Tracking Filter Engineering – The Gauss-Newton and Polynomial Filters (2016)

EEE 5132Z (2016) Tracking Filter Engineering - Class Photo

Course Information

Dates: 29 February to 4 March 2016

Course code: EEE5132Z – Special Topics in Radar F

Venue: Menzies Seminar Room, 6th Floor, Menzies Building (Upper Campus), University of Cape Town

Credits: 20 points


Course Description

Course Handout: Tracking Filter Engineering 2016
Download Course Handout: Tracking Filter Engineering 2016

The course provides a detailed introduction to tracking filter engineering based on the Gauss-Newton and polynomial filters.

At the start of the Satellite Age in 1958, three tracking filters competed for acceptance at Bell Labs:

  • Gauss-Newton filters were the first to be tried, but they had to be ruled out for real time use because of the speed limitations of the existing computers.
  • The second to be tried were the Swerling filters, which could be run in near real time on the existing machines.
  • Two years later, the Swerling filters were replaced by the Kalman filters.

Nevertheless, a number of facts were noted, among them the following:

  • Swerling and Kalman yielded identical numerical results.
  • Swerling and Kalman both suffered from the same problems of unpredictable instability.
  • Swerling was in some ways superior to Kalman.

Apart from the fact that they were unusable at the time, Gauss-Newton was observed to be the best of the three: Gauss-Newton filters were unconditionally stable, they produced better numerical results, and they were better suited to the tracking of manoeuvring targets. The speed of today’s computers is vastly greater than those of 1958, and so Gauss-Newton need no longer be ruled out for near real time use.

This course:

  • Touches briefly on the Swerling and Kalman filters;
  • Covers Gauss-Newton in full depth;
  • Covers in full depth the widely used polynomial filters, which were devised by the lecturer when he worked at Bell Labs between 1964 and 1968.



Dr Norman Morrison holds degrees in electrical engineering and applied mathematics. He worked in US military defence for thirteen years, including four years at Bell Labs on ballistic missile defence, where he first learned about tracking filters. After returning to South Africa in 1986, he taught applied mathematics at the University of Cape Town for twenty years until 2007.

From 2008 to 2013, he was employed by Armscor (South African Department of Defence) and assigned to work with Reutech, on the development of a new type of TWS radar that was to operate in conjunction with surface-to-air missiles provided by Denel Aerospace.

His book, “Tracking Filter Engineering: The Gauss-Newton and Polynomial Filters” came out of this work.