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Dolphins are known to outperform man-made sonar in detecting and classifying targets in a shallow water environment where the returned signal is dominated by clutter in the vicinity of targets. During target interrogation, some species (such as the Atlantic bottlenose dolphin, Tursiops truncatus) emit trains of clicks. Each click can be modelled as consisting of two distinct down-chirping components over differing frequency bands. This study proposes a processing scheme called biased pulse summation sonar (BiaPSS) by which such trains can be interpreted to enhance target detection and reduce clutter in bubbly water, provided that the animal changes the amplitude of the clicks within the click train. A theoretical study is carried out using two dolphin-like clicks of different amplitude to determine the efficacy of such a pulse train in target discrimination in a bubble-filled environment. By adding and subtracting the responses from the two similar pulses, which are identical except that one has twice the amplitude of the other, the linear backscatter contribution from the target (e.g. a fish) can be discriminated from the non-linear backscattered reverberation (e.g. bubbles). For the bubble population used, the detection rate of the linear target using the pulse pair is showed to outperform the `standard sonar` processing.