Kalman Filtering with Newton's Method [Lecture Notes]

In this article, Kalman filter using Newton's method for root finding is derived. We show that the one-step Kalman filter 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, 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 filter for nonlinear systems.