Square-Root Algorithms for the Continuous-Time Linear Least Squares Estimation Problem.

摘要

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 square-roots 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. (Author)