This book provides a complete discussion of the Gauss-Newton filters@ including all necessary theoretical background. This book also covers the expanding and fading memory polynomial filters based on the Legendre and Laguerre orthogonal polynomials@ and how these can serve as pre-filters for Gauss-Newton. Of particular interest is a new approach to the tracking of manoeuvring targets that the Gauss-Newton filters make possible. Fourteen carefully constructed computer programs demonstrate the use and power of Gauss-Newton and the polynomial filters. Two of these also include Kalman and Swerling filters in addition to Gauss-Newton@ all three of which process identical data that have been pre-filtered by polynomial filters. These two programs demonstrate Kalman and Swerling instability@ to which Gauss-Newton is immune@ and also the fact that if an attempt is made to forestall Kalman/ Swerling instability by the use of a Q matrix@ then they cease to be Crame?r-Rao consistent and become less accurate than the always Cramer-Rao consistent Gauss-Newton filters. Author Norman Morrison