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

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.