A New Approach to Estimation of Initial Conditions and Smoothing Problems

A unified approach utilizing the Kalman-Bucy filtering technique istaken to solve the estimation problem of initial conditions and thesmoothing problem in linear dynamic systems. The equivalencebetween the forward integration method and the backward integrationmethod of the smoothing solution is proved. Complete analyticalsolutions of filtering and smoothing problems of rectilinear motion ofa randomly accelerated spacecraft are derived when the vehicle istracked by the ranging system at the ground station.