Superimposed chirped pulse parameter estimation based on the Extended Kalman Filter (EKF)

An extended Kalman filter (EKF) is proposed to estimate the frequencies and chirp rate of multiple superimposed chirped pulses. The estimation problem is a difficult one, where maximum likelyhood methods are very complex especially if more than two pulses are superimposed. It is shown that for the EKF an arbitrary number of pulses can be tracked, and it will be shown that for the case of two superimposed pulses tracking is achieved after sufficient samples for minimum required frequency resolution. Mean square error (MSE) performance is shown to compare well to the Cramer-Rao bounds even for difficult cases where the number of samples is close to the inverse of the difference in normalized frequencies.