Likelihood Gradient Evaluation Using Square-Root Covariance Filters

TL;DR

This paper introduces a numerically stable square-root algorithm for evaluating the log-likelihood gradient in Kalman filtering, enhancing robustness and avoiding instabilities of conventional methods.

Contribution

A new square-root algorithm for likelihood gradient evaluation using covariance quantities and array square-root filters, improving numerical stability.

Findings

Enhanced numerical stability in likelihood gradient computation

Reduced roundoff errors compared to conventional Kalman filter methods

Applicable to robust state estimation in noisy systems

Abstract

Using the array form of numerically stable square-root implementation methods for Kalman filtering formulas, we construct a new square-root algorithm for the log-likelihood gradient (score) evaluation. This avoids the use of the conventional Kalman filter with its inherent numerical instabilities and improves the robustness of computations against roundoff errors. The new algorithm is developed in terms of covariance quantities and based on the "condensed form" of the array square-root filter.