A regularised EEG informed Kalman filtering algorithm

Abstract

The conventional Kalman filter assumes a constant process noise covariance according to the system's dynamics. However, in practice, the dynamics might alter and the initial model for the process noise may not be adequate to adapt to abrupt dynamics of the system. In this paper, we provide a novel informed Kalman filter (IKF) which is informed by an extrinsic data channel carrying information about the system's future state. Thus, each state can be represented with a corresponding process noise covariance, i.e. the Kalman gain is automatically adjusted according to the detected state. As a real-world application, we demonstrate for the first time how the analysis of electroencephalogram (EEG) can be used to predict the voluntary body movement and inform the tracking Kalman algorithm about a possible state transition. Furthermore, we provide a rigorous analysis to establish a relationship between the Kalman performance and the detection accuracy. Simulations on both synthetic and real-world data support our analysis.

Modeling time-varying brain networks with a self-tuning optimized Kalman filter

“…The single constant c is a smoothing parameter in the exponential smoothing of the state and determines the exponential decay of weights assigned to past predicted states, as they get older—the fading memory of the system. Whereas a fixed adaptation constant assumes a steady memory decay of the system, which could not be appropriate in modelling neuronal processes and dynamics [ 74 ], solutions for variable fading factors have been widely explored (see [ 126 ] for a comprehensive list), also in relation to intrinsic dynamics of physiological signals [ 127 ]. Here we propose a new method based on monitoring the proportional change in innovation residuals from consecutive segments of time, according to: where b is a baseline constant ( b = 0.05) that prevents the filter to perform at excessively slow tracking speed, such that c ∈ (0.05,0.95), and is the trace of the estimated measurements innovation covariance for consecutive segments of data: new is a segment comprising samples from t to t − p , and old is a segment from t − ( p + 1) to t − 2 p .…”

“…The single constant c is a smoothing parameter in the exponential smoothing of the statex ðþÞ t and determines the exponential decay of weights assigned to past predicted states, as they get older-the fading memory of the system. Whereas a fixed adaptation constant assumes a steady memory decay of the system, which could not be appropriate in modelling neuronal processes and dynamics [74], solutions for variable fading factors have been widely explored (see [126] for a comprehensive list), also in relation to intrinsic dynamics of physiological signals [127]. Here we propose a new method based on monitoring the proportional change in innovation residuals from consecutive segments of time, according to:…”

Flexible Textile-Based Pressure Sensing System Applied in the Operating Room for Pressure Injury Monitoring of Cardiac Operation Patients

“…To obtain a high efficiency and precision of the flexible pressure sensor, the Kalman filter with the variables of prediction and measurement was applied in the readout system. There are 5 formulas of the Kalman filter from the variance of signal and noise in both prediction and measurement, which are already used for the dynamic system of multi-variables, including electrocardiogram (ECG) [ 30 ], electroencephalogram (EEG) [ 31 ], robotics and vision [ 32 , 33 ], and industrial applications [ 27 ]. Due to the single variable of capacitance, these 5 equations can be simplified as follows: …”