The Gauss-Newton algorithm applied to track-while-scan radar

The Gauss-Newton (GN) algorithm is the minimum-variance non-recursive estimation procedure invented by Gauss in 1809 [3, 4, 7]. Mathematicians refer to it by that name; statisticians refer to it as nonlinear regression; astronomers call it differential correction. In 1959 Swerling reworked Gauss' non-recursive algorithm into a recursive format [9], giving rise to the Bayes-Swerling filter. In 1960/61, Kalman and Bucy published their algorithm [5, 6], which, in the absence of process noise, can be derived from Swerling's recursive format [7]. The huge advances in computing power and affordability of RAM since the early 60's have made it desirable that we re-examine Gauss' original algorithm which avoids the problems and/or limitations incurred by either the Swerling or the Kalman recursive formats, and at the same time opens up tremendous flexibility in terms of access to internal filter values. This paper examines the GN algorithm and how it has been applied to Track-While-Scan (TWS) radar. A companion paper in these proceedings discusses the application of GN to Passive Coherent Location (PCL) radar [8].