In this paper, we propose a new approach to signal smoothing when the data are generated (or represented) by an autoregressive moving average with exogenous inputs (ARMAX) model. In this approach, the original ARMAX recurrence relation is directly employed and combined with a constrained least squares optimization framework to filter out both system and measurement noise components and estimate the desired signal in form of block-wise matrix formulation. The approach is also driven from a forward backward filtering, which is accomplished through linear time invariant system. While the impulse response of the proposed filter can be found using deconvolution operator, a closed-form expression is presented for its impulse response without resorting to any transform methods. Two examples of its applications for variable-Q filter design and spectral density estimation are given, which demonstrate the present approach is more effective and robust than the existing variable-Q filter designs in the literature and it can he used to improve the spectral density estimation.

A New Approach to ARMAX Signals Smoothing: Application to Variable-Q ARMA Filter Design / A. Kheirati Roonizi. - In: IEEE TRANSACTIONS ON SIGNAL PROCESSING. - ISSN 1053-587X. - 67:17(2019), pp. 4535-4544. [10.1109/tsp.2019.2928986]

A New Approach to ARMAX Signals Smoothing: Application to Variable-Q ARMA Filter Design

A. Kheirati Roonizi
2019

Abstract

In this paper, we propose a new approach to signal smoothing when the data are generated (or represented) by an autoregressive moving average with exogenous inputs (ARMAX) model. In this approach, the original ARMAX recurrence relation is directly employed and combined with a constrained least squares optimization framework to filter out both system and measurement noise components and estimate the desired signal in form of block-wise matrix formulation. The approach is also driven from a forward backward filtering, which is accomplished through linear time invariant system. While the impulse response of the proposed filter can be found using deconvolution operator, a closed-form expression is presented for its impulse response without resorting to any transform methods. Two examples of its applications for variable-Q filter design and spectral density estimation are given, which demonstrate the present approach is more effective and robust than the existing variable-Q filter designs in the literature and it can he used to improve the spectral density estimation.
ARMAX; least squares optimization; matrix formulation; LTI system; filtering and smoothing; impulse response; variable-Q ARMA filter; spectral density estimation
Settore INF/01 - Informatica
2019
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/952852
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