The need for accurate monitoring and analysis of sequential data arises in many scientic, industrial and nancial problems. Although the Kalman lter is effective in the linear-Gaussian case, new methods of dealing with sequential data are required with non-standard models. Recently, there has been renewed interest in simulation-based techniques. The basic idea behind these techniques is that the current state of knowledge is encapsulated in a representative sample from the appropriate posterior distribution. As time goes on, the sample evolves and adapts recursively in accordance with newly acquired data. We give a critical review of recent developments, by reference to oil well monitoring, ion channel monitoring and tracking problems, and propose some alternative algorithms that avoid the weaknesses of the current methods.
