Abstract: Road grade is modeled over a region in which a vehicle is driven on roadways having a grade that varies over a plurality of predetermined grade ranges. A succession of grade values are generated while operating the vehicle at a predetermined rate, wherein each grade value identifies a respective grade range then being encountered. A Markov chain road-grade model is updated in response to the succession of grade values, wherein the model represents respective elements of probability in a matrix of transition events from each predetermined grade range to a respective next-in-succession grade range. Each element of the matrix has a value ?i,j representing a weighted frequency of transition events from a first respective grade value to a second respective grade value divided by a weighted frequency of transition events initiating from the first respective grade value, so that the matrix successively approximates the road grade of the region.

Abstract: Road grade is modeled over a region in which a vehicle is driven on roadways having a grade that varies over a plurality of predetermined grade ranges. A succession of grade values are generated while operating the vehicle at a predetermined rate, wherein each grade value identifies a respective grade range then being encountered. A Markov chain road-grade model is updated in response to the succession of grade values, wherein the model represents respective elements of probability in a matrix of transition events from each predetermined grade range to a respective next-in-succession grade range. Each element of the matrix has a value ?i,j representing a weighted frequency of transition events from a first respective grade value to a second respective grade value divided by a weighted frequency of transition events initiating from the first respective grade value, so that the matrix successively approximates the road grade of the region.