# Convergence analysis of a family of robust Kalman filters based on the contraction principle

## TL;DR

This paper investigates the convergence properties of a family of robust Kalman filters, demonstrating that under certain conditions, the filters reliably converge when model uncertainty is appropriately controlled.

## Contribution

It provides a convergence analysis for robust Kalman filters using the contraction principle, linking filter stability to the tolerance parameter and system properties.

## Key findings

- Filters converge when the tolerance parameter is sufficiently small.
- The Riccati-like mapping is strictly contractive under the given conditions.
- Convergence is guaranteed for reachable and observable models.

## Abstract

In this paper we analyze the convergence of a family of robust Kalman filters. For each filter of this family the model uncertainty is tuned according to the so called tolerance parameter. Assuming that the corresponding state-space model is reachable and observable, we show that the corresponding Riccati-like mapping is strictly contractive provided that the tolerance is sufficiently small, accordingly the filter converges.