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.
