A seismic streamer system and associated methods for estimating the shape of a laterally steered seismic streamer. The streamer is divided into a series of contiguous streamer segments by lateral-steering devices. Heading sensors positioned in forward and aft portions of each segment produce heading readings. Each segment is modeled as having a linear shape in the forward portion and a curved shape in the aft portion. The shape of the segment is estimated according to the model from the heading readings on the segment.