We present a method to optimally estimate when a slip state transition occurs for a slip-steered vehicle. A slip-steered vehicle's contact state with the ground must slip sideways in order for the vehicle to turn. This slipping generates uncertainties for an autonomous controller. These uncertainties can be be reduced if an estimate of when the vehicle switches between slipping and sticking is provided to the controller. We present an estimator that optimally determines when a switch between slipping and sticking occurs by comparing simulations of the slip-steered vehicle with its measured configurations. We demonstrate that steepest descent-based optimization has slow convergence and show how this issue can be rectified by using Newton's Method. This is a primary stress of our paper. The paper concludes with the introduction of an algorithm that uses second-order optimization in a manner that is appropriate for online implementation.