Tracking Filter Engineering: The Gauss-Newton and Polynomial Filters (repost)

For almost 50 years the Kalman filter has been the accepted approach to tracking filter engineering. At the start of the Satellite Age in 1958, Gauss-Newton tracking filters were tried but had to be ruled out for real-time use because of the speed limitations of existing computers.

In their place two new algorithms were devised, first the Swerling filter and then the Kalman filter, both of which could be run in real time on the machines of that era. It was nevertheless observed that Gauss-Newton possessed some superior properties, particularly with regard to stability.

Computer speed has now vastly increased and so Gauss-Newton need no longer be ruled out. The almost one hour that it took to execute Gauss-Newton in 1958 is now down to a few tens of milliseconds on readily available machines, and could soon be down to microseconds if computer technology continues to progress as it has done in recent years.

It is on this basis that Morrison presents his approach. The book provides a complete theoretical background, and then discusses in detail the Gauss-Newton filters. Of particular interest is a new approach to the tracking of maneuvering targets that is made possible by these filters. The book also covers the expanding and fading memory polynomial filters based on the Legendre and Laguerre orthogonal polynomials, and how these can be used in conjunction with Gauss-Newton.

Fourteen carefully constructed computer programs cover the theoretical background, and also demonstrate the power of the Gauss-Newton and polynomial filters. Two of these programs include Kalman, Swerling and Gauss-Newton filters, all three processing identical data. These demonstrate Kalman and Swerling instability to which Gauss-Newton is immune, and also the fact that if an attempt is made to forestall Kalman and Swerling instability by the use of a Q matrix, then they are no longer Cramer-Rao consistent and become noticeably less accurate than the always Cramer-Rao consistent Gauss-Newton filters.