Fixed memory filter for real-time estimation of noise-corrupted signals

Abstract

Introduction I N many engineering applications, such as guidance and navigation of aeronautical vehicles, the signals need to be estimated from noisy measurements in real time. The (minimum-variance) Kalman-Bucy filter' that relies on a finite-dimensional state-space model of the plant dynamics and the measurement history is extensively used for this purpose. Techniques of adaptive filtering' that are based on the principle of recursive least squares algorithm and rely on an inputoutput relationship of the plant dynamics are also used. Given a linear (or linearized) time-invariant finite-dimensional model of plant dynamics in the autoregressive moving average (ARMA) setting, we propose a fixed-memory, nonrecursive filter for real-time signal estimation. The key idea is to construct a simple, nonrecursive filter based on weighted averaging of a finite array of past values of measured inputs and outputs of the plant. A fixed memory filter is very useful in the applications of smart sensors and/or active sensors where memory constraints are tight and computationally efficient algorithms are required for real-time implementation on a microchip collocated with the sensor. The filter memory length depends on the plant dynamics and the allowable bound of estimation error and, for real-time applications, is often selected as a tradeoff between execution time and accuracy of the filter. This Engineering Note presents the concept and formulation of a fixed-memory filter based on an ARMA model of plant dynamics. The criteria for selection of the filter memory length are not included in this Note. Although the filter algorithm is derived for single-input single-output (SISO) systems, the proposed filter can be extended to multi-input multioutput (MIMO) systems.