Deinterleaving pulse trains using discrete-time stochastic dynamic-linear models

Pulse trains from a number of different sources are often received on the one communication channel. It is then of interest to identify which pulses are from which source, based on different source characteristics. This sorting task is termed deinterleaving. the authors propose time-domain techniques for deinterleaving pulse trains from a finite number of periodic sources based on the time of arrival (TOA) and pulse energy, if available, of the pulses received on the one communication channel. They formulate the pulse train deinterleaving problem as a stochastic discrete-time dynamic linear model (DLM), the “discrete-time” variable k being associated with the kth received pulse. The time-varying parameters of the DLM depend on the sequence of active sources. The deinterleaving detection/estimation task can then be done optimally via linear signal processing using the Kalman filter (or recursive least squares when the source periods are constant) and tree searching. The optimal solution, however, is computationally infeasible for other than small data lengths since the number of possible sequences grow exponentially with data length. The authors propose and study two of a number of possible suboptimal solutions: 1) forward dynamic programming with fixed look-ahead rather than total look-ahead as required for the optimal scheme; 2) a probabilistic teacher Kalman filtering for the detection/estimation task