Adaptive Filtering Approach With Forgetting Factor for Stochastic Signals Applied to EEG

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 estimationidentification, 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).

Variable Forgetting Factor-Based Adaptive Kalman Filter With Disturbance Estimation Considering Observation Noise Reduction

“…The KFD can considerably remove noise influences from the estimates; however, disturbances and unmeasured variable estimates have a large time delay. By contrast, to develop the DKF model, ( 15) is replaced by (21).…”

“…In (21), the system noiseQ is defined as a diagonal matrix and is treated as uncertainty in each augmented state variable. The system can estimate the augmented state vector quickly; however, the estimates are affected by the observation noise.…”

“…In this paper, a novel KFD technique, which provides an accurate simultaneous estimation of state and disturbance under the observation noise, including quantization noise, is proposed. To solve the trade-off in the conventional method, the proposed method employs the adaptive Kalman filter (AKF) [18]- [20], which uses a forgetting factor [21]. AKF is a method used for dynamic system state and parameter identifications and can correspond to the variations in the system using the forgetting factor.…”