This paper presents a new method, in an underwater context, of estimating the trajectory of a target assumed to be in constant velocity motion. The observer system is composed of a transmitter (emitting continuously, said also in high duty cycle mode) and a set of passive underwater acoustic sensors (e.g. receiving sonobuoys) not necessarily collocated with the transmitter. Each receiver detects the single-tone signal emitted by the transmitter after its reflection on the target. The two sets of doubly Dopplershifted frequency measurements for each receiver make the target motion analysis (TMA) feasible, even when only one receiver is available. First, we develop the exact model of the bistatic received frequencies and then we compute the Cramér-Rao lower bound (CRLB) when the number of receivers is 1, 2, or 3, the measurements being corrupted by an additive and time-independent Gaussian noise. Finally, using some realistic scenarios, we show that the maximum likelihood estimated is actually efficient.