Towards the time varying estimation of complex brain connectivity networks by means of a General Linear Kalman Filter approach

2012 ◽  
Author(s):  
J. Toppi ◽  
F. Babiloni ◽  
G. Vecchiato ◽  
F. De Vico Fallani ◽  
D. Mattia ◽  
...  
Keyword(s):  
Kalman Filter ◽  
Brain Connectivity ◽  
General Linear ◽  
Time Varying ◽  
Filter Approach

Identification of Linear Time-Varying Systems

2010 ◽  
pp. 221-237
Author(s):  
Vinayak G. Asutkar ◽  
Balasaheb M. Patre
Keyword(s):  
Kalman Filter ◽  
Physical Situation ◽  
Time Varying ◽  
Varying Parameters ◽  
System Parameters ◽  
Optimal Estimator ◽  
Time Varying Parameters ◽  
Time Varying Systems ◽  
Filter Approach ◽  
Kalman Filter Method

This chapter deals with identification of time-varying systems using Kalman filter approach. Most physical systems exhibit some degree of time-varying behaviour for many reasons. These systems cannot effectively be modelled using time invariant models. A time-varying autoregressive with exogenous input (TVARX) model is good to model these time-varying systems. The Kalman filter approach is a superior way to estimate the system parameters. This approach can track the time-varying parameters and is suitable for recursive estimation. It works well even when there are abrupt changes in the system parameters. Kalman filter is known to be an optimal estimator even when there is significant noise. In the proposed approach, for the purpose of simulation, we employ first order TVARX model and its parameters are estimated using recursive Kalman filter method. The system parameters are varied in continuous and abruptly changing manner to reveal the physical situation. To show the efficacy of the proposed approach, the time-varying parameters are estimated for different noise conditions. The performance is evaluated by calculating error performance measures. The results are found to be satisfactory with reasonable accuracy for noisy conditions even for fast changing parameters. The numerical examples illustrate efficacy of the proposed Kalman filter based approach for identification of time-varying systems.

The Kalman Filter Approach for Time-varying ß Estimation

2003 ◽  
Vol 43 (8) ◽  
pp. 1033-1042 ◽  
Author(s):  
Massimo Gastaldi ◽  
Annamaria Nardecchia
Keyword(s):  
Kalman Filter ◽  
Time Varying ◽  
Filter Approach

scholarly journals A Kalman Filter for Nonlinear Attitude Estimation Using Time Variable Matrices and Quaternions

Sensors ◽  
2020 ◽  
Vol 20 (23) ◽  
pp. 6731
Author(s):  
Álvaro Deibe ◽  
José Augusto Antón Nacimiento ◽  
Jesús Cardenal ◽  
Fernando López Peña
Keyword(s):  
Kalman Filter ◽  
Dynamic Behavior ◽  
State Vector ◽  
Time Variable ◽  
Explicit Calculation ◽  
Time Varying ◽  
Input And Output ◽  
Filter Approach ◽  
Augmented State ◽  
Physical Quantities

The nonlinear problem of sensing the attitude of a solid body is solved by a novel implementation of the Kalman Filter. This implementation combines the use of quaternions to represent attitudes, time-varying matrices to model the dynamic behavior of the process and a particular state vector. This vector was explicitly created from measurable physical quantities, which can be estimated from the filter input and output. The specifically designed arrangement of these three elements and the way they are combined allow the proposed attitude estimator to be formulated following a classical Kalman Filter approach. The result is a novel estimator that preserves the simplicity of the original Kalman formulation and avoids the explicit calculation of Jacobian matrices in each iteration or the evaluation of augmented state vectors.

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