Abstract: In shallow waters, regular striations can be observed from the broad-band range-frequency spectrogram radiated by a moving ship, whose structure can be interpreted by the waveguide invariant theory and has been applied for sediment geoacoustic inversion and source ranging, etc. We present an algorithm to sequentially estimate the source range by observing the striation geometrical characteristics with an extended Kalman filter. This approach is based on the waveguide invariant theory and has the advantage of no requirement of a prior environmental information and forward sound field calculation. The at-sea ship noise data is tested, and the results are in high agreement with GPS data, besides, this approach is also demonstrated to be robust to initial state values.