictions of local filters at the observation sampling points. They have the reduced computational cost and a good real-time property. Then, the cross-covariance matrices between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators and the cross-covariance matrices. An example shows the effectiveness of the proposed algorithms