The limits of extended Kalman filtering for pulse train deinterleaving

Some signals, such as in radar systems, communication systems, and neural s ystems, are transmitted as periodic pulse trains. If more than one pulse tr ain is transmitted over the same communication channel, a challenge is to s eparate them for source identification at the receiver, This is known as pu lse 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 e stimating their periods using an extended Kalman filter (EKF). A naive appl ication of EKF theory is not attractive because of discontinuities in the s ignal model. Here, a form of smoothing of the discontinuities is proposed s o that the EKF approach becomes attractive. The advantage of this EKF appro ach is that it is less computationally expensive than most previously propo sed methods, which are of order N-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, particu larly when there is some a priori information on the pulse frequencies, whi ch can be obtained using computations of order N log N.