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Summary form only given. The talk discusses various computational techniques for solving complex inference problems in signal processing. The focus of the talk would be Monte Carlo methods, and in particular the sequential Monte Carlo methods which are currently proving extremely powerful for non-linear/non-Gaussian sequential environments. The author review the basic formulation of the sequential Monte Carlo framework, or particle filter, from the perspective of sequential updating of a general probability distribution, such as the posterior distribution of a hidden state or signal parameter. These methods, in their most basic forms, have proved very powerful for solving of non-linear problems in radar tracking, financial time series, communications, robotics and computer vision. In recent years increases in available computer power and memory have facilitated substantial algorithmic advances in these methods, allowing for more accurate inference and solution of more complex problems. In the second part of the talk the author describe some of these recent advances in sequential Monte Carlo, including Monte Carlo smoothers and trans-dimensional filters, which allow for on-line model selection. The methods described would be illustrated with examples from radar tracking, audio signal extraction and inference of musical beat from an audio waveform.