A number of geophysical observing techniques, including ocean acoustic tomography, obtain sequences of records of which the observed relative maxima (“peaks”) are used to infer properties of the system via inversions. Traditionally, these peaks first are tracked (followed from one record to another) and identified separately, before they can be used in an inversion scheme. In this paper, a method is presented for identifying and tracking ensembles of such peaks in one step and simultaneously with the inversion. A priori information, in our case knowledge about the ocean, can thus be used to constrain the allowed peak identifications, enabling the usage of irregularly appearing or more closely spaced peaks. The best identification is defined to be the one that upon inversion minimizes a cost function that involves data residual and smoothness in time, subject to two constraints bounding the solution and residual size. For the presented cases, the minimum can be found by simply trying inversions with all possible peak identifications. Sample applications of the method from an acoustic tomography experiment are shown in order to illustrate the approach and results.