Relative position estimation of moving distributed sources using the extended Kalman filter

The relative positions of moving distributed sources are estimated by the Doppler frequency shift estimate of each source using the extended Kalman filter (EKF). Each source is assumed to radiate a different frequency with a different spatial position. The Doppler frequency shift of each source along the Closest Point of Approach (CPA) is unique with respect to time and frequency and this is mapped with respect to each source position. Since the Doppler frequency shift should be estimated with a high time resolution and a high frequency resolution particularly for a moving source with a relatively fast time-varying amplitude, the EKF frequency-amplitude estimator is proposed to fulfill this goal. The performance of the technique is examined by an illustrative numerical example and is verified by an experiment using loudspeaker sources on the roof of a car.