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This paper addresses the problem of time-varying field directionality mapping (FDM) or spatial spectrum estimation in dynamic environments with a maneuverable towed acoustic array. Array processing algorithms for towed arrays are typically designed assuming the array is straight, and are thus degraded during tow ship maneuvers. In this paper, maneuvering the array is treated as a feature allowing for left and right disambiguation as well as improved resolution towards endfire. A new method for online spatial spectrum estimation is presented. The maximum likelihood of the time-varying field is solved for using a single expectation maximization step after each received data snapshot. A multi-source simulation is used to illustrate the proposed algorithm's ability to suppress ambiguous towed-array backlobes and resolve closely spaced interferers near endfire which pose challenges for conventional beamforming approaches, especially during array maneuvers.