Worst-case Prediction Performance Analysis of the Kalman Filter

TL;DR

This paper analyzes the worst-case prediction performance of the Kalman filter within a minimax framework, providing bounds on prediction errors based on comparator complexity and drift, bridging control theory and online learning.

Contribution

It introduces a worst-case analysis of the Kalman filter's prediction errors, connecting control theory with online learning and providing bounds based on comparator drift.

Findings

Derived bounds on cumulative squared prediction errors.

Performance linked to the best reference predictor and its drift.

Bridged control theory and online learning frameworks.

Abstract

In this paper, we study the prediction performance of the Kalman filter (KF) in a worst-case, minimax setting as studied in online machine learning, information - and game theory. The aim is to predict the sequence of observations almost as well as the best reference predictor (comparator) sequence in a comparison class. We prove worst-case bounds on the cumulative squared prediction errors using a priori knowledge about the complexity of reference predictor sequence. In fact, the performance of the KF is derived as a function of the performance of the best reference predictor and the total amount of drift occurs in the schedule of the best comparator.