Likelihood Gradient Evaluation Using Square-Root Covariance Filters
For practitioners using Kalman filters, this provides a more numerically stable method for gradient evaluation, though it is an incremental improvement over existing square-root filtering techniques.
The paper presents a new square-root algorithm for evaluating the log-likelihood gradient (score) in Kalman filtering, which improves numerical stability and robustness against roundoff errors compared to conventional methods.
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.