Single-hydrophone localization

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Abstract
It is shown that Clay’s single-hydrophone time-domain localization algorithm is a member of a large class of algorithms {χmn} that require exact knowledge of the source time function w(t). The single-hydrophone Clay algorithm is χ∞2; however, χ∞1 often localizes better than χ∞2. Next, five new families of single-hydrophone localization algorithms are introduced. The first of these, {μmn}, also requires a knowledge of w(t), and is introduced mainly to emphasize that Clay localization is the ratio of norms. The four new localizer families, {φmn}, {θmn}, {βmn}, and {νmn}, require almost no knowledge of w(t). These new algorithms actually yield an estimate of the source spectrum W(ω), as well as the location of the source. The localizers φ, θ and ν work best when ‖W(ω)‖, the amplitude spectrum of the source, is smooth, although w(t) need not be a pulse. The β localizers work best when w(t) is a pulse. If it happens that an estimate of W(ω) is available, then φ, θ, β, and ν can use this information and their performance is enhanced. A similar enhancement is obtained when two hydrophones are available.

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