Likelihood Gradient Evaluation Using Square-Root Covariance Filters

IEEE Transactions on Automatic Control, 54(3) (2009), 646-651
http://dx.doi.org/10.1109/TAC.2008.2010989

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 ldquocondensed formrdquo of the array square-root filter.