Josefa Linares-Pérez

Recursive estimators of signals from measurements with stochastic delays using covariance information

Least-squares linear one-stage prediction, filtering and fixed-point smoothing algorithms for signal estimation using measurements with stochastic delays contaminated by additive white noise are derived. The delay is considered to be random and modelled by a binary white noise with values zero or one; these values indicate that the measurements arrive in time or they are delayed by one sampling time. Recursive estimation algorithms are obtained without requiring the state-space model generating the signal, but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities.

Extended and unscented filtering algorithms using one-step randomly delayed observations

In this paper, the least squares filtering problem is investigated for a class of nonlinear discrete-time stochastic systems using observations with stochastic delays contaminated by additive white noise. The delay is considered to be random and modelled by a binary white noise with values of zero or one; these values indicate that the measurement arrives on time or that it is delayed by one sampling time. Using two different approximations of the first and second-order statistics of a nonlinear transformation of a random vector, we propose two filtering algorithms; the first is based on linear approximations of the system equations and the second on approximations using the scaled unscented transformation. These algorithms generalize the extended and unscented Kalman filters to the case in which the arrival of measurements can be one-step delayed and, hence, the measurement available to estimate the state may not be up-to-date. The accuracy of the different approximations is also analyzed and the performance of the proposed algorithms is compared in a numerical simulation example.

Signal estimation with multiple delayed sensors using covariance information

Recursive filtering and smoothing algorithms to estimate a signal from noisy measurements coming from multiple randomly delayed sensors, with different delay characteristics, are proposed. To design these algorithms an innovation approach is used, assuming that the state-space model of the signal is unknown and using only covariance information. To measure the precision of the proposed estimators formulas to calculate the filtering and smoothing error covariance matrices are also derived. The effectiveness of the estimators is illustrated by a numerical simulation example where a signal is estimated using observations from two randomly delayed sensors having different delay properties.

Optimal state estimation for networked systems with random parameter matrices, correlated noises and delayed measurements

In this paper, the optimal least-squares state estimation problem is addressed for a class of discrete-time multisensor linear stochastic systems with state transition and measurement random parameter matrices and correlated noises. It is assumed that at any sampling time, as a consequence of possible failures during the transmission process, one-step delays with different delay characteristics may occur randomly in the received measurements. The random delay phenomenon is modelled by using a different sequence of Bernoulli random variables in each sensor. The process noise and all the sensor measurement noises are 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. Based on the proposed model and using an innovation approach, the optimal linear filter is designed by a recursive algorithm which is very simple computationally and suitable for online applications. A numerical simulation is exploited to illustrate the feasibility of the proposed filtering algorithm.

Linear recursive discrete-time estimators using covariance information under uncertain observations

This paper, using the covariance information, proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain observations in linear discrete-time stochastic systems. The observation equation is given by y(k) = γ(k)Hx(k) + v(k), where {γ(k)} is a binary switching sequence with conditional probability distribution verifying Eq. (3). This observation equation is suitable for modeling the transmission of data in multichannels as in remote sensing situations. The estimators require the information of the system matrix Φ concerning the state variable which generates the signal, the observation vector H, the crossvariance function Kxz(k,k) of the state variable with the signal, the variance R(k) of the white observation noise, the observed values, the probability p(k): P{γ(k)= 1} that the signal exists in the uncertain observation equation and the (2,2) element [P(k|j)]2,2 of the conditional probability matrix of γ(k), given γ(j).

Information fusion algorithms for state estimation in multi-sensor systems with correlated missing measurements

In this paper, centralized and distributed fusion estimation problems in linear discrete-time stochastic systems with missing observations coming from multiple sensors are addressed. At each sensor, the Bernoulli random variables describing the phenomenon of missing observations are assumed to be correlated at instants that differ m units of time. By using an innovation approach, recursive linear filtering and fixed-point smoothing algorithms for the centralized fusion problem are derived in the least-squares sense. The distributed fusion estimation problem is addressed based on the distributed fusion criterion weighted by matrices in the linear minimum variance sense. For each sensor subsystem, local least-squares linear filtering and fixed-point smoothing estimators are given and the estimation error cross-covariance matrices between any two sensors are derived to obtain the distributed fusion estimators. The performance of the proposed estimators is illustrated by numerical simulation examples where scalar and two-dimensional signals are estimated from missing observations coming from two sensors, and the estimation accuracy is analyzed for different missing probabilities and different values of m.

New design of estimators using covariance information with uncertain observations in linear discrete-time systems

This paper proposes recursive least-squares (RLS) filtering and fixed-point smoothing algorithms with uncertain observations in linear discrete-time stochastic systems. The estimators require the information of the auto-covariance function in the semi-degenerate kernel form, the variance of white observation noise, the observed value and the probability that the signal exists in the observed value. The auto-covariance function of the signal is factorized in terms of the observation vector, the system matrix and the cross-variance function of the state variable, that generates the signal, with the signal. These quantities are obtained from the auto-covariance data of the signal. It is shown that the semi-degenerate kernel is expressed in terms of these quantities.

Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.

Fusion estimation using measured outputs with random parameter matrices subject to random delays and packet dropouts

This paper investigates the centralized and distributed fusion estimation problems for discrete-time random signals from multi-sensor noisy measurements, perturbed by random parameter matrices, which are transmitted to local processors through different communication channel links. It is assumed that both one-step delays and packet dropouts can randomly occur during the data transmission, and different white sequences of Bernoulli random variables with known probabilities are introduced to depict the transmission delays and losses at each sensor. Using only covariance information, without requiring the evolution model of the signal process, a recursive algorithm for the centralized least-squares linear prediction and filtering estimators is derived by an innovation approach. Also, local least-squares linear estimators based on the measurements received by the processor of each sensor are obtained, and the distributed fusion method is then used to generate fusion predictors and filters by a matrix-weighted linear combination of the local estimators, using the mean squared error as optimality criterion. In order to compare the performance of the centralized and distributed fusion estimators, recursive formulas for the estimation error covariance matrices are also derived. A numerical example illustrates how some usual network-induced uncertainties can be dealt with the current observation model with random matrices. HighlightsMulti-sensor noisy measurements with random delays and dropouts are considered.A recursive least-squares centralized fusion estimation algorithm is proposed.Least-squares matrix-weighted distributed fusion estimators are also proposed.The algorithms, based on covariances, are derived by an innovation approach.Recursive formulas for the estimation error covariance matrices are also proposed.

Second-order polynomial estimators from uncertain observations using covariance information

This paper presents recursive least mean-squared error second-order polynomial filtering and fixed-point smoothing algorithms to estimate a signal, from uncertain observations, when only the information on the moments up to fourth-order of the signal and observation noise is available. The estimators require the autocovariance and crosscovariance functions of the signal and their second-order powers in a semidegenerate kernel form, and the probability that the signal exists in the observed values.