Abstract
This paper presents a new stochastic adaptive estimation-identification technique for nonstationary systems. The proposed method enhances the initial results from an on average estimation, and its identification, through a generalized adaptable function based on the Exponential Forgetting Factor (EFF), and the Sliding Mode (SM) regarding the error identification. In this form, the presented process includes the function implementation in three stages-estimation, adaptive estimation, and adaptive estimation-identification, allowing us to observe the gradual convergence to a nonstationary reference signal. Simulations first introduce convergence level checks obtained from the estimation and identification of artificial signals. After that, the algorithm is applied for real references, considering the Electroencephalogram (EEG) signals taken from a public database, finding their internal nonstationary gains, indirectly. Finally, the results include a performance comparison between the proposed strategy concerning the Recursive Least Square (RLS), the Least Mean Square (LMS), and the Kalman Filter (KF).
Highlights
The processes or systems analyses require the creation of simplified representations for their study
INNOVATIVE CONTRIBUTION to provide a new filtering tool for stochastic signals, keeping a low complexity, we propose an adaptive estimation and identification process considering the Exponential Forgetting Factor (EFF) and the Sliding Mode (SM) described in [11]
The additive noise included in the reference signal (42) incorporates pseudorandom variations, representing a signal without preprocessing, as raw sampled signals would be, and with unknown behavior
Summary
The processes or systems analyses require the creation of simplified representations for their study. The signals are quantitative representations of measurable characteristics from phenomena or systems The analysis of these signals is useful to define relationships between them, creating empirical models without requiring a priori knowledge, contrary to the models based on physical first principles. B. INNOVATIVE CONTRIBUTION to provide a new filtering tool for stochastic signals, keeping a low complexity, we propose an adaptive estimation and identification process considering the EFF and the SM described in [11]. To accomplish the tracking of nonstationary signals, we take advantage of the EFF features, incorporating the sign function and the identification error as a part of the adaptive function arguments With this form, the proposed method increases the convergence rate to the reference without establishing special conditions in each nonstationary evolution. It focuses on signal tracking and not on providing a diagnosis [27]
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