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Low frequency passive sonar systems often use towed line arrays. In order to properly beamform the elements in the array, an accurate estimate of the array shape is required. We consider a submarine towed instrumented with 12 heading sensors used to estimate its shape. Submarines may make drastic maneuvers, producing significant bends in the array. These maneuvers also produce vibrations which introduce severe noise into the heading sensors. A Kalman filter has been developed to produce an accurate estimate of the array shape in the presence of severe heading noise. The Kalman filter uses an adaptively weighted average of the heading sensor data with an improved dynamic model to produce the estimate of shape. During periods of nominally straight tow, the filter relies strongly on the heading sensor data. The filter adaptively estimates the variance of the heading sensors, so that it automatically recognizes vibration-inducing maneuvers, and relies more heavily on the dynamic model during those times. Performance of the filter is controlled by adjusting the ratio of the sensor to process noise. Since the filter works on all sensors simultaneously to produce a single shape estimate, it is capable of recognizing a few bad sensors that are inconsistent with the majority. The Kalman filter algorithm has been successfully applied to eliminate contaminations from noisy sensors.