A Novel Technique based on up-sampling for addressing Modeling Issues in Sampled Data Nonlinear Filtering

We address sampled data non-linear filtering problems where there is an underlying continuous-time system. In the case of linear systems, it is well known that there is an exact discrete model that describes the second order properties at the sampling instants. However, in the nonlinear case, one must use an approximate model. In practice, simple Euler expansions are typically used. However, an Euler model is known to give a poor approximation especially with moderate sample period. Here we propose a resolution of this difficulty via the use of an up-sampling strategy. We show that, as the up-sampling rate increases, then in the linear case the up-sampled filter converges to the true filter. We illustrate by an example.