Topic: Stochastic Filtering and the Kalman-Bucy Filter

The Zakai Equation for Unnormalized Filtering

The Innovations Process and Its Brownian Character

The Filtering Problem as Conditional State Estimation

Steady-State Kalman-Bucy Gain

Scalar Filtering of a Constant Hidden Signal

Orthogonal Projection in Linear Filtering

Linear Gaussian Signal and Observation Models

Innovation Residuals and Filtering Diagnostics

Gaussian Conditioning and Covariance Updates

Filtering an Ornstein-Uhlenbeck Signal