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A class of baseband correlation receivers is developed for estimating the time-of-flight of a narrowband signal. In contrast to conventional correlation receivers that contain a perfectly known replica of the signal, the signal shape is unknown to the proposed receiver. A parametric model of the signal envelope is therefore built, concurrently with the process of time-of-flight estimation. The identification of the model parameters can be pursued by assuming that a few signal constraints are satisfied at the time instant of signal onset: the constraints concern the value of the signal envelope and of its first time derivative. The correlation receivers perform a series expansion of the signal envelope by a set of Laguerre basis functions; the outputs of the Laguerre filter bank that computes the running Laguerre transform are used to build a parametric model of the unknown envelope and to estimate its time-of-flight. Simple variations of the correlation receivers are proposed, which differ from each other in the use they make of the signal constraints. The correlation receivers are applied to process narrowband echoes from in-air ultrasonic sensors. Potential applications are object identification and surface profiling in the robotic field. Computer simulations and experiments using a simple pulse-echo sensor system are presented.