MACSYMA-Generated closed-form solutions to some matrix Riccati equations

摘要

Closed-form solutions to some continuous-time matrix Riccati equations have been generated by employing MACSYMA, the symbolic manipulation program developed at MIT. These equations, whose solution by hand would be prohibitive, occur in a description of the performance of imaging infrared trackers. Solutions have been obtained for both second-order and third-order matrices (corresponding, respectively, to the application to the target of a white-noise or a Poisson-type stochastic force), and for the cases in which the variance matrix is initially either zero or singular.