1. A vehicle comprising: an engine configured for automatic shutdown and restart; a controller configured to filter a longitudinal acceleration using a low pass filter having a bandwidth selected from a plurality of bandwidths based on a derivative of the longitudinal acceleration, generate output indicative of a static road gradient estimation based on the filtered longitudinal acceleration, wherein the controller is further configured to shutdown and restart the engine based on the static road gradient estimation; wherein an initial value of the static road gradient estimation corresponds to at least one of a kinematic road gradient estimation and a dynamic road gradient estimation.