Demystifying Kalman Filters: From Classical Estimation to Bayesian Inference
In this post, we will discuss the Kalman filters from two perspectives: classical parameter estimation and Bayesian estimation. Each perspective provides a unique way to derive the Kalman filter. Parameter estimation is more flexible as it allows you to easily add constraints, revise the transition and observation models, and derive other related smoothing and filtering methods. Meanwhile, Bayesian estimation is more intuitive and provides a clearer probabilistic interpretation, helping us understand the underlying principles better. By examining both approaches, we can gain a more comprehensive understanding of how Kalman filters work. ...