  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.
