We consider the problem of estimating the position of a concentrated inhomogeneity on a stationary acoustic path organized between a single sound source and a vertical receiving antenna in a shallow waveguide in the presence of background disturbances. A local bottom rise and a soliton-like internal wave are chosen as model inhomogeneities. It is proposed to determine the distance from the source to the inhomogeneity by cepstral analysis of the amplitude of the first waveguide mode isolated on the antenna, with preliminary deformation of the frequency axis. Using numerical modeling, the stability of this approach is studied in the presence of several concentrated inhomogeneities or additional disturbances: bottom slope, background internal waves, wind waves, bottom irregularities. Estimates of the signal-to-noise ratio required to implement the proposed approach are provided.