Nonlinear Kalman Filtering for Censored Observations

TL;DR

This paper introduces a modified extended Kalman filter designed to accurately estimate system states and parameters from censored nonlinear observations, validated through simulations and real-world medical data analysis.

Contribution

It develops a novel nonlinear censored Kalman filter that effectively handles censored data, improving estimation accuracy in such challenging scenarios.

Findings

Accurately reconstructs state variables with censored data.

Effectively tracks system parameters despite observation limitations.

Demonstrates practical utility with medical datasets.

Abstract

The use of Kalman filtering, as well as its nonlinear extensions, for the estimation of system variables and parameters has played a pivotal role in many fields of scientific inquiry where observations of the system are restricted to a subset of variables. However in the case of censored observations, where measurements of the system beyond a certain detection point are impossible, the estimation problem is complicated. Without appropriate consideration, censored observations can lead to inaccurate estimates. Motivated by the work of [1], we develop a modified version of the extended Kalman filter to handle the case of censored observations in nonlinear systems. We validate this methodology in a simple oscillator system first, showing its ability to accurately reconstruct state variables and track system parameters when observations are censored. Finally, we utilize the nonlinear censored filter to analyze censored datasets from patients with hepatitis C and human immunodeficiency virus.