Sequential localization of a radiating source by Doppler-shifted frequency measurements

For a single omnidirectional sensor in contact with a constant velocity source that radiates a constant frequency tone, the measurements of the Doppler-shifted frequencies over time do not provide sufficient information to localize the source. Instead, only the parameters of source rest frequency, speed, and range relative to a sensor can be determined. However, if over time three or more sensors sequentially come in contact with the source, the source trajectory can then be specified. This is termed sequential localization. A two-dimensional grid search technique to find the Doppler parameters from measurements taken by a single sensor alone is presented. From these parameters, it is next shown how sequential localization is accomplished. Two simulation examples are provided to verify the development. The localization root mean squared errors (RMSEs) are found to be very close to the Cramer-Rao bound