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. In this paper we next 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. We 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. Here we 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. In simulation studies we show that when the number of sources is small, the proposed suboptimal schemes yield near-optimal estimates even in the presence of relatively large jitter noise. Also, issues of robustness and generalizations of the approach to the case of missing pulses, unknown source number, and non-Gaussian jitter noise are addressed.