RLS Wiener Fixed-Point Smoother and Filter with Randomly Delayed or Uncertain Observations in Linear Discrete-Time Stochastic Descriptor Systems

The purpose of this paper is to design the recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time descriptor systems. The signal process is observed with additional observation noise. The observed value is randomly delayed by multiple sampling intervals or has the possibility of uncertainty that the observed value does not include the signal and contains the observation noise only. It is assumed that the probability of the observation delay and the probability that the observation does not contain the signal are known. The delayed or uncertain measurements are characterized by the Bernoulli random variables. The characteristic of this paper is that the RLS Wiener estimators are proposed from the randomly delayed, by multiple sampling intervals, or uncertain observations particularly for the descriptor systems in linear discrete-time stochastic systems

Design of H-infinity Extended Recursive Wiener Estimators in Discrete-Time Stochastic Systems

This paper designs (1) the H-infinity RLS Wiener fixed-point smoother and filter for the observation equation with the linear modulation and (2) the extended H-infinity recursive Wiener fixed-point smoother and filter in discrete-time wide-sense stationary stochastic systems. ln the extended estimatars, it is assumed that the signal is observed with the nonlinear modulation and with additional white observation noise. In the estimators, the system matrix Φ for the state vector x(k), the observation vector C for the state vector, the variance K(k,k) = K(0) of the state vector, the nonlinear observation function and the variance of the white observation noise are used. Φ, C and K(0) axr calculated from the auto covariance data of the signal. A simulation example, on the estimation of a speech signal in the phase demodulation problem, is demonstrated to show the estimation characteristics of the proposed extended H-infinity recursive Wiener estimatoxs

Bibliographic Review on Distributed Kalman Filtering

In recent years, a compelling need has arisen to understand the effects of distributed information structures on estimation and filtering. In this paper, a bibliographical review on distributed Kalman filtering (DKF) is provided.\ud The paper contains a classification of different approaches and methods involved to DKF. The applications of DKF are also discussed and explained separately. A comparison of different approaches is briefly carried out. Focuses on the contemporary research are also addressed with emphasis on the practical applications of the techniques. An exhaustive list of publications, linked directly or indirectly to DKF in the open literature, is compiled to provide an overall picture of different developing aspects of this area

Design of discrete time controllers and estimators.

This thesis considers optimal linear least-squares filtering smoothing prediction and regulation for discrete-time processes. A finite interval smoothing filter is derived in the z domain giving a transfer function solution. The resulting time-invariant smoother can be applied to problems where, a time varying solution using matrix Riccati equations would diverge if the process is modelled inaccurately. A self-tuning algorithm is given for the filtering and fixed lag smoothing problems as applied to square multi-variable ARMA processes when only the order of the process is assumed known. The dynamics of the process can also be slowly time varying. If the dynamics remain constant and unknown, it is shown how the self-tuning filter or smoother algorithm converges asymptotically to the optimal Wiener solutions. LQG self-tuning regulation is considered. The LQG algorithms rely on input-output data rather than from the conventional state-space approach employing the Kalman filter. An explicit algorithm is given which is similar to certain pole placement self-tuning regulators, requiring the solution of a diophantine equation. Following this, an implicit algorithm is shown to overcome the problem of solving a diophantine equation by estimating the regulator parameters directly using recursive least squares. The LQG algorithms are shown to be able to cope with processes which are non-minimum phase, open loop unstable and with an unknown time delay