A problem that arises in many applications is to compute the conditional distributions of stochastic models given observed data. While exact computations are rarely possible, particle filtering algorithms have proved to be very useful for approximating such conditional distributions. Unfortunately, the approximation error of particle filters grows exponentially with dimension. This phenomenon has rendered particle filters of limited use in complex data assimilation problems that arise, for example, in weather forecasting or oceanography. In this talk, I will argue that it should be possible, at least in theory, to develop "local" particle filtering algorithms whose approximation error is dimension-free by exploiting conditional decay of correlations properties of high-dimensional models. As a proof of concept, we prove for the simplest possible algorithm of this type an error bound that is uniform both in time and in the model dimension. (Joint work with P. Rebeschini)