A polynomial algorithm for noise identification in linear systems

Abstract

The implementation of an optimal adaptive filter in a composite system consisting of a Kalman filter and a noise covariance identifier is addressed. A method of noise identification employing a polynomial transformation of the system output is presented. The method eliminates batch processing, indirect observation through filtering apparatus, and the need for a priori estimates for tuning the noise estimation apparatus. The result is a robust method, suitable for online incremental update, and time-varying systems, free of tunable parameters or a priori assumptions other than the values of the deterministic system parameters, and highly parallelizable.