Seiichi Nakamori

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.

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.

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).

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.

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.

Estimation technique using covariance information with uncertain observations in linear discrete-time systems

Abstract This paper proposes the recursive estimation technique using the covariance information in linear stationary discrete-time systems when the uncertain observations are given. At first, recursive least-squares algorithms for the filtering, fixed-point smoothing and one-step ahead prediction estimates are designed. The estimators use the crossvariance function of the state variable, that generates the signal process, with the signal, the observation vector, the system matrix, the variance of white Gaussian observation noise, the observed value and the probability that the signal exists in the uncertain observation. Second, to obtain the necessary information related to the covariance function of the signal in the estimators, we show the factorization method for the observation vector, the crossvariance function and the system matrix from the autocovariance function of the signal. As a result, the proposed technique uses finite number of autocovariance data of the stationary stochastic signal, the variance of white Gaussian observation noise, the uncertain observations and the probability.

Linear estimation from uncertain observations with white plus coloured noises using covariance information

Abstract This paper considers the least mean-squared error linear estimation problems, using covariance information, in linear discrete-time stochastic systems with uncertain observations for the case of white plus coloured observation noises. The different kinds of estimation problems treated include one-stage prediction, filtering, and fixed-point smoothing. The recursive algorithms are derived by employing the Orthogonal Projection Lemma and assuming that both, the signal and the coloured noise autocovariance functions, are given in a semi-degenerate kernel form.

Signal estimation based on covariance information from observations featuring correlated uncertainty and coming from multiple sensors

The linear least-squares estimation problem of signals from observations coming from multiple sensors is addressed when there is a non-zero probability that each observation does not contain the signal to be estimated (uncertain observations). At each sensor, this uncertainty in the observations is modeled by a sequence of Bernoulli random variables correlated at consecutive sampling times. To estimate the signal, recursive filtering and (fixed-point and fixed-interval) smoothing algorithms are derived without requiring the knowledge of the signal state-space model but only the means and covariance functions of the processes involved in the observation equations, the uncertainty probabilities and the correlation between the variables modeling the uncertainty. To measure the estimation accuracy, recursive expressions for the estimation error covariance matrices are also proposed. The theoretical results are illustrated by a numerical simulation example where a signal is estimated from observations featuring correlated uncertainty and coming from two sensors with different uncertainty characteristics.

Recursive estimation of discrete-time signals from nonlinear randomly delayed observations

In this paper, one-stage prediction, filtering, and fixed-point smoothing problems are addressed for nonlinear discrete-time stochastic systems with randomly delayed measurements perturbed by additive white noise. The observation delay is modelled by a sequence of independent Bernoulli random variables whose values-zero or one-indicate that the real observation arrives on time or it is delayed one sampling time and, hence, the available measurement to estimate the signal is not updated. Assuming that the state-space model generating the signal to be estimated is unknown and only the covariance functions of the processes involved in the observation equation are available, recursive estimation algorithms based on linear approximations of the real observations are proposed.

Least-Squares Linear Smoothers from Randomly Delayed Observations with Correlation in the Delay

This paper discusses the least-squares linear filtering and smoothing (fixed-point and fixed-interval) problems of discrete-time signals from observations, perturbed by additive white noise, which can be randomly delayed by one sampling time. It is assumed that the Bernoulli random variables characterizing delay measurements are correlated in consecutive time instants. The marginal distribution of each of these variables, specified by the probability of a delay in the measurement, as well as their correlation function, are known. Using an innovation approach, the filtering, fixed-point and fixed-interval smoothing recursive algorithms are obtained without requiring the state-space model generating the signal; they use only the covariance functions of the signal and the noise, the delay probabilities and the correlation function of the Bernoulli variables. The algorithms are applied to a particular transmission model with stand-by sensors for the immediate replacement of a failed unit.