The limits of extended Kalman filtering for pulse train deinterleaving

Some signals are transmitted as periodic pulse trains. If more than one pulse train is transmitted over the same communication channel, a challenge is to separate them for source identification at the receiver. This is known as pulse train deinterleaving and is clearly a fundamental problem in the study of discrete-event systems. Frequently, the only relevant information at the receiver is the time of arrival (TOA) data, which is usually contaminated by jitter noise. Perhaps there are also missing or overlapping pulses. In this paper, we present an approach for deinterleaving pulse trains and estimating their periods using an extended Kalman filter (EKF). A naive application of EKF theory is not attractive because of discontinuities in the signal model. Here, a form of smoothing of the discontinuities is proposed so that the EKF approach becomes attractive. The advantage of this EKF approach is that it is less computationally expensive than most previously proposed methods, which are of order N/sup 2/, where N is the number of pulses being processed. The computation required here is of order N. The method proposed appears to give useful results for up to seven or so pulse trains, particularly when there is some a priori information on the pulse frequencies, which can be obtained using computations of order N log N.