1. A seismic streamer system comprising: a seismic streamer extending in length from a head end to a tail end; a plurality of lateral-steering devices attached to the streamer to apply a lateral force at spaced apart steering positions along the length of the streamer, wherein the lateral-steering devices divide the streamer into a series of contiguous streamer segments, each segment extending from a fore end at a steering position to an aft end at the next consecutive steering position closer to the tail end of the streamer; a plurality of first heading sensors disposed along the length of the streamer, each of the first heading sensors disposed in one of the streamer segments closer to the fore end than to the aft end and producing heading readings; a plurality of second heading sensors disposed along the length of the streamer, each of the second heading sensors disposed in one of the streamer segments proximate the aft end of the streamer segment and producing heading readings; and means for estimating streamer shape by modeling the shape of each of the streamer segments with a linear portion extending from the fore end to an intermediate point between the fore end and the aft end and a curved portion extending from the intermediate point to the aft end and computing a shape estimate of each of the streamer segments between consecutive lateral-steering devices from the model of the shape and the heading readings of the first and second heading sensors in the streamer segment.