A higher order correlation unscented Kalman filter

TL;DR

This paper introduces a higher order correlation measurement update for the unscented Kalman filter, enabling sequential estimation of parameters like volatility that are uncorrelated with observations.

Contribution

It extends the Gaussian two-moment filters with a higher order correlation update, allowing estimation of uncorrelated diffusion parameters.

Findings

Successfully applied to Ornstein-Uhlenbeck process parameter estimation

Demonstrates improved estimation of uncorrelated parameters

Provides explicit formulas for the higher order filter

Abstract

Many nonlinear extensions of the Kalman filter, e.g., the extended and the unscented Kalman filter, reduce the state densities to Gaussian densities. This approximation gives sufficient results in many cases. However, this filters only estimate states that are correlated with the observation. Therefore, sequential estimation of diffusion parameters, e.g., volatility, which are not correlated with the observations is not possible. While other filters overcome this problem with simulations, we extend the measurement update of the Gaussian two-moment filters by a higher order correlation measurement update. We explicitly state formulas for a higher order unscented Kalman filter within a continuous-discrete state space. We demonstrate the filter in the context of parameter estimation of an Ornstein-Uhlenbeck process.