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Description
This paper investigates the limits of acoustic source localization when using multipole-based models in a two-dimensional cylindrical-wave framework. A small displacement of a monopolar sound source generates additional spatial patterns beyond the basic monopole field. These patterns carry essential information about the source position. When estimating the source location from noisy measurements, we show that including more multipole components in the model can unintentionally remove this information. For example, adding components such as dipoles and quadrupoles to the estimation model can absorb the effects of source displacement, making the position increasingly difficult to identify. This leads to a loss of identifiability and a significant degradation in estimation accuracy. More generally, we show that the estimation behavior is governed by the lowest-order remaining term in the field expansion with respect to the source displacement. These results are derived analytically and confirmed through numerical simulations, showing strong agreement between theory and practice.