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A sequential extended Kalman filter and optimal smoothing algorithm was developed to provide real time estimates of torpedo position and depth on the three dimensional underwater tracking range at the Naval Torpedo Station, Keyport, Washington. The measurements consisted of acoustic pulse transit times from the torpedo to receiving array, which are nonlinear functions of the positions and the depth of the torpedo, were linearized and filter gains and filtered estimates of states calculated. By running the smoothing subroutine, all past filtered estimates of states and error covariance were smoothed. The program was tested, using simulated torpedo trajectories that traversed both single and multiple arrays, on an IBM-PC. The results showed that filter performance was dependent on system noise and the distance to the hydrophone array from the torpedeo and the smoothed estimates of states and error covariances were better than or equal ot the filtered estimates.

A sequential extended Kalman -filter and optimal smoothing algorithm was developed to provide real time estimates o-f torpedo position and depth on the three dimensional underwater tracking range at the Naval Torpedo Station, Keyport , Washington. The measurements consisted o-f acoustic pulse transit times -from the torpedo to receiving array, which are nonlinear -functions o-f the positions and the depth o-f the torpedo, were linearized and -filter gains and -filtered estimates o-f states calculated. By running the smoothing subroutine, all past -filtered estimates o-f states and error covariance were smoothed. The program was tested, using simulated torpedo trajectories that traversed both single and multiple arrays, on an IBM-PC. The results showed that -filter performance was dependent on system noise and the distance to the hydrophone array -from the torpedo and the smoothed estimates of states and error covariances were better than or equal to the filtered estimates.