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 Cramer-Rao consistent and become less accurate than the always Cramer-Rao consistent Gauss-Newton filters.