School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
Kulikova, M.V., School of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, Wits 2050, South Africa
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. © 2009 IEEE.
Block codes; Control theory; Convergence of numerical methods; Gradient methods; Kalman filters; Turbo codes; Condensed forms; Identification; Implementation methods; Kalman filtering; Log likelihoods; Numerical instabilities; Numerical stability; Round-off errors; Square roots; Square-root algorithms; Maximum likelihood estimation