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