Strategic Objectives
• Master the mathematical foundations of Recursive Least Squares (RLS).
• Ensure filter stability in non-stationary neural environments.
• Optimize convergence speeds for real-time brain-computer interfaces.
• Implement forgetting factors to handle temporal signal decay.
The Core Challenge
Traditional static filters fail the moment brain activity shifts, leading to model drift and system instability in real-time applications.
01
The Nature of Non-Stationarity
02
Foundations of Adaptive Filter Theory
03
Linear Estimation Theory
04
The Recursive Least Squares Algorithm
05
Optimal Filter Convergence
06
Matrix Inversion Lemma
07
The Forgetting Factor
08
Stability and Lyapunov Criteria
09
Stochastic Gradient Descent vs. RLS
10
The Wiener Filter Connection
11
Kalman Filtering for Neural States
12
Numerical Stability in Real-Time
13
The Autocorrelation Matrix
14
Fast Transversal Filters
15
Tracking Performance Analysis
16
Regularization in Neural Models
17
System Identification of the Brain
18
Lattice Filters for Neural Data
19
Mean Square Error Minimization
20
The Bayesian Perspective
21
Future Directions in Adaptive BCIs
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