ARMA Innovation Model Research Articles

Measurement Feedback Self‐Tuning Weighted Measurement Fusion Kalman Filter for Systems with Correlated Noises

For the linear discrete stochastic systems with multiple sensors and unknown noise statistics, an online estimators of the noise variances and cross‐covariances are designed by using measurement feedback, full‐rank decomposition, and weighted least squares theory. Further, a self‐tuning weighted measurement fusion Kalman filter is presented. The Fadeeva formula is used to establish ARMA innovation model with unknown noise statistics. The sampling correlated function of the stationary and reversible ARMA innovation model is used to identify the noise statistics. It is proved that the presented self‐tuning weighted measurement fusion Kalman filter converges to the optimal weighted measurement fusion Kalman filter, which means its asymptotic global optimality. The simulation result of radar‐tracking system shows the effectiveness of the presented algorithm.

Covariance Intersection Fusion Kalman Estimators

By the CI (Covariance Intersection) fusion algorithm, based on the ARMA innovation model, the two-sensor CI fusion Kalman estimators are presented for the systems with unknown cross-covariance. It is proved that their estimation accuracies are higher than those of the local Kalman estimators, and are lower than those of the optimal fused Kalman estimators. A Monte-Carlo simulation result shows that the actual accuracy of the presented CI fusion Kalman estimator are close to those of the optimal fused Kalman estimators with known cross-covariance.

A New Approach To Optimal and Self‐Tuning Filtering, Smoothing and Prediction For Discrete‐Time Systems

ABSTRACTA new approach to optimal and self‐tuning state estimation of linear discrete time‐invariant systems is presented, using projection theory and innovation analysis method in time domain. The optimal estimators are calculated by means of spectral factorization. The filter, predictor, and smoother are given in a unified form. Comparisons are made to the previously known techniques such as the Kalman filtering and the polynomial method initiated by Kucera. When the noise covariance matrices are not available, self‐tuning estimators are obtained through the identification of an ARMA innovation model. The self‐tuning estimator asymptotically converges to the optimal estimator.

H∞ deconvolution filtering, prediction, and smoothing: a Krein space polynomial approach

This correspondence is concerned with the infinite horizon H/spl infin/ deconvolution for discrete time-invariant systems described by polynomial equations. A simple frequency domain approach in Krein space is developed for the deconvolution problem. With the help of an ARMA innovation model, solutions to the problems of deconvolution filtering, prediction, and fixed lag smoothing are obtained. The estimators are calculated by performing one J-spectral factorization.

Optimal recursive filtering, prediction, and smoothing for singular stochastic discrete-time systems

A new and simple approach to optimal recursive filtering, prediction, and smoothing for singular stochastic discrete-time systems is presented by using a time-domain innovation analysis method. The estimators are calculated based on an ARMA innovation model which can be obtained using spectral factorization or a recursive identifier. The prediction problem for the singular systems is solved with the aid of an output predictor. Further, a simple solution is presented for the complex smoothing problem.

A Unified Approach to Optimal State Estimation for Stochastic Singular Systems

The steady-state optimal state estimation problem for discrete-time stochastic singular linear systems is considered via the innovation analysis method in the time domain. The filter, predictor and smoother are derived by using the projection formula and are calculated based on the ARMA innovation model. The three cases of filter, predictor and smoother are shown to have a unified form. Also, the optimal white noise estimation method, including both input and measurement noises, is presented. Asymptotic stability of the estimators is proved. The results of this paper can be applied to normal systems as a special case.

White-Noise Filter and Smoother with Application to Seismic Data Deconvolution

The problem of estimating white noise is discussed. Using the time series analysis method, based on the vector ARMA innovation model this paper presents the new multiple-channel steady-state optimal white noise filter and smoother applied to seismic data deconvolution, which are different from Mendel's single-channel steady-state white noise estimators that are based on the state-space model and Kalman filtering