Adaptive signal processing by particle filters and discounting of old measurements

In adaptive signal processing the principle of exponentially weighted recursive least-squares plays a major role in developing various estimation algorithms. It is based on the concept of discounting of old measurements and allows for better performance in problems with time-varying signals and signals in nonstationary noise. We show how this concept can be combined with the Bayesian methodology. We propose that the discounting of old measurements within the Bayesian framework be implemented by employing particle filters. The main idea is presented by way of a simple example. The methodology is very attractive and can be used in a very wide range of scenarios including ones that involve highly nonlinear models and non-Gaussian noise.