We introduce a limit orderbook modelling (LOB) framework, based on the decomposition of a LOB in terms of its instantaneous volume and instantaneous shape. The optimal LOB shape is determined as the unique shape describing a set of market features and maximizing entropy. We show that for any LOB, one can adjust the evolution of the limit orderbook volume in such a way that the reference measure becomes an ELMM for each of the market prices. We show that the shape of the limit orderbook can be estimated using an infinite-dimensional non-Euclidean filtering scheme. The filtering scheme is reduced to a familiar and computationally tractable finite dimensional Euclidean filtering problem by exploiting the geometry of the limit orderbook’s shape.