Groupe d’études et de recherche en analyse des décisions

Optimization perspective on Kalman filtering and smoothing

Aleksandr Aravkin IBM TJ Watson Research Center, États-Unis

Since its debut in 1960, the Kalman filter, and subsequent smoothing algorithms, have played a key role in a broad range of signal processing applications, including navigation, healthcare, finance, and weather. While there are many ways to attack inference for dynamic systems, the optimization perspective allows us to view many classic algorithms as particular ways to solve a structured least squares problem.

With this understanding, we can attack a broad range of more sophisticated problems, including inference for nonlinear dynamic systems, situations where measurements are contaminated, systems with prior knowledge encoded through constraints, and systems for tracking sudden errors in the states. We show that we can design optimization methods for all of these formulations that preserve the computational efficiency of the classic RTS and Mayne-Fraser algorithms.