Approximate Kalman filtering for large-scale systems with an application to hyperthermia cancer treatments

TL;DR

This paper introduces a real-time feasible approximate Kalman filtering method for large-scale systems, especially those modeled by PDEs, demonstrated through a hyperthermia cancer treatment case study.

Contribution

It develops a novel approximation scheme that reduces computational complexity while maintaining accuracy for large-scale PDE-based systems.

Findings

Significant reduction in computation time compared to traditional methods

Maintains accurate state estimates in large-scale systems

Effective application demonstrated in hyperthermia cancer treatment

Abstract

Accurate state estimates are required for increasingly complex systems, to enable, for example, feedback control. However, available state estimation schemes are not necessarily real-time feasible for certain large-scale systems. Therefore, we develop in this paper, a real-time feasible state-estimation scheme for a class of large-scale systems that approximates the steady state Kalman filter. In particular, we focus on systems where the state-vector is the result of discretizing the spatial domain, as typically seen in Partial Differential Equations. In such cases, the correlation between states in the state-vector often have an intuitive interpretation on the spatial domain, which can be exploited to obtain a significant reduction in computational complexity, while still providing accurate state estimates. We illustrate these strengths of our method through a hyperthermia cancer treatment case study. The results of the case study show significant improvements in the computation time, while simultaneously obtaining good state estimates, when compared to Ensemble Kalman filters and Kalman filters using reduced-order models.