Square-root algorithms for the continuous-time linear least squares estimation problem

A simple differential equation for the triangular square-root of the error covariance of the linear state estimator is derived. Previous algorithms involved an antisymmetric matrix in the square-root differential equation. In the constant model case, Chandrasekhar-type equations are shown to constitute a set of fast square-root algorithms for the derivative of the error variance. Square-root algorithms for the smoothing problem are presented and as in the discrete case, an array method for handling continuous squareroots is developed. This method also yields very naturally the usual normalizations of stochastic calculus, suggesting extensions to more general stochastic equations, even to estimators for nonlinear models.