Estimation theory with applications to communications and control

This paper proposes the robust estimation technique for the signal and the state variables with respect to the state-space model having the general types of system matrices in linear discrete-time stochastic systems with the uncertain parameters. It is assumed that the signal and degraded signal processes are fitted to the finite order autoregressive (AR) models. By fitting the signal process to the AR model, the system matrix for the signal is transformed into the controllable canonical form. By using the system matrix, the existing robust RLS Wiener filter and fixed-point smoother are adopted to estimate the signal. Concerning the state estimation, the existing robust RLS Wiener filter calculates the filtering estimate of the signal. By replacing the observed value with the robust filtering estimate of the signal in the existing RLS Wiener filtering and fixed-point smoothing algorithms, the robust filtering and fixed-point smoothing estimates of the signal and the state variables are calculated.
The simulation result shows the superior estimation characteristics of the proposed robust estimation technique for the signal and the state variables in comparison with the existing  RLS Wiener filter, the robust Kalman filter, and the existing robust RLS Wiener filter and fixed-point smoother.

/pdf/robust-rls-wiener-state-estimators-in-linear-discrete-time-ji6crbj2f0.pdf

Robust RLS Wiener State Estimators In Linear Discrete-Time Stochastic Systems With Uncertain Parameters

This paper proposes the robust RLS Wiener filter and fixed-interval smoothing algorithms based on the innovation approach. As a result, the robust RLS Wiener filtering algorithm is same as the existing robust RLS Wiener filtering algorithm. The estimation accuracy of the fixed-interval smoother is compared with the robust RLS Wiener filter and the following fixed-interval smoothers. In the proposed robust RLS Wiener fixed-interval smoother, the case, where the observed value is replaced with the robust filtering estimate of the signal, is also simulated. (1) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (2) The RTS (Rauch-Tung-Striebel) fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate. (3) The  RLS Wiener fixed-interval smoother and the  RLS Wiener filter. (4) The RLS Wiener fixed-interval smoother in which the filtering estimate of the state is replaced with the robust RLS Wiener filtering estimate and the observed value is replaced with the robust RLS Wiener filtering estimate of the signal. From the simulation results, the most feasible estimation technique for the fixed-interval smoothing estimate is the RLS Wiener fixed-interval smoother. Here, the robust filtering estimate is used and the observed value is replaced with the robust filtering estimate.

Robust RLS Wiener Fixed-Interval Smoother in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

As an extension of the linear robust recursive least-squares Wiener fixed-point smoother and filter,
this paper originally designs the robust extended recursive Wiener fixed-point smoother and filter for
estimating the signal in discrete-time wide-sense stationary stochastic systems. It is a characteristic in this paper
that the signal is modulated with the nonlinear mechanism. As a step to the estimation problem for the
observation mechanism with the nonlinear modulation, the robust signal estimators are proposed for the
observation equation with the linear amplitude modulation of the signal. The observation noise is additional
white noise. The system matrix in the state equation contains uncertain parameters. The robust extended
recursive Wiener estimators are derived from the Wiener-Hopf equation. In the simulation example, it is shown
that the proposed robust extended recursive Wiener fixed-point smoother and filter are superior in estimation
accuracy to the extended recursive Wiener estimators

/pdf/robust-extended-recursive-wiener-fixed-point-smoother-and-5bhn78bo2l.pdf

Robust Extended Recursive Wiener Fixed-Point Smoother and Filter in Discrete-Time Stochastic Systems

/pdf/robust-recursive-least-squares-finite-impulse-response-siv4qox1ua.pdf

Robust Recursive Least-Squares Finite Impulse Response Predictor in Linear Discrete-Time Stochastic Systems with Uncertain Parameters

This paper proposes the robust recursive least-squares (RLS) Wiener fixed-point smoother and filter in linear discrete-time stochastic systems with parameter uncertainties. The uncertain parameters exist in the observation matrix and the system matrix. The uncertain parameters cause to generate the degraded signal. In this paper, the degraded signal process is fitted to the finite order autoregressive (AR) model. The robust RLS Wiener estimators use the system matrices and the observation matrices for both the signal and the degraded signal, the variance of the state vector for the degraded signal, the cross-variance of the state vector for the signal with the state vector for the degraded signal, and the variance of the white observation noise. Also, this paper proposes the robust recursive fixed-point smoother and filter, by using the covariance information of the state vector for the degraded signal, the cross-covariance information of the state vector for the signal with the state vector for the degraded signal, the observation matrices for both the degraded signal and the signal besides the variance of the white observation noise. In estimating the signal process expressed by the second order AR model, the proposed robust RLS Wiener filter is superior in estimation accuracy to the robust Kalman filter and the RLS Wiener filter.

/pdf/robust-rls-wiener-signal-estimators-for-discrete-time-3evojserv6.pdf

Seiichi Nakamori

Papers

Robust RLS Wiener Signal Estimators for Discrete-Time Stochastic Systems with Uncertain Parameters