A method by applying Doppler frequency shift of multi-line in radiated noise spectrum to estimate the vertical range from a receiver to a moving vessel, which is supposed to move along a straight line at a constant velocity, is developed. This method is based on passive ranging by a single sensor and the depth of the sea and other environment parameters are not necessarily known. First the Wigner-Ville distribution is used as the instantaneous frequency estimator to find out the instantaneous frequencies of the muti-lines as a signal. Then define Doppler frequency shift basis functions, based on an algorithm called matching pursuit, by a searching strategy of variable span, and explore the minimum spatial distance between the signal and the Doppler frequency shift basis functions in a five-dimension space. The basis function of the obtained minimum spatial distance corresponds to the estimation of range and speed of the moving vessel. Computer simulations yield statistics errors in the range and speed estimates with differing intensities of noise. If the white noise deviation is less than 10% of the maximum Doppler frequency shift and time-window width is 1.47 times of reference-duration,relative error of range estimate is less than 5.4% and relative error of speed estimate is less than 1.4%. This estimation method has been tested and the result conforms to data collected during an experiment on the sea, the estimated speed is 52 knots and the estimated range is 42 m. The single point passive ranging method can be used for ranging purposes in sonar-buoys, mines,movement analysis of an underwater object in underwater acoustics experiment, and soundsource level measurements.
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