Filtering notes (III): the Kalman filter

Part III of the filtering notes series: Part I: signal plus noise models Part II: state-space-models Part III: the Kalman filter Introduction In this post, we derive the Kalman filter (KF) algorithm and explore how it can be applied to time series forecasting and sequential (online) learning. As we will see, the KF algorithm arises naturally from the covariance properties of state-space models…