Kalman Filtering with Newton's Method

Abstract

fi nding. We show that the one-step Kalman fi lter is given by a single iteration of Newton’s method on the gradient of a quadratic objective function, and with a judiciously chosen initial guess. This derivation is different from those found in standard texts [2]‐[6], since it provides a more general framework for recursive state estimation. Although not presented here, this approach can also be used to derive the extended Kalman fi lter for nonlinear systems.