On the number of samples to be drawn in particle filtering

In this paper we look at the nonlinear filtering problem. In particular we look at filters of the sampling kind, also referred to as particle filters. In a setting where the system is nonlinear, and/or the load disturbance and measurement noise are not Gaussian, the (extended) Kalman filter may exhibit poor performance. In this case one is forced to look at alternative filtering methods. A method that works fine in many situations is the application of a so called sampling filter. The main disadvantage of these sampling types of filter is their computational load, which, especially in real time applications, is of paramount importance. The computation time consuming part of the sampling types of filter is the sampling part. The computational load of this stage of the filter algorithm is determined by two factors, namely: 1. The way in which the sampling stage is implemented. 2. The number of samples that is used. While the first issue has received broad attention in the literature the second one has not. In this report we try to fill this gap and suggest a method to relate the required number of samples in a quantitative way to the accuracy and the level of confidence by which the sampling stage is performed. This method is based on inequalities from probability theory and statistical learning theory. These inequalities then provide bounds for the sample size